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	<title>Comments on: N Bodies</title>
	<atom:link href="http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/feed/" rel="self" type="application/rss+xml" />
	<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/</link>
	<description>Random samplings from a universe of ideas.</description>
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		<title>By: Napka&#8217;s Top Science &#187; The N Body Problem</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18994</link>
		<dc:creator>Napka&#8217;s Top Science &#187; The N Body Problem</dc:creator>
		<pubDate>Fri, 16 Nov 2007 15:41:18 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18994</guid>
		<description>[...] read more &#124; digg story [...]</description>
		<content:encoded><![CDATA[<p>[...] read more | digg story [...]</p>
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		<title>By: General Sciences &#187; The N Body Problem</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18969</link>
		<dc:creator>General Sciences &#187; The N Body Problem</dc:creator>
		<pubDate>Wed, 16 Aug 2006 13:45:44 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18969</guid>
		<description>[...] The N-body problem is one of the most famous, and easily stated, problems in mathematical physics: find exact solutions to point masses moving under their mutual Newtonian gravitational forces (i.e. the inverse-square law). But let N=3 and chaos breaks loose, quite literally.read more&#160;&#124;&#160;digg story [...]</description>
		<content:encoded><![CDATA[<p>[...] The N-body problem is one of the most famous, and easily stated, problems in mathematical physics: find exact solutions to point masses moving under their mutual Newtonian gravitational forces (i.e. the inverse-square law). But let N=3 and chaos breaks loose, quite literally.read more&nbsp;|&nbsp;digg story [...]</p>
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		<title>By: Dynamics of Cats</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18965</link>
		<dc:creator>Dynamics of Cats</dc:creator>
		<pubDate>Wed, 26 Jul 2006 15:46:35 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18965</guid>
		<description>&lt;strong&gt;Experimental Astrophysics&lt;/strong&gt;

 Doug Hamilton as a nifty Astronomy Workshop web page, with lots of fun little tools....</description>
		<content:encoded><![CDATA[<p><strong>Experimental Astrophysics</strong></p>
<p> Doug Hamilton as a nifty Astronomy Workshop web page, with lots of fun little tools&#8230;.</p>
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		<title>By: Tony</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18968</link>
		<dc:creator>Tony</dc:creator>
		<pubDate>Wed, 26 Jul 2006 08:49:41 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18968</guid>
		<description>bobocopy:

I can guess why anyone with limited time might not want to risk editing Wikipedia. The finer the sculpture, the more likely it is to have its nose knocked off by drunken 16-year-old vandals. The &quot;no original research&quot; policy is infinitely regressive. There&#039;s no mechanism to identify authority whatsoever.

You might consider adding a taunting footnote, in hopes that a seasoned warrior will see it and brave the gauntlet.</description>
		<content:encoded><![CDATA[<p>bobocopy:</p>
<p>I can guess why anyone with limited time might not want to risk editing Wikipedia. The finer the sculpture, the more likely it is to have its nose knocked off by drunken 16-year-old vandals. The &#8220;no original research&#8221; policy is infinitely regressive. There&#8217;s no mechanism to identify authority whatsoever.</p>
<p>You might consider adding a taunting footnote, in hopes that a seasoned warrior will see it and brave the gauntlet.</p>
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		<title>By: Jawad Shuaib</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18966</link>
		<dc:creator>Jawad Shuaib</dc:creator>
		<pubDate>Tue, 25 Jul 2006 16:50:52 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18966</guid>
		<description>owww this is amazing. Though, a lil&#039; bit of mathematics would&#039;ve been appreciated. But beautiful work nonetheless, thank you!</description>
		<content:encoded><![CDATA[<p>owww this is amazing. Though, a lil&#8217; bit of mathematics would&#8217;ve been appreciated. But beautiful work nonetheless, thank you!</p>
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		<title>By: bobocopy</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18967</link>
		<dc:creator>bobocopy</dc:creator>
		<pubDate>Tue, 25 Jul 2006 13:56:19 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18967</guid>
		<description>You mention that, &quot;The Wikipedia entry on PoincarÃ© tells a much less interesting, and less accurate, version of the story.&quot;  May I ask why if the story is so woefully inadequate 1) you link to it and 2) you have yet to fix the article?</description>
		<content:encoded><![CDATA[<p>You mention that, &#8220;The Wikipedia entry on PoincarÃ© tells a much less interesting, and less accurate, version of the story.&#8221;  May I ask why if the story is so woefully inadequate 1) you link to it and 2) you have yet to fix the article?</p>
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		<title>By: Steinn Sigurdsson</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18992</link>
		<dc:creator>Steinn Sigurdsson</dc:creator>
		<pubDate>Mon, 24 Jul 2006 15:24:42 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18992</guid>
		<description>There has been some exploration of the N-body problem for potentials other than the inverse square law - a 1/r^D-1 generlization follows from extending Gauss&#039;s law to extra dimensions (standard grad problem is to consider &quot;the problem&quot; in arbitary dimensions).
Most orbits are unstable in D != 3, so the problem is not as interesting is the short answer. The long answer is that the problem has not been studied as hard.

