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	<title>Comments on: What if Time Really Exists?</title>
	<atom:link href="http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/feed/" rel="self" type="application/rss+xml" />
	<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/</link>
	<description>Random samplings from a universe of ideas.</description>
	<lastBuildDate>Mon, 09 Nov 2009 00:09:16 -0600</lastBuildDate>
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		<title>By: Les Natures du Temps &#171; Dr. Goulu</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-69320</link>
		<dc:creator>Les Natures du Temps &#171; Dr. Goulu</dc:creator>
		<pubDate>Sat, 28 Mar 2009 19:20:24 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-69320</guid>
		<description>[...] à Sean Carroll pour “What if Time Really Exists?”. (Sean maintient le blog Cosmic Variance grâce auquel j&#8217;ai découvert ce [...]</description>
		<content:encoded><![CDATA[<p>[...] à Sean Carroll pour “What if Time Really Exists?”. (Sean maintient le blog Cosmic Variance grâce auquel j&#8217;ai découvert ce [...]</p>
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	<item>
		<title>By: The Envelope Please&#8230; &#124; Cosmic Variance &#124; Discover Magazine</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-65974</link>
		<dc:creator>The Envelope Please&#8230; &#124; Cosmic Variance &#124; Discover Magazine</dc:creator>
		<pubDate>Mon, 09 Mar 2009 03:54:53 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-65974</guid>
		<description>[...] Questions Institute essay competition on “The Nature of Time,&#8221; which we discussed here. And the winners are: First Juried [...]</description>
		<content:encoded><![CDATA[<p>[...] Questions Institute essay competition on “The Nature of Time,&#8221; which we discussed here. And the winners are: First Juried [...]</p>
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	<item>
		<title>By: Richard Feynman on Boltzmann Brains &#124; Cosmic Variance &#124; Discover Magazine</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-55771</link>
		<dc:creator>Richard Feynman on Boltzmann Brains &#124; Cosmic Variance &#124; Discover Magazine</dc:creator>
		<pubDate>Mon, 29 Dec 2008 16:34:30 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-55771</guid>
		<description>[...] The Boltzmann Brain paradox is an argument against the idea that the universe around us, with its incredibly low-entropy early conditions and consequential arrow of time, is simply a statistical fluctuation within some eternal system that spends most of its time in thermal equilibrium. You can get a universe like ours that way, but you&#8217;re overwhelmingly more likely to get just a single galaxy, or a single planet, or even just a single brain &#8212; so the statistical-fluctuation idea seems to be ruled out by experiment. (With potentially profound consequences.) [...]</description>
		<content:encoded><![CDATA[<p>[...] The Boltzmann Brain paradox is an argument against the idea that the universe around us, with its incredibly low-entropy early conditions and consequential arrow of time, is simply a statistical fluctuation within some eternal system that spends most of its time in thermal equilibrium. You can get a universe like ours that way, but you&#8217;re overwhelmingly more likely to get just a single galaxy, or a single planet, or even just a single brain &#8212; so the statistical-fluctuation idea seems to be ruled out by experiment. (With potentially profound consequences.) [...]</p>
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	<item>
		<title>By: Interested</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-52681</link>
		<dc:creator>Interested</dc:creator>
		<pubDate>Tue, 16 Dec 2008 17:21:02 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-52681</guid>
		<description>Jonathan, 

