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  1. <?xml version="1.0" encoding="iso-8859-1"?>
  2. <feed version="0.3" xmlns="" xmlns:dc="" xml:lang="en">
  3. <title>selling waves</title>
  4.  <link rel="alternate" type="text/html" href="" />
  5.  <modified>2005-03-18T07:30:06Z</modified>
  6.  <tagline>A graduate student in mathematics and a philosophy major take on politics and culture with the following aspirational motto: &amp;#8216;Deregulate your mind.&amp;#8217;</tagline>
  7.  <id>,2008://1</id>
  8.  <generator url="" version="2.661">Movable Type</generator>
  9.  <copyright></copyright>
  10.  <entry>
  11.    <title>RSS feed moved</title>
  12.    <link rel="alternate" type="text/html" href="" />
  13.    <modified>2005-03-18T07:30:06Z</modified>
  14.    <issued>2005-03-18T02:30:06-05:00</issued>
  15.    <id>,2005://1.596</id>
  16.    <created>2005-03-18T07:30:06Z</created>
  17.    <summary type="text/plain">Special to RSS readers: the selling waves feed has moved. (36 words)</summary>
  18.    <author>
  19.      <name>shonk</name>
  20.      <url></url>
  21.    </author>
  22.    <dc:subject>Blogging</dc:subject>
  23.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  24.      <![CDATA[<p>For any of you that may be reading this via RSS, the change from Movable Type to WordPress means that the RSS feed for selling waves is now located at</p>
  26. <p>If you&#8217;re interested, that is.</p>
  27. ]]>
  30.    </content>
  31.  </entry>
  32.  <entry>
  33.    <title>Okay, so you won the argument.  So what?</title>
  34.    <link rel="alternate" type="text/html" href="" />
  35.    <modified>2005-03-12T00:35:04Z</modified>
  36.    <issued>2005-03-11T19:35:04-05:00</issued>
  37.    <id>,2005://1.594</id>
  38.    <created>2005-03-12T00:35:04Z</created>
  39.    <summary type="text/plain">Don&apos;t underestimate the importance of winning arguments, but don&apos;t overestimate it either (plus more Wittgenstein!). (842 words)</summary>
  40.    <author>
  41.      <name>shonk</name>
  42.      <url></url>
  43.    </author>
  44.    <dc:subject>Language</dc:subject>
  45.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  46.      <![CDATA[<p>Over at Catallarchy, Micha Ghertner discusses <a href="" title="Catallarchy &#187; How To Tell You've Won An Argument">&#8220;How To Tell You&#8217;ve Won An Argument;&#8221;</a> namely, when your opponent concedes that his position is less coherent than your own, you&#8217;ve won.  Now, I don&#8217;t want to dispute his point, but rather to question how relevant it is.  I&#8217;ve <a href=";id=419" title=" : Legality Is Not Morality, by Clay Shonkwiler">touched on this before</a>, but I&#8217;m a bit dubious of the notion that the &#8220;correct&#8221; position is the one that wins arguments between advocates of two different positions.  </p>
  48. <p>Obviously, in the first place, there&#8217;s nothing to prevent <em>both</em> arguers from being wrong; the relative lack of coherence of one of their positions means, at best, that the other&#8217;s position is &#8220;less&#8221; wrong (assuming that even makes sense and assuming that coherence is a measure of correctness).<sup><a href="#argfn1">1</a></sup>  But this is somewhat superficial (and besides, already mentioned and acknowledged in the comments to Ghertner&#8217;s post); more importantly, I want to cast doubts upon the parenthetical assumption I made above, that coherence is some sort of infallible metric for measuring correctness/validity.  </p>
  50. <p>In fact, Ghertner (perhaps unconsciously) alludes to this very issue when he quotes Wittgenstein&#8217;s famous seventh proposition from the <a href="" title="Tractatus Logico-Philosophicus (English)"><em>Tractatus</em></a>: &#8220;Whereof one cannot speak, thereof one must be silent.&#8221;  Within the context of the <em>Tractatus</em> (as an attempt to construct or at least describe a perfect language), this supports the notion that being right and being coherent are synonymous, but Wittgenstein himself later rejects this perspective and, to me, the more <em>apropos</em> quotation is: &#8220;Explanations come to an end somewhere&#8221; (<a href=";code=xm2" title=" Philosophical Investigations: The German Text, With a Revised English Translation: Explore similar items"><em>Philosophical Investigations</em></a>, I&#167;1).  That is, no argument (and certainly none about abstract principles) is completely coherent; we always run up against that whereof we cannot speak and therefore must be silent.  The question is simply at what stage in the investigation we enter the realm of unsupported assertion.</p>
  52. <p>And even if we scale back our expectations and choose to embrace the position that manages to maintain coherence as far back as possible, there&#8217;s still no guarantee that we&#8217;re on the right track.  Although much of the world can apparently be explained without the need to stipulate a deity, this doesn&#8217;t really make it any less likely that theism is right.  In the words of <a href=";code=xm2" title=" Sex, Drugs, and Cocoa Puffs : A Low Culture Manifesto: Explore similar items">Chuck Klosterman</a>: </p>
  54. <blockquote>
  55. <p>Math [or, perhaps more fittingly in this context, logic] is the antireligion, because it splinters the gravity of life&#8217;s only imperative equation: Either something is true, or it isn&#8217;t.</p>
  56. </blockquote>
  58. <p>In fact, if we really want to get all Wittgensteinian about this (not that we necessarily should), we might even begin to question those positions which <em>do</em> appear to be coherent: </p>
  60. <blockquote>
  61. <p>In the actual use of expressions we make detours, we go by side roads. We see the straight highway before us, but of course we cannot use it, because it is permanently closed. (PI, I&#167;426)</p>
  62. </blockquote>
  64. <p>Anyway, getting back to whatever semblance of a point I was trying to make, when someone admits that their position is incoherent, that does indeed mean that they&#8217;ve lost the argument, but I just wonder how important that really is.  Giving up your high-paying job and live-in girlfriend to go back home and take care of your sick mother isn&#8217;t going to win a lot of arguments if we&#8217;re taking logical coherence as the criterion of victory (seriously, think about it), but that doesn&#8217;t mean it&#8217;s not the right thing to do.  That doesn&#8217;t mean that coherence is totally <em>irrelevant</em> to what is right/correct, either (and, I should point out, in the above example helping your sick mom <em>isn&#8217;t</em> necessarily the right thing to do; as is almost always true, it depends on the circumstances), but let&#8217;s not give argument-winning more importance than it merits.  Or, as some smarmy new-age intellectual might put it, in the pursuit of knowledge, our goal shouldn&#8217;t be to <em>win arguments</em>, but, rather, to <em>discover truth</em>.  </p>
  66. <p><hr />
  67. <a name="argfn1"></a>
  68. <small>1. Since I&#8217;m quoting Wittgenstein anyway, I might as well include the relevant quote for this as well:</p>
  70. <blockquote>
  71. <p>The law of the excluded middle says here: It must either look like this, or like that. So it really&#8212;and this is a truism&#8212;says nothing at all, but gives us a picture. And the problem ought now to be: does reality accord with the picture or not? And this picture seems to determine what we have to do, what to look for, and how&#8212;but it does not do so, just because we do not know how it is to be applied. Here saying &#8220;There is no third possibility&#8221; or &#8220;But there can&#8217;t be a third possibility!&#8221;&#8212;expresses our inability to turn our eyes away from this picture: a picture which looks as if it must already contain both the problem and its solution, while all the time we feel that it is not so. (PI I&#167;352)</small></p>
  72. </blockquote>
  73. ]]>
  76.    </content>
  77.  </entry>
  78.  <entry>
  79.    <title>Comments dead</title>
  80.    <link rel="alternate" type="text/html" href="" />
  81.    <modified>2005-03-02T04:24:46Z</modified>
  82.    <issued>2005-03-01T23:24:46-05:00</issued>
  83.    <id>,2005://1.590</id>
  84.    <created>2005-03-02T04:24:46Z</created>
  85.    <summary type="text/plain">All my recent posts seem to be about death (figurative, in this case). (123 words)</summary>
  86.    <author>
  87.      <name>shonk</name>
  88.      <url></url>
  89.    </author>
  90.    <dc:subject>Blogging</dc:subject>
  91.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  92.      <![CDATA[<p>I just got an email from my <a href="" title=" - The Ultimate in Web Hosting">hosting company</a>&#8230;apparently the old <a href="" title="Movable Type">Movable Type</a> comment script is causing some sort of server malfunction, so they&#8217;ve disabled all comments on this site.  </p>
  94. <p>Since I refuse to pay for the new version of MT, I may end up doing what I&#8217;ve been thinking about for a while: namely, switching to <a href="" title="WordPress &#8250; Home">WordPress</a> or some other alternative.  Which seems to be the thing to do these days, anyway.  Fortunately, spring break is coming up next week, so I may actually have some free time to wrestle with it.</p>
  96. <p>In the meantime, feel free to email any comments you may have.</p>
  97. ]]>
  100.    </content>
  101.  </entry>
  102.  <entry>
