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	<title>Comments on: Reflections upon Emergent Events</title>
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	<link>http://www.ephblog.com/2006/07/21/reflections-upon-emergent-events/</link>
	<description>All Things Eph</description>
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		<title>By: Alexander Woo</title>
		<link>http://www.ephblog.com/2006/07/21/reflections-upon-emergent-events/#comment-7247</link>
		<dc:creator>Alexander Woo</dc:creator>
		<pubDate>Sun, 23 Jul 2006 02:25:47 +0000</pubDate>
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		<description>Some reflections on &quot;my head hurts&quot;.  Mathematics is all about making your head hurt, so I have some authority on this.

The complexity of the situation is here.  It will not go away.  Simplification is not a matter of doing away the complexity; it is a matter of organizing it.

One of the &quot;principles&quot; of doing mathematics is the &quot;conservation of proof energy&quot;.  This says that, for any given mathematical statement, all proofs require roughly the same amount of work.  One can give a long complicated proof using elementary techniques (in many cases comprehensible using only mathematics learned in high school), or a shorter proof using a complicated, well-developed theory.  In the case of the shorter proof, all the complications are hidden in the theory.  The shorter proof doesn&#039;t make my head hurt, but that&#039;s only because I understand the that particular theory (and, hopefully, made my head hurt with it in my first couple years in grad school).

Historically, usually (but not always), the long complicated proof comes first, and then the theory is developed which abstracts part of this proof and other similar proofs, putting the idea into some nice container we can conveniently refer to later.

So the &quot;my head hurts&quot; reaction is partly a response to the lack of theory which simplifies by hiding part of the complexity from us.  In this I am a little mystified.  Failed and disputed elections have been actually quite frequent in the past 50 years or so.  Just about every African country has had a few, not to mention Pakistan.  Have the political scientists doing comparitive politics not come up with a theory to help here?  Or is each case so different that no theory can help?  Or perhaps the ideology that &quot;close enough to free and fair&quot; elections implies the existence of democracy, and that we should not make judgements on internal politics beyond this point, has hindered the development or distribution of such a theory?
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		<content:encoded><![CDATA[<p>Some reflections on &#8220;my head hurts&#8221;.  Mathematics is all about making your head hurt, so I have some authority on this.</p>
<p>The complexity of the situation is here.  It will not go away.  Simplification is not a matter of doing away the complexity; it is a matter of organizing it.</p>
<p>One of the &#8220;principles&#8221; of doing mathematics is the &#8220;conservation of proof energy&#8221;.  This says that, for any given mathematical statement, all proofs require roughly the same amount of work.  One can give a long complicated proof using elementary techniques (in many cases comprehensible using only mathematics learned in high school), or a shorter proof using a complicated, well-developed theory.  In the case of the shorter proof, all the complications are hidden in the theory.  The shorter proof doesn&#8217;t make my head hurt, but that&#8217;s only because I understand the that particular theory (and, hopefully, made my head hurt with it in my first couple years in grad school).</p>
<p>Historically, usually (but not always), the long complicated proof comes first, and then the theory is developed which abstracts part of this proof and other similar proofs, putting the idea into some nice container we can conveniently refer to later.</p>
<p>So the &#8220;my head hurts&#8221; reaction is partly a response to the lack of theory which simplifies by hiding part of the complexity from us.  In this I am a little mystified.  Failed and disputed elections have been actually quite frequent in the past 50 years or so.  Just about every African country has had a few, not to mention Pakistan.  Have the political scientists doing comparitive politics not come up with a theory to help here?  Or is each case so different that no theory can help?  Or perhaps the ideology that &#8220;close enough to free and fair&#8221; elections implies the existence of democracy, and that we should not make judgements on internal politics beyond this point, has hindered the development or distribution of such a theory?</p>
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