Gravity as an emergent phenomenon

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Re: Gravity as an emergent phenomenon

Nick Thompson
Yes!  YES!  THANKYOU Grant!!!!!!  I keep forgetting that crucial point. 
 
OK, all you wise guys out there.  What do you say to that?
 
Nick
 
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://www.cusf.org [City University of Santa Fe]
 
 
 
 
----- Original Message -----
Sent: 7/14/2010 7:38:45 AM
Subject: Re: [FRIAM] Gravity as an emergent phenomenon

Verlinde makes the same unfortunate argument that is made by scores of scientists - even noted thermodynamicsists - about so-called "disorder": namely that certain permutations are "disordered", while other permutations are not. To wit:

"Think of the universe as a box of scrabble letters. There is only one way to have the letters arranged to spell out the Gettysburg Address, but an astronomical number of ways to have them spell nonsense. Shake the box and it will tend toward nonsense, disorder will increase and information will be lost as the letters shuffle toward their most probable configurations. Could this be gravity?"

I find this argument specious.

Just because, from an anthropomorphic, English-speaking bias, he finds the Gettysburg address "more ordered" than any other permutation of the same length - it is not. They are all permutation of the same number of letters. Each is as well-defined, and well-ordered, as the other.

Anyway, "order" is an ill-defined, conflated term within the discussion of thermodynamics. It enjoys two distinct usages that get oft-conflated in the conversation regarding entropy. One usage is that it means "disorganization", "absence of arrangement", "dispersed", etc. This is approximately the meaning had originally by R. Clausius. The other usage is that of  "uncertainty" or "unpredictability".  This is the meaning had by Shannon. "Disorganized" and "uncertain" do not mean the same thing. I can prove this because they can vary independently - and, the same phenomenon can exhibit one without the other - the Organized state can sometimes be Uncertain...

In between the meanings of Clausius and Shannon are the meanings of entropy put forth by Boltzmann and Gibbs. Those meanings are often taken to be about "disorganization", but they are actually about "uncertainty". They involve probabilities. So, there is much confusion within statistical thermodynamics about "entropy", because the conversation often assumes that "disorder" is about "disorganization", when it is actually about "unpredictability". Certainly, it is confusing since Clausius was all about "dispersion",  "disorganization", while these other two physicists, Boltzmann and Gibbs, were actually about "uncertainty".

On the other hand, Shannon was not behaving as a physicist, when he "borrowed" the word "entropy" (upon the insistence of von Neumann) for his measure of uncertainty. Indeed, he even "borrowed" most of his formula from Gibbs. However, with his definition of entropy, Gibbs ( and Boltzmann before him) was doing physics - he was describing a specific physical phenomenon.

On the other hand, Shannon was not doing physics. Rather he was doing mathematical statistics. His definition of entropy is a mathematical function whose domain space is probability distributions (to use the term loosely). With Shannon's entropy, any probability distribution now has a "measure of unpredictability". Some PDFs have more unpredictability built into them than others, and he measures it.

Harold Morowitz also makes this point:

[Shannon’s entropy] is a meaningful measure over any probability distribution, while [Gibb’s thermodynamic entropy] has meaning only if the pi are the probabilities of a system being in the ith quantum state when the system is at equilibrium, as rigorously defined for thermodynamics….[Shannon’s entropy] is a measure on a probability distribution; it is not a physical quantity.” [Morowitz 1992]

This is obviously a pet peeve of mine. Welcome any comments!

Grant

Pamela McCorduck wrote:
Great food for thought. Gravity might be no more than an emergent phenomenon:


http://www.nytimes.com/2010/07/13/science/13gravity.html?_r=1&partner=rss&emc=rss





"God keep me from ever completing anything. This whole book is but a draft--nay, but the draft of a draft. Oh, Time, Strength, Cash, and Patience!"

			Melville, "Moby Dick"


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-- 
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Re: Gravity as an emergent phenomenon

glen e. p. ropella-2
In reply to this post by Russell Standish
Russell Standish wrote  circa 07/14/2010 02:09 PM:
> On Tue, Jul 13, 2010 at 10:07:14PM -0600, Roger Critchlow wrote:
>> Working from the context, I'd guess: the tensor product between the
>> components <i>dx<sup>a</sup></i> and <i>dx<sup>b</sup></i>of the stress
>> energy tensor <i>T<sub>ab</sub></i>, but I've never been too sure about
>> tensors.
>>
>
> Not a tensor product, but an exterior product. It's somewhat related to
> a cross product of two 3D vectors.