Thank you. You are welcomed. I cannot imagine such a computer, though one sees the likes of it in movies, where the computer takes on a life of its own. One of my favorites was the robot who opened his own bank account, and decided to go out and find other robots like him and he found none and lived by himself near the sea. But this http://www.poodwaddle.com/worldclock.swf  that is circulating among my husband’s friends and sent to me just now, is a far cry but still something  : - )))</description>
		<content:encoded><![CDATA[<p>Jonathan, </p>
<p>Thank you. You are welcomed. I cannot imagine such a computer, though one sees the likes of it in movies, where the computer takes on a life of its own. One of my favorites was the robot who opened his own bank account, and decided to go out and find other robots like him and he found none and lived by himself near the sea. But this <a href="http://www.poodwaddle.com/worldclock.swf" rel="nofollow">http://www.poodwaddle.com/worldclock.swf</a>  that is circulating among my husband’s friends and sent to me just now, is a far cry but still something  : &#8211; )))</p>
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		<title>By: Jonathan Vos Post</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-52556</link>
		<dc:creator>Jonathan Vos Post</dc:creator>
		<pubDate>Tue, 16 Dec 2008 07:14:24 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-52556</guid>
		<description>Thank you, Interested.  Although my wife and I have earned over $100,000.00 in consulting for top Intellectual Property law firms, I now delegate that subject to my son.  My son, after all, is smarter than me.  I was a ripe old 16 when I arrived at Caltech on full scholarship and worked with family friend Feynman. My son started full time at university at age 13, and got his double B.S. in Math and Computer Science at 18.  He&#039;s halfway through his J.D. program, specializing in Intellectual Property, at the Gould School of Law, University of Southern California. Stephen Wolfram (who met my son when my son presented a paper years ago at a Wolfram NKS conference) is in no way naive about IP, having won his showdown with Caltech, a complicated story dating back to when Wolfram left his Computational Physics professorship to commercialize Mathematica.

Referring back to the title of this blog thread, &quot;What if Time Really Exists?&quot;, the deeper questions involve the period with which IP grants monopoly to the patent holder, versus the benefits to Arts &amp; Sciences that it confers on society as a whole.  Once computers have legal rights (inevitable when a system that passes the Turing Test has a good enough lawyer) then the whole game changes.  Time really exists alright (though Sean Carroll opened a cute loophole with the uncountably infinite Hilbert Space notion) but the computers of the future, merged in ways we can&#039;t yet describe with human beings, explore the Ideocosm dramatically faster with quantum hardware and genetic algorithm software.</description>
		<content:encoded><![CDATA[<p>Thank you, Interested.  Although my wife and I have earned over $100,000.00 in consulting for top Intellectual Property law firms, I now delegate that subject to my son.  My son, after all, is smarter than me.  I was a ripe old 16 when I arrived at Caltech on full scholarship and worked with family friend Feynman. My son started full time at university at age 13, and got his double B.S. in Math and Computer Science at 18.  He&#8217;s halfway through his J.D. program, specializing in Intellectual Property, at the Gould School of Law, University of Southern California. Stephen Wolfram (who met my son when my son presented a paper years ago at a Wolfram NKS conference) is in no way naive about IP, having won his showdown with Caltech, a complicated story dating back to when Wolfram left his Computational Physics professorship to commercialize Mathematica.</p>
<p>Referring back to the title of this blog thread, &#8220;What if Time Really Exists?&#8221;, the deeper questions involve the period with which IP grants monopoly to the patent holder, versus the benefits to Arts &#038; Sciences that it confers on society as a whole.  Once computers have legal rights (inevitable when a system that passes the Turing Test has a good enough lawyer) then the whole game changes.  Time really exists alright (though Sean Carroll opened a cute loophole with the uncountably infinite Hilbert Space notion) but the computers of the future, merged in ways we can&#8217;t yet describe with human beings, explore the Ideocosm dramatically faster with quantum hardware and genetic algorithm software.</p>
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	<item>
		<title>By: Interested</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-52550</link>
		<dc:creator>Interested</dc:creator>
		<pubDate>Tue, 16 Dec 2008 06:43:39 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-52550</guid>
		<description>Jonathan: “Stephen Wolfram asked me the sneaky question: if you have a computer search for you, who owns the intellectual property to what is discovered?” 

http://www.outlinedepot.com/textbookoutlines.aspx?textbookid=385
If you go to Outlinedepot.com you can preview the various law school outlines on intellectual property , and purchase them. I think they cost about $ 10 per subject outline. Many schools offer their outlines and so you have a choice of outlines. The preview section will give you an idea of the writing and pedagogical style that suits your taste. 
To answer your question, will require visiting those outlines and then framing them in a way that meets your expectations. It will take very much time and some cost. Maybe it may be done if circumstances permit, but otherwise this is the direction you are looking at on the net. 
In a broad brush, some things you want to watch out for- (i) intellectual property rights to protect writing (books) music [ copy right] patents, trademarks, service marks (?)  and of course intellectual property rights and technology (ii) intellectual property rights at international level, TRIPS – Trade Related Intellectual Property rightS and concomitant 153 states’ obligation vide TRIPS Agreement and interlinked with about 40 (?) agreements through membership of World Trade Organisation, of which it was about 120 in 1994 at inception and 153 today. 

