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	<title>Comments on: Complexity and abstraction</title>
	<atom:link href="http://www.langabi.name/blog/2005/07/10/complexity-and-abstraction/feed" rel="self" type="application/rss+xml" />
	<link>http://langabi.name/blog/2005/07/10/complexity-and-abstraction</link>
	<description>Paul Cook's blog</description>
	<pubDate>Fri, 10 Feb 2012 00:23:06 +0000</pubDate>
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		<title>By: paulcook</title>
		<link>http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-7393</link>
		<dc:creator>paulcook</dc:creator>
		<pubDate>Thu, 22 Feb 2007 07:26:11 +0000</pubDate>
		<guid isPermaLink="false">http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-7393</guid>
		<description>When reality seems really complicated, one can always abstract away all the nitty-gritty linear details of logic or ordered discourse. Apparently.

"Generally finite beings" -- does that mean sometimes we aren't? Or that some of us aren't?</description>
		<content:encoded><![CDATA[<p>When reality seems really complicated, one can always abstract away all the nitty-gritty linear details of logic or ordered discourse. Apparently.</p>
<p>&#8220;Generally finite beings&#8221; &#8212; does that mean sometimes we aren&#8217;t? Or that some of us aren&#8217;t?</p>
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		<title>By: Raj</title>
		<link>http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-7392</link>
		<dc:creator>Raj</dc:creator>
		<pubDate>Thu, 22 Feb 2007 04:14:16 +0000</pubDate>
		<guid isPermaLink="false">http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-7392</guid>
		<description>In a greater scheme of things it is always in balance, including at the national, racial, religious and profession level(s).

In order to acheive the Buddha (Avtar) mind body states, you should correct the issues in the past.

The mind (brain) is non linear.

We are generally finite beings.</description>
		<content:encoded><![CDATA[<p>In a greater scheme of things it is always in balance, including at the national, racial, religious and profession level(s).</p>
<p>In order to acheive the Buddha (Avtar) mind body states, you should correct the issues in the past.</p>
<p>The mind (brain) is non linear.</p>
<p>We are generally finite beings.</p>
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		<title>By: MDA</title>
		<link>http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-427</link>
		<dc:creator>MDA</dc:creator>
		<pubDate>Tue, 12 Jul 2005 19:55:14 +0000</pubDate>
		<guid isPermaLink="false">http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-427</guid>
		<description>You'll need the cutoff to be an intensive property.  In fact, the cutoff related to any abstraction of physical laws should always be dimensionless.  In the case of thermodynamics (well... let me talk statistical mechanics) one typical parameter is proportional to the average distance between particles divided by the typical wavelength of a particle (as I recall, this number is actually reported using densities &lt;code&gt;=&#62; ^3&lt;/code&gt;... and perhaps inverted).

If that parameter is large, things simplify nicely (everyone likes classical mechanics and counting problems right?).  Pack things too tightly, though, and you need to worry about serious quantum effects.  Of course, a different level of abstraction, as you call it, would just try to average these quantum effects (to low order) and roll them into some other (it better be dimensionless!) parameter.

This is all a &lt;em&gt;little&lt;/em&gt; naive, though, since you obviously can't get classical thermodynamics out of just one particle.  So there's also an absolute number requirement as you suggest Paul, and over which Adam mulls.  How do we turn such an (extensive) requirement into an intensive (and dimensionless) number?  Stastics to the rescue again.  It's related to the relative distribution of the particles' energies.  A tight distribution, and you've got a well defined thermodynamic Temperature. That is, only one parameter is really needed to specify the distribution: it's average.  A broad one, and you've got to do more work; you need more parameters.</description>
		<content:encoded><![CDATA[<p>You&#8217;ll need the cutoff to be an intensive property.  In fact, the cutoff related to any abstraction of physical laws should always be dimensionless.  In the case of thermodynamics (well&#8230; let me talk statistical mechanics) one typical parameter is proportional to the average distance between particles divided by the typical wavelength of a particle (as I recall, this number is actually reported using densities <code>=&gt; ^3</code>&#8230; and perhaps inverted).</p>
<p>If that parameter is large, things simplify nicely (everyone likes classical mechanics and counting problems right?).  Pack things too tightly, though, and you need to worry about serious quantum effects.  Of course, a different level of abstraction, as you call it, would just try to average these quantum effects (to low order) and roll them into some other (it better be dimensionless!) parameter.</p>
<p>This is all a <em>little</em> naive, though, since you obviously can&#8217;t get classical thermodynamics out of just one particle.  So there&#8217;s also an absolute number requirement as you suggest Paul, and over which Adam mulls.  How do we turn such an (extensive) requirement into an intensive (and dimensionless) number?  Stastics to the rescue again.  It&#8217;s related to the relative distribution of the particles&#8217; energies.  A tight distribution, and you&#8217;ve got a well defined thermodynamic Temperature. That is, only one parameter is really needed to specify the distribution: it&#8217;s average.  A broad one, and you&#8217;ve got to do more work; you need more parameters.</p>
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		<title>By: Adam</title>
		<link>http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-426</link>
		<dc:creator>Adam</dc:creator>
		<pubDate>Tue, 12 Jul 2005 06:43:17 +0000</pubDate>
		<guid isPermaLink="false">http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-426</guid>
		<description>One mole == Number of carbon-12 atoms in 0.012 kg of carbon-12 ~= 6.0221415(10) x 10^23 particles

