View Full Version : arrow of time
Roman Arce
May11-04, 07:04 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n"if the laws of nature do not distinguish between past and future, why are\neggs seen to break but broken eggs never seen to recombine" from\nhttp://physicsweb.org/article/review/17/5/1.\n\nIt\'s not the first time I read that.\nAn egg can be in many states, a small percentage of those states would be\ncalled unbroken and arbitrarily called order, the majority of the states\nwould be called broken and arbitrarily called disorder, starting from a\nstate with low probability (order) and going to one of less probability\n(disorder) will be more likely than the opposite, but that doesn\'t challenge\nthe arbitrariness of "order". Using a dice instead of an egg if I call 1\norder and 2-6 disorder then the chance of going from 1 to 2-6 is 5/6, now if\nyou ask what\'s the opposite probability, the trick is there:\nIncorrect "opposite" probability: if I start with a 2 (disorder) the\nprobabily of going to 1 (order) is 1/6.\nCorrect "opposite" probability: if I add the probabilities of all disorder\nstates going to order: (2 to 1)+...+(6 to 1) I have 5 initial states with\n1/6 each with a total of 5/6.\nThe choice of a specific initial state like 2 in the incorrect case was\ntotally arbitrary and therefore unphysical when in the correct (at least\nphysically meaningful) case there was no arbitrariness.\nNote the arbitrariness of choosing 1 as order instead of any other number in\nthe same way that unbroken egg is chosen as order, unbroken is just an\narbitrary state and the question could be asked with any states as long as\nthe "order" states represent a tiny percentage of the possible\nconfigurations.\nPlease tell me if I\'m saying something wrong or something "not even wrong"\n:).\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"if the laws of nature do not distinguish between past and future, why are
eggs seen to break but broken eggs never seen to recombine" from
http://physicsweb.org/article/review/17/5/1.
It's not the first time I read that.
An egg can be in many states, a small percentage of those states would be
called unbroken and arbitrarily called order, the majority of the states
would be called broken and arbitrarily called disorder, starting from a
state with low probability (order) and going to one of less probability
(disorder) will be more likely than the opposite, but that doesn't challenge
the arbitrariness of "order". Using a dice instead of an egg if I call 1
order and 2-6 disorder then the chance of going from 1 to 2-6 is 5/6, now if
you ask what's the opposite probability, the trick is there:
Incorrect "opposite" probability: if I start with a 2 (disorder) the
probabily of going to 1 (order) is 1/6.
Correct "opposite" probability: if I add the probabilities of all disorder
states going to order: (2 to 1)+...+(6 to 1) I have 5 initial states with
1/6 each with a total of 5/6.
The choice of a specific initial state like 2 in the incorrect case was
totally arbitrary and therefore unphysical when in the correct (at least
physically meaningful) case there was no arbitrariness.
Note the arbitrariness of choosing 1 as order instead of any other number in
the same way that unbroken egg is chosen as order, unbroken is just an
arbitrary state and the question could be asked with any states as long as
the "order" states represent a tiny percentage of the possible
configurations.
Please tell me if I'm saying something wrong or something "not even wrong"
:).
tessel@tum.bot
May12-04, 05:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Roman Arce asked about "Ehrenfest urn" type "toy models" (Markov chain\nmodels) of classical statistical mechanical phenomena such as gaseous\nmixing. We have often discussed these here in the past; a good\nsemipopular discussion can be found in\n\nauthor = {Lawrence Sklar},\ntitle = {Space, Time, and Spacetime},\npublisher = {University of California Press},\nyear = 1976}\n\nThere is a huge literature on this topic; some more technical references\ninclude (in very rougly increasing order of difficulty):\n\nauthor = {Olle Haggstrom},\ntitle = {Finite {M}arkov chains and algorithmic applications},\nseries = {London Mathematical Society student texts},\nvolume = 52,\npublisher = {Cambridge University Press},\nyear = 2002}\n\nauthor = {John G. Kemeny and J. Laurie Snell},\ntitle = {Finite Markov Chains},\npublisher = {Van Nostrand},\nyear = 1960}\n\nauthor = {M. Pollicott and M. Yuri},\ntitle = {Ergodic Theory and Dynamical Systems},\npublisher = {London Mathematical Society},\nseries = {Student Texts},\nnumber = 40,\nyear = 1998}\n\nauthor = {Gerhard Keller},\ntitle = {Equilibrium States in Ergodic Theory},\npublisher = {London Mathematical Society},\nseries = {Student Texts},\nnumber = 42,\nyear = 1998}\n\nauthor = {Andrzej Lasota and Michael C. Mackey},\ntitle = {Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics},\nedition = {Second},\nseries = {Applied Mathematical Sciences},\nvolume = 97,\npublisher = {Springer-Verlag},\nyear = 1994}\n\nauthor = {Karl Petersen},\ntitle = {Ergodic Theory},\npublisher = {University of Cambridge Press},\nseries = {Cambridge Series in Advanced Mathematics},\nvolume = 2,\nyear = 1983}\n\nauthor = {Peter Walters},\ntitle = {Introduction to Ergodic Theory},\npublisher = {Springer},\nyear = 1981}\n\nMore generally, there are many books on the "second law". One adopting a\npoint of view which should be congenial to your question is\n\nauthor = {Michael C. Mackey},\ntitle = {Time\'s arrow: the origins of thermodynamic behavior},\npublisher = {Springer-Verlag},\nyear = 1992}\n\nUnfortunately, I believe that this book unaccountably begins with a fatal\nerror of interpretation! To wit, IIRC, Mackey studies the putative (and\ndubious) -increase- of a certain unbounded and negative quantity\n(incorrect!, say I), rather than the (easily proven) -decrease- of a a\nquite different bounded positive quantity (correct). He understandably\nprotested when I said this some years ago, without trying to justify my\ncomment. Unfortunately I couldn\'t then (nor can I now) muster the energy\nto explain myself other than pointing interested readers at\n\nauthor = {Silviu Guiasu},\ntitle = {Information Theory with Applications},\npublisher = {McGraw-Hill},\nyear = 1977}\n\nauthor = {Thomas M. Cover and Joy A. Thomas},\ntitle = {Elements of information theory},\npublisher = {Wiley},\nyear = 1991}\n\nwhere one can find discussion of the above mentioned bounded positive\nquantity. Be careful--- terminology is notoriously muddled in the\nliterature; you can never assume that when two authors discuss\n"conditional entropy" they mean the same thing; you need to check their\ndefinitions. Same for all other constructions of the form "<modifier>\nentropy". See also Giuasu for a crucial observation about "discrete"\nversus "continuous" entropies.\n\nRe the question in another thread about the impact today of Einstein\'s\nlife work, I forgot to mention that one interesting Einstein/Bohr\ncontroversy (dating back to 1907 or so) concerns the Lorentz\ntransformation properties of temperature. IIRC, this question arose\nduring a conference whose proceedings I once read; E & B advanced to the\nboard, and reached mutually contradictory conclusions. The original\nproceedings offer a rare if contemporary account of Bohr and Einstein\narguing about physics, in their own lightly edited words. I urge\ninterested readers to think for themselves about the question! For the\nanswer, see Adami\'s recent and easily readable review, quant-ph/0405005.\n\n"T. Essel" (hiding somewhere in cyberspace)\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Roman Arce asked about "Ehrenfest urn" type "toy models" (Markov chain
models) of classical statistical mechanical phenomena such as gaseous
mixing. We have often discussed these here in the past; a good
semipopular discussion can be found in
author = {Lawrence Sklar},
title = {Space, Time, and Spacetime},
publisher = {University of California Press},
year = 1976}
There is a huge literature on this topic; some more technical references
include (in very rougly increasing order of difficulty):
author = {Olle Haggstrom},
title = {Finite {M}arkov chains and algorithmic applications},
series = {London Mathematical Society student texts},
volume = 52,
publisher = {Cambridge University Press},
year = 2002}
author = {John G. Kemeny and J. Laurie Snell},
title = {Finite Markov Chains},
publisher = {Van Nostrand},
year = 1960}
author = {M. Pollicott and M. Yuri},
title = {Ergodic Theory and Dynamical Systems},
publisher = {London Mathematical Society},
series = {Student Texts},
number = 40,
year = 1998}
author = {Gerhard Keller},
title = {Equilibrium States in Ergodic Theory},
publisher = {London Mathematical Society},
series = {Student Texts},
number = 42,
year = 1998}
author = {Andrzej Lasota and Michael C. Mackey},
title = {Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics},
edition = {Second},
series = {Applied Mathematical Sciences},
volume = 97,
publisher = {Springer-Verlag},
year = 1994}
author = {Karl Petersen},
title = {Ergodic Theory},
publisher = {University of Cambridge Press},
series = {Cambridge Series in Advanced Mathematics},
volume = 2,
year = 1983}
author = {Peter Walters},
title = {Introduction to Ergodic Theory},
publisher = {Springer},
year = 1981}
More generally, there are many books on the "second law". One adopting a
point of view which should be congenial to your question is
author = {Michael C. Mackey},
title = {Time's arrow: the origins of thermodynamic behavior},
publisher = {Springer-Verlag},
year = 1992}
Unfortunately, I believe that this book unaccountably begins with a fatal
error of interpretation! To wit, IIRC, Mackey studies the putative (and
dubious) -increase- of a certain unbounded and negative quantity
(incorrect!, say I), rather than the (easily proven) -decrease- of a a
quite different bounded positive quantity (correct). He understandably
protested when I said this some years ago, without trying to justify my
comment. Unfortunately I couldn't then (nor can I now) muster the energy
to explain myself other than pointing interested readers at
author = {Silviu Guiasu},
title = {Information Theory with Applications},
publisher = {McGraw-Hill},
year = 1977}
author = {Thomas M. Cover and Joy A. Thomas},
title = {Elements of information theory},
publisher = {Wiley},
year = 1991}
where one can find discussion of the above mentioned bounded positive
quantity. Be careful--- terminology is notoriously muddled in the
literature; you can never assume that when two authors discuss
"conditional entropy" they mean the same thing; you need to check their
definitions. Same for all other constructions of the form "<modifier>
entropy". See also Giuasu for a crucial observation about "discrete"
versus "continuous" entropies.