  103.    <title>Bentham&apos;s mummified corpse, like Lenin&apos;s,  remains fresh in appearance</title>
  104.    <link rel="alternate" type="text/html" href="" />
  105.    <modified>2005-02-26T13:27:40Z</modified>
  106.    <issued>2005-02-26T08:27:40-05:00</issued>
  107.    <id>,2005://1.589</id>
  108.    <created>2005-02-26T13:27:40Z</created>
  109.    <summary type="text/plain">It&amp;#8217;s almost comforting that such invidious fluffy-minded sludge as this is floating around, as it seems, like religion, to keep the middle-brows hypnotized by &amp;#8220;beautiful sentiments&amp;#8221; which are so vague as to keep them from actually getting together and doing... (1629 words)</summary>
  110.    <author>
  111.      <name>Curt</name>
  113.    </author>
  114.    <dc:subject>Geek Talk</dc:subject>
  115.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  116.      <![CDATA[<p>It&#8217;s almost comforting that such invidious fluffy-minded sludge <a href="">as this</a> is floating around, as it seems, like religion, to keep the middle-brows hypnotized by &#8220;beautiful sentiments&#8221; which are so vague as to keep them from actually getting together and doing anything.  It&#8217;s sort of weird to hear this weakly Marxist social-democratic pap which used to be shouted from the rooftops now being whispered in a low monotonous whine.  The author avows his fealty to Jeremy Bentham, not Marx, and calls it utilitarianism not Marxism, but there are many illegitimate fathers along this line of thought.  </p>
  118. <p>The root of the idea is that, now that neuroscience has supposedly made it possible to actually identify what makes us happy, the idea of happiness has become quantifiable, and hence a program of providing the greatest happiness to the greatest number of people has become objectively possible.  However, the author does not make the slightest effort to apply these wonders of modern science to actually determining what the alleged sources of human happiness are.  The neuroscience tack is really just a defensive ploy to ward off the eternal charges that utilitarinism is simply a euphemism for an authoritarian imposition of values.  As for espousing his positive program for what constitutes human happiness, it is simply the usual liberal middle-class canards, with not surprisingly a socialist edge: more time to spend with family, a decent wage for everyone, blah blah blah.  But he seems to make two pretty criminally unsubstantiated assumptions: one is these sources are essentially the same for everyone, or at least could be under certain conditions, and the other is that they do not inherently conflict with anyone else&#8217;s.  </p>
  120. <p>I say under certain conditions could be, because in evaluating our current society he seems to privilege envy of other&#8217;s material well-being as the principal determinant of happiness.  His theory is that above a certain level of material subsistence people are motivated primarily by status-seeking and the desire for a high rank within their social group.  Therefore, the increasing wealth of the society will not increase happiness because people measure their well-being relative to the group, not by their absolute prosperity.  This is always been a flaw in the concept of the &#8220;war against poverty&#8221;; I&#8217;m not sure it&#8217;s much of an argument for socialist economic redistribution.  But actually if you read his section on the value of income taxes carefully, he doesn&#8217;t even seem to be arguing that they are useful insofar as they can be redirected to the less prosperous, although he does evidently believe that a certain amount of money contributes more to the happiness of a poor person than to a rich one&#8217;s.  Rather, he seems to think that taking money away from the properous is valuable <i>in and of itself</i>, because it will supposedly make them less focused on the &#8220;rat race,&#8221; more family-oriented, etc., etc.  In short he seems to be advocating a <i>net impoverishment</i> of society.  </p>
  122. <p>All of which may be consistent with the program of a good little socialist, but does not necessarily accord marvelously with his own evidence about the supposedly quantified happiness of humanity.  The research that he cites non-specifically supposedly indicates that people&#8217;s feeling of happiness has not risen in the last half-century, but he does not cite anything which indicates that it has necessarily declined.  He cites rising rates of depression and crime as presumably implicit indicators of greater unhappiness, but he does not seem to acknowledge the possibility that in our hyper-medicated and surveillance-based society perhaps people simply report depression and crime more.  In any event, if roughly similar numbers of people today as in the &#8216;50&#8217;s report themselves happy (and we believe them), despite the increase in prosperity, that might perhaps indicate that happiness is not fixed to material well-being.  Which may be consistent with his general point, but not with his idea of increasing happiness by manipulating income levels.  </p>
  124. <p>And even if it did, it seems rather difficult to countenance any social program predicated upon appealing to one of humanity&#8217;s most depraved instincts, namely envy.  The author acknowledges that his ideal of taxation is mainly motivated by the desire to pander to people&#8217;s envy, but he seems to think that their envy will be sated by the loss of prosperity of those around them and that after that point there will be no more.  So the envy of the less prosperous will be satisfied by the losses accrued by the more prosperous, which will somehow not be counter-balanced by the chagrin of the more prosperous at the prospect of seeing their status diminished.  Very logical.</p>
  126. <p>One of the more egregious presumptions of utilitarians is that non-utilitarian social systems somehow aren&#8217;t concerned with seeking the greatest good for the greatest number of people.  On the contrary, that&#8217;s the defining problem of practically every social and political theory I can think of, and they all either seek or claim to have found the answer&#8212;whether such a solution exists, I have my doubts, but that&#8217;s why I&#8217;m a skeptic about politics.  This is a handy trick by utilitarians: they say &#8220;I believe in the greatest good for the greatest number of people.&#8221;  Which is practically begging the question: &#8220;As opposed to whom?&#8221;  It&#8217;s useful because it tends to conceal the fact that their real agenda is generally somewhat more specific, and tends to consist in the autocratic notion that one or two measures of social living can be authoritatively determined to be the sources of happiness, and then divided up in a centralized fashion.  Those that are the most insistent on the idea of liberty are generally those that are the most skeptical about the possibility of the notion of happiness being either quantitatively defined or generalizable.  In other words, only indviduals can determine their own sources of happiness.</p>
  128. <p>For the author, on the other hand, the fact that certain stimuli trigger certain areas of the brain at the times when test subjects profess pleasure has solved the problem of determining happiness.  Of course, as mentioned, he never really bothers with the results that those studies have yielded.  Somehow the fact that he considers envy to be a principal element of human happiness does not place very severe limits on the harmoniousness of individual happiness.  Nor does it constitute a tyranny of the majority, because he claims that in an ideal utilitarian society the happiness of the most unhappy would be considered of pre-eminent importance.  Of course, at the beginning of the article he cited the equal importance of each individual&#8217;s happiness as the fouding tenet of his theory, but I&#8217;m sure it all sorts out in the end.</p>
  130. <p>Among social factors responsible for unhappiness, he cites divorce and unemployment as of pre-eminent importance.  Of course, rates of both divorce and unemployment in the crassly materialistic and religious United States are much lower than in the much more overtly utilitarian-embracing Europe, but it would be a bit embarassing for him to admit this after avowing that all traditional value-systems outside of utilitarianism and &#8220;individualism&#8221; are dead.  </p>
  132. <p>Personally the question of the greatest happiness for the greatest number of people doesn&#8217;t exactly compel me constantly, although the issue of personal happiness tends to impose itself intransigently.  I would have thought that evolutionary biology would have provided an adequate explanation of this, as well as the recurrence of what we call altruism.  But such an idea of course suggests that happiness, whatever that is, is not really the point of our little existences, and that the more imperious competitiveness of life will ultimately subvert all of these little trifles of pleasure and pain.  But in the meantime, we have these debased statistical notions of happiness to amuse us in an idle hour.</p>