&lt;a href="http://en.wikipedia.org/wiki/Mole_(unit)" rel="nofollow"&gt;Wikipedia: Mole&lt;/a&gt;
&lt;a href="http://en.wikipedia.org/wiki/Avogadro's_number" rel="nofollow"&gt;Wikipedia: Avogadro's Number&lt;/a&gt;
&lt;a href="http://www.moleday.org/" rel="nofollow"&gt;National Mole Day Foundation&lt;/a&gt;

Incidentally, I would put the cutoff for "macroscopic" amounts of gas at much smaller than one mole.  In fact, consider a liter of very low pressure gas (I'm talking millitorr here) at non-cryogenic temperatures.  Gas at that pressure contains much less than one mole of particles, but the typical gas laws will still apply.  To tell the truth, I'm not quite sure where to put the cutoff above which gas can be considered "bulk".</description>
		<content:encoded><![CDATA[<p>One mole == Number of carbon-12 atoms in 0.012 kg of carbon-12 ~= 6.0221415(10) x 10^23 particles</p>
<p><a href="http://en.wikipedia.org/wiki/Mole_(unit)" rel="nofollow">Wikipedia: Mole</a><br />
<a href="http://en.wikipedia.org/wiki/Avogadro's_number" rel="nofollow">Wikipedia: Avogadro&#8217;s Number</a><br />
<a href="http://www.moleday.org/" rel="nofollow">National Mole Day Foundation</a></p>
<p>Incidentally, I would put the cutoff for &#8220;macroscopic&#8221; amounts of gas at much smaller than one mole.  In fact, consider a liter of very low pressure gas (I&#8217;m talking millitorr here) at non-cryogenic temperatures.  Gas at that pressure contains much less than one mole of particles, but the typical gas laws will still apply.  To tell the truth, I&#8217;m not quite sure where to put the cutoff above which gas can be considered &#8220;bulk&#8221;.</p>
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		<title>By: paulcook</title>
		<link>http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-425</link>
		<dc:creator>paulcook</dc:creator>
		<pubDate>Mon, 11 Jul 2005 22:44:18 +0000</pubDate>
		<guid isPermaLink="false">http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-425</guid>
		<description>Yes, there's a very good reason I picked 10^27: I thought that was how large a mole was. But you quite rightly point out that it's more like 10^23. Oops. I blame it on inflation.

Thanks for the comment!</description>
		<content:encoded><![CDATA[<p>Yes, there&#8217;s a very good reason I picked 10^27: I thought that was how large a mole was. But you quite rightly point out that it&#8217;s more like 10^23. Oops. I blame it on inflation.</p>
<p>Thanks for the comment!</p>
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		<title>By: Adam</title>
		<link>http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-424</link>
		<dc:creator>Adam</dc:creator>
		<pubDate>Mon, 11 Jul 2005 22:35:31 +0000</pubDate>
		<guid isPermaLink="false">http://langabi.name/blog/2005/07/10/complexity-and-abstraction#comment-424</guid>
		<description>Very good post!  I look forward to reading the second part.  However, I have one criticism and one addition.

Criticism: At Standard Temperature and Pressure (0 C, 1 Atm), one mole (6.02x10^23 molecules) of gas occupies 22.4 L of space.  Thus, I would say that your cutoff for macroscopic quantities of gas (10^27 molecules) is several orders of magnitude too high.  Is there a reason you picked this number?

Addition: An example of where higher prices result in higher demand: Name brand foods versus store brand foods.  Consider Kellogg's Corn Flakes versus Ralph's brand corn flakes.  The Ralph's brand flakes are probably made by Kellogg's, thus there is no difference, nutritional- or taste-wise, between the two.  However, most people will shun the store brand cereal and go straight for the name brand cereal.  The only difference between the two is price (name brand is higher) and packaging (name brand is fancier).</description>
		<content:encoded><![CDATA[<p>Very good post!  I look forward to reading the second part.  However, I have one criticism and one addition.</p>
<p>Criticism: At Standard Temperature and Pressure (0 C, 1 Atm), one mole (6.02&#215;10^23 molecules) of gas occupies 22.4 L of space.  Thus, I would say that your cutoff for macroscopic quantities of gas (10^27 molecules) is several orders of magnitude too high.  Is there a reason you picked this number?</p>
<p>Addition: An example of where higher prices result in higher demand: Name brand foods versus store brand foods.  Consider Kellogg&#8217;s Corn Flakes versus Ralph&#8217;s brand corn flakes.  The Ralph&#8217;s brand flakes are probably made by Kellogg&#8217;s, thus there is no difference, nutritional- or taste-wise, between the two.  However, most people will shun the store brand cereal and go straight for the name brand cereal.  The only difference between the two is price (name brand is higher) and packaging (name brand is fancier).</p>
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