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	<title>Comments on: How many dimensions are there?</title>
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	<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/</link>
	<description>Random samplings from a universe of ideas.</description>
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		<title>By: Brad Schuman</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8363</link>
		<dc:creator>Brad Schuman</dc:creator>
		<pubDate>Fri, 24 Mar 2006 23:18:37 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8363</guid>
		<description>It would seem that there should be as many dimensions as there are numbers to denote them.  An infinite number that can go on forever in a &quot;positive field&quot;, as well as an infinite number in a &quot;negative&quot; field.
I see no reason that there need be a finite number of dimensions anymore than there can be a finite numeric system.
Perhaps &quot;zero&quot; and &quot;infinity&quot; are actually one and the same.
I&#039;ve heard of the higher dimensions in string theory being spoken of as &quot;existing within a realm that&#039;s smaller than we can measure&quot;...which just sounds like a complicated explanation of describing the attributes of the &quot;infinitely small&quot;.
Any reason this assumption should be considered &quot;in error&quot;??</description>
		<content:encoded><![CDATA[<p>It would seem that there should be as many dimensions as there are numbers to denote them.  An infinite number that can go on forever in a &#8220;positive field&#8221;, as well as an infinite number in a &#8220;negative&#8221; field.<br />
I see no reason that there need be a finite number of dimensions anymore than there can be a finite numeric system.<br />
Perhaps &#8220;zero&#8221; and &#8220;infinity&#8221; are actually one and the same.<br />
I&#8217;ve heard of the higher dimensions in string theory being spoken of as &#8220;existing within a realm that&#8217;s smaller than we can measure&#8221;&#8230;which just sounds like a complicated explanation of describing the attributes of the &#8220;infinitely small&#8221;.<br />
Any reason this assumption should be considered &#8220;in error&#8221;??</p>
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		<title>By: Plato</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8362</link>
		<dc:creator>Plato</dc:creator>
		<pubDate>Wed, 08 Mar 2006 23:54:23 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8362</guid>
		<description>I know I am &lt;a href=&quot;http://eskesthai.blogspot.com/2006/03/new-search-paradigm.html&quot; rel=&quot;nofollow&quot;&gt;Physic-ally&lt;/a&gt; challenged sometimes, but I can&#039;t just take that for granted Claire. :)</description>
		<content:encoded><![CDATA[<p>I know I am <a href="http://eskesthai.blogspot.com/2006/03/new-search-paradigm.html" rel="nofollow">Physic-ally</a> challenged sometimes, but I can&#8217;t just take that for granted Claire. <img src='http://blogs.discovermagazine.com/cosmicvariance/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> </p>
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		<title>By: Claire</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8361</link>
		<dc:creator>Claire</dc:creator>
		<pubDate>Wed, 08 Mar 2006 17:21:28 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8361</guid>
		<description>There are 129600 dimensions. Don&#039;t ask why...</description>
		<content:encoded><![CDATA[<p>There are 129600 dimensions. Don&#8217;t ask why&#8230;</p>
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		<title>By: Plato</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8360</link>
		<dc:creator>Plato</dc:creator>
		<pubDate>Tue, 13 Dec 2005 18:12:24 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8360</guid>
		<description>In the perfect world, I like circles that are &lt;a href=&quot;http://eskesthai.blogspot.com/2005/12/string-theory-displays-golden-ratio.html&quot; rel=&quot;nofollow&quot;&gt;smoothly expressed&lt;/a&gt;, but it is not always like that?</description>
		<content:encoded><![CDATA[<p>In the perfect world, I like circles that are <a href="http://eskesthai.blogspot.com/2005/12/string-theory-displays-golden-ratio.html" rel="nofollow">smoothly expressed</a>, but it is not always like that?</p>
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		<title>By: Elliot</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8294</link>
		<dc:creator>Elliot</dc:creator>
		<pubDate>Tue, 13 Dec 2005 04:41:33 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8294</guid>
		<description>when speaking of physics inventions
there is none like the extra dimensions
but how many you query
well there&#039;s more than one theory
and discussion increases the tension