Re the question in another thread about the impact today of Einstein's
life work, I forgot to mention that one interesting Einstein/Bohr
controversy (dating back to 1907 or so) concerns the Lorentz
transformation properties of temperature. IIRC, this question arose
during a conference whose proceedings I once read; E & B advanced to the
board, and reached mutually contradictory conclusions. The original
proceedings offer a rare if contemporary account of Bohr and Einstein
arguing about physics, in their own lightly edited words. I urge
interested readers to think for themselves about the question! For the
answer, see Adami's recent and easily readable review, http://www.arxiv.org/abs/quant-ph/0405005.
"T. Essel" (hiding somewhere in cyberspace)
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>shampoo@fibertel.com.ar (Roman Arce) wrote in message news:<3ec0ba0c.0405110053.6d54520a@posting.google. com>...\n> "if the laws of nature do not distinguish between past and future, why are\n> eggs seen to break but broken eggs never seen to recombine" from\n> http://physicsweb.org/article/review/17/5/1.\n>\n> It\'s not the first time I read that.\n> An egg can be in many states, a small percentage of those states would be\n> called unbroken and arbitrarily called order, the majority of the states\n> would be called broken and arbitrarily called disorder, starting from a\n> state with low probability (order) and going to one of less probability\n> (disorder) will be more likely than the opposite, but that doesn\'t challenge\n> the arbitrariness of "order". Using a dice instead of an egg if I call 1\n> order and 2-6 disorder then the chance of going from 1 to 2-6 is 5/6, now if\n> you ask what\'s the opposite probability, the trick is there:\n> Incorrect "opposite" probability: if I start with a 2 (disorder) the\n> probabily of going to 1 (order) is 1/6.\n> Correct "opposite" probability: if I add the probabilities of all disorder\n> states going to order: (2 to 1)+...+(6 to 1) I have 5 initial states with\n> 1/6 each with a total of 5/6.\n> The choice of a specific initial state like 2 in the incorrect case was\n> totally arbitrary and therefore unphysical when in the correct (at least\n> physically meaningful) case there was no arbitrariness.\n> Note the arbitrariness of choosing 1 as order instead of any other number in\n> the same way that unbroken egg is chosen as order, unbroken is just an\n> arbitrary state and the question could be asked with any states as long as\n> the "order" states represent a tiny percentage of the possible\n> configurations.\n> Please tell me if I\'m saying something wrong or something "not even wrong"\n> :).\n\nThere is no way to define "order" versus "disorder" or "random" versus\n"not random" separate from the human psychology, the prejudice or bias\nof the observer. If you "see a pattern" you call it "order" and if you\ndon\'t "see a pattern", you call it disorder. If you showed a list of\nprime numbers to someone who never heard of prime numbers, they would\ncall it random. However, any possible list of numbers could be\nproduced by some algorithmn even if we don\'t know what it is. If you\nshow someone a series of numbers, and they don\'t see any pattern, and\nthey call it "disordered", and then you give them the algorithmn that\nproduces it, does that mean the series changed from "disordered" to\n"ordered" just because of the change in the observer\'s knowledge.\n\nIf you are playing poker and receive a royal flush, you think, "Wow!\nThat was very unlikely!", but of course a royal flush isn\'t any less\nlikely than any other possible combination of the cards. The\ndifference is, in our society, most combinations of the cards are\ncalled "nothing", and don\'t correspond to any hand in our game of\npoker. If you are dealt a hand we call "nothing", you don\'t notice\nanything unusual. If you are dealt a hand we call a "royal flush", you\nnotice it, and feel like something very unlikely has happened, even\nthough both hands are equally likely. We would call a royal flush\n"ordered" and the nothing hand "disordered" but that\'s totally\narbitrary.\n\nPeople invented the second law of thermodynamics to explain why you\ndon\'t see the air rush to the corners of the room you are in, but\nthere is no need to invent such a thing because you can totally\nexplain the fact you don\'t see the air rush to the corners of the room\nby the mere fact that it is a tiny percentage of all possible\ntrajectories of all the molecules in the room that lead to that\nconfiguration, about 1 in 10^10^20. It\'s the same as the fact that if\nyou roll a dice, you probably won\'t roll a 6 because the likelihood is\n1 in 6. Therefore, there\'s no need for any second law of\nthermodynamics. Furthermore, there is no objective logical reason to\nattach any significance to a set of trajectories of all the air\nmolecules in the room that lead to a configuration where all the air\nis in the corners of the room, versus any other configuration. It\'s\nthe same as attaching an arbitary significance to the number 6 when\nrolling a dice. The only reason we attach a significance to it is\nbecause we notice all the air rushing to the corners of the room.\nWell, so what? You cares if we notice it or not. Some alien\ncivilization might notice eddies in the air in the room or something\nelse we would never notice. If your definition of ordered versus\ndisordered depends on what a given observer would "notice" then it\ndepends on the observer. Calling the air rushing to the corners of the\nroom "ordered" is like rolling a dice and calling rolling a six\n"ordered" and rolling any other number "disordered".\n\nDavid\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>shampoo@fibertel.com.ar (Roman Arce) wrote in message news:<3ec0ba0c.0405110053.6d54520a@posting.google.com>...
> "if the laws of nature do not distinguish between past and future, why are
> eggs seen to break but broken eggs never seen to recombine" from
> http://physicsweb.org/article/review/17/5/1.
>
> It's not the first time I read that.
> An egg can be in many states, a small percentage of those states would be
> called unbroken and arbitrarily called order, the majority of the states
> would be called broken and arbitrarily called disorder, starting from a
> state with low probability (order) and going to one of less probability
> (disorder) will be more likely than the opposite, but that doesn't challenge
> the arbitrariness of "order". Using a dice instead of an egg if I call 1
> order and 2-6 disorder then the chance of going from 1 to 2-6 is 5/6, now if
> you ask what's the opposite probability, the trick is there:
> Incorrect "opposite" probability: if I start with a 2 (disorder) the
> probabily of going to 1 (order) is 1/6.
> Correct "opposite" probability: if I add the probabilities of all disorder
> states going to order: (2 to 1)+...+(6 to 1) I have 5 initial states with
> 1/6 each with a total of 5/6.
> The choice of a specific initial state like 2 in the incorrect case was
> totally arbitrary and therefore unphysical when in the correct (at least
> physically meaningful) case there was no arbitrariness.
> Note the arbitrariness of choosing 1 as order instead of any other number in
> the same way that unbroken egg is chosen as order, unbroken is just an
> arbitrary state and the question could be asked with any states as long as
> the "order" states represent a tiny percentage of the possible
> configurations.
> Please tell me if I'm saying something wrong or something "not even wrong"
> :).
There is no way to define "order" versus "disorder" or "random" versus
"not random" separate from the human psychology, the prejudice or bias
of the observer. If you "see a pattern" you call it "order" and if you
don't "see a pattern", you call it disorder. If you showed a list of
prime numbers to someone who never heard of prime numbers, they would
call it random. However, any possible list of numbers could be
produced by some algorithmn even if we don't know what it is. If you
show someone a series of numbers, and they don't see any pattern, and
they call it "disordered", and then you give them the algorithmn that
produces it, does that mean the series changed from "disordered" to
"ordered" just because of the change in the observer's knowledge.
If you are playing poker and receive a royal flush, you think, "Wow!
That was very unlikely!", but of course a royal flush isn't any less
likely than any other possible combination of the cards. The
difference is, in our society, most combinations of the cards are
called "nothing", and don't correspond to any hand in our game of
poker. If you are dealt a hand we call "nothing", you don't notice
anything unusual. If you are dealt a hand we call a "royal flush", you
notice it, and feel like something very unlikely has happened, even
though both hands are equally likely. We would call a royal flush
"ordered" and the nothing hand "disordered" but that's totally
arbitrary.
People invented the second law of thermodynamics to explain why you
don't see the air rush to the corners of the room you are in, but
there is no need to invent such a thing because you can totally
explain the fact you don't see the air rush to the corners of the room
by the mere fact that it is a tiny percentage of all possible
trajectories of all the molecules in the room that lead to that
configuration, about 1 in 10^10^20. It's the same as the fact that if
you roll a dice, you probably won't roll a 6 because the likelihood is
1 in 6. Therefore, there's no need for any second law of
thermodynamics. Furthermore, there is no objective logical reason to
attach any significance to a set of trajectories of all the air
molecules in the room that lead to a configuration where all the air
is in the corners of the room, versus any other configuration. It's
the same as attaching an arbitary significance to the number 6 when
rolling a dice. The only reason we attach a significance to it is
because we notice all the air rushing to the corners of the room.
Well, so what? You cares if we notice it or not. Some alien
civilization might notice eddies in the air in the room or something
else we would never notice. If your definition of ordered versus
disordered depends on what a given observer would "notice" then it
depends on the observer. Calling the air rushing to the corners of the
room "ordered" is like rolling a dice and calling rolling a six
"ordered" and rolling any other number "disordered".
David
Jerzy Karczmarczuk
May13-04, 05:25 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nUlmo wrote:\n\n> There is no way to define "order" versus "disorder" or "random" versus\n> "not random" separate from the human psychology, the prejudice or bias\n> of the observer. If you "see a pattern" you call it "order" and if you\n> don\'t "see a pattern", you call it disorder. If you showed a list of\n> prime numbers to someone who never heard of prime numbers, they would\n> call it random. However, any possible list of numbers could be\n> produced by some algorithmn even if we don\'t know what it is. If you\n> show someone a series of numbers, and they don\'t see any pattern, and\n> they call it "disordered", and then you give them the algorithmn that\n> produces it, does that mean the series changed from "disordered" to\n> "ordered" just because of the change in the observer\'s knowledge.\n\nThis is a metaphysical, not an operational viewpoint. When I launch a\nrandom number generator, I KNOW that the sequence is perfectly determi-\nnistic and repeatable, yeat I *call it random*.\n\nPhysicists are rarely medieval scholastics. There *ARE* ways of defining\nrandomness, e.g. the quality of a RN generator through proofs of ergodicity,\nstatistical tests, etc. There are ways of defining - not always but\nfrequently - the notion of order as the breakdown of a symmetry.\n\nSorry for being a bit brutal, but reducing notions which are analysable by\nthe theory of measure, etc. to human prejudices and psychology doesn\'t\nsound very scientific.\n\nJerzy Karczmarczuk\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Ulmo wrote:
> There is no way to define "order" versus "disorder" or "random" versus
> "not random" separate from the human psychology, the prejudice or bias
> of the observer. If you "see a pattern" you call it "order" and if you
> don't "see a pattern", you call it disorder. If you showed a list of
> prime numbers to someone who never heard of prime numbers, they would
> call it random. However, any possible list of numbers could be
> produced by some algorithmn even if we don't know what it is. If you
> show someone a series of numbers, and they don't see any pattern, and
> they call it "disordered", and then you give them the algorithmn that
> produces it, does that mean the series changed from "disordered" to
> "ordered" just because of the change in the observer's knowledge.
