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<div>#REDIRECT [[Template:Cite doi/10.1038.2Fnature01279]]</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=120078Main Page2014-08-26T20:27:24Z<p>10.68.16.65: Replaced content with "[https://wiki.Kastnet.at/The_Emerging_Opportunities_In_Speedy_Tactics_For_Riad_Marrakech. Riad To Renovate For Sale In Marrakech] <br><br><br><br><br><br><br><br><br..."</p>
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| name = Missouri Tigers athletic director navbox<br />
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<div>{{#if:yes|<noinclude>[[Category:Passed DYK nominations&nbsp;from November 2013]]<div style="background-color: #F3F9FF; margin: 2em 0 0 0; padding: 0 10px 0 10px; border: 1px solid #AAAAAA;"><br />
:''The following discussion is an archived discussion of the DYK nomination of the article below. <span style="color:red">'''Please do not modify this page.'''</span> Subsequent comments should be made on the appropriate discussion page (such as [[{{TALKPAGENAME}}|this nomination's talk page]], [[Talk:{{SUBPAGENAME}}|the article's talk page]] or [[Wikipedia talk:Did you know]]), unless there is consensus to re-open the discussion at this page. '''No further edits should be made to this page'''.''<br />
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The result was: '''promoted''' by [[User:PFHLai|PFHLai]] ([[User talk:PFHLai|talk]]) 17:37, 1 December 2013 (UTC)<br />}}<br />
{{DYKC}}<br />
====Pilgrim of Eternity====<br />
{{DYK nompage links|nompage=Pilgrim of Eternity|Pilgrim of Eternity}}<br />
<div style="float:right;margin-left:0.5em;"><br />
[[File:James Doohan Scotty Star Trek.JPG|100x100px|James Doohan as Chief Engineer Scott]]<br />
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* ... that [[Chris Doohan]], son of original Chief Engineer [[Montgomery Scott]] portrayer [[James Doohan]] ''(pictured)'', played the role in the [[Star Trek fandom|''Star Trek'' fan]] production, '''''[[Pilgrim of Eternity]]'''''?<br />
:*<br />
:* ''Comment'': may just need inline citations, which i actually dont know how to do with multiple usages of a single ref.<br />
<small>Created by [[User:Igottheconch|Igottheconch]] ([[User talk:Igottheconch|talk]]).&nbsp; nominated by [[User:Mercurywoodrose|Mercurywoodrose]] ([[User talk:Mercurywoodrose|talk]]) at 05:32, 6 November 2013 (UTC)</small>.<br />
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:* I did some copy editing, and I think more needs to be done to the prose. References have been moved down into the body of the article, rather than in the lead. I'm not sure all references apply to existing prose. Any photo you use in DYK needs to also be in the article (it's nice to see Scotty). I like the article, and am a fan of all things Trek. However, I would advise some copy editing and scrutiny by an editor who is experienced with similar articles. [[User:Maile66|— Maile ]] ([[User talk:Maile66|talk]]) 00:01, 24 November 2013 (UTC)<br />
::*I agree, I have little experience either with DYK's, or with Star Trek or webtv articles. I have included this in the various wikiprojects, but i am reluctant to canvass, as I understand its a little tasteless. I just added the scotty image to the article. I really wish we had an image of Chris Doohan. thanks so much for moving the refs down, i should be able to parse that, but so far i remain stubbornly ignorant of the techniques. I have no doubt my prose needs some work, but im pretty sure its all ref'd (except the plot summary), and i will try to see if it matches up now.[[User:Mercurywoodrose|Mercurywoodrose]] ([[User talk:Mercurywoodrose|talk]]) 05:09, 24 November 2013 (UTC)<br />
:::[[File:Symbol confirmed.svg|16px]] Length, history and reference verified. [[User:Daniel Case|Daniel Case]] ([[User talk:Daniel Case|talk]]) 22:14, 29 November 2013 (UTC)<br />
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{{-}}{{#if:yes|</div></noinclude>|{{#ifeq:{{FULLPAGENAME}}|Template talk:Did you know/{{SUBPAGENAME}}|[[Category:Pending DYK nominations]][[Category:DYK/Nominations|Pending]]|{{#ifeq:{{FULLPAGENAME}}|Template:Did you know nominations/{{SUBPAGENAME}}|[[Category:DYK/Nominations|Pending]][[Category:Pending DYK nominations]]}}}}}}<!--Please do not write below this line or remove this line. Place comments above this line.--></div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=112795Main Page2014-08-26T09:47:33Z<p>10.68.16.65: </p>
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== Stacey Walked Hive Mind Doesn't Belong ==<br />
<br />
This article is supposed to be about Malthusian catastrophe, and the following quote and reference certainly does NOT belong in the section where it has been placed:<br />
<br />
"In her book Humanity and it's foolishness, Stacey Walker invites readers to challenge previous views on individuality looking instead for a paradigm shift towards a collective Hive Mind. Once in Humanity has entered the 'Hive State' Walker postulates an end to resource depletion via the Druidic virtue of 'Survival of the Fittest'."<br />
<br />
That should be removed and if necessary placed into some sort of "related works" section. <br />
<br />
Addendum to note: I would also beg to differ with the statement implying that Druids are somehow responsible for the theory of 'Survival of the Fittest'.<br />
<br />
<span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/74.46.43.230|74.46.43.230]] ([[User talk:74.46.43.230|talk]]) 23:01, 29 June 2009 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
==Exponential growth annual growth chart==<br />
<br />
It says next to this image "The annual increase graph does not appear as one would expect for exponential growth. For exponential growth, it should itself be an upward trending exponential curve whereas it has actually been trending downward since 1986. " I don't think this is quite correct. In an exponential growth situation, the annual growth rate (given in % like the graph), should remain constant, not trend upwards exponentially. Comments? [[User:Edsanville|Ed Sanville]] 21:33, 22 April 2006 (UTC)<br />
:This is because on 27 March, [[User:Casito|Casito]] edited the image file because "Excel Graphs look unprofessional", and changed it to percentage growth because it is "more useful", but didn't adjust the description; the original image, which you can still find [http://upload.wikimedia.org/wikipedia/en/archive/9/95/20060327181454%21World_population_increase_history.png here] showed absolute growth. Either the image should be converted back to absoute growth rate, or the description adjusted accordingly. For the time being I've adjusted the description to correct the inconsistency, but don't take that as a vote either way. (Worryingly, this image edit did not trigger my watchlists, even though that image was on my watchlist.) -- [[User:Securiger|Securiger]] 11:11, 24 April 2006 (UTC)<br />
<br />
I have completed the edits I planned to make to this page. I would be interested to see any comments.<br />
<br />
Buzz Bloom<br />
<br />
Some of this article's information has been moved to ''[[Neanderthals Bandits and Farmers]]'' or ''[[Cannibals and Kings]]'' articles where it more rightfully belongs. The remainder contained some pretty basic errors (e.g. supply and demand) and has been mostly rewritten. I am pretty confident about this, but if you think it was correct we can discuss it here. [[User:H7asan]]<br />
<br />
H7asan<br />
<br />
We obviously have a disagreement regarding the relevance of "[[Beyond the Limits]]".<br />
I found the entire book exactly on the point. It deals with the exhaustion of food (and other resources) as a result of unconstrained population growth (as well as the unconstrained growth of consumption). I definitely think this book should be referenced from a discussion of neo-Malthusean theory. Why do you think otherwise? Also, what is the proper mechanism for getting a disagreement of this kind resolved?<br />
<br />
By the way, I thought your moving of the discussion about the Harris and Tudge books to their own pages was a good idea.<br />
<br />
Buzz Bloom<br />
<br />
<br />
I have nothing against the ''Beyond the Limits'' book. (Actually I know nothing about it.) My problem was with the article which was empty. [[User:H7asan]]<br />
<br />
----<br />
<br />
I plan to remove the two paragraphs beginning with "Another problem is that there is no strong evidence ... " including the two graphs. This discussion is irrelevant to the topic of the Mathusuan catastrophe. Malthus never described population growth as being [[exponential]]. He said the growth would be expoential in unchecked, and then only until a subsistance level was reached. Growth of a population until a subsistance level would correspond to what Securiger describes in the current text I plan to remove as a Logistic curve. All that the curves show is that the current trend of world population from 1950-2000 may be begining to reach a new limit of a kind that Malthus discusses: use of contraception, which Malthus called a vice.<br />
<br />
I put this notice of intent here to elicit comments or alternative suggestions before doing it.<br />
<br />
I also plan to edit the remaining material in the "Non-occurrence of the catastrophe" section cbecajuse I think it un fairly represents the state of the world at the end of the 19th century, which the anthropoligist [[Marvin Harris]] describes as one of approaching catastrophe as predicted by Malthus. The section should discuss the innovations of the twentieth century that offer opportunities to avoid the catastrophe, or only postpose it. From this perspective, I would change he title of the section to "Postponement or non-occurrence of the catastrophe".<br />
<br />
I also elicit comments or alternative suggestions regarding these intentions.<br />
<br />
[[User:BuzzB]] Feb 28, 2004<br />
<br />
:I disagree with both proposed edits, quite strongly. Firstly, the paragraphs beginning "Another problem is..." are highly relevant. Malthus proposed a particular theory, which was essentially premised on three claims, one of them being the idea that a human population undergoes geometric growth if unchecked. Malthus' ''Essay'' has been disputed by many, and one major point of disputation - indeed one of the few points, pro- or anti-, that bothers to look at empirical facts - is that there is absolutely no evidence in support of this basic premise. It was pointed out as soon as the ''Essay'' was published, and continues to be pointed out today; if you like you can propose hypotheses to explain that fact away, but simply removing all evidence of it would severely bias the article.<br />
<br />
:Equally, we could point out that there is no evidence that food supply increases arithmetically, and that in fact it patently does not. One of the nicer summaries is this, written by Hazlitt in 1822:<br />
<br />
::''All that is true of Mr Malthus's doctrine then, is this, that the tendency of population to increase remains after the power of the earth to produce more food is gone; that the one is limited, the other unlimited. This is enough for the morality of the question: his mathematics are altogether spurious.''<br />
<br />
:Secondly, you propose to edit the remaining material in that section, because you claim that it "un fairly represents the state of the world at the end of the 19th century, which the anthropoligist Marvin Harris describes as one of approaching catastrophe as predicted by Malthus". Huh? That section doesn't even discuss the end of the nineteenth century! If you meant "end of the '''18th''' century", which is mentioned, then of that time it says "At the time Malthus wrote, most societies had populations at or near their agricultural limits" - which is not contradicted by your point!? (Although there is plenty of evidence to believe that that statement is also somewhat exaggerated).<br />
<br />
:I should point out that when I get time to do it justice, I plan to make extensive additions to this article, which in my opinion is currently very shallow and unencyclopedic. It currently represents the shallow, ill-defined, handwaving version of the Malthusian theory that is frequently dragged out in the pub or at dinner parties in support of some political argument or another. But in fact Malthus had a much more complete theory than is represented here, which was one of the seminal theories that gave rise to economics. (Although there is very little of the detail that is still widely accepted.) We need to work in its r&ocirc;le in the development of economics. Additionally the current article needs to mention Wallace, who had the idea first. Oh, and it also doesn't even mention the basic Malthusian idea that increased food supply automatically ''generated'' increased population until everyone was starving again, which segues into the r&ocirc;le the theory in had in justifying the oppression of the poor in nineteenth century politics - again from Hazlitt:<br />
::''The instant, however, any increase in population, with or without an increase in the means of subsistence, is hinted, the disciples of Mr Malthus are struck with horror at the vice and misery which must ensue to keep this double population down; nay, mention any improvement, any reform, any addition to the comforts or necessaries of life, any diminution of vice and misery, and the infallible result in their apprehensive imagination is only an incalculable increase of vice and misery, from the increased means of subsistence, and increased population that would follow. They have but this one idea in their heads; it comes in at every turn, and nothing can drive it out.''<br />
: [[User:Securiger|Securiger]] 11:28, 1 Mar 2004 (UTC)<br />
<br />
----<br />
<br />
I have extended the graph using the same data source, out to the years 1800-2005. Unfortunately, there seems to be some problem with the new image. Sometimes it appears when the article is displayed, and sometimes I see only a reference to an image. I have posted a query over at WikiMedia, and I hope to have it resolved in a day or two. Meanwhile, if you are looking for the image, please have some patience! --[[User:Aetheling|Aetheling]] 16:53, 30 September 2006 (UTC)<br />
<br />
----<br />
<br />
Addressing the original question of this section, an exponential curve does not have a constant growth rate. A constant growth rate yields a linear curve (for example, y=2x, a linear curve, has a growth rate of 2, a constant). An exponential curve has a growth rate that is, itself, an exponential curve (simplest example is y=e^x, a curve whose growth rate is equal to itself y'=e^x). For more information on this, you could visit the wikipedia page on [[exponential growth]]. I corrected the incorrect sentence.<br />
<br />
Matt<br />
<br />
* You have misunderstood the meaning of the term "growth rate". When we say that a population of size X grows at a rate of 5%, for example, we mean that the growth this year will be 0.05X. If you solve the difference equation X(t+1)-X(t) = rX(t), the solution is exponential growth: X(t) = (1+r)^t X(0). I have therefore reverted your edit. —[[User:Aetheling|Aetheling]] ([[User talk:Aetheling|talk]]) 07:29, 12 February 2008 (UTC)<br />
<br />
----<br />
<br />
I have updated the figures for world population and world population growth rate, to reflect the latest figures and estimates from the US Bureau of the Census. I also took the opportunity to improve these charts a little. I narrowed the range of the first and converted the vertical scale from semilog, so as to bring out more detail. If you look at this chart in its highest resolution, you can see that we have been following pretty closely the UN Medium projection (though it is still way too early to make any definitive judgement on this point). For the growth rate chart I added the latest projections by the US Bureau of the Census out to 2025, in red. Cheers! —[[User:Aetheling|Aetheling]] ([[User talk:Aetheling|talk]]) 18:16, 19 September 2008 (UTC).<br />
<br />
-------------<br />
<br />
I wanted to point out that this approach to exponential growth is to limited. In the article it is suggested that you should view the population as different groups with different growth rates. You could compare a population that is decreasing with 2,5% per year with a population that consists of two groups. Lets say half of the population is a group that decreases with 10% and the other half increases with 5%. The latter would have a decrease of 2,5 percent in the first year. But this would slowly change over time. After 15 years you will see a growth of about three percent. And over time the growth of the entire population will be five percent. The group with the largest growth wins.<br />
<br />
This is an important aspect because people will respond differently to the changes in society. There are a lot of explanations why population growth slowes when gdp rises. There will be more contraceptives and more luxury etc. However there will be a group within the population that despite all these changes still has a preference for having children. <br />
M. Meijer <small><span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Meijer1973|Meijer1973]] ([[User talk:Meijer1973|talk]] • [[Special:Contributions/Meijer1973|contribs]]) 20:05, 29 August 2010 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Graph of World Population ==<br />
<br />
Hmm. I just wanted to object to a few things:<br />
*The World Population graph is described as "''clearly... close to linear''". Really? To me it looks "clearly curved". (In fact, I think I see evidence of the [[logistic curve]], but that could well be spurious.) As alluded to in the article, 50 years is an awfully short time to get a good idea of how human population levels are changing. In fact, graphing the data from 1804-1999 given in the [http://www.geohive.com/global/linkg.php?xml=hist2&xsl=hist2 first external link] at that point in the article, would give a strong impression of ''exponential'' growth. Yes, maybe we're starting to see the beginning of the "slowing down" in growth that's predicted by the logistic model, but it's relatively early in that process, IMO, so I would be very hesitant to claim that the growth is no longer exponential &mdash; certainly not based on the data given here. ([[User:Dcljr|dcljr]], continued below)<br />
** Yes, graphing the 6 points 1804-1999 does look ''closer'' to exponential (see below) - but the data prior to 1950 are extrapolations or approximations, based partly on the ''assumption'' of exponential growth prior to 1950 (and of course data after 2004 is purely extrapolated with some unstated model). Only the data highlighted in blue are based largely on actual census counts. (In any case, it looks closer still to two linear segments with an critical point near 1960). So the reason for concentrating on the last 50 years is because that is the sole period for which we have reasonably reliable data. And when you graph that real data, you get something that offers little support for the common assumption that "it's obviously exponential". Also it was not stated that it's "no longer exponential", but rather that there is no strong evidence that it ever has been. In fact it could be a very slow exponential, or maybe a very slow logistical, or perhaps linear, or quadratic - the point is we really don't know, and at any rate it certainly isn't a simple function. But at least the reason for choosing this period should be clarified. ([[User:Securiger|Securiger]])<br/>[[Image:Extrapolated world population history.png]]<br />
*** Hmm... Part of the reason it might ''look'' closer to two linear segments is because the interpolating curve is (I assume) a cubic spline (and there's no point for it to go through between c. 1805 and 1925). Anyway, I agree with the rest of your paragraph. - [[User:Dcljr|dcljr]] 22:53, 7 Sep 2004 (UTC)<br />
<br />
*Note that the plot of World Population Increase suggests that the rate of increase may actually still be going up, perhaps even (approximately) linearly (you always have to expect short-term fluctuations from the overall trend), which would imply '''quadratic''' growth. ([[User:Dcljr|dcljr]])<br />
** How do you figure that? Apart from two years, it has been going down every year since 1987 - which is a third of the period for which we actually have reliable data! (Overall, there has been downturn in the growth rate for 26 of the 54 years considered.) ([[User:Securiger|Securiger]])<br />
*The sentence that begins "''Also the rate of increase should increase, whereas, of the increase between [[1960]] and today, five-sixths occurred in the early [[1960s]]''", aside from being confusing, is '''completely misleading''', since a mere glance of the Increase graph shows something highly unusual happening in the years [[1957]]-[[1962]], resulting in a lcoal minimum in 1960! That dip in the graph is '''''the only reason''''' the statement above is true (to the extent that it is). ([[User:Dcljr|dcljr]])<br />
**I'll try to rephrase the sentence you find confusing. The point is that in a positive exponential, the first [[difference equation|difference]] (and second difference, and all other differences) is also a positive, upward trending exponential. Thus when you get a true exponential growth curve and plot the differences between years, that rate-of-growth curve is itself an upward curving exponential. The rate-of-growth curve for human population clearly does not look like that at all. This is seen even more so in the 2nd difference curve (below), which however I would not include on the main page because second differences are heavily affected by noise. If population was exponential, the second difference curve should also be exponential, in fact it has a lot of noise oscillating around zero but with an overall downward trend. As for the statement which you claim is "completely misleading", umm, your "objection" agrees almost exactly with the point and meaning of that sentence: if we were looking at exponential growth, most of the growth would be recent, but in fact most of the growth is due to "something highly unusual" happening back then - the big dip from '57 to '60, and also the huge surge from '60 to '63. And even if we interpolate the years '57 to '63 to remove this curious feature, 75% of the growth increase between 1950 and the peak year, 1990, occurred in the first half of that period. This is just not at all consistent with a positive exponential growth. It seems I need to make some clarifications on why this chart, and the data it represents, are wholly inconsistent with the implications of exponential growth. ([[User:Securiger|Securiger]])<br/>[[Image:Population 2nd derivative.png]]<br />
***Maybe I misunderstood your purpose of pointing out the circa-1960 thing. I don't know. In any case, I wouldn't read much into the data of around that time. The "hiccup" might just be "noise" or might be due to a completely ''administrative'' cause (a change, say, in how censuses were taken or recorded in one or more large countries at the time &mdash; who knows?). I think most of our "differences" can be summed up by the following statement from the article: "''...short-term trends, even on the scale of decades or centuries, do not necessarily disprove the underlying mechanisms...''". I've been taking a much more long-term perspective, figuring that things like the 1960-ish "hiccup" and the "decrease in the increase" since 1986 are likely short-term deviations from the overall pattern over centuries (which is essentially unknowable anyway, but at least an exponential [and logistical] model has some theoretical basis). Anyway, I think both of us can agree that in the last 50 years or so the trend has not ''appeared to be'' exponential. On a completely different note, it would be interesting to consider (not in the article itself &mdash; or even here, necessarily) what role (tele)communications and transportation plays in all of this. Might population growth be "stabilizing" (''2nd derivative'' graph above) as a result of the increased interconnectedness of human populations? Perhaps that's the reason behind the "critical point" of around 1960? - [[User:Dcljr|dcljr]] 22:53, 7 Sep 2004 (UTC)<br />
<br />
*Finally, I think the [[correlation coefficient]] is a pretty useless measure of anything in this context; someone should do an appropriate [[statistical test]] on the yearly data instead (I suggest an F-test to see whether an exponential term is needed over linear <nowiki>[intercept and slope]</nowiki> terms, and possibly an approximate lack of fit test). - [[User:Dcljr|dcljr]] 08:00, 6 Aug 2004 (UTC)<br />
**Why do you think it is useless here? <math>r^2</math> is supposed to measure the fraction of the variability in y explained by the function of x - in this case, a linear model and exponential one explain the variability about equally well. I don't understand what you mean by "F-test to see whether an exponential term is needed over linear", but an F-test finds no significant difference in the residuals from linear and exponential models. [[User:Securiger|Securiger]] 16:58, 7 Aug 2004 (UTC)<br />
***Why is it useless? Because an exponential with slow growth can ''look'' linear and have a correlation close to 1! As for ''r''&sup2;, the article mentions the correlation coefficient not the coefficient of determination. Although obviously they're computationally the same in this case, the author was using it specifically to indicate linearity. In any case, even if you grant that "''practically'' speaking" the correlation is close to 1, consider what "practice" we're putting this information to: we're using these models to predict population levels far into the future (sometimes as far into the future as we have "reliable" data in the past, in fact &mdash; see above graph) and there can be a ''big'' difference between [[extrapolation]] using a linear model and one using an exponential. (Of course. That's why we're discussing this in the first place.) Oh, and I meant an ''ANOVA'' "F-test" for testing whether a coefficient in a regression model is zero (as opposed to an "F-test" for testing the equality of two population variances). I should have been more specific. I'm not sure what "F-test" you did. - [[User:Dcljr|dcljr]] 22:53, 7 Sep 2004 (UTC)<br />
<br />
== Depletion of resources. ==<br />
<br />
I think these things should be included because they strongly effect what decisions should be made regarding Malthusian theory.<br />
I find it impossible to argue with or doubt the basic theory. Almost the only requirements for its applicability are that life exists and there is no centralized control.<br />
What is in question are the time scale and the nature of the catastrophe. Both of these are strongly effected by pollution and resource depletion, especially energy and farm land.<br />
One can consider food the "fuel" of non-industrial man, so energy is the modern equivalent.<br />
<br />
The only way I feel I am being pessimistic is that nuclear (breader fission and/or fusion) power may well be able to replace fossil fuels with acceptable pollution and hazard, but no-one is sure of that. Anyway it can't support the kind of increase in energy consumption we are seeing.<br />
<br />
David R. Ingham<br />
<br />
== Citations Needed ==<br />
<br />
There is no cite given for the following assertion:<br />
<br />
''In fact, currently, food supply per person is several times higher than when Malthus wrote his essay''<br />
<br />
Reference #10 links to the International Data Base home page, but does not contain a reference to any particular article.<br />
<br />
== Only showing to 1950 in the chart ==<br />
<br />
I read what was discussed before, and I still think it is misleading to only show data from 1950-2000. Regardless of the precision of the data before 1950, the numbers can still be shown to be in the right ballpark. (One reader commented that the data before 1950 were often approxomations that, in part, assumed exponential growth - but one can not possibly assume linear growth, or there would have been no people before 1900! And the numbers for earlier dates are based on real data, not merely assumptions.) <br />
<br />
It's obvious that the period from 1950 to 2000 looks much more linear than, say, 1750 to 2000, and gives a misleading impression. The correct answer is, as has been said, that world population appears to follow a more complex function than simple linear, exponential, or quadratic growth. So why show only the select portion that appears linear? &ndash; [[User:Quadell|Quadell]] <sup>([[User_talk:Quadell|talk]])</sup> 13:47, 10 October 2005 (UTC)<br />
<br />
:Since there has been no discussion for 2 weeks on this, I'm going to change the article. &ndash; [[User:Quadell|Quadell]] <sup>([[User_talk:Quadell|talk]])</sup> 15:19, 23 October 2005 (UTC)<br />
<br />
== An Inaccurate Interpretation ==<br />
<br />
When you say: <br />
<br />
:"[Malthus] predicted that population growth would eventually outrun food supply," <br />
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(this being one of many statements you've made in support of your interpretation) you seem to be claiming that Malthus was describing (and predicting) a future catastrophic global event - one that has yet to occur. That is not what he was saying, at all.<br />
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Malthus posited a doubling of world population every 25 years '''under ideal conditions''' (no shortage of food and none of the "positive" constraints of, for example, war and disease). It is wrong to assume that Malthus actually thought the world population would double every 25 years until some future event in which there would not be enough food to sustain the population. (Given his ideal conditions and a population at the close of the 18th century of 1 billion, the world population would now be in excess of 250 billion.) <br />
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What he predicted was not some apocalyptic event but ''ongoing catastrophes'' playing out simultaneously in localized areas all over the world, wherever and whenever any group of people could not sustain themselves because their population had outrun the local area's food production capacity. His intent is quite clear in his statement (when discussing the American Indian):<br />
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:"Yet, [...] the effort towards population, even in this people, seems to be ''always'' greater than the means to support it." [emphasis added]<br />
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It is also implicitly clear that when Darwin found in Malthus' essay the mechanism that drives evolution - a constant competition for survival due to limited resources - he didn't think Malthus was predicting some future global catastrophe. <br />
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Malthus was addressing the idea of utopian societies gaining popularity at the time he wrote his essay. The point of his essay was to show that there could ''never'' be a population free from poverty and hunger and, therefore, the dream of a utopian society was just that - a dream. While your point that food production is now far greater than Malthus could ever imagine is true, what Malthus was saying remains valid. There are more people living in extreme poverty today than there were people (in total) at the time Malthus wrote his essay. <br />
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[[User:Paul Pomeroy|Paul Pomeroy]] 06:14, 24 December 2005 (UTC)<br />
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I was going to make those very points (see above) about the logistic curve behaviour not contradicting Malthus's ideas, i.e. that he did not predict exponential growth but rather a tendency towards it, always modified by "checks", which is precisely where the logistics curve comes from. But then, why hasn't that change yet been made?<br />
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I'd also like to draw attention to [Nassau Senior]'s work on wages, which has some of this thinking behind it. The particular point I want to bring out is his idea that machinery could theoretically compete with people for food, if only it needed fuel that drew on the same resources - which using more renewable fuels might soon cause. PML.<br />
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== Population, WHEN UNCHECKED, increases in a geometrical ratio ==<br />
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Hi,<br />
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when discussing the correctness of the geometric growth assumption and Malthus' theory in general it's important to keep Malthus' exact words in mind: ''"Population, WHEN UNCHECKED, increases in a geometrical ratio"''. Since the late 18th century occured plenty of Malthusian' checks to the human population: wars and epidemics, unhealthy living conditions, still existing infant mortality, contraception and abortion etc.<br />
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Arguing that the Malthusian population model is void because we can't see a perfect exponential growth in the world population chart seems somewhat dubios; without considering the existence of checks (that, in Malthus' thinking, avoid, or delay, the "big catastrophe").<br />
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-- [[User:212.144.193.196|212.144.193.196]] 12:01, 19 February 2006 (UTC)<br />
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:user 212.144.193.196 is right on target. i wish she or he would get a name :) [[User:Anlace|Anlace]] 21:16, 23 June 2006 (UTC)<br />
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== Fertility Rate ==<br />
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There has been enormous decrease in female fertility worldwide and this is something that is not just specific to the west. The average worldwide fertility is now 2.59 (2.1 is the replacement rate fertility at which no population growth will occur in the long term). For instance the fertility rate in India is now 2.73. This implies that growth is not exponential since a constant fertility rate would be required for exponential growth. This is the reason for the UN estimates. A scientific approach (scientific does not mean environmentalist) implies that population growth must level off due to decreasing fertility. Therefore neo-malthusian theory makes no sense and has just been debunked. QED bitches.<br />
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:the anonymous author above makes little sense. the birth rate of India for example would lead to tens of millions more people in that country in the next decades if the rate is left unchecked and death rates do not escalate severely. moreover there are many ways population growth can "level off" besides decreased fertility. thus the author above has revealed his or her inherent lack of scientific approach. [[User:Anlace|Anlace]] 04:39, 2 July 2006 (UTC)<br />
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:I'm not sure what the commenter means by 'female fertility'. There is no reason to think that women are physiologically less fertile than they used to be. The reduction in actual birth rates is due mainly to contraception, abortion, and to the increasing economic independence of women, which means they do not need to marry as soon as possible. I don't know about 'neo-Malthusian theory', but Malthus himself was aware of the primitive methods of birth control available in his day, and deplored them as immoral 'violations of the marriage bed'. His own preferred method of birth control was 'moral restraint', i.e. abstention from marriage by those who cannot afford to raise children, combined with chastity by the unmarried. Which is a bit grim, but don't forget he was a clergyman.[[Special:Contributions/109.158.128.2|109.158.128.2]] ([[User talk:109.158.128.2|talk]]) 13:33, 20 January 2014 (UTC)<br />
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That assumes fertility does not continue to decrease and we have no reason to expect that will happen given that it has decreased from 6 to less that 3 worldwide from 1960 to 1990. You say India will continue to experience population increase. It will but at a slower rate which is completely inconsistent with Malthus. Showing an increase in population is not enough. You are required to show an exponential increase. A decrease from 6 to 3 definitely implies that growth is not exponential since exponential growth requires constant fertility.<br />
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:Could we please have a moratorium on comments about Malthus by people who have never read him? Malthus never claimed that population actually increases at an exponential rate, only that it would do if there were no 'checks' on reproduction. He then devoted hundreds of pages (in the later editions of his Essay) to analyzing what those 'checks' were.[[Special:Contributions/109.158.128.2|109.158.128.2]] ([[User talk:109.158.128.2|talk]]) 13:37, 20 January 2014 (UTC)<br />
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::i think someone is missing the big picture here. have you seen the "low" projections for india and many lesser developed countries (i am not considering India lesser developed by the way). the real issue is carrying capacity. do you honestly believe there is carrying capacity for these burgeoning billions when over one billion people today do not have safe drinking water? this is not a simple matter of sharing the wealth. we are simply living on a finite planet, whose resources are stretched thinly. wake up and smell the coffee. the catatastrophe is occurring now. by the way your credibility would grow exponentially if you would create an account :) [[User:Anlace|Anlace]] 05:15, 2 July 2006 (UTC)<br />
::: Carrying capacity is a variable in the [[Logistic curve]], it is not part of malthus' original theory afaik. [[User:Kim Bruning|Kim Bruning]] 09:07, 20 July 2006 (UTC)<br />
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== Logistic curve and lotka-volterra ==<br />
They're already mentioned, but not emphasized. Could we maybe stress that there are currently improved population models available. Both these newer models *do* actually have malthusian style exponential growth for certain parameters. They just also have different behaviour under other parameters. --[[User:Kim Bruning|Kim Bruning]] 09:01, 20 July 2006 (UTC)<br />