Not a lot of people know that there is an exact perturbation expansion solution to the three body problem, but it has rather poor convergence...</description>
		<content:encoded><![CDATA[<p>There has been some exploration of the N-body problem for potentials other than the inverse square law &#8211; a 1/r^D-1 generlization follows from extending Gauss&#8217;s law to extra dimensions (standard grad problem is to consider &#8220;the problem&#8221; in arbitary dimensions).<br />
Most orbits are unstable in D != 3, so the problem is not as interesting is the short answer. The long answer is that the problem has not been studied as hard.</p>
<p>Not a lot of people know that there is an exact perturbation expansion solution to the three body problem, but it has rather poor convergence&#8230;</p>
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		<title>By: nigel cook</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18993</link>
		<dc:creator>nigel cook</dc:creator>
		<pubDate>Mon, 24 Jul 2006 09:07:56 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18993</guid>
		<description>&#039;... the &#039;inexorable laws of physics&#039; ... were never really there ... Newton could not predict the behaviour of three balls ... In retrospect we can see that the determinism of pre-quantum physics kept itself from ideological bankruptcy only by keeping the three balls of the pawnbroker apart.&#039; â€&quot; Tim Poston and Ian Stewart, Analog, November 1981.

It isn&#039;t quantum physics that is the oddity, but actually classical physics! The normal teaching of Newtonian physics (at least at low levels) falsely claims/indoctrinates the persistent lie that it allows the positions of the planets to be exactly calculated (determinism) when it does not if you have 3+ bodies, which you do.  Richard P. Feynman conceded this in his book QED:

&#039;when the space through which a photon moves becomes too small (such as the tiny holes in the screen) ... we discover that ... there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, &lt;strong&gt;such as inside an atom, the space is so small&lt;/strong&gt; that ... interference becomes very important.&#039;

The interference is due to many vacuum virtual charges:

&#039;All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs.&#039; â€&quot; I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

The duration and maximum range of these charges is easily estimated: take the energy-time form of Heisenberg&#039;s uncertainty principle and put in the energy of an electron-positron pair and you find it can exist for ~10^-21 second; the maximum possible range is therefore this time multiplied by c, or 10^-12 metre.  This is far enough to deflect electrons but not enough to be observed as vacuum radioactivity.  Like Brownian motion, it introduces chaos on small scales, not lare ones:

&#039;... the Heisenberg formulae can be most naturally interpreted as statistical scatter relations, as I proposed [in the 1934 book &#039;The Logic of Scientific Discovery&#039;]. ... There is, therefore, no reason whatever to accept either Heisenberg&#039;s or Bohr&#039;s subjectivist interpretation ...&#039; â€&quot; Sir Karl R. Popper, Objective Knowledge, Oxford University Press, 1979, p. 303.