This is a metaphysical, not an operational viewpoint. When I launch a
random number generator, I KNOW that the sequence is perfectly determi-
nistic and repeatable, yeat I *call it random*.
Physicists are rarely medieval scholastics. There *ARE* ways of defining
randomness, e.g. the quality of a RN generator through proofs of ergodicity,
statistical tests, etc. There are ways of defining - not always but
frequently - the notion of order as the breakdown of a symmetry.
Sorry for being a bit brutal, but reducing notions which are analysable by
the theory of measure, etc. to human prejudices and psychology doesn't
sound very scientific.
Jerzy Karczmarczuk
David Williams
May13-04, 09:17 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>-> Physicists are rarely medieval scholastics. There *ARE* ways of defining\n-> randomness, e.g. the quality of a RN generator through proofs of ergodicity,\n-> statistical tests, etc. There are ways of defining - not always but\n-> frequently - the notion of order as the breakdown of a symmetry.\n\nBut every *finite* sequence of truly randomly generated numbers has a\nnonzero probability of *failing* any test for randomness. Sequences\nsuch as 11111111...., going on for the whole length of the sequence,\n*can* occur. If they can\'t, the method of generating the sequence is\n*not* random!\n\nAnd this is the point. The essence of randomness is not in the\nsequences themselves, but in the methods by which they are generated. A\ncomputer pseudo-random number generator is *not* random, although finite\nsequences it produces usually pass tests for randomness. A device based\non radioactive decay *is* (if properly designed and constructed) a\ntruly random number generator, even though it must, very rarely,\nproduce finite sequences that fail tests for randomness.\n\nShuffling a deck of cards, if done thoroughly and without trickery,\nproduces a good randomization of the order of the cards. The fact that\na "royal flush" occasionally appears does not prove otherwise.\n\ndow\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>-> Physicists are rarely medieval scholastics. There *ARE* ways of defining
-> randomness, e.g. the quality of a RN generator through proofs of ergodicity,
-> statistical tests, etc. There are ways of defining - not always but
-> frequently - the notion of order as the breakdown of a symmetry.
But every *finite* sequence of truly randomly generated numbers has a
nonzero probability of *failing* any test for randomness. Sequences
such as 11111111...., going on for the whole length of the sequence,
*can* occur. If they can't, the method of generating the sequence is
*not* random!
And this is the point. The essence of randomness is not in the
sequences themselves, but in the methods by which they are generated. A
computer pseudo-random number generator is *not* random, although finite
sequences it produces usually pass tests for randomness. A device based
on radioactive decay *is* (if properly designed and constructed) a
truly random number generator, even though it must, very rarely,
produce finite sequences that fail tests for randomness.
Shuffling a deck of cards, if done thoroughly and without trickery,
produces a good randomization of the order of the cards. The fact that
a "royal flush" occasionally appears does not prove otherwise.
dow
Douglas Natelson
May14-04, 04:09 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Ulmo wrote:\n\n> There is no way to define "order" versus "disorder" or "random" versus\n> "not random" separate from the human psychology, the prejudice or bias\n> of the observer.\n\nWhile there is some truth to your later statements, I disagree\nwith this. One can define a correlation function, for example,\nthat measures the periodicity of the spacings of particles.\nCrystals produce diffraction spots; liquids do not. This kind\nof structural order is well-defined mathematically, and in fact\nis related to the fundamental concepts of symmetry and\nsymmetry breaking (and phase transitions and so forth).\n\nThose correlations, independent of whether one chooses to\nquantify them, are certainly there in crystals and not in\nliquids.\n\n<snip>\n\n> Calling the air rushing to the corners of the\n> room "ordered" is like rolling a dice and calling rolling a six\n> "ordered" and rolling any other number "disordered".\n\nSo, don\'t you think it\'s surprising that, from the hugely\nlarge number of possible microstates of all the matter in the\nuniverse, the universe apparently started out in a configuration\nsuch that we can easily prepare an empty room for air to\nrush into? One of the great mysteries, to many physicists,\nis why the universe started off in such a low-entropy state.\n\n--DN\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Ulmo wrote:
> There is no way to define "order" versus "disorder" or "random" versus
> "not random" separate from the human psychology, the prejudice or bias
> of the observer.
While there is some truth to your later statements, I disagree
with this. One can define a correlation function, for example,
that measures the periodicity of the spacings of particles.
Crystals produce diffraction spots; liquids do not. This kind
of structural order is well-defined mathematically, and in fact
is related to the fundamental concepts of symmetry and
symmetry breaking (and phase transitions and so forth).
Those correlations, independent of whether one chooses to
quantify them, are certainly there in crystals and not in
liquids.
<snip>
> Calling the air rushing to the corners of the
> room "ordered" is like rolling a dice and calling rolling a six
> "ordered" and rolling any other number "disordered".
So, don't you think it's surprising that, from the hugely
large number of possible microstates of all the matter in the
universe, the universe apparently started out in a configuration
such that we can easily prepare an empty room for air to
rush into? One of the great mysteries, to many physicists,
is why the universe started off in such a low-entropy state.
--DN
Thomas Dent
May14-04, 06:14 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\ndavid.williams@bayman.org (David Williams) wrote\n\n> -> Physicists are rarely medieval scholastics. There *ARE* ways of defining\n> -> randomness, e.g. the quality of a RN generator through proofs of ergodicity,\n> -> statistical tests, etc. There are ways of defining - not always but\n> -> frequently - the notion of order as the breakdown of a symmetry.\n>\n> But every *finite* sequence of truly randomly generated numbers has a\n> nonzero probability of *failing* any test for randomness. Sequences\n> such as 11111111...., going on for the whole length of the sequence,\n> *can* occur. If they can\'t, the method of generating the sequence is\n> *not* random!\n>\n> And this is the point. The essence of randomness is not in the\n> sequences themselves, but in the methods by which they are generated. A\n> computer pseudo-random number generator is *not* random, although finite\n> sequences it produces usually pass tests for randomness. A device based\n> on radioactive decay *is* (if properly designed and constructed) a\n> truly random number generator, even though it must, very rarely,\n> produce finite sequences that fail tests for randomness.\n>\n> Shuffling a deck of cards, if done thoroughly and without trickery,\n> produces a good randomization of the order of the cards. The fact that\n> a "royal flush" occasionally appears does not prove otherwise.\n>\n\nSurely information theory has something to say about this: whether any\ngiven sequence can be specified by a shorter recipe. (e.g.\n0.142857142856142857... = 0.142857 repeating = 1/7.) The longer the\nrecipe, the more information and the greater the information-theoretic\nentropy and the greater the randomness (if we take this as a\n*scientific* measure of randomness, aside from its colloquial\nmeaning). It is completely consistent with the probabilistic notion of\nentropy, since the number of possible recipes increases exponentially\nwith the length of the recipe, so you are exponentially more likely to\nproceed into a "state" of higher entropy and greater randomness which\nrequires a longer recipe to specify it.\n\nThe state with all molecules in one corner of the room has lower\nentropy because there are fewer possible arrangements and it requires\nless information to specify any given arrangement. In this sense it is\nless random.\n\nOf course, there is a nonzero probability to proceed in the direction\nof smaller entropy, i.e. less randomness as defined above, but this is\nexponentially tiny. Am I saying that the Second Law fails sometimes?\nYes. But, any observable violation probably won\'t happen more than\nonce in a period of time greater than the age of the Universe.\n"Random" evolution (in the sense of ergodic) will sometimes lead to a\nstate which is highly "nonrandom" (as measured by\ninformation-theoretic entropy)!\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>david.williams@bayman.org (David Williams) wrote
> -> Physicists are rarely medieval scholastics. There *ARE* ways of defining
> -> randomness, e.g. the quality of a RN generator through proofs of ergodicity,
> -> statistical tests, etc. There are ways of defining - not always but
> -> frequently - the notion of order as the breakdown of a symmetry.
>
> But every *finite* sequence of truly randomly generated numbers has a
> nonzero probability of *failing* any test for randomness. Sequences
> such as 11111111...., going on for the whole length of the sequence,
> *can* occur. If they can't, the method of generating the sequence is
> *not* random!
>
> And this is the point. The essence of randomness is not in the
> sequences themselves, but in the methods by which they are generated. A
> computer pseudo-random number generator is *not* random, although finite
> sequences it produces usually pass tests for randomness. A device based
> on radioactive decay *is* (if properly designed and constructed) a
> truly random number generator, even though it must, very rarely,
> produce finite sequences that fail tests for randomness.
>
> Shuffling a deck of cards, if done thoroughly and without trickery,
> produces a good randomization of the order of the cards. The fact that
> a "royal flush" occasionally appears does not prove otherwise.
>
Surely information theory has something to say about this: whether any
given sequence can be specified by a shorter recipe. (e.g.
.142857142856142857... = .142857 repeating = 1/7.) The longer the
recipe, the more information and the greater the information-theoretic
entropy and the greater the randomness (if we take this as a
*scientific* measure of randomness, aside from its colloquial
meaning). It is completely consistent with the probabilistic notion of
entropy, since the number of possible recipes increases exponentially
with the length of the recipe, so you are exponentially more likely to
proceed into a "state" of higher entropy and greater randomness which
requires a longer recipe to specify it.
The state with all molecules in one corner of the room has lower
entropy because there are fewer possible arrangements and it requires
less information to specify any given arrangement. In this sense it is
less random.
Of course, there is a nonzero probability to proceed in the direction
of smaller entropy, i.e. less randomness as defined above, but this is
exponentially tiny. Am I saying that the Second Law fails sometimes?
Yes. But, any observable violation probably won't happen more than
once in a period of time greater than the age of the Universe.
"Random" evolution (in the sense of ergodic) will sometimes lead to a
state which is highly "nonrandom" (as measured by
information-theoretic entropy)!