....oh wait this was supposed to go over on the poetry thread.... ;)

Elliot</description>
		<content:encoded><![CDATA[<p>when speaking of physics inventions<br />
there is none like the extra dimensions<br />
but how many you query<br />
well there&#8217;s more than one theory<br />
and discussion increases the tension</p>
<p>&#8230;.oh wait this was supposed to go over on the poetry thread&#8230;. <img src='http://blogs.discovermagazine.com/cosmicvariance/wp-includes/images/smilies/icon_wink.gif' alt=';)' class='wp-smiley' /> </p>
<p>Elliot</p>
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		<title>By: rof</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8295</link>
		<dc:creator>rof</dc:creator>
		<pubDate>Tue, 13 Dec 2005 02:45:11 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8295</guid>
		<description>Fyodor says: &lt;i&gt;Now you want to assert that mathematically indistinguishable situations are *equally real*. Maybe you can persuade us, but you won&#039;t do it by means of analogies with special relativity. You will do it by describing *precisely* how an observer who waves his arms about can possibly describe his experiences in terms of two different dimensionalities.&lt;/i&gt;

Exactly.

Moshe: I&#039;m sorry if my tone was too aggressive. I did get carried away on my high horse. Still, I stand by everything I said. Fyodor has expressed it perhaps more succinctly than I did. Good luck with the war on reality.

Fyodor: I believe that the answer from string theory would be the following. The observer would wave his arms around and count a certain number of dimensions. Then he would learn string theory and do experiments with an LHC and conclude from the particle spectrum that there are extra dimensions that he didn&#039;t count while waving his arms around. Some observers would be able to count all the dimensions by waving their arms and others would have a very difficult time finding them. What is indistinguishable is the final string-theoretic description of the world that the two would reach (which is what string theorists would call the real world), and the differences in the respective worlds that they see around them would be attributed to the fact that the observers would regard themselves as embedded in the stringy world in different ways. An observer imprisoned in a D-brane would be able to wave his arms in fewer directions than an observer who wasn&#039;t so imprisoned.</description>
		<content:encoded><![CDATA[<p>Fyodor says: <i>Now you want to assert that mathematically indistinguishable situations are *equally real*. Maybe you can persuade us, but you won&#8217;t do it by means of analogies with special relativity. You will do it by describing *precisely* how an observer who waves his arms about can possibly describe his experiences in terms of two different dimensionalities.</i></p>
<p>Exactly.</p>
<p>Moshe: I&#8217;m sorry if my tone was too aggressive. I did get carried away on my high horse. Still, I stand by everything I said. Fyodor has expressed it perhaps more succinctly than I did. Good luck with the war on reality.</p>
<p>Fyodor: I believe that the answer from string theory would be the following. The observer would wave his arms around and count a certain number of dimensions. Then he would learn string theory and do experiments with an LHC and conclude from the particle spectrum that there are extra dimensions that he didn&#8217;t count while waving his arms around. Some observers would be able to count all the dimensions by waving their arms and others would have a very difficult time finding them. What is indistinguishable is the final string-theoretic description of the world that the two would reach (which is what string theorists would call the real world), and the differences in the respective worlds that they see around them would be attributed to the fact that the observers would regard themselves as embedded in the stringy world in different ways. An observer imprisoned in a D-brane would be able to wave his arms in fewer directions than an observer who wasn&#8217;t so imprisoned.</p>
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		<title>By: Qubit</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8296</link>
		<dc:creator>Qubit</dc:creator>
		<pubDate>Tue, 13 Dec 2005 00:28:04 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8296</guid>
		<description>IMO, there are no dimensions at all. My existance, along with all of yours, is a virtual one. At some time, me and everybody else will die. From your own point of veiw at that moment, the universe, space-time, everything will come to an end and this will mean that; you will, never have existed.

My virtual existance, one day reached a singularity. To become real, meant I had to escape from the edge of an horizon and fall into a black hole, at the same time. This was not to live forever, I did this... Just to be born. When I was born, you all! Was already dead. For you all to have existed, would mean I had no choice, other than to escape, I did and I did become real and I was born.