  134. <p>It seems to me that if one&#8217;s &#8220;objective&#8221; measure of happiness is electrical stimulation in the cerebral cortex, the most efficient utilitarian solution to the problem of human happiness would be strap everyone onto hospital gurneys and stimulate the &#8220;happiness&#8221; part of their brain all day long.  If one does not wish to be this deterministic about it, perhaps one should allow more latitute to individuals to discover their own conception of happiness.  Personally, I have found happiness generally to be an idea for the unhappy and something rarely spoken of by the happiness; mention of practically guarantees that it is not present in the environment where it is uttered.  I don&#8217;t deny that what you might call love is the real bridge between personal happiness and moral obligations, and the only true means by which the desires of oneself and of others are united, but such a sentiment can never be mandated; it is entirely resistant to intellectual compulsion.  Utilitarianism, which sometimes does a decent job of faking morality, is nevertheless ultimately predicated on the pleasure principle, and hence is wholly inadequate to uniting the moral and the pleasurable except when love truly pertains.  In that case, of course, political theory is entirely superfluous, which is why this is all a waste of time.</p>
  136. <p>p.s.  I don&#8217;t claim that people&#8217;s behavior necessarily reflects what really would make them happy, but presumably it does at least reflect what they consciously value.  Hence, if I were the author I would have been a bit skeptical of using the results of &#8220;surveys&#8221; of what people claim to value when the results don&#8217;t correlate with their behavior, i.e. they claim that spending time with family is most important, but they spend a disproportiante amount of time working (at least according to him).  So either people are not really being forthright (consciously or unconsciously) in responding to surveys, or there is not actually a problem of priorities.  In either case, he&#8217;s way over-valuing surveys as a guide to what will make people happy.</p>
  137. ]]>
  140.    </content>
  141.  </entry>
  142.  <entry>
  143.    <title>The Doctor is out</title>
  144.    <link rel="alternate" type="text/html" href="" />
  145.    <modified>2005-02-23T03:00:59Z</modified>
  146.    <issued>2005-02-22T22:00:59-05:00</issued>
  147.    <id>,2005://1.587</id>
  148.    <created>2005-02-23T03:00:59Z</created>
  149.    <summary type="text/plain">Saying goodbye to Doctor Gonzo (44 words)</summary>
  150.    <author>
  151.      <name>shonk</name>
  152.      <url></url>
  153.    </author>
  154.    <dc:subject>Ramblings</dc:subject>
  155.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  156.      <![CDATA[<p><a href="" title="OpinionJournal - Leisure &#38; Arts">RIP, H.S.T.</a></p>
  158. <p>(See also <a href=";and&#95;loathing&#95;in&#95;las&#95;vegas/" title="selling waves: Fear and Loathing in Las Vegas">&#8220;Fear and Loathing in Las Vegas,&#8221;</a> <a href="" title="selling waves: Regrettably necessary">&#8220;Regrettably necessary,&#8221;</a> and <a href=";vote/" title="selling waves: Don't Vote!">&#8220;Don&#8217;t Vote!&#8221;</a>)</p>
  159. ]]>
  162.    </content>
  163.  </entry>
  164.  <entry>
  165.    <title>&quot; just get used to them&quot;</title>
  166.    <link rel="alternate" type="text/html" href="" />
  167.    <modified>2005-02-13T09:37:18Z</modified>
  168.    <issued>2005-02-13T04:37:18-05:00</issued>
  169.    <id>,2005://1.584</id>
  170.    <created>2005-02-13T09:37:18Z</created>
  171.    <summary type="text/plain">Math is hard, but if you have the right picture in mind, it&apos;s slightly easier. (2097 words)</summary>
  172.    <author>
  173.      <name>shonk</name>
  174.      <url></url>
  175.    </author>
  176.    <dc:subject>Geek Talk</dc:subject>
  177.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  178.      <![CDATA[<blockquote>
  179. <p>&#8220;Young man, in mathematics you don&#8217;t understand things, you just get used to them.&#8221;
  180. &#8212;John von Neumann<a href="#calculusfn1"><sup>1</sup></a></p>
  181. </blockquote>
  183. <p>This, in a sense, is at the heart of why mathematics is so hard.  Math is all about abstraction, about generalizing the stuff you can get a sense of to apply to crazy situations about which you otherwise have no insight whatsoever.  Take, for example, one way of understanding the manifold structure on <i>SO(3)</i>, the <a href="" title="Special Orthogonal Group -- from MathWorld">special orthogonal group</a> on 3-space.  In order to explain what I&#8217;m talking about, I&#8217;ll have to give several definitions and explanations and each, to a greater or lesser extent, illustrates both my point about abstraction and von Neumann&#8217;s point about getting used to things.  </p>
  185. <p>First off, <i>SO(3)</i> has a purely algebraic definition as the set of all real (that is to say, the entries are real numbers) 3 &times; 3 matrices <i>A</i> with the property <i>A<sup>T</sup>A = I</i> and the determinant of <i>A</i> is 1.  That is, if you take <i>A</i> and flip rows and columns, you get the transpose of <i>A</i>, denoted <i>A<sup>T</sup></i>; if you then multiply this transpose by <i>A</i>, you get the identity matrix <i>I</i>.  The <a href="" title="Determinant -- from MathWorld">determinant</a> has its own complicated algebraic definition (the unique alternating, multilinear functional&#8230;), but it&#8217;s easy to compute for small matrices and can be intuitively understood as a measure of how much the matrix &#8220;stretches&#8221; vectors.  Now, as with all algebraic definitions, this is a bit abstruse; also, as is unfortunately all too common in mathematics, I&#8217;ve presented all the material slightly backwards.  </p>
  187. <p>This is natural, because it seems obvious that the first thing to do in any explication is to define what you&#8217;re talking about, but, in reality, the best thing to do in almost every case is to first explain what the things you&#8217;re talking about (in this case, special orthogonal matrices) <em>really are</em> and why we should care about them, and only then give the technical definition.  In this case, special orthogonal matrices are &#8220;really&#8221; the set of all rotations of plain ol&#8217; 3 dimensional space that leave the origin fixed (another way to think of this is as the set of linear transformations that preserve length and orientation; if I apply a special orthogonal transformation to you, you&#8217;ll still be the same height and width and you won&#8217;t have been flipped into a &#8220;mirror image&#8221;).  Obviously, this is a handy thing to have a grasp on and this is why we care about special orthogonal matrices.  In order to deal with such things rigorously it&#8217;s important to have the algebraic definition, but as far as <em>understanding</em> goes, you need to have the picture of rotations of 3 space in your head.</p>
  189. <p>Okay, so I&#8217;ve explained part of the sentence in the first paragraph where I started throwing around arcane terminology, but there&#8217;s a bit more to clear up; specifically, what the hell is a &#8220;<a href="" title="Manifold -- from MathWorld">manifold</a>&#8221;, anyway?  Well, in this case I&#8217;m talking about differentiable (as opposed to topological) manifolds, but I don&#8217;t imagine that explanation helps.  In order to understand what a manifold is, it&#8217;s very important to have the right picture in your head, because the technical definition is about ten times worse than the special orthogonal definition, but the basic idea is probably even simpler.  The intuitive picture is that of a smooth surface.  For example, the surface of a sphere is a nice 2-dimensional manifold.  So is the surface of a donut, or a saddle, or an idealized version of the rolling hills of your favorite pastoral scene.  Slightly more abstractly, think of a rubber sheet stretched and twisted into any configuration you like so long as there are no holes, tears, creases, black holes or sharp corners.  </p>
  191. <p>In order to rigorize this idea, the important thing to notice about all these surfaces is that, if you&#8217;re a small enough ant living on one of these surfaces, it looks indistinguishable from a flat plane.  This is something we can all immediately understand, given that we live on an oblate spheroid that, because it&#8217;s so much bigger than we are, looks flat to us.  In fact, this is very nearly the precise definition of a manifold, which basically says that a manifold is a topological space (read: set of points with some important, but largely technical, properties) where, at any point in the space, there is some neighborhood that looks identical to &#8220;flat&#8221; euclidean space; a 2-dimensional manifold is one that looks locally like a plane, a 3-dimensional manifold is one that looks locally like normal 3-dimensional space, a 4-dimensional manifold is one that looks locally like normal 4-dimensional space, and so on.  </p>
  193. <p>In fact, these spaces look so much like normal space that we can do calculus on them, which is why the subject concerned with manifolds is called &#8220;differential geometry&#8221;.  Again, the reason why we would want to do calculus on spaces that look a lot like normal space but aren&#8217;t is obvious: if we live on a sphere (as we basically do), we&#8217;d like to be able to figure out how to, e.g., minimize our distance travelled (and, thereby, fuel consumed and time spent in transit) when flying from Denver to London, which is the sort of thing for which calculus is an excellent tool that gives good answers; unfortunately, since the Earth isn&#8217;t flat, we can&#8217;t use regular old freshman calculus.<a href="#calculusfn2"><sup>2</sup></a>  As it turns out, there are all kinds of applications of this stuff, from relatively simple engineering to theoretical physics.</p>