153: -
[Albania  8 September 2000 Angola  23 November 1996 Antigua and Barbuda  1 January 1995 Argentina  1 January 1995 Armenia  5 February 2003 Australia  1 January 1995 Austria  1 January 1995 Bahrain, Kingdom of  1 January 1995 Bangladesh  1 January 1995 Barbados  1 January 1995 Belgium  1 January 1995 Belize  1 January 1995 Benin  22 February 1996 Bolivia  12 September 1995 Botswana  31 May 1995 Brazil  1 January 1995 Brunei Darussalam  1 January 1995 Bulgaria  1 December 1996 Burkina Faso  3 June 1995 Burundi  23 July 1995 Cambodia 13 October 2004 Cameroon  13 December 1995 Canada  1 January 1995 Cape Verde 23 July 2008 Central African Republic  31 May 1995 Chad  19 October 1996 Chile  1 January 1995 China  11 December 2001 Colombia  30 April 1995 Congo  27 March 1997 Costa Rica  1 January 1995 Côte d&#039;Ivoire  1 January 1995 Croatia    30 November 2000 Cuba  20 April 1995 Cyprus  30 July 1995 Czech Republic  1 January 1995 Democratic Republic of the Congo  1 January 1997 Denmark  1 January 1995 Djibouti  31 May 1995 Dominica  1 January 1995 Dominican Republic  9 March 1995 Ecuador  21 January 1996 Egypt  30 June 1995 El Salvador  7 May 1995  Estonia  13 November 1999 European Communities  1 January 1995  Fiji  14 January 1996
Finland  1 January 1995 Former Yugoslav Republic of Macedonia (FYROM)  4 April 2003 France  1 January 1995 Gabon  1 January 1995 The Gambia    23 October 1996 Georgia  14 June 2000 Germany  1 January 1995 Ghana  1 January 1995 Greece  1 January 1995 Grenada  22 February 1996 Guatemala  21 July 1995 Guinea  25 October 1995 Guinea Bissau  31 May 1995 Guyana  1 January 1995 Haiti  30 January 1996 Honduras  1 January 1995 Hong Kong, China  1 January 1995 Hungary  1 January 1995 Iceland  1 January 1995 India  1 January 1995 Indonesia  1 January 1995 Ireland  1 January 1995 Israel  21 April 1995 Italy  1 January 1995 Jamaica  9 March 1995 Japan  1 January 1995
Jordan  11 April 2000 Kenya  1 January 1995 Korea, Republic of  1 January 1995 Kuwait  1 January 1995 Kyrgyz Republic  20 December 1998 Latvia  10 February 1999 Lesotho  31 May 1995 Liechtenstein  1 September 1995 Lithuania  31 May 2001 Luxembourg  1 January 1995 Macao, China  1 January 1995 Madagascar  17 November 1995 Malawi  31 May 1995 Malaysia  1 January 1995 Maldives  31 May 1995 Mali  31 May 1995 Malta  1 January 1995
Mauritania  31 May 1995 Mauritius  1 January 1995 Mexico  1 January 1995 Moldova  26 July 2001 Mongolia  29 January 1997 Morocco  1 January 1995 Mozambique  26 August 1995 Myanmar  1 January 1995 Namibia  1 January 1995 Nepal  23 April 2004 Netherlands — For the Kingdom in Europe and for the Netherlands Antilles  1 January 1995 New Zealand  1 January 1995 Nicaragua  3 September 1995 Niger  13 December 1996 Nigeria  1 January 1995 Norway  1 January 1995 Oman  9 November 2000 Pakistan  1 January 1995 Panama  6 September 1997 Papua New Guinea  9 June 1996 Paraguay  1 January 1995 Peru  1 January 1995 Philippines  1 January 1995 Poland  1 July 1995
Portugal  1 January 1995 Qatar  13 January 1996 Romania  1 January 1995 Rwanda  22 May 1996 Saint Kitts and Nevis  21 February 1996 Saint Lucia  1 January 1995 Saint Vincent &amp; the Grenadines  1 January 1995 Saudi Arabia  11 December 2005 Senegal  1 January 1995 Sierra Leone  23 July 1995
Singapore  1 January 1995 Slovak Republic  1 January 1995 Slovenia  30 July 1995 Solomon Islands  26 July 1996 South Africa  1 January 1995 Spain  1 January 1995 Sri Lanka  1 January 1995 Suriname  1 January 1995 Swaziland  1 January 1995 Sweden  1 January 1995 Switzerland  1 July 1995 Chinese Taipei 1 January 2002 Tanzania  1 January 1995 Thailand  1 January 1995 Togo  31 May 1995 Tonga  27 July 2007 Trinidad and Tobago  1 March 1995 Tunisia  29 March 1995 Turkey  26 March 1995 Uganda  1 January 1995 Ukraine 16 May 2008 United Arab Emirates  10 April 1996 United Kingdom  1 January 1995 United States of America  1 January 1995 Uruguay  1 January 1995
Venezuela (Bolivarian Republic of)  1 January 1995 Viet Nam  11 January 2007 Zambia  1 January 1995 Zimbabwe  5 March 1995 ] 