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==NPOV & Factual accuracy==<br />
The section on "is the catastrophe happening?" seems to have a Non-NPOV and perhaps even some factual accuracy. I just stumbled on this article and don't know enough to necessarily correct it all myself, but tagged the section. For example, the unsourced and original opinion that the UN study is "less scientific" than contradicting studies. There are weasel words/phrases like "numerous scholars accept...", "some analysts consider...", etc. I think the section has definitely been massaged to push a subtly apocalyptic point of view.--[[User:160.39.213.64|160.39.213.64]] 01:54, 27 September 2006 (UTC)<br />
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I did enjoy the bit about one lone economist suggessting that global starvation might not be inevitable! Most economists (and others with a half a brain!) regard theories of Malthusian catastophes as a 19th century goof, and comprehensively disproven! Neo-Malthusianism is up there with those who believe that reading the Bible backwards reveals Satanic messages! --[[User:Nmcmurdo|Nmcmurdo]] 19:02, 23 October 2006 (UTC)<br />
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I agree that the earlier version had some serious problems with bias. As time permits, I have been trying to improve this section with both text and figures that let readers make up their own minds based on the most impartial and accurate graphics that I can devise. — [[User:Aetheling|Aetheling]] 20:55, 24 October 2006 (UTC)<br />
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As first user states. There are lots of NPOV issues with that section. Whoever authored that section was determined to reject all notions that the Malthusian Catastrophe is shoved back/not happening at all. Then again murdo, isn't it a bit personal to talk, ad hominem, to the Neo-Malthusians?<br />
We sure could use a little tact everywhere in Wikipedia. [[User:Pasonia|Pasonia]] 03:31, 18 November 2006 (UTC)<br />
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True. The way I heard it, the world food supply is more than enough to comfortably sustain the entire population, and famine is due mostly to politics and poor distribution. [[User:Vultur|Vultur]] 9:48 PM, 16 December 2006 (UTC)<br />
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:there is no question that more sourcing is needed on this article (along with 99 percent of all wikipedia articles}. Vultur, the way you "heard it" is factually in error. the world food supply is presently being produced by un[[sustainable]] agricultural methods. in some of the biggest production areas (eg great plains of USA and north China plain) groundwater is being exhausted. there are countless other factual examples of the fact that food production is not foreseeably adequate...let alone adequate [[drinking water]]. thus i hope the zeal expressed above will translate into acquiring fact based sources. regards. [[User:Anlace|Anlace]] 15:31, 17 December 2006 (UTC)<br />
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== Malthusian catastrophe in popular culture ==<br />
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Maybe this article is asking for a "Malthusian catastrophe in popular culture" section, as popular on many other articles? To seed such a section, here's a piece of trivia: the [[Guardians of the Universe]], from DC Comics, originated in a planed named Maltus, and were called Maltusians. Some of them evolved into the Guardians and left for Oa, while most stayed behind, and were later depicted as much less advanced than Earth, presumably due to Malthusian effects. It may be that the name is only a coincidence, and as such I'd rather not touch the article, but I believe it's intentional. I'm sure other people can remember lots of other pop references. [[User:LaloMartins|LaloMartins]] 05:01, 12 October 2006 (UTC)<br />
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== Critics of Malthusian catastrophe ==<br />
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Following are the sections I wrote on critics of malthusian catastrophe. However, they might first be further discussed before any display on the article page again, so I moved them here. Please state if you find them reasonable or not. [[User:Mortsggah|Mikael Häggström]] 06:54, 9 June 2007 (UTC)<br />
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===Economically===<br />
By the simple rule of supply and demand, an increasing population would lead to an increasing demand for food. If then the supply of food isn't increasing at the same rate, the price of food will increase. Thus, more people would find it worth to work agricultural, and if the land area of agriculture isn't enough, find alternatives for producing food. Such alternatives could be food based on [[algae]] or [[fungi]] <ref>www.ias.ac.in/resonance/May2004/pdf/May2004p33-40.pdf</ref> or, on the long term, purely [[synthetic food]].<br />
On the other hand, increasing prices of food would render the consumers to find cheaper alternatives. Thus, the worst catastrophe that could happen is that all people would have to become vegetarians, instead of the wasting system of eating animals eating vegetables. Alternatively, the population would have to eat more algae or seaweed.<br />
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:The problem is that you run into limits of what can physically be produced. Prolonged exponential growth would lead to absurdities like having more people than there are atoms in the universe, or a vast ball of humans expanding into space faster than the speed of light. Supply and demand isn't going to make those scenarios any less absurd. Even to get remotely close to those scenarios would require sci-fi-style technology (think [[Ringworld]]), which, while it may appear in the future, should not be taken for granted. Currently feasible things like eating seaweed would buy us a few doubling times, at best, and the population doubles every 70 years at a modest 1% growth rate. <br />
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:Malthus agreed with you that agricultural output could be increased, but he didn't believe it could increase as fast as a growing population.[[User:Rsheridan6|Rsheridan6]] 03:25, 15 June 2007 (UTC)<br />
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Shouldn't the growing occurrence of obesity in the developing world render Malthus' theory (at least as it relates to food) void once and for all? I mean now we can manufacture junk food with ridiculously high calorie content for next to nothing. The number of obese individuals worldwide has now equalled the number of underfed. This should be mentioned somewhere http://www.fao.org/FOCUS/E/obesity/obes1.htm[[User:81.153.62.232|81.153.62.232]] 20:23, 10 July 2007 (UTC)<br />
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:That has nothing to do with the essence of the theory. Read the paragraph above yours: where is the cheap junk food going to come from when there are 12, 24, 48, 96, or 192 billion people? The theory is based on the fundamental nature of food production and population growth, and the fact that farming productivity outstripped population growth for a century or two (really not a long time on an evolutionary or historical scale) doesn't render the theory null and void forever, any more than the fact that oil production increased for a few centuries proves that there's an infinite supply of oil in the ground. To render it void forever, you would have to either show that we can reliably have food production increases similar to the green revolution on a regular basis, or that population growth will cease forever. [[User:Rsheridan6|Rsheridan6]] 05:53, 11 July 2007 (UTC)<br />
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===Distribution===<br />
The starvation we see on earth today isn't a result of an insufficiency of the earth to supply food, even without prospects of purely [[synthetic food]] and a shift to eating algae and fungi. Rather, it's a result of inability to transport it to all areas where it is needed.<br />
By the [[Malthusian catastrophe#economically|economic reasons]] above, this will continue into the future as well. Thus, there will be no deterioration of mankind due to the Malthusian catastrophe, although an unfair distribution of supply might persist.<br />
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:The sections (Distribution in particular) are stating opinion as fact, and not crediting the opinion to any source. [[Wikipedia:No original research#Primary, secondary, and tertiary sources|Wikipedia is a tertiary source]], and must also be written from a [[WP:NPOV|neutral point of view]]. We cannot say "it's obvious that this theory is wrong because blah", we must say "John F. Doe and Dr. Foo disagree with this theory due to blah". [[User:Capi|Capi]] 14:55, 14 June 2007 (UTC)<br />
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::Yeah, right. [http://ipsnews.net/news.asp?idnews=38372] Guess the U.N. know what they are talking about when they say that there's already enough food for 12 billion people. And the population is expected to reach a maximum of 9 billion. Actually in many parts of the world the population already stopped growing. So I don't think figuring out how to grow stuff in space is our primary problem to stop people starving and I also don't think the Malthusian catastrophe is about to happen any time soon. --[[User:Mudd1|Mudd1]] 13:44, 25 August 2007 (UTC)<br />
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== Load of clap-trap ==<br />
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What a load of clap-trap! Even Malthus agreed that since his predicted catastrophe never happened, he was wrong. Would that his modern-day supporters were as intelligent and honest as he. <br />
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==Man does not live by bread alone==<br />
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In most discussions/articles RE: the sustaniability or otherwise of future (or even current) population levels there is far too much emphisis on the feasibility (or otherwise) of meeting projected demands of FOOD but what of other resources required by modern people to lead worthwhile lives like housing, clean water, clothing, energy, transport, medicine and all manner of manufactured goods. There are serious question marks over the long term availability of sufficent supplies of raw materials to meet these needs even at current population levels. And what pollution ? All other considerations being equal surely twelve billion people will produce a lot more than say two billion. [[User:80.229.222.48|80.229.222.48]] 11:14, 11 August 2007 (UTC)<br />
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==Population growth==<br />
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http:Disablelink//www.optimumpopulation.org/ your right about this one... it is a spam one really here ... because of the donation thing pov. etc... thanks for catching that NJGW it is not a good link here at all... and I guess you agree that you probably mistakenly removed this one previously... that is excellent information ''M. King Hubbert on the Nature of Growth. 1974'' Thanks for being alert on the other one. [[User:Skipsievert|skip sievert]] ([[User talk:Skipsievert|talk]]) 18:46, 5 September 2008 (UTC)<br />
:The Hubbert link doesn't really belong either... it doesn't mention Malthus or speak of population drops due to catastrophe. It deals with population growth. I think other editors should look very closely at that link and consider removing it. It has also been inserted into other articles recently to which it is only tangentially related. [[User:NJGW|NJGW]] ([[User talk:NJGW|talk]]) 07:33, 6 September 2008 (UTC)<br />
::Sorry I think you are wrong. It is all about exponential growth and use of resources .. and future consequences.. Why would it have to mention Malthus to be pertinent? It goes way beyond Malthus... Malthus would have swooned over Hubberts charts and graphs. Hubbert was probably was the most well known Geo-scientist produced by the U.S. -- Removing that link ... is removing very good information. Not suggested. Look at Hubberts exponential growth explanation in the article. For that reason alone it is good... also here is a sample from the paper in question:<br />
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::''Yet, during the last two centuries of unbroken industrial growth we have evolved what amounts to an exponential-growth culture. Our institutions, our legal system, our financial system, and our most cherished folkways and beliefs are all based upon the premise of continuing growth. Since physical and biological constraints make it impossible to continue such rates of growth indefinitely, it is inevitable that with the slowing down in the rates of physical growth cultural adjustments must be made.''[http://www.technocracy.org/natureofgrowth.htm] Now that is purely Malthusian. [[User:Skipsievert|skip sievert]] ([[User talk:Skipsievert|talk]]) 15:40, 6 September 2008 (UTC)<br />
:::Malthusian? Perhaps (though it's your word against Hubbert's lack of using the name Malthus for now), but how is it related to Malthusian catastrophes? Lots of folks have written works which may be traced back in some way to Malthus, but we shouldn't list every one of those papers here, or even at Malthus' article for that matter. The external links should be a stand-out resource which speaks about the topic itself, or else we'll have every single person who likes a tangentially related website wanting to link it here. <br />
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:::Better idea: try finding a way to use it as a ref here or at Malthus in a way which doesn't violate [[wp:OR]]. [[User:NJGW|NJGW]] ([[User talk:NJGW|talk]]) 19:18, 6 September 2008 (UTC)<br />
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::::E.T's are supposed to expand the information not directly in the article but pertinent.<br />
::::''Wikipedia does not publish original research or original thought. This includes unpublished facts, arguments, speculation, and ideas; and any unpublished analysis or synthesis of published material that serves to advance a position. This means that Wikipedia is not the place to publish your own opinions, experiences, or arguments.''<br />
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::::How it is you interpret that file as such is not known. This is a scientist who was called before a subcommittee of the Congress to testify about energy, as it relates the environment and consequences of lack of energy in the future. Energy is what supports our system. If you loose access to it the system stops. Original research? Hubbert was called before these politicians to try and explain a very Malthusian problem... We use petrol also for making fertilizer and pesticides... That is the [[green revolution]]... or what powers it. [[User:Skipsievert|skip sievert]] ([[User talk:Skipsievert|talk]]) 20:56, 6 September 2008 (UTC)<br />
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:::::I think you mean ELs, not ETs. In any case, you should read [[wp:EL]], and especially [[wp:ELYES|the list of suggested external links]] and the thirteenth entry in [[wp:ELNO|the list of links to avoid]] (which reads in part "Sites that are only indirectly related to the article's subject: the link should be directly related to the subject of the article"). The article is not about Malthusian catastrophies, Malthus and catastrophies are not mentioned, and besides your interpretation we have no indication that this was essay was written to "explain a very Malthusian problem". I'm not trying to be mean, and I see why you believe what you believe (and even agree with your main points regarding Hubbert peaks and population growth), but that doesn't make it appropriate to link this essay in this and other tangentially related articles. Besides, it exists appropriately as a link in at least 6 other articles already. [[User:NJGW|NJGW]] ([[User talk:NJGW|talk]]) 21:36, 6 September 2008 (UTC)<br />
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I agree with NJGW here. The [[WP:OR]] violation he is referring to is not in the contents of the linked article itself; it's in your tacit assumption that the latter relates to the main topic of Malthusian Catastrophe. That is far from being a given. I echo his guidance in trying to place it within the body of the article. It's compliance or lack thereof will then become apparent. ~ [[User:Alcmaeonid|Alcmaeonid]] ([[User talk:Alcmaeonid|talk]]) 22:06, 6 September 2008 (UTC)<br />
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::Ok... but I do not agree... [[peak oil]] is about Malthusian as it gets, in every sense. [[User:Skipsievert|skip sievert]] ([[User talk:Skipsievert|talk]]) 05:25, 7 September 2008 (UTC)<br />
:::I think it's more accurate to say that some of the predictions of [[oil depletion]] resemble Malthusian catastrophes, but that's already covered [[Malthusian_catastrophe#Application_to_energy.2Fresource_consumption|here]] and a link to Peak oil exists in the see also section. I see no reason to violate wp:ELNO-13 in this case. [[User:NJGW|NJGW]] ([[User talk:NJGW|talk]]) 15:09, 7 September 2008 (UTC)<br />
::::You have a point there. Bartlett does a good job explaining things. I am thinking now that I agree with your points in general, after looking more into the issues you discussed. [[User:Skipsievert|skip sievert]] ([[User talk:Skipsievert|talk]]) 22:33, 8 September 2008 (UTC)<br />
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== Anarcho-primitivism connection? ==<br />
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First I just want to point out that links within the See also section shouldn't have the same level of scrutiny as those in the EL sections. That said, this connection is a bit loose... I can see how one might argue that an Anarcho-primitivist might support the return to a different lifestyle in order to ''avoid'' a Malthusian catastrophy, but couldn't the same be said for any type of primitivst? Maybe a section could be inserted in the text which discusses movements which aim to mitigate a catastrophy and primitivism could be mentioned there (but since this is essentially a population issue, a sudden drop in technology levels worldwide would create an instant and artificial--rather than organic--Malthusian catastrophy).<br />
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This seems a bit tricky, but if done correctly could improve the article. [[User:NJGW|NJGW]] ([[User talk:NJGW|talk]]) 18:11, 18 September 2008 (UTC)<br />
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It's complicated to distinguish "artificial" from "organic" social phenomenon. The connection is very clear if you consider that the "Malthusian catastrophe" is in itself part of the anarcho-primitivist theory on why civilization is unsustainable. In this sense, the anarcho-primitivists are not exactly looking to “mitigate” the problem, but to find alternatives of sustainable survival trough the inevitable collapse. [[User:Maziotis|Maziotis]] ([[User talk:Maziotis|talk]]) 21:05, 18 September 2008 (UTC)<br />
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:[[Anarcho-primitivism]] is an [[Anarchism|anarchist]] critique of the origins and progress of [[civilization]]. According to anarcho-primitivism, the shift from [[hunter-gatherer]] to [[Agriculture|agricultural]] subsistence gave rise to [[Social_stratification#Non-stratified_societies|social stratification]], [[coercion]], and [[Social alienation|alienation]]. Anarcho-primitivists advocate a return to non-"civilized" ways of life through [[Industrialisation|deindustrialisation]], abolition of [[division of labour]] or [[specialization (functional)|specialization]], and abandonment of [[technology]]. There are other non-anarchist forms of [[primitivism]], and not all primitivists point to the same phenomenon as the source of modern, civilized problems. I fail to see how this is related... much to Malthus, if at all. [[User:Skipsievert|skip sievert]] ([[User talk:Skipsievert|talk]]) 02:10, 19 September 2008 (UTC)<br />
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::Maybe you should try to read more than the first paragraph of an article in wikipedia when trying to understand a subject. [[User:Maziotis|Maziotis]] ([[User talk:Maziotis|talk]]) 09:32, 19 September 2008 (UTC)<br />
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I believe there is not exactly a Marx in anarcho-primitivism like there is one in marxism. There is this general assumption that civilization is a two second disease in our biological history. Other than that, there is a space for different interpretations to what the unsustainability of civilization means. I never meant to argue that the Malthusian theory is a corner stone in anarcho-primitivist theory. Simply, if I understood it well, this theory is an explanation on how agriculture is unsustainable for human beings in the long run. This in turn is central to a political philosophy called anarcho-primitivism. There is where I see a clear connection. [[User:Maziotis|Maziotis]] ([[User talk:Maziotis|talk]]) 11:52, 19 September 2008 (UTC)<br />
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::Yeah probably that is the angle that would have to be tried to get at... if a link were to be made. As NJGW said ''Maybe a section could be inserted in the text which discusses movements which aim to mitigate a catastrophy and primitivism could be mentioned there (but since this is essentially a population issue, a sudden drop in technology levels worldwide would create an instant and artificial--rather than organic--Malthusian catastrophy).''... Another section might list a bunch of alternative concepts... but still Anarcho-primitivism being in my opinion... a kind of political social movement... that is possibly a couple of steps from even mainstream hetorodox thinking, although I am familiar with Tainter and his ideas, and also some of the other well known advocates of this movement. [[User:Skipsievert|skip sievert]] ([[User talk:Skipsievert|talk]]) 14:25, 19 September 2008 (UTC)<br />
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== does not belong in lede ==<br />
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"An August 2007 science review in The New York Times raised the claim that the Industrial Revolution had enabled the modern world to break out of the Malthusian Trap,[1] " ... uh... the idea the that the Industrial Revolution enabled the modern world to break out of the Malthusian Trap goes back to ... well, shortly after Malthus. Certainly it was widely accepted among economists by the early 20th century. And that's way, way, way before 2007. This is so outdated (2007 vs. 1900) and trite ("raised the claim" to characterize a widely held view completely supported by empirical evidence) that it just does not belong in the article, and definitely not in the lede.[[User:Radeksz|radek]] ([[User talk:Radeksz|talk]]) 22:23, 1 August 2009 (UTC)<br />
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I am curious if Malthusian theory can be applied to other areas of growth. For example, educational institutions continually birthing graduates in relation to the number of jobs available. In trying to ease the problem, different organizations or government entities are wanting to create new jobs. This is not stated as reality but to only an example. <br />
[[User:Beetlebailey75|Beetlebailey75]] ([[User talk:Beetlebailey75|talk]]) 09:01, 3 April 2010 (UTC)beetlebailey75<br />
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== This sentence is questionable ==<br />
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"In some cases, population growth occurs due to increasing life expectancies, even though fertility rates are below replacement."<br />
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Does not seem to make mathematical sense. The mechanism where increasing life expectancies creates population growth works in the way that: greater life expectancies cause increasing fertility rates, which causes population growth. Increasing life expectancies cannot create population growth without increasing fertility rates about replacement first. Think about the arithmetic of it:<br />
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If you have an initial number, say, 0, and can (only) add or subtract as many 1s from it anytime, you need to add more times than you subtract to get a greater number. I'm no mathematician, by the way, so I don't know if this is always true, but I'm pretty true it applies here. Anyways, if "fertility rates are below replacement," as in the sentence in question, it corresponds to subtracting more times than adding, if the resulting number corresponds to the population, but since you need to add more times than you subtract to get a greater number, the population could only decrease. If the population could only decrease, it wouldn't make sense how "population growth occurs". If no one objects, I'll remove this statement at February. [[Special:Contributions/173.180.202.22|173.180.202.22]] ([[User talk:173.180.202.22|talk]]) 06:36, 2 January 2012 (UTC)<br />
:And also, the example where there's "1.3 children/woman" doesn't seem to be a replacement rate because the children's parents don't necessarily have to be replaced. [[Special:Contributions/173.180.202.22|173.180.202.22]] ([[User talk:173.180.202.22|talk]]) 07:10, 2 January 2012 (UTC)<br />
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== Rename ==<br />
<br />
Wouldn't it be better to have this article, with a slight rewrite and shift of focus, under [[Malthusian theory]] (currently a redirect here) rather than "catastrophe"? The way the idea works is that there are demographic checks on income per capita but a "catastrophe" in the sense of something sudden and very bad is not necessarily a consequence of the model.[[User:Volunteer Marek|<font color="Orange">Volunteer</font><font color="Blue">Marek</font>]] 08:13, 4 July 2012 (UTC)</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=97495Main Page2014-08-24T01:51:47Z<p>10.68.16.65: </p>
<hr />
<div>{{Cite journal <br />
| last1 = Gillespie | first1 = D. T. | authorlink1 = Daniel Gillespie<br />
| title = Approximate accelerated stochastic simulation of chemically reacting systems <br />
| doi = 10.1063/1.1378322 <br />
| journal = The Journal of Chemical Physics <br />
| volume = 115 <br />
| issue = 4 <br />
| pages = 1716–1711 <br />
| year = 2001 <br />
| pmid = <br />
| pmc = <br />
| url = http://users.soe.ucsc.edu/~msmangel/Gillespie01.pdf<br />
}}<noinclude>{{template doc|Template:cite_doi/subpage}}</noinclude></div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=95725Main Page2014-08-23T16:09:28Z<p>10.68.16.65: </p>
<hr />
<div>{{National squad no numbers<br />
| name = Belgium football squad 1900 Summer Olympics<br />
| bg = #d4071a<br />
| fg = #ffce4a<br />
| bordercolor = black<br />
| country = Belgium<br />
| comp link = Football at the 1900 Summer Olympics<br />
| comp = 1900 Olympic Bronze Medalists<br />
| pos1 = GK | p1 = [[Marcel Leboutte|Leboutte]]<br />
| pos2 = | p2 = [[Albert Delbecque|Delbecque]]<br />
| pos3 = | p3 = [[Hendrik van Heuckelum|van Heuckelum]] (Dutch player)<br />
| pos4 = | p4 = [[Raul Kelecom|Kelecom]]<br />
| pos5 = | p5 = [[Lucien Londot|Londot]]<br />
| pos6 = | p6 = [[Ernest Moreau de Melen|Moreau de Melen]] <br />
| pos7 = | p7 = [[Eugène Neefs|Neefs]]<br />
| pos8 = | p8 = [[Georges Pelgrims|Pelgrims]] (captain) <br />
| pos9 = | p9 = [[Alphonse Renier|Renier]]<br />
| pos10 = | p10 = [[Émile Spannoghe|Spannoghe]]<br />
| pos11 = | p11 = [[Eric Thornton|Thornton]] (English player)<br />
| pos12 = | p12 = [[Camille Van Hoorden|Van Hoorden]] (reserve)<br />
| coach = <br />
}}<noinclude><br />
[[Category:Belgium national football team navigational boxes|Olympics 1900]]<br />
[[Category:1900 Summer Olympics football squad navigational boxes]]<br />
</noinclude></div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=92628Main Page2014-08-23T08:05:51Z<p>10.68.16.65: </p>
<hr />
<div>#REDIRECT [[Template:Events at the 1970 Asian Games]]</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=92458Main Page2014-08-23T07:15:22Z<p>10.68.16.65: </p>
<hr />
<div>{{Cite journal <br />
| last1 = Bourlat | first1 = S. <br />
| last2 = Nielsen | first2 = C. <br />
| last3 = Economou | first3 = A. <br />
| last4 = Telford | first4 = M. <br />
| title = Testing the new animal phylogeny: A phylum level molecular analysis of the animal kingdom <br />
| doi = 10.1016/j.ympev.2008.07.008 <br />
| journal = Molecular Phylogenetics and Evolution <br />
| volume = 49 <br />
| issue = 1 <br />
| pages = 23–31 <br />
| year = 2008 <br />
| pmid = 18692145<br />
| pmc = <br />
}}<noinclude>{{template doc|Template:cite_doi/subpage}}</noinclude></div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=91328Main Page2014-08-23T01:18:39Z<p>10.68.16.65: </p>
<hr />
<div>{{Cite journal <br />
| last1 = Austin | first1 = J. L. <br />
| last2 = Soeda | first2 = J. M. <br />
| editor1-last = Vollmer <br />
| editor1-first = Timothy <br />
| doi = 10.1901/jaba.2008.41-279 <br />
| title = Fixed-Time Teacher Attention to Decrease Off-Task Behaviors of Typically Developing Third Graders <br />
| journal = Journal of Applied Behavior Analysis <br />
| volume = 41 <br />
| issue = 2 <br />
| pages = 279–283 <br />
| year = 2008 <br />
| pmid = 18595294<br />
| pmc =2408347 <br />
}}<noinclude>{{template doc|Template:cite_doi/subpage}}</noinclude></div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=90461Main Page2014-08-22T21:20:59Z<p>10.68.16.65: </p>
<hr />
<div>{{cite journal<br />
|authorlink=J. Davy Kirkpatrick<br />
|last=Kirkpatrick |first=J. Davy<br />
|author2=Beichman, Charles A.; Skrutskie, Michael F.<br />
|title=The Coolest Isolated M Dwarf and Other 2MASS Discoveries<br />
|year=1997<br />
|journal=[[The Astrophysical Journal]]<br />
|volume=476 | issue= | pages=311<br />
|arxiv=<br />
|doi=10.1086/303613<br />
|bibcode=1997ApJ...476..311K}}</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=90389Main Page2014-08-22T21:10:36Z<p>10.68.16.65: </p>
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<div>{{#if:yes|<noinclude>[[Category:Passed DYK nominations&nbsp;from August 2013]]<div style="background-color: #F3F9FF; margin: 2em 0 0 0; padding: 0 10px 0 10px; border: 1px solid #AAAAAA;"><br />
:''The following discussion is an archived discussion of the DYK nomination of the article below. <span style="color:red">'''Please do not modify this page.'''</span> Subsequent comments should be made on the appropriate discussion page (such as [[{{TALKPAGENAME}}|this nomination's talk page]], [[Talk:{{SUBPAGENAME}}|the article's talk page]] or [[Wikipedia talk:Did you know]]), unless there is consensus to re-open the discussion at this page. '''No further edits should be made to this page'''.''<br />
<br />
The result was: '''promoted''' by ''[[User: Allen3|Allen3]]''&nbsp;<sup>[[User talk:Allen3|talk]]</sup> 09:46, 13 September 2013 (UTC)<br />}}<br />
{{DYKC}}<br />
====Doin' It Right====<br />
{{DYK nompage links|nompage=Doin&#39; It Right|Doin' It Right}}<br />
<div style="float:right;margin-left:0.5em;"><br />
[[File:Panda Bear, the musician.jpg|100x100px|Panda Bear]]<br />
</div><br />
{{*mp}}... that [[Daft Punk]]'s "'''[[Doin' It Right]]'''", featuring [[Panda Bear (musician)|Panda Bear]] ''(pictured)'' of the [[Animal Collective]], was considered by both [[Pitchfork Media]] and Paperblog to be the best track out of their fourth album ''[[Random Access Memories]]''?<br />
:{{*mp}}<br />
<small>Created/expanded by [[User:EditorE|EditorE]] ([[User talk:EditorE|talk]]).&nbsp;Self nominated at 14:03, 18 August 2013 (UTC)</small>.<br />
<br />
:* [[File:Symbol question.svg|16px]] New article stemming from a redirect. The hook needs to be rewritten. Pitchfork doesn't say "best", they call it the "simplest and prettiest" and their "strongest statement of purpose". Paperblog considers it the most "highly anticipated". &ndash;&nbsp;[[User:Muboshgu|Muboshgu]]&nbsp;([[User talk:Muboshgu#top|talk]]) 15:20, 3 September 2013 (UTC)<br />
::'''ALT2''':... that [[Daft Punk]]'s "'''[[Doin' It Right]]'''", featuring [[Panda Bear (musician)|Panda Bear]] ''(pictured)'' of the [[Animal Collective]], was considered by [[Pitchfork Media]] as the "simplest and prettiest" and their "strongest statement of purpose" out of their fourth album ''[[Random Access Memories]]''?<br />
::<s>Also, I don't think the article is stemming for a redirect. There is enough information outside of critical reviews, such as a review of the song itself by Pitchfork Media and Paperblog, and a fair amount of chart positions. Not worth redirecting, in my opinion. [[User:EditorE|<font style="color:Green; font-family:OCR A Extended">和DITOR</font>]][[User talk:EditorE|<font style = "color:black">'''E'''</font>]][[User:EditorE/Details|tails]] 15:26, 3 September 2013 (UTC)</s><br />
:::Opps. I misread what you said. Sorry. [[User:EditorE|<font style="color:Green; font-family:OCR A Extended">和DITOR</font>]][[User talk:EditorE|<font style = "color:black">'''E'''</font>]][[User:EditorE/Details|tails]] 15:37, 3 September 2013 (UTC)<br />
:::*[[File:Symbol confirmed.svg|16px]] That's okay. Sorry I forgot to watchlist this template so I didn't notice your response until now. ALT hook approved. &ndash;&nbsp;[[User:Muboshgu|Muboshgu]]&nbsp;([[User talk:Muboshgu#top|talk]]) 18:04, 12 September 2013 (UTC)<br />
{{-}}{{#if:yes|</div></noinclude>|{{#ifeq:{{FULLPAGENAME}}|Template talk:Did you know/{{SUBPAGENAME}}|[[Category:Pending DYK nominations]][[Category:DYK/Nominations|Pending]]|{{#ifeq:{{FULLPAGENAME}}|Template:Did you know nominations/{{SUBPAGENAME}}|[[Category:DYK/Nominations|Pending]][[Category:Pending DYK nominations]]}}}}}}<!--Please do not write below this line or remove this line. Place comments above this line.--></div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=89466Main Page2014-08-20T22:49:21Z<p>10.68.16.65: </p>
<hr />
<div>{| style="padding:0.3em; float:right; margin-left:15px; border:1px solid #B8C7D9; background:#f5faff; text-align:left; font-size:90%; line-height:1.5em"<br />
|- style="background:#cedff2; text-align:center;"<br />
!colspan=5|[[:Category:2013 IPC Swimming World Championships|Events]] at the<br/>[[2013 IPC Swimming World Championships|2013 World Championships]]<br/>[[File:Swimming pictogram (Paralympics).svg|40px]]<br />
|- style="background:#deeaf6; text-align:center;"<br />
!colspan=5|Meet events<br />
|-<br />
|50m freestyle<br />
|&nbsp;<br />
|[[2013 IPC Swimming World Championships – Men's 50 metre freestyle|men]]<br />
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|[[2013 IPC Swimming World Championships – Women's 50 metre freestyle |women]]<br />
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|[[2013 IPC Swimming World Championships – Men's 200 metre freestyle|men]]<br />
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|[[2013 IPC Swimming World Championships – Men's 50 metre backstroke|men]]<br />
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|[[2013 IPC Swimming World Championships – Men's 50 metre breaststroke|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 50 metre breaststroke|women]]<br />
|-<br />
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|<br />
|[[2013 IPC Swimming World Championships – Men's 100 metre breaststroke|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 100 metre breaststroke|women]]<br />
|-<br />
|50m butterfly<br />
|<br />
|[[2013 IPC Swimming World Championships – Men's 50 metre butterfly|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 50 metre butterfly|women]]<br />
|-<br />
|100m butterfly<br />
|<br />
|[[2013 IPC Swimming World Championships – Men's 100 metre butterfly|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 100 metre butterfly|women]]<br />
|-<br />
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|<br />
|[[2013 IPC Swimming World Championships – Men's 150 metre medley|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 150 metre medley|women]]<br />
|-<br />
|200m medley<br />
|<br />
|[[2013 IPC Swimming World Championships – Men's 200 metre medley|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 200 metre medley|women]]<br />
|-<br />
|4&times;50m freestyle relay<br />
|<br />
|[[2013 IPC Swimming World Championships – Men's 4 x 50 metre freestyle relay|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 4 x 50 metre freestyle relay|women]]<br />
|-<br />
|4&times;50m medley relay<br />
|<br />
|[[2013 IPC Swimming World Championships – Men's 4 x 50 metre medley relay|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 4 x 50 metre medley relay|women]]<br />
|-<br />
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|<br />
|[[2013 IPC Swimming World Championships – Men's 4 x 100 metre freestyle relay|men]]<br />
|<br />
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|4&times;100m medley relay<br />
|<br />
|[[2013 IPC Swimming World Championships – Men's 4 x 100 metre medley relay|men]]<br />
|<br />
|[[2013 IPC Swimming World Championships – Women's 4 x 100 metre medley relay|women]]<br />
|- style="background:#deeaf6; text-align:center;"<br />
!colspan=5 style="text-align: center; |{{navbar|Swimming2013IPCWorldChamps}}<br />
|}<noinclude><br />
[[Category:World Championships in Swimming navigational boxes|{{PAGENAME}}]]<br />
[[Category:2013 IPC Swimming World Championships|τ]]<br />
<br />
</noinclude></div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=89082Main Page2014-08-20T19:06:58Z<p>10.68.16.65: </p>
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<div>{{Infobox World Aquatics Championships country<br />
|NF=KEN<br />
|NFname=Kenya Swimming Federation<br />
|website=www.swimkenya.org<br />
|championships={{{championships|}}}<br />
|competitors={{{competitors|}}}<br />
|sports={{{sports|}}}<br />
|officials={{{officials|}}}<br />
|gold={{{gold|0}}}<br />
|silver={{{silver|0}}}<br />