  195. <p>So, anyway, the point is that manifolds look, at least locally, like plain vanilla euclidean space.  Of course, even the notion of &#8220;plain vanilla euclidean space&#8221; is an abstraction beyond what we can really visualize for dimensions higher than three, but this is exactly the sort of thing von Neumann was talking about: you can&#8217;t really visualize 10 dimensional space, but you &#8220;know&#8221; that it looks pretty much like regular 3 dimensional space with 7 more axes thrown in at, to quote Douglas Adams, &#8220;right angles to reality&#8221;.  </p>
  197. <p>Okay, so the claim is that <em>SO(3)</em>, our set of special orthogonal matrices, is a 3-dimensional manifold.  On the face of it, it might be surprising that the set of rotations of three space should itself look anything like three space.  On the other hand, this sort of makes sense: consider a single vector (say of unit length, though it doesn&#8217;t really matter) based at the origin and then apply <em>every</em> possible rotation to it.  This will give us a set of vectors based at the origin, all of length 1 and pointing any which way you please.  In fact, if you look just at the heads of all the vectors, you&#8217;re just talking about a sphere of radius 1 centered at the origin.  So, in a sense, the special orthognal matrices look like a sphere.  This is both right and wrong; the special orthogonal matrices <em>do</em> look a lot like a sphere, but like a 3-sphere (that is, a sphere living in four dimensions), not a 2-sphere (i.e., what we usually call a &#8220;sphere&#8221;).  </p>
  199. <p>In fact, locally <em>SO(3)</em> looks almost <em>exactly</em> like a 3-sphere; globally, however, it&#8217;s a different story.  In fact, <em>SO(3)</em> looks globally like <img src="" alt="R" title="R" /><img src="" alt="P" title="P" /><img src="" alt="3" title="3" />, which requires one more excursion into the realm of abstraction.  <img src="" alt="R" title="R" /><img src="" alt="P" title="P" /><img src="" alt="3" title="3" />, or <a href=";space" title="Projective space - Wikipedia, the free encyclopedia">real projective 3-space</a>, is an abstract space where we&#8217;ve taken regular 3-space and added a &#8220;plane at infinity&#8221;.  This sounds slightly wacky, but it&#8217;s a generalization of what&#8217;s called the <a href="" title="Real Projective Plane -- from MathWorld">projective plane</a>, which is basically the same thing but in a lower dimension.  To get the projective plane, we add a &#8220;line at infinity&#8221; rather than a plane, and the space has this funny property that if you walk through the line at infinity, you get flipped into your mirror image; if you were right-handed, you come out the other side left-handed (and on the &#8220;other end&#8221; of the plane).  But not to worry, if you walk across the infinity line again, you get flipped back to normal.  </p>
  201. <p>Okay, sounds interesting, but how do we visualize such a thing?  Well, the &#8220;line at infinity&#8221; thing is good, but infinity is pretty hard to visualize, too.  Instead we think about twisting the sphere <a href="" title="HogBlog: Vector Bundles">in a funny way</a>:</p>
  203. <blockquote>
  204. <p>You can construct the projective plane as follows: take a sphere. Imagine taking a point on the sphere, and its antipodal point, and pulling them together to meet somewhere inside the sphere. Now do it with another pair of points, but make sure they meet somewhere else. Do this with every single point on the sphere, each point and its antipodal point meeting each other but meeting no other points. It&#8217;s a weird, collapsed sphere that can&#8217;t properly live in three dimensions, but I imagine it as looking a bit like a seashell, all curled up on itself. And pink.</p>
  205. </blockquote>
  207. <p>This gives you the real projective plane, <img src="" alt="R" title="R" /><img src="" alt="P" title="P" /><img src="" alt="2" title="2" />.  If you do the same thing, but with a 3-sphere (again, remember that this is the sphere living in four dimensions), you get <img src="" alt="R" title="R" /><img src="" alt="P" title="P" /><img src="" alt="3" title="3" />.  Of course, you can&#8217;t even really visualize <img src="" alt="R" title="R" /><img src="" alt="P" title="P" /><img src="" alt="2" title="2" /> or, for that matter, a 3-sphere, so <em>really</em> visualizing <img src="" alt="R" title="R" /><img src="" alt="P" title="P" /><img src="" alt="3" title="3" /> is going to be out of the question, but we have a pretty good idea, at least by analogy, of what it is.  This is, as von Neumann indicates, one of those things you &#8220;just get used to&#8221;.  </p>
  209. <p>Now, as it turns out, if you <a href="" title="Special groups and projective planes">do the math</a>, <em>SO(3)</em> and <img src="" alt="R" title="R" /><img src="" alt="P" title="P" /><img src="" alt="3" title="3" /> look the same in a very precise sense (specifically, they&#8217;re diffeomorphic).  On the face of it, of course, this is patently absurd, but if you have the right picture in mind, this is the sort of thing you might have guessed.  The basic idea behind the proof linked above is that we can visualize 3-space as living inside 4-space (where it makes sense to talk about multiplication); here, a rotation (remember, that&#8217;s all the special orthogonal matrices/transformations really are) is just like conjugating by a point on the sphere.  And certainly conjugating by a point is the same as conjugating by its antipodal point, since the minus signs will cancel eachother in the latter case.  But this is exactly how we visualized <img src="" alt="R" title="R" /><img src="" alt="P" title="P" /><img src="" alt="3" title="3" />, as the points on the sphere with antipodal points identified!  </p>
  211. <p>I&#8217;m guessing that most of the above doesn&#8217;t make a whole lot of sense, but I would urge you to heed von Neumann&#8217;s advice: don&#8217;t necessarily try to &#8220;understand&#8221; it so much as just to &#8220;get used to it&#8221;; the understanding can only come after you&#8217;ve gotten used to the concepts and, most importantly, the pictures.  Which was really, I suspect, von Neumann&#8217;s point, anyway: of course we can understand things in mathematics, but we can only understand them after we suspend our disbelief and allow ourselves to get used to them.  And, of course, make good pictures.</p>
  213. <p><hr />
  214. <a name="calculusfn1"></a>
  215. <sup>1</sup> This, by the way, is my second-favorite math quote of the year, behind my complex analysis professor&#8217;s imprecation, right before discussing poles vs. essential singularities, to &#8220;distinguish problems that are real but not serious from those that are really serious.&#8221;</p>
  217. <p><a name="calculusfn2"></a>
  218. <sup>2</sup> As a side note, calculus itself is a prime example of mathematical abstraction.  The problem with the world is that most of the stuff in it isn&#8217;t straight.  If it were, we could have basically stopped after the Greeks figured out a fair amount of geometry.  And, even worse, not only is non-straight stuff (like, for example, a graph of the position of a falling rock plotted against time) all over the place, but it&#8217;s hard to get a handle on.  So, instead of just giving up and going home, we <em>approximate</em> the curvy stuff in the world with straight lines, which we have a good grasp of.  As long as we&#8217;re dealing with stuff that&#8217;s curvy (rather than, say, broken into pieces) this actually works out pretty well and, once you get used to it all, it&#8217;s easy to forget what the whole point was, anyway (this, I suspect, is the main reason calculus instruction is so uniformly bad; approximating curvy stuff with straight lines works <em>so well</em> that those who who are supposed to teach the process lose sight of what&#8217;s really going on).</p>
  219. ]]>
  222.    </content>
  223.  </entry>
  224.  <entry>
  225.    <title>But what about the antiquarians?</title>
  226.    <link rel="alternate" type="text/html" href="" />
  227.    <modified>2005-02-12T12:44:35Z</modified>
  228.    <issued>2005-02-12T07:44:35-05:00</issued>
  229.    <id>,2005://1.583</id>
  230.    <created>2005-02-12T12:44:35Z</created>
  231.    <summary type="text/plain">&quot;Those who do not learn from the mistakes of the past are doomed to repeat them.&quot; This is good advice, especially for democracies, which tend (as even Plato and Thucydides noted) to have short-term attention spans. But we shouldn&apos;t forget... (132 words)</summary>
  232.    <author>
  233.      <name>Curt</name>
  235.    </author>
  236.    <dc:subject>Words of Wisdom</dc:subject>