David Williams
May14-04, 09:19 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>-> While there is some truth to your later statements, I disagree\n-> with this. One can define a correlation function, for example,\n-> that measures the periodicity of the spacings of particles.\n-> Crystals produce diffraction spots; liquids do not. This kind\n-> of structural order is well-defined mathematically, and in fact\n-> is related to the fundamental concepts of symmetry and\n-> symmetry breaking (and phase transitions and so forth).\n\n-> Those correlations, independent of whether one chooses to\n-> quantify them, are certainly there in crystals and not in\n-> liquids.\n\nThis is true only if the sample is large enough that the probabilities\nbecome virtual certainties. Liquids *do* have "short range" ordering of\nthe molecules. A sample only a few hundred molecules in size would\nproduce a diffraction pattern pretty much like that of a solid. Only\nwith much larger samples would the disorder in a liquid become obvious.\n\ndow\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>-> While there is some truth to your later statements, I disagree
-> with this. One can define a correlation function, for example,
-> that measures the periodicity of the spacings of particles.
-> Crystals produce diffraction spots; liquids do not. This kind
-> of structural order is well-defined mathematically, and in fact
-> is related to the fundamental concepts of symmetry and
-> symmetry breaking (and phase transitions and so forth).
-> Those correlations, independent of whether one chooses to
-> quantify them, are certainly there in crystals and not in
-> liquids.
This is true only if the sample is large enough that the probabilities
become virtual certainties. Liquids *do* have "short range" ordering of
the molecules. A sample only a few hundred molecules in size would
produce a diffraction pattern pretty much like that of a solid. Only
with much larger samples would the disorder in a liquid become obvious.
dow
Thomas Dent
May14-04, 11:25 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nJerzy Karczmarczuk <karczma@info.unicaen.fr> wrote\n\n> Ulmo wrote:\n>\n> > There is no way to define "order" versus "disorder" or "random" versus\n> > "not random" separate from the human psychology, the prejudice or bias\n> > of the observer. If you "see a pattern" you call it "order" and if you\n> > don\'t "see a pattern", you call it disorder. If you showed a list of\n> > prime numbers to someone who never heard of prime numbers, they would\n> > call it random. However, any possible list of numbers could be\n> > produced by some algorithmn even if we don\'t know what it is. If you\n> > show someone a series of numbers, and they don\'t see any pattern, and\n> > they call it "disordered", and then you give them the algorithmn that\n> > produces it, does that mean the series changed from "disordered" to\n> > "ordered" just because of the change in the observer\'s knowledge.\n>\n> This is a metaphysical, not an operational viewpoint. When I launch a\n> random number generator, I KNOW that the sequence is perfectly determi-\n> nistic and repeatable, yeat I *call it random*.\n>\n> Physicists are rarely medieval scholastics. There *ARE* ways of defining\n> randomness, e.g. the quality of a RN generator through proofs of ergodicity,\n> statistical tests, etc. There are ways of defining - not always but\n> frequently - the notion of order as the breakdown of a symmetry.\n>\n> Sorry for being a bit brutal, but reducing notions which are analysable by\n> the theory of measure, etc. to human prejudices and psychology doesn\'t\n> sound very scientific.\n>\n> Jerzy Karczmarczuk\n\nTo expand on this a little, one can use Shannon\'s\ninformation-theoretic entropy to give a very precise definition of\n"randomness" as it applies to entropy. The more bits of information\nneeded to completely specify a state, the more "random" it is\nconsidered and the greater its entropy. Now, of course, the number of\npossible states grows exponentially with the amount of information\nneeded, and hence with the entropy, so given a minimal assumption of\nergodicity, you are exponentially more likely to make a transition\ninto a state of higher entropy.\n\nOf course, you could interpret "random" to mean ergodic, so you get\nthe apparent paradox that "random" (ergodic) evolution can sometimes\nlead to a "less random" (i.e. lower entropy) state! (And yes, this\nmeans that the Second Law is violated - but only very very rarely!)\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote
> Ulmo wrote:
>
> > There is no way to define "order" versus "disorder" or "random" versus
> > "not random" separate from the human psychology, the prejudice or bias
> > of the observer. If you "see a pattern" you call it "order" and if you
> > don't "see a pattern", you call it disorder. If you showed a list of
> > prime numbers to someone who never heard of prime numbers, they would
> > call it random. However, any possible list of numbers could be
> > produced by some algorithmn even if we don't know what it is. If you
> > show someone a series of numbers, and they don't see any pattern, and
> > they call it "disordered", and then you give them the algorithmn that
> > produces it, does that mean the series changed from "disordered" to
> > "ordered" just because of the change in the observer's knowledge.
>
> This is a metaphysical, not an operational viewpoint. When I launch a
> random number generator, I KNOW that the sequence is perfectly determi-
> nistic and repeatable, yeat I *call it random*.
>
> Physicists are rarely medieval scholastics. There *ARE* ways of defining
> randomness, e.g. the quality of a RN generator through proofs of ergodicity,
> statistical tests, etc. There are ways of defining - not always but
> frequently - the notion of order as the breakdown of a symmetry.
>
> Sorry for being a bit brutal, but reducing notions which are analysable by
> the theory of measure, etc. to human prejudices and psychology doesn't
> sound very scientific.
>
> Jerzy Karczmarczuk
To expand on this a little, one can use Shannon's
information-theoretic entropy to give a very precise definition of
"randomness" as it applies to entropy. The more bits of information
needed to completely specify a state, the more "random" it is
considered and the greater its entropy. Now, of course, the number of
possible states grows exponentially with the amount of information
needed, and hence with the entropy, so given a minimal assumption of
ergodicity, you are exponentially more likely to make a transition
into a state of higher entropy.
Of course, you could interpret "random" to mean ergodic, so you get
the apparent paradox that "random" (ergodic) evolution can sometimes
lead to a "less random" (i.e. lower entropy) state! (And yes, this
means that the Second Law is violated - but only very very rarely!)
Ken S. Tucker
May16-04, 12:57 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>david.williams@bayman.org (David Williams) wrote in message news:<1089361372.1572.1089360308@bayman.org>...\n>-> Physicists are rarely medieval scholastics. There *ARE* ways of defining\n>-> randomness, e.g. the quality of a RN generator through proofs of ergodicity,\n>-> statistical tests, etc. There are ways of defining - not always but\n>-> frequently - the notion of order as the breakdown of a symmetry.\n[...]\n>And this is the point. The essence of randomness is not in the\n>sequences themselves, but in the methods by which they are generated. A\n>computer pseudo-random number generator is *not* random, although finite\n>sequences it produces usually pass tests for randomness. A device based\n>on radioactive decay *is* (if properly designed and constructed) a\n>truly random number generator, even though it must, very rarely,\n>produce finite sequences that fail tests for randomness.\n\nIs it possible to formulate a algorithm to generate Random\nNumbers?\n\nIf Yes, then certain *apparently* random physical\nprocesses like radioactive decay, would need to\ninclude that algorithm somewhere, albiet implicit,\nbut the the process is casual, since random would\nbe a function of time.\n\nIf No, then it would be impossible to describe\nrandom natural processes with an algorithm. The\nprocess would not be a function of time and\ntherefore would be impssible to prove is casual.\nIf acasual, the arrow of time could not have any\nmeaning in said process as the arrow is defined by\ncasual assumptions.\n\nIf the algorithm is possible, it generates a sequence,\nand should produce\nRandom Number = function (time) = casual.\n\nKen S. Tucker\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>david.williams@bayman.org (David Williams) wrote in message news:<1089361372.1572.1089360308@bayman.org>...
>-> Physicists are rarely medieval scholastics. There *ARE* ways of defining
>-> randomness, e.g. the quality of a RN generator through proofs of ergodicity,
>-> statistical tests, etc. There are ways of defining - not always but
>-> frequently - the notion of order as the breakdown of a symmetry.
[...]
>And this is the point. The essence of randomness is not in the
>sequences themselves, but in the methods by which they are generated. A
>computer pseudo-random number generator is *not* random, although finite
>sequences it produces usually pass tests for randomness. A device based
>on radioactive decay *is* (if properly designed and constructed) a
>truly random number generator, even though it must, very rarely,
>produce finite sequences that fail tests for randomness.
Is it possible to formulate a algorithm to generate Random
Numbers?
If Yes, then certain *apparently* random physical
processes like radioactive decay, would need to
include that algorithm somewhere, albiet implicit,
but the the process is casual, since random would
be a function of time.
If No, then it would be impossible to describe
random natural processes with an algorithm. The
process would not be a function of time and
therefore would be impssible to prove is casual.
If acasual, the arrow of time could not have any
meaning in said process as the arrow is defined by
casual assumptions.
If the algorithm is possible, it generates a sequence,
and should produce
Random Number = function (time) = casual.
Ken S. Tucker
Kirk Gregory Czuhai
May17-04, 02:03 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>tdent@auth.gr (Thomas Dent) wrote in message news:<cb504c2c.0405140745.29695d48@posting.google. com>...\n> Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote\n>\n> > Ulmo wrote:\n> >\n> > > There is no way to define "order" versus "disorder" or "random" versus\n> > > "not random" separate from the human psychology, the prejudice or bias\n> > > of the observer. If you "see a pattern" you call it "order" and if you\n> > > don\'t "see a pattern", you call it disorder. If you showed a list of\n> > > prime numbers to someone who never heard of prime numbers, they would\n> > > call it random. However, any possible list of numbers could be\n> > > produced by some algorithmn even if we don\'t know what it is. If you\n> > > show someone a series of numbers, and they don\'t see any pattern, and\n> > > they call it "disordered", and then you give them the algorithmn that\n> > > produces it, does that mean the series changed from "disordered" to\n> > > "ordered" just because of the change in the observer\'s knowledge.\n> >\n> > This is a metaphysical, not an operational viewpoint. When I launch a\n> > random number generator, I KNOW that the sequence is perfectly determi-\n> > nistic and repeatable, yeat I *call it random*.\n> >\n> > Physicists are rarely medieval scholastics. There *ARE* ways of defining\n> > randomness, e.g. the quality of a RN generator through proofs of ergodicity,\n> > statistical tests, etc. There are ways of defining - not always but\n> > frequently - the notion of order as the breakdown of a symmetry.\n> >\n> > Sorry for being a bit brutal, but reducing notions which are analysable by\n> > the theory of measure, etc. to human prejudices and psychology doesn\'t\n> > sound very scientific.\n> >\n> > Jerzy Karczmarczuk\n>\n> To expand on this a little, one can use Shannon\'s\n> information-theoretic entropy to give a very precise definition of\n> "randomness" as it applies to entropy. The more bits of information\n> needed to completely specify a state, the more "random" it is\n> considered and the greater its entropy. Now, of course, the number of\n> possible states grows exponentially with the amount of information\n> needed, and hence with the entropy, so given a minimal assumption of\n> ergodicity, you are exponentially more likely to make a transition\n> into a state of higher entropy.\n>\n> Of course, you could interpret "random" to mean ergodic, so you get\n> the apparent paradox that "random" (ergodic) evolution can sometimes\n> lead to a "less random" (i.e. lower entropy) state! (And yes, this\n> means that the Second Law is violated - but only very very rarely!)\n\nI am pondering the statement, "The more bits of information\nneeded to completely specify a state, the more "random" it is\nconsidered and the greater its entropy." and wondering if this applies\nalways to living organisms OR if I may jump ahead to what many have\nfaith in, God !!!\n\nWould not God have to have infinite entropy or total disorder based on\nthis definition? Pardon me if this topic is not allowed discussion\nhere.\n\nBack to the life forms:\n\nConsider two two rabbits that were twin siblings. Suppose one was\nstarved of vitamin C and eventually died as a consequence. Would you\nsay that while it lived with scurvey that it was more ordered and had\na lower entropy than its healthier twin that was recieving an adequet\ndiet? Surely you see, less information was needed to describe the diet\nof the rabbit that was gonna die.\n\npeace and love,\n\n(kirk) kirk gregory czuhai\n\nhttp://www.altelco.net/~churches\n\nhttp://heavensense.intranets.com\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>tdent@auth.gr (Thomas Dent) wrote in message news:<cb504c2c.0405140745.29695d48@posting.google.com>...
> Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote
>
> > Ulmo wrote:
> >
> > > There is no way to define "order" versus "disorder" or "random" versus
> > > "not random" separate from the human psychology, the prejudice or bias
> > > of the observer. If you "see a pattern" you call it "order" and if you
> > > don't "see a pattern", you call it disorder. If you showed a list of
> > > prime numbers to someone who never heard of prime numbers, they would
> > > call it random. However, any possible list of numbers could be
> > > produced by some algorithmn even if we don't know what it is. If you
> > > show someone a series of numbers, and they don't see any pattern, and
> > > they call it "disordered", and then you give them the algorithmn that
> > > produces it, does that mean the series changed from "disordered" to
> > > "ordered" just because of the change in the observer's knowledge.
> >
> > This is a metaphysical, not an operational viewpoint. When I launch a
> > random number generator, I KNOW that the sequence is perfectly determi-
> > nistic and repeatable, yeat I *call it random*.
> >
> > Physicists are rarely medieval scholastics. There *ARE* ways of defining
> > randomness, e.g. the quality of a RN generator through proofs of ergodicity,
> > statistical tests, etc. There are ways of defining - not always but
> > frequently - the notion of order as the breakdown of a symmetry.
> >
> > Sorry for being a bit brutal, but reducing notions which are analysable by
> > the theory of measure, etc. to human prejudices and psychology doesn't
> > sound very scientific.
> >
> > Jerzy Karczmarczuk
>
> To expand on this a little, one can use Shannon's
> information-theoretic entropy to give a very precise definition of
> "randomness" as it applies to entropy. The more bits of information
> needed to completely specify a state, the more "random" it is
> considered and the greater its entropy. Now, of course, the number of
> possible states grows exponentially with the amount of information
> needed, and hence with the entropy, so given a minimal assumption of
> ergodicity, you are exponentially more likely to make a transition
> into a state of higher entropy.
>
> Of course, you could interpret "random" to mean ergodic, so you get
> the apparent paradox that "random" (ergodic) evolution can sometimes
> lead to a "less random" (i.e. lower entropy) state! (And yes, this
> means that the Second Law is violated - but only very very rarely!)
I am pondering the statement, "The more bits of information
needed to completely specify a state, the more "random" it is
considered and the greater its entropy." and wondering if this applies
always to living organisms OR if I may jump ahead to what many have
faith in, God !!!
Would not God have to have infinite entropy or total disorder based on
this definition? Pardon me if this topic is not allowed discussion
here.
Back to the life forms:
Consider two two rabbits that were twin siblings. Suppose one was
starved of vitamin C and eventually died as a consequence. Would you
say that while it lived with scurvey that it was more ordered and had
a lower entropy than its healthier twin that was recieving an adequet
diet? Surely you see, less information was needed to describe the diet
of the rabbit that was gonna die.
peace and love,
(kirk) kirk gregory czuhai
http://www.altelco.net/~churches
http://heavensense.intranets.com
David Williams
May17-04, 05:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n-> Is it possible to formulate a algorithm to generate Random\n-> Numbers?\n\n-> If Yes, then certain *apparently* random physical\n-> processes like radioactive decay, would need to\n-> include that algorithm somewhere, albiet implicit,\n-> but the the process is casual, since random would\n-> be a function of time.\n\n-> If No, then it would be impossible to describe\n-> random natural processes with an algorithm. The\n-> process would not be a function of time and\n-> therefore would be impssible to prove is casual.\n-> If acasual, the arrow of time could not have any\n-> meaning in said process as the arrow is defined by\n-> casual assumptions.\n\n-> If the algorithm is possible, it generates a sequence,\n-> and should produce\n-> Random Number = function (time) = casual.\n\n-> Ken S. Tucker\n\nI\'m not sure what you mean by an "algorithm" that includes some process\nsuch as radioactive decay.\n\nIt is possible to make a very good random-number generator by using a\nGeiger counter and a small chunk of some radioactive material. In some\nshort periood of time, say one second, the counter will register a\nlarge number of counts. If this number is even, your "random" number is\n0. If the number of counts is odd, the random number is 1. Do this a\nlarge number of times, and you get a sequence of 0\'s and 1\'s that is\nvery random.\n\nI take it you meant "causal", rather than "casual". No? But I still\ndon\'t follow your argument.\n\ndow\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>-> Is it possible to formulate a algorithm to generate Random
-> Numbers?
-> If Yes, then certain *apparently* random physical
-> processes like radioactive decay, would need to
-> include that algorithm somewhere, albiet implicit,
-> but the the process is casual, since random would
-> be a function of time.
-> If No, then it would be impossible to describe
-> random natural processes with an algorithm. The
-> process would not be a function of time and
-> therefore would be impssible to prove is casual.
-> If acasual, the arrow of time could not have any
-> meaning in said process as the arrow is defined by
-> casual assumptions.
-> If the algorithm is possible, it generates a sequence,
-> and should produce
-> Random Number = function (time) = casual.
-> Ken S. Tucker
I'm not sure what you mean by an "algorithm" that includes some process
such as radioactive decay.
It is possible to make a very good random-number generator by using a
Geiger counter and a small chunk of some radioactive material. In some
short periood of time, say one second, the counter will register a
large number of counts. If this number is even, your "random" number is
. If the number of counts is odd, the random number is 1. Do this a
large number of times, and you get a sequence of 0's and 1's that is
very random.
I take it you meant "causal", rather than "casual". No? But I still
don't follow your argument.
dow
Phillip Helbig---remove CLOTHES to reply
May17-04, 05:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nIn article <68c18740.0405161853.753737cf@posting.google.com>, \nlovekgc@altelco.net (Kirk Gregory Czuhai) writes:\n\n> I am pondering the statement, "The more bits of information\n> needed to completely specify a state, the more "random" it is\n> considered and the greater its entropy." and wondering if this applies\n> always to living organisms OR if I may jump ahead to what many have\n> faith in, God !!!\n\nIt depends on the definitions of "information" and "randomness". In\nsome sense (the sense alluded to above), the more one can compress\nsomething (say, a text file with a compression program), the less\ninformation it contains, since there is some redundancy (otherwise it\ncouldn\'t be compressed). In this sense, something random cannot be\ncompressed, and thus has a high information content. Intuitively, one\nwould attribute "complexity" neither to something completely random, nor\nto something completely predictable, but somewhere in-between.\n\nThere is a reasonably good discussion of this in Murray Gell-Mann\'s\npopular book THE QUARK AND THE JAGUAR.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <68c18740.0405161853.753737cf@posting.google.com>,
lovekgc@altelco.net (Kirk Gregory Czuhai) writes:
> I am pondering the statement, "The more bits of information
> needed to completely specify a state, the more "random" it is
> considered and the greater its entropy." and wondering if this applies
> always to living organisms OR if I may jump ahead to what many have
> faith in, God !!!
It depends on the definitions of "information" and "randomness". In
some sense (the sense alluded to above), the more one can compress
something (say, a text file with a compression program), the less
information it contains, since there is some redundancy (otherwise it
couldn't be compressed). In this sense, something random cannot be
compressed, and thus has a high information content. Intuitively, one
would attribute "complexity" neither to something completely random, nor
to something completely predictable, but somewhere in-between.
There is a reasonably good discussion of this in Murray Gell-Mann's
popular book THE QUARK AND THE JAGUAR.
Douglas Natelson
May17-04, 06:24 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>David Williams wrote:\n\n[regarding correlations and diffraction patterns]\n> This is true only if the sample is large enough that the probabilities\n> become virtual certainties. Liquids *do* have "short range" ordering of\n> the molecules. A sample only a few hundred molecules in size would\n> produce a diffraction pattern pretty much like that of a solid. Only\n> with much larger samples would the disorder in a liquid become obvious.\n\nSure - diffraction patterns are only really sharp in the\nthermodynamic limit. Still, the density-density correlations\nfor mesoscale amounts of liquid do look different from those\nof mesoscale amounts of solid, unless the liquid is extremely\nconstrained. Anyway, you know the point I was trying to make:\nthe correlations in a crystal are a real measure of order, while\nthe original poster was claiming essentially that "order" and\n"disorder" are purely semantic terms.\n\n--DN\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>David Williams wrote:
[regarding correlations and diffraction patterns]
> This is true only if the sample is large enough that the probabilities
> become virtual certainties. Liquids *do* have "short range" ordering of
> the molecules. A sample only a few hundred molecules in size would
> produce a diffraction pattern pretty much like that of a solid. Only
> with much larger samples would the disorder in a liquid become obvious.
Sure - diffraction patterns are only really sharp in the
thermodynamic limit. Still, the density-density correlations
for mesoscale amounts of liquid do look different from those
of mesoscale amounts of solid, unless the liquid is extremely
constrained. Anyway, you know the point I was trying to make:
the correlations in a crystal are a real measure of order, while
the original poster was claiming essentially that "order" and
"disorder" are purely semantic terms.
