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	<title>Comments on: The Mathematics of Biodiversity (Part 2)</title>
	<atom:link href="http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/feed/" rel="self" type="application/rss+xml" />
	<link>http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/</link>
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	<item>
		<title>By: John Baez</title>
		<link>http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/#comment-16208</link>
		<dc:creator><![CDATA[John Baez]]></dc:creator>
		<pubDate>Mon, 25 Jun 2012 17:17:18 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=10293#comment-16208</guid>
		<description><![CDATA[Yes, good point.]]></description>
		<content:encoded><![CDATA[<p>Yes, good point.</p>
]]></content:encoded>
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	<item>
		<title>By: arch1</title>
		<link>http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/#comment-16207</link>
		<dc:creator><![CDATA[arch1]]></dc:creator>
		<pubDate>Mon, 25 Jun 2012 17:07:01 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=10293#comment-16207</guid>
		<description><![CDATA[The approximation&#039;s validity seems pretty consistent w/ intuition even for those w/o deep math background.  For large $latex N$, the species with the largest contributions to both the singleton and the undiscovered formulas are not surprisingly among the rarest species, i.e. precisely those for which $latex (1-p_i)$ is closest to 1, i.e. precisely those for which the $latex N$th and the $latex (N+1)$st powers of $latex (1-p_i)$ are most nearly equal.]]></description>
		<content:encoded><![CDATA[<p>The approximation&#8217;s validity seems pretty consistent w/ intuition even for those w/o deep math background.  For large <img src='http://s0.wp.com/latex.php?latex=N&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='N' title='N' class='latex' />, the species with the largest contributions to both the singleton and the undiscovered formulas are not surprisingly among the rarest species, i.e. precisely those for which <img src='http://s0.wp.com/latex.php?latex=%281-p_i%29&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='(1-p_i)' title='(1-p_i)' class='latex' /> is closest to 1, i.e. precisely those for which the <img src='http://s0.wp.com/latex.php?latex=N&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='N' title='N' class='latex' />th and the <img src='http://s0.wp.com/latex.php?latex=%28N%2B1%29&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='(N+1)' title='(N+1)' class='latex' />st powers of <img src='http://s0.wp.com/latex.php?latex=%281-p_i%29&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='(1-p_i)' title='(1-p_i)' class='latex' /> are most nearly equal.</p>
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	<item>
		<title>By: WebHubTelescope</title>
		<link>http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/#comment-16159</link>
		<dc:creator><![CDATA[WebHubTelescope]]></dc:creator>
		<pubDate>Sun, 24 Jun 2012 19:00:27 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=10293#comment-16159</guid>
		<description><![CDATA[Lou Jost gets around. I first heard of him when a fellow oil economics blogger caught wind of what I was working on and said it was similar to Jost&#039;s work, who was a friend of his.  See the comment at the bottom of this post of mine:
http://mobjectivist.blogspot.com/2010/04/entroplet-species-area-relationships.html

I rather believe species diversity is governed more by dispersion and chance than by specific mechanism. So it is more about filling up the state space of possible growth paths, leading to a spread in agglomeration values.

BTW, Is anyone following the work of David Mumford on Pattern Theory?]]></description>
		<content:encoded><![CDATA[<p>Lou Jost gets around. I first heard of him when a fellow oil economics blogger caught wind of what I was working on and said it was similar to Jost&#8217;s work, who was a friend of his.  See the comment at the bottom of this post of mine:<br />
<a href="http://mobjectivist.blogspot.com/2010/04/entroplet-species-area-relationships.html" rel="nofollow">http://mobjectivist.blogspot.com/2010/04/entroplet-species-area-relationships.html</a></p>
<p>I rather believe species diversity is governed more by dispersion and chance than by specific mechanism. So it is more about filling up the state space of possible growth paths, leading to a spread in agglomeration values.</p>
<p>BTW, Is anyone following the work of David Mumford on Pattern Theory?</p>
]]></content:encoded>
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	<item>
		<title>By: John Baez</title>
		<link>http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/#comment-16147</link>
		<dc:creator><![CDATA[John Baez]]></dc:creator>
		<pubDate>Sun, 24 Jun 2012 15:30:38 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=10293#comment-16147</guid>
		<description><![CDATA[Thanks, I&#039;ll fix that!]]></description>
		<content:encoded><![CDATA[<p>Thanks, I&#8217;ll fix that!</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: John Baez</title>
		<link>http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/#comment-16142</link>
		<dc:creator><![CDATA[John Baez]]></dc:creator>
		<pubDate>Sun, 24 Jun 2012 12:52:14 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=10293#comment-16142</guid>
		<description><![CDATA[I&#039;m more confident, not less.  These days I mainly post about global warming &lt;a href=&quot;https://plus.google.com/u/0/b/104603011082997519952/104603011082997519952/posts&quot; rel=&quot;nofollow&quot;&gt;here&lt;/a&gt;.  The big question for me is &lt;i&gt;what should I do about it?&lt;/i&gt;  Publicizing information is useful, but not sufficiently satisfying to make it my full-time career.  I&#039;m good at math.  It doesn&#039;t make sense for me to become a journalist or a climate scientist.  So, I&#039;m focusing on shifting my career away from pure mathematics toward mathematics that is:

1) attractive to ambitious mathematicians, for example good grad students 

yet:

2) eventually relevant to environmental issues.  