|bronze={{{bronze|0}}}<br />
|rank={{{rank|}}}<br />
|appearances=<br />
* [[Kenya at the 2001 World Aquatics Championships|2001]]<br />
* [[Kenya at the 2003 World Aquatics Championships|2003]]<br />
* [[Kenya at the 2005 World Aquatics Championships|2005]]<br />
* [[Kenya at the 2007 World Aquatics Championships|2007]]<br />
* [[Kenya at the 2009 World Aquatics Championships|2009]]<br />
* [[Kenya at the 2011 World Aquatics Championships|2011]]<br />
* [[Kenya at the 2013 World Aquatics Championships|2013]]<br />
}}<noinclude><br />
[[Category:World Aquatics Championships by country infobox templates|Kenya]]<br />
[[Category:Kenya multi-sport events infobox templates|World Aquatics Championships]]<br />
</noinclude></div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=86583Main Page2014-08-20T02:20:31Z<p>10.68.16.65: </p>
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<div>[[Image:Ephesus library-650px.jpg|thumb|275px|Front of [[Celsus]] Library with aediculae in [[Ephesus]].]]<br />
[[File:Jerusalem Holy Sepulchre BW 7.JPG|The Aedicule|thumb|200px|The Aedicula where, according to [[Christianity|Christian religious tradition]], the body of [[Jesus]] was buried.]]<br />
[[File:Cathedral of exeter.jpg|thumb|275px|Gothic facade of [[Exeter Cathedral]], with rows of figures in aedicular or tabernacle frames above the door, and two above the [[crenellation]]s]] <br />
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In [[religion in ancient Rome|ancient Roman religion]], an '''''aedicula''''' (plural '''''aediculae''''') is a small [[shrine]]. The word ''aedicula'' is the [[diminutive]] of the [[Latin]] ''[[aedes (Roman)|aedes]]'', a temple building or house.<br />
<br />
Many aediculae were household [[shrine]]s that held small [[altar]]s or [[statue]]s of the [[Lares]] and [[Penates]]. The Lares were [[Religion in ancient Rome|Roman deities]] protecting the house and the family household gods. The Penates were originally [[patron gods]] (really [[genius (mythology)|genii]]) of the storeroom, later becoming household gods guarding the entire house.<br />
<br />
Other aediculae were small shrines within larger [[temple]]s, usually set on a base, surmounted by a pediment and surrounded by columns. In Roman architecture the aedicula has this representative function in the society. They are installed in public buildings like the [[Triumphal arch]], [[City gate]], or [[Therm]]es. The [[Celsus]] Library in [[Ephesus]] (2. c. AD) is a good example. From the 4th century Christianization of the Roman Empire onwards such shrines, or the framework enclosing them, are often called by the Biblical term [[tabernacle]], which becomes extended to any elaborated framework for a niche, window or picture.<br />
<br />
==Gothic aediculae==<br />
As in [[Classical architecture]], in [[Gothic architecture]], too, an aedicule or tabernacle frame is a structural framing device that gives importance to its contents, whether an inscribed plaque, a [[cult object]], a bust or the like, by assuming the tectonic vocabulary of a little building that sets it apart from the wall against which it is placed. A tabernacle frame on a wall serves similar hieratic functions as a free-standing, three-dimensional architectural [[baldaquin]] or a [[Ciborium (architecture)|ciborium]] over an [[altar]].<br />
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In Late Gothic settings, [[altarpiece]]s and [[devotional image]]s were customarily crowned with [[gable]]s and canopies supported by clustered-column piers, echoing in small the architecture of Gothic churches. Painted ædicules frame figures from sacred history in initial letters of [[Illuminated manuscript]]s.<br />
<br />
==Renaissance aediculae==<br />
[[File:Palazzo medici riccardi finestre inginocchiate.JPG|thumb|Two "tabernacle windows" in the [[Palazzo Medici Riccardi]] in Florence. These are of the type known as "inginocchiata", "kneeling" on two brackets.]] <br />
Classicizing architectonic structure and decor ''all'antica'', in the "ancient [Roman] mode", became a fashionable way to frame a painted or bas-relief portrait, or protect an expensive and precious mirror<ref>[http://www.metmuseum.org/toah/hd/fram/ho_1975.1.1638.htm Metropolitan Museum: tabernacle frame, Florence, ca 1510]</ref> during the [[High Renaissance]]; Italian precedents were imitated in France, then in Spain, England and Germany during the later 16th century.<ref>[http://www.nga.gov/exhibitions/tabernacleinfo.shtm National Gallery of Art: Tabernacle frames from the Samuel H. Kress collection]</ref><br />
<br />
==Post-Renaissance classicism==<br />
Aedicular door surrounds that are architecturally treated, with pilasters or columns flanking the doorway and an [[entablature]] even with a [[pediment]] over it came into use with the 16th century. In the [[neo-Palladian]] revival in Britain, architectonic aedicular or tabernacle frames, carved and gilded. are favourite schemes for English [[Palladian]] mirror frames of the late 1720s through the 1740s, by such designers as [[William Kent]].<br />
<br />
==Other aedicula==<br />
Similar small shrines, called ''[[naiskos|naiskoi]]'', are found in [[Religion in ancient Greece|Greek religion]], but their use was strictly religious.<br />
<br />
Aediculae exist today in Roman [[cemeteries]] as a part of funeral architecture.<br />
<br />
Presently the most famous Aedicule is situated inside the [[Church of the Holy Sepulchre]] in city of [[Jerusalem]].<br />
<br />
==Notes==<br />
{{Reflist|2}}<br />
<br />
==See also==<br />
*[[Pilaster]]<br />
*[[Portico]]<br />
<br />
==References==<br />
*Adkins, Lesley & Adkins, Roy A. (1996). ''Dictionary of Roman Religion''. Facts on File, inc. ISBN 0-8160-3005-7.<br />
*{{1911}}<br />
<br />
==External links==<br />
{{commons category|Aediculae}}<br />
*[http://www.trp.dundee.ac.uk/research/glossary/aedicule.html Conservation glossary]<br />
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[[Category:Ancient Roman temples]]<br />
[[Category:Architectural elements]]<br />
[[Category:Ancient Roman architectural elements]]</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=84956Main Page2014-08-19T16:23:48Z<p>10.68.16.65: </p>
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<div>{{About|the chemical compounds alkaloids|the [[pharmaceutical company]] in the [[Republic of Macedonia]]|Alkaloid (company)}}<br />
<br />
[[File:Papaver somniferum 01.jpg|thumb|250px|The first individual alkaloid, [[morphine]], was isolated in 1804 from [[opium poppies|poppy]] (''Papaver somniferum'').<ref>{{cite book|url=http://books.google.com/?id=MtOiLVWBn8cC&pg=PA20|page=20|title=Molecular, clinical and environmental toxicology|author=Andreas Luch|publisher=Springer|year=2009|isbn=3-7643-8335-6}}</ref>]]<br />
<br />
'''Alkaloids''' are a group of naturally occurring [[chemical compound]]s that contain mostly [[base (chemistry)|basic]] [[nitrogen]] atoms. This group also includes some related compounds with neutral<ref name="goldbook.iupac.org">[http://goldbook.iupac.org/A00220.html IUPAC. Compendium of Chemical Terminology], 2nd ed. (The "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997) ISBN 0-9678550-9-8 {{doi|10.1351/goldbook}}</ref> and even weakly [[acid]]ic properties.<ref>R. H. F. Manske. ''The Alkaloids. Chemistry and Physiology''. Volume VIII. – New York: [[Academic Press]], 1965, p. 673</ref> Some synthetic compounds of similar structure are also attributed to alkaloids.<ref>Robert Alan Lewis. [http://books.google.com/books?id=caTqdbD7j4AC&pg=PA51 ''Lewis' dictionary of toxicology'']. CRC Press, 1998, p. 51 ISBN 1-56670-223-2</ref> In addition to [[carbon]], [[hydrogen]] and [[nitrogen]], alkaloids may also contain [[oxygen]], [[sulfur]] and more rarely other elements such as [[chlorine]], [[bromine]], and [[phosphorus]].<ref name="XimE: alkaloidy">[http://www.xumuk.ru/encyklopedia/119.html Chemical Encyclopedia: alkaloids]. xumuk.ru</ref><br />
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Alkaloids are produced by a large variety of organisms, including [[bacteria]], [[fungus|fungi]], [[plant]]s, and [[animal]]s, and are part of the group of [[natural product]]s (also called [[secondary metabolite]]s). Many alkaloids can be purified from crude extracts by [[acid-base extraction]]. Many alkaloids are [[toxicity|toxic]] to other organisms. They often have [[pharmacology|pharmacological]] effects and are used as [[medication]]s, as [[recreational drug]]s, or in [[entheogenic]] rituals. Examples are the [[local anesthetic]] and [[stimulant]] [[cocaine]], the psychedelic [[psilocin]], the stimulant [[caffeine]], [[nicotine]],<ref>{{cite web|title=Alkaloid|url=http://science.howstuffworks.com/alkaloid-info.htm}}</ref> the [[analgesic]] [[morphine]], the antibacterial [[berberine]], the anticancer compound [[vincristine]], the antihypertension agent [[reserpine]], the cholinomimeric [[galantamine]], the spasmolysis agent [[atropine]], the vasodilator [[vincamine]], the anti-arrhythmia compound [[quinidine]], the anti-asthma therapeutic [[ephedrine]], and the [[antimalarial drug]] [[quinine]].<br />
Although alkaloids act on a diversity of metabolic systems in humans and other animals, they almost uniformly invoke a [[Bitter (taste)#Bitterness|bitter taste]].<ref name=Rhoades1979>{{cite book|year=1979 |author=Rhoades, David F |chapter=Evolution of Plant Chemical Defense against Herbivores |editor=Rosenthal, Gerald A., and Janzen, Daniel H|title=Herbivores: Their Interaction with Secondary Plant Metabolites |place=New York |publisher=Academic Press |page=41 |isbn=0-12-597180-X}}</ref><br />
<br />
The boundary between alkaloids and other nitrogen-containing natural compounds is not clear-cut.<ref name="Meyers">Robert A. Meyers ''Encyclopedia of Physical Science and Technology'' – Alkaloids, 3rd edition. ISBN 0-12-227411-3</ref> Compounds like [[amino acid]] [[peptide]]s, [[protein]]s, [[nucleotide]]s, [[nucleic acid]], [[amine]]s, and [[antibiotics]] are usually not called alkaloids.<ref name="goldbook.iupac.org"/> Natural compounds containing nitrogen in the [[Alicyclic compound|exocyclic]] position ([[mescaline]], [[serotonin]], [[dopamine]], etc.) are usually attributed to [[amine]]s rather than alkaloids.<ref>Leland J. Cseke [http://books.google.com/books?id=wV2T41nGFc4C&pg=PA30 Natural Products from Plants] Second Edition. – CRC, 2006, p. 30 ISBN 0-8493-2976-0</ref> Some authors, however, consider alkaloids a special case of amines.<ref>A. William Johnson [http://books.google.com/books?id=0X4cQus2gz8C&pg=PA433 Invitation to Organic Chemistry], Jones and Bartlett, 1999, p. 433 ISBN 0-7637-0432-6</ref><ref>Raj K Bansal [http://books.google.com/books?id=1B6ijcTkD5EC&pg=PA644 A Text Book of Organic Chemistry]. 4th Edition, New Age International, 2004, p. 644 ISBN 81-224-1459-1</ref><ref name="Aniszewski 110">[[#Aniszewski|Aniszewski]], p. 110</ref><br />
<br />
==Naming==<br />
[[File:Meissner alkalod definition article 1819.png|thumb|160px|The article that introduced the concept of "alkaloid".]]<br />
<br />
The name "alkaloids" ({{lang-de|Alkaloide}}) was introduced in 1819 by the German chemist [[:de:Carl Friedrich Wilhelm Meißner|Carl Friedrich Wilhelm Meißner]], and is derived from late Latin root ''{{lang-la|alkali}}'' (which, in turn, comes from the Arabic ''al-qalwī'' – "ashes of plants") and the suffix ''{{lang-el|-οειδής}}'' – "like".<ref group="nb">In the penultimate sentence of his article – W. Meissner (1819) "Über Pflanzenalkalien: II. Über ein neues Pflanzenalkali (Alkaloid)" (On plant alkalis: II. On a new plant alkali (alkaloid)), ''Journal für Chemie und Physik'', '''25''' : 379–381 ; available on-line at: [http://babel.hathitrust.org/cgi/pt?id=nyp.33433069069056;view=1up;seq=415 Hathi Trust] – Meissner wrote: "''Überhaupt scheint es mir auch angemessen, die bis jetzt bekannten Pflanzenstoffe nicht mit dem Namen Alkalien, sondern Alkaloide zu belegen, da sie doch in manchen Eigenschaften von den Alkalien sehr abweichen, sie würden daher in dem Abschnitt der Pflanzenchemie vor den Pflanzensäuren ihre Stelle finden''." (In general, it seems appropriate to me to impose on the currently known plant substances not the name "alkalis" but "alkaloids", since they differ greatly in some properties from the alkalis; among the chapters of plant chemistry, they would therefore find their place before plant acids [since "Alkaloid" would precede "Säure" (acid)].)</ref> However, the term came into wide use only after the publication of a review article by Oscar Jacobsen in the chemical dictionary of [[Albert Ladenburg]] in the 1880s.<ref>[[#Hesse|Hesse]], pp. 1–3</ref><ref>Oscar Jacobsen, "Alkaloide" in: Ladenburg, ''Handwörterbuch der Chemie'' (Breslau, Germany: Eduard Trewendt, 1882), vol. 1, [http://books.google.com/books?id=-9fUAAAAMAAJ&pg=PA213 pp. 213–422].</ref><br />
<br />
There is no unique method of naming alkaloids.<ref name="Hesse 5">[[#Hesse|Hesse]], p. 5</ref> Many individual names are formed by adding the suffix "ine" to the species or genus name.<ref>The suffix "ine" is a Greek feminine patronymic suffix and means "daughter of"; hence, for example, "atropine" means "daughter of Atropa (belladonna)": [https://webspace.yale.edu/chem125/125/history99/5Valence/Nomenclature/alkanenames.html Development of Systematic Names for the Simple Alkanes]. yale.edu</ref> For example, [[atropine]] is isolated from the plant [[Atropa belladonna]], [[strychnine]] is obtained from the seed of [[Strychnine tree]] (''Strychnos nux-vomica'' L.).<ref name="XimE: alkaloidy"/> If several alkaloids are extracted from one plant then their names often contain suffixes "idine", "anine", "aline", "inine", etc. There are also at least 86 alkaloids containing the root "vin" (extracted from the [[Vinca]] plant).<ref>[[#Hesse|Hesse]], p. 7</ref><br />
<br />
== History ==<br />
[[File:Friedrich Wilhelm Adam Sertuerner.jpg|thumb|left|[[Friedrich Sertürner]], the German chemist who first isolated [[morphine]] from [[opium]].]]<br />
Alkaloid-containing plants have been used by humans since ancient times for therapeutic and recreational purposes. For example, medicinal plants have been known in the [[Mesopotamia]] at least around 2000 BC.<ref name="Aniszewski 182">[[#Aniszewski|Aniszewski]], p. 182</ref> The ''[[Odyssey]]'' of [[Homer]] referred to a gift given to Helen by the Egyptian queen, a drug bringing oblivion. It is believed that the gift was an opium-containing drug.<ref>[[#Hesse|Hesse]], p. 338</ref> A Chinese book on houseplants written in 1st–3rd centuries BC mentioned a medical use of [[Ephedra]] and [[Opium poppy|opium poppies]].<ref>[[#Hesse|Hesse]], p. 304</ref> Also, [[coca]] leaves have been used by [[South America]]n Indians since ancient times.<ref>[[#Hesse|Hesse]], p. 350</ref><br />
<br />
[[Extracts]] from plants containing toxic alkaloids, such as [[aconitine]] and [[tubocurarine]], were used since antiquity for poisoning arrows.<ref name="Aniszewski 182"/><br />
<br />
Studies of alkaloids began in the 19th century. In 1804, the German chemist [[Friedrich Sertürner]] isolated from opium a "soporific principle" ({{lang-la|principium somniferum}}), which he called "morphium" in honor of [[Morpheus (mythology)|Morpheus]], the [[Ancient Greece|Greek]] god of dreams; in German and some other Central-European languages, this is still the name of the drug. The term "morphine", used in English and French, was given by the French physicist [[Joseph Louis Gay-Lussac]].<br />
<br />
A significant contribution to the chemistry of alkaloids in the early years of its development was made by the French researchers [[Pierre Joseph Pelletier]] and [[Joseph Bienaimé Caventou]], who discovered [[quinine]] (1820) and [[strychnine]] (1818). Several other alkaloids were discovered around that time, including [[xanthine]] (1817), [[atropine]] (1819), [[caffeine]] (1820), [[coniine]] (1827), [[nicotine]] (1828), [[colchicine]] (1833), [[sparteine]] (1851), and [[cocaine]] (1860).<ref>[[#Hesse|Hesse]], pp. 313–316</ref><br />
<br />
The first complete synthesis of an alkaloid was achieved in 1886 by the German chemist [[Albert Ladenburg]]. He produced [[coniine]] by reacting 2-methylpyridine with [[acetaldehyde]] and reducing the resulting 2-propenyl pyridine with [[sodium]].<ref name="BSE: koniin">[http://slovari.yandex.ru/dict/bse/article/00036/77600.htm Кониин]. [[Great Soviet Encyclopedia]] (1969–1978)</ref><ref>[[#Hesse|Hesse]], p. 204</ref> The development of the chemistry of alkaloids was accelerated by the emergence of [[spectroscopy|spectroscopic]] and [[Chromatography|chromatographic]] methods in the 20th century, so that by 2008 more than 12,000 alkaloids had been identified.<ref>[[#Begley|Begley]], Natural Products in Plants</ref><br />
<br />
[[File:Bufotenin.svg|thumb|160px|[[Bufotenin]], an alkaloid from some toads, contains an [[indole]] core and is produced in living organisms from the amino acid [[tryptophan]].]]<br />
<br />
== Classification ==<br />
[[File:Nicotine.svg|thumb|160px|The [[nicotine]] molecule contains both [[pyridine]] (left) and [[pyrrolidine]] rings (right).]]<br />
<br />
Compared with most other classes of natural compounds, alkaloids are characterized by a great structural diversity and there is no uniform classification of alkaloids.<ref name="ref15">[[#Hesse|Hesse]], p. 11</ref> First classification methods have historically combined alkaloids by the common natural source, e.g., a certain type of plants. This classification was justified by the lack of knowledge about the chemical structure of alkaloids and is now considered obsolete.<ref name="XimE: alkaloidy"/><ref>[[#Orekhov|Orekhov]], p. 6</ref><br />
<br />
More recent classifications are based on similarity of the carbon skeleton (e.g., [[indole]]-, [[isoquinoline]]-, and [[pyridine]]-like) or biogenetic precursor ([[ornithine]], [[lysine]], [[tyrosine]], [[tryptophan]], etc.).<ref name="XimE: alkaloidy"/> However, they require compromises in borderline cases;<ref name="ref15" /> for example, [[nicotine]] contains a pyridine fragment from [[nicotinamide]] and [[pyrrolidine]] part from ornithine<ref>[[#Aniszewski|Aniszewski]], p. 109</ref> and therefore can be assigned to both classes.<ref name="ref19">[[#Dewick|Dewick]], p. 307</ref><br />
<br />
Alkaloids are often divided into the following major groups:<ref>[[#Hesse|Hesse]], p. 12</ref><br />
<br />
# "True alkaloids", which contain [[nitrogen]] in the [[heterocycle]] and originate from [[amino acid]]s.<ref name="ref21">[[#Plemenkov|Plemenkov]], p. 223</ref> Their characteristic examples are [[atropine]], [[nicotine]], and [[morphine]]. This group also includes some alkaloids that besides nitrogen heterocycle contain [[terpene]] (e.g., [[evonine]]<ref>[[#Aniszewski|Aniszewski]], p. 108</ref>) or peptide fragments (e.g. [[ergotamine]]<ref name="ref23">[[#Hesse|Hesse]], p. 84</ref>). This group also includes piperidine alkaloids [[coniine]] and [[coniceine]]<ref name="ref24">[[#Hesse|Hesse]], p. 31</ref> although they do not originate from amino acids.<ref name="ref25">[[#Dewick|Dewick]], p. 381</ref><br />
# "Protoalkaloids", which contain [[nitrogen]] and also originate from amino acids.<ref name="ref21" /> Examples include [[mescaline]], [[adrenaline]] and [[ephedrine]].<br />
# Polyamine alkaloids – derivatives of [[putrescine]], [[spermidine]], and [[spermine]].<br />
# Peptide and cyclopeptide alkaloids.<ref name="ref27">{{cite journal|author = Dimitris C. Gournelif, Gregory G. Laskarisb and Robert Verpoorte|title = Cyclopeptide alkaloids|doi = 10.1039/NP9971400075|journal = Nat. Prod. Rep.|year = 1997|volume = 14|pages = 75–82|pmid = 9121730|issue = 1}}</ref><br />
# Pseudalkaloids – alkaloid-like compounds that do not originate from amino acids.<ref>[[#Aniszewski|Aniszewski]], p. 11</ref> This group includes, [[terpene]]-like and [[steroid]]-like alkaloids,<ref>[[#Plemenkov|Plemenkov]], p. 246</ref> as well as [[purine]]-like alkaloids such as [[caffeine]], [[theobromine]], [[theacrine]] and [[theophylline]].<ref name="ref30">[[#Aniszewski|Aniszewski]], p. 12</ref> Some authors classify as pseudoalkaloids such compounds such as [[ephedrine]] and [[cathinone]]. Those originate from the amino acid [[phenylalanine]], but acquire their nitrogen atom not from the amino acid but through [[transamination]].<ref name="ref30" /><ref name="ref31">[[#Dewick|Dewick]], p. 382</ref><br />
<br />
Some alkaloids do not have the carbon skeleton characteristic of their group. So, [[galantamine]] and homoaporphines do not contain [[isoquinoline]] fragment, but are, in general, attributed to isoquinoline alkaloids.<ref>[[#Hesse|Hesse]], pp. 44, 53</ref><br />
<br />
Main classes of monomeric alkaloids are listed in the table below:<br />
<!--the table is translated from the ru.wiki article. Please fix translation glitches --><br />
{| Class = "wikitable"<br />
|-<br />
! Class<br />
!Major groups<br />
!Main synthesis steps<br />
!Examples<br />
|-<br />
| colspan="4" style="text-align:center; background:# DADADA;"|''Alkaloids with nitrogen heterocycles (true alkaloids)''<br />
|-<br />
| [[Pyrrolidine]] derivatives<ref name="ref34">[[#Plemenkov|Plemenkov]], p. 224</ref><br />
[[File:Pyrrolidine structure.svg|50px|center]]<br />
|<br />
| [[Ornithine]] or [[arginine]] → [[putrescine]] → N-methylputrescine → N-methyl-Δ<sup>1</sup>-pyrroline <ref name="ref35">[[#Aniszewski|Aniszewski]], p. 75</ref><br />
| [[Cuscohygrine]], [[hygrine]], hygroline, stachydrine<ref name="ref34" /><ref>[[#Orekhov|Orekhov]], p. 33</ref><br />
|-<br />
| Rowspan = "2"|[[Tropane]] derivatives<ref name="ref38">[http://www.xumuk.ru/encyklopedia/2/4609.html Chemical Encyclopedia: Tropan alkaloids]. xumuk.ru</ref><br />
[[File:Tropane numbered.svg|100px|center]]<br />
| Atropine group<br /><small>Substitution in positions 3, 6 or 7 </small><br />
| Rowspan = "2"|[[Ornithine]] or [[arginine]] → [[putrescine]] → N-methylputrescine → N-methyl-Δ<sup>1</sup>-pyrroline <ref name = "ref35 "/><br />
| [[Atropine]], [[scopolamine]], [[hyoscyamine]]<ref name="ref34" /><ref name="ref38" /><ref>[[#Hesse|Hesse]], p. 34</ref><br />
|-<br />
| Cocaine group<br /> <small>Substitution in positions 2 and 3 </small><br />
| [[Cocaine]], [[ecgonine]] <ref name="ref38" /><ref>[[#Aniszewski|Aniszewski]], p. 27</ref><br />
|-<br />
| Rowspan = "4"|[[Pyrrolizidine]] derivatives<ref name="ref45">[http://www.xumuk.ru/encyklopedia/2/3370.html Chemical Encyclopedia: Pyrrolizidine alkaloids]. xumuk.ru</ref><br />
[[File:Pyrrolizidine.svg|80px|center]]<br />
| Non-esters<br />
| Rowspan = "3"|In plants: [[ornithine]] or [[arginine]] → [[putrescine]] → [[homospermidine]] → [[retronecine]] <ref name="ref35" /><br />
| [[Retronecine]], heliotridine, laburnine <ref name="ref45" /><ref>[[#Plemenkov|Plemenkov]], p. 229</ref><br />
|-<br />
| Complex [[esters]] of monocarboxylic acids<br />
| Indicine, lindelophin, sarracine <ref name="ref45" /><br />
|-<br />
| Macrocyclic diesters<br />
| [[Platyphylline]], trichodesmine<ref name="ref45" /><br />
|-<br />
| 1-aminopyrrolizidines ([[Loline alkaloids|lolines]])<br />
| In [[Neotyphodium|fungi]]: [[Proline|<small>L</small>-proline]] + [[homoserine|<small>L</small>-homoserine]] → ''N''-(3-amino-3-carboxypropyl)proline → norloline<ref name="Blankenship">{{cite journal|author=Blankenship JD, Houseknecht JB, Pal S, Bush LP, Grossman RB, Schardl CL|year= 2005|title=Biosynthetic precursors of fungal pyrrolizidines, the loline alkaloids|journal=Chembiochem|volume=6|pages=1016–1022|pmid=15861432|doi=10.1002/cbic.200400327|issue=6}}</ref><ref name="Faulkner et al. 2006">{{cite journal|author=Faulkner JR, Hussaini SR, Blankenship JD, Pal S, Branan BM, Grossman RB, Schardl CL|year= 2006|title=On the sequence of bond formation in loline alkaloid biosynthesis|journal=Chembiochem|volume=7|pages=1078–1088|pmid=16755627|doi=10.1002/cbic.200600066|issue=7}}</ref><br />
|Loline, ''N''-formylloline, ''N''-acetylloline<ref name="Schardl et al. 2007">{{cite journal|author=Schardl CL, Grossman RB, Nagabhyru P, Faulkner JR, Mallik UP|year=2007|title=Loline alkaloids: currencies of mutualism|journal = [[Phytochemistry (journal)|Phytochemistry]]|volume=68|pages=980–996|doi=10.1016/j.phytochem.2007.01.010|pmid=17346759|issue=7}}</ref><br />
|-<br />
| Rowspan = "2"|[[Piperidine]] derivatives<ref>[[#Plemenkov|Plemenkov]], p. 225</ref><br />
[[File:Piperidin.svg|50px|center]]<br />
|<br />
| [[Lysine]] → [[cadaverine]] → Δ<sup>1</sup>-piperideine <ref>[[#Aniszewski|Aniszewski]], p. 95</ref><br />
| [[Sedamine]], lobeline, anaferine, [[piperine]] <ref name="ref24" /><ref>[[#Orekhov|Orekhov]], p. 80</ref><br />
|-<br />
|<br />
| [[Caprylic acid|Octanoic acid]] → coniceine → [[coniine]] <ref name="ref25" /><br />
| [[Coniine]], coniceine <ref name="ref25" /><br />
|-<br />
| Rowspan = "5"|[[Quinolizidine]] derivatives<ref name="ref57">[http://www.xumuk.ru/encyklopedia/2/5011.html Chemical Encyclopedia: Quinolizidine alkaloids]. xumuk.ru</ref><ref>[[#Saxton|Saxton]], Vol. 1, p. 93</ref><br />
[[File:Quinolizidine.svg|80px|center]]<br />
| [[Lupinine]] group<br />
| Rowspan = "5"|[[Lysine]] → [[cadaverine]] → Δ<sup>1</sup>-piperideine <ref>[[#Aniszewski|Aniszewski]], p. 98</ref><br />
| [[Lupinine]], nupharidin <ref name="ref57" /><br />
|-<br />
| [[Cytisine]] group<br />
| [[Cytisine]] <ref name="ref57" /><br />
|-<br />
| [[Sparteine]] group<br />
| [[Sparteine]], [[lupanine]], [[anahygrine]]<ref name="ref57" /><br />
|-<br />
| [[Matrine]] group<br />
| Matrine, oxymatrine, allomatridine<ref name="ref57" /><ref>[[#Saxton|Saxton]], Vol. 1, p. 91</ref><ref>{{cite journal|author = Joseph P. Michael|title = Indolizidine and quinolizidine alkaloids|doi = 10.1039/b208137g|journal=Nat. Prod. Rep|year = 2002|volume = 19|pages = 458–475}}</ref><br />
|-<br />
| [[Ormosanine]] group<br />
| Ormosanine, piptantine<ref name="ref57" /><ref>[[#Saxton|Saxton]], Vol. 1, p. 92</ref><br />
|-<br />
| [[Indolizidine]] derivatives<ref>[[#Dewick|Dewick]], p. 310</ref><br />
[[File:Indolizidine.svg|80px|center]]<br />
|<br />
| [[Lysine]] → δ-semialdehyde of [[alpha-Aminoadipic acid|α-aminoadipic acid]] → [[pipecolic acid]] → 1 indolizidinone <ref>[[#Aniszewski|Aniszewski]], p. 96</ref><br />
| [[Swainsonine]], [[castanospermine]] <ref>[[#Aniszewski|Aniszewski]], p. 97</ref><br />
|-<br />
| Rowspan = "4"|[[Pyridine]] derivatives<ref name="ref72">[[#Plemenkov|Plemenkov]], p. 227</ref><ref name="ref73">[http://www.xumuk.ru/encyklopedia/2/3336.html Chemical Encyclopedia: pyridine alkaloids]. xumuk.ru</ref><br />
[[File:Pyridine.svg|50px|center]]<br />
| Simple derivatives of pyridine<br />
| Rowspan = "3"|[[Nicotinic acid]] → dihydronicotinic acid → 1,2-dihydropyridine <ref name="ref74">[[#Aniszewski|Aniszewski]], p. 107</ref><br />
| [[Trigonelline]], ricinine, [[arecoline]] <ref name="ref72" /><ref name="ref76">[[#Aniszewski|Aniszewski]], p. 85</ref><br />
|-<br />
| Polycyclic noncondensing pyridine derivatives<br />
| [[Nicotine]], [[nornicotine]], [[anabasine]], anatabine <ref name="ref72" /><ref name="ref76" /><br />
|-<br />
| Polycyclic condensed pyridine derivatives<br />
| [[Actinidine]], gentianine, pediculinine <ref>[[#Plemenkov|Plemenkov]], p. 228</ref><br />
|-<br />
| [[Sesquiterpene]] pyridine derivatives<br />
| [[Nicotinic acid]], [[isoleucine]] <ref name="Aniszewski 110"/><br />
| Evonine, hippocrateine, triptonine <ref name="ref73" /><ref name="ref74" /><br />
|-<br />
| Rowspan = "26"|[[Isoquinoline]] derivatives and related alkaloids <ref name="Hesse 36">[[#Hesse|Hesse]], p. 36</ref><br />
[[File:Isoquinoline numbered.svg|90px|center]]<br />
| Simple derivatives of isoquinoline <ref name="XimE: izoxinolin">[http://www.xumuk.ru/encyklopedia/1642.html Chemical Encyclopedia: isoquinoline alkaloids]. xumuk.ru</ref><br />
| Rowspan = "26"|[[Tyrosine]] or [[phenylalanine]] → [[dopamine]] or [[tyramine]] (for alkaloids Amarillis) <ref>[[#Aniszewski|Aniszewski]], pp. 77–78</ref><ref name="Begley">[[#Begley|Begley]], Alkaloid Biosynthesis</ref><br />
| Salsoline, lophocerine <ref name="Hesse 36"/><ref name="XimE: izoxinolin"/><br />
|-<br />
| Derivatives of 1- and 3-isoquinolines <ref name="Saxton 122">[[#Saxton|Saxton]], Vol. 3, p. 122</ref><br />
| N-methylcoridaldine, noroxyhydrastinine <ref name="Saxton 122"/><br />
|-<br />
| Derivatives of 1- and 4-phenyltetrahydroisoquinolines <ref name="XimE: izoxinolin"/><br />
| Cryptostilin <ref name="XimE: izoxinolin"/><ref name="Hesse 54">[[#Hesse|Hesse]], p. 54</ref><br />
|-<br />
| Derivatives of 5-naftil-isoquinoline <ref name="ref83">[[#Hesse|Hesse]], p. 37</ref><br />
| Ancistrocladine <ref name="ref83" /><br />
|-<br />
| Derivatives of 1- and 2-benzyl-izoquinolines <ref>[[#Hesse|Hesse]], p. 38</ref><br />
| [[Papaverine]], [[laudanosine]], sendaverine<br />
|-<br />
| [[Cularine]] group<ref name="ref86">[[#Hesse|Hesse]], p. 46</ref><br />
| Cularine, yagonine <ref name="ref86" /><br />
|-<br />
| [[Pavine (molecule)|Pavine]]s and isopavines <ref name="ref88">[[#Hesse|Hesse]], p. 50</ref><br />
| Argemonine, [[amurensine]] <ref name="ref88" /><br />
|-<br />
| Benzopyrrocolines <ref name="ref90">{{cite journal|author = Kenneth W. Bentley|title = β-Phenylethylamines and the isoquinoline alkaloids|doi = 10.1039/NP9971400387|journal=Nat. Prod. Rep|year = 1997|volume = 14|pages = 387–411|pmid = 9281839|issue = 4|url=http://chemistry.mdma.ch/hiveboard/rhodium/pdf/archive/merbst/phenethylamines%20and%20isoquinolines%202001.pdf}}</ref><br />
| Cryptaustoline <ref name="XimE: izoxinolin"/><br />
|-<br />
| Protoberberines <ref name="XimE: izoxinolin"/><br />
| [[Berberine]], [[canadine]], ophiocarpine, mecambridine, corydaline <ref name="ref91">[[#Hesse|Hesse]], p. 47</ref><br />
|-<br />
| Phthalidisoquinolines <ref name="XimE: izoxinolin"/><br />
| [[Hydrastine]], [[narcotine]] (Noscapine) <ref>[[#Hesse|Hesse]], p. 39</ref><br />
|-<br />
| Spirobenzylisoquinolines <ref name="XimE: izoxinolin"/><br />
| Fumaricine <ref name="ref88" /><br />
|-<br />
| [[Psychotria ipecacuanha|Ipecacuanha]] alkaloids<ref name="ref94">[[#Hesse|Hesse]], p. 41</ref><br />
| Emetine, protoemetine, ipecoside <ref name="ref94" /><br />
|-<br />
| Benzophenanthridines <ref name="XimE: izoxinolin"/><br />
| Sanguinarine, oxynitidine, corynoloxine <ref name="ref96">[[#Hesse|Hesse]], p. 49</ref><br />
|-<br />
| [[Aporphine]]s <ref name="XimE: izoxinolin"/><br />
| [[Glaucine]], coridine, liriodenine <ref>[[#Hesse|Hesse]], p. 44</ref><br />
|-<br />
| Proaporphines <ref name="XimE: izoxinolin"/><br />
| Pronuciferine, glaziovine <ref name="XimE: izoxinolin"/><ref name="ref90" /><br />
|-<br />
| Homoaporphines <ref name="ref99">[[#Saxton|Saxton]], Vol. 3, p. 164</ref><br />
| Kreysiginine, multifloramine <ref name="ref99" /><br />
|-<br />
| Homoproaporphines <ref name="ref99" /><br />
| Bulbocodine <ref name="ref86" /><br />
|-<br />
| [[Morphine]]s<ref name="ref103">[[#Hesse|Hesse]], p. 51</ref><br />
| [[Morphine]], [[codeine]], [[thebaine]], [[sinomenine]] <ref name="ref104">[[#Plemenkov|Plemenkov]], p. 236</ref><br />
|-<br />
| Homomorphines <ref>[[#Saxton|Saxton]], Vol. 3, p. 163</ref><br />
| Kreysiginine, androcymbine <ref name="ref103" /><br />
|-<br />
| Tropoloisoquinolines <ref name="XimE: izoxinolin"/><br />
| Imerubrine <ref name="XimE: izoxinolin"/><br />
|-<br />
| Azofluoranthenes <ref name="XimE: izoxinolin"/><br />
| Rufescine, imeluteine <ref>[[#Saxton|Saxton]], Vol. 3, p. 168</ref><br />
|-<br />
| [[Amaryllis]] alkaloids<ref>[[#Hesse|Hesse]], p. 52</ref><br />
| [[Lycorine]], ambelline, tazettine, [[galantamine]], montanine <ref>[[#Hesse|Hesse]], p. 53</ref><br />
|-<br />
| [[Erythrina]] alkaloids<ref name="Hesse 54"/><br />
| Erysodine, erythroidine <ref name="Hesse 54"/><br />
|-<br />
| [[Phenanthrene]] derivatives <ref name="XimE: izoxinolin"/><br />
| Atherosperminine <ref name="XimE: izoxinolin"/><ref name="ref91" /><br />
|-<br />
| [[Protopin]]s <ref name="XimE: izoxinolin"/><br />
| Protopine, oxomuramine, corycavidine <ref name="ref96" /><br />
|-<br />
| Aristolactam <ref name="XimE: izoxinolin"/><br />
| Doriflavin <ref name="XimE: izoxinolin"/><br />
|-<br />
| [[Oxazole]] derivatives<ref name="Plemenkov 241">[[#Plemenkov|Plemenkov]], p. 241</ref><br />
[[File:Oxazole structure.svg|80px|center]]<br />
|<br />
| [[Tyrosine]] → [[tyramine]] <ref>[[#Brossi|Brossi]], Vol. 35, p. 261</ref><br />
| Annuloline, halfordinol, texaline, texamine<ref>[[#Brossi|Brossi]], Vol. 35, pp. 260–263</ref><br />
|-<br />
| [[Isoxazole]] derivatives<br />
[[Image:isoxazole structure.png|80px|center]]<br />
|<br />
|[[Ibotenic acid]] → [[Muscimol]]<br />
|Ibotenic acid, Muscimol<br />
|-<br />
| [[Thiazole]] derivatives<ref name="ref114">[[#Plemenkov|Plemenkov]], p. 242</ref><br />
[[File:Thiazole structure.svg|80px|center]]<br />
|<br />
| [[1-Deoxy-D-xylulose 5-phosphate]] (DOXP), [[tyrosine]], [[cysteine]] <ref>[[#Begley|Begley]], Cofactor Biosynthesis</ref><br />
| Nostocyclamide, thiostreptone <ref name="ref114" /><ref>{{cite journal|author = John R. Lewis|title = Amaryllidaceae, muscarine, imidazole, oxazole, thiazole and peptide alkaloids, and other miscellaneous alkaloids|journal = Nat. Prod. Rep|year = 2000|volume = 17|pages = 57–84|pmid = 10714899|issue = 1|doi = 10.1039/a809403i}}</ref><br />
|-<br />
| Rowspan = "3"|[[Quinazoline]] derivatives<ref>[http://www.xumuk.ru/encyklopedia/2/5003.html Chemical Encyclopedia: Quinazoline alkaloids]. xumuk.ru</ref><br />
[[File:Quinazoline numbered.svg|90px|center]]<br />
| 3,4-Dihydro-4-quinazolone derivatives<br />
| Rowspan = "3"|[[Anthranilic acid]] or [[phenylalanine]] or [[ornithine]] <ref>[[#Aniszewski|Aniszewski]], p. 106</ref><br />
| [[Febrifugine]]<ref name="ref120">[[#Aniszewski|Aniszewski]], p. 105</ref><br />
|-<br />
| 1,4-Dihydro-4-quinazolone derivatives<br />
| Glycorine, arborine, glycosminine<ref name="ref120" /><br />
|-<br />
| Pyrrolidine and piperidine quinazoline derivatives<br />
| [[Vazicine]] (peganine) <ref name="Plemenkov 241"/><br />
|-<br />
| [[Acridine]] derivatives<ref name="Plemenkov 241"/><br />
[[File:Acridine.svg|100px|center]]<br />
|<br />
| [[Anthranilic acid]] <ref>{{cite journal|author = Richard B. Herbert|title = The biosynthesis of plant alkaloids and nitrogenous microbial metabolites|journal=Nat. Prod. Rep|year = 1999|volume = 16|pages = 199–208|doi = 10.1039/a705734b|last2 = Herbert|first2 = Richard B.|last3 = Herbert|first3 = Richard B.}}</ref><br />
| Rutacridone, [[acronicine]]<ref>[[#Plemenkov|Plemenkov]], pp. 231, 246</ref><ref>[[#Hesse|Hesse]], p. 58</ref><br />
|-<br />
| Rowspan = "4"|[[Quinoline]] derivatives<ref>[[#Plemenkov|Plemenkov]], p. 231</ref><ref name="ref126">[http://www.xumuk.ru/encyklopedia/2/5014.html Chemical Encyclopedia: Quinoline alkaloids]. xumuk.ru</ref><br />
[[File:Quinoline numbered.svg|90px|center]]<br />
| Simple derivatives of quinoline derivatives of 2 – [[quinolones]] and 4-quinolone<br />
| Rowspan = "3"|[[Anthranilic acid]] → 3-carboxyquinoline <ref name="ref127">[[#Aniszewski|Aniszewski]], p. 114</ref><br />
| Cusparine, [[echinopsine]], evocarpine<ref name="ref126" /><ref>[[#Orekhov|Orekhov]], p. 205</ref><ref>[[#Hesse|Hesse]], p. 55</ref><br />
|-<br />
| Tricyclic terpenoids<br />
| Flindersine<ref name="ref126" /><ref name="ref131">[[#Plemenkov|Plemenkov]], p. 232</ref><br />
|-<br />
| Furanoquinoline derivatives<br />
| [[Dictamnine]], fagarine, skimmianine<ref name="ref126" /><ref>[[#Orekhov|Orekhov]], p. 212</ref><ref>[[#Aniszewski|Aniszewski]], p. 118</ref><br />
|-<br />
| [[Quinine]]s<br />
| [[Tryptophan]] → [[tryptamine]] → [[strictosidine]] (with [[secologanin]]) → korinanteal → [[cinhoninon]] <ref name="Begley"/><ref name = " ref127 "/><br />
| [[Quinine]], [[quinidine]], [[cinchonine]], cinhonidine <ref name="ref131" /><br />
|-<br />
| Rowspan = "10"|[[Indole]] derivatives<ref name="ref104" /><br />
[[File:Indole numbered.svg|100px|center]]<br />
{{See also|indole alkaloids}}<br />
| colspan="3" style="text-align:center;"|''Non-isoprene indole alkaloids''<br />
|-<br />
| Simple indole derivatives <ref name="ref140">[[#Aniszewski|Aniszewski]], p. 112</ref><br />
| Rowspan = "3"|[[Tryptophan]] → [[tryptamine]] or 5-hydroxitriptofan <ref name="ref141">[[#Aniszewski|Aniszewski]], p. 113</ref><br />
| [[Serotonin]], [[psilocybin]], [[dimethyltryptamine]] (DMT), [[bufotenin]] <ref>[[#Hesse|Hesse]], p. 15</ref><ref>[[#Saxton|Saxton]], Vol. 1, p. 467</ref><br />
|-<br />
| Simple derivatives of [[beta-carboline|β-carboline]] <ref>[[#Dewick|Dewick]], pp. 349–350</ref><br />
| Harman, [[harmine]], [[harmaline]], eleagnine <ref name="ref140" /><br />
|-<br />
| Pyrroloindole alkaloids <ref name="ref152">[[#Aniszewski|Aniszewski]], p. 119</ref><br />
| [[Physostigmine]] (eserine), etheramine, physovenine, eptastigmine<ref name="ref152" /><br />
|-<br />
| colspan="3" style="text-align:center;"|''Semiterpenoid indole alkaloids''<br />
|-<br />
| [[Ergoline|Ergot alkaloids]]<ref name="ref104" /><br />
| [[Tryptophan]] → chanoclavine → agroclavine → elimoclavine → [[paspalic acid]] → [[lysergic acid]] <ref name="ref152" /><br />
| [[Ergotamine]], ergobasine, ergosine<ref>[[#Hesse|Hesse]], p. 29</ref><br />
|-<br />
| colspan="3" style="text-align:center;"|''Monoterpenoid indole alkaloids''<br />
|-<br />
| ''Corynanthe'' type alkaloids<ref name="ref141" /><br />
| Rowspan = "3"|[[Tryptophan]] → [[tryptamine]] → [[strictosidine]] (with [[secologanin]]) <ref name="ref141" /><br />
| Ajmalicine, sarpagine, vobasine, [[ajmaline]], [[yohimbine]], [[reserpine]], [[mitragynine]],<ref>[[#Hesse|Hesse]], pp. 23–26</ref><ref>[[#Saxton|Saxton]], Vol. 1, p. 169</ref> group [[strychnine]] and ([[Strychnine]] [[brucine]], aquamicine, [[vomicine]] <ref>[[#Saxton|Saxton]], Vol. 5, p. 210</ref>)<br />
|-<br />
| [[Iboga]]-type alkaloids<ref name="ref141" /><br />
| [[Ibogamine]], [[ibogaine]], [[voacangine]]<ref name="ref141" /><br />
|-<br />
| [[Aspidosperma]]-type alkaloids<ref name="ref141" /><br />
| [[Vincamine]], [[vinca alkaloids]], vincotine, aspidospermine<ref>[[#Hesse|Hesse]], pp. 17–18</ref><ref>[[#Dewick|Dewick]], p. 357</ref><br />
|-<br />
| [[Imidazole]] derivatives<ref name="Plemenkov 241"/><br />
[[File:Imidazole structure.svg|50px|center]]<br />
|<br />
| Directly from [[histidine]]<ref name="Aniszewski 104">[[#Aniszewski|Aniszewski]], p. 104</ref><br />
| [[Histamine]], pilocarpine, pilosine, stevensine<ref name="Plemenkov 241"/><ref name="Aniszewski 104"/><br />