--DN
Italo Vecchi
May17-04, 07:52 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>david.williams@bayman.org (David Williams) wrote in message news:<1089361372.1572.1089360308@bayman.org>...\n\ n....\n\n> The essence of randomness is not in the\n> sequences themselves, but in the methods by which they are generated. A\n> computer pseudo-random number generator is *not* random, although finite\n> sequences it produces usually pass tests for randomness. A device based\n> on radioactive decay *is* (if properly designed and constructed) a\n> truly random number generator, even though it must, very rarely,\n> produce finite sequences that fail tests for randomness.\n>\n> Shuffling a deck of cards, if done thoroughly and without trickery,\n> produces a good randomization of the order of the cards. The fact that\n> a "royal flush" occasionally appears does not prove otherwise.\n>\n\nI wonder whether shuffling a deck of cards is a quantum process, i.e.\nI wonder whether any "true" randomisation is a quantum phenomenon. I\nconjecture it is.\n\nPhysical "classical" randomness (admitting that there is such a\nthing) arises from processes exhibiting chaotic behaviour, such as\nBrownian motion or dice being shaken in a can. Now in a chaotic system\nany initial "quantum scale" indeterminacy determined by Heisenberg\'s\nprinciple will quickly grow macroscopic ([1]).\n\nSo when we talk about concrete instances of randomness we are\nreferring to phenomena whose quantum character is fundamental.\n\nI conjecture also that randomness may be observer-dependent. For a\ncard-sharper that "royal flush" may not be random after all.\n\nCheers,\n\nIV\n\n\n[1] "Newtonian Chaos + Heisenberg Uncertainty = macroscopic\nindeterminacy" by Barone, S.R., Kunhardt, E.E., Bentson, J., and\nSyljuasen, A., American Journal of Physics, Vol 61, No. 5, May 1993.\n\n----------------------------\n\n"In dubio non est recedendum a propria significatione verborum"\n\n"When in doubt, never back away from the proper meaning of words"\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>david.williams@bayman.org (David Williams) wrote in message news:<1089361372.1572.1089360308@bayman.org>...
....
> The essence of randomness is not in the
> sequences themselves, but in the methods by which they are generated. A
> computer pseudo-random number generator is *not* random, although finite
> sequences it produces usually pass tests for randomness. A device based
> on radioactive decay *is* (if properly designed and constructed) a
> truly random number generator, even though it must, very rarely,
> produce finite sequences that fail tests for randomness.
>
> Shuffling a deck of cards, if done thoroughly and without trickery,
> produces a good randomization of the order of the cards. The fact that
> a "royal flush" occasionally appears does not prove otherwise.
>
I wonder whether shuffling a deck of cards is a quantum process, i.e.
I wonder whether any "true" randomisation is a quantum phenomenon. I
conjecture it is.
Physical "classical" randomness (admitting that there is such a
thing) arises from processes exhibiting chaotic behaviour, such as
Brownian motion or dice being shaken in a can. Now in a chaotic system
any initial "quantum scale" indeterminacy determined by Heisenberg's
principle will quickly grow macroscopic ([1]).
So when we talk about concrete instances of randomness we are
referring to phenomena whose quantum character is fundamental.
I conjecture also that randomness may be observer-dependent. For a
card-sharper that "royal flush" may not be random after all.
Cheers,
IV
[1] "Newtonian Chaos + Heisenberg Uncertainty = macroscopic
indeterminacy" by Barone, S.R., Kunhardt, E.E., Bentson, J., and
Syljuasen, A., American Journal of Physics, Vol 61, No. 5, May 1993.
----------------------------
"In dubio non est recedendum a propria significatione verborum"
"When in doubt, never back away from the proper meaning of words"
George Buyanovsky
May17-04, 08:09 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>dynamics@vianet.on.ca (Ken S. Tucker) wrote in message news:<2202379a.0405150802.2e33ff14@posting.google. com>...\n> david.williams@bayman.org (David Williams) wrote in message news:<1089361372.1572.1089360308@bayman.org>...\n> >-> Physicists are rarely medieval scholastics. There *ARE* ways of defining\n> >-> randomness, e.g. the quality of a RN generator through proofs of ergodicity,\n> >-> statistical tests, etc. There are ways of defining - not always but\n> >-> frequently - the notion of order as the breakdown of a symmetry.\n> [...]\n> >And this is the point. The essence of randomness is not in the\n> >sequences themselves, but in the methods by which they are generated. A\n> >computer pseudo-random number generator is *not* random, although finite\n> >sequences it produces usually pass tests for randomness. A device based\n> >on radioactive decay *is* (if properly designed and constructed) a\n> >truly random number generator, even though it must, very rarely,\n> >produce finite sequences that fail tests for randomness.\n>\n> Is it possible to formulate a algorithm to generate Random\n> Numbers?\n\nSince computer is a finite automata, the maximum number of states you\ncan get is finite. Let assume that computer has 4GB RAM (2^40 bit) the\nmaximum period of random sequences cannot be more that factorial of\n(2^40). If to take into account HD (1TB), the boundary is (2^50)!.\nHowever, as the rule, the practical random generator algorithms\ngenerate the unique sequence with length not more than (2^10)!.\nHowever this length is enormously huge the sequence is predetermined.\nThe knowledge of initial state and applied algorithm describes all\nsequence. It means that to remember (2^10)! sequence some one needs to\nremember 2^10 bit of initial state plus number of deployed algorithm\nlog2i(|algorithms_set|). To get the true random generator the outside\ndisturbance has to be involved (like radioactive decay).\n\nGeorge\n\n[Moderator\'s note: Unless there\'s some clear connection to physics,\nlet\'s not continue the discussion along this particular\ndirection. -TB]\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>dynamics@vianet.on.ca (Ken S. Tucker) wrote in message news:<2202379a.0405150802.2e33ff14@posting.google.com>...
> david.williams@bayman.org (David Williams) wrote in message news:<1089361372.1572.1089360308@bayman.org>...
> >-> Physicists are rarely medieval scholastics. There *ARE* ways of defining
> >-> randomness, e.g. the quality of a RN generator through proofs of ergodicity,
> >-> statistical tests, etc. There are ways of defining - not always but
> >-> frequently - the notion of order as the breakdown of a symmetry.
> [...]
> >And this is the point. The essence of randomness is not in the
> >sequences themselves, but in the methods by which they are generated. A
> >computer pseudo-random number generator is *not* random, although finite
> >sequences it produces usually pass tests for randomness. A device based
> >on radioactive decay *is* (if properly designed and constructed) a
> >truly random number generator, even though it must, very rarely,
> >produce finite sequences that fail tests for randomness.
>
> Is it possible to formulate a algorithm to generate Random
> Numbers?
Since computer is a finite automata, the maximum number of states you
can get is finite. Let assume that computer has 4GB RAM (2^{40} bit) the
maximum period of random sequences cannot be more that factorial of
(2^{40}). If to take into account HD (1TB), the boundary is (2^{50})!.
However, as the rule, the practical random generator algorithms
generate the unique sequence with length not more than (2^{10})!.
However this length is enormously huge the sequence is predetermined.
The knowledge of initial state and applied algorithm describes all
sequence. It means that to remember (2^{10})! sequence some one needs to
remember 2^{10} bit of initial state plus number of deployed algorithm
log2i(|algorithms_set|). To get the true random generator the outside
disturbance has to be involved (like radioactive decay).
George
[Moderator's note: Unless there's some clear connection to physics,
let's not continue the discussion along this particular
direction. -TB]
Kirk Gregory Czuhai
May17-04, 08:19 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to reply) wrote in message news:<c89oio\\$c6f\\$2@online.de>...\n> In article <68c18740.0405161853.753737cf@posting.google.com>, \n> lovekgc@altelco.net (Kirk Gregory Czuhai) writes:\n>\n> > I am pondering the statement, "The more bits of information\n> > needed to completely specify a state, the more "random" it is\n> > considered and the greater its entropy." and wondering if this applies\n> > always to living organisms OR if I may jump ahead to what many have\n> > faith in, God !!!\n>\n> It depends on the definitions of "information" and "randomness". In\n> some sense (the sense alluded to above), the more one can compress\n> something (say, a text file with a compression program), the less\n> information it contains, since there is some redundancy (otherwise it\n> couldn\'t be compressed). In this sense, something random cannot be\n> compressed, and thus has a high information content. Intuitively, one\n> would attribute "complexity" neither to something completely random, nor\n> to something completely predictable, but somewhere in-between.\n>\n> There is a reasonably good discussion of this in Murray Gell-Mann\'s\n> popular book THE QUARK AND THE JAGUAR.\n\nThank you for the explanation. I admit my basic lack of education in\ninformation theory. Seems somehow intuitive (and apparently wrong) to\nme that the more information something contained would make something\nhave more order not less! (neglecting any compression ability). I have\nbeen subjected enough to both classical and quantum mechanical physics\nand have seen Murray Gell-Mann\'s work in other areas to see that we\nindeed for many reasons live in a very Complex Universe!\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to reply) wrote in message news:<c89oio$c6f$2@online.de>...
> In article <68c18740.0405161853.753737cf@posting.google.com>,
> lovekgc@altelco.net (Kirk Gregory Czuhai) writes:
>
> > I am pondering the statement, "The more bits of information
> > needed to completely specify a state, the more "random" it is
> > considered and the greater its entropy." and wondering if this applies
> > always to living organisms OR if I may jump ahead to what many have
> > faith in, God !!!
>
> It depends on the definitions of "information" and "randomness". In
> some sense (the sense alluded to above), the more one can compress
> something (say, a text file with a compression program), the less
> information it contains, since there is some redundancy (otherwise it
> couldn't be compressed). In this sense, something random cannot be
> compressed, and thus has a high information content. Intuitively, one
> would attribute "complexity" neither to something completely random, nor
> to something completely predictable, but somewhere in-between.
>
> There is a reasonably good discussion of this in Murray Gell-Mann's
> popular book THE QUARK AND THE JAGUAR.
Thank you for the explanation. I admit my basic lack of education in
information theory. Seems somehow intuitive (and apparently wrong) to
me that the more information something contained would make something
have more order not less! (neglecting any compression ability). I have
been subjected enough to both classical and quantum mechanical physics
and have seen Murray Gell-Mann's work in other areas to see that we
indeed for many reasons live in a very Complex Universe!