The legal text for TRIPS agreement and others are in the website http://www.wto.org/ . Your question also crosses states borders through technology and you might wish to look at the user in any of the above 153 states or outside those 153 states, that is 42 states   [ 195-153]</description>
		<content:encoded><![CDATA[<p>Jonathan: “Stephen Wolfram asked me the sneaky question: if you have a computer search for you, who owns the intellectual property to what is discovered?” </p>
<p><a href="http://www.outlinedepot.com/textbookoutlines.aspx?textbookid=385" rel="nofollow">http://www.outlinedepot.com/textbookoutlines.aspx?textbookid=385</a><br />
If you go to Outlinedepot.com you can preview the various law school outlines on intellectual property , and purchase them. I think they cost about $ 10 per subject outline. Many schools offer their outlines and so you have a choice of outlines. The preview section will give you an idea of the writing and pedagogical style that suits your taste.<br />
To answer your question, will require visiting those outlines and then framing them in a way that meets your expectations. It will take very much time and some cost. Maybe it may be done if circumstances permit, but otherwise this is the direction you are looking at on the net.<br />
In a broad brush, some things you want to watch out for- (i) intellectual property rights to protect writing (books) music [ copy right] patents, trademarks, service marks (?)  and of course intellectual property rights and technology (ii) intellectual property rights at international level, TRIPS – Trade Related Intellectual Property rightS and concomitant 153 states’ obligation vide TRIPS Agreement and interlinked with about 40 (?) agreements through membership of World Trade Organisation, of which it was about 120 in 1994 at inception and 153 today. </p>
<p>153: -<br />
[Albania  8 September 2000 Angola  23 November 1996 Antigua and Barbuda  1 January 1995 Argentina  1 January 1995 Armenia  5 February 2003 Australia  1 January 1995 Austria  1 January 1995 Bahrain, Kingdom of  1 January 1995 Bangladesh  1 January 1995 Barbados  1 January 1995 Belgium  1 January 1995 Belize  1 January 1995 Benin  22 February 1996 Bolivia  12 September 1995 Botswana  31 May 1995 Brazil  1 January 1995 Brunei Darussalam  1 January 1995 Bulgaria  1 December 1996 Burkina Faso  3 June 1995 Burundi  23 July 1995 Cambodia 13 October 2004 Cameroon  13 December 1995 Canada  1 January 1995 Cape Verde 23 July 2008 Central African Republic  31 May 1995 Chad  19 October 1996 Chile  1 January 1995 China  11 December 2001 Colombia  30 April 1995 Congo  27 March 1997 Costa Rica  1 January 1995 Côte d'Ivoire  1 January 1995 Croatia    30 November 2000 Cuba  20 April 1995 Cyprus  30 July 1995 Czech Republic  1 January 1995 Democratic Republic of the Congo  1 January 1997 Denmark  1 January 1995 Djibouti  31 May 1995 Dominica  1 January 1995 Dominican Republic  9 March 1995 Ecuador  21 January 1996 Egypt  30 June 1995 El Salvador  7 May 1995  Estonia  13 November 1999 European Communities  1 January 1995  Fiji  14 January 1996<br />