|-<br />
| [[Purine]] derivatives<ref>[[#Hesse|Hesse]], p. 72</ref><br />
[[File:Purin2.svg|90px|center]]<br />
|<br />
| [[Xanthosine]] (formed in purine biosynthesis) → 7 methylxantosine → 7-methyl [[xanthine]] → [[theobromine]] → [[caffeine]] <ref name="Begley"/><br />
| [[Caffeine]], [[theobromine]], [[theophylline]], [[saxitoxin]] <ref>[[#Hesse|Hesse]], p. 73</ref><ref>[[#Dewick|Dewick]], p. 396</ref><br />
|-<br />
| colspan="4" style="text-align:center; background:# DADADA;"|''Alkaloids with nitrogen in the side chain (protoalkaloids)''<br />
|-<br />
| β-[[Phenylethylamine]] derivatives<ref name="ref90" /><br />
[[File:Phenylethylamine numbered.svg|110px|center]]<br />
|<br />
| [[Tyrosine]] or [[phenylalanine]] → [[dioxyphenilalanine]] → [[dopamine]] → [[adrenaline]] and [[mescaline]] [[tyrosine]] → [[tyramine]] phenylalanine → 1-phenylpropane-1,2-dione → [[cathinone]] → [[ephedrine]] and [[pseudoephedrine]] <ref name="Aniszewski 110"/><ref name="ref31" /><ref>[http://www.plantcyc.org:1555/PLANT/NEW-IMAGE?type=NIL&object=PWY-5883 PlantCyc Pathway: ephedrine biosynthesis]{{dead link|date=March 2013}}</ref><br />
| [[Tyramine]], [[ephedrine]], [[pseudoephedrine]], [[mescaline]], [[cathinone]], [[catecholamines]] ([[adrenaline]], [[noradrenaline]], [[dopamine]])<ref name="Aniszewski 110"/><ref>[[#Hesse|Hesse]], p. 76</ref><br />
|-<br />
| [[Colchicine]] alkaloids <ref name="ref179">[http://www.xumuk.ru/encyklopedia/2069.html Chemical Encyclopedia: colchicine alkaloids]. xumuk.ru</ref><br />
[[File:Colchicine.svg|120px|center]]<br />
|<br />
| [[Tyrosine]] or [[phenylalanine]] → [[dopamine]] → [[autumnaline]] → [[colchicine]] <ref>[[#Aniszewski|Aniszewski]], p. 77</ref><br />
| [[Colchicine]], colchamine<ref name="ref179" /><br />
|-<br />
| [[Muscarine]] <ref name="ref182">[[#Hesse|Hesse]], p. 81</ref><br />
[[File:Muscarine.svg|100px|center]]<br />
|<br />
| [[Glutamic acid]] → 3-ketoglutamic acid → muscarine (with [[pyruvic acid]])<ref>[[#Brossi|Brossi]], Vol. 23, p. 376</ref><br />
| [[Muscarine]], allomuscarine, epimuscarine, epiallomuscarine<ref name="ref182" /><br />
|-<br />
| Benzylamine<ref name="ref185">[[#Hesse|Hesse]], p. 77</ref><br />
[[File:Benzylamine.svg|90px|center]]<br />
|<br />
| [[Phenylalanine]] with [[valine]], [[leucine]] or [[isoleucine]]<ref>[[#Brossi|Brossi]], Vol. 23, p. 268</ref><br />
| [[Capsaicin]], [[dihydrocapsaicin]], nordihydrocapsaicin <ref name="ref185" /><ref>[[#Brossi|Brossi]], Vol. 23, p. 231</ref><br />
|-<br />
| colspan="4" style="text-align:center; background:# DADADA;"|''Polyamines alkaloids''<br />
|-<br />
| [[Putrescine]] derivatives<ref name="ref189">[[#Hesse|Hesse]], p. 82</ref><br />
[[File:Putrescine.svg|90px|center]]<br />
|<br />
| Rowspan = "3"|[[ornithine]] → [[putrescine]] → [[spermidine]] → [[spermine]]<ref>[http://www.chem.qmul.ac.uk/iubmb/enzyme/reaction/misc/spermine.html Spermine Biosynthesis]</ref><br />
| Paucine <ref name="ref189" /><br />
|-<br />
| [[Spermidine]] derivatives<ref name="ref189" /><br />
[[File:Spermidine.svg|110px|center]]<br />
|<br />
| Lunarine, codonocarpine<ref name="ref189" /><br />
|-<br />
| [[Spermine]] derivatives<ref name="ref189" /><br />
[[File:Spermine.svg|130px|center]]<br />
|<br />
| Verbascenine, aphelandrine <ref name="ref189" /><br />
|-<br />
| colspan="4" style="text-align:center; background:# DADADA;"|''Peptide (cyclopeptide) alkaloids''<br />
|-<br />
| Rowspan = "2"|Peptide alkaloids with a 13-membered cycle <ref name="ref27" /><ref name="ref196">[[#Plemenkov|Plemenkov]], p. 243</ref><br />
| Nummularine C type<br />
| Rowspan = "8"|From different amino acids <ref name="ref27" /><br />
| Nummularine C, Nummularine S <ref name="ref27" /><br />
|-<br />
| [[Ziziphine]] type<br />
| Ziziphine A, sativanine H <ref name="ref27" /><br />
|-<br />
| Rowspan = "5"|Peptide alkaloids with a 14-membered cycle <ref name="ref27" /><ref name="ref196" /><br />
| Frangulanine type<br />
| Frangulanine, scutianine J <ref name="ref196" /><br />
|-<br />
| Scutianine A type<br />
| Scutianine A <ref name="ref27" /><br />
|-<br />
| Integerrine type<br />
| Integerrine, discarine D <ref name="ref196" /><br />
|-<br />
| Amphibine F type<br />
| Amphibine F, spinanine A <ref name="ref27" /><br />
|-<br />
| Amfibine B type<br />
| Amphibine B, lotusine C <ref name="ref27" /><br />
|-<br />
| Peptide alkaloids with a 15-membered cycle <ref name="ref196" /><br />
| Mucronine A type<br />
| Mucronine A <ref name="ref23" /><ref name="ref196" /><br />
|-<br />
| colspan="4" style="text-align:center; background:# DADADA;"|''Pseudoalkaloids ([[terpenes]] and [[steroids]])''<br />
|-<br />
| Diterpenes <ref name="ref23" /><br />
[[File:Isoprene.svg|80px|center]]<br />
| Lycoctonine type<br />
| [[Mevalonic acid]] → [[izopentenilpyrophosfate]] → [[geranyl pyrophosphate]] <ref>[http://www.xumuk.ru/encyklopedia/2/4392.html Chemical Encyclopedia: Terpenes]. xumuk.ru</ref><ref>[[#Begley|Begley]], Natural Products: An Overview</ref><br />
| [[Aconitine]], [[delphinine]] <ref name="ref23" /><ref>{{cite journal|author = Atta-ur-Rahman and M. Iqbal Choudhary|title = Diterpenoid and steroidal alkaloids|url = http://www.rsc.org/publishing/journals/NP/article.asp?doi=NP9971400191|journal=Nat. Prod. Rep|year = 1997|volume = 14|pages = 191–203|pmid = 9149410|issue = 2|doi = 10.1039/np9971400191}}</ref><br />
|-<br />
| [[Steroids]]<ref>[[#Hesse|Hesse]], p. 88</ref><br />
[[File:Cyclopentenophenanthrene.svg|100px|center]]<br />
|<br />
| [[Cholesterol]], [[arginine]]<ref>[[#Dewick|Dewick]], p. 388</ref><br />
| Solasodine, [[solanidine]], veralkamine, [[batrachotoxin]]<ref>[[#Plemenkov|Plemenkov]], p. 247</ref><br />
|}<br />
<br />
== Properties ==<br />
[[File:Cyclopelamb2.jpg|thumb|Head of a lamb born by a sheep that ate leaves of the [[Veratrum californicum|corn lily]] plant. The [[cyclopia]] in the calf is induced by the alkaloid [[cyclopamine]] present in the plant.]]<br />
Most alkaloids contain oxygen in their molecular structure; those compounds are usually colorless crystals at ambient conditions. Oxygen-free alkaloids, such as [[nicotine]]<ref>[http://slovari.yandex.ru/dict/bse/article/00052/84600.htm Никотин]. [[Great Soviet Encyclopedia]] (1969–1978)</ref> or [[coniine]],<ref name="BSE: koniin"/> are typically volatile, colorless, oily liquids.<ref name="ref222">[[#Grinkevich|Grinkevich]], p. 131</ref> Some alkaloids are colored, like [[berberine]] (yellow) and [[sanguinarine]] (orange).<ref name="ref222" /><br />
<br />
Most alkaloids are weak bases, but some, such as [[theobromine]] and [[theophylline]], are [[amphoteric]].<ref name="ref225">G. A. Spiller [http://books.google.com/books?id=Rgs_rVOceZwC&pg=PA140 ''Caffeine''], CRC Press, 1997 ISBN 0-8493-2647-8</ref> Many alkaloids dissolve poorly in water but readily dissolve in [[organic solvent]]s, such as [[diethyl ether]], [[chloroform]] or [[1,2-dichloroethane]]. [[Caffeine]],<ref>{{cite web|title=Caffeine|url=http://www.drugbank.ca/drugs/DB00201|work=DrugBank|accessdate=12 February 2013}}</ref> [[cocaine]],<ref>{{cite web|title=Cocaine|url=http://www.drugbank.ca/drugs/DB00907|work=DrugBank|accessdate=12 February 2013}}</ref> [[codeine]]<ref>{{cite web|title=Codeine|url=http://www.drugbank.ca/drugs/DB00318|work=DrugBank|accessdate=12 February 2013}}</ref> and [[nicotine]]<ref>{{cite web|title=Nicotine|url=http://www.drugbank.ca/drugs/DB00184|work=DrugBank|accessdate=12 February 2013}}</ref> are water soluble (with a solubility of ≥1g/L), whereas others, including [[morphine]]<ref>{{cite web|title=Morphine|url=http://www.drugbank.ca/drugs/DB00295|work=DrugBank|accessdate=12 February 2013}}</ref> and [[yohimbine]]<ref>{{cite web|title=Yohimbine|url=http://www.drugbank.ca/drugs/DB01392|work=DrugBank|accessdate=12 February 2013}}{{dead link|date=March 2013}}</ref> are highly water soluble (0.1–1 g/L). Alkaloids and acids form salts of various strengths. These salts are usually soluble in water and [[alcohol]] and poorly soluble in most organic solvents. Exceptions include [[scopolamine]] hydrobromide, which is soluble in organic solvents, and the water-soluble quinine sulfate.<ref name="ref222" /><br />
<br />
Most alkaloids have a bitter taste or are poisonous when ingested. Alkaloid production in plants appeared to have evolved in response to feeding by herbivorous animals; however, some animals have evolved the ability to detoxify alkaloids.<ref>[[#Fattorusso|Fattorusso]], p. 53</ref> Some alkaloids can produce developmental defects in the offspring of animals that consume but cannot detoxify the alkaloids. One example is the alkaloid [[cyclopamine]], produced in the leaves of [[Veratrum californicum|corn lily]]. During the 1950s, up to 25% of lambs born by sheep that had grazed on corn lily had serious facial deformations. These ranged from deformed jaws to [[cyclopia]] (see picture). After decades of research, in the 1980s, the compound responsible for these deformities was identified as the alkaloid 11-deoxyjervine, later renamed to cyclopamine.<ref>{{cite book|page=362|url=http://books.google.com/?id=nixyqfGIGHcC&pg=PA362|title=Poisonous plants and related toxins, Volume 2001|author=Thomas Acamovic, Colin S. Stewart, T. W. Pennycott|publisher=CABI|year= 2004|isbn=0-85199-614-0}}</ref><br />
<br />
==Distribution in nature==<br />
[[File:Strychnos nux-vomica - Köhler–s Medizinal-Pflanzen-266.jpg|thumb|[[Strychnine tree]]. Its seeds are rich in [[strychnine]] and [[brucine]].]]<br />
<br />
Alkaloids are [[anabolism|generated]] by various living organisms, especially by [[Vascular plant|higher plants]] – about 10 to 25% of those contain alkaloids.<ref>[[#Aniszewski|Aniszewski]], p. 13</ref><ref>[[#Orekhov|Orekhov]], p. 11</ref> Therefore, in the past the term "alkaloid" was associated with plants.<ref name="Hesse 4">[[#Hesse|Hesse]], p.4</ref><br />
<br />
The alkaloids content in plants is usually within a few percent and is inhomogeneous over the plant tissues. Depending on the type of plants, the maximum concentration is observed in the leaves ([[black henbane]]), [[fruit]]s or [[seed]]s ([[Strychnine tree]]), root ([[Rauwolfia serpentina]]) or bark ([[cinchona]]).<ref>[[#Grinkevich|Grinkevich]], pp. 122–123</ref> Furthermore, different tissues of the same plants may contain different alkaloids.<ref>[[#Orekhov|Orekhov]], p. 12</ref><br />
<br />
Beside plants, alkaloids are found in certain types of [[fungi]], such as [[psilocybin]] in the fungus of the genus [[Psilocybe]], and in animals, such as [[bufotenin]] in the skin of some toads.<ref name="Hesse 5" /> Many marine organisms also contain alkaloids.<ref>[[#Fattorusso|Fattorusso]], p. XVII</ref> Some [[amines]], such as [[adrenaline]] and [[serotonin]], which play an important role in higher animals, are similar to alkaloids in their structure and biosynthesis and are sometimes called alkaloids.<ref>[[#Aniszewski|Aniszewski]], pp. 110–111</ref><br />
<br />
==Extraction==<br />
[[File:Piperine crystals.jpg|thumb|Crystals of [[piperine]] extracted from [[black pepper]].]]<br />
<br />
Because of the structural diversity of alkaloids, there is no single method of their extraction from natural raw materials.<ref name="Hesse 116">[[#Hesse|Hesse]], p. 116</ref> Most methods exploit the property of most alkaloids to be soluble in organic solvents but not in water, and the opposite tendency of their salts.<br />
<br />
Most plants contain several alkaloids. Their mixture is extracted first and then individual alkaloids are separated.<ref name="ref236">[[#Grinkevich|Grinkevich]], p. 132</ref> Plants are thoroughly ground before extraction.<ref name="Hesse 116"/><ref>[[#Grinkevich|Grinkevich]], p. 5</ref> Most alkaloids are present in the raw plants in the form of salts of organic acids.<ref name="Hesse 116"/> The extracted alkaloids may remain salts or change into bases.<ref name="ref236" /> Base extraction is achieved by processing the raw material with alkaline solutions and extracting the alkaloid bases with organic solvents, such as 1,2-dichloroethane, chloroform, diethyl ether or benzene. Then, the impurities are dissolved by weak acids; this converts alkaloid bases into salts that are washed away with water. If necessary, an aqueous solution of alkaloid salts is again made alkaline and treated with an organic solvent. The process is repeated until the desired purity is achieved.<br />
<br />
In the acidic extraction, the raw plant material is processed by a weak acidic solution (e.g., [[acetic acid]] in water, ethanol, or methanol). A base is then added to convert alkaloids to basic forms that are extracted with organic solvent (if the extraction was performed with alcohol, it is removed first, and the remainder is dissolved in water). The solution is purified as described above.<ref name="Hesse 116"/><ref>[[#Grinkevich|Grinkevich]], pp. 132–134</ref><br />
<br />
Alkaloids are separated from their mixture using their different solubility in certain solvents and different reactivity with certain reagents or by [[distillation]].<ref>[[#Grinkevich|Grinkevich]], pp. 134–136</ref><br />
<br />
==Biosynthesis==<br />
Biological precursors of most alkaloids are [[amino acid]]s, such as [[ornithine]], [[lysine]], [[phenylalanine]], [[tyrosine]], [[tryptophan]], [[histidine]], [[aspartic acid]], and [[anthranilic acid]].<ref name="Plemenkov 253">[[#Plemenkov|Plemenkov]], p. 253</ref> [[Nicotinic acid]] can be synthesized from tryptophan or aspartic acid. Ways of alkaloid biosynthesis are too numerous and cannot be easily classified.<ref name="Begley"/> However, there are a few typical reactions involved in the biosynthesis of various classes of alkaloids, including synthesis of [[Schiff bases]] and [[Mannich reaction]].<ref name="Plemenkov 253"/><br />
<br />
===Synthesis of Schiff bases===<br />
{{Main|Schiff base}}<br />
<br />
Schiff bases can be obtained by reacting amines with ketones or aldehydes.<ref>[[#Plemenkov|Plemenkov]], p. 254</ref> These reactions are a common method of producing C=N bonds.<ref name="Dewick 19">[[#Dewick|Dewick]], p. 19</ref><br />
<br />
[[File:Schiff base formation.svg|center]]<br />
<br />
In the biosynthesis of alkaloids, such reactions may take place within a molecule,<ref name="Plemenkov 253"/> such as in the synthesis of piperidine:<ref name="ref19"/><br />
<br />
[[File:Schiff base formation intramolecular.svg|center]]<br />
<br />
===Mannich reaction===<br />
{{Main|Mannich reaction}}<br />
<br />
An integral component of the Mannich reaction, in addition to an amine and a [[carbonyl]] compound, is a [[carbanion]], which plays the role of the nucleophile in the [[nucleophilic addition]] to the ion formed by the reaction of the amine and the carbonyl.<ref name = "Dewick 19" /><br />
<br />
[[File:Mannich.png|center]]<br />
<br />
The Mannich reaction can proceed both intermolecularly and intramolecularly:<ref>[[#Plemenkov|Plemenkov]], p. 255</ref><ref>[[#Dewick|Dewick]], p. 305</ref><br />
<br />
[[File:Mannich reaction intramolecular.svg|center]]<br />
<br />
==Dimer alkaloids==<br />
In addition to the described above monomeric alkaloids, there are also [[Dimer (chemistry)|dimer]]ic, and even [[trimer (chemistry)|trimer]]ic and [[tetramer]]ic alkaloids formed upon condensation of two, three, and four monomeric alkaloids. Dimeric alkaloids are usually formed from monomers of the same type through the following mechanisms:<ref>[[#Hesse|Hesse]], pp. 91–105</ref><br />
* [[Mannich reaction]], resulting in, e.g., voacamine<br />
* [[Michael reaction]] (villalstonine)<br />
* Condensation of aldehydes with amines (toxiferine)<br />
* Oxidative addition of phenols (dauricine, tubocurarine)<br />
* [[Lactone|Lactonization]] (carpaine).<br />
<br />
<center><br />
<gallery widths="220px" perrow="3"><br />
File:Voacamine chemical structure.png|[[Voacamine]]<br />
File:Villalstonine.svg|[[Villalstonine]]<br />
File:Toxiferine I.png|[[Toxiferine]]<br />
File:Dauricine.svg|[[Dauricine]]<br />
File:Tubocurarine.svg|[[Tubocurarine]]<br />
File:Carpaine.png|[[Carpaine]]<br />
</gallery><br />
</center><br />
<br />
==The biological role==<br />
The role of alkaloids for living organisms that produce them is still unclear.<ref>[[#Aniszewski|Aniszewski]], p. 142</ref> It was initially assumed that the alkaloids are the final products of [[nitrogen]] [[metabolism]] in plants, as [[urea]] in mammals. It was later shown that alkaloid concentrations varies over time, and this hypothesis was refuted.<ref name="Meyers"/><br />
<br />
Most of the known functions of alkaloids are related to protection. For example, [[aporphine]] alkaloid [[liriodenine]] produced by the [[Liriodendron tulipifera|tulip tree]] protects it from parasitic mushrooms. In addition, presence of alkaloids in the plant prevents insects and [[chordate]] animals from eating it. However, some animals adapted to alkaloids and even use them in their own metabolism.<ref>[[#Hesse|Hesse]], pp. 283–291</ref> Such alkaloid-related substances as [[serotonin]], [[dopamine]] and [[histamine]] are important [[neurotransmitter]]s in animals. Alkaloids are also known to regulate plant growth.<ref>[[#Aniszewski|Aniszewski]], pp. 142–143</ref> Another example of an organism that uses alkaloids for protection is the ''[[Utetheisa ornatrix]]'', more commonly known as the Ornate Moth. Pyrrolizidine alkaloids render these larvae and adult moths unpalatable to many of their natural enemies like coccinelid beetles, green lacewings, insectivorous hemiptera and insectivorous bats.<ref>W.E. Conner (2009). ''Tiger Moths and Woolly Bears—behaviour, ecology, and evolution of the Arctiidae''. New York: Oxford University Press. pp. 1–10. ISBN 0195327373.</ref><br />
<br />
== Applications ==<br />
<br />
===In medicine===<br />
Medical use of alkaloid-containing plants has a long history, and, thus, when the first alkaloids were isolated in the 19th century, they immediately found application in clinical practice.<ref>[[#Hesse|Hesse]], p. 303</ref> Many alkaloids are still used in medicine, usually in the form of salts, including the following:<ref name="Meyers"/><ref>[[#Hesse|Hesse]], pp. 303–309</ref><br />
<br />
{| Class = "wikitable"<br />
|-<br />
! Alkaloid<br />
! Action<br />
|-<br />
| [[Ajmaline]]<br />
| [[Antiarrhythmic agent|antiarrhythmic]]<br />
|-<br />
| [[Atropine]], [[scopolamine]], [[hyoscyamine]]<br />
| [[anticholinergic]]<br />
|-<br />
| [[Caffeine]]<br />
| [[Stimulant]], [[Adenosine receptor]] antagonist<br />
|-<br />
| [[Codeine]]<br />
| [[cough medicine]], [[analgesic]]<br />
|-<br />
| [[Colchicine]]<br />
| remedy for [[gout]]<br />
|-<br />
| [[Emetine]]<br />
| [[antiprotozoal agent]]<br />
|-<br />
| [[Ergoline|Ergot alkaloids]]<br />
| [[Sympathomimetics|sympathomimetic]], vasodilator, antihypertensive<br />
|-<br />
| [[Morphine]]<br />
| [[analgesic]]<br />
|-<br />
| [[Nicotine]]<br />
| [[Stimulant]], [[Nicotinic agonist|Nicotinic acetylcholine receptor agonist]]<br />
|-<br />
| [[Physostigmine]]<br />
| inhibitor of [[acetylcholinesterase]]<br />
|-<br />
| [[Quinidine]]<br />
| antiarrhythmic<br />
|-<br />
| [[Quinine]]<br />
| antipyretics, antimalarial<br />
|-<br />
| [[Reserpine]]<br />
| [[Antihypertensive drug|antihypertensive]]<br />
|-<br />
| [[Tubocurarine]]<br />
| Muscle relaxant<br />
|-<br />
| [[Vinblastine]], [[vincristine]]<br />
| [[Chemotherapy|antitumor]]<br />
|-<br />
| [[Vincamine]]<br />
| [[Vasodilation|vasodilating]], [[Antihypertensive drug|antihypertensive]]<br />
|-<br />
| [[Yohimbine]]<br />
| [[Stimulant]], [[Aphrodisiac]]<br />
|}<br />
<br />
Many synthetic and semisynthetic drugs are structural modifications of the alkaloids, which were designed to enhance or change the primary effect of the drug and reduce unwanted side-effects.<ref>[[#Hesse|Hesse]], p. 309</ref> For example, [[naloxone]], an [[opioid receptor]] [[receptor antagonist|antagonist]], is a derivative of [[thebaine]] that is present in [[opium]].<ref>[[#Dewick|Dewick]], p. 335</ref><br />
<br />
<center><br />
<gallery widths="200px" perrow="2"><br />
File:Thebaine skeletal.svg|[[Thebaine]]<br />
File:Naloxone.svg|[[Naloxone]]<br />
</gallery><br />
</center><br />
<br />
=== In agriculture ===<br />
Prior to the development of a wide range of relatively low-toxic synthetic [[pesticide]]s, some alkaloids, such as salts of nicotine and [[anabasine]], were used as [[insecticide]]s. Their use was limited by their high toxicity to humans.<ref>György Matolcsy, Miklós Nádasy, Viktor Andriska [http://books.google.com/books?id=fPiRSsUOpLEC&pg=PA21 ''Pesticide chemistry''], Elsevier, 2002, pp. 21–22 ISBN 0-444-98903-X</ref><br />
<br />
=== Use as psychoactive drugs ===<br />
Preparations of plants containing alkaloids and their extracts, and later pure alkaloids, have long been used as [[Psychoactive drug|psychoactive substances]]. [[Cocaine]] and [[cathinone]] are [[stimulant]]s of the [[central nervous system]].<ref>[[#Veselovskaya|Veselovskaya]], p. 75</ref><ref>[[#Hesse|Hesse]], p. 79</ref> [[Mescaline]] and many of indole alkaloids (such as [[psilocybin]], [[dimethyltryptamine]] and [[ibogaine]]) have [[hallucinogen]]ic effect.<ref>[[#Veselovskaya|Veselovskaya]], p. 136</ref><ref>Geoffrey A. Cordell ''The Alkaloids: Chemistry and Biology''. [http://www.sciencedirect.com/science/bookseries/10994831/56 Vol. 56], Elsevier, 2001, p. 8, ISBN 978-0-12-469556-6.</ref> [[Morphine]] and [[codeine]] are strong narcotic pain killers.<ref>[[#Veselovskaya|Veselovskaya]], p. 6</ref><br />
<br />
There are alkaloids that do not have strong psychoactive effect themselves, but are [[precursor (chemistry)|precursor]]s for semi-synthetic psychoactive drugs. For example, [[ephedrine]] and [[pseudoephedrine]] are used to produce [[methcathinone]] and [[methamphetamine]].<ref>[[#Veselovskaya|Veselovskaya]], pp. 51–52</ref> [[Thebaine]] is used in the synthesis of many painkillers such as [[oxycodone]].<br />
<br />
== See also ==<br />
{{colbegin|3}}<br />
* [[Amine]]<br />
* [[Base (chemistry)]]<br />
* [[Natural products]]<br />
* [[Palau'amine]]<br />
* [[Secondary metabolite]]<br />
* [[Mayer's reagent]]<br />
{{colend}}<br />
<br />
== Notes ==<br />
{{Reflist|group="nb"}}<br />
<br />
== References ==<br />
{{Reflist|25em}}<br />
<br />
== Bibliography ==<br />
{{Commons|Alkaloid}}<br />
* {{cite book|ref=Aniszewski|author = Aniszewski, Tadeusz |title = Alkaloids – secrets of life|location = Amsterdam|publisher = [[Elsevier]]|year = 2007|isbn = 978-0-444-52736-3}}<br />
* {{cite book|ref=Begley|author = Begley, Tadhg P. |title = Encyclopedia of Chemical Biology|year = 2009|publisher = Wiley|isbn = 978-0-471-75477-0|doi=10.1002/cbic.200900262}}<br />
* {{cite book|ref=Brossi|author =Brossi, Arnold |title=The Alkaloids: Chemistry and Pharmacology|publisher= Academic Press|year= 1989}}<br />
* {{cite book|ref=Dewick|author = Dewick, Paul M |title = Medicinal Natural Products. A Biosynthetic Approach. Second Edition|year = 2002|publisher = Wiley|isbn = 0-471-49640-5}}<br />
* {{cite book|ref=Fattorusso|author = Fattorusso, E. and Taglialatela-Scafati, O. |title = Modern Alkaloids: Structure, Isolation, Synthesis and Biology|year = 2008|publisher = Wiley-VCH|isbn = 978-3-527-31521-5}}<br />
* {{cite book|ref=Grinkevich|author = Grinkevich NI Safronich LN|title = The chemical analysis of medicinal plants: Proc. allowance for pharmaceutical universities|location = M|year = 1983}}<br />
* {{cite book|ref=Hesse|author = Hesse, Manfred |title = Alkaloids: Nature's Curse or Blessing?|year = 2002|publisher = Wiley-VCH|isbn = 978-3-906390-24-6}}<br />
* {{cite book|ref=Knunyants|author = Knunyants, IL|title = Chemical Encyclopedia|url = http://www.cnshb.ru/AKDiL/0048/base/RA/140004.shtm|publisher = Soviet Encyclopedia|year = 1988}}<br />
* {{cite book|ref=Orekhov|author = Orekhov, AP|title = Chemistry alkaloids|edition = Acad. 2|location = M.|publisher = USSR|year = 1955}}<br />
* {{cite book|ref=Plemenkov|author = Plemenkov, VV|title = Introduction to the Chemistry of Natural Compounds|location = Kazan|year = 2001}}<br />
*{{cite book|ref=Saxton|author =Saxton, J. E. |title=The Alkaloids. A Specialist Periodical Report|place= London|publisher= The Chemical Society|year=1971}}<br />
* {{cite book|ref=Veselovskaya|author =Veselovskaya, N. B., Kovalenko, A.E |title=Drugs|place=Moscow|publisher= Triada-X|year=2000}}<br />
<br />
{{alkaloids}}<br />
<br />
[[Category:Alkaloids|*]]<br />
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{{Link GA|ru}}</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=84132Main Page2014-08-19T04:21:49Z<p>10.68.16.65: </p>
<hr />
<div>[[File:Alpha Decay.svg|thumb|240px|right|Visual representation of alpha decay]]<br />
{{Nuclear physics}}<br />
'''Alpha decay''', or α-decay, is a type of [[radioactivity|radioactive decay]] in which an [[atomic nucleus]] emits an [[alpha particle]] and thereby transforms (or 'decays') into an atom with a [[mass number]] 4 less and [[atomic number]] 2 less. For example, [[uranium-238]] decaying through α-particle emission to form [[thorium-234]] can be expressed as:<ref name="suchocki">Suchocki, John. ''Conceptual Chemistry'', 2007. Page 119.</ref><br />
<br />
:<math>\mathrm{~^{238}_{92}U}\rightarrow\mathrm{~^{234}_{90}Th} + {\alpha }</math><br />
<br />
Because an [[alpha particle]] is the same as the nucleus of a [[helium-4]] atom - consisting of two [[proton]]s and two [[neutron]]s and thus having [[mass number]] 4 and [[atomic number]] 2 - this can also be written as:<br />
<br />
:<math>\mathrm{~^{238}_{92}U}\rightarrow\mathrm{~^{234}_{90}Th} + \mathrm{~^{4}_{2}He}</math><br />
<br />
Notice how, on either side of the nuclear equation, both the mass number and the atomic number are conserved: the mass number is 238 on the left side and (234 + 4) on the right side, and the atomic number is 92 on the left side and (90 + 2) on the right side.<br />
<br />
The alpha particle also has a charge +2, but the charge is usually not written in nuclear equations, which describe nuclear reactions without considering the electrons. This convention is not meant to imply that the nuclei necessarily occur in neutral atoms. Alpha decay typically occurs in the heaviest nuclides. In theory it can occur only in nuclei somewhat heavier than nickel (element 28), where overall [[binding energy]] per [[nucleon]] is no longer a minimum, and the nuclides are therefore unstable toward spontaneous fission-type processes. In practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitter being the lightest [[isotope]]s (mass numbers 106–110) of [[tellurium]] (element 52).<br />
<br />
Alpha decay is by far the most common form of [[cluster decay]] where the parent [[atom]] ejects a defined [[decay product|daughter]] collection of [[nucleon]]s, leaving another defined product behind (in [[nuclear fission]], a number of different pairs of daughters of approximately equal size are formed). Alpha decay is the most likely cluster decay because of the combined extremely high [[binding energy]] and relatively small mass of the helium-4 product nucleus (the alpha particle). Alpha decay, like other cluster decays, is fundamentally a [[quantum tunneling]] process. Unlike [[beta decay]], alpha decay is governed by the interplay between the [[nuclear force]] and the [[electromagnetic force]].<br />
<br />
[[Alpha particle]]s have a typical kinetic energy of 5&nbsp;MeV (that is, ≈&nbsp;0.13% of their total energy, i.e. 110&nbsp;TJ/kg) and a speed of 15,000&nbsp;km/s. This corresponds to a speed of around 0.05&nbsp;''[[Speed of light|c]]''. There is surprisingly small variation around this energy, due to the heavy dependence of the half-life of this process on the energy produced (see equations in the [[Geiger–Nuttall law]]). Because of their relatively large mass, +2 [[electric charge]] and relatively low velocity, alpha particles are very likely to interact with other atoms and lose their energy, so their forward motion is effectively stopped within a few centimeters of [[air]]. Most of the [[helium]] produced on [[Earth]] (approximately 99% of it) is the result of the alpha decay of underground deposits of [[mineral]]s containing [[uranium]] or [[thorium]]. The helium is brought to the surface as a byproduct of [[natural gas]] production.<br />
<br />
==History==<br />
[[Image:Alphaspektroskopie.JPG|thumb|right|Alpha source beneath a radiation detector]]<br />
Alpha particles were first described in the investigations of radioactivity by [[Ernest Rutherford]] in 1899, and by 1907 they were identified as He<sup>2+</sup> ions. For more details of this early work, see [[Alpha particle#History of discovery and use]].<br />
<br />
By 1928, [[George Gamow]] had solved the theory of the alpha decay via tunneling. The alpha particle is trapped in a [[potential well]] by the nucleus. Classically, it is forbidden to escape, but according to the (then) newly discovered principles of [[quantum mechanics]], it has a tiny (but non-zero) probability of "[[quantum tunnelling|tunneling]]" through the [[potential barrier|barrier]] and appearing on the other side to escape the nucleus. Gamow solved a model potential for the nucleus and derived, from first principles, a relationship between the [[half-life]] of the decay, and the energy of the emission, which had been previously discovered empirically, and was known as the [[Geiger–Nuttall law]].<ref>[http://www.phy.uct.ac.za/courses/phy300w/np/ch1/node38.html For Gamow's derivation of this law, see]</ref><br />
<br />
==Uses==<br />
[[Americium-241]], an [[alpha emitter]], is used in [[smoke detector]]s. The alpha particles [[Ionization|ionize]] air in an open [[ion chamber]] and a small [[Electric current|current]] flows through the ionized air. Smoke particles from fire that enter the chamber reduce the current, triggering the smoke detector's alarm. ''See [[Smoke_detector#Ionization|Smoke_Detector-Ionization]] for details''.<br />
<br />
Alpha decay can provide a safe power source for [[radioisotope thermoelectric generator]]s used for [[space probe]]s<ref>{{cite web |url=http://solarsystem.nasa.gov/rps/rtg.cfm |title=Radioisotope Thermoelectric Generator |work=Solar System Exploration |publisher=[[NASA]] |accessdate=25 March 2013}}</ref> and [[Artificial pacemaker|artificial heart pacemakers]].<ref>{{cite web |url=http://osrp.lanl.gov/pacemakers.shtml |title=Nuclear-Powered Cardiac Pacemakers |work=Off-Site Source Recovery Project |publisher=[[Los Alamos National Laboratory|LANL]] |accessdate=25 March 2013}}</ref> Alpha decay is much more easily shielded against than other forms of radioactive decay. [[Plutonium-238]], for example, requires only 2.5 millimetres of [[lead]] shielding to protect against unwanted radiation.{{cn|date=March 2014}}<br />
<br />
[[Static eliminator]]s typically use [[polonium-210]], an alpha emitter, to ionize air, allowing the 'static cling' to more rapidly dissipate.<br />
<br />
==Toxicity==<br />
Being relatively heavy and positively charged, alpha particles tend to have a very short [[mean free path]], and quickly lose kinetic energy within a short distance of their source. This results in several [[MeV]] being deposited in a relatively small volume of material. This increases the chance of cellular damage in cases of internal contamination. In general, external alpha radiation is not harmful since alpha particles are effectively shielded by a few centimeters of air, a piece of paper, or the thin layer of dead skin cells that make up the [[epidermis (skin)|epidermis]]. Even touching an alpha source is typically not harmful, though many alpha sources also are accompanied by [[beta decay|beta-emitting]] radio daughters, and alpha emission is also accompanied by gamma photon emission. If substances emitting alpha particles are ingested, inhaled, injected or introduced through the skin, then it could result in a measurable [[Equivalent dose|dose]].<br />
<br />
The [[relative biological effectiveness]] (RBE) of alpha radiation is higher than that of beta or gamma radiation. RBE quantifies the ability of radiation to cause certain biological effects, notably either [[cancer]] or [[necrosis|cell-death]], for equivalent radiation exposure. The higher value for alpha radiation is generally attributable to the high [[linear energy transfer]] (LET) coefficient, which is about one ionization of a chemical bond for every [[angstrom]] of travel by the alpha particle. The RBE has been set at the value of 20 for alpha radiation by various government regulations. The RBE is set at 10 for [[neutron]] irradiation, and at 1 for [[Beta decay|beta radiation]] and ionizing photons.<br />
<br />
However, another component of alpha radiation is the [[recoil]] of the parent nucleus, termed alpha recoil. Due to the [[conservation of momentum]] requiring the parent nucleus to recoil, the effect acts much like the 'kick' of a rifle butt when a bullet goes in the opposite direction. This gives a significant amount of energy to the recoiling nucleus, which also causes ionization damage (see [[ionizing radiation]]). The total energy of the recoil nucleus is readily calculable, and is roughly the weight of the alpha (4&nbsp;[[Atomic mass unit|u]]) divided by the weight of the parent (typically about 200&nbsp;u) times the total energy of the alpha. By some estimates, this might account for most of the internal radiation damage, as the recoil nuclei are typically [[heavy metal (chemistry)|heavy metals]] which preferentially collect on the [[chromosome]]s. In some studies,<ref><br />
{{cite journal<br />
|author=Winters TH, Franza JR<br />
|year=1982<br />
|title=Radioactivity in Cigarette Smoke<br />
|journal=[[New England Journal of Medicine]]<br />
|volume=306 |issue=6 |pages=364–365<br />
|doi=10.1056/NEJM198202113060613<br />
}}</ref> this has resulted in a RBE approaching 1,000 instead of the value used in governmental regulations.<br />
<br />
The largest natural contributor to public radiation dose is [[radon]], a naturally occurring, radioactive gas found in soil and rock.<ref>[http://www.ans.org/pi/resources/dosechart/ ANS : Public Information : Resources : Radiation Dose Chart<!-- Bot generated title -->]</ref> If the gas is inhaled, some of the radon particles may attach to the inner lining of the lung. These particles continue to decay, emitting alpha particles which can damage cells in the lung tissue.<ref>EPA Radiation Information: Radon. October 6, 2006, [http://www.epa.gov/radiation/radionuclides/radon.htm], Accessed December 6, 2006</ref> The death of [[Marie Curie]] at age 66 from [[leukemia]] was probably caused by prolonged exposure to high doses of ionizing radiation, but it is not clear if this was due to alpha radiation or X-rays. Curie worked extensively with radium, which decays into radon,<ref>Health Physics Society, "Did Marie Curie die of a radiation overexposure?" [http://www.hps.org/publicinformation/ate/q535.html]</ref> along with other radioactive materials that emit [[beta decay|beta]] and [[gamma ray]]s. However, Curie also worked with unshielded X-ray tubes during World War I, and analysis of her skeleton during a reburial showed a relatively low level of radioisotope burden.<br />
<br />
Russian dissident [[Alexander Litvinenko]]'s 2006 murder by [[radiation poisoning]] is thought to have been carried out with [[polonium-210]], an alpha emitter.<br />
<br />
== See also ==<br />
*[[Alpha particle]]<br />
*[[Beta decay]]<br />
<br />
==References==<br />
{{reflist}}<br />
*[http://www.ct.infn.it/~rivel/Didat/SilDet.pdf Alpha emitters by increasing energy (Appendix 1)]<br />
<br />
== External links ==<br />
* [[Image:Ndslivechart.png]] '''[http://www-nds.iaea.org/livechart The LIVEChart of Nuclides - IAEA ]''' with filter on alpha decay<br />
* [http://nagysandor.eu/AsimovTeka/AlphaExamples/index_en.html Alpha decay with 3 animated examples] showing the recoil of daughter<br />
<br />
{{Nuclear processes}}<br />
<br />
{{DEFAULTSORT:Alpha Decay}}<br />
[[Category:Nuclear physics]]<br />
[[Category:Radioactivity]]</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=83984Main Page2014-08-19T03:01:48Z<p>10.68.16.65: </p>
<hr />
<div>{{Austrian School sidebar |expanded=all}}<br />
{{Neoliberalism sidebar |expanded=Economics}}<br />
The '''Austrian School''' is a [[Schools of economic thought|school of economic thought]] that is based on the analysis of the purposeful actions of individuals (see [[methodological individualism]]).<ref>Carl Menger, Prinicples of Economics, online at http://www.mises.org/etexts/menger/principles.asp</ref><ref name="econlib">{{cite encyclopedia |last1=Boettke |first1=Peter J. |authorlink1= Peter Boettke |last2= |first2= |authorlink2= |editor= [[David R. Henderson]] (ed.) |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Austrian School of Economics |url=http://www.econlib.org/library/Enc/AustrianSchoolofEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |isbn=978-0865976658 |oclc=237794267}}</ref><ref>[http://plato.stanford.edu/entries/methodological-individualism/ Methodological Individualism at the Stanford Encyclopedia of Philosophy ]</ref><ref name="Mises_Action">Ludwig von Mises. [[Human Action]], p. 11, "r. Purposeful Action and Animal Reaction". Referenced 2011-11-23.</ref> It originated in late-19th and early-20th century Vienna with the work of [[Carl Menger]], [[Eugen von Böhm-Bawerk]], [[Friedrich von Wieser]], and others.<ref>Joseph A. Schumpeter, History of economic analysis, Oxford University Press 1996, ISBN 978-0195105599.</ref> Current-day economists working in this tradition are located in many different countries, but their work is referred to as '''Austrian economics'''.<br />
<br />
Among the theoretical contributions of the early years of the Austrian School are the [[subjective theory of value]], [[marginalism]] in [[price theory]], and the formulation of the [[economic calculation problem]], each of which has become an accepted part of [[mainstream economics]].<ref>{{Cite book | last1 = Birner | first1 = Jack | first2 = Rudy | last2 = van Zijp | title = Hayek, Co-ordination and Evolution: His Legacy in Philosophy, Politics, Economics and the History of Ideas | location = London, New York | publisher = [[Routledge]] | year= 1994 | page = 94 | isbn = 978-0-415-09397-2}}</ref><br />
<br />