These goals are somewhat in conflict, since real-world issues tend to involve lots of domain-specific knowledge and number-crunching, which are exactly what mathematicians dislike.  Nonetheless there&#039;s a lot of room for mathematicians to develop new formalisms that can &lt;i&gt;eventually&lt;/i&gt; be helpful, when applied and adapted by other more practical people.  Mathematicians are never near the front of the battle lines.  But they can do things other people can&#039;t.

So, I&#039;ve been spending lots of time thinking about complex systems made of many interacting parts, using ideas from probability theory, information theory and game theory.  And that&#039;s what the &lt;a href=&quot;http://math.ucr.edu/home/baez/information/&quot; rel=&quot;nofollow&quot;&gt;information geometry&lt;/a&gt;, &lt;a href=&quot;http://math.ucr.edu/home/baez/networks/&quot; rel=&quot;nofollow&quot;&gt;network theory&lt;/a&gt; and &lt;a href=&quot;http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/&quot; rel=&quot;nofollow&quot;&gt;biodiversity&lt;/a&gt; posts are about.  All these posts are actually about the same big subject.   I hope that by the time I go back to U.C. Riverside in September, I&#039;ll have enough material developed that I can run an interesting seminar about it and attract a crew of good grad students.

When it comes to global warming, a lot of programmers on the Azimuth Forum are working to develop &lt;a href=&quot;http://azimuth.mathforge.org/discussion/892/a-simple-online-climate-model/#Item_0&quot; rel=&quot;nofollow&quot;&gt;simple online climate models&lt;/a&gt; for educational purposes.  These will appear on the blog.  My involvement has been limited mainly because I don&#039;t like to program, but also because I&#039;m busy trying to shift careers.  I hope to get back into that in a while.]]></description>
		<content:encoded><![CDATA[<p>I&#8217;m more confident, not less.  These days I mainly post about global warming <a href="https://plus.google.com/u/0/b/104603011082997519952/104603011082997519952/posts" rel="nofollow">here</a>.  The big question for me is <i>what should I do about it?</i>  Publicizing information is useful, but not sufficiently satisfying to make it my full-time career.  I&#8217;m good at math.  It doesn&#8217;t make sense for me to become a journalist or a climate scientist.  So, I&#8217;m focusing on shifting my career away from pure mathematics toward mathematics that is:</p>
<p>1) attractive to ambitious mathematicians, for example good grad students </p>
<p>yet:</p>
<p>2) eventually relevant to environmental issues.  </p>
<p>These goals are somewhat in conflict, since real-world issues tend to involve lots of domain-specific knowledge and number-crunching, which are exactly what mathematicians dislike.  Nonetheless there&#8217;s a lot of room for mathematicians to develop new formalisms that can <i>eventually</i> be helpful, when applied and adapted by other more practical people.  Mathematicians are never near the front of the battle lines.  But they can do things other people can&#8217;t.</p>
<p>So, I&#8217;ve been spending lots of time thinking about complex systems made of many interacting parts, using ideas from probability theory, information theory and game theory.  And that&#8217;s what the <a href="http://math.ucr.edu/home/baez/information/" rel="nofollow">information geometry</a>, <a href="http://math.ucr.edu/home/baez/networks/" rel="nofollow">network theory</a> and <a href="http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/" rel="nofollow">biodiversity</a> posts are about.  All these posts are actually about the same big subject.   I hope that by the time I go back to U.C. Riverside in September, I&#8217;ll have enough material developed that I can run an interesting seminar about it and attract a crew of good grad students.</p>
<p>When it comes to global warming, a lot of programmers on the Azimuth Forum are working to develop <a href="http://azimuth.mathforge.org/discussion/892/a-simple-online-climate-model/#Item_0" rel="nofollow">simple online climate models</a> for educational purposes.  These will appear on the blog.  My involvement has been limited mainly because I don&#8217;t like to program, but also because I&#8217;m busy trying to shift careers.  I hope to get back into that in a while.</p>
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	<item>
		<title>By: S</title>
		<link>http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/#comment-16137</link>
		<dc:creator><![CDATA[S]]></dc:creator>
		<pubDate>Sun, 24 Jun 2012 11:03:00 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=10293#comment-16137</guid>
		<description><![CDATA[A typo: &quot;Similarly, the probability that we find exactly one orchid of the $latex i$th species is $latex N p_i (1-p_i)^N$&quot;. The exponent should be N-1.]]></description>
		<content:encoded><![CDATA[<p>A typo: &#8220;Similarly, the probability that we find exactly one orchid of the <img src='http://s0.wp.com/latex.php?latex=i&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='i' title='i' class='latex' />th species is <img src='http://s0.wp.com/latex.php?latex=N+p_i+%281-p_i%29%5EN&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='N p_i (1-p_i)^N' title='N p_i (1-p_i)^N' class='latex' />&#8220;. The exponent should be N-1.</p>
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		<title>By: Arrow</title>
		<link>http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/#comment-16121</link>
		<dc:creator><![CDATA[Arrow]]></dc:creator>
		<pubDate>Sun, 24 Jun 2012 06:59:00 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=10293#comment-16121</guid>
		<description><![CDATA[A bit off topic, but it seems that there are hardly any posts about global warming these days. 

I wonder, as you learned more about climate research did you become more or less confident man made emissions are the main driver of recent climate change and that global warming is a serious threat to our civilization and other species in the near term (this century)?]]></description>
		<content:encoded><![CDATA[<p>A bit off topic, but it seems that there are hardly any posts about global warming these days. </p>
<p>I wonder, as you learned more about climate research did you become more or less confident man made emissions are the main driver of recent climate change and that global warming is a serious threat to our civilization and other species in the near term (this century)?</p>
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