Finland  1 January 1995 Former Yugoslav Republic of Macedonia (FYROM)  4 April 2003 France  1 January 1995 Gabon  1 January 1995 The Gambia    23 October 1996 Georgia  14 June 2000 Germany  1 January 1995 Ghana  1 January 1995 Greece  1 January 1995 Grenada  22 February 1996 Guatemala  21 July 1995 Guinea  25 October 1995 Guinea Bissau  31 May 1995 Guyana  1 January 1995 Haiti  30 January 1996 Honduras  1 January 1995 Hong Kong, China  1 January 1995 Hungary  1 January 1995 Iceland  1 January 1995 India  1 January 1995 Indonesia  1 January 1995 Ireland  1 January 1995 Israel  21 April 1995 Italy  1 January 1995 Jamaica  9 March 1995 Japan  1 January 1995<br />
Jordan  11 April 2000 Kenya  1 January 1995 Korea, Republic of  1 January 1995 Kuwait  1 January 1995 Kyrgyz Republic  20 December 1998 Latvia  10 February 1999 Lesotho  31 May 1995 Liechtenstein  1 September 1995 Lithuania  31 May 2001 Luxembourg  1 January 1995 Macao, China  1 January 1995 Madagascar  17 November 1995 Malawi  31 May 1995 Malaysia  1 January 1995 Maldives  31 May 1995 Mali  31 May 1995 Malta  1 January 1995<br />
Mauritania  31 May 1995 Mauritius  1 January 1995 Mexico  1 January 1995 Moldova  26 July 2001 Mongolia  29 January 1997 Morocco  1 January 1995 Mozambique  26 August 1995 Myanmar  1 January 1995 Namibia  1 January 1995 Nepal  23 April 2004 Netherlands — For the Kingdom in Europe and for the Netherlands Antilles  1 January 1995 New Zealand  1 January 1995 Nicaragua  3 September 1995 Niger  13 December 1996 Nigeria  1 January 1995 Norway  1 January 1995 Oman  9 November 2000 Pakistan  1 January 1995 Panama  6 September 1997 Papua New Guinea  9 June 1996 Paraguay  1 January 1995 Peru  1 January 1995 Philippines  1 January 1995 Poland  1 July 1995<br />
Portugal  1 January 1995 Qatar  13 January 1996 Romania  1 January 1995 Rwanda  22 May 1996 Saint Kitts and Nevis  21 February 1996 Saint Lucia  1 January 1995 Saint Vincent &#038; the Grenadines  1 January 1995 Saudi Arabia  11 December 2005 Senegal  1 January 1995 Sierra Leone  23 July 1995<br />
Singapore  1 January 1995 Slovak Republic  1 January 1995 Slovenia  30 July 1995 Solomon Islands  26 July 1996 South Africa  1 January 1995 Spain  1 January 1995 Sri Lanka  1 January 1995 Suriname  1 January 1995 Swaziland  1 January 1995 Sweden  1 January 1995 Switzerland  1 July 1995 Chinese Taipei 1 January 2002 Tanzania  1 January 1995 Thailand  1 January 1995 Togo  31 May 1995 Tonga  27 July 2007 Trinidad and Tobago  1 March 1995 Tunisia  29 March 1995 Turkey  26 March 1995 Uganda  1 January 1995 Ukraine 16 May 2008 United Arab Emirates  10 April 1996 United Kingdom  1 January 1995 United States of America  1 January 1995 Uruguay  1 January 1995<br />
Venezuela (Bolivarian Republic of)  1 January 1995 Viet Nam  11 January 2007 Zambia  1 January 1995 Zimbabwe  5 March 1995 ] </p>
<p>The legal text for TRIPS agreement and others are in the website <a href="http://www.wto.org/" rel="nofollow">http://www.wto.org/</a> . Your question also crosses states borders through technology and you might wish to look at the user in any of the above 153 states or outside those 153 states, that is 42 states   [ 195-153]</p>
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	<item>
		<title>By: Jonathan Vos Post</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-52473</link>
		<dc:creator>Jonathan Vos Post</dc:creator>
		<pubDate>Mon, 15 Dec 2008 19:29:56 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-52473</guid>
		<description>See also equation (5) of On the consistency of the constraint algebra in spin network quantum gravity, R Gambini, J Lewandowski, D Marolf, J Pullin - Arxiv preprint gr-qc/9710018, 1997:

&quot;While this sum involves an (uncountable) infinity of terms, its action on spin network states&#124;Γ′is well-defined since only one term (the one in which σ maps the vertices of Γ to the vertices of Γ′ in the proper way) can be nonzero...&quot;

And also:

Unimodular eigenvalues and linear chaos in Hilbert spaces 
Journal Geometric And Functional Analysis 
Publisher Birkhäuser Basel 
ISSN 1016-443X (Print) 1420-8970 (Online) 
Issue Volume 5, Number 1 / January, 1995 
DOI 10.1007/BF01928214 
Pages 1-13 

PDF (722.1 KB)

Unimodular eigenvalues and linear chaos in Hilbert spaces
E. Flytzanis1

(1)  Athens University of Economics and Business, 76 Patission Street, 104 34 Athens, Greece 

Received: 15 May 1993  Accepted: 15 October 1994  

Abstract  For linear operators T in a complex separable Hilbert space H we consider the problem of existence of invariant Gaussian measuresm:
mT^–1 = m. We relate the size of the unimodular point spectrum of T to mixing properties of the measure preserving transformations defined by T with respect to such invariant measures, and we draw some conclusions concerning orbit structure properties of T.
The research for this work has been supported by a grant from the Research Center (KoE) of the Athens University of Economics and Business.

&quot;Unimodular eignevalues of linear operators in Hilbert space are usually associated with periodic or quasiperiodic orbits. We will show that this is indeed the case if they are countable. However if the unimodular point spectrum is uncountable then we will show that the orbits of the operator are also characterized by erratic behavior associated with chaotic motion. This happens because the linear transformations defined by such operators accept invariant probability measures having mixing properties in the context of ergodic theory.&quot;

Does someone want to draw a Cosmological conclusion from this?</description>
		<content:encoded><![CDATA[<p>See also equation (5) of On the consistency of the constraint algebra in spin network quantum gravity, R Gambini, J Lewandowski, D Marolf, J Pullin &#8211; Arxiv preprint gr-qc/9710018, 1997:</p>
<p>&#8220;While this sum involves an (uncountable) infinity of terms, its action on spin network states|Γ′is well-defined since only one term (the one in which σ maps the vertices of Γ to the vertices of Γ′ in the proper way) can be nonzero&#8230;&#8221;</p>
<p>And also:</p>
<p>Unimodular eigenvalues and linear chaos in Hilbert spaces<br />
Journal Geometric And Functional Analysis<br />
Publisher Birkhäuser Basel<br />
ISSN 1016-443X (Print) 1420-8970 (Online)<br />
Issue Volume 5, Number 1 / January, 1995<br />
DOI 10.1007/BF01928214<br />
Pages 1-13 </p>
<p>PDF (722.1 KB)</p>
<p>Unimodular eigenvalues and linear chaos in Hilbert spaces<br />
E. Flytzanis1</p>
<p>(1)  Athens University of Economics and Business, 76 Patission Street, 104 34 Athens, Greece </p>
<p>Received: 15 May 1993  Accepted: 15 October 1994  </p>
<p>Abstract  For linear operators T in a complex separable Hilbert space H we consider the problem of existence of invariant Gaussian measuresm:<br />
mT^–1 = m. We relate the size of the unimodular point spectrum of T to mixing properties of the measure preserving transformations defined by T with respect to such invariant measures, and we draw some conclusions concerning orbit structure properties of T.<br />
The research for this work has been supported by a grant from the Research Center (KoE) of the Athens University of Economics and Business.</p>
<p>&#8220;Unimodular eignevalues of linear operators in Hilbert space are usually associated with periodic or quasiperiodic orbits. We will show that this is indeed the case if they are countable. However if the unimodular point spectrum is uncountable then we will show that the orbits of the operator are also characterized by erratic behavior associated with chaotic motion. This happens because the linear transformations defined by such operators accept invariant probability measures having mixing properties in the context of ergodic theory.&#8221;</p>
<p>Does someone want to draw a Cosmological conclusion from this?</p>
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		<title>By: Interested</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-52464</link>
		<dc:creator>Interested</dc:creator>
		<pubDate>Mon, 15 Dec 2008 18:26:14 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-52464</guid>
		<description>Jonathan: “The issue is not to store all ideas, but to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas.”