  237.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  238.      <![CDATA[<p><i>"Those who do not learn from the mistakes of the past are doomed to repeat them." This is good advice, especially for democracies, which tend (as even Plato and Thucydides noted) to have short-term attention spans. But we shouldn't forget an equally important lesson, articulated most forcefully by Nietzsche: The health of a person and a people also depends vitally on the capacity to forget. Forgetting is necessary to free ourselves from imperfectly understood "lessons of history," so that we can see the challenges ahead clearly, without preconceptions or prejudice. Forgetting is also the better part of forgiving, and there are whole domains of political controversy -- indeed, whole regions of the world -- where a little less history could be of service in this respect. </i><br />
  239.                                          --Eliot Noyes, <a href="">Getting Past the Past</a></p>]]>
  241.    </content>
  242.  </entry>
  243.  <entry>
  244.    <title>Superstring cultists--tough luck</title>
  245.    <link rel="alternate" type="text/html" href="" />
  246.    <modified>2005-02-10T13:37:18Z</modified>
  247.    <issued>2005-02-10T08:37:18-05:00</issued>
  248.    <id>,2005://1.582</id>
  249.    <created>2005-02-10T13:37:18Z</created>
  250.    <summary type="text/plain">At the conjunction of this critique of reductionism in physics and this interview with Benoit Mandelbrot I think one sees the same basic dynamic at work: a devaluation of simplicity and generalization in math and science, what I suppose Mandelbrot... (537 words)</summary>
  251.    <author>
  252.      <name>Curt</name>
  254.    </author>
  255.    <dc:subject>Science</dc:subject>
  256.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  257.      <![CDATA[<p>At the conjunction of <a href="">this critique</a> of reductionism in physics and <a href="">this interview with Benoit Mandelbrot</a> I think one sees the same basic dynamic at work: a devaluation of simplicity and generalization in math and science, what I suppose Mandelbrot might call &#8220;smoothness,&#8221; and a preference for the complex and the multifarious.  To some extent this seems to cut against the basic scientific impulse to simplify, to generalize, which is what a law or an equation generally does.  In Laughlin I think there is even a certain disillusionment with realism perhaps not totally dissimilar from that in the analysis of language by <a href="">dear friend Wittgenstein</a>.  Although, by encouraging investigation of the specifics and intricacies of phenomena which seem to be superficially covered by the most general and basic laws and to give up idle speculation about the far nether regions of the universe in space and time which cannot in any way be corroborated, he seems to be trying to bring physics back into the solid world of relative certainties and reasonable evidence, it seems to me that this is a tacit admission that the theories which seem to cover and explain adequately all phenomena except for those extreme edges are in actuality insufficient to represent the richness of even the most mundane levels of reality.</p>
  259. <p>Just as in the case of the over-heated discoveries of Wittgeinstein and Cambridge group, this sudden realization that the broad and universal physical laws established and the abstract shapes used to represent them don&#8217;t really reflect the full multiplicity of reality seems a little phony to me.  I mean, isn&#8217;t that the entire point?  Isn&#8217;t that abstractness and simplicity supposed to yoke all of that complexity within a reasonable level of comprehensibility sufficient to possibly predict other phenomena, or at least relate them to what we have already seen?  Now maybe we see a revision in the valuation of these ideals, and in both Laughlin and Mandelbrot a movement away from final solutions, formulations and summations.  Seemingly nothing out-of-the-ordinary about that, but if one ceases to regard oneself as capturing the <i>essence</i> of a phenomenon in an equation or image describing it, then that necessarily leads to a re-evaluation of the type of work one is doing and the standard by which it is judged.  Let&#8217;s put it this way: although there are many rules which often govern both the form and content of a form (some, granted, quite idiosyncratic and individual), it would be quite ludicrous to suggest that a listing of those rules would be an adequate reflection or description of the poem, let alone itself be a poem, or equivalent to the poem.</p>
  261. <p>Philosophically, I&#8217;m not troubled by this as many scientists seem to be.  Despite the many declarations that Newton had discovered the very mechanism by which God controlled the universe, he himself complained famously that he felt like a dilettante on the shoreline picking up stones and shells that amused him while neglecting the vast ocean before him.  This seems unnecessary if one regards theorems as essentially creations, not mirrors of nature, and hence judge the cathedral of scientific knowledge by its height above the ground rather than as an incomplete ladder to the heavens.</p>
  262. ]]>
  265.    </content>
  266.  </entry>
  267.  <entry>
  268.    <title>Abuse?  I&apos;ll show you abuse!</title>
  269.    <link rel="alternate" type="text/html" href="" />
  270.    <modified>2005-02-05T07:19:38Z</modified>
  271.    <issued>2005-02-05T02:19:38-05:00</issued>
  272.    <id>,2005://1.579</id>
  273.    <created>2005-02-05T07:19:38Z</created>
  274.    <summary type="text/plain">Why Curt is wrong. (145 words)</summary>
  275.    <author>
  276.      <name>shonk</name>
  277.      <url></url>
  278.    </author>
  279.    <dc:subject>Economics</dc:subject>
  280.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  281.      <![CDATA[<p>Note to <a href=";abuse&#95;of&#95;a&#95;college&#95;education/" title="selling waves: The abuse of a college education">Curt</a>:</p>
  283. <p>Just because the state claims the authority to apprehend and punish rapists doesn&#8217;t mean that apprehending and punishing rapists is a form of state coercion.  Nor is the notion that rape is bad an example of state coercion.  Depending on your perspective, this is either a moral truth derived from God/reason/whatever or a widely-accepted social convention.  Similarly, the notion that one can own property is (again, depending on your perspective) either morally necessary or a widely-accepted social convention that seems to work pretty well (here I&#8217;m dispensing with Communists and other fools who have nothing intelligent to say on the matter).  Either way, the fact that the state claims ultimate authority to adjudicate property disputes does not make private property a form of state coercion.  (<a href="" title="selling waves: Slummin'">Further reading</a>)</p>
  284. ]]>
  287.    </content>
  288.  </entry>
  289.  <entry>
  290.    <title>The abuse of a college education</title>
  291.    <link rel="alternate" type="text/html" href="" />
  292.    <modified>2005-02-02T00:25:38Z</modified>
  293.    <issued>2005-02-01T19:25:38-05:00</issued>
  294.    <id>,2005://1.577</id>
  295.    <created>2005-02-02T00:25:38Z</created>
  296.    <summary type="text/plain">&amp;#8220;Perhaps you&amp;#8217;re familiar with &amp;#8220;the tragedy of the commons,&amp;#8221; a social dilemma outlined by the late biologist Garrett Hardin in a famous 1968 essay of the same name. The dilemma is that when individuals pursue personal gain, the net result... (528 words)</summary>
  297.    <author>
  298.      <name>Curt</name>
  300.    </author>
  301.    <dc:subject>Economics</dc:subject>
  302.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  303.      <![CDATA[<p><i>&#8220;Perhaps you&#8217;re familiar with &#8220;the tragedy of the commons,&#8221; a social dilemma outlined by the late biologist Garrett Hardin in a famous 1968 essay of the same name. The dilemma is that when individuals pursue personal gain, the net result for society as a whole may be impoverishment. (Pollution is the most familiar example.) Such thinking has fallen out of fashion amid President Bush&#8217;s talk of an &#8220;ownership society,&#8221; but its logic is unassailable.&#8221;</i></p>
  305. <p><a href="">That response</a> seems like a pretty damn obtuse interpretation of the essay, simply because the essay is nothing if not a plea for the creation of property rights.  Furthermore, while it is true that Hardin claims that pursuing individual gain leads to group catastrophe, the word &#8220;when&#8221; in the paragraph above implies that there are times when the individual doesn&#8217;t, whereas Hardin claims that individuals basically always pursue their own interest, which is the problem in high-density situations where some amout of coordination is necessary.  However, upon re-reading it, I realize that for Hardin property rights only forms a part of a wished-for imposition of coercive measures which will prevent individuals from pursuing personal gain at the expense of their environment.  Which makes sense, because property rights, for all this may get lost in the ceaseless ideological wrangling today, are themselves forms of <i>state-imposed coercion</i>.  Dismiss the semi-metaphysical nonsense in Locke and Kant about gaining &#8220;just propriety&#8221; over an object by making a visible mark on it.  Think about it: animals control exactly as much &#8220;property&#8221; as they can defend; cheetahs peeing on trees only works because they will fight to defend what they have claimed.  By contrast, think about who adjudicates the (in theory) incontestable property rights: <i>the authorities</i>, i.e. in our society, the State.  The corollary of this, of course, is that nationalized or federal property is not &#8220;public property,&#8221; in the sense of property owned by the public&#8212;quite the contrary.  The dichotomy between it and &#8220;private property&#8221; is spurious.  &#8220;Public property&#8221; is simply property owned by the government.  This no doubt seems obvious and intuitive, but based on the foolishness I cited above, it bears repeating that property rights, whether granted to others by the government or to itself, are not opposed to coercive state power but are in fact <i>the very essence of it</i>.  That fact is perhaps more apparent in regards to so-called &#8220;intellectual property.&#8221;</p>