Teddy bears dont work, Quantum physics is nonsense, there are no magic boxes, CATS SEE WITH TWO EYES and one day I will die!!</description>
		<content:encoded><![CDATA[<p>IMO, there are no dimensions at all. My existance, along with all of yours, is a virtual one. At some time, me and everybody else will die. From your own point of veiw at that moment, the universe, space-time, everything will come to an end and this will mean that; you will, never have existed.</p>
<p>My virtual existance, one day reached a singularity. To become real, meant I had to escape from the edge of an horizon and fall into a black hole, at the same time. This was not to live forever, I did this&#8230; Just to be born. When I was born, you all! Was already dead. For you all to have existed, would mean I had no choice, other than to escape, I did and I did become real and I was born.</p>
<p>Teddy bears dont work, Quantum physics is nonsense, there are no magic boxes, CATS SEE WITH TWO EYES and one day I will die!!</p>
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		<title>By: Plato</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8297</link>
		<dc:creator>Plato</dc:creator>
		<pubDate>Mon, 12 Dec 2005 16:07:15 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8297</guid>
		<description>&lt;a href=&quot;http://eskesthai.blogspot.com/2005/12/poincare-conjecture.html&quot; rel=&quot;nofollow&quot;&gt;&lt;blockquote&gt;Moshe is leaving me hanging on a limb now that he moves into the fighting reality while the poor clod like me is trying to live in the world created by scientists/ theorists.&lt;/blockquote&gt;&lt;/a&gt;</description>
		<content:encoded><![CDATA[<p><a href="http://eskesthai.blogspot.com/2005/12/poincare-conjecture.html" rel="nofollow"><br />
<blockquote>Moshe is leaving me hanging on a limb now that he moves into the fighting reality while the poor clod like me is trying to live in the world created by scientists/ theorists.</p></blockquote>
<p></a></p>
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		<title>By: Moshe</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8298</link>
		<dc:creator>Moshe</dc:creator>
		<pubDate>Mon, 12 Dec 2005 14:31:28 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8298</guid>
		<description>Guys, there are too many high horses around for my comfort. I believe I stated precisely what I mean, let me try to get over some confusions I can identify, and maybe for the rest you can try to read what I actually write.

First, I emphasize I did not mention string theory at all when talking about observables of quantum gravity, whether in 4 dimensions or in higher dimensions. If you define &quot;observables&quot; as those things that can be observed, where observation includes and actual observer and a measuring device, the only things that we know exist are S-matrix elements. Those include everything we ever measured. Now this was not a statement about string theory at all, and please try to contain your passion and wait for me to actually make an arrogant and ill-informed statement. Yes &quot;string theory observables&quot; is a term you made up yourself rof.

Second, since the beginning of quantum theory physics is defined as the attempt to describe and predict results of measurments, I have no interest in &quot;reality&quot; beyond that, whatever that may mean. That is precisely why I caution talking about all kinds of comfortable notions one may have, and try to concentrate on precise statements about results of measurments.

All I had to say about T-duality was in the context of string theory, where this thing exist. It was not a statement about the real world where we don&#039;t have experimental evidence for T-duality.  If string thoery describes the world and it has a compact circle, there are no measurements that will distinguish a small circle from a large one. Since I am only interested in results of measurments there is no reason for me to choose.