Books are stored in libraries, catalogued, so they can be searched by topic, specific subject matter, author, etc. Abstracts enable easy overview of the longer works. 

What then would be methodologies to systematically explore the Ideocosm? How different would they be from that used by libraries? 

One apparent difference between “to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas” for  public use versus private system of Zwicky ( not having spoken to him, nor met him, and not being called ....... [ seven letters] by him would be design of the system, made easier when ( imagine) Zwicky employs it for his own research &amp; his area of interest is limited to his field of study. 
Given that, the world has many areas of studies that humanity has come up with and more yet to come, how can there be same methodologies for different areas of studies? For example, sciences differ from social sciences &amp; humanities &amp; arts. Even within broad categorisation, differences would appear in the different sub fields. 

How can mankind conceive of perfecting “methodologies” to cover all areas of human studies and explorations? 

Who determines what ‘really great ideas” are? If that be the criteria to selection  for the Ideocosm? 

What is this ideocosm? The reality of nature , of the universe? Who determines what is the ideocosm? Zwicky? Based on what he collected and stored and the method he employed for himself for his limited area of study? Is that to be exponentially transferred to the whole world, whole of humanity, whole of universe, from beginning of time to end of time ( if there is a beginning and if there is an end since there is some doubt serious doubt whether time even exists)</description>
		<content:encoded><![CDATA[<p>Jonathan: “The issue is not to store all ideas, but to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas.”</p>
<p>Books are stored in libraries, catalogued, so they can be searched by topic, specific subject matter, author, etc. Abstracts enable easy overview of the longer works. </p>
<p>What then would be methodologies to systematically explore the Ideocosm? How different would they be from that used by libraries? </p>
<p>One apparent difference between “to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas” for  public use versus private system of Zwicky ( not having spoken to him, nor met him, and not being called &#8230;&#8230;. [ seven letters] by him would be design of the system, made easier when ( imagine) Zwicky employs it for his own research &#038; his area of interest is limited to his field of study.<br />
Given that, the world has many areas of studies that humanity has come up with and more yet to come, how can there be same methodologies for different areas of studies? For example, sciences differ from social sciences &#038; humanities &#038; arts. Even within broad categorisation, differences would appear in the different sub fields. </p>
<p>How can mankind conceive of perfecting “methodologies” to cover all areas of human studies and explorations? </p>
<p>Who determines what ‘really great ideas” are? If that be the criteria to selection  for the Ideocosm? </p>
<p>What is this ideocosm? The reality of nature , of the universe? Who determines what is the ideocosm? Zwicky? Based on what he collected and stored and the method he employed for himself for his limited area of study? Is that to be exponentially transferred to the whole world, whole of humanity, whole of universe, from beginning of time to end of time ( if there is a beginning and if there is an end since there is some doubt serious doubt whether time even exists)</p>
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		<title>By: Jonathan Vos Post</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-52370</link>
		<dc:creator>Jonathan Vos Post</dc:creator>
		<pubDate>Mon, 15 Dec 2008 05:46:18 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-52370</guid>
		<description>The issue is not to store all ideas, but to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas.  I&#039;ve discussed that with Zwicky himself (whose first words to me were &quot;who the hell are you?&quot;) and Herman Kahn, and Linus Pauling, Jr. -- they all agreed on this.  Stephen Wolfram asked me the sneaky question: if you have a computer search for you, who owns the intellectual property to what is discovered?</description>
		<content:encoded><![CDATA[<p>The issue is not to store all ideas, but to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas.  I&#8217;ve discussed that with Zwicky himself (whose first words to me were &#8220;who the hell are you?&#8221;) and Herman Kahn, and Linus Pauling, Jr. &#8212; they all agreed on this.  Stephen Wolfram asked me the sneaky question: if you have a computer search for you, who owns the intellectual property to what is discovered?</p>
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		<title>By: Interested</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/comment-page-1/#comment-52363</link>
		<dc:creator>Interested</dc:creator>
		<pubDate>Mon, 15 Dec 2008 05:07:36 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2008/11/24/what-if-time-really-exists/#comment-52363</guid>
		<description>Jonathan : Philosophically, this relates to a question that I’ve been asking for 35 years:“what is the topology of the space of all possible ideas (what Fritz Zwicky called the “ideocosm”)? 