  307. <p>As a marginal note, Hardin&#8217;s essay, despite the pithiness of its central analogy, is rather dispiriting insofar as it takes Hegel&#8217;s statement that &#8220;Freedom lies in the recognition of necessity&#8221; as its motto and guiding spirit.  That formulation is, as I believe I have said before, perfectly monstruous.  Freedom means nothing if it is not the absence of restriction, and it is perhaps a sign of the evasive confusion of priorities in Western culture that one would pretend to celebrate this value in such a way while in fact describing its opposite.  Freedom is not an act or a thought, but rather a set of conditions under which action and thought occur.  This is the same idealistic debasement of the language that has turned love into a deed: <i>making love</i>.   </p>
  308. ]]>
  311.    </content>
  312.  </entry>
  313.  <entry>
  314.    <title>So much for the End of History</title>
  315.    <link rel="alternate" type="text/html" href="" />
  316.    <modified>2005-01-31T00:05:39Z</modified>
  317.    <issued>2005-01-30T19:05:39-05:00</issued>
  318.    <id>,2005://1.576</id>
  319.    <created>2005-01-31T00:05:39Z</created>
  320.    <summary type="text/plain">Just some cheerful words to chew on while our politicians wear their enamels off congratulating themselves about the Iraqi election: &amp;#8220;The collapse of the rival giant [the Soviet Union] has exaggerated America\x92s apparent strength because it has so much more... (231 words)</summary>
  321.    <author>
  322.      <name>Curt</name>
  324.    </author>
  325.    <dc:subject>Politics</dc:subject>
  326.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  327.      <![CDATA[<p>Just <a href=",,1065-1451138,00.html">some cheerful words</a> to chew on while our politicians wear their enamels off congratulating themselves about the Iraqi election:</p>
  329. <p>&#8220;The collapse of the rival giant [the Soviet Union] has exaggerated America\x92s apparent strength because it has so much more economic muscle than any single rival.  But for many decades America\x92s share of the world\x92s economic output has been in decline. Think of a see-saw. America at one end is now easily outweighed by any substantial grouping at the other, and most of those powers are on friendly terms with each other. America\x92s modesty in 1945 understated its muscle, just as Bushite vanity overstates it today. He has over-reached. His country is overstretched, losing economic momentum, losing world leadership, and losing the philosophical plot. America is running into the sand.&#8221;</p>
  331. <p>Maybe I&#8217;ve been hanging out in France, where declinism (both French and American) never goes out of fashion, for too long, but that assessment seems more convincing than <a href="">this disappointing &#8220;We are so great&#8212;right now&#8221; rebuttal</a> by Victor Hanson.  And the CIA <a href="">seems to concur</a> (though admittedly in more neutral language):</p>
  333. <p>&#8220;The likely emergence of China and India &#8230; as new major global players\x97similar to the advent of a united Germany in the 19th century and a powerful United States in the early 20th century\x97will transform the geopolitical landscape with impacts potentially as dramatic as those in the previous two centuries.&#8221;</p>
  334. ]]>
  337.    </content>
  338.  </entry>
  339.  <entry>
  340.    <title>The anthropomorphism of religion</title>
  341.    <link rel="alternate" type="text/html" href="" />
  342.    <modified>2005-01-28T21:07:33Z</modified>
  343.    <issued>2005-01-28T16:07:33-05:00</issued>
  344.    <id>,2005://1.575</id>
  345.    <created>2005-01-28T21:07:33Z</created>
  346.    <summary type="text/plain">I might deduce one final consequence of a skepticism in regards to temporality and causality. If our only experience of the world is of an existent reality, such that something uncreated or destroyed is literally unimaginable, the superfluity of religion... (104 words)</summary>
  347.    <author>
  348.      <name>Curt</name>
  350.    </author>
  351.    <dc:subject>Geek Talk</dc:subject>
  352.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  353.      <![CDATA[<p>I might deduce one final consequence of a skepticism in regards to temporality and causality.  If our only experience of the world is of an existent reality, such that something uncreated or destroyed is literally unimaginable, the superfluity of religion becomes very evident.  Since it is on the basis of a parallel between finite objects, which are presumed to be necessarily created, and the universe in its totality, which in turn therefore needs its Creator, that modern religions ultimately justify themselves, if creation, rather than lack of creation, is taken to be the phenomenon unjustified by experience then the concept of God is unwarranted.</p>
  354. ]]>
  357.    </content>
  358.  </entry>
  359.  <entry>
  360.    <title>And Prospero broke his soap box</title>
  361.    <link rel="alternate" type="text/html" href="" />
  362.    <modified>2005-01-26T21:26:50Z</modified>
  363.    <issued>2005-01-26T16:26:50-05:00</issued>
  364.    <id>,2005://1.574</id>
  365.    <created>2005-01-26T21:26:50Z</created>
  366.    <summary type="text/plain">I may have bored everyone to death about this topic, but I have my last exam tomorrow, so here is my final thought about what distinguishes science. Most of the descriptions of science that I know of don&amp;#8217;t really explain... (1410 words)</summary>
  367.    <author>
  368.      <name>Curt</name>
  370.    </author>
  371.    <dc:subject>Science</dc:subject>
  372.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  373.      <![CDATA[<p>I may have bored everyone to death about this topic, but I have my last exam tomorrow, so here is my final thought about what distinguishes science.  Most of the descriptions of science that I know of don&#8217;t really explain how science progresses without falling into a quaint mythology about approaching some metaphysical truth.  Kuhn doesn&#8217;t, Popper doesn&#8217;t, Pierre Duhem doesn&#8217;t, and I myself have neglected to account for it to some extent.  </p>
  375. <p>I think the key is that science, at least experimental science, is essentially concerned with predicting the future.  Every hypothesis, in essence, is a prediction about the future.  What distinguishes science from other forms of prediction is the emphasis on verification, the insistence on framing predictions in such a way that when they are tested they can be decisively answered positively or negatively.  In other, the goal is not to not be wrong but to achieve a definitive positive answer.  Even a definite negative answer is preferable to none at all.</p>
  377. <p>Some philosophers, like Duhem, claim that individual hypotheses can neither be verified nor falsified, because a whole body of theories and assumptions lies behind, and is implicated in, every hypothesis, and thus one can never be sure just what has been validated or failed.  While that&#8217;s true, it is also nonetheless true that when the result of an experiment does not match a hypothetical prediction the hypothesis has been proven invalid <i>as it stands</i>.  In other words, no matter what went wrong, the body of theories and assumptions that led to the hypothesis do not work as they now stand.  Thus, things will have to be changed until they produce accurate predictions.  Conversely, if a hypotheis is corroborated with a positive answer, the theories behind it stand validated until a hypothesis receives a negative answer.</p>
  379. <p>In other words, experimentation does not serve to lead by induction to new theories, but rather theories serve to make possible specific predictions about the future which can be verified decisively.  This at least is the goal.  The goal is not a description which is true or corresponds to the truth, or at least that is not the immediate goal.  When the facts or events are given, anyone can interpret them, and the fact that these events are known can mask the relative merits of the theory which interprets them.  The idea that theories are validated by their correspondence to experimental results is tautological: the first condition of any theory is that it accounts for the experimental results that gave rise to it.  But the only way to determine whether it is simply a theory to fit the facts or whether it is truly generalizable is to test it against unknown facts via prediction.  Of course, predictions are almost always only approximately true, so the specific point of acceptability is not provided for by the general concept, but, at least in theory, decisive verification of predictions provides a simple, clear, and immensely useful criterion by which to evaluate theories.  In my opinion, this explains much of the evolutionary capacity of science (I mean evolution in the more contemporary sense of diversification and selection rather than the old idea of teleological perfectibility).  </p>