I think I will leave it at that, there is too much war on reality to do this week.</description>
		<content:encoded><![CDATA[<p>Guys, there are too many high horses around for my comfort. I believe I stated precisely what I mean, let me try to get over some confusions I can identify, and maybe for the rest you can try to read what I actually write.</p>
<p>First, I emphasize I did not mention string theory at all when talking about observables of quantum gravity, whether in 4 dimensions or in higher dimensions. If you define &#8220;observables&#8221; as those things that can be observed, where observation includes and actual observer and a measuring device, the only things that we know exist are S-matrix elements. Those include everything we ever measured. Now this was not a statement about string theory at all, and please try to contain your passion and wait for me to actually make an arrogant and ill-informed statement. Yes &#8220;string theory observables&#8221; is a term you made up yourself rof.</p>
<p>Second, since the beginning of quantum theory physics is defined as the attempt to describe and predict results of measurments, I have no interest in &#8220;reality&#8221; beyond that, whatever that may mean. That is precisely why I caution talking about all kinds of comfortable notions one may have, and try to concentrate on precise statements about results of measurments.</p>
<p>All I had to say about T-duality was in the context of string theory, where this thing exist. It was not a statement about the real world where we don&#8217;t have experimental evidence for T-duality.  If string thoery describes the world and it has a compact circle, there are no measurements that will distinguish a small circle from a large one. Since I am only interested in results of measurments there is no reason for me to choose.</p>
<p>I think I will leave it at that, there is too much war on reality to do this week.</p>
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		<title>By: Fyodor</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/comment-page-1/#comment-8299</link>
		<dc:creator>Fyodor</dc:creator>
		<pubDate>Mon, 12 Dec 2005 09:50:05 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2005/12/07/how-many-dimensions-are-there/#comment-8299</guid>
		<description>Moshe said:
&quot;rof, both descriptions of the same model have precisely the same set of answers to precsicely the same sets of questions. The set of things &quot;observers&quot; can do on a small or large circles is precisely identical, they both can wave their arms in the same number of independent ways (9), and it is up to them what portion of it they describe geometrically and what they attribute to &quot;stringy&quot; physics.&quot;

Perhaps you can justify this apparently strange assertion?

Let me explain. If you look at the history [say 1930] of Kaluza Klein theory, you will find that there were two schools of thought. One said that the 5th dimension was real, the other that it was just a mathematical formalism. Of course, nobody disputed that the KK equations were *exactly equivalent* mathematically to the Einstein-Maxwell system, but nobody assumed that *exact mathematical equivalence* was the same thing as &quot;equally real&quot;. Similarly, string theorists circa 1985 surely knew that a purely formal interpretation of  Calabi-Yau compactifications was possible, but evidently nobody felt moved to attach any importance to this observation.

Now you want to assert that mathematically indistinguishable situations are *equally real*. Maybe you can persuade us, but you won&#039;t do it by means of analogies with special relativity. You will do it by describing *precisely* how an observer who waves his arms about can possibly describe his experiences in terms of two different dimensionalities. More generally, a string-theoretic analysis of the concept of &quot;reality&quot; would do the trick nicely.</description>
		<content:encoded><![CDATA[<p>Moshe said:<br />
&#8220;rof, both descriptions of the same model have precisely the same set of answers to precsicely the same sets of questions. The set of things &#8220;observers&#8221; can do on a small or large circles is precisely identical, they both can wave their arms in the same number of independent ways (9), and it is up to them what portion of it they describe geometrically and what they attribute to &#8220;stringy&#8221; physics.&#8221;</p>
<p>Perhaps you can justify this apparently strange assertion?</p>
<p>Let me explain. If you look at the history [say 1930] of Kaluza Klein theory, you will find that there were two schools of thought. One said that the 5th dimension was real, the other that it was just a mathematical formalism. Of course, nobody disputed that the KK equations were *exactly equivalent* mathematically to the Einstein-Maxwell system, but nobody assumed that *exact mathematical equivalence* was the same thing as &#8220;equally real&#8221;. Similarly, string theorists circa 1985 surely knew that a purely formal interpretation of  Calabi-Yau compactifications was possible, but evidently nobody felt moved to attach any importance to this observation.</p>
<p>Now you want to assert that mathematically indistinguishable situations are *equally real*. Maybe you can persuade us, but you won&#8217;t do it by means of analogies with special relativity. You will do it by describing *precisely* how an observer who waves his arms about can possibly describe his experiences in terms of two different dimensionalities. More generally, a string-theoretic analysis of the concept of &#8220;reality&#8221; would do the trick nicely.</p>
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