Of what good would it do to collect and store and archive all possible ideas? Not knowing what ideas Fritz  Zwicky stored and archived, and retrieved for his research use, would it not suggest a storage has to be tailored to the intended use and needs of the specific user/s? The usual general storage area is the library. Some may collect and archive many things, like a human sponge. It is said that babies before age 5 are like sponges, and they can absorb many new things easily and learning is effortless then. It is said that Sanskrit is difficult to learn but a child below 5 who lives in that environment can learn it easily and speak it then. Those who collect sort out and compartmentalise and archive, are like the before 5 babies, human sponges, brains that absorb all.  http://www.amazon.com/Absorbent-Mind-Maria-Montessori/dp/0805041567  Is that one of the further along human evolutionary process/es? On a parallel tangent, I have met 2 people who have told me that when some very good meditator monks die, and are cremated, their remains, include some crystals besides the ashes and bones ( as they have been privileged by circumstances to have a few of them.) I have also read that in one book on the monk who purchased the land in Northern CA, for his temple (something like ten thousand buddhas) and before he died, he donated a part of the forest land to the monks of a different buddhist branch (something like Redwood Valley area in Northern CA). ( I just pulled out the book to get his name Hsuan Hua, city of ten thousand buddhas) These people do not collect such worldly knowledge but it seems they are different and their difference is in what forms their body so that when cremated they leave behind things that others do not. 

What is the topology of the space of all mathematical theories?

Do not know 

How do we make a hyperplane or hypersurface to separate the physical theories from the nonphysical theories within the space of all mathematical theories?

Do not know</description>
		<content:encoded><![CDATA[<p>Jonathan : Philosophically, this relates to a question that I’ve been asking for 35 years:“what is the topology of the space of all possible ideas (what Fritz Zwicky called the “ideocosm”)? </p>
<p>Of what good would it do to collect and store and archive all possible ideas? Not knowing what ideas Fritz  Zwicky stored and archived, and retrieved for his research use, would it not suggest a storage has to be tailored to the intended use and needs of the specific user/s? The usual general storage area is the library. Some may collect and archive many things, like a human sponge. It is said that babies before age 5 are like sponges, and they can absorb many new things easily and learning is effortless then. It is said that Sanskrit is difficult to learn but a child below 5 who lives in that environment can learn it easily and speak it then. Those who collect sort out and compartmentalise and archive, are like the before 5 babies, human sponges, brains that absorb all.  <a href="http://www.amazon.com/Absorbent-Mind-Maria-Montessori/dp/0805041567" rel="nofollow">http://www.amazon.com/Absorbent-Mind-Maria-Montessori/dp/0805041567</a>  Is that one of the further along human evolutionary process/es? On a parallel tangent, I have met 2 people who have told me that when some very good meditator monks die, and are cremated, their remains, include some crystals besides the ashes and bones ( as they have been privileged by circumstances to have a few of them.) I have also read that in one book on the monk who purchased the land in Northern CA, for his temple (something like ten thousand buddhas) and before he died, he donated a part of the forest land to the monks of a different buddhist branch (something like Redwood Valley area in Northern CA). ( I just pulled out the book to get his name Hsuan Hua, city of ten thousand buddhas) These people do not collect such worldly knowledge but it seems they are different and their difference is in what forms their body so that when cremated they leave behind things that others do not. </p>
<p>What is the topology of the space of all mathematical theories?</p>
<p>Do not know </p>
<p>How do we make a hyperplane or hypersurface to separate the physical theories from the nonphysical theories within the space of all mathematical theories?</p>
<p>Do not know</p>
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