  381. <p>If experimental prediction is the mark of science, this leaves the question of whether purely descriptive disciplines like zoology and areas like quantum theory where predictions are inherently statistical and ambiguous are scientific.  Zoology and the like I think are, because hypothetical prediction inherently implies classification.  In other words, by saying &#8220;under these conditions, such an event will happen,&#8221; one classifies, in other words sets parameters.  The goal of zoology seems to be not simply to describe members of a group but to describe all the characteristics which define the group, set the parameters of the group, which is the first step towards making predictions about the group.  So it is an element of science, but incomplete.  As for quantum, I avow my profound ignorance of it, so let my opinion be taken in that light.  As far as I understand, the stastical laws in that realm allow predictions in aggregate, so I am inclined to view it as still within the domain of science, at least in spirit, but of course the lack of decisiveness of statistical predictions gravely weakens the predictive power of science in this area, and I have already suggested that the rise of relativity and quantum in my view are intimately tied to the waning of the scientific age.  Finally, it should be noted that while making correct predictions is the goal of science, that should be qualified by saying that the predictions are intended to answer general questions concerning the nature of things and establish specific knowledge.  Optics or engineering, for example, are not science, although they once were, because all the major questions have been answered, and they no longer concern gaining further knowledge of the future and the universe, but rather in applying that knowledge to constructing specific objects.</p>
  383. <p>So the goal and value of science is in predicting, and thus establishing knowledge of, the future, and the scientific method is the means of arriving at correct predictions.  This is not to discard my earlier contention about the ideological basis of science, because the efficacy of prediction is based on the relative value of induction, and successful induction relies on the essential regularity and stability of the universe.  In other words, in order to draw a general theory from a specific experimental result and vice versa, the universe must be considered as basically the same everywhere and at  every time, which in turn implies that it be material, matter being defined as that which cannot change itself and is therefore static.  It seems to me that if in quantum theory, for example, phenomena become genuinely dependent on the observeer in ways that are neither generalizable nor predicatable, it cannot continue to remain truly a science.  It would seem to me that the branches of physics which are entirely theoretical are for practical purposes basically metaphysics.</p>
  385. <p>This model depends on a linear notion of time.  It might seem the opposite, that if the physical laws are eternal and universal time is actually opposed to this insofar as it represents dynamism, change.  But in reality the sameness of the universe upon which science is predicated is not a a sameness at any particular moment, but rather a sameness of behavior.  In other words, a view of the universe from a materialist perspective at any given moment shows that everything in the univese is different in the sense of being distinct.  However, the idea is that under the same conditions all matter (or whatever you call the fundamental substances) will act in the same way.  Without the steady march of time, this unity of behavior disappears, and there are simply a million disparate entities.  Thus, space (and time) as <i>properties</i> of the universe are essential to science.</p>
  387. <p>As for what the <i>value</i> of science is, I&#8217;m afraid I can&#8217;t generalize about that.  From reading my recent posts one can most likely guess at my views, but I will simply say that one&#8217;s view of the efficacy of science in making the universe understandable will probably depend on entirely on whether one a) believes that linear time is a real property of the universe and b) if so, whether true induction is possible. </p>
  389. <p>p.s.  I should note that Henri Poincaré anticipates me in seeing the epistemological value of science as consisting mainly of its ability to make predictions rather than its descriptive correspondence to reality.  However, he also thinks that theories are conventions and definitions of concepts, not true descriptions of physical phenomena based necessarily on experimental results.  He thinks the conjunction of these two make theories relatively independent of their experimental bases, which he regards as a good thing because it creates a body of stable principles in which we can trust.  I think that that is neither true nor a good value.  The emphasis is on predicting correctly, not creating stable beliefs (if you want unchanging beliefs, what not join the Church?), and if generating true predictions is the goal, theories should be more rather than less sensitive to their experimental roots.</p>
  391. <p>p.p.s.  Since my exam was about scientific laws and causality, I should add that while scientific <i>activity</i> depends on a belief in time, not all scientific <i>theories</i> do: the law of conservation of energy, for example, I believe is essentially atemporal.</p>
  392. ]]>
  395.    </content>
  396.  </entry>
  397.  <entry>
  398.    <title>Einstein and Gödel, at the Königsberg café</title>
  399.    <link rel="alternate" type="text/html" href="" />
  400.    <modified>2005-01-22T21:38:04Z</modified>
  401.    <issued>2005-01-22T16:38:04-05:00</issued>
  402.    <id>,2005://1.572</id>
  403.    <created>2005-01-22T21:38:04Z</created>
  404.    <summary type="text/plain">About a month ago I wrote this entry which was, I think, somewhat misunderstood, at least by the one confirmed reader of it. In it I tried to argue that there are some fundamental problems involved in conceptualizing time which,... (729 words)</summary>
  405.    <author>
  406.      <name>Curt</name>
  408.    </author>
  409.    <dc:subject>Science</dc:subject>
  410.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  411.      <![CDATA[<p>About a month ago I wrote <a href="">this entry</a> which was, I think, somewhat misunderstood, at least by the one confirmed reader of it.  In it I tried to argue that there are some fundamental problems involved in conceptualizing time which, in my mind, appear intractable, and hence its existence as a concept contradictory, impossible.  To which it was replied that of course time has an existence, as a social convention, a mental framework.  Of that I have no doubt-it would be impossible for me to refute even if I wanted to.  My point was about metaphysics, not sociology, and in that regard I don&#8217;t think it was that much different from that expressed by St. Augustine regarding time: &#8220;if no one asks me what it is I know what it is, but if someone asks me I don&#8217;t know.&#8221;  Or, even more notably, Kant, who regarded time, in addition to space, not as an entity, process, or property of the physical world, but as a filter of percpetion, the mental framework which orders our experience of the world.  </p>
  413. <p>Which brings me back to science.  I just finished reading <i><a href=;s=books>The Evolution of Physics</a></i>, by Einstein and Leopold Infeld.  Of course Einstein is justly famed for, among many other things, pioneering the idea of space-time.  However, I was quite intrigued to discover, while perusing the science section at the National Library in Paris, that Gödel claimed that his late work on relativity and physics, upon which I touched in my earlier post, was inspired by an intense study of Kant.  Now, assuming such a dour man as Gödel was not simply being facetious, the implications of this are immediate.  In the (apparent) somewhat paradoxical act of tearing down the structure of Einstein&#8217;s work while bringing some of its deepest tendencies to fruition, he was working under the influence of a theory which denies the type of external, property-based existence which Einstein implicitly ascribes to time (and space)!  As I understand special relativity (always a dubious premise, I grant you), it holds that space and time, <i>as properties of the universe</i>, are perceived differently at every point of view, or coordinate system, as he calls them.  But for me it seems a question of the simplest explanation: if everyone is in a relative frame of reference with respect to space and time, is it simpler and more likely that time and space are real properties which are different at every point in the universe, or simply that they are perceived differently by each observer?  It seems to me that if one takes Kant&#8217;s idea of space and time as elements perception and not of external reality, none of these problems come up, although there may of course be others.  Again, it&#8217;s hard for me to say what Gödel&#8217;s interpretation of all of this is, since no one seems to have engaged and propogated his work on this subject much, but if he was following in the line of Kant&#8217;s thinking as well as the tradition of relativity, it would be interesting to see the resuscitation, by &#8220;a commodius vicus of recirculation,&#8221; of a very powerful and cogent point of view which has nonetheless been largely dismissed by scientists as non-pertinently metaphysical.  Perhaps interesting also to note that, in dealing with Kant last year, I protested against his classification of space as a perceptual framework, and even managed to convince my philosophy professor that it is rather the fundamental visual property, before reversing myself and concluding that light is actually the fundamental visible property.  Light is also in some ways the fundamental property in Einstein&#8217;s system, or at least the one constant in all of the warping of space-time, which somehow doesn&#8217;t seem so surprising now&#8230;</p>