Many economists are critical of the current-day Austrian School and consider its rejection of [[econometrics]], [[experimental economics]], and aggregate [[macroeconomic]] analysis to be outside of [[Mainstream economics|mainstream economic theory]], or "[[Heterodox economics|heterodox]]."<ref name="Austrian Economists: Boettke">{{Cite web|url=http://austrianeconomists.typepad.com/weblog/2008/05/is-austrian-eco.html|title=Is Austrian Economics Heterodox Economics?|last=Boettke |first=Peter|publisher=The Austrian Economists|accessdate=2009-02-13| archiveurl= https://web.archive.org/web/20090328232903/http://austrianeconomists.typepad.com/weblog/2008/05/is-austrian-eco.html| archivedate= 28 March 2009 <!--DASHBot-->| deadurl= no}}</ref><ref name="Boettke and Leeson">{{Cite book|last=Boettke|first=Peter J.|author2=[[Peter T. Leeson]]|title=A Companion to the History of Economic Thought|editor=[[Warren Samuels]], Jeff E. Biddle, and John B. Davis|pages=446–452|chapter=28A: The Austrian School of Economics 1950-2000|url=http://books.google.com/?id=3H8gBQv5MysC&pg=PA445&dq=austrian+school+heterodox+economics |publisher=Blackwell Publishing |year=2003 |isbn=978-0-631-22573-7}}</ref><ref>{{cite news | url=http://www.economist.com/node/21542174 | title=Heterodox economics: Marginal revolutionaries | publisher=The Economist | date=December 31, 2011 | accessdate=February 22, 2012}}</ref><ref name="Caplan">{{Cite web|url=http://www.gmu.edu/departments/economics/bcaplan/whyaust.htm|title=Why I Am Not an Austrian Economist |last=Caplan |first=Bryan |publisher=Byan Caplan at [[George Mason University]] faculty page |accessdate=2008-07-04 | quote=...More than anything else, what prevents Austrians from getting more publications in mainstream journals is that their papers rarely use mathematics or econometrics, research tools that Austrians reject on principle. ...Mises and Rothbard however err when they say that economic history can ''only'' illustrate economic theory. In particular, empirical evidence is often necessary to determine whether a theoretical factor is ''quantitatively significant''. ...Austrians reject econometrics on principle because economic theory is true a priori, so statistics or historical study cannot 'test' theory....}}</ref> Austrians are likewise critical of mainstream economics.<ref>[http://mises.org/journals/qjae/pdf/qjae3_2_3.pdf Austrian Economics and the Mainstream: View from the Boundary], Roger E. Backhouse</ref> Although the Austrian School has been considered heterodox since the late 1930s, it began to attract renewed academic and public interest starting in the 1970s.<ref name="Meijer 1995">{{cite book |last=Meijer |first=G. |title=New Perspectives on Austrian Economics |publisher=Routledge |location=New York |year=1995 |isbn=978-0-415-12283-2 }}</ref><br />
<br />
==Methodology==<br />
{{Main|Action axiom|Catallactics|Praxeology}}<br />
<br />
The Austrian School believes that the subjective choices of individuals underlie all economic phenomena. Austrians seek to understand the observed economy by examining the social ramifications of such individual choice. This approach, termed ''[[methodological individualism]]'', differs significantly from many other schools of economic thought, which have placed less importance on individual knowledge, time, expectation, and other subjective factors and focused instead on aggregate variables, equilibrium analysis, and the consideration of societal groups rather than individuals.<ref name="White Methodology">{{cite book|last=White|first=Lawrence H.|title=The Methodology of the Austrian School Economists|year=revised ed. 2003|publisher=Mises Institute|url=https://mises.org/mofase.asp}}</ref><br />
<br />
[[File:Ludwig von Mises.jpg|right|thumb|130px|[[Ludwig von Mises]]]]<br />
In the twentieth and twenty-first centuries, many diverse approaches and theoretical orientations have developed among economists whose methodological lineage can be traced back to the early Austrian School. For example, in 1949, [[Ludwig von Mises]] codified his version of the subjectivist approach, which he called "[[praxeology]]", in a book published in English as ''[[Human Action]]''.<ref name="Ludwigvon">Ludwig von Mises, Nationalökonomie (Geneva: Union, 1940), p. 3; Human Action (Auburn, Ala.: Mises Institute, [1949] 1998), p. 3.</ref> In it, Mises presented an extensive statement of his method, and stated that praxeology could be used to deduce ''a priori'' theoretical economic truths. Mises also argued against the use of probabilities in economic models. According to Mises, deductive economic [[thought experiment]] can yield conclusions which follow irrefutably from the underlying assumptions and could not be inferred from empirical observation or statistical analysis.<ref>{{Cite web|url=http://mises.org/books/ufofes/ |title=The Ultimate Foundation of Economic Science by Ludwig von Mises |publisher=Mises.org |date= |accessdate=2012-08-13}}</ref><br />
<br />
Since Mises time, many, but certainly not all, Austrian thinkers have accepted his praxeological approach. Some have adopted alternative methodologies.<ref>Bruce J. Caldwell "Praxeology and its Critics: an Appraisal" History of Political Economy Fall 1984 16(3): 363–379; {{DOI|10.1215/00182702-16-3-363}} [http://public.econ.duke.edu/~bjc18/docs/Praxeology%20and%20Its%20Critics.pdf]</ref> For example, [[Fritz Machlup]], [[Friedrich Hayek]], and others, did not take Mises' strong ''[[A priori and a posteriori|a priori]]'' approach to economics.<ref>Richard N. Langlois, "FROM THE KNOWLEDGE OF ECONOMICS TO THE ECONOMICS OF KNOWLEDGE: FRITZ MACHLUP ON METHODOLOGY AND ON THE "KNOWLEDGE SOCIETY" Research in the History of Economic Thought and Methodology, Volume 3, pp. 225–235 [http://web.uconn.edu/ciom/Machlup%20Knowledge%20(1985).pdf]</ref> Prof. Ludwig Lachmann, a radical subjectivist, also largely rejected Mises' formulation of Praxeology in favor of the ''verstehende Methode'' (interpretive method) articulated by [[Max Weber]].<ref name="White Methodology"/><ref name=Ludwig>{{cite book|last=Lachmann|first=Ludwig|title=Macroeconomic Thinking and the Market Economy|year=1973|publisher=Institute of Economic Affairs|url=http://mises.org/books/macrothinking.pdf}}</ref><br />
<br />
Economist [[Paul A. Samuelson]] has written that most economists believe that economic conclusions reached by pure logical deduction are limited and weak.<ref name="Samuelson">{{Cite book |last=Samuelson |first=Paul |title=Economics |publisher=New York: McGraw-Hill |year=1964 |edition=6th |page=736 |isbn=978-0-07-074741-8}}</ref> According to Samuelson and economist [[Bryan Caplan]], Mises' deductive methodology (also embraced by [[Murray Rothbard]] and to a lesser extent by Mises' student, Israel Kirzner) has been widely dismissed within mainstream economics.<ref name="tremble"/> Caplan has written that the Misesian challenge to the realism of neoclassical assumptions has helped work towards making those assumptions more plausible.<ref name="Austrian Search">{{cite journal|last=Caplan|first=Bryan|title=The Austrian Search for Realistic Foundations|journal=Southern Economic Journal|year=1999|volume=65|issue=4|pages=823–838|jstor=1061278|doi=10.2307/1061278 |url=http://econfaculty.gmu.edu/bcaplan/pdfs/aussearch.pdf }}</ref><br />
<br />
Starting in the 20th century, various Austrians incorporated models and mathematics into their analysis of the economy. Austrian economist [[Steven Horwitz]] argues that Austrian methodology is consistent with [[macroeconomics]] and that Austrian macroeconomics can be expressed in terms of [[microeconomics|microeconomic]] foundations.<ref name="Horwitz, Steven 2000">Horwitz, Steven: Microfoundations and Macroeconomics: An Austrian Perspective (2000)|''Routledge''</ref> Austrian economist Roger Garrison argues that Austrian macroeconomic theory can be correctly expressed in terms of [[diagram|diagrammatic models]].<ref>http://library.mises.org/books/Roger%20W%20Garrison/Austrian%20Macroeconomics%20A%20Diagrammatical%20Exposition.pdf Garrison, Roger: Austrian Macroeconomics: A Diagrammatical Exposition (1978)|''Institute for Humane Studies''</ref> In 1944, Austrian economist Oskar Morgenstern presented a rigorous schematization of an ordinal utility function (the [[Von Neumann–Morgenstern utility theorem]]) in [[Theory of Games and Economic Behavior]].<ref>Neumann, John von and Morgenstern, Oskar Theory of Games and Economic Behavior. Princeton, NJ. Princeton University Press. 1944</ref><br />
<br />
==Fundamental tenets==<br />
<br />
[[Fritz Machlup]] listed the typical views of Austrian economic thinking.<ref name="Machlup Mises">{{cite web|last=Machlup |first=Fritz |authorlink=Fritz Machlup |title=Homage to Mises |url=http://www.mises.org/daily/1700 |publisher=Hillsdale College |accessdate=8 August 2013|pages=19–27|year=1981}}</ref><br />
<br />
{{quote|<br />
:(1) Methodological Individualism: In the explanation of economic phenomena we have to go back to the actions (or inaction) of individuals; groups or "collectives" cannot act except through the actions of individual members.<br />
:(2) Methodological Subjectivism: In the explanation of economic phenomena we have to go back to judgments and choices made by individuals on the basis of whatever knowledge they have or believe to have and whatever expectations they entertain regarding external developments and especially the consequences of their own intended actions.<br />
:(3) Tastes and Preferences: Subjective valuations of goods and services determine the demand for them so that their prices are influenced by (actual and potential) consumers.<br />
:(4) Opportunity Costs: The costs with which producers and other economic actors calculate reflect the alternative opportunities that must be foregone; as productive services are employed for one purpose, all alternative uses have to be sacrificed.<br />
:(5) Marginalism: In all economic designs, the values, costs, revenues, productivity, etc., are determined by the significance of the last unit added to or subtracted from the total.<br />
:(6) Time Structure of Production and Consumption: Decisions to save reflect "time preferences" regarding consumption in the immediate, distant, or indefinite future, and investments are made in view of larger outputs expected to be obtained if more time-taking production processes are undertaken.<br />
<br />
Two important tenets held by the Misesian branch of Austrian economics may also be added to the list:<br />
:(7) Consumer Sovereignty: The influence consumers have on the effective demand for goods and services and, through the prices which result in free competitive markets, on the production plans of producers and investors, is not merely a hard fact but also an important objective, attainable only by complete avoidance of governmental interference with the markets and of restrictions on the freedom of sellers and buyers to follow their own judgment regarding quantities, qualities, and prices of products and services.<br />
:(8) Political Individualism: Only when individuals are given full economic freedom will it be possible to secure political and moral freedom. Restrictions on economic freedom lead, sooner or later, to an extension of the coercive activities of the state into the political domain, undermining and eventually destroying the essential individual liberties which the capitalistic societies were able to attain in the nineteenth century.}}<br />
<br />
==Contributions to economic thought==<br />
<br />
===Opportunity cost===<br />
{{Main|Opportunity cost}}<br />
[[File:1wieser.jpg|right|thumb|130px|[[Friedrich von Wieser]]]]<br />
The opportunity cost doctrine was first explicitly formulated by the Austrian economist [[Friedrich von Wieser]] in the late 19th century.<ref>{{Cite book |title=Subjectivism, intelligibility and economic understanding: essays in honor of Ludwig M. Lachmann on his eightieth birthday |last1=Kirzner |first1=Israel M. |last2=Lachman |first2=Ludwig M. |publisher=McMillan |year=1986 |edition=Illustrated |isbn=978-0-333-41788-1}}</ref> Opportunity cost is the cost of any activity measured in terms of the value of the next best alternative foregone (that is not chosen). It is the sacrifice related to the second best choice available to someone, or group, who has picked among several [[mutually exclusive]] choices.<ref name="investopedia">{{cite web |work=Investopedia |title=Opportunity Cost |url=http://www.investopedia.com/terms/o/opportunitycost.asp |accessdate=2010-09-18| archiveurl= https://web.archive.org/web/20100914214221/http://www.investopedia.com/terms/o/opportunitycost.asp| archivedate= 14 September 2010 <!--DASHBot-->| deadurl= no}}</ref> This view is currently held by contemporary economists of all mainstream schools of thought.<br />
<br />
Opportunity cost is a key concept in [[economics]], and has been described as expressing "the basic relationship between [[scarcity]] and [[utility|choice]]".<ref>{{cite encyclopedia |url=http://www.dictionaryofeconomics.com/search_results?q=opportunity+cost&edition=current&button_search=GO |title=Opportunity cost |encyclopedia=The New Palgrave Dictionary of Economics Online |author=James M. Buchanan |authorlink=James M. Buchanan |year=2008 |edition=Second |accessdate=2010-09-18 |ref=harv }}</ref> The notion of opportunity cost plays a crucial part in ensuring that resources are used efficiently.<ref>{{cite news |url=http://www.economist.com/research/Economics/alphabetic.cfm?letter=O#opportunitycost |title=Opportunity Cost |work=Economics A-Z |publisher=The Economist |accessdate=2010-09-18 | archiveurl= https://web.archive.org/web/20101009122334/http://www.economist.com/research/Economics/alphabetic.cfm?letter=O| archivedate= 9 October 2010 <!--DASHBot-->| deadurl= no}}</ref><br />
<br />
===Capital and interest===<br />
{{See also|Capital and Interest|Marginalism|Neutrality of money|Time preference}}<br />
[[File:1Bawerk.gif|right|thumb|130px|[[Eugen von Böhm-Bawerk]]]]<br />
The Austrian theory of capital and interest was first developed by [[Eugen von Böhm-Bawerk]]. He stated that interest rates and profits are determined by two factors, namely, [[supply and demand]] in the market for final goods and time preference.<ref name="BohmBawerkEugen">Böhm-Bawerk, Eugen Ritter von; ''Kapital Und Kapitalizns. Zweite Abteilung: Positive Theorie des Kapitales'' (1889). Translated as ''Capital and Interest. II: Positive Theory of Capital'' with appendices rendered as ''Further Essays on Capital and Interest''.</ref><ref name="econlib_a">http://www.econlib.org/library/Enc/bios/BohmBawerk.html</ref><br />
<br />
Böhm-Bawerk's theory was a response to Marx's [[labor theory of value]] and capital. Böhm-Bawerk's theory attacked the viability of the labor theory of value in the light of the [[transformation problem]]. His conception of interest countered [[Exploitation theory|Marx's exploitation theory]]. Marx famously argued that capitalists exploit workers by paying them less than the fruits of their labor sell for. Bohm-Bawerk countered this claim by invoking the concept of [[time preference]] to demonstrate that everyone values present consumption more than future consumption, and therefore that a difference between the (smaller) salary laborers are paid in the present and the (greater) price for which the goods they produce are later sold need not be exploitative.<ref name="econlib_a" /><br />
<br />
Böhm-Bawerk's theory equates [[capital intensity]] with the degree of [[roundaboutness]] of production processes. Böhm-Bawerk also argued that the law of [[marginal utility]] necessarily implies the classical law of costs.<ref name="BohmBawerkEugen" /> Some Austrian economists therefore entirely reject the notion that interest rates are affected by [[liquidity preference]].{{citation needed|date=March 2013}}<br />
<br />
===Inflation===<br />
{{See also|Monetary Inflation}}<br />
Mises believed that money prices and wages will inevitably rise when the supply of money and bank credit is increased.<ref>{{Cite book |first=Ludwig |last=von Mises |chapter=Economic Freedom and Interventionism |editor1-first=Bettina B. |editor1-last=Greaves |title=Economics of Mobilization |publisher=The Commercial and Financial Chronicle |location=Sulphur Springs, West Virginia |pages= |year=1980 |isbn= |chapterurl=http://mises.org/efandi/ch20.asp |ref=harv |quote="Inflation, as this term was always used everywhere and especially in this country, means increasing the quantity of money and bank notes in circulation and the quantity of bank deposits subject to check. But people today use the term "inflation" to refer to the phenomenon that is an inevitable consequence of inflation, that is the tendency of all prices and wage rates to rise. The result of this deplorable confusion is that there is no term left to signify the cause of this rise in prices and wages. There is no longer any word available to signify the phenomenon that has been, up to now, called inflation. . . . As you cannot talk about something that has no name, you cannot fight it. Those who pretend to fight inflation are in fact only fighting what is the inevitable consequence of inflation, rising prices. Their ventures are doomed to failure because they do not attack the root of the evil. They try to keep prices low while firmly committed to a policy of increasing the quantity of money that must necessarily make them soar. As long as this terminological confusion is not entirely wiped out, there cannot be any question of stopping inflation."}}</ref> He therefore used the term "inflation" to mean an excessive increase of the money supply and not, as is the common usage, to refer to [[inflation|price inflation]]. In Mises' view, inflation is the result of policies of the government or central bank which result in an increase in the circulating money supply.<ref>Ludwig von Mises, [http://mises.org/books/Theory_Money_Credit/Contents.aspx The Theory of Money and Credit]", ISBN 978-0-913966-70-9</ref>{{primary source claim|date=June 2013}} Mises wrote: <blockquote>In theoretical investigation there is only one meaning that can rationally be attached to the expression Inflation: an increase in the quantity of money (in the broader sense of the term, so as to include fiduciary media as well), that is not offset by a corresponding increase in the need for money (again in the broader sense of the term), so that a fall in the objective exchange-value of money must occur.<ref name="TheTheory">The Theory of Money and Credit, Mises (1912, [1981], p. 272)</ref></blockquote><br />
<br />
Economist [[Richard Timberlake]] criticized von Mises' view that ''inflation'' must refer to an increase in the money supply. Timberlake noted that economists since the time of [[John Stuart Mill]] have recognized the distinction between increases in the money stock and increases in the general level of money prices. Timberlake stated that Mises' view has repeatedly been proven false and that statistical measurement of the aggregate price level is necessary in order test the empirical validity of Mises' theory.<ref name=Timberlake>{{cite journal|last=Timberlake|first=Richard H.|title=Austrian Inflation, Austrian Money, and Federal Reserve Policy|journal=The Freeman|date=September 1, 2000|url=http://www.fee.org/the_freeman/detail/austrian-inflation-austrian-money-and-federal-reserve-policy#axzz2JZKoJIRE|accessdate=31 January 2013}}</ref><br />
<br />
Economist Paul Krugman has criticized Austrians' views on inflation and the failure to test their views against empirical evidence. In late 2011 he pointed out that the monetary base had tripled in the previous three years, but the average annual inflation rate was only 1.5 percent. There was no "devastating inflation" as predicted by Austrians.<ref name=Madness>{{cite news|last=Krugman|first=Paul|title=G.O.P. Monetary Madness|url=http://www.nytimes.com/2011/12/16/opinion/gop-monetary-madness.html|accessdate=11 June 2013|newspaper=NY Times|date=Dec 15, 2011}}</ref> In late 2012 he chided those who failed to "let the evidence speak" when it disproved the Austrian theory of inflation. Krugman wrote: "If you believe that... expanding credit will simply result in too much money chasing too few goods, and hence a lot of inflation... [Then] the failure of high inflation to materialize amounts to a decisive rejection of [the Austrian] model."<ref>Paul Krugman, [http://krugman.blogs.nytimes.com/2012/11/29/varieties-of-error/ Varieties of Error], 2012.</ref><br />
<br />
===Economic calculation problem===<br />
{{Main|Economic calculation problem}}<br />
{{refimprove section|date=May 2013}}<br />
[[File:Friedrich Hayek portrait.jpg|right|thumb|130px|[[Friedrich Hayek]]]]<br />
The economic calculation problem refers to a criticism of [[socialist economics|socialism]] which was first stated by [[Max Weber]] in 1920. Mises subsequently discussed Weber's idea with his student Friedrich Hayek, who developed it in various works including [[The Road to Serfdom]].<ref name=autogenerated5>{{cite book |title=Economic calculation in the Socialist Commonwealth |accessdate=2008-09-08 |last=Von Mises |first=Ludwig |authorlink=Ludwig von Mises |year=1990|format=PDF |publisher=[[Ludwig von Mises Institute]] |url=http://mises.org/pdf/econcalc.pdf |isbn=0-945466-07-2 | archiveurl= https://web.archive.org/web/20080923191714/http://mises.org/pdf/econcalc.pdf| archivedate= 23 September 2008 <!--DASHBot-->| deadurl= no}}</ref><ref>F. A. Hayek, (1935), "The Nature and History of the Problem" and "The Present State of the Debate," om in F. A. Hayek, ed. ''Collectivist Economic Planning'', pp. 1–40, 201–243.</ref> The problem concerns the means by which resources are allocated and distributed in an economy.<br />
<br />
Austrian theory emphasizes the [[spontaneous order|organizing power]] of markets. Hayek stated that market prices reflect information, the totality of which is not known to any single individual, which determines the allocation of resources in an economy. Because socialist systems lack the individual incentives and [[price discovery]] processes by which individuals act on their personal information, Hayek argued that the decisions of socialist economic planners lack all of the knowledge to make optimal decisions. Those who agree with this criticism view it is a refutation of socialism and that it shows that it is not a viable or sustainable form of economic organization. The debate rose to prominence in the 1920s and 1930s, and that specific period of the debate has come to be known by historians of economic thought as ''The Socialist Calculation Debate.''<ref name="School">[http://cepa.newschool.edu/het/essays/paretian/social.htm The socialist calculation debate]{{Dead link|date=August 2011}}</ref><br />
<br />
Mises argued in a 1920 article "[[Economic Calculation in the Socialist Commonwealth]]" that the pricing systems in socialist economies were necessarily deficient because if government owned the [[means of production]], then no prices could be obtained for [[capital goods]] as they were merely internal transfers of goods in a socialist system and not "objects of exchange," unlike final goods. Therefore, they were unpriced and hence the system would be necessarily inefficient since the central planners would not know how to allocate the available resources efficiently.<ref name="School" /> This led him to write "…that rational economic activity is impossible in a socialist commonwealth."<ref name="Mises">{{Cite web|url=http://mises.org/humanaction/chap2sec4.asp|author=Ludwig von Mises|title=The Principle of Methodological Individualism|work=Human Action|publisher=Ludwig von Mises Institute|accessdate=2009-04-24| archiveurl= https://web.archive.org/web/20090422004804/http://mises.org/humanaction/chap2sec4.asp| archivedate= 22 April 2009 <!--DASHBot-->| deadurl= no}}</ref> Economist [[Bryan Caplan]] has written that Mises's has been criticized as overstating the strength of his case, in describing socialism as impossible, rather than that it may need to establish non-market institutions to deal with a source of inefficiency.<ref name="Caplan" /><ref name="Caplan_soc">{{cite journal |last1=Caplan |first1=Bryan |title=Is socialism really "impossible"? |journal=Critical Review |volume=16 |pages=33–52 |year=2004 |doi=10.1080/08913810408443598 |ref=harv}}</ref><br />
<br />
===Business cycles===<br />
{{Main|Austrian business cycle theory}}<br />
{{refimprove section|date=May 2013}}<br />
The Austrian theory of the [[business cycles|business cycle]] ("ABCT") focuses on banks' issuance of credit as the cause of economic fluctuations. Although later elaborated by Hayek and others, the theory was first set forth by von Mises, who believed that banks extend credit at artificially low interest rates, causing businesses to invest in relatively [[Roundaboutness|roundabout]] production processes. Mises stated that this led to a misallocation of resources which he called ''[[malinvestment]]''.<br />
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According to the theory, malinvestment is induced by banks' excessive and unsustainable expansion of credit to businesses.<ref name="econlib.org">[http://www.econlib.org/library/Mises/msT.html Theory of Money and Credit], Ludwig von Mises, Part III, Part IV</ref> Businesses borrow at unsustainably low interest rates and overinvest in capital-intensive production processes, which in turn leads to a diversion of investment from consumer goods industries to capital goods industries. Austrians contend that this shift is unsustainable and must eventually be reversed, and that the re-adjustment process will be more violent and disruptive the longer the putative malinvestment in capital goods industries continues.<br />
<br />
According to the Austrian view, the proportion of income allocated to [[Consumption (economics)|consumption]] rather than saving is determined by the interest rate and people's [[time preference]], which is the degree to which they prefer present to future satisfactions. According to this view, the pure interest rate is determined by the time preferences of the individuals in society. If the market rate of interest offered by banks is set lower than this, business borrowing will be excessive and will be allocated to malinvestment.<ref>[http://www.econlib.org/library/Mises/msT.html Theory of Money and Credit], Ludwig von Mises, Part II</ref><br />
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Newly extended credit thus malinvested will circulate from the business borrowers to the factors of production: landowners, capital goods producers, and capital goods workers. Austrians state that, because individuals' time preferences have not changed, the market will tend to reestablish the old proportions between current and future production. Depositors will tend to remove cash from the banking system and spend it (not save it), banks will then ask their borrowers for repayment, and the excessive capital goods will be liquidated at lower prices to retire the now-unprofitable loans.<ref name="econlib.org"/>{{citation needed|date=June 2013}}<br />
<br />
====Role of government disputed====<br />
According to Mises, [[central bank]]s enable the commercial banks to fund loans at artificially low interest rates, thereby inducing an unsustainable expansion of bank credit and impeding any subsequent contraction.<ref name="econlib.org"/><ref name="The Mystery of Banking">[http://www.mises.org/Books/mysteryofbanking.pdf The Mystery of Banking], Murray Rothbard, 1983</ref>{{citation needed|date=June 2013}} <ref name="econlib.org">[http://www.econlib.org/library/Mises/msT.html Theory of Money and Credit], Ludwig von Mises, Part III, Part IV</ref><ref name="ReferenceA">''[[America's Great Depression]]'', [[Murray Rothbard]]</ref> Friedrich Hayek disagreed. Hayek did not favor [[laissez-faire]] in banking and said that a freely competitive banking industry tends to be endogenously destabilizing and pro-cyclical, mimicking the effects which Rothbard attributed to central bank policy. Hayek stated that the need for [[central banking]] control was inescapable.<ref>{{cite journal|last=White|first=Lawrence H.|title=Why Didn't Hayek Favor Laissez Faire in Banking?|journal=History of Political Economy|year=1999|volume=31|issue=4|url=http://cameroneconomics.com/white-hayek-hope.pdf|accessdate=11 April 2013|doi=10.1215/00182702-31-4-753|pages=753}}</ref><br />
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====Criticism====<br />
Most research regarding the theory finds that it is inconsistent with empirical evidence. Economists such as [[Gordon Tullock]],<ref name="Tullock1988">{{cite journal |author=Gordon Tullock |title=Why the Austrians are wrong about depressions |journal=The Review of Austrian Economics |volume=2 |issue=1 |year=1988 |pages=73–78 |format=PDF |url=http://mises.org/journals/rae/pdf/RAE2_1_4.pdf |accessdate=2009-06-24 |doi=10.1007/BF01539299 |ref=harv}}</ref> Bryan Caplan,<ref name=autogenerated3>{{cite web |url=http://econlog.econlib.org/archives/2008/01/whats_wrong_wit_6.html |title=What's Wrong With Austrian Business Cycle Theory |last=Caplan |first=Bryan |date=2008-01-02 |publisher=Library of Economics and Liberty |accessdate=2008-07-28}}</ref> [[Milton Friedman]],<ref name="Friedman1969">{{cite book |last=Friedman |first=Milton |title=The Optimal Quantity of Money and Other Essays |publisher=Aldine |location=Chicago |pages=261–284 |chapter=The Monetary Studies of the National Bureau, 44th Annual Report}}</ref><ref name="Friedman93">{{cite journal |last=Friedman |first=Milton |title=The 'Plucking Model' of Business Fluctuations Revisited |journal=Economic Inquiry |pages=171–177 |ref=harv}}</ref> and [[Paul Krugman]]<ref name="Krugman">{{cite web |url=http://www.slate.com/id/9593 |title=The Hangover Theory |last=Krugman |first=Paul |authorlink=Paul Krugman |date=1998-12-04 |publisher=Slate |accessdate=2008-06-20| archiveurl = http://www.webcitation.org/5u40jRL5e | archivedate = 2010-11-07| deadurl=no}}</ref> have said that they regard the theory as incorrect. Austrian economist Ludwig Lachmann noted that the Austrian theory was rejected during the 1930s:<br />
<blockquote>The promise of an Austrian theory of the trade cycle, which might also serve to explain the severity of the Great Depression, a feature of the early 1930s that provided the background for Hayek’s successful appearance on the London scene, soon proved deceptive. Three giants – Keynes, Knight and Sraffa – turned against the hapless Austrians who, in the middle of that black decade, thus had to do battle on three fronts. Naturally it proved a task beyond their strength.<ref>Ludwig M. Lachmann, in The Market as an Economic Process (Oxford, 1986), p. ix</ref></blockquote><br />
In 1969, Milton Friedman argued that the theory is not consistent with empirical evidence<ref>Friedman, Milton. "The Monetary Studies of the National Bureau, 44th Annual Report". The Optimal Quantity of Money and Other Essays. Chicago: Aldine. pp. 261–284.</ref> and using newer data in 1993 reached the same conclusion.<ref>Friedman, Milton. "The 'Plucking Model' of Business Fluctuations Revisited". Economic Inquiry: 171–177.</ref> In 1986, Austrian economist Roger Garrison reviewed Hayek's development of the Austrian Business Cycle Theory and discussed the factors that have sustained interest in the theory despite its longtime rejection by mainstream economics.<ref>{{cite journal|last=Garrison|first=Roger|title=Hayekian Trade Cycle Theory: A Reappraisal|journal=Cato Journal|year=2001|volume=6|issue=2|url=http://www.auburn.edu/~garriro/c4refah.htm|accessdate=19 May 2013}}</ref><br />
<br />
==History==<br />
[[File:Jean-baptiste Say.jpg|right|thumb|130px|[[Jean-Baptiste Say]]]]<br />
<br />
===Origin of the name Austrian school===<br />
The School owes its name to members of the German [[Historical school of economics]], who argued against the Austrians during the ''[[Methodenstreit]]'' ("methodology struggle"), in which the Austrians defended the role of theory in economics as distinct from the study or compilation of historical circumstance. In 1883, Menger published ''Investigations into the Method of the Social Sciences with Special Reference to Economics'', which attacked the methods of the Historical school. [[Gustav von Schmoller]], a leader of the Historical school, responded with an unfavorable review, coining the term "Austrian School" in an attempt to characterize the school as outcast and provincial.<ref>"Menger’s approach – haughtily dismissed by the leader of the German Historical School, Gustav Schmoller, as merely “Austrian,” the origin of that label – led to a renaissance of theoretical economics in Europe and, later, in the United States." [[Peter G. Klein]], 2007; in the Foreword to ''Principles of Economics'', Carl Menger; trns. James Dingwall and Bert F. Hoselitz, 1976; Ludwig von Mises Institute, Alabama; 2007; ISBN 978-1-933550-12-1</ref> The label endured and was adopted by the adherents themselves.<ref>{{cite book|last=von Mises|first=Ludwig|title=The Historical Setting of the Austrian School of Economics|year=1984 ed.|publisher=Ludwig von Mises Institute.|url=http://mises.org/etexts/histsetting.pdf}}</ref><br />
<br />
===First Wave===<br />
[[File:CarlMenger.png|right|thumb|130px|[[Carl Menger]]]]<br />
The school originated in [[Vienna]], in the [[Austrian Empire]]. [[Carl Menger]]'s 1871 book, ''[[Principles of Economics]]'', is generally considered the founding of the Austrian School. The book was one of the first modern treatises to advance the theory of [[marginal utility]]. The Austrian School was one of three founding currents of the marginalist revolution of the 1870s, with its major contribution being the introduction of the subjectivist approach in economics.<ref name=keizer>{{cite book |last=Keizer |first=Willem |title=Austrian Economics in Debate |publisher=Routledge |location=New York |year=1997 |isbn=978-0-415-14054-6 }}</ref>{{Page needed|date=August 2011}} While marginalism was generally influential, there was also a more specific school that began to coalesce around Menger's work, which came to be known as the “Psychological School,” “Vienna School,” or “Austrian School.”<ref>Israel M. Kirzner (1987). "Austrian School of Economics," ''[[The New Palgrave: A Dictionary of Economics]]'', v. 1, pp. 145–151.</ref><br />
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Menger's contributions to economic theory were closely followed by those of Böhm-Bawerk and Friedrich von Wieser. These three economists became what is known as the "first wave" of the Austrian School. Böhm-Bawerk wrote extensive critiques of [[Karl Marx]] in the 1880s and 1890s, as was part of the Austrians' participation in the late 19th Century ''[[Methodenstreit]]'', during which they attacked the [[Georg Wilhelm Friedrich Hegel|Hegelian]] doctrines of the [[Historical school of economics|Historical School]].<br />
<br />
===Early Twentieth Century in Vienna===<br />
Several important Austrian economists trained at the University of Vienna in the 1920s and later participated in the private seminar of von Mises. These included Gottfried Haberler,<ref>http://mises.org/page/1452/Biography-of-Gottfried-Haberler-19011995</ref> Friedrich Hayek, Fritz Machlup,<ref>{{cite web|title=Biography of Fritz Machlup|url=http://mises.org/page/1457/Biography-of-Fritz-Machlup-19021983|accessdate=16 June 2013}}</ref> Karl Menger (son of Carl Menger),<ref>http://www.iit.edu/csl/am/about/menger/about.shtml</ref> Oskar Morgenstern,<ref>http://library.duke.edu/rubenstein/findingaids/morgenst/</ref> Paul Rosenstein-Rodan<ref>http://archives.lse.ac.uk/Record.aspx?src=CalmView.Catalog&id=COLL+MISC+0324 Archive at London School of Economics</ref> <br />
Abraham Wald,<ref>{{cite journal|title=Abraham Wald, 1902-1950|author=Oskar Morgenstern|journal=Econometrica<br />
|volume=19|number=4|date=Oct., 1951|pages=361-367|publisher=The Econometric Society|jstor=1907462}}</ref> among others.<br />
<br />
===Later Twentieth century===<br />
[[File:Israel Kirzner.jpg|right|thumb|130px|[[Israel Kirzner]]]]<br />
<br />
By the mid-1930s, most economists had embraced what they considered the important contributions of the early Austrians.<ref name="Boettke and Leeson"/> After [[World War II]], Austrian economics was disregarded or derided by most economists because it rejected mathematical and statistical methods in the study of economics.<ref>"[http://www.springerlink.com/content/kq577622488v4447/fulltext.pdf Austrian economics and the mainstream: View from the boundary]" by Roger E. Backhouse, $34 to view {{Dead link|date=March 2011}}</ref> Fritz Machlup quoted Hayek's statement, "the greatest success of a school is that it stops existing because its fundamental teachings have become parts of the general body of commonly accepted thought." <ref>http://mises.org/daily/1700/Ludwig-von-Mises-A-Scholar-Who-Would-Not-Compromise Homage to Mises by Fritz Machlup 1981</ref> Mises' student, [[Israel Kirzner]] recalled that in 1954, when Kirzner was pursuing his PhD, there was no separate Austrian School as such. When Kirzner was deciding which graduate school to attend, Mises had advised him to accept an offer of admission at Johns Hopkins because it was a prestigious university and Fritz Machlup taught there.<ref>{{cite web|last=Kirzner|first=Israel|title=Interview of Israel Kirzner|url=http://www.mises.org/journals/aen/aen17_1_1.asp|publisher=Mises Institute|accessdate=17 June 2013}}</ref><br />
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After 1940, Austrian economics can be divided into two schools of economic thought, and the school "split" to some degree in the late 20th century. One camp of Austrians, exemplified by Mises, regards neoclassical methodology to be irredeemably flawed; the other camp, exemplified by Friedrich Hayek, accepts a large part of neoclassical methodology and is more accepting of government intervention in the economy.<ref name="Caplan"/><ref>http://mises.org/journals/qjae/pdf/qjae7_1_3.pdf</ref><br />
<br />
[[Henry Hazlitt]] wrote economics columns and editorials for a number of publications and wrote many books on the topic of Austrian economics from the 1930s to the 1980s. Hazlitt's thinking was influenced by Mises.<ref>{{cite web|url=http://www.thefreemanonline.org/featured/remembering-henry-hazlitt/ |title=Remembering Henry Hazlitt |publisher=[[The Freeman]] |date= |accessdate=2013-03-11}}</ref> His book ''[[Economics in One Lesson]]'' (1946) sold over a million copies, and he is also known for ''[[The Failure of the New Economics|The Failure of the "New Economics"]]'' (1959), a line-by-line critique of [[John Maynard Keynes]]'s ''[[The General Theory of Employment, Interest and Money|General Theory]]''.<ref>{{cite web |url=http://mises.org/about/3233 |title=Biography of Henry Hazlitt |publisher=The Ludwig von Mises Institute |date= |accessdate=2013-03-11}}</ref><br />