The Schroedinger wave equation arises naturally from a sea of particles because we know that you get waves in particle-based fluids: http://feynman137.tripod.com/#b</description>
		<content:encoded><![CDATA[<p>&#8216;&#8230; the &#8216;inexorable laws of physics&#8217; &#8230; were never really there &#8230; Newton could not predict the behaviour of three balls &#8230; In retrospect we can see that the determinism of pre-quantum physics kept itself from ideological bankruptcy only by keeping the three balls of the pawnbroker apart.&#8217; â€&#8221; Tim Poston and Ian Stewart, Analog, November 1981.</p>
<p>It isn&#8217;t quantum physics that is the oddity, but actually classical physics! The normal teaching of Newtonian physics (at least at low levels) falsely claims/indoctrinates the persistent lie that it allows the positions of the planets to be exactly calculated (determinism) when it does not if you have 3+ bodies, which you do.  Richard P. Feynman conceded this in his book QED:</p>
<p>&#8216;when the space through which a photon moves becomes too small (such as the tiny holes in the screen) &#8230; we discover that &#8230; there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, <strong>such as inside an atom, the space is so small</strong> that &#8230; interference becomes very important.&#8217;</p>
<p>The interference is due to many vacuum virtual charges:</p>
<p>&#8216;All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs.&#8217; â€&#8221; I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.</p>
<p>The duration and maximum range of these charges is easily estimated: take the energy-time form of Heisenberg&#8217;s uncertainty principle and put in the energy of an electron-positron pair and you find it can exist for ~10^-21 second; the maximum possible range is therefore this time multiplied by c, or 10^-12 metre.  This is far enough to deflect electrons but not enough to be observed as vacuum radioactivity.  Like Brownian motion, it introduces chaos on small scales, not lare ones:</p>
<p>&#8216;&#8230; the Heisenberg formulae can be most naturally interpreted as statistical scatter relations, as I proposed [in the 1934 book 'The Logic of Scientific Discovery']. &#8230; There is, therefore, no reason whatever to accept either Heisenberg&#8217;s or Bohr&#8217;s subjectivist interpretation &#8230;&#8217; â€&#8221; Sir Karl R. Popper, Objective Knowledge, Oxford University Press, 1979, p. 303.</p>
<p>The Schroedinger wave equation arises naturally from a sea of particles because we know that you get waves in particle-based fluids: <a href="http://feynman137.tripod.com/#b" rel="nofollow">http://feynman137.tripod.com/#b</a></p>
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		<title>By: Ambitwistor</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18970</link>
		<dc:creator>Ambitwistor</dc:creator>
		<pubDate>Mon, 24 Jul 2006 02:56:14 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18970</guid>
		<description>See the bottom of &lt;a href=&quot;http://www.burtleburtle.net/bob/physics/kempler.html&quot; rel=&quot;nofollow&quot;&gt;this page&lt;/a&gt; for an animation of the &lt;a href=&quot;http://en.wikipedia.org/wiki/Klemperer_rosette&quot; rel=&quot;nofollow&quot;&gt;Klemperer rosette&lt;/a&gt; of the puppeteer Fleet of Worlds in the Larry Niven novel &lt;i&gt;Ringworld&lt;/i&gt;.</description>
		<content:encoded><![CDATA[<p>See the bottom of <a href="http://www.burtleburtle.net/bob/physics/kempler.html" rel="nofollow">this page</a> for an animation of the <a href="http://en.wikipedia.org/wiki/Klemperer_rosette" rel="nofollow">Klemperer rosette</a> of the puppeteer Fleet of Worlds in the Larry Niven novel <i>Ringworld</i>.</p>
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		<title>By: bittergradstudent</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/comment-page-1/#comment-18971</link>
		<dc:creator>bittergradstudent</dc:creator>
		<pubDate>Mon, 24 Jul 2006 01:52:47 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2006/07/23/n-bodies/#comment-18971</guid>
		<description>chris #6--

nuclear physics is inherently quantum mechanical, so you can&#039;t get away with using the cold determinism of classical mechanics and hope to get answers corresponding to what experimentalists observe--you run into all sorts of odd probleems having to do with the indistinguishability of particles inside the nucleus, as well as the probabilistic nature of quantum mechanics.</description>
		<content:encoded><![CDATA[<p>chris #6&#8211;</p>
<p>nuclear physics is inherently quantum mechanical, so you can&#8217;t get away with using the cold determinism of classical mechanics and hope to get answers corresponding to what experimentalists observe&#8211;you run into all sorts of odd probleems having to do with the indistinguishability of particles inside the nucleus, as well as the probabilistic nature of quantum mechanics.</p>
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