  415. <p>p.s.  For all of those intersted in Spanish literature (which at this point probably composes nearly 100% of our readership), I also came across <a href=,,1059-1449680,00.html>this article</a> with the following sub-headline: <i>&#8220;It is the 400th anniversary of Don Quixote, a more important work than all of Einstein&#8217;s theories.&#8221;</i>  To the extent that the article follows up on this point, I think the claim about the inevitability of scientific discovery is at the very least highly disputable (and even if Cervantes&#8217; work is more inimitable, that does not in itself mean that it is more &#8220;important&#8221;), but nonetheless a provocative idea, and gratifying to my humanities-leaning heart.</p>
  416. ]]>
  419.    </content>
  420.  </entry>
  421.  <entry>
  422.    <title>Philosophical Investigations</title>
  423.    <link rel="alternate" type="text/html" href="" />
  424.    <modified>2005-01-07T00:47:23Z</modified>
  425.    <issued>2005-01-06T19:47:23-05:00</issued>
  426.    <id>,2005://1.562</id>
  427.    <created>2005-01-07T00:47:23Z</created>
  428.    <summary type="text/plain">...not my own, of course. (989 words)</summary>
  429.    <author>
  430.      <name>shonk</name>
  431.      <url></url>
  432.    </author>
  433.    <dc:subject>Ramblings</dc:subject>
  434.    <content type="text/html" mode="escaped" xml:lang="en" xml:base="">
  435.      <![CDATA[<p>As promised, quotations from Wittgenstein&#8217;s <a href=";code=xm2" title=" Philosophical Investigations: The German Text, With a Revised English Translation: Explore similar items"><em>Philosophical Investigations</em></a> are <a href=";investigations.html" title="Books: Philosophical Investigations">now available</a>.  Again, both German and English versions of each are reproduced, though the task was made considerably easier than in other cases by the fact that the edition I used was a dual-language edition.</p>
  437. <p>I (like, I suspect, many others) find Wittgenstein simultaneously fascinating and annoying.  On the one hand, he makes interesting and insightful observations on all sorts of phenomena; on the other, he never really synthesizes those observations into a single, coherent argument.  For example, when he says that &#8220;Uttering a word is like striking a note on the keyboard of the imagination&#8221; (I&#167;6) or that &#8220;Philosophy is a battle against the bewitchment of our intelligence by means of our language&#8221; (I&#167;109) or that &#8220;The fluctuation of scientific definitions: what to-day counts as an observed concomitant of a phenomenon will to-morrow be used to define it&#8221; (I&#167;79) I find myself saying &#8220;Right on!&#8221;; but I also find myself frustrated by the fact that he can&#8217;t even decide on what, exactly, his purpose in writing this all down is.  For example, at one point Wittgenstein claims that his &#8220;aim in philosophy&#8221; is &#8220;To shew the fly the way out of the fly-bottle&#8221; (I&#167;309), while elsewhere he says: &#8220;My aim is: to teach you to pass from a piece of disguised nonsense to something that is patent nonsense&#8221; (I&#167;464) and still elsewhere he suggests that he&#8217;s merely making obvious remarks that presumably everybody already knows:</p>
  439. <blockquote>
  440. <p>What we are supplying are really remarks on the natural history of human beings; we are not contributing curiosities, however, but observations which no one has doubted, but which have escaped remark only because they are always before our eyes. (I&#167;415)</p>
  441. </blockquote>
  443. <p>As I say, this can be frustrating, but, in a way, is also understandable.  In one sense, Wittgenstein isn&#8217;t <em>trying</em> to provide answers, but rather to show that there aren&#8217;t really any problems (as he says in <a href=";code=xm2" title=" Books: Philosophical Grammar: Explore similar items"><em>Philosophical Grammar</em></a>: &#8220;While thinking philosophically we see problems in places where there are none.  It is for philosophy to show that there are no problems.&#8221;).  And why aren&#8217;t there any problems?  Because &#8220;philosophical problems arise when language <em>goes on holiday</em>&#8221; (I&#167;38); our problems derive from an inability to properly express ourselves.  </p>
  445. <p>(INTERPOLATION: This isn&#8217;t stated very well, so I want to expand just a bit.  The idea, as I understand it, is that we ask <em>too much</em> of language; that is, we ignore the fact that &#8220;Explanations come to an end somewhere&#8221; (I§1), that, as quoted below, &#8220;language itself cannot be explained&#8221;, but, rather, that it can only be understood by its use.  In failing to recognize this, we find ourselves unable to express the explanations we seek.)</p>
  447. <p>Within this context, I think Wittgenstein&#8217;s thesis (to the extent that he even has one) boils down to the following:</p>
  449. <blockquote>
  450. <p>What we have rather to do is to <em>accept</em> the everyday language-game, and to note <em>false</em> accounts of the matter as false. The primitive language-game which children are taught needs no justification; attempts at justification need to be rejected. (II.xi)</p>
  451. </blockquote>
  453. <p>Or, from a different direction:</p>
  455. <blockquote>
  456. <p>&#8220;So you are saying that human agreement decides what is true and what is false?&#8221;&#8212;It is what human beings say that is true and false; and they agree in the language they use. That is not agreement in opinions but in form of life. (I&#167;241)</p>
  457. </blockquote>
  459. <p>Viewed from this perspective, then, it is, perhaps, not so surprising that Wittgenstein has a tendency to be frustratingly vague at times; after all, as he himself says, &#8220;What is most difficult here is to put this indefiniteness, correctly and unfalsified, into words&#8221; (II.xi).  Personally, I find his perspective compelling, but I can understand why some might find it rather superficial, especially since it can lead to seemingly-trivial statements like: &#8220;One wants to say: a significant sentence is one which one can not merely say, but also think&#8221; (I&#167;511).</p>
  461. <p>All this aside, though, there are two other things I really like about Wittgenstein.  First, the fact that he has a real sense of humor and isn&#8217;t afraid to deploy it.  For example, I couldn&#8217;t help laughing aloud at reading this:</p>
  463. <blockquote>
  464. <p>Think of a picture of a landscape, an imaginary landscape with a house in it.&#8212;Someone asks &#8220;Whose house is that?&#8221;&#8212;The answer, by the way, might be &#8220;It belongs to the farmer who is sitting on the bench in front of it&#8221;.  But then he cannot for example enter his house. (I&#167;398)</p>
  465. </blockquote>
  467. <p>Of course, it probably helps that his sense of humor has that bone-dry, literalistic bent that is characteristic of mathematicians (if you don&#8217;t see the humor in the above, re-read the last two sentences like a died-in-the-wool literalist).  Which brings me to the second appeal Wittgenstein has for me: he has at least some understanding and awareness of mathematics.  And, of course, I can&#8217;t help but be excited when someone seems to agree with my own quasi-Intuitionist perspective:</p>
  469. <blockquote>
  470. <p>Of course, in one sense mathematics is a branch of knowledge,&#8212;but still it is also an activity.  And &#8216;false moves&#8217; can only exist as the exception.  For if what we now call by that name became the rule, the game in which they were false moves would have been abrogated. (II.xi)</p>
  471. </blockquote>
  473. <p>And, though it doesn&#8217;t explicitly refer to mathematics, Wittgenstein&#8217;s initial (or final, depending on how you look at it) conclusion has a distinctly mathematical feel to it (especially within the context of <a href=";paradox" title="Russell's paradox - Wikipedia, the free encyclopedia">Russell&#8217;s paradox</a>): </p>
  475. <blockquote>
  476. <p>What is spoken can only be explained in language, and so in this sense language itself cannot be explained.</p>
  477. <p>Language must speak for itself.</p>
  478. </blockquote>
  480. <p>(Actually from <em>Philosophical Grammar</em>, but echoed throughout <em>Philosophical Investigations</em>)</p>
  482. <p>Okay, enough book-reviewing; <a href=";investigations.html" title="Books: Philosophical Investigations">check out the quotations</a>.</p>
  483. ]]>
  486.    </content>
  487.  </entry>
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