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The reputation of the Austrian School rose in the late-20th century due in part to the work of Israel Kirzner and [[Ludwig Lachmann]] at New York University, and to renewed public awareness of the work of Hayek after he won the 1974 Nobel Memorial Prize in Economic Sciences.<ref name="Meijer 1995">{{cite book |editor=Meijer, Gerrit |title=New Perspectives on Austrian Economics |publisher=Routledge |location=New York |year=1995 |isbn=978-0-415-12283-2 |oclc= 70769328 }}</ref> Hayek's work was influential in the revival of ''laissez-faire'' thought in the 20th century.<ref name=raico>{{cite web |url= http://mises.org/etexts/austrianliberalism.asp |title=Austrian Economics and Classical Liberalism |first=Ralph |last=Raico |work=mises.org |publisher=Mises Institute |year=2011 |quote=despite the particular policy views of its founders ..., Austrianism was perceived as the economics of the free market |accessdate=27 July 2011}}</ref><ref>{{cite book |last=Kasper |first=Sherryl Davis |title=The Revival of Laissez-faire in American Macroeconomic Theory |publisher=Edward Elgar Publishing |year=2002 |isbn=978-1-84064-606-1 |page=66}}</ref><br />
<br />
===Split among contemporary Austrians===<br />
According to economist Bryan Caplan, by the late twentieth century, a split had developed among those who self-identify with the Austrian School. One group, building on the work of Hayek, follows the broad framework of mainstream neoclassical economics, including its use of mathematical models and general equilibrium, and merely brings a critical perspective to mainstream methodology influenced by the Austrian notions such as the [[economic calculation problem]] and the independent role of logical reasoning in developing economic theory.<ref name="Austrian Search"/><br />
<br />
[[File:MurrayBW.jpg|right|thumb|130px|[[Murray Rothbard]]]]<br />
A second group, following Mises and Rothbard, rejects the neoclassical theories of consumer and welfare economics, dismisses empirical methods and mathematical and statistical models as inapplicable to economic science, and asserts that economic theory went entirely astray in the twentieth century; they offer the Misesian view as a radical alternative paradigm to mainstream theory. Caplan wrote that if "Mises and Rothbard are right, then [mainstream] economics is wrong; but if Hayek is right, then mainstream economics merely needs to adjust its focus."<ref name="Austrian Search"/><br />
<br />
Economist [[Leland Yeager]] discussed the late twentieth century rift and referred to a discussion written by Murray Rothbard, Hans-Hermann Hoppe, Joseph Salerno, and others in which they attack and disparage Hayek. "To try to drive a wedge between Mises and Hayek on [the role of knowledge in economic calculation], especially to the disparagement of Hayek, is unfair to these two great men, unfaithful to the history of economic thought" and went on to call the rift subversive to economic analysis and the historical understanding of the fall of Eastern European communism.<ref>{{cite book|last=Yaeger|first=Leland|title=Is the Market a Test of Truth and Beauty?: Essays in Political Economy|page=93ff|year=2011|publisher=Mises Institute}}</ref><br />
<br />
In a 1999 book published by the Mises Institute,<ref>{{cite book|last=Hoppe|first=Herr Hans-Hermann|title=15 Great Austrian Economists -- Murray Rothbard|year=1999|publisher=von Mises Institute|location=Alabama|pages=223 ff.|url=http://mises.org/books/15great.pdf}}</ref> Hans-Hermann Hoppe asserted that Murray Rothbard was the leader of the "mainstream within Austrian Economics" and contrasted Rothbard with Nobel Laureate Friedrich Hayek, who he identified as a [[British empiricism|British empiricist]] and an opponent of the thought of Mises and Rothbard. Hoppe acknowledged that Hayek was the most prominent Austrian economist within academia, but stated that Hayek was an opponent of the Austrian tradition which led from Carl Menger and Böhm-Bawerk through Mises to Rothbard.<br />
<br />
Economists of the Hayekian view are affiliated with the [[Cato Institute]], George Mason University, and New York University, among other institutions. They include [[Peter Boettke]], [[Roger Garrison]], [[Steven Horwitz]], [[Peter Leeson]] and [[George Reisman]]. Economists of the Mises-Rothbard view include [[Walter Block]], [[Hans-Hermann Hoppe]], [[Jesús Huerta de Soto]] and [[Robert P. Murphy]], each of whom is associated with the [[Ludwig von Mises Institute]]<ref name="faculty">{{cite web |url=http://mises.org/Faculty |title=Senior Fellows, Faculty Members, and Staff |publisher=Mises.org |accessdate=July 21, 2013}}</ref> and some of them also with academic institutions.<ref name="faculty"/> According to Murphy, a "truce between (for lack of better terms) the GMU Austro-libertarians and the Auburn Austro-libertarians" was signed around 2011.<ref>[http://consultingbyrpm.com/blog/2011/12/in-defense-of-the-mises-institute.html Robert Murphy blog, December 31, 2011.]</ref><ref name="Yaeger Truth and Beauty">{{cite book|last=Yeager|first=Leland|title=Is the Market a Test of Truth and Beauty?|year=2011|publisher=Mises Institute|page=103|url=http://books.google.com/books?id=-z7Q4rsgdhAC&source=gbs_navlinks_s}}</ref><br />
<br />
==Influence==<br />
Many theories developed by "first wave" Austrian economists have been absorbed into [[mainstream economics]]. These include Carl Menger's theories on marginal utility, Friedrich von Wieser's theories on [[opportunity cost]], and Eugen von Böhm-Bawerk's theories on time preference, as well as Menger and Böhm-Bawerk's criticisms of [[Marxian economics]].{{citation needed|date=June 2013}}<br />
<br />
Former [[U.S. Federal Reserve]] Chairman [[Alan Greenspan]] said that the founders of the Austrian School "reached far into the future from when most of them practiced and have had a profound and, in my judgment, probably an irreversible effect on how most mainstream economists think in this country."<ref>Greenspan, Alan. "Hearings before the U.S. House of Representatives' Committee on Financial Services." U.S. House of Representatives' Committee on Financial Services. Washington D.C.. 25 July 2000.</ref> In 1987, Nobel Laureate [[James M. Buchanan]] told an interviewer, "I have no objections to being called an Austrian. Hayek and Mises might consider me an Austrian but, surely some of the others would not."<ref>[http://mises.org/journals/aen/aen9_1_1.asp An Interview with Laureate James Buchanan] Austrian Economics Newsletter: Volume 9, Number 1; Fall 1987</ref><br />
<br />
Chinese economist [[Zhang Weiying]], supports some Austrian theories such as the Austrian theory of the business cycle.<ref>Weiyin, Zhang, "Completely bury Keynesianism", http://finance.sina.com.cn/20090217/10345864499_3.shtml (February 17, 2009)</ref> Currently, universities with a significant Austrian presence are [[George Mason University]], [[New York University]], [[Loyola University New Orleans]], and [[Auburn University]] in the United States and [[Universidad Francisco Marroquín]] in Guatemala. Austrian economic ideas are also promoted by privately funded organizations such as the [[Mises Institute]],<ref>{{cite web |url=http://mises.org/page/1448/About-The-Mises-Institute |title=About the Mises Institute |publisher=Mises.org |accessdate=July 21, 2013}}</ref> and the [[Cato Institute]].<br />
<br />
==Criticisms==<br />
<br />
===General criticisms===<br />
Mainstream economists have argued that Austrians are often averse to the use of mathematics and statistics in economics.<ref name="white1"/><br />
<br />
Economist Bryan Caplan argues that many Austrians have not understood valid contributions of modern mainstream economics, causing them to overstate their differences with it. For example, Murray Rothbard stated that he objected to the use of [[cardinal utility]] in microeconomic theory. Caplan says that Rothbard did not understand the position he was attacking, because microeconomic theorists go to great pains to show that their results are derived for any [[monotonic]] transformation of an [[ordinal utility]] function, and do not entail cardinal utility.<ref name="Austrian Search"/><ref name="Caplan_ord">{{Cite web|url=http://www.gmu.edu/departments/economics/bcaplan/whyaust.htm|title=Why I Am Not an Austrian Economist |last=Caplan |first=Bryan |publisher=[[George Mason University]] |accessdate=2008-07-04 | quote=According to Rothbard, the mainstream approach credulously accepted the use of cardinal utility, when only the use of ordinal utility is defensible. As Rothbard insists, "Value scales of each individual are purely ordinal, and there is no way whatever of measuring the distance between the rankings; indeed, any concept of such distance is a fallacious one." ...As plausible as Rothbard sounds on this issue, he simply does not understand the position he is attacking. The utility function approach is based as squarely on ordinal utility as Rothbard's is. The modern neoclassical theorists – such as Arrow and Debreau – who developed the utility function approach went out of their way to avoid the use of cardinal utility. ...To sum up, Rothbard falsely accused neoclassical utility theory of assuming cardinality. It does not.}}</ref> The result is that conclusions about utility preferences hold no matter what values are assigned to them.{{Citation needed|date=June 2013}}<br />
<br />
Economist [[Paul Krugman]] has stated that because Austrians do not use "explicit models" they are unaware of holes in their own thinking.<ref name="Krugman 2">{{Cite web|url=http://krugman.blogs.nytimes.com/2010/04/07/martin-and-the-austrians |title=The Conscience of a Liberal: Martin And The Austrians |last=Krugman |first=Paul |date=4-7-2010 |publisher=''[[The New York Times]]'' |accessdate=2011-09-21}}</ref> In February 2013, Krugman further criticized Austrian School economists on their failure to revise their theory of inflation in light of their incorrect prophecies of government-induced inflation following the 2008 financial crisis.<ref name=Whines>{{cite news|last=Krugman|first=Paul|title=Fine Austrian Whines|url=http://krugman.blogs.nytimes.com/2013/02/20/fine-austrian-whines/|accessdate=11 June 2013|newspaper=New York Times|date=February 20, 2013}}</ref><br />
<br />
Economist Benjamin Klein has criticized the economic methodological work of Austrian economist [[Israel M. Kirzner]]. While praising Kirzner for highlighting shortcomings in traditional methodology, Klein argued that Kirzner did not provide a viable alternative for economic methodology.<ref>Klein, Benjamin. "Book review: ''Competition and Entrepreneurship''" (by [[Israel M. Kirzner]], University of Chicago Press, 1973) ''[[Journal of Political Economy]]''. Vol. 83: No. 6, 1305–1306, December 1975.<!--JSTOR has the first page of Klein's review at http://www.jstor.org/pss/1830872. Can this be used as a reference instead please? --></ref> Economist Tyler Cowen has written that Kirzner's theory of entrepreneurship can ultimately be reduced to a neoclassical search model and is thus not in the radical subjectivist tradition of Austrian praxeology. Cowen states that Kirzner's entrepreneurs can be modeled in mainstream terms of search.<ref>{{cite journal|last=Cowen|first=Tyler|title=Entrepreneurship, Austrian Economics, and the Quarrel Between Philosophy and Poetry|journal=Review of Austrian Economics|date=May 2003|volume=16|issue=1|doi=10.1023/A:1022958406273|pages=5}}</ref><br />
<br />
Economist [[Jeffrey Sachs]] argues that among developed countries, those with high rates of taxation and high social welfare spending perform better on most measures of economic performance compared to countries with low rates of taxation and low social outlays. He concludes that Friedrich Hayek was wrong to argue that high levels of government spending harms an economy, and "a generous social-welfare state is not a road to serfdom but rather to fairness, economic equality and international competitiveness."<ref>{{Cite journal|title=The Social Welfare State, Beyond Ideology |last=Sachs|first=Jeffrey |date = October 2006|journal=Scientific American |url=http://www.sciam.com/article.cfm?id=the-social-welfare-state |accessdate=2008-06-20|ref=harv }}</ref> Austrian economist [[Sudha Shenoy]] responded by arguing that countries with large public sectors have grown more slowly.<ref>Sudha R. Shenoy, ''Are High Taxes the Basis of Freedom and Prosperity?'', http://www.thefreemanonline.org/featured/are-high-taxes-the-basis-of-freedom-and-prosperity/</ref><br />
<br />
===Methodology===<br />
Critics generally argue that Austrian economics lacks scientific rigor and rejects scientific methods and the use of empirical data in modelling economic behavior.<ref name="Caplan"/><ref name="white1">{{Cite journal |title=The research program of Austrian economics |publisher=Emerald Group Publishing Limited |first=Lawrence H. |last=White |journal=Advances in Austrian Economics |year=2008 |page=20 |ref=harv }}</ref><ref name="Newton1999">"Rules for the study of [[natural philosophy]]", {{harvnb |Newton |1999 |pp=794–6 }}, from Book '''3''', ''The System of the World''.</ref> Some economists describe Austrian methodology as being ''[[A priori and a posteriori|a priori]]'' or [[empirical|non-empirical]].<ref name="Caplan" /><ref name="tremble">{{cite journal |first=Paul A. |last=Samuelson |title=Theory and Realism: A Reply |publisher=[[American Economic Association]] |journal=The [[American Economic Review]] |date=September 1964 |pages=736–739 |quote=Well, in connection with the exaggerated claims that used to be made in economics for the power of deduction and a priori reasoning ..... – I tremble for the reputation of my subject. Fortunately, we have left that behind us. |ref=harv}}</ref><ref name="white1"><br />
{{Cite journal |title=The research program of Austrian economics |publisher=Emerald Group Publishing Limited |first=Lawrence H.<br />
|last=White |journal=Advances in Austrian Economics |year=2008 |page=20 |ref=harv |postscript= }}</ref><ref name="Mayer1998">{{cite journal<br />
|first=Thomas |last=Mayer |title=Boettke's Austrian critique of mainstream economics: An empiricist's response |publisher=Routledge<br />
|journal=Critical Review |date=Winter 1998 |pages=151–171 |ref=harv<br />
|doi=10.1080/08913819808443491<br />
|volume=12}}</ref><br />
<br />
Economist [[Mark Blaug]] has criticized over-reliance on methodological individualism, arguing it would rule out all macroeconomic propositions that cannot be reduced to microeconomic ones, and hence reject almost the whole of received macroeconomics.<ref name=Blaug>{{Cite book|last=Blaug|first=Mark|title=The Methodology of Economics: Or, How Economists Explain|year=1992|publisher=Cambridge University Press|isbn=0-521-43678-8|pages=45–46}}</ref><br />
<br />
Economist [[Thomas Mayer]] has stated that Austrians advocate a rejection of the [[scientific method]] which involves the development of empirically falsifiable [[Scientific theory#Pedagogical definition|theories]].<ref name="Newton1999" /><ref name="Mayer1998" /> Furthermore, many supporters of using models of market behavior to analyze and test economic theory argue that economists have developed numerous experiments that elicit useful information about individual preferences.<ref>{{cite web |url=http://www.dictionaryofeconomics.com/article?id=pde2008_M000391 |title=Models |first=Mary S. |last=Morgan |work=The New Palgrave Dictionary of Economics |year=2008 |accessdate=22 November 2011}}</ref><ref>{{cite web |url= http://www.dictionaryofeconomics.com/article?id=pde2008_C000569 |title=Causality in economics and econometrics |first=Kevin D. |last=Hoover |work=The New Palgrave Dictionary of Economics |year=2008 |accessdate=22 November 2011}}</ref><br />
<br />
Economist Leland Yeager rejects many favorite views of the Misesian group of Austrians, in particular, "These include the specifics of their business-cycle theory, ultra-subjectivism in value theory and particularly in interest-rate theory, their insistence on unidirectional causality rather than general interdependence, and their fondness for methodological brooding, pointless profundities, and verbal gymnastics. Provoked by mainstream abuses of mathematics, including the frequent merely decorative and pretentious use of symbols, some Austrians have wanted to ban mathematics from economics. But is it not arrogant for someone who does not see how to use certain techniques constructively to suppose that no one else will ever see how either? These Austrians should remember how, in other contexts, they emphasize the openness of the future and scope for novelty."<ref name="Leland Yaeger Truth">{{cite book|last=Yeager|first=Leland|title=Is the Market a Test of Truth and Beauty?: Essays in Political Economy|year=2011|page=103|url=http://mises.org/document/6508/Is-the-Market-a-Test-of-Truth-and-Beauty-Essays-in-Political-Economy}}</ref><br />
<br />
===Business cycle theory===<br />
{{main|Austrian business cycle theory}}<br />
According to [[John Quiggin]], most economists believe that the Austrian business cycle theory is incorrect because of its incompleteness and other problems.<ref name="Quiggin">{{cite web |url= http://johnquiggin.com/index.php/archives/2009/05/03/austrian-business-cycle-theory/ |title=John Quiggin " Austrian Business Cycle Theory |work=johnquiggin.com |accessdate=19 July 2010 }}</ref>{{elucidate|date=January 2013}} Economists such as [[Gottfried von Haberler]], [[Milton Friedman]],<ref name="Friedman1969">{{cite book |last=Friedman |first=Milton |title=The Optimal Quantity of Money and Other Essays |publisher=Aldine |location=Chicago |pages=261–284 |chapter=The Monetary Studies of the National Bureau, 44th Annual Report}}</ref><ref name="Friedman93">{{cite journal |last=Friedman |first=Milton |title=The 'Plucking Model' of Business Fluctuations Revisited |journal=Economic Inquiry |pages=171–177}}</ref> [[Gordon Tullock]],<ref name="Tullock1988">{{cite journal |author=Gordon Tullock |title=Why the Austrians are wrong about depressions |journal=The Review of Austrian Economics |volume=2 |issue=1 |year=1988 |pages=73–78 |format=PDF |url=http://mises.org/journals/rae/pdf/RAE2_1_4.pdf |accessdate=2009-06-24 |doi=10.1007/BF01539299}}</ref> [[Bryan Caplan]],<ref name="Caplan">{{cite web |url=http://econlog.econlib.org/archives/2008/01/whats_wrong_wit_6.html |title=What's Wrong With Austrian Business Cycle Theory |last=Caplan |first=Bryan |date=2008-01-02 |publisher=Library of Economics and Liberty |accessdate=2008-07-28}}</ref> and [[Paul Krugman]]<ref name="Krugman">{{cite web |url=http://www.slate.com/id/9593 |title=The Hangover Theory |last=Krugman |first=Paul |date=1998-12-04 |publisher=Slate |accessdate=2008-06-20| archiveurl= https://web.archive.org/web/20080706173751/http://www.slate.com/id/9593| archivedate= 6 July 2008 <!--DASHBot-->| deadurl= no}}</ref> have argued that the theory is incorrect.<br />
<br />
====Theoretical objections====<br />
Some economists argue that Austrian business cycle theory requires bankers and investors to exhibit a kind of irrationality, because the Austrian theory posits that investors will be fooled repeatedly (by temporarily low interest rates) into making unprofitable investment decisions.<ref name="Caplan"/><ref name="Tullock1988"/><ref>[http://www.reasonpapers.com/pdf/05/rp_5_4.pdf Problems with Austrian Business Cycle Theory]</ref> Bryan Caplan writes: "Why does Rothbard think businessmen are so incompetent at forecasting government policy? He credits them with entrepreneurial foresight about all market-generated conditions, but curiously finds them unable to forecast government policy, or even to avoid falling prey to simple accounting illusions generated by inflation and deflation... Particularly in interventionist economies, it would seem that natural selection would weed out businesspeople with such a gigantic blind spot."<ref name="caplan_abct"><br />
{{cite web<br />
| first = Bryan<br />
| last = Caplan<br />
| title = What's Wrong With Austrian Business Cycle Theory<br />
| publisher = Liberty Fund, Inc.<br />
| date = February 12, 2009<br />
| url = http://econlog.econlib.org/archives/2008/01/whats_wrong_wit_6.html<br />
| format = news<br />
| accessdate = 2010-05-17}}<br />
</ref><br />
<br />
Economist Paul Krugman has argued that the theory cannot explain changes in unemployment over the business cycle. Austrian business cycle theory postulates that business cycles are caused by the misallocation of resources from consumption to investment during "booms", and out of investment during "busts". Krugman argues that because total spending is equal to total income in an economy, the theory implies that the reallocation of resources during "busts" would increase employment in consumption industries, whereas in reality, spending declines in all sectors of an economy during recessions. He also argues that according to the theory the initial "booms" would also cause resource reallocation, which implies an increase in unemployment during booms as well.<ref name="Krugman" /><br />
<br />
In response, historian [[David Gordon (philosopher)|David Gordon]] argues that Krugman's analysis misrepresents Austrian theory. Gordon states, "unemployment, as Austrians see matters, stems mainly from rigid wage rates. If workers accept a fall in wages, liquidation of the boom is compatible with full employment."<ref>[http://mises.org/daily/3579 Hangover Theory: How Paul Krugman Has Misconceived Austrian Theory – David Gordon – Mises Daily<!-- Bot generated title -->]</ref> Austrian economist Roger Garrison states that a false boom caused by artificially low interest rates would cause a boom in consumption goods as well as investment goods (with a decrease in "middle goods"), thus explaining the jump in unemployment at the end of a boom.<ref>{{Cite web|author=Auburn User |url=http://www.auburn.edu/~garriro/strigl.htm |title=Overconsumption And Forced Saving |publisher=Auburn.edu |date= |accessdate=2012-08-15}}</ref> Garrison has also stated that capital allocated to investment goods cannot always be redeployed to create consumption goods.<ref>{{Cite web|author=Roger W. Garrison |url=http://mises.org/daily/1215 |title=Hayek on Industrial Fluctuations – Roger W. Garrison – Mises Daily |publisher=Mises.org |date= |accessdate=2012-08-13}}</ref><br />
<br />
Economist Jeffery Hummel is critical of Hayek's explanation of labor asymmetry in booms and busts. He argues that Hayek makes peculiar assumptions about demand curves for labor in his explanation of how a decrease in investment spending creates unemployment. He also argues that the labor asymmetry can be explained in terms of a change in real wages, but this explanation fails to explain the business cycle in terms of resource allocation.<ref name="Hummel">{{Cite web|url=http://www.reasonpapers.com/pdf/05/rp_5_4.pdf ''Reason Papers'' |title=Problems with Austrian Business Cycle Theory |last=Hummel |first=Jeffery Rogers|date=Winter 1979|format=PDF |pages=41–53|accessdate=2011-09-17}}</ref><br />
<br />
Milton Friedman objected to the policy implications of the theory, stating the following in a 1998 interview:<br />
<br />
<blockquote>I think the Austrian business-cycle theory has done the world a great deal of harm. If you go back to the 1930s, which is a key point, here you had the Austrians sitting in London, Hayek and Lionel Robbins, and saying you just have to let the bottom drop out of the world. You’ve just got to let it cure itself. You can’t do anything about it. You will only make it worse. You have Rothbard saying it was a great mistake not to let the whole banking system collapse. I think by encouraging that kind of do-nothing policy both in Britain and in the United States, they did harm.<ref>Interview in ''Barron's Magazine'', August 24, 1998 archived at Hoover Institution [http://www.hoover.org/publications/hoover-digest/article/6459]</ref></blockquote><br />
<br />
====Empirical objections====<br />
Hummel argues that the Austrian explanation of the business cycle fails on empirical grounds. In particular, he notes that investment spending remained positive in all recessions where there are data, except for the [[Great Depression]]. He argues that this casts doubt on the notion that recessions are caused by a reallocation of resources from industrial production to consumption, since he argues that the Austrian business cycle theory implies that net investment should be below zero during recessions.<ref name="Hummel"/> In response, Austrian economist [[Walter Block]] argues that the misallocation during booms does not preclude the possibility of demand increasing overall.<ref>http://www.reasonpapers.com/pdf/30/rp_30_4.pdf</ref><br />
<br />
In 1969, economist Milton Friedman, after examining the history of business cycles in the U.S., concluded that "The Hayek-Mises explanation of the business cycle is contradicted by the evidence. It is, I believe, false."<ref name=Friedman1969/> He analyzed the issue using newer data in 1993, and again reached the same conclusion.<ref name="Friedman93"/><br />
<br />
Referring to Friedman's discussion of the business cycle, Austrian economist Roger Garrison stated, "Friedman's empirical findings are broadly consistent with both Monetarist and Austrian views", and goes on to argue that although Friedman's model "describes the economy's performance at the highest level of aggregation; Austrian theory offers an insightful account of the market process that might underlie those aggregates."<ref>{{Cite web|author=Auburn User |url=http://www.auburn.edu/~garriro/fm1pluck.htm |title=Plucking Model |publisher=Auburn.edu |date=1982-10-25 |accessdate=2012-08-13}}</ref><ref>Milton Friedman, "The 'Plucking Model' of Business Fluctuations Revisited" Economic Inquiry April, 1993</ref><br />
<br />
==Principal works==<br />
* ''[[Capital and Interest]]'' by [[Eugen von Böhm-Bawerk]]<ref name="econlib"/><br />
* ''[[Individualism and Economic Order]]'' by [[Friedrich Hayek]]<ref name="econlib"/><br />
* ''[[Principles of Economics]]'' by [[Carl Menger]]<ref name="econlib"/><br />
* ''[[Human Action]]'' by [[Ludwig von Mises]]<ref name="econlib"/><br />
* ''[[Man, Economy, and State]]'' by [[Murray Rothbard|Murray N. Rothbard]]<ref name="econlib"/><br />
<br />
==See also==<br />
{{Portal|Economics|Libertarianism}}<br />
* [[List of Austrian School economists]]<br />
* [[List of Austrian intellectual traditions]]<br />
* [[Perspectives on capitalism]]<br />
* ''[[Quarterly Journal of Austrian Economics]]''<br />
<br />
==References and notes==<br />
{{Reflist|2}}<br />
<br />
==Further reading==<br />
* Alejandro Agafonow (2012). [http://ideas.repec.org/a/taf/revpoe/v24y2012i2p273-287.html “The Austrian Dehomogenization Debate, or the Possibility of a Hayekian Planner,”] ''Review of Political Economy'', Vol. 24, No. 02.<br />
* Harald Hagemann, Tamotsu Nishizawa, and Yukihiro Ikeda, eds. ''Austrian Economics in Transition: From Carl Menger to Friedrich Hayek'' (Palgrave Macmillan; 2010) 339 pages<br />
* Stephen Littlechild, ed. (1990). ''Austrian economics'', 3 v. Edward Elgar. [http://www.e-elgar.co.uk/bookentry_mainUS.lasso?id=682 Description] and scroll to chapter preview [http://books.google.com/books?id=XoZXUkYGj-oC&printsec=frontcover&source=gbs_v2_summary_r&cad=0#v=onepage&q&f=false links] for v. 1.<br />
<br />
==External links==<br />
{{Commons category|Austrian School}}<br />
* [http://wiki.mises.org/wiki/Austrian_School Austrian School] at Mises Wiki<br />
* {{dmoz|Science/Social_Sciences/Economics/Schools_of_Thought/Austrian_School/}}<br />
<br />
{{Austrian School economists}}<br />
{{macroeconomics-footer}}<br />
{{Schools of economic thought}}<br />
<br />
[[Category:Austrian School| ]]<br />
[[Category:Conservatism in the United States]]<br />
[[Category:Economic theories]]<br />
[[Category:Heterodox economics]]<br />
[[Category:Libertarian theory]]<br />
[[Category:Articles with inconsistent citation formats]]<br />
<br />
{{Link GA|de}}</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=83965Main Page2014-08-19T02:53:50Z<p>10.68.16.65: </p>
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{{pp-move-indef}}{{calendar}}<br />
{{This date in recent years}}<br />
{{Day}}<br />
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==Events==<br />
*[[46 BC]] &ndash; [[Julius Caesar]] defeats Caecilius Metellus Scipio and [[Cato the Younger|Marcus Porcius Cato (Cato the Younger)]] in the [[battle of Thapsus]].<br />
* [[402]] &ndash; [[Stilicho]] stymies the [[Visigoths]] under [[Alaric I|Alaric]] in the [[Battle of Pollentia]].<br />
*[[1199]] &ndash; [[King Richard I]] of England dies from an infection following the removal of an arrow from his shoulder.<br />
*[[1250]] &ndash; [[Seventh Crusade]]: [[Ayyubid dynasty|Ayyubids]] of Egypt capture King [[Louis IX of France]] in the [[Battle of Fariskur]].<br />
*[[1320]] &ndash; The [[Scotland|Scots]] reaffirm their independence by signing the [[Declaration of Arbroath]].<br />
*[[1327]] &ndash; The [[poet]] [[Petrarch]] first sees his idealized love, Laura, in the church of [[Saint Clare of Assisi|Saint Clare]] in [[Avignon]].<br />
*[[1385]] &ndash; John, Master of the [[Order of Aviz]], is made king [[John I of Portugal]].<br />
*[[1453]] &ndash; [[Mehmed II]] begins his siege of [[Constantinople]] ([[Istanbul]]), which falls on [[May 29]].<br />
*[[1580]] &ndash; One of the [[1580 Dover Straits earthquake|largest earthquakes]] recorded in the history of England, Flanders, or Northern France, takes place.<br />
*[[1652]] &ndash; At the [[Cape of Good Hope]], [[Netherlands|Dutch]] sailor [[Jan van Riebeeck]] establishes a resupply camp that eventually becomes [[Cape Town]].<br />
*[[1667]] &ndash; An [[earthquake]] devastates [[Dubrovnik]], then an independent [[city-state]].<br />
*[[1712]] &ndash; The [[New York Slave Revolt of 1712]] begins near [[Broadway (New York City)|Broadway]].<br />
*[[1776]] &ndash; [[American Revolutionary War]]: Ships of the [[Continental Navy]] fail in their [[Battle of Block Island|attempt to capture]] a [[Royal Navy]] [[dispatch boat]].<br />
*[[1782]] &ndash; King [[Buddha Yodfa Chulaloke]] (Rama I) of Siam (modern day [[Thailand]]) founded the Chakri dynasty.<br />
*[[1793]] &ndash; During the [[French Revolution]], the [[Committee of Public Safety]] becomes the executive organ of the republic.<br />
*[[1808]] &ndash; [[John Jacob Astor]] incorporates the [[American Fur Company]], that would eventually make him America's first millionaire.<br />
*[[1812]] &ndash; British forces under the command of the [[Duke of Wellington]] assault the fortress of [[Siege of Badajoz (1812)|Badajoz]]. This would be the turning point in the [[Peninsular War]] against [[Napoleon]]-led [[France]].<br />
*[[1814]] &ndash; Nominal beginning of the [[Bourbon Restoration]]; anniversary date that Napoleon abdicates and is exiled to [[Elba]].<br />
*[[1830]] &ndash; [[The Church of Jesus Christ of Latter Day Saints]], the original church of the [[Latter Day Saint movement]], is organized by [[Joseph Smith, Jr.]] and others at [[Fayette, New York|Fayette]] or [[Manchester (town), New York|Manchester, New York]].<br />
*[[1860]] &ndash; The [[Reorganized Church of Jesus Christ of Latter Day Saints]]—later renamed [[Community of Christ]]—is organized by [[Joseph Smith III]] and others at [[Amboy, Illinois]]<br />
*[[1861]] &ndash; First performance of [[Arthur Sullivan]]'s debut success, his suite of [[incidental music]] for ''[[The Tempest (Sullivan)|The Tempest]]'', leading to a career that included the famous [[Gilbert and Sullivan]] operas.<br />
*[[1862]] &ndash; [[American Civil War]]: The [[Battle of Shiloh]] begins &ndash; in [[Tennessee]], forces under [[Union (American Civil War)|Union]] [[General (United States)|General]] [[Ulysses S. Grant]] meet [[Confederate States of America|Confederate]] troops led by General [[Albert Sidney Johnston]].<br />
*[[1865]] &ndash; American Civil War: The [[Battle of Sayler's Creek]] &ndash; Confederate General [[Robert E. Lee]]'s [[Army of Northern Virginia]] fights its last major battle while in retreat from [[Richmond, Virginia]].<br />
*[[1866]] &ndash; The [[Grand Army of the Republic]], an American patriotic organization composed of Union veterans of the American Civil War, is founded. It lasts until [[1956]].<br />
*[[1869]] &ndash; [[Celluloid]] is patented.<br />
*[[1888]] &ndash; [[Thomas Green Clemson]] dies, bequeathing his estate to the State of [[South Carolina]] to establish [[Clemson University|Clemson Agricultural College]].<br />
*[[1893]] &ndash; [[Salt Lake Temple]] of The Church of Jesus Christ of Latter-day Saints is dedicated by [[Wilford Woodruff]].<br />
*[[1895]] &ndash; [[Oscar Wilde]] is arrested in the [[Cadogan Hotel]], [[London]] after losing a [[libel]] case against the [[John Sholto Douglas, 9th Marquess of Queensberry|Marquess of Queensberry]].<br />
*[[1896]] &ndash; In [[Athens]], the opening of the [[1896 Summer Olympics|first modern Olympic Games]] is celebrated, 1,500 years after the original games are banned by [[Roman Emperor]] [[Theodosius I]].<br />
*[[1909]] &ndash; [[Robert Edwin Peary|Robert Peary]] and [[Matthew Henson]] reach the [[North Pole]].<br />
*[[1911]] &ndash; During the [[Battle of Deçiq]], [[Ded Gjo Luli|Dedë Gjon Luli Dedvukaj]], leader of the [[Malësori]] [[Albania]]ns, raises the Albanian flag in the town of [[Tuzi]], [[Montenegro]], for the first time after [[George Kastrioti]] ([[Skenderbeg]]).<br />
*[[1917]] &ndash; [[World War I]]: The United States declares war on [[Germany]] (see [[:s:Woodrow Wilson declares war on Germany|President Woodrow Wilson's address to Congress]]).<br />
*[[1919]] &ndash; [[Mohandas Karamchand Gandhi]] orders a [[general strike]].<br />
*[[1923]] &ndash; The first Prefects Board in [[Southeast Asia]] is formed in [[Victoria Institution]], [[Malaysia]].<br />
*[[1924]] &ndash; [[First aerial circumnavigation|First round-the-world]] flight commences.<br />
*[[1926]] &ndash; [[Varney Airlines]] makes its first commercial flight (Varney is the root company of [[United Airlines]]).<br />
*[[1929]] &ndash; [[Huey P. Long]] [[Governor of Louisiana]] is [[impeach]]ed by the [[Louisiana House of Representatives]].<br />
*[[1930]] &ndash; Gandhi raises a lump of mud and salt and declares, "With this, I am shaking the foundations of the [[British Empire]]," beginning the [[Salt Satyagraha]].<br />
*[[1936]] &ndash; [[Tupelo-Gainesville tornado outbreak]]: Another tornado from the same storm system as the Tupelo tornado hits [[Gainesville, Georgia]], killing 203.<br />
*[[1941]] &ndash; [[World War II]]: [[Nazi Germany]] launches [[Invasion of Yugoslavia|Operation 25]] (the invasion of Kingdom of Yugoslavia) and [[Operation Marita]] (the invasion of [[Greece]]).<br />
*[[1945]] &ndash; World War II: [[Sarajevo]] is liberated from [[Germany|German]] and [[Croatia]]n forces by the [[Yugoslav Partisans]].<br />
* 1945 &ndash; World War II: the [[Battle of Slater's Knoll]] on Bougainville comes to an end.<br />
*[[1947]] &ndash; The first [[Tony Awards]] are presented for theatrical achievement.<br />
*[[1957]] &ndash; Greek shipping tycoon [[Aristotle Onassis]] buys the Hellenic National Airlines (TAE) and founds [[Olympic Airlines]].<br />
*[[1962]] &ndash; [[Leonard Bernstein]] causes controversy with his remarks from the podium during a [[New York Philharmonic]] [[New York Philharmonic concert of April 6, 1962|concert]] featuring [[Glenn Gould]] performing [[Johannes Brahms|Brahms]]' [[Piano Concerto No. 1 (Brahms)|First Piano Concerto]].<br />
*[[1965]] &ndash; Launch of [[Intelsat I|Early Bird]], the first communications [[satellite]] to be placed in [[geosynchronous orbit]].<br />
* 1965 &ndash; The British Government announces the cancellation of the [[BAC TSR-2|TSR-2]] aircraft project.<br />
*[[1968]] &ndash; In [[Richmond, Indiana]]'s downtown district, a [[Richmond, Indiana explosion|double explosion]] kills 41 and injures 150.<br />
* 1968 &ndash; [[Pierre Elliot Trudeau]] wins the [[Liberal Party of Canada leadership election, 1968|Liberal Leadership Election]], and becomes Prime Minister of [[Canada]] soon after.<br />
*[[1970]] &ndash; [[Newhall Incident]]: Four [[California Highway Patrol]] officers are killed in a shootout.<br />
*[[1972]] &ndash; [[Vietnam War]]: [[Easter Offensive]] &ndash; American forces begin sustained air strikes and naval bombardments.<br />
*[[1973]] &ndash; Launch of ''[[Pioneer 11]]'' [[spacecraft]].<br />
* 1973 &ndash; The [[American League]] of [[Major League Baseball]] begins using the [[designated hitter]].<br />
*[[1982]] &ndash; [[Estonian Communist Party]] bureau declares "fight against bourgeois TV"—meaning [[Finland|Finnish]] TV—a top priority of the propagandists of [[Estonian SSR]]<br />
*[[1984]] &ndash; Members of [[Cameroon]]'s Republican Guard unsuccessfully attempt to overthrow the [[government]] headed by [[Paul Biya]].<br />
*[[1994]] &ndash; The [[Rwandan Genocide]] begins when the aircraft carrying [[Rwanda]]n [[president]] [[Juvénal Habyarimana]] and [[Burundi]]an president [[Cyprien Ntaryamira]] is shot down.<br />
*[[1998]] &ndash; [[Pakistan]] tests medium-range missiles capable of reaching [[India]].<br />
* 1998 &ndash; [[Travelers Group]] announces an agreement to undertake the $76 billion merger between Travelers and [[Citicorp]], and the merger is completed on [[October 8]], of that year, forming [[Citibank]].<br />
*[[2004]] &ndash; [[Rolandas Paksas]] becomes the first president of [[Lithuania]] to be peacefully removed from office by [[impeachment]].<br />
*[[2005]] &ndash; Kurdish leader [[Jalal Talabani]] becomes [[Iraq]]i president; Shiite Arab Ibrahim al-Jaafari is named [[premier]] the next day.<br />
*[[2008]] &ndash; [[2008 Egyptian general strike]] starts led by [[Egypt]]ian workers later to be adopted by [[April 6 Youth Movement]] and [[Egypt]]ian activities .<br />
*[[2009]] &ndash; A [[2009 L'Aquila earthquake|6.3 magnitude earthquake]] strikes near [[L'Aquila]], [[Italy]], killing 307.<br />