David Williams
May18-04, 03:44 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>-> I am pondering the statement, "The more bits of information\n-> needed to completely specify a state, the more "random" it is\n\nIt can\'t be *that* simple. Suppose I have a very short sequence of\nnumbers that I want to test for randomness. Let\'s go to the extreme,\nand suppose that the sequence is just one bit long. So obviously one\nbit of information is enough to specify this "sequence". What does that\nmean? Was the one-bit sequence produced by some random method such as\nflipping a coin, or was it determined in some non-random way?\n\nIf the sequence is longer, but still finite, the same difficulty\narises. The sequence may have been produced randomly, but still\naccidentally contain some regularities that would allow it to be\ndescribed quite briefly. Or it may have been produced non-randomly,\nsuch as by a computer pseudo-random number generator, but be short\nenough that its briefest description would equal the sequence itself,\nmaking it appear random. Only if the sequence is extremely long\n(billions of bits, in most cases), would the pseudo-random numbers\nstart to repeat, allowing a shorter description.\n\nBasically, it is impossible to determine whether a *finite* sequence\nhas been generated randomly or not by looking at the sequence itself.\n"Tests of randomness" are themselves uncertain. They can give a\nprobabilistic estimate, subject to arbitary initial assumptions, but\nthey can never decide with certainty.\n\nOnly by looking at the method by which the sequence was generated is it\npossible to know if it is random or not.\n\ndow\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>-> I am pondering the statement, "The more bits of information
-> needed to completely specify a state, the more "random" it is
It can't be *that* simple. Suppose I have a very short sequence of
numbers that I want to test for randomness. Let's go to the extreme,
and suppose that the sequence is just one bit long. So obviously one
bit of information is enough to specify this "sequence". What does that
mean? Was the one-bit sequence produced by some random method such as
flipping a coin, or was it determined in some non-random way?
If the sequence is longer, but still finite, the same difficulty
arises. The sequence may have been produced randomly, but still
accidentally contain some regularities that would allow it to be
described quite briefly. Or it may have been produced non-randomly,
such as by a computer pseudo-random number generator, but be short
enough that its briefest description would equal the sequence itself,
making it appear random. Only if the sequence is extremely long
(billions of bits, in most cases), would the pseudo-random numbers
start to repeat, allowing a shorter description.
Basically, it is impossible to determine whether a *finite* sequence
has been generated randomly or not by looking at the sequence itself.
"Tests of randomness" are themselves uncertain. They can give a
probabilistic estimate, subject to arbitary initial assumptions, but
they can never decide with certainty.
Only by looking at the method by which the sequence was generated is it
possible to know if it is random or not.
dow
David Williams
May18-04, 03:44 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>-> constrained. Anyway, you know the point I was trying to make:\n-> the correlations in a crystal are a real measure of order, while\n-> the original poster was claiming essentially that "order" and\n-> "disorder" are purely semantic terms.\n\n-> --DN\n\nShould we be making a distinction between "order" and "organization"? A\njumble such as the molecules in a liquid is in some "order", which\nmight be held to be only semantically different from the "order" of\nmolecules in a crystal. But the crystal structure is definitely more\n"organized".\n\ndow\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>-> constrained. Anyway, you know the point I was trying to make:
-> the correlations in a crystal are a real measure of order, while
-> the original poster was claiming essentially that "order" and
-> "disorder" are purely semantic terms.
-> --DN
Should we be making a distinction between "order" and "organization"? A
jumble such as the molecules in a liquid is in some "order", which
might be held to be only semantically different from the "order" of
molecules in a crystal. But the crystal structure is definitely more
"organized".
dow
George Buyanovsky
May20-04, 03:47 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>tdent@auth.gr (Thomas Dent) wrote in message news:<cb504c2c.0405140745.29695d48@posting.google. com>...\n> Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote\n>\n> To expand on this a little, one can use Shannon\'s\n> information-theoretic entropy to give a very precise definition of\n> "randomness" as it applies to entropy. The more bits of information\n> needed to completely specify a state, the more "random" it is\n> considered and the greater its entropy.\n\nShannon\'s entropy is defined for simples 0-order context model; the\nhigher orders will produce different entropy for each probabilistic\nset of outcomes. So entropy is a product of source modeling. More\nprecise definition of complexity (randomness) has to account the\nmodeling algorithm as well. If some one proposed the predictive\napparatus (let\'s assume "Quantum Mechanics"), which is implemented as\na computer program to predict the probabilistic set of outcomes, then\ncomplexity of modeled process can be defined as entropy of\nprobabilistic set of outcomes multiplied by set size plus amount of\nmemory necessary for modeling algorithm to accomplish prediction.\n\nStill "amount of memory necessary for modeling algorithm" is weakly\ndefined since there is significant variation of algorithm\nimplementations.\n\nBest,\nGeorge\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>tdent@auth.gr (Thomas Dent) wrote in message news:<cb504c2c.0405140745.29695d48@posting.google.com>...
> Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote
>
> To expand on this a little, one can use Shannon's
> information-theoretic entropy to give a very precise definition of
> "randomness" as it applies to entropy. The more bits of information
> needed to completely specify a state, the more "random" it is
> considered and the greater its entropy.
Shannon's entropy is defined for simples 0-order context model; the
higher orders will produce different entropy for each probabilistic
set of outcomes. So entropy is a product of source modeling. More
precise definition of complexity (randomness) has to account the
modeling algorithm as well. If some one proposed the predictive
apparatus (let's assume "Quantum Mechanics"), which is implemented as
a computer program to predict the probabilistic set of outcomes, then
complexity of modeled process can be defined as entropy of
probabilistic set of outcomes multiplied by set size plus amount of
memory necessary for modeling algorithm to accomplish prediction.
Still "amount of memory necessary for modeling algorithm" is weakly
defined since there is significant variation of algorithm
implementations.
Best,
George
alistair
May22-04, 04:49 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to reply) wrote in message news:<c89oio\\$c6f\\$2@online.de>...\nIntuitively, one\nwould attribute "complexity" neither to something completely random,\nnor\nto something completely predictable, but somewhere in-between\n\n\nA good example of this is prime numbers, some of which can be\npredicted and follow a pattern but primes as a whole cannot be\npredicted by one equation\nand the greatest mathematicians in history have failed to solve this\nproblem\n-people like Bernard Riemann.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>helbig@astro.multiCLOTHESvax.de (Phillip Helbig---remove CLOTHES to reply) wrote in message news:<c89oio$c6f$2@online.de>...
Intuitively, one
would attribute "complexity" neither to something completely random,
nor
to something completely predictable, but somewhere in-between
A good example of this is prime numbers, some of which can be
predicted and follow a pattern but primes as a whole cannot be
predicted by one equation
and the greatest mathematicians in history have failed to solve this
problem
-people like Bernard Riemann.
alistair
May23-04, 03:13 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>> > Jerzy Karczmarczuk\n>\nto make a transition\n> into a state of higher entropy.\n>\nevolution can sometimes\n> lead to a "less random" (i.e. lower entropy) state! (And yes, this\n> means that the Second Law is violated - but only very very rarely!)\n\nBut the second law will not\nbe violated - the entropy of the surroundings in which the lower\nentropy state was created will increase.The total entropy is what\ncounts.\nEntropy cannot be interpreted in terms of isolated systems because\nthere is no known system that is isolated in the real world, apart,\nperhaps from the universe itself.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>> > Jerzy Karczmarczuk
>
to make a transition
> into a state of higher entropy.
>
evolution can sometimes
> lead to a "less random" (i.e. lower entropy) state! (And yes, this
> means that the Second Law is violated - but only very very rarely!)
But the second law will not
be violated - the entropy of the surroundings in which the lower
entropy state was created will increase.The total entropy is what
counts.
Entropy cannot be interpreted in terms of isolated systems because
there is no known system that is isolated in the real world, apart,
perhaps from the universe itself.
Jerzy Karczmarczuk
May24-04, 05:24 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nalistair wrote:\n>>>Jerzy Karczmarczuk\n>>\n> to make a transition\n>\n>>into a state of higher entropy.\n>>\n>\n> evolution can sometimes\n>\n>>lead to a "less random" (i.e. lower entropy) state! (And yes, this\n>>means that the Second Law is violated - but only very very rarely!)\n>\n>\n> But the second law will not\n> be violated - the entropy of the surroundings in which the lower\n> entropy state was created will increase.The total entropy is what\n> counts.\n> Entropy cannot be interpreted in terms of isolated systems because\n> there is no known system that is isolated in the real world, apart,\n> perhaps from the universe itself.\n\nFirst, I am not the author of words which follow my name; they are echos\nof subsequent postings. In fact, I didn\'t want to jump into the can of worms\nwhich remains open since the tragic death of Boltzmann..., I just suggested\nthat entropy, randomness, etc. are NOT JUST the results of the observer\nspeculations and modelling, that there are objective measures. Now I will\ncontradict myself a bit, but just a bit.\n\nThe point is that if we believe that the *fundamental*, microscopic theory\nis absolutely exact and deterministic, there is *no* "fundamental" entropy.\nIt is zero, since the probability of all microstates *but one*, the one\nimposed by God and His initial conditions, vanish...\n\nWe can get entropy, if we agree to play along the "thin red line". To make\nfuzzy the initial conditions, to introduce some coarse-graining, some inde-\nterminacy of interactions, whatever...\n\nOr, independently of all that, and not introducing any extra dybbuks, we can\nget something \'statistical\' if we *apply the ergodicity at the CONCEPTUAL\nlevel*. We say: the movement is chaotic (or alike). Sampling the trajectories\nthrough time *with some coarse-graining*, gives us - we believe - the\nstatistical distribution of them in an artificial \'ensemble\' of states. For\ntrue bedlam, we should get the microcanonical ensemble, don\'t we?\n\nIn such a context WE CAN OF COURSE speak of entropy of a completely isolated\nsystem, and it is true that for some crazy initial conditions all the air in\nmy room gets into one corner. It is not necessarily combined with the growth\nof the entropy elsewhere, so the real author of the statement criticized by\nAlistair seems to be - in my eyes - right. But I won\'t bet my head, I am not\neven a physicist...\n\n\nJerzy Karczmarczuk\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>alistair wrote:
>>>Jerzy Karczmarczuk
>>
> to make a transition
>
>>into a state of higher entropy.