*[[2010]] &ndash; [[Communist Party of India (Maoist)|Maoist rebels]] [[April 2010 Maoist attack in Dantewada|kill]] 76 [[Central Reserve Police Force|CRPF]] officers in [[Dantewada district]], [[India]].<br />
*[[2011]] &ndash; In [[San Fernando, Tamaulipas]], [[Mexico]], over 193 bodies were exhumed from several [[2011 San Fernando massacre|mass graves]] made by [[Los Zetas]].<br />
*[[2012]] &ndash; [[Azawad Declaration of Independence]] is declared.<br />
<br />
==Births==<br />
*[[1632]] &ndash; [[Maria Leopoldine of Austria]], Empress of the Holy Roman Empire (d. 1649)<br />
*[[1651]] &ndash; [[André Dacier]], French scholar (d. 1722)<br />
*[[1660]] &ndash; [[Johann Kuhnau]], German organist and composer (d. 1722)<br />
*[[1664]] &ndash; [[Arvid Horn]], Swedish soldier and politician (d. 1742)<br />
*[[1671]] &ndash; [[Jean-Baptiste Rousseau]], French poet (d. 1741)<br />
*[[1672]] &ndash; [[André Cardinal Destouches]], French composer (d. 1749)<br />
*[[1706]] &ndash; [[Louis de Cahusac]], French playwright (d. 1759)<br />
*[[1708]] &ndash; [[Georg Reutter II]], Austrian composer (d. 1772)<br />
*[[1725]] &ndash; [[Pasquale Paoli]], French commander (d. 1807)<br />
*[[1726]] &ndash; [[Gerard Majella]], Italian saint (d. 1755)<br />
*[[1741]] &ndash; [[Nicolas Chamfort]], French author and playwright (d. 1794)<br />
*[[1766]] &ndash; [[Wilhelm von Kobell]], German painter (d. 1853)<br />
*[[1773]] &ndash; [[James Mill]], Scottish historian, economist, and philosopher (d. 1836)<br />
*[[1810]] &ndash; [[Philip Henry Gosse]], English biologist (d. 1888)<br />
*[[1812]] &ndash; [[Alexander Herzen]], Russian philosopher and author (d. 1870)<br />
*[[1815]] &ndash; [[Robert Volkmann]], German composer (d. 1883)<br />
*[[1818]] &ndash; [[Aasmund Olavsson Vinje]], Norwegian journalist and poet (d. 1870)<br />
*[[1820]] &ndash; [[Nadar (photographer)|Nadar]], French photographer, journalist, and author (d. 1910)<br />
*[[1823]] &ndash; [[Joseph Medill]], American publisher and politician, 26th [[Mayor of Chicago]] (d. 1899)<br />
*[[1826]] &ndash; [[Gustave Moreau]], French painter (d. 1898)<br />
*[[1841]] &ndash; [[Karl Binding]], German jurist and author (d. 1920)<br />
*[[1851]] &ndash; [[Guillaume Bigourdan]], French astronomer (d. 1932)<br />
*[[1855]] &ndash; [[Charles Huot]], Canadian painter and illustrator (d. 1930)<br />
*[[1860]] &ndash; [[René Lalique]], French sculptor (d. 1945)<br />
*[[1861]] &ndash; [[Stanislas de Guaita]], French poet (d. 1897)<br />
*[[1864]] &ndash; [[William Bate Hardy]], English biochemist (d. 1934)<br />
*[[1866]] &ndash; [[Felix-Raymond-Marie Rouleau]], Canadian cardinal (d. 1931)<br />
*[[1869]] &ndash; [[Levon Shant]], Armenian author, poet, and playwright (d. 1951)<br />
*[[1878]] &ndash; [[Erich Mühsam]], German author, poet, and playwright (d. 1934)<br />
*[[1881]] &ndash; [[Karl Staaf]], Swedish pole vaulter and hammer thrower (d. 1953)<br />
*[[1884]] &ndash; [[Walter Huston]], Canadian-American actor (d. 1950)<br />
* 1884 &ndash; [[J. G. Parry-Thomas]], Welsh race car driver and engineer (d. 1927)<br />
*[[1886]] &ndash; [[Patriarch Athenagoras I of Constantinople]] (d. 1972)<br />
* 1886 &ndash; [[Walter Dandy]], American neurosurgeon (d. 1946)<br />
* 1886 &ndash; [[Osman Ali Khan, Asaf Jah VII]] of Hyderabad (d. 1967)<br />
*[[1888]] &ndash; [[Hans Richter (artist)|Hans Richter]], Swiss painter, illustrator, and director (d. 1976)<br />
* 1888 &ndash; [[Gerhard Ritter]], German historian (d. 1967)<br />
*[[1890]] &ndash; [[Anthony Fokker]], Dutch engineer and businessman, founded [[Fokker|Fokker Aircraft Manufacturer]] (d. 1939)<br />
*[[1892]] &ndash; [[Donald Wills Douglas, Sr.]], American businessman, founded the [[Douglas Aircraft Company]] (d. 1981)<br />
* 1892 &ndash; [[Lowell Thomas]], American journalist (d. 1981)<br />
*[[1894]] &ndash; [[Gertrude Baines]], American super-centenarian (d. 2009)<br />
*[[1895]] &ndash; [[Dudley Nichols]], American screenwriter, director, and producer (d. 1960)<br />
*[[1898]] &ndash; [[Jeanne Hébuterne]], French painter (d. 1920)<br />
*[[1900]] &ndash; [[Leo Robin]], American composer and songwriter (d. 1984)<br />
*[[1901]] &ndash; [[Pier Giorgio Frassati]], Italian activist (d. 1925)<br />
*[[1902]] &ndash; [[Julien Torma]], French author, poet, and playwright (d. 1933)<br />
*[[1903]] &ndash; [[Mickey Cochrane]], American baseball player and manager (d. 1962)<br />
* 1903 &ndash; [[Harold Eugene Edgerton]], American engineer and academic (d. 1990)<br />
*[[1904]] &ndash; [[Kurt Georg Kiesinger]], German politician, 3rd [[Chancellor of Germany]] (d. 1988)<br />
*[[1908]] &ndash; [[Marcel-Marie Desmarais]], Canadian preacher, author, and broadcaster (d. 1994)<br />
*[[1909]] &ndash; [[William M. Branham]], American minister (d. 1965)<br />
* 1909 &ndash; [[Hermann Lang]], German race car driver (d. 1987)<br />
*[[1911]] &ndash; [[Feodor Felix Konrad Lynen]], German biochemist, [[Nobel Prize in Physiology or Medicine|Nobel Prize]] laureate (d. 1979)<br />
*[[1913]] &ndash; [[Shannon Boyd-Bailey McCune]], North Korean-American geographer (d. 1993)<br />
*[[1915]] &ndash; [[Tadeusz Kantor]], Polish director, painter, and set designer (d. 1990)<br />
*[[1916]] &ndash; [[Phil Leeds]], American actor (d. 1998)<br />
* 1916 &ndash; [[Vincent Ellis McKelvey]], American geologist (d. 1987)<br />
*[[1917]] &ndash; [[Leonora Carrington]], English-Mexican painter and author (d. 2011)<br />
*[[1918]] &ndash; [[Alfredo Ovando Candía]], Bolivian general and politician, 56th [[President of Bolivia]] (d. 1982)<br />
*[[1918]] &ndash; [[Big Walter Horton]], American blues harmonica player (d. 1981)<br />
*[[1919]] &ndash; [[Georgios Mylonas]], Greek politician (d. 1998)<br />
*[[1920]] &ndash; [[Jack Cover]], American pilot and scientist, invented the [[Taser|Taser gun]] (d. 2009)<br />
* 1920 &ndash; [[Edmond H. Fischer]], Chinese-American biochemist, [[Nobel Prize in Physiology or Medicine|Nobel Prize]] laureate<br />
*[[1926]] &ndash; [[Sergio Franchi]], Italian-American singer and actor (d. 1990)<br />
* 1926 &ndash; [[Gil Kane]], Latvian-American illustrator (d. 2000)<br />
* 1926 &ndash; [[Ian Paisley]], Irish minister and politician, 2nd [[First Minister of Northern Ireland]]<br />
*[[1927]] &ndash; [[Gerry Mulligan]], American saxophonist, clarinet player, and composer (d. 1996)<br />
*[[1928]] &ndash; [[James Watson]], American biologist and geneticist, [[Nobel Prize in Physiology or Medicine|Nobel Prize]] laureate<br />
*[[1929]] &ndash; [[Willis Hall]], English playwright and author (d. 2005)<br />
* 1929 &ndash; [[Joi Lansing]], American model, actress, and singer (d. 1972)<br />
* 1929 &ndash; [[André Previn]], German-American pianist, composer, and conductor<br />
*[[1931]] &ndash; [[Ram Dass]], American author and educator<br />
* 1931 &ndash; [[Ivan Dixon]], American actor, director, and producer (d. 2008)<br />
* 1931 &ndash; [[Suchitra Sen]], Indian actress (d. 2014)<br />
*[[1932]] &ndash; [[Connie Broden]], Canadian ice hockey player (d. 2013)<br />
* 1932 &ndash; [[Helmut Griem]], German actor and director (d. 2004)<br />
*[[1933]] &ndash; [[Roy Goode]], English lawyer and academic<br />
* 1933 &ndash; [[Tom Korologos]], American diplomat<br />
* 1933 &ndash; [[Eduardo Malapit]], American politician, [[Mayor of Kauai]] (d. 2007)<br />
*[[1934]] &ndash; [[Enrique Álvarez Félix]], Mexican actor (d. 1996)<br />
* 1934 &ndash; [[Anton Geesink]], Dutch martial artist (d. 2010)<br />
* 1934 &ndash; [[Guy Peellaert]], Belgian painter, illustrator, and photographer (d. 2008)<br />
*[[1935]] &ndash; [[Douglas Hill]], Canadian author (d. 2007)<br />
*[[1936]] &ndash; [[Helen Berman]], Dutch-Israeli painter and illustrator<br />
* 1936 &ndash; [[Jean-Pierre Changeux]], French biologist<br />
*[[1937]] &ndash; [[Merle Haggard]], American singer-songwriter and guitarist ([[The Strangers (American band)|The Strangers]] and [[The Buckaroos]])<br />
* 1937 &ndash; [[Terrence Hardiman]], English actor<br />
* 1937 &ndash; [[Peter Maivia]], Samoan-American wrestler (d. 1982)<br />
* 1937 &ndash; [[Billy Dee Williams]], American actor and singer<br />
*[[1938]] &ndash; [[Paul Daniels]], English magician<br />
* 1938 &ndash; [[Roy Thinnes]], American actor<br />
*[[1939]] &ndash; [[André Ouellet]], Canadian politician, 1st [[Minister of Foreign Affairs (Canada)|Minister of Foreign Affairs for Canada]]<br />
* 1939 &ndash; [[John Sculley]], American businessman<br />
*[[1940]] &ndash; [[Homero Aridjis]], Mexican journalist, author, and poet<br />
* 1940 &ndash; [[Pedro Armendáriz, Jr.]], Mexican-American actor (d. 2011)<br />
*[[1941]] &ndash; [[Phil Austin]], American comedian, actor, and screenwriter<br />
* 1941 &ndash; [[Hans W. Geißendörfer]], German director and producer<br />
* 1941 &ndash; [[Don Prudhomme]], American race car driver<br />
* 1941 &ndash; [[Gheorghe Zamfir]], Romanian flute player and composer<br />
*[[1942]] &ndash; [[Barry Levinson]], American actor, director, screenwriter, and producer<br />
*[[1943]] &ndash; [[Mitchell Melton]], American politician (d. 2013)<br />
*[[1944]] &ndash; [[Anita Pallenberg]], Italian-English model, actress, and fashion designer<br />
* 1944 &ndash; [[Felicity Palmer]], English soprano<br />
*[[1945]] &ndash; [[Neal Boortz]], American radio host and author<br />
*[[1947]] &ndash; [[John Ratzenberger]], American actor<br />
* 1947 &ndash; [[Mike Worboys]], English mathematician and computer scientist<br />
* 1947 &ndash; [[André Weinfeld]], French-American director, screenwriter, and producer<br />
*[[1948]] &ndash; [[Patrika Darbo]], American actress<br />
*[[1949]] &ndash; [[Patrick Hernandez]], French singer-songwriter<br />
* 1949 &ndash; [[Horst Ludwig Störmer]], German physicist, [[Nobel Prize in Physics|Nobel Prize]] laureate<br />
*[[1950]] &ndash; [[Cleo Odzer]], American author (d. 2001)<br />
*[[1951]] &ndash; [[Bert Blyleven]], Dutch-American baseball player and sportscaster<br />
* 1951 &ndash; [[Jean-Marc Boivin]], French skier, mountaineer, and pilot (d. 1990)<br />
*[[1952]] &ndash; [[Udo Dirkschneider]], German singer-songwriter ([[Accept (band)|Accept]] and [[U.D.O.]])<br />
* 1952 &ndash; [[Marilu Henner]], American actress, producer, and author<br />
* 1952 &ndash; [[Michel Larocque (ice hockey b. 1952)|Michel Larocque]], Canadian ice hockey player and manager (d. 1992)<br />
*[[1953]] &ndash; [[Christopher Franke]], German-American drummer and songwriter ([[Tangerine Dream]] and [[Agitation Free]])<br />
*[[1955]] &ndash; [[Rob Epstein]], American director and producer<br />
* 1955 &ndash; [[Keith Hunter Jesperson]], Canadian-American serial killer<br />
* 1955 &ndash; [[Cathy Jones]], Canadian comedian and actor<br />
* 1955 &ndash; [[Blind Mississippi Morris]], American singer and harmonica player<br />
* 1955 &ndash; [[Michael Rooker]], American actor<br />
*[[1956]] &ndash; [[Normand Corbeil]], Canadian composer (d. 2013)<br />
* 1956 &ndash; [[Sebastian Spreng]], Argentinian-American painter and journalist<br />
* 1956 &ndash; [[Dilip Vengsarkar]], Indian cricketer<br />
* 1956 &ndash; [[Michele Bachmann]], American politician<br />
*[[1957]] &ndash; [[Jaroslava Maxová]], Czech soprano<br />
* 1957 &ndash; [[Paolo A. Nespoli]], Italian engineer and astronaut<br />
*[[1958]] &ndash; [[Graeme Base]], Australian author and illustrator<br />
*[[1959]] &ndash; [[Gail Shea]], Canadian politician<br />
*[[1960]] &ndash; [[Batem]], Congolese-Belgian illustrator<br />
* 1960 &ndash; [[Warren Haynes]], American singer-songwriter and guitarist ([[The Allman Brothers Band]], [[Gov't Mule]], and [[The Dead (band)|The Dead]])<br />
* 1960 &ndash; [[John Pizzarelli]], American singer-songwriter and guitarist<br />
*[[1961]] &ndash; [[Rory Bremner]], Scottish actor and screenwriter<br />
*[[1962]] &ndash; [[Iris Häussler]], German sculptor<br />
* 1962 &ndash; [[Marco Schällibaum]], Swiss footballer, coach, and manager<br />
*[[1963]] &ndash; [[Rafael Correa]], Ecuadorian politician, 54th [[President of Ecuador]]<br />
*[[1964]] &ndash; [[Phil Gayle]], English journalist<br />
*[[1965]] &ndash; [[Black Francis]], American singer-songwriter and guitarist ([[Pixies]] and [[Grand Duchy (band)|Grand Duchy]])<br />
* 1965 &ndash; [[Sterling Sharpe]], American football player<br />
* 1965 &ndash; [[Lieve Slegers]], Belgian runner<br />
*[[1966]] &ndash; [[Vince Flynn]], American author (d. 2013)<br />
* 1966 &ndash; [[Young Man Kang]], South Korean-American director and producer<br />
*[[1967]] &ndash; [[Jonathan Firth]], English actor<br />
* 1967 &ndash; [[Mika Koivuniemi]], Finnish-American bowler<br />
*[[1968]] &ndash; [[Affonso Giaffone]], Brazilian race car driver<br />
*[[1969]] &ndash; [[Bret Boone]], American baseball player and manager<br />
* 1969 &ndash; [[Jack Canfora]], American actor, singer, and playwright<br />
* 1969 &ndash; [[Bison Dele]], American basketball player (d. 2002)<br />
* 1969 &ndash; [[Ari Meyers]], Puerto Rican-American actress<br />
* 1969 &ndash; [[Philipp Peter]], Austrian race car driver<br />
* 1969 &ndash; [[Paul Rudd]], American actor, screenwriter, and producer<br />
* 1969 &ndash; [[Louie Spence]], English dancer and choreographer<br />
* 1969 &ndash; [[Spencer Wells]], American geneticist and anthropologist<br />
*[[1970]] &ndash; [[Olaf Kölzig]], South African-German ice hockey player and coach<br />
* 1970 &ndash; [[Roy Mayorga]], American drummer, songwriter, and producer ([[Stone Sour]], [[Soulfly]], [[Amebix]], [[Black President (band)|Black President]], and [[Nausea (band)|Nausea]])<br />
* 1970 &ndash; [[Huang Xiaomin]], Chinese swimmer<br />
*[[1971]] &ndash; [[Lou Merloni]], American baseball player and radio host<br />
* 1971 &ndash; [[Sanjay Suri]], Indian actor and producer<br />
*[[1972]] &ndash; [[Scott Martin Brooks]], American actor<br />
* 1972 &ndash; [[Chad Eaton]], American football player and coach<br />
* 1972 &ndash; [[Jason Hervey]], American actor and producer<br />
* 1972 &ndash; [[Ami James]], Israeli-American tattoo artist<br />
* 1972 &ndash; [[Anders Thomas Jensen]], Danish director and screenwriter<br />
* 1972 &ndash; [[Dickey Simpkins]], American basketball player<br />
* 1972 &ndash; [[Jo Van Daele]], Belgian discus thrower<br />
*[[1973]] &ndash; [[Donnie Edwards]], American football player<br />
* 1973 &ndash; [[Randall Godfrey]], American football player<br />
* 1973 &ndash; [[Joe Machine]], English painter and poet<br />
* 1973 &ndash; [[Rie Miyazawa]], Japanese model and actress<br />
* 1973 &ndash; [[Sun Wen (footballer)|Sun Wen]], Chinese footballer<br />
*[[1974]] &ndash; [[Camilla Dallerup]], Danish-English dancer and model<br />
* 1974 &ndash; [[Érica García]], Argentinian-American singer-songwriter and actress ([[Fool's Gold (band)|Fool's Gold]])<br />
* 1974 &ndash; [[Robert Kovač]], Croatian footballer and coach<br />
* 1974 &ndash; [[Jeff Tymoschuk]], Canadian composer<br />
* 1974 &ndash; [[Gina Yashere]], English comedian and actor<br />
*[[1975]] &ndash; [[Zach Braff]], American actor, director, screenwriter, and producer<br />
* 1975 &ndash; [[Hal Gill]], American ice hockey player<br />
* 1975 &ndash; [[Sonia Lopes]], Cape Verdean middle distance and long-distance runner<br />
* 1975 &ndash; [[Joel West]], American actor<br />
*[[1976]] &ndash; [[Candace Cameron Bure]], American actress, producer, and author<br />
* 1976 &ndash; [[James Fox (singer)|James Fox]], Welsh singer-songwriter, guitarist, and actor<br />
* 1976 &ndash; [[Chris Hoke]], American football player<br />
* 1976 &ndash; [[Georg Hólm]], Icelandic bass player ([[Sigur Rós]])<br />
* 1976 &ndash; [[Hirotada Ototake]], Japanese author and educator<br />
*[[1977]] &ndash; [[Ville Nieminen]], Finnish ice hockey player<br />
* 1977 &ndash; [[Andy Phillips]], American baseball player and coach<br />
* 1977 &ndash; [[Teddy Sears]], American actor<br />
*[[1978]] &ndash; [[Tim Hasselbeck]], American football player and sportscaster<br />
* 1978 &ndash; [[Myleene Klass]], English singer, pianist, and model ([[Hear'Say]])<br />
* 1978 &ndash; [[Martin Mendez]], Uruguayan bass player and songwriter ([[Opeth]])<br />
* 1978 &ndash; [[Blaine Neal]], American baseball player<br />
* 1978 &ndash; [[Igor Semshov]], Russian footballer<br />
* 1978 &ndash; [[Kendra Todd]], American real estate agent and author<br />
*[[1979]] &ndash; [[Sam Atwell]], Australian actor<br />
* 1979 &ndash; [[Eilen Jewell]], American singer-songwriter and guitarist<br />
* 1979 &ndash; [[Christine Smith (model)|Christine Smith]], American model and actress<br />
* 1979 &ndash; [[Lord Frederick Windsor]], English journalist and financier<br />
*[[1980]] &ndash; [[Matthew Carey]], American actor<br />
* 1980 &ndash; [[Tommi Evilä]], Finnish long jumper<br />
* 1980 &ndash; [[Tanja Poutiainen]], Finnish skier<br />
*[[1981]] &ndash; [[Eliza Coupe]], American actress<br />
* 1981 &ndash; [[Robert Earnshaw]], Zambian-Welsh footballer<br />
* 1981 &ndash; [[Jeff Faine]], American football player<br />
* 1981 &ndash; [[Kari Jobe]], American singer-songwriter and guitarist ([[Gateway Worship]])<br />
* 1981 &ndash; [[Anastassia Morkovkina]], Estonian footballer<br />
* 1981 &ndash; [[Alex Suarez]], American bass player ([[Cobra Starship]] and [[This Is Ivy League]])<br />
*[[1982]] &ndash; [[Alana Austin]], American actress<br />
* 1982 &ndash; [[Sofia Boutella]], Algerian-American dancer and actress<br />
* 1982 &ndash; [[Michael Guy Chislett]], Australian-American guitarist, songwriter, and producer ([[The Academy Is...]] and [[Hillsong United (band)|Hillsong United]])<br />
* 1982 &ndash; [[Herculez Gomez]], American soccer player<br />
* 1982 &ndash; [[Ilan Hall]], American chef<br />
* 1982 &ndash; [[Bret Harrison]], American actor and singer<br />
* 1982 &ndash; [[Travis Moen]], Canadian ice hockey player<br />
* 1982 &ndash; [[Miguel Ángel Silvestre]], Spanish actor<br />
* 1982 &ndash; [[Euclides Varela]], Cape Verdean long-distance runner<br />
*[[1983]] &ndash; [[Diora Baird]], American model and actress<br />
* 1983 &ndash; [[Mehdi Ballouchy]], Moroccan footballer<br />
* 1983 &ndash; [[Jerome Kaino]], New Zealand rugby player<br />
* 1983 &ndash; [[Mitsuru Nagata]], Japanese footballer<br />
* 1983 &ndash; [[Remi Nicole]], English singer-songwriter and actress<br />
* 1983 &ndash; [[Jekaterina Patjuk]], Estonian runner<br />
* 1983 &ndash; [[Jade Seah]], Singaporean model and actress<br />
* 1983 &ndash; [[Bobbi Starr]], American porn actress<br />
* 1983 &ndash; [[James Wade]], English darts player<br />
* 1983 &ndash; [[Katie Weatherston]], Canadian ice hockey player<br />
*[[1984]] &ndash; [[Max Bemis]], American singer-songwriter ([[Say Anything (band)|Say Anything]], [[Two Tongues]], and [[Max Bemis and the Painful Splits]])<br />
* 1984 &ndash; [[Michaël Ciani]], French footballer<br />
* 1984 &ndash; [[Siboniso Gaxa]], South African footballer<br />
*[[1985]] &ndash; [[Clarke MacArthur]], Canadian ice hockey player<br />
* 1985 &ndash; [[Ali Mukaddam]], Canadian actor, director, and producer<br />
* 1985 &ndash; [[Frank Ongfiang]], Cameroonian footballer<br />
*[[1986]] &ndash; [[Nikolas Asprogenis]], Cypriot footballer<br />
* 1986 &ndash; [[Aaron Curry (American football)|Aaron Curry]], American football player<br />
* 1986 &ndash; [[Ryota Moriwaki]], Japanese footballer<br />
* 1986 &ndash; [[Tara Osseck]], American model, [[Miss Missouri|Miss Missouri 2009]]<br />
*[[1987]] &ndash; [[Juan Adriel Ochoa]], Mexican footballer<br />
* 1987 &ndash; [[Levi Porter]], English footballer<br />
* 1987 &ndash; [[Hilary Rhoda]], American supermodel<br />
* 1987 &ndash; [[Benjamin Corgnet]], French footballer<br />
*[[1988]] &ndash; [[Jucilei]], Brazilian footballer<br />
* 1988 &ndash; [[Leigh Adams (footballer)|Leigh Adams]], Australian footballer<br />
* 1988 &ndash; [[Mike Bailey (actor)|Mike Bailey]], English actor and singer<br />
* 1988 &ndash; [[Melisa Cantiveros]], Filipino actress<br />
* 1988 &ndash; [[Daniele Gasparetto]], Italian footballer<br />
* 1988 &ndash; [[Carlton Mitchell]], American football player<br />
* 1988 &ndash; [[Fabrice Muamba]], Congolese-English footballer<br />
* 1988 &ndash; [[Ivonne Orsini]], Puerto Rician model, [[Miss World Puerto Rico 2008]]<br />
*[[1989]] &ndash; [[Rigard van Klooster]], Dutch cyclist and speed skater<br />
* 1989 &ndash; [[Renārs Rode]], Latvian football player<br />
*[[1990]] &ndash; [[Charlie McDermott]], American actor<br />
* 1990 &ndash; [[Andrei Veis]], Estonian footballer<br />
*[[1995]] &ndash; [[Darya Lebesheva]], Belarusian tennis player<br />
* 1995 &ndash; [[Ryutaro Morimoto]], Japanese actor and singer ([[Hey! Say! JUMP]])<br />
*[[1998]] &ndash; [[Lily Jackson]], American actress<br />
* 1998 &ndash; [[Peyton List (actress born 1998)|Peyton List]], American actress<br />
* 1998 &ndash; [[Spencer List]], American actor<br />
*[[1999]] &ndash; [[Kwesi Boakye]], American actor<br />
*[[2000]] &ndash; [[CJ Adams]], American actor<br />
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==Deaths==<br />
* [[885]] &ndash; [[Saints Cyril and Methodius|Saint Methodius]], Byzantine missionary (b. 815)<br />
*[[1147]] &ndash; [[Frederick II, Duke of Swabia]] (b. 1090)<br />
*[[1199]] &ndash; [[Richard I of England]] (b. 1157)<br />
*[[1362]] &ndash; [[James I, Count of La Marche]] (b. 1319)<br />
*[[1490]] &ndash; [[Matthias Corvinus]], Hungarian king (b. 1443)<br />
*[[1520]] &ndash; [[Raphael]], Italian painter and architect (b. 1483)<br />
*[[1528]] &ndash; [[Albrecht Dürer]], German painter, engraver, and mathematician (b. 1471)<br />
*[[1551]] &ndash; [[Joachim Vadian]], Swiss scholar and politician (b. 1484)<br />
*[[1571]] &ndash; [[John Hamilton (archbishop of St Andrews)|John Hamilton]], Scottish archbishop (b. 1512)<br />
*[[1590]] &ndash; [[Francis Walsingham]], English politician (b. 1532)<br />
*[[1605]] &ndash; [[John Stow]], English historian (b. 1525)<br />
*[[1655]] &ndash; [[David Blondel]], French clergyman and scholar (b. 1591)<br />
*[[1686]] &ndash; [[Arthur Annesley, 1st Earl of Anglesey]], Irish-English politician (b. 1614)<br />
*[[1707]] &ndash; [[Willem van de Velde the Younger]], Dutch painter (b. 1633)<br />
*[[1755]] &ndash; [[Richard Rawlinson]], English minister and historian (b. 1690)<br />
*[[1790]] &ndash; [[Louis IX, Landgrave of Hesse-Darmstadt]] (b. 1719)<br />
*[[1825]] &ndash; [[Vladimir Borovikovsky]], Ukrainian-Russian painter (b. 1757)<br />
*[[1829]] &ndash; [[Niels Henrik Abel]], Norwegian mathematician (b. 1802)<br />
*[[1833]] &ndash; [[Adamantios Korais]], Greek scholar (b. 1748)<br />
*[[1838]] &ndash; [[José Bonifácio de Andrada]], Brazilian politician (b. 1763)<br />
*[[1860]] &ndash; [[James Kirke Paulding]], American author and politician, 11th [[United States Secretary of the Navy]] (b. 1778)<br />
*[[1862]] &ndash; [[Albert Sidney Johnston]], American general (b. 1803)<br />
*[[1883]] &ndash; [[Benjamin Wright Raymond]], American politician, 3rd [[Mayor of Chicago]] (b. 1801)<br />
*[[1899]] &ndash; [[Alvan Wentworth Chapman]], American physician and botanist (b. 1809)<br />
*[[1906]] &ndash; [[Alexander Kielland]], Norwegian author (b. 1849)<br />
*[[1935]] &ndash; [[Edwin Arlington Robinson]], American poet (b. 1869)<br />
*[[1947]] &ndash; [[Herbert Backe]], German politician (b. 1896)<br />
*[[1950]] &ndash; [[Louis Wilkins]], American pole vaulter (b. 1882)<br />
*[[1953]] &ndash; [[Idris Davies]], Welsh poet (b. 1905)<br />
*[[1959]] &ndash; [[Leo Aryeh Mayer]], Israeli scholar (b. 1895)<br />
*[[1961]] &ndash; [[Jules Bordet]], Belgian microbiologist, [[Nobel Prize in Physiology or Medicine|Nobel Prize]] laureate (b. 1870)<br />
*[[1963]] &ndash; [[Otto Struve]], Russian-American astronomer (b. 1897)<br />
*[[1970]] &ndash; [[Sam Sheppard]], American physician (b. 1923)<br />
* 1970 &ndash; [[Maurice Stokes]], American basketball player (b. 1933)<br />
*[[1971]] &ndash; [[Igor Stravinsky]], Russian-American pianist, composer, and conductor (b. 1882)<br />
*[[1974]] &ndash; [[Willem Marinus Dudok]], Dutch architect (b. 1884)<br />
* 1974 &ndash; [[Hudson Fysh]], Australian pilot and businessman, co-founded [[Qantas|Qantas Airways Limited]] (b. 1895)<br />
*[[1977]] &ndash; [[Kōichi Kido]], Japanese politician, 13th [[Lord Keeper of the Privy Seal of Japan]] (b. 1889)<br />
*[[1979]] &ndash; [[Ivan Vasilyov]], Bulgarian architect, designed the [[SS. Cyril and Methodius National Library]] (b. 1893)<br />
*[[1984]] &ndash; [[Ral Donner]], American singer (b. 1943)<br />
*[[1992]] &ndash; [[Isaac Asimov]], Russian-American author and educator (b. 1920)<br />
*[[1994]] &ndash; [[Juvénal Habyarimana]], Rwandan politician, 3rd [[President of Rwanda]] (b. 1937)<br />
* 1994 &ndash; [[Cyprien Ntaryamira]], Burundian politician, 5th [[President of Burundi]] (b. 1956)<br />
*[[1995]] &ndash; [[Ioannis Alevras]], Greek politician, [[President of Greece]] (b. 1912)<br />
*[[1996]] &ndash; [[Greer Garson]], English-American actress (b. 1904)<br />
*[[1998]] &ndash; [[Norbert Schmitz]], German footballer (b. 1958)<br />
* 1998 &ndash; [[Wendy O. Williams]], American singer-songwriter ([[Plasmatics]]) (b. 1949)<br />
* 1998 &ndash; [[Tammy Wynette]], American singer-songwriter (b. 1942)<br />
*[[1999]] &ndash; [[Red Norvo]], American vibraphone player and composer (b. 1908)<br />
*[[2000]] &ndash; [[Habib Bourguiba]], Tunisian politician, 1st [[President of Tunisia]] (b. 1903)<br />
*[[2001]] &ndash; [[Charles Pettigrew]], American singer-songwriter ([[Charles & Eddie]]) (b. 1963)<br />
*[[2003]] &ndash; [[David Bloom]], American journalist (b. 1963)<br />
* 2003 &ndash; [[Gerald Emmett Carter]], Canadian cardinal (b. 1912)<br />
* 2003 &ndash; [[Babatunde Olatunji]], Nigerian drummer, educator, and activist (b. 1927)<br />
*[[2004]] &ndash; [[Lou Berberet]], American baseball player (b. 1929)<br />
* 2004 &ndash; [[Larisa Bogoraz]], Russian linguist and activist (b. 1929)<br />
* 2004 &ndash; [[Niki Sullivan]], American guitarist ([[The Crickets]]) (b. 1937)<br />
*[[2005]] &ndash; [[Rainier III, Prince of Monaco]] (b. 1923)<br />
*[[2006]] &ndash; [[Maggie Dixon]], American basketball player and coach (b. 1977)<br />
* 2006 &ndash; [[Francis L. Kellogg]], American diplomat (b. 1917)<br />
* 2006 &ndash; [[Stefanos Stratigos]], Greek actor (b. 1926)<br />
*[[2007]] &ndash; [[Luigi Comencini]], Italian director and producer (b. 1916)<br />
*[[2009]] &ndash; [[J. M. S. Careless]], Canadian historian (b. 1919)<br />
* 2009 &ndash; [[Shawn Mackay]], Australian rugby player (b. 1982)<br />
*[[2010]] &ndash; [[Wilma Mankiller]], American tribal leader (b. 1945)<br />
* 2010 &ndash; [[Neva Morris]], American super-centenarian (b. 1895)<br />
* 2010 &ndash; [[Corin Redgrave]], English actor (b. 1939)<br />
*[[2011]] &ndash; [[Sujatha (actress)|Sujatha]], Indian actress (b. 1952)<br />
* 2011 &ndash; [[Nabi Bux Khan Baloch]], Pakistani scholar (b. 1917)<br />
* 2011 &ndash; [[Gerald Finnerman]], American cinematographer (b. 1931)<br />
*[[2012]] &ndash; [[Roland Guilbault]], American admiral (b. 1934)<br />
* 2012 &ndash; [[Thomas Kinkade]], American painter (b. 1958)<br />
* 2012 &ndash; [[Fang Lizhi]], Chinese astrophysicist (b. 1936)<br />
* 2012 &ndash; [[Reed Whittemore]], American poet and critic (b. 1919)<br />
*[[2013]] &ndash; [[Hilda Bynoe]], Grenadian politician, 2nd [[Governor of Grenada]] (b. 1921)<br />
* 2013 &ndash; [[Johnny Esaw]], Canadian sportscaster (b. 1925)<br />
* 2013 &ndash; [[Matt Gilsenan]], Irish footballer, coach, and manager (b. 1915)<br />
* 2013 &ndash; [[Bill Guttridge]], English footballer and manager (b. 1931)<br />
* 2013 &ndash; [[Bigas Luna]], Spanish director and screenwriter (b. 1946)<br />
* 2013 &ndash; [[Michael Norgrove]], Zambian-English boxer (b. 1981)<br />
* 2013 &ndash; [[Miguel Poblet]], Spanish cyclist (b. 1928)<br />
* 2013 &ndash; [[Ottmar Schreiner]], German lawyer and politician (b. 1946)<br />
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==Holidays and observances==<br />
* [[Public holidays in Thailand|Chakri Day]], commemorating the reign of the [[Chakri Dynasty]]. ([[Thailand]])<br />
*Christian [[Feast Day]]:<br />
**[[Brychan]]<br />
**[[Patriarch Eutychius of Constantinople|Eutychius of Constantinople]] ([[Byzantine Church]])<br />
**[[Saint Marcellinus of Carthage|Marcellinus of Carthage]]<br />
**[[Pope Celestine I]] ([[Roman Catholic Church]])<br />
**[[Pope Sixtus I]]<br />
**[[April 6 (Eastern Orthodox liturgics)]]<br />
*[[Tartan Day]] ([[United States]] & [[Canada]])<br />
<br />
==External links==<br />
{{commons}}<br />
* [http://www.april6.org International Day of Sport for Development and Peace]<br />
* [http://news.bbc.co.uk/onthisday/hi/dates/stories/april/6 BBC: On This Day]<br />
* {{NYT On this day|month=04|day=06}}<br />
* [http://www1.sympatico.ca/cgi-bin/on_this_day?mth=Apr&day=06 On This Day in Canada]<br />
{{months}}<br />
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{{DEFAULTSORT:April 06}}<br />
[[Category:Days of the year]]<br />
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'''Computable topology''' studies the topological and algebraic structure of computation. Computable topology includes algorithmic topology and therefore encompasses computer science. [[Computational topology]] is equivalent to the topology of [[lambda calculus|&lambda;-calculus]]. Within [[computer science]] computational forms can be reduced to λ-calculus's functional based mathematics. As shown by [[Allan Turing]] and [[Alonzo Church]], the λ-calculus is strong enough to describe all mechanically computable functions (see [[Church-Turing thesis]]).<ref>Church 1934:90 footnote in Davis 1952</ref><ref>Turing 1936–7 in Davis 1952:149</ref><ref>Barendregt, H.P., The Lambda Calculus Syntax and Semantics. North-Holland Publishing Company. 1981</ref> Lambda-calculus is then a foundational mathematics easily made into a principle programming language from which other languages can be built. For this reason when considering the [[topology]] of computation it is suitable to focus on the topology of λ-calculus. Functional programming, e.g. type free [[lambda Calculus]], originated as a theoretical [[foundation of mathematics]]. The premise relies on functional computability, where objects and functions are of the same type. The [[topology]] of λ-calculus is the [[#Scott Topology|Scott topology]], and when restricted to continuous functions the type free λ-Calculus amounts to a [[topological space]] reliant on the [[tree topology]]. Both the Scott and Tree topologies exhibit continuity with respect to the [[binary operators]] of application ( f ''applied to'' a = fa ) and abstraction ((λx.t(x))a = t(a)) with a modular equivalence relation based on a [[congruence relation|congruency]]. The algebraic structure of computation may also be considered as equivalent to the algebraic structure of λ-calculus, meaning the λ-algebra. The λ-algebra is found to be an extension of the combinatory algebra, with an element introduced to accommodate abstraction.<br />
<br />
A primary concern of algorithmic topology, as its name suggests, is to develop efficient [[algorithm]]s for solving topological problems, or using topological methods to solve algorithmic problems from other fields.<br />
<br />
==Computational topology from &lambda;-calculus topology==<br />
Type free λ-calculus treats functions as rules and does not differentiate functions and the objects which they are applied to, meaning λ-calculus is [[data type|type]] free. A by-product of type free λ-Calculus is an [[effective method|effective computability]] equivalent to [[recursion|general recursion]] and [[Turing machine]]s.<ref name="Barendregt">Barendregt, H.P., The Lambda Calculus Syntax and Semantics. North-Holland Publishing Company. 1981.</ref> The set of λ -terms can be considered a functional topology in which a function space can be [[embedding|embedded]], meaning λ mappings within the space X are such that λ:X → X.<ref name="Barendregt" /><ref name="ScottModels">D. S. Scott. Models for the &lambda;-calculus. Informally distributed, 1969. Notes, December 1969, Oxford Univ.</ref> Introduced November 1969, [[Dana Scott]]'s untyped set theoretic model constructed a proper topology for any λ-calculus model whose function space is limited to continuous functions.<ref name="Barendregt" /><ref name="ScottModels" /> The result of a [[Scott continuous]] λ-calculus topology is a function space built upon a programming semantic allowing fixed point combinatorics, such as the [[Y Combinator]], and data types.<ref>Gordon, M.J.C., The Denotational Description of Programming Languages. Springer Verlag, Berlin. 1979.</ref><ref>Scott, D. S. and Strachey, C. Toward a Mathematical Semantics for Computer Languages, Proc. Symp. on Computers and Automata, Polytechnic Institute of Brooklyn, 21, pp. 19-46. 1971.</ref> By 1971, λ-calculus was equipped to define any sequential computation and could be easily adapted to parallel computations.<ref>G. Berry, Sequential algorithms on concrete data structures, Theoretical Computer Science 20, 265-321 (1982).</ref> The reducibility of all computations to λ-calculus allows these λ-topological properties to become adopted by all programming languages.<ref name="Barendregt" /><br />
<br />
==Computational Algebra from &lambda;-calculus algebra==<br />
Based on the operators within [[lambda calculus]], application and abstraction, it is possible to develop an algebra whose group structure uses application and abstraction as binary operators. Application is defined as an operation between [[lambda term]]s producing a λ-term, e.g. the application of λ onto the lambda term ''a'' produces the lambda term ''&lambda;a''. Abstraction incorporates undefined variables by denoting λx.t(x) as the function assigning the variable ''a'' to the lambda term with value ''t(a)'' via the operation ((λ x.t(x))a = t(a)). Lastly, an [[equivalence relation]] emerges which identifies λ-terms modulo convertible terms, an example being [[beta normal form]].<br />
<br />
==Scott Topology==<br />
The Scott Topology is essential in understanding the topological structure of computation as expressed through the λ-calculus. Scott found that after constructing a function space using λ-calculus one obtains a [[Kolmogorov space]], a <math>T_o</math> topological space which is [[homeomorphic]] to itself and exhibits [[pointwise convergence]], in short the [[product topology]].<ref>D. S. Scott. “Continuous Lattices.” Oxford University Computing Laboratory August, 1971.</ref> It is the ability of self homeomorphism as well as the ability to embed every space into such a space, denoted [[Scott continuous]], as previously described which allows Scott's topology to be applicable to logic and recursive function theory. Scott approaches his derivation using a [[complete lattice]], resulting in a topology dependent on the lattice structure. It is possible to generalise Scott's theory with the use of [[complete partial order]]s. For this reason a more general understanding of the computational topology is provided through complete partial orders. We will re-iterate to familiarize ourselves with the notation to be used during the discussion of Scott topology.<br />
<br />
Complete partial orders are defined as follows:<br />
<br />
First, given the [[partially ordered set]] D=(D,≤) where a subset ''X'' of ''D'', ''X'' ≤ ''D'' is directed, i.e.:<br />
::if ''X'' &ne; <math>\empty</math> and<br />
::<math>\forall</math> ''x,y'' &isin; ''X'' <math>\exists</math> ''z'' &isin; ''X'' where ''x''&le; ''z'' & ''y'' &le; ''z''<br />
<br />
<br />
''D'' is a [[complete partial order]] (cpo) if:<br />
<br />
::<math>\exists</math> ''bottom'' element <math>\perp</math> such that <math>\perp</math> &isin; ''D'' & <math>\forall</math> ''x'' &isin; ''D'' <math>\perp</math> &le; ''x''<br />
<br />
::<math>\cdot</math> Every directed X <math>\subseteq</math>D there exists a [[supremum]].<br />
<br />
We are now able to define the '''Scott Topology''' over a cpo (D, ≤ ).<br />
<br />
''O'' <math>\subseteq</math> ''D'' is ''open'' if:<br />
<br />
::(1) for x &isin; O, and x &le; y, then y &isin; O, i.e. O is an [[upper set]].<br />
<br />
::(2) for a directed set X <math>\subseteq</math> D, and [[supremum]](X) &isin; O, then X <math>\cap</math> O <math>\neq</math> <math>\empty </math>.<br />
<br />
<br />
Using the Scott topological definition of open it is apparent that all topological properties are met. <br />
<br />
::<math>\cdot</math><math>\empty</math> and D, i.e. the empty set and whole space, are open.<br />
<br />
::<math>\cdot</math>Open sets are open under arbitrary unions and under intersection:<br />
:::: ''Proof'': Assume <math>U_i</math> is open where i &isin; I, I being the index set. We define U = <math>\cup</math>{ <math>U_i</math> ; i &isin; I}. Take ''b'' as an element of the upper set of U, therefore a &le; ''b'' for some ''a'' &isin; U It must be that ''a'' &isin; <math>U_i</math> for some i, likewise ''b'' &isin; upset(<math>U_i</math>). U must therefore be upper as well since <math>U_i</math> &isin; U.<br />
<br />
::::Lastly, if D is a directed set with a supremum in U, then by assumption sup(D) &isin; <math>U_i </math>where <math>U_i </math>is open. There is necessarily a ''b'' &isin; D where upper(b) <math>\cap</math> D <math>\subseteq U_{i} \subseteq</math> U. The union of open sets <math> U_i </math>is therefore open.<br />
<br />
::<math>\cdot</math>Open sets under intersection are open:<br />
::::''Proof'': Given two open sets, U and V, we define W = U<math>\cap</math>V. If W=<math>\empty</math> then W is open. If non-empty say ''b'' &isin; upset(W) (the upper set of W), then for some ''a'' &isin; W, ''a'' &le; ''b''. Since a &isin; U <math>\cap</math>V, and b an element of the upper set of both U and V, then ''b'' &isin; W. W being open implies the intersection of open sets is open.<br />
<br />
<br />
Though not shown here, it is the case that the map <math>f: D \rightarrow D^{'}</math> is continuous iff f(sup(X)) = sup(f(X)) for all directed X<math>\subseteq</math> D, where f(X) = {f(x) | x ∈ X} and the second supremum in <math>D^{'}</math>.<ref name="Barendregt" /><br />
<br />
Before we begin explaining that application as common to λ-calculus is continuous within the Scott topology we require a certain understanding of the behavior of supremums over continuous functions as well as the conditions necessary for the product of spaces to be continuous namely<br />
<br />
:(1) With <math>{f_{i}}_{i}</math> <math>\subseteq [D \rightarrow D^{'}]</math> be a directed family of maps, then <math>f(x) = \cup_{i}f_{i}(x)</math> if well defined and continuous.<br />
<br />
:(2) If F <math>\subseteq [D \rightarrow D^{'}]</math> is directed and cpo and <math> [D \rightarrow D^{'}]</math> a cpo where sup({f(x) | f &isin; F).<br />
<br />
<br />
<br />
We now show the continuity of ''application''. Using the definition of application as follows: <br />
<br />
:::Ap: <math>[D\rightarrow D^{'}] \times D \rightarrow D^{'}</math> where Ap(f,x) = f(x).<br />
<br />
Ap is continuous with respect to the Scott topology on the product (<math> [D \rightarrow D^{'}] \times D \rightarrow D^{'}</math>) :<br />
<br />
::''Proof'': &lambda;x.f(x) = f is continuous. Let h = &lambda; f.f(x). For directed F<math>\subseteq [D \rightarrow D^{'}]</math><br />
<br />
::h(sup(F)) = sup(F)(x)<br />
<br />
:::: = sup( {f(x) | f &isin; F} )<br />
<br />
:::: = sup( {h(f) | f &isin; F} )<br />
<br />
:::: = sup( h(F) )<br />
<br />
::By definition of Scott continuity h has been shown continuous. All that is now required to prove is that ''application'' is continuous when it's separate arguments are continuous, i.e. <math>[D \rightarrow D^{'}] </math>and <math>D \rightarrow D^{'} </math>are continuous, in our case ''f'' and ''h''.<br />
<br />
::Now abstracting our argument to show <math>f:D \times D^{'} \rightarrow D^{''} </math> with ''g'' = &lambda; x.f(x,<math>x_{0}</math>) and ''d'' = &lambda;<math> x^'.f(x_0,x^')</math> as the arguments for D and <math>D^'</math> respectively, then for a directed X <math>\subseteq</math> D<br />
<br />
::g(sup(X)) = f( sup(X),<math>x_{0}^{'})</math> )<br />
<br />
:::: = f( sup( (x,<math>x_{0}^{'}</math>) | x &isin; X} ))<br />
<br />
:::: (since ''f'' is continuous and {(x,<math>x_{0}^{'}</math>) | x &isin; X}) is directed):<br />
<br />
:::: = sup( {f(x,<math>x_{0}^{'}</math>) | x &isin; X} )<br />
<br />
:::: = sup(g(X))<br />
<br />
::g is therefore continuous. The same process can be taken to show d is continuous.<br />
::It has now been shown application is continuous under the Scott topology.<br />
<br />
<br />
In order to demonstrate the Scott topology is a suitable fit for λ-calculus it is necessary to prove ''abstraction'' remains continuous over the Scott topology. Once completed it will have been shown that the mathematical foundation of λ-calculus is a well defined and suitable candidate functional paradigm for the Scott topology.<br />
<br />
<br />
With f ∈ [D <math>\times D^{'} \rightarrow D^{''}</math>] we define <math>\check{f}</math> (x) =λ y ∈ <math>D^{'}</math>f(x,y)We will show:<br />
<br />
:(i) <math>\check{f} </math> is continuous, meaning <math>\check{f}</math> &isin; <math>[D \rightarrow [D^{'} \rightarrow D^{''}] </math><br />
<br />
:(ii) &lambda; <math> f.\check{f}: [D \times D^{'} \rightarrow D^{''}]\rightarrow [D\rightarrow [D^{'}\rightarrow D^{''}]</math> is continuous.<br />
<br />
::''Proof'' (i): Let X <math>\subseteq</math> D be directed, then<br />
<br />
::<math>\check{f}</math>(sup(X)) = &lambda; y.f( sup(X),y )<br />
<br />
:::: = &lambda; y.<math>sup_{x \isin X}</math>( f(x,y) )<br />
<br />
:::: = <math>sup_{x \isin X}</math>( &lambda;y.f(x,y) )<br />
<br />
:::: = sup(<math>\check{f}</math>(X))<br />
<br />
::''Proof'' (ii): Defining L = &lambda; <math> f.\check{f} </math> then for F <math> \subseteq [D \times D^{'} \rightarrow D^{''}]</math> directed<br />
<br />
::L(sup(F)) = &lambda; x &lambda; y. (sup(F))(x,y))<br />
<br />
:::: = &lambda; x &lambda; y. <math>sup_{y \isin F}</math>f(x,y)<br />
<br />
:::: = <math>sup_{y \isin F} </math>&lambda;x &lambda;y.f(x,y)<br />
<br />
:::: = sup(L(F))<br />
It has not been demonstrated how and why the λ-calculus defines the Scott topology.<br />
<br />
==Böhm trees and Computational Topology==<br />
[[Böhm trees]], easily represented graphically, express the computational behavior of a [[lambda term]]. It is possible to predict the functionality of a given lambda expression from reference to its correlating Böhm tree.<ref name="Barendregt" /> Böhm trees can be seen somewhat analogous to <math>\mathbb{R}</math> where the Böhm tree of a given set is similar to the continued fraction of a real number, and what is more, the Böhm tree corresponding to a sequence in [[normal form]] is finite, similar to the rational subset of the Reals.<br />
<br />
Böhm trees are defined by a mapping of elements within a sequence of numbers with ordering (≤, lh) and a binary operator * to a set of symbols. The Böhm tree is then a relation among a set of symbols through a partial mapping <math>\psi</math>.<br />
<br />
Informally Böhm trees may be conceptualized as follows:<br />
<br />
:Given: <math>\Sigma</math> = <math>\perp \cup </math> { &lambda; x_{1} <math>\cdots </math>x_{n} . y | n &isin; <math> \mathbb{N}, x_{1} ... x_{n}</math>y are variables and denoting BT(M) as the Böhm tree for a lambda term M we then have:<br />
<br />
:BT(M) = <math>\perp</math> if M is unsolvable (therefore a single node)<br />
<poem> <br />
BT(M) = λ<math>\vec{x}</math>.y<br />
/&nbsp;&nbsp;&nbsp;&nbsp;\ <br />
BT(<math> M_{1} )</math>&nbsp;&nbsp;&nbsp;BT(<math> M_{m}</math> ) ; if M is solvable<br />
</poem> <br />
More Formally:<br />
<br />
<math>\Sigma</math> is defined as a set of symbols. The Böhm tree of a λ term M, denoted BT(M), is the <math>\Sigma</math> labelled tree defined as follows:<br />
<br />
::If M is unsolvable:<br />
<br />
::BT(M)(< >) = <math>\perp</math>,<br />
<br />
::BT(M)(<math><k> * \alpha</math>) is unsolvable <math>\forall k, \alpha</math><br />
<br />
If M is solvable, where M = λ x_{1}<math> \cdots x_{n}.y M_{0} \cdots M_{m-1}</math>:<br />
<br />
::BT(M)(< >) = &lambda; x_{1} <math>\cdots x_{n}.y</math><br />
<br />
::BT(M)(<math><k> * \alpha</math>) = BT(M_k)(<math>\alpha</math>) <math>\forall \alpha</math> and k < m<br />
<br />
:::::= undefined <math>\forall \alpha</math> and k <math>\ge</math> m<br />
<br />
We may now move on to show that Böhm trees act as suitable mappings from the tree topology to the scott topology. Allowing one to see computational constructs, be it within the Scott or tree topology, as Böhm tree formations.<br />
<br />
===Böhm tree and tree topology===<br />
<br />
It is found that [[Böhm tree]]'s allow for a [[continuous]] mapping from the tree topology to the Scott topology. More specifically:<br />
<br />
We begin with the cpo B = (B,<math>\subseteq</math>) on the Scott topology, with ordering of Böhm tree's denoted M<math>\subseteq</math> N, meaning M, N are trees and M results from N. The [[tree topology]] on the set <math>\Gamma</math> is the smallest set allowing for a continuous map<br />
<br />
::BT:<math>\Gamma \rightarrow </math>''B''.<br />
<br />
An equivalent definition would be to say the open sets of <math>\Gamma</math> are the image of the inverse Böhm tree <math> BT^{-1}</math> (O) where O is Scott open in B.<br />
<br />
The applicability of the Bömh trees and the tree topology has many interesting consequences to λ-terms expressed topologically:<br />
<br />
:Normal forms are found to exist as isolated points.<br />
<br />
:Unsolvable &lambda;-terms are compactification points.<br />
<br />
:Application and abstraction, similar to the Scott topology, are continuous on the tree topology.<br />
<br />
==Algebraic structure of Computation==<br />
<br />
New methods of interpretation of the λ-calculus are not only interesting in themselves but allow new modes of thought concerning the behaviors of computer science. The binary operator within the λ-algebra A is application. Application is denoted <math>\cdot</math> and is said to give structure <math>A=(X, \cdot)</math>. A [[Combinatory algebra]] allows for the application operator and acts as a useful starting point but remains insufficient for the λ-calculus in being unable to express abstraction. The λ algebra becomes a combinatory algebra M combined with a syntactic operator λ* that transforms a term ''B(x,y)'', with constants in ''M'', into C(<math>\hat{y}</math>)<math>\equiv</math> λ* x.B(x,<math>\hat{y}</math>). It is also possible to define an [[extension]] model to circumvent the need of the λ* operator by allowing <math>\forall</math>x (fx =gx) <math>\rightarrow</math> f =g . The construction of the λ-algebra through the introduction of an abstraction operator proceeds as follows:<br />
<br />
We must construct an algebra which allows for solutions to equations such as axy = xyy such that a = λ xy.xyy there is need for the combinatory algebra. Relevant attributes of the combinatory algebra are:<br />
<br />
Within combinatory algebra there exists ''applicative structures''. An applicative structure W is a combinatory algebra provided:<br />
::<math>\cdot</math>W is non-trival, meaning W has [[cardinality]] > 1<br />
::<math>\cdot</math>W exibits combinatory completeness (see [[combinatory logic|completeness of the S-K basis]]). More specifically: for every term A &isin; the set of terms of W, and <math> x_1, ... , x_n </math> with the free variables of A within <math>{x_1, ... ,x_n}</math> then:<br />
::: <math> \exists f \forall x_1 \cdot \cdot \cdot x_n</math> where <math> fx_1 \cdot \cdot \cdot x_n = A </math><br />
<br />
The combiniatory algebra is:<br />
<br />
:<math>\cdot</math>Never commutative<br />
<br />
:<math>\cdot</math>Not associative.<br />
<br />
:<math>\cdot</math>Never finite.<br />
<br />
:<math>\cdot</math>Never recursive.<br />
<br />
Combinatory algebras remain unable to act as the algebraic structure for λ-calculus, the lack of recursion being a major disadvantage. However the existence of an applicative term <math>A(x, \vec{y}</math>) provides a good starting point to build a λ-calculus algebra. What is needed is the introduction of a [[lambda term]], i.e. include λx.A(x, <math>\vec{y}</math>). <br />
<br />
We begin by exploiting the fact that within a combinatory algebra M, with A(x, <math>\vec{y}</math>) within the set of terms, then:<br />
::<math>\forall \vec{y}</math> <math>\exists b</math> s.t. bx = A(x, <math>\vec{y}</math>).<br />
We then require b have a dependence on <math> \vec{y}</math> resulting in:<br />
:::<math>\forall x</math> B(<math>\vec{y}</math>)x = A(x, <math>\vec{y}</math>).<br />
B(<math>\vec{y}</math>) becomes equivalent to a λ term, and is therefore suitably defined as follows: B(<math>\vec{y}) \equiv</math> λ*.<br />
<br />
A ''pre-&lambda;-algebra'' (pλA) can now be defined.<br />
::p&lambda;A is an applicative structure W = (X,<math>\cdot</math>) such that for each term A within the set of terms within W and for every x there is a term &lambda;*x.A &isin; T(W) (T(W) <math>\equiv</math> the terms of W) where (the set of free variables of &lambda;*x.A) = (the set of free variables of A) - {x}. W must also demonstrate:<br />
::<math>(\beta)</math> (&lambda;*x.A)x = A<br />
::<math>\alpha_{1}</math>&lambda;*x.A<math>\equiv</math> &lambda;*x.A[x:=y] provided y is not a free variable of A<br />
::<math>\alpha_{2}</math>(&lambda;*x.A)[y:=z]<math>\equiv</math>&lambda;*x.A[x:=y] provided y,z &ne; x and z is not a free variable of A<br />
<br />
Before defining the full λ-algebra we must introduce the following definition for the set of λ-terms within W denoted <math>\Gamma(W) </math> with the following requirements:<br />
::a &isin; W <math>\Rightarrow c_{a} \isin \Gamma(W) </math><br />
::x &isin; <math> \Gamma(W) </math> for x &isin; (<math> v_0, v_1, ... </math>)<br />
::M,N &isin; <math>\Gamma(W) \Rightarrow </math> (MN) &isin; <math> \Gamma(W) </math><br />
::M &isin; <math>\Gamma(W) \Rightarrow</math> (&lambda;x.M) &isin; <math>\Gamma(W)</math><br />
<br />
A mapping from the terms within <math>\Gamma(W)</math> to all λ terms within W, denoted '''*''' : <math>\Gamma(W)\rightarrow \Tau(W) </math>, can then be designed as follows:<br />
::<math>v_{i}^{*} = w_i, c_{a}^{*} = c_a </math><br />
::(MN)* = M* N*<br />
::(&lambda;x.M)* = &lambda;* x*.M*<br />
<br />
We now define '''λ'''(M) to denote the extension after evaluating the terms within <math>\Gamma(W)</math>. <br />
::&lambda;x.(&lambda;y.yx)<math>c_a</math> = &lambda;x.<math>c_a</math>x in '''&lambda;'''(W).<br />
<br />
Finally we obtain the full ''&lambda;-algebra'' through the following definition:<br />
::(1) A &lambda;-algebra is a p&lambda;A W such that for M,N &isin; <math>\Gamma</math>(W):<br />
:::'''&lambda;'''(W) [[turnstile (symbol)|<math>\vdash</math>]] M = N <math>\Rightarrow</math> W <math> \vDash </math> M = N.<br />
<br />
Though arduous, the foundation has been set for a proper algebraic framework for which the λ-calculus, and therefore computation, may be investigated in a [[group theory|group theoretic]] manner.<br />
<br />
==References==<br />
<br />
{{reflist}}<br />
<br />
[[Category:Computational topology]]<br />
[[Category:Computational complexity theory]]<br />
[[Category:Computational science|Topology]]</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=82959Main Page2014-08-18T19:09:38Z<p>10.68.16.65: </p>
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<div>In [[statistical classification]], the '''Bayes error rate''' is the lowest possible error rate for a given class of classifier.<ref name=stat >Fukunaga, Keinosuke (1990) ''Introduction to Statistical Pattern Recognition'' by ISBN 0122698517 pages 3 and 97</ref><ref name=Tumer >K. Tumer, K. (1996) "Estimating the Bayes error rate through classifier combining" in ''Proceedings of the 13th International Conference on Pattern Recognition'', Volume 2, 695–699 </ref><br />
<br />
A number of approaches to the estimation of the Bayes error rate exist. One method seeks to obtain analytical bounds which are inherently dependent on distribution parameters, and hence difficult to estimate. Another approach focuses on class densities, while yet another method combines and compares various classifiers.<ref name=Tumer /><br />
<br />
The Bayes error rate finds important use in the study of patterns and [[machine learning]] techniques.<br />
<br />
==Error Determination==<br />
In terms of machine learning and pattern classification, the data set can be discretely divided into 2 or more classes. Each element of the dataset is called an '''instance''' and the class it belongs to is called the '''lable'''.<br />
The bayes error rate of the dataset classifier is probability of the classifier to incorrectly classify an instance. <br />
For an n-multiclass classifier, the bayes error rate may be calculated as follows :<br />
<br /><br /><br />
<math>\sum_{i=1}^{i=n}\textstyle \int\limits_{x\in H_{i}}P(C_{i}|x)p(x)\, dx</math><br />
<br /> <br /><br />
Where x is an instance, C is the class into which an instance is classified, H<math>_{i}</math> is the area/region that the classifier function '''h''' classifies as C<math>_{i}</math><br />
<br /><br />
A bayes error is non-zero if the distributions of the instances overlap, i.e. a certain instance x can wear more than one lable.<br />
<br />
==See also==<br />
* [[Naive Bayes classifier]]<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
[[Category:Statistical classification]]<br />
[[Category:Bayesian statistics|Error rate]]<br />
<br />
{{Statistics-stub}}</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=82926Main Page2014-08-18T18:59:59Z<p>10.68.16.65: </p>
<hr />
<div>'''Multidimensional sampling''' is the process of converting a function of a multidimensional variable into a discrete collection of values of the function measured on a discrete set of points. This article presents the basic result due to Petersen and Middleton<ref name="petmid62">D. P. Petersen and D. Middleton, "Sampling and Reconstruction of Wave-Number-Limited Functions in N-Dimensional Euclidean Spaces", Information and Control, vol. 5, pp. 279–323, 1962.</ref> on conditions for perfectly reconstructing a [[wavenumber]]-limited function from its measurements on a discrete [[Lattice (group)|lattice]] of points. This result, also known as the '''Petersen–Middleton theorem''', is a generalization of the [[Nyquist–Shannon sampling theorem]] for sampling one-dimensional bandlimited functions to higher-dimensional Euclidean spaces.<br />
<br />
In essence, the Petersen–Middleton theorem shows that a wavenumber-limited function can be perfectly reconstructed from its values on an infinite [[Lattice (group)|lattice]] of points, provided the lattice is fine enough. The theorem provides conditions on the lattice under which perfect reconstruction is possible. <br />
<br />
As with the Nyquist–Shannon sampling theorem, this theorem also assumes an idealization of any real-world situation, as it only applies to functions that are sampled over an infinitude of points. Perfect reconstruction is mathematically possible for the idealized model but only an approximation for real-world functions and sampling techniques, albeit in practice often a very good one.<br />
<br />
==Preliminaries==<br />
[[Image:Hexagonal_sampling_lattice.png|thumb|Fig. 1: A hexagonal sampling lattice <math>\Lambda</math> and its basis vectors ''v''<sub>1</sub> and ''v''<sub>2</sub>|right|200px]]<br />
[[Image:Reciprocal_lattice.png|thumb|Fig. 2: The reciprocal lattice <math>\Gamma</math> corresponding to the lattice <math>\Lambda</math> of Fig. 1 and its basis vectors ''u''<sub>1</sub> and ''u''<sub>2</sub> (figure not to scale).|right|200px]]<br />
The concept of a [[Bandlimiting|bandlimited]] function in one dimension can be generalized to the notion of a wavenumber-limited function in higher dimensions. Recall that the [[Fourier transform]] of an integrable function ''ƒ(.)'' on ''n''-dimensional Euclidean space is defined as:<br />
:<math>\hat{f}(\xi) = \mathcal{F}(f)(\xi) = \int_{\Re^n} f(x) e^{-2\pi i \langle x,\xi \rangle} \, dx</math><br />
where ''x'' and ''ξ'' are ''n''-dimensional [[vector (mathematics)|vectors]], and <math>\langle x,\xi \rangle</math> is the [[inner product]] of the vectors. The function ''ƒ(.)'' is said to be wavenumber-limited to a set <math>\Omega</math> if the Fourier transform satisfies <math>\hat{f}(\xi) = 0</math> for <math>\xi \notin \Omega</math>. <br />
<br />
Similarly, the configuration of uniformly spaced sampling points in one-dimension can be generalized to a [[Lattice (group)|lattice]] in higher dimensions. A lattice is a collection of points <math>\Lambda \subset \Re^n</math> of the form <br />
<math><br />
\Lambda = \left\{ \sum_{i=1}^n a_i v_i \; | \; a_i \in\Bbb{Z} \right\}<br />
</math><br />
where {''v''<sub>1</sub>, ..., ''v''<sub>''n''</sub>} is a [[Basis (linear algebra)|basis]] for <math>\Re^n</math>. The [[reciprocal lattice]] <math>\Gamma</math> corresponding to <math>\Lambda</math> is defined by<br />
:<math><br />
\Gamma = \left\{ \sum_{i=1}^n a_i u_i \; | \; a_i \in\Bbb{Z} \right\}<br />
</math><br />
where the vectors <math>u_i</math> are chosen to satisfy <math>\langle u_i, v_j \rangle = \delta_{ij}</math>. An example of a sampling lattice is a [[hexagonal lattice]] depicted in Figure 1. The corresponding reciprocal lattice is shown in Figure 2.<br />
<br />
==The theorem==<br />
<br />
Let <math>\Lambda</math> denote a lattice in <math>\Re^n</math> and <math>\Gamma</math> the corresponding reciprocal lattice. The theorem of Petersen and Middleton<ref name="petmid62"></ref> states that a function ''f(.)'' that is wavenumber-limited to a set <math>\Omega \subset \Re^n</math> can be exactly reconstructed from its measurements on <math>\Lambda</math> provided that the set <math>\Omega</math> does not overlap with any of its shifted versions <math>\Omega + x </math> where the shift ''x'' is any nonzero element of the reciprocal lattice <math>\Gamma</math>. In other words, ''f(.)'' can be exactly reconstructed from its measurements on <math>\Lambda</math> provided that <math>\Omega \cap \{x+y:y\in\Omega\} = \phi </math> for all <math>x \in \Gamma\setminus\{0\}</math>.<br />
<br />
==Reconstruction==<br />
[[Image:Unaliased_sampled_spectrum_in_2D.png|thumb|Fig. 3: Support of the sampled spectrum <math>\hat f_s(.)</math> obtained by hexagonal sampling of a two-dimensional function wavenumber-limited to a circular disc. The blue circle represents the support <math>\Omega</math> of the original wavenumber-limited field, and the green circles represent the repetitions. In this example the spectral repetitions do not overlap and hence there is no aliasing. The original spectrum can be exactly recovered from the sampled spectrum.|right|300px]]<br />
The generalization of the [[Poisson summation formula]] to higher dimensions <ref name="stewei71">E. M. Stein and G. Weiss, "Introduction to Fourier Analysis on Euclidean Spaces", Princeton University Press, Princeton, 1971.</ref> can be used to show that the samples, <math>\{f(x): x \in \Lambda\} </math>, of the function ''f(.)'' on the lattice <math>\Lambda</math> are sufficient to create a [[periodic summation]] of the function <math>\hat f(.)</math>. The result is:<br />
<br />
{{NumBlk|:|<math>\hat f_s(\xi)\ \stackrel{\mathrm{def}}{=} \sum_{y \in \Gamma} \hat f\left(\xi - y\right) = \sum_{x \in \Lambda} |\Lambda|f(x) \ e^{-i 2\pi \langle x, \xi \rangle},</math>|{{EquationRef|Eq.1}}}}<br />
where <math>|\Lambda| </math> represents the volume of the [[parallelepiped]] formed by the vectors {''v''<sub>1</sub>, ..., ''v''<sub>''n''</sub>}. This periodic function is often referred to as the sampled spectrum and can be interpreted as the analogue of the [[discrete-time Fourier transform]] (DTFT) in higher dimensions. If the original wavenumber-limited spectrum <math>\hat f(.)</math> is supported on the set <math>\Omega</math> then the function <math>\hat f_s(.)</math> is supported on periodic repetitions of <math>\Omega</math> shifted by points on the reciprocal lattice <math>\Gamma</math>. If the conditions of the Petersen-Middleton theorem are met, then the function <math>\hat f_s(\xi)</math> is equal to <math>\hat f(\xi)</math> for all <math>\xi \in \Omega</math>, and hence the original field can be exactly reconstructed from the samples. In this case the reconstructed field matches the original field and can be expressed in terms of the samples as<br />
<br />
{{NumBlk|:|<math>f(x) = \sum_{y \in \Lambda} |\Lambda| f(y) \check \chi_\Omega(y - x)</math>,|{{EquationRef|Eq.2}}}}<br />
where <math>\check \chi_\Omega(.)</math> is the inverse Fourier transform of the [[Indicator function|characteristic function]] of the set <math>\Omega</math>. This interpolation formula is the higher-dimensional equivalent of the [[Whittaker–Shannon interpolation formula]]. <br />
<br />
As an example suppose that <math>\Omega</math> is a circular disc. Figure 3 illustrates the support of <math>\hat f_s(.)</math> when the conditions of the Petersen-Middleton theorem are met. We see that the spectral repetitions do not overlap and hence the original spectrum can be exactly recovered.<br />
<br />
==Implications==<br />
<br />
===Aliasing===<br />
{{main|Aliasing}}<br />
[[Image:Aliased_sampled_spectrum_in_2D.png|thumb|Fig. 4: Support of the sampled spectrum <math>\hat f_s(.)</math> obtained by hexagonal sampling of a two-dimensional function wavenumber-limited to a circular disc. In this example, the sampling lattice is not fine enough and hence the discs overlap in the sampled spectrum. Thus the spectrum within <math>\Omega</math> represented by the blue circle cannot be recovered exactly due to the overlap from the repetitions (shown in green), thus leading to aliasing.|right|300px]]<br />
<br />
[[File:Moire pattern of bricks small.jpg|thumb|205px|Fig. 5: Spatial aliasing in the form of a [[Moiré pattern]].]]<br />
[[File:Moire pattern of bricks.jpg|thumb|205px|Fig. 6: Properly sampled image of brick wall.]]<br />
The theorem gives conditions on sampling lattices for perfect reconstruction of the sampled. If the lattices are not fine enough to satisfy the Petersen-Middleton condition, then the field cannot be reconstructed exactly from the samples in general. In this case we say that the samples may be [[Aliasing|aliased]]. Again, consider the example in which <math>\Omega</math> is a circular disc. If the Petersen-Middleton conditions do not hold, the support of the sampled spectrum will be as shown in Figure 4. In this case the spectral repetitions overlap leading to aliasing in the reconstruction.<br />
<br />
A simple illustration of aliasing can be obtained by studying low-resolution images. A gray-scale image can be interpreted as a function in two-dimensional space. An example of aliasing is shown in the images of brick patterns in Figure 5. The image shows the effects of aliasing when the sampling theorem's condition is not satisfied. If the lattice of pixels is not fine enough for the scene, aliasing occurs as evidenced by the appearance of the [[Moiré pattern]] in the image obtained. The image in Figure 6 is obtained when a smoothened version of the scene is sampled with the same lattice. In this case the conditions of the theorem are satisfied and no aliasing occurs.<br />
<br />
===Optimal sampling lattices===<br />
One of the objects of interest in designing a sampling scheme for wavenumber-limited fields is to identify the configuration of points that leads to the minimum sampling density, i.e., the density of sampling points per unit spatial volume in <math>\Re^n</math>. Typically the cost for taking and storing the measurements is proportional to the sampling density employed. Often in practice, the natural approach to sample two-dimensional fields is to sample it at points on a [[Lattice_(group)|rectangular lattice]]. However, this is not always the ideal choice in terms of the sampling density. The theorem of Petersen and Middleton can be used to identify the optimal lattice for sampling fields that are wavenumber-limited to a given set <math>\Omega \subset \Re^d</math>. For example, it can be shown that the lattice in <math>\Re^2</math> with minimum spatial density of points that admits perfect reconstructions of fields wavenumber-limited to a circular disc in <math>\Re^2</math> is the hexagonal lattice<ref name="mer79">D. R. Mersereau, “The processing of hexagonally sampled two-dimensional signals,” Proceedings of the IEEE, vol. 67, no. 6, pp. 930 – 949, June 1979.</ref>. As a consequence, hexagonal lattices are preferred for sampling [[Isotropy|isotropic fields]] in <math>\Re^2</math>.<br />
<br />
==Applications==<br />
<br />
The Petersen–Middleton theorem is useful in designing efficient sensor placement strategies in applications involving measurement of spatial phenomena such as seismic surveys, environment monitoring and spatial audio-field measurements.<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
<br />
{{DSP}}<br />
[[Category:Digital signal processing]]<br />
[[Category:Theorems in Fourier analysis]]</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=82778Main Page2014-08-18T18:08:58Z<p>10.68.16.65: </p>
<hr />
<div>In mathematics, the '''Kervaire semi-characteristic''', introduced by {{harvs|txt|last=Kervaire|authorlink=Michel Kervaire|year=1956}}, is an invariant of manifolds ''M'' of dimension 4''n''+1 taking values in '''Z'''/2'''Z''', given by <br />
:k(M) = <math>\sum_{i=0}^n \dim H^{2i}(M,R)\bmod 2</math><br />
{{harvtxt|Atiyah|Singer|1971}} showed that it is given by the index of a skew-adjoint elliptic operator.<br />
<br />
==References==<br />
<br />
*{{citation|last1= Atiyah|first1= Michael F. |author1-link=Michael Atiyah|last2=Singer|first2= Isadore M. |author2-link=Isadore Singer|title=The Index of Elliptic Operators V|journal=[[Annals of Mathematics. Second Series]]|volume= 93|issue= 1|year= 1971|pages= 139–149|doi= 10.2307/1970757|publisher= The Annals of Mathematics, Vol. 93, No. 1 |jstor=1970757}}<br />
*{{Citation | last1=Kervaire | first1=Michel | title=Courbure intégrale généralisée et homotopie | doi=10.1007/BF01342961 |mr=0086302 | year=1956 | journal=[[Mathematische Annalen]] | issn=0025-5831 | volume=131 | pages=219–252}}<br />
<br />
[[Category:Differential topology]]</div>10.68.16.65https://en.formulasearchengine.com/index.php?title=Main_Page&diff=82314Main Page2014-08-18T16:04:39Z<p>10.68.16.65: </p>
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<div>{| class=wikitable width=280 align=right<br />
!<math>{\tilde{A}}_2</math><br />
!<math>{\tilde{A}}_3</math><br />
|-<br />
![[Triangular tiling]]<br />
![[Tetrahedral-octahedral honeycomb]]<br />
|-<br />
|[[File:Uniform_tiling_333-t1.png|120px]]<BR>With red and yellow equilateral triangles<br />
|[[File:Tetrahedral-octahedral honeycomb2.png|160px]]<BR>With cyan and yellow [[tetrahedron|tetrahedra]], and red rectified tetrahedra ([[octahedron]])<br />
|-<br />
!{{CDD|node_1|split1|branch}}<br />
!{{CDD|node_1|split1|nodes|split2|node}}<br />
|}<br />
In [[geometry]], the '''simplectic honeycomb''' (or '''n-simplex honeycomb''') is a dimensional infinite series of [[Honeycomb (geometry)|honeycomb]]s, based on the <math>{\tilde{A}}_n</math> affine [[Coxeter group]] symmetry. It is given a [[Schläfli symbol]] {3<sup>[n+1]</sup>}, and is represented by a [[Coxeter-Dynkin diagram]] as a cyclic graph of ''n+1'' nodes with one node ringed. It is composed of n-[[simplex]] facets, along with all [[Rectification (geometry)|rectified]] n-simplices. The [[vertex figure]] of an ''n-simplex honeycomb'' is an [[Expansion (geometry)|expanded]] n-[[simplex]].<br />
<br />
In 2 dimensions, the honeycomb represents the [[triangular tiling]], with Coxeter graph {{CDD|node_1|split1|branch}} filling the plane with alternately colored triangles. In 3 dimensions it represents the [[tetrahedral-octahedral honeycomb]], with Coxeter graph {{CDD|node_1|split1|nodes|split2|node}} filling space with alternately tetrahedral and octahedral cells. In 4 dimensions it is called the [[5-cell honeycomb]], with Coxeter graph {{CDD|node_1|split1|nodes|3ab|branch}}, with [[5-cell]] and [[rectified 5-cell]] facets. In 5 dimensions it is called the [[5-simplex honeycomb]], with Coxeter graph {{CDD|node_1|split1|nodes|3ab|nodes|split2|node}}, filling space by [[5-simplex]], [[rectified 5-simplex]], and [[birectified 5-simplex]] facets. In 6 dimensions it is called the [[6-simplex honeycomb]], with Coxeter graph {{CDD|node_1|split1|nodes|3ab|nodes|3ab|branch}}, filling space by [[6-simplex]], [[rectified 6-simplex]], and [[birectified 6-simplex]] facets.<br />
<br />
== By dimension ==<br />
{| class="wikitable"<br />
!height=30|n<br />
!<math>{\tilde{A}}_{2+}</math><br />
!Tessellation<br />
!Vertex figure<br />
!Facets per vertex figure<br />
!Vertices per vertex figure<br />
!Edge figure<br />
|-<br />
|1<br />
|<math>{\tilde{A}}_1</math><br />
|[[File:Regular_apeirogon.png|80px]]<BR>[[Apeirogon]]<BR>{{CDD|node_1|infin|node}}<br />
|{{CDD|node_1}}<br />
|1<br />
|2<br />
| -<br />
|-<br />
|2<br />
|<math>{\tilde{A}}_2</math><br />
|[[Image:Uniform tiling 333-t1.png|80px]]<BR>[[Triangular tiling]]<BR>2-simplex honeycomb<BR>{{CDD|node_1|split1|branch}}<br />
|[[Image:Truncated triangle.png|80px]]<BR>[[Hexagon]]<BR>(Truncated triangle)<BR>{{CDD|node_1|3|node_1}}<br />
|3 [[triangle]]s<BR>3 [[hexagon|rectified triangles]]<br />
|6<br />
|[[Line segment]]<BR>{{CDD|node_1}}<br />
|-<br />
|3<br />
|<math>{\tilde{A}}_3</math><br />
|[[File:Tetrahedral-octahedral honeycomb2.png|80px]]<BR>[[Tetrahedral-octahedral honeycomb]]<BR>3-simplex honeycomb<BR>{{CDD|node_1|split1|nodes|split2|node}}<br />
|[[Image:Uniform polyhedron-33-t02.png|80px]]<BR>[[Cuboctahedron]]<BR>(Cantellated tetrahedron)<BR>{{CDD|node_1|3|node|3|node_1}}<br />
|4+4 [[tetrahedron]]<BR>6 [[octahedron|rectified tetrahedra]]<br />
|12<br />
|[[Rectangle]]<BR>{{CDD|node_1|2|node_1}}<br />
|-<br />
|4<br />
|<math>{\tilde{A}}_4</math><br />
|[[4-simplex honeycomb]]<BR>{{CDD|node_1|split1|nodes|3ab|branch}}<br />
|[[Image:Schlegel half-solid runcinated 5-cell.png|80px]]<BR>[[Runcinated 5-cell]]<BR>{{CDD|node_1|3|node|3|node|3|node_1}}<br />
|5+5 [[5-cell]]s<BR>10+10 [[rectified 5-cell]]s<br />
|20<br />
|[[File:Runcinated_5-cell_verf.png|60px]]<BR>Triangular antiprism<BR>{{CDD|node_h|3|node_h|2|node_h}}<br />
|-<br />
|5<br />
|<math>{\tilde{A}}_5</math><br />
|[[5-simplex honeycomb]]<BR>{{CDD|node_1|split1|nodes|3ab|nodes|split2|node}}<br />
|[[File:5-simplex_t04.svg|80px]]<BR>[[Stericated 5-simplex]]<BR>{{CDD|node_1|3|node|3|node|3|node|3|node_1}}<br />
|6+6 [[5-simplex]]<BR>15+15 [[rectified 5-simplex]]<BR>20 [[birectified 5-simplex]]<br />
|30<br />
|[[File:Stericated_hexateron_verf.png|60px]]<BR>Tetrahedral antiprism<BR>{{CDD|node_h|4|node|3|node|2|node_h}}<br />
|-<br />
|6<br />
|<math>{\tilde{A}}_6</math><br />
|[[6-simplex honeycomb]]<BR>{{CDD|node_1|split1|nodes|3ab|nodes|3ab|branch}}<br />
|[[File:6-simplex_t05.svg|80px]]<BR>[[Pentellated 6-simplex]]<BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1}}<br />
|7+7 [[6-simplex]]<BR>21+21 [[rectified 6-simplex]]<BR>35+35 [[birectified 6-simplex]]<br />
|42<br />
|4-simplex antiprism<br />
|-<br />
|7<br />
|<math>{\tilde{A}}_7</math><br />
|[[7-simplex honeycomb]]<BR>{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}<br />
|[[File:7-simplex_t06.svg|80px]]<BR>[[Hexicated 7-simplex]]<BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />
|8+8 [[7-simplex]]<BR>28+28 [[rectified 7-simplex]]<BR>56+56 [[birectified 7-simplex]]<BR>70 [[trirectified 7-simplex]]<br />
|56<br />
|5-simplex antiprism<br />
|-<br />
|8<br />
|<math>{\tilde{A}}_8</math><br />
|[[8-simplex honeycomb]]<BR>{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch}}<br />
|[[File:8-simplex_t07.svg|80px]]<BR>[[Heptellated 8-simplex]]<BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />
|9+9 [[8-simplex]]<BR>36+36 [[rectified 8-simplex]]<BR>84+84 [[birectified 8-simplex]]<BR>126+126 [[trirectified 8-simplex]]<br />
|72<br />
|6-simplex antiprism<br />
|-<br />
|9<br />
|<math>{\tilde{A}}_9</math><br />
|[[9-simplex honeycomb]]<BR>{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|nodes|split2|node}}<br />
|[[File:9-simplex_t08.svg|80px]]<BR>[[Octellated 9-simplex]]<BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />
|10+10 [[9-simplex]]<BR>45+45 [[rectified 9-simplex]]<BR>120+120 [[birectified 9-simplex]]<br>210+210 [[trirectified 9-simplex]]<br>252 [[quadrirectified 9-simplex]]<br />
|90<br />
|7-simplex antiprism<br />
|-<br />
|10<br />
|<math>{\tilde{A}}_{10}</math><br />
|[[10-simplex honeycomb]]<BR>{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|nodes|3ab|branch}}<br />
|[[File:10-simplex_t09.svg|80px]]<BR>[[Ennecated 10-simplex]]<BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />
|11+11 [[10-simplex]]<BR>55+55 [[rectified 10-simplex]]<BR>165+165 [[birectified 10-simplex]]<BR>330+330 [[trirectified 10-simplex]]<BR>462+462 [[quadrirectified 10-simplex]]<br />
|110<br />
|8-simplex antiprism<br />
|-<br />
|11<br />
|<math>{\tilde{A}}_{11}</math><br />
|11-simplex honeycomb<br />
|...<br />
|...<br />
|...<br />
|...<br />
|}<br />
<br />
== Projection by folding ==<br />
<br />
The (2n-1)-simplex honeycombs and 2n-simplex honeycombs can be projected into the n-dimensional [[hypercubic honeycomb]] by a [[Coxeter–Dynkin diagram#Geometric folding|geometric folding]] operation that maps two pairs of mirrors into each other, sharing the same [[vertex arrangement]]:<br />
<br />
{|class=wikitable<br />
|- <br />
!<math>{\tilde{A}}_2</math><br />
|{{CDD|node_1|split1|branch}}<br />
!<math>{\tilde{A}}_4</math><br />
|{{CDD|node_1|split1|nodes|3ab|branch}}<br />
!<math>{\tilde{A}}_6</math><br />
|{{CDD|node_1|split1|nodes|3ab|nodes|3ab|branch}}<br />
!<math>{\tilde{A}}_8</math><br />
|{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch}}<br />
!<math>{\tilde{A}}_{10}</math><br />
|{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|nodes|3ab|branch}}<br />
|...<br />
<br />
|- <br />
!<math>{\tilde{A}}_3</math><br />
|{{CDD|nodes_10r|splitcross|nodes}}<br />
!<math>{\tilde{A}}_3</math><br />
|{{CDD|node_1|split1|nodes|split2|node}}<br />
!<math>{\tilde{A}}_5</math><br />
|{{CDD|node_1|split1|nodes|3ab|nodes|split2|node}}<br />
!<math>{\tilde{A}}_7</math><br />
|{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|split2|node}}<br />
!<math>{\tilde{A}}_9</math><br />
|{{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|nodes|split2|node}}<br />
|...<br />
|- <br />
!<math>{\tilde{C}}_1</math><br />
|{{CDD|node_1|infin|node}}<br />
!<math>{\tilde{C}}_2</math><br />
|{{CDD|node_1|4|node|4|node}}<br />
!<math>{\tilde{C}}_3</math><br />
|{{CDD|node_1|4|node|3|node|4|node}}<br />
!<math>{\tilde{C}}_4</math><br />
|{{CDD|node_1|4|node|3|node|3|node|4|node}}<br />
!<math>{\tilde{C}}_5</math><br />
|{{CDD|node_1|4|node|3|node|3|node|3|node|4|node}}<br />
|...<br />
|}<br />
<br />
== Kissing number ==<br />
<br />
These honeycombs, seen as tangent n-spheres located at the center of each honeycomb vertex have a fixed number of contacting spheres and correspond to the number of vertices in the [[vertex figure]]. For 2 and 3 dimensions, this represents the highest [[kissing number]] for 2 and 3 dimensions, but fall short on higher dimensions. In 2-dimensions, the triangular tiling defines a circle packing of 6 tangent spheres arranged in a regular hexagon, and for 3 dimensions there are 12 tangent spheres arranged in an [[cuboctahedron|cuboctahedral]] configuration. For 4 to 8 dimensions, the kissing numbers are [[Expanded 4-simplex|20]], [[Expanded 5-simplex|30]], [[Expanded 5-simplex|42]], [[Expanded 6-simplex|56]], and [[Expanded 7-simplex|72]] spheres, while the greatest solutions are 24, 40, 72, 126, and 240 spheres respectively.<br />
<br />
== See also==<br />
* [[Truncated simplectic honeycomb]]<br />
* [[Omnitruncated simplectic honeycomb]]<br />
<br />
== References ==<br />
* [[George Olshevsky]], ''Uniform Panoploid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)''<br />
* [[Branko Grünbaum]], Uniform tilings of 3-space. [[Geombinatorics]] 4(1994), 49 - 56.<br />
* [[Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)<br />
* [[Coxeter|Coxeter, H.S.M.]] ''[[Regular Polytopes (book)|Regular Polytopes]]'', (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 <br />
* '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]<br />
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)<br />
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]<br />
<br />
{{Honeycombs}}<br />
<br />
[[Category:Honeycombs (geometry)]]<br />
[[Category:Polytopes]]</div>10.68.16.65