>>
>
> evolution can sometimes
>
>>lead to a "less random" (i.e. lower entropy) state! (And yes, this
>>means that the Second Law is violated - but only very very rarely!)
>
>
> But the second law will not
> be violated - the entropy of the surroundings in which the lower
> entropy state was created will increase.The total entropy is what
> counts.
> Entropy cannot be interpreted in terms of isolated systems because
> there is no known system that is isolated in the real world, apart,
> perhaps from the universe itself.
First, I am not the author of words which follow my name; they are echos
of subsequent postings. In fact, I didn't want to jump into the can of worms
which remains open since the tragic death of Boltzmann..., I just suggested
that entropy, randomness, etc. are NOT JUST the results of the observer
speculations and modelling, that there are objective measures. Now I will
contradict myself a bit, but just a bit.
The point is that if we believe that the *fundamental*, microscopic theory
is absolutely exact and deterministic, there is *no* "fundamental" entropy.
It is zero, since the probability of all microstates *but one*, the one
imposed by God and His initial conditions, vanish...
We can get entropy, if we agree to play along the "thin red line". To make
fuzzy the initial conditions, to introduce some coarse-graining, some inde-
terminacy of interactions, whatever...
Or, independently of all that, and not introducing any extra dybbuks, we can
get something 'statistical' if we *apply the ergodicity at the CONCEPTUAL
level*. We say: the movement is chaotic (or alike). Sampling the trajectories
through time *with some coarse-graining*, gives us - we believe - the
statistical distribution of them in an artificial 'ensemble' of states. For
true bedlam, we should get the microcanonical ensemble, don't we?
In such a context WE CAN OF COURSE speak of entropy of a completely isolated
system, and it is true that for some crazy initial conditions all the air in
my room gets into one corner. It is not necessarily combined with the growth
of the entropy elsewhere, so the real author of the statement criticized by
Alistair seems to be - in my eyes - right. But I won't bet my head, I am not
even a physicist...
Jerzy Karczmarczuk
alistair
May25-04, 01:32 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote in message news:<40B1C176.8010108@info.unicaen.fr>...\n....\n \nWe can get entropy, if we agree to play along the "thin red line". To make\nfuzzy the initial conditions, to introduce some coarse-graining, some inde-\nterminacy of interactions, whatever...\n\n\nAlistair writes:\n\nYou can fuzzy the initial conditions as much as you want\nbut you would only be trying to supplant a concept\nthat has solid foundations in the real world.\nTheories in which entropy is used make predictions\nthat are found to agree with experiment.Not one exception\nto the second law of thermodynamics has been found.\nPeople associate the word "disorder" with entropy\nbut the great thing about the concept is that it makes\nthe physical world more understandable and less fuzzy.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote in message news:<40B1C176.8010108@info.unicaen.fr>...
....
We can get entropy, if we agree to play along the "thin red line". To make
fuzzy the initial conditions, to introduce some coarse-graining, some inde-
terminacy of interactions, whatever...
Alistair writes:
You can fuzzy the initial conditions as much as you want
but you would only be trying to supplant a concept
that has solid foundations in the real world.
Theories in which entropy is used make predictions
that are found to agree with experiment.Not one exception
to the second law of thermodynamics has been found.
People associate the word "disorder" with entropy
but the great thing about the concept is that it makes
the physical world more understandable and less fuzzy.
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0405240805.33c7e886@posting.google. com>...\n> Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote in message news:<40B1C176.8010108@info.unicaen.fr>...\n> ...\n>\n> We can get entropy, if we agree to play along the "thin red line". To make\n> fuzzy the initial conditions, to introduce some coarse-graining, some inde-\n> terminacy of interactions, whatever...\n>\n>\n> Alistair writes:\n>\n> You can fuzzy the initial conditions as much as you want\n> but you would only be trying to supplant a concept\n> that has solid foundations in the real world.\n> Theories in which entropy is used make predictions\n> that are found to agree with experiment.Not one exception\n> to the second law of thermodynamics has been found.\n\noh please... It\'s like if you rolled a dice twice, and neither time\ngot a 6, and then invented a so-called law of physics that stated it\nwas impossible to roll a 6. If you rolled a dice 20 times, you would\nget a 6. Similarly, if you waited a googolplex years, you would see\nall the air in the room rush to the corners of the room. The only\nreason "Not one exception to the second law of thermodynamics has been\nfound" is because it\'s such a rare occurance. If you could wait long\nenough you would find such exceptions.\n\n\n\n> People associate the word "disorder" with entropy\n> but the great thing about the concept is that it makes\n> the physical world more understandable and less fuzzy.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0405240805.33c7e886@posting.google.com>...
> Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote in message news:<40B1C176.8010108@info.unicaen.fr>...
> ...
>
> We can get entropy, if we agree to play along the "thin red line". To make
> fuzzy the initial conditions, to introduce some coarse-graining, some inde-
> terminacy of interactions, whatever...
>
>
> Alistair writes:
>
> You can fuzzy the initial conditions as much as you want
> but you would only be trying to supplant a concept
> that has solid foundations in the real world.
> Theories in which entropy is used make predictions
> that are found to agree with experiment.Not one exception
> to the second law of thermodynamics has been found.
oh please... It's like if you rolled a dice twice, and neither time
got a 6, and then invented a so-called law of physics that stated it
was impossible to roll a 6. If you rolled a dice 20 times, you would
get a 6. Similarly, if you waited a googolplex years, you would see
all the air in the room rush to the corners of the room. The only
reason "Not one exception to the second law of thermodynamics has been
found" is because it's such a rare occurance. If you could wait long
enough you would find such exceptions.
> People associate the word "disorder" with entropy
> but the great thing about the concept is that it makes
> the physical world more understandable and less fuzzy.
Thomas Dent
May31-04, 06:26 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nJerzy Karczmarczuk <karczma@info.unicaen.fr> wrote\n\n> alistair wrote:\n\n> > > (Edited for correct author) THOMAS DENT:\n> > evolution can sometimes\n> > lead to a "less random" (i.e. lower entropy) state! (And yes, this\n> > means that the Second Law is violated - but only very very rarely!)\n>\n> First, I am not the author of words which follow my name;\n\nI am!\n\n> The point is that if we believe that the *fundamental*, microscopic theory\n> is absolutely exact and deterministic, there is *no* "fundamental" entropy.\n> It is zero, since the probability of all microstates *but one*, the one\n> imposed by God and His initial conditions, vanish...\n\nAs I said, we can use some other formulation of entropy which does not\ninvolve probabilities, alternative universes, quantum mechanics, etc.\nAlthough it was pointed out that information-theoretic entropy is\nsubject to some ambiguities, I don\'t think it is content-free, even in\na completely deterministic universe.\n\n> We can get entropy, if we agree to play along the "thin red line". To make\n> fuzzy the initial conditions, to introduce some coarse-graining, some inde-\n> terminacy of interactions, whatever...\n\nI don\'t think this is strictly necessary for information-theoretic\nentropy.\n\n> (...)\n> In such a context WE CAN OF COURSE speak of entropy of a completely isolated\n> system, and it is true that for some crazy initial conditions all the air in\n> my room gets into one corner. It is not necessarily combined with the growth\n> of the entropy elsewhere, so the real author of the statement criticized by\n> Alistair seems to be - in my eyes - right. But I won\'t bet my head, I am not\n> even a physicist...\n\nYes, it is quite true, the Second Law as thought of in stat. mech. is\nonly statistically valid, in that it says that transitions to states\nof higher entropy are enormously more likely than transitions to\nstates of lower entropy. The breaking of the naive Second Law "entropy\nincreases in a closed system" is not impossible, only very improbable.\n\nThe Poincare return theorem shows that in a deterministic closed\nsystem the entropy *must* increase significantly at least once in a\ngiven (extremely long) time period.\n\nSince S = k log Omega, and Omega is the number of states involved, it\nis trivial that there are exponentially more states with higher S, and\ngiven ergodicity, an increase of S is exponentially more likely.\n\nThere remains the problem of how to classify states such that an\nin-principle-measurable entropy S can be defined in the first place,\nand as I said, information theory or algorithmic complexity offers one\nmethod to do this.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jerzy Karczmarczuk <karczma@info.unicaen.fr> wrote
> alistair wrote:
> > > (Edited for correct author) THOMAS DENT:
> > evolution can sometimes
> > lead to a "less random" (i.e. lower entropy) state! (And yes, this
> > means that the Second Law is violated - but only very very rarely!)
>
> First, I am not the author of words which follow my name;
I am!
> The point is that if we believe that the *fundamental*, microscopic theory
> is absolutely exact and deterministic, there is *no* "fundamental" entropy.
> It is zero, since the probability of all microstates *but one*, the one
> imposed by God and His initial conditions, vanish...
As I said, we can use some other formulation of entropy which does not
involve probabilities, alternative universes, quantum mechanics, etc.
Although it was pointed out that information-theoretic entropy is
subject to some ambiguities, I don't think it is content-free, even in
a completely deterministic universe.
> We can get entropy, if we agree to play along the "thin red line". To make
> fuzzy the initial conditions, to introduce some coarse-graining, some inde-
> terminacy of interactions, whatever...
I don't think this is strictly necessary for information-theoretic
entropy.
> (...)
> In such a context WE CAN OF COURSE speak of entropy of a completely isolated
> system, and it is true that for some crazy initial conditions all the air in
> my room gets into one corner. It is not necessarily combined with the growth
> of the entropy elsewhere, so the real author of the statement criticized by
> Alistair seems to be - in my eyes - right. But I won't bet my head, I am not
> even a physicist...
Yes, it is quite true, the Second Law as thought of in stat. mech. is
only statistically valid, in that it says that transitions to states
of higher entropy are enormously more likely than transitions to
states of lower entropy. The breaking of the naive Second Law "entropy
increases in a closed system" is not impossible, only very improbable.
The Poincare return theorem shows that in a deterministic closed
system the entropy *must* increase significantly at least once in a
given (extremely long) time period.
Since S = k log \Omega, and \Omega is the number of states involved, it
is trivial that there are exponentially more states with higher S, and
given ergodicity, an increase of S is exponentially more likely.
There remains the problem of how to classify states such that an
in-principle-measurable entropy S can be defined in the first place,
and as I said, information theory or algorithmic complexity offers one
method to do this.
vBulletin® v3.8.7, Copyright ©2000-2012, vBulletin Solutions, Inc.