Thanks for all the answers!  It's interesting to me that this page:

   http://en.wikipedia.org/wiki/Differential_form#Wedge_product

is less understandable to me than this page:

   http://mathworld.wolfram.com/WedgeProduct.html

which is _less_ understandable to me than this page:

   http://en.wikipedia.org/wiki/Exterior_algebra

A usual, each answer is different enough to provide a parallax.  I
always wonder what it would look like to circumscribe my (or anyone's)
knowledge (or, at least, familiarity).  Would the surface of such a
circumscription have a very rough texture?  Or would it be smooth[ish]?
 Would it have great big divots?  Would the "things one knows (of)" even
form a connected set?  Everyone talks about wise people knowing when
they don't know something.  That seems easier said than done.


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Re: Gravity as an emergent phenomenon

lrudolph
In reply to this post by Nick Thompson
Glen Ropella asked:
>What is that ^ symbol between dx^a and dx^b?

Roger Critchlow writes:
> Working from the context, I'd guess: the tensor
>product between the components <i>dx<sup>a</sup></i>
>and <i>dx<sup>b</sup></i>of the stress energy tensor
> <i>T<sub>ab</sub></i>, but I've never been too sure '
>about tensors.

I haven't read the Verlinde paper (and don't intend
to; I find that treating string theoretical physicists
as ignorable crackpots who, alas, have immense institutional
power makes my life much simpler), but my guess about
the "^" symbol is that it's meant to be the "wedge
product" or "exterior product" rather than the general
tensor product--in other words, it's skew-symmetric.
As an example, in old fashioned terms, the tensor
product of two vectors in R3, a = a1x1+a2x2+a3x3
and b = b1x1+b2x2+b3x3, where you can make the indices
of ai and bj be lower and those on x be upper if you
like, is the "dyad" ab = a1b1x1x1+a1b2x1x2+...+a3b3x3x3,
which skew-symmetrizes to a^b = (a1b2-a2b1)x1^x2 +
(a1b3-a3b1)x1^x3 + (a2b3-a3b2)x2^x3 (or maybe, depending
on taste, to that divided by 2 or 3 factorial).  


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Re: Gravity as an emergent phenomenon

Roger Critchlow-2
In reply to this post by Nick Thompson

It doesn't matter, the bell jar serves to isolate the vapors inside from those outside.

-- rec --

On Jul 14, 2010 9:38 AM, "Nicholas Thompson" <[hidden email]> wrote:
> Roger,
>
> Some how that seems less mysterious if you say, seal a beaker of SUGAR and a beaker of water in a bell jar. In time the sugar will become damp. By the way, help me out with the technology, here. Initially, what is the atmosphere in the bell jar composed of?
>
> Nick
>
> Nicholas S. Thompson
> Emeritus Professor of Psychology and Ethology,
> Clark University ([hidden email])
> http://home.earthlink.net/~nickthompson/naturaldesigns/
> http://www.cusf.org [City University of Santa Fe]
>
>
>
>
> ----- Original Message -----
> From: Roger Critchlow
> To: The Friday Morning Applied Complexity Coffee Group
> Sent: 7/14/2010 12:07:45 AM
> Subject: Re: [FRIAM] Gravity as an emergent phenomenon
>
>
> Working from the context, I'd guess: the tensor product between the components <i>dx<sup>a</sup></i> and <i>dx<sup>b</sup></i>of the stress energy tensor <i>T<sub>ab</sub></i>, but I've never been too sure about tensors.
>
>
> I was lost in the introduction.
>
>
> The proposition of entropy causing action at a distance reminded me of a notorious demonstration. A beaker of water and a beaker of sugar dissolved in water are sealed together inside a bell jar. Over time the level of liquid in the beaker of water will drop and the level of liquid in the beaker of sugar water will rise.
>
>
> -- rec --
>
>
> On Tue, Jul 13, 2010 at 7:30 PM, glen e. p. ropella <[hidden email]> wrote:
>
>
> So, Verlinde lost me in section 4. But I usually try to continue reading even if I don't understand (just like I continue talking about stuff I don't understand ;-). And equation 5.35 (attached) had a surprise for me. What is that ^ symbol between dx^a and dx^b?
>
>
> --
> glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com
>
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org


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Re: Gravity as an emergent phenomenon

Tom Carter
In reply to this post by David Eric Smith
I can also recommend Harley Flander's book on Differential Forms ...

tom

On Jul 14, 2010, at 5:53 AM, Eric Smith <[hidden email]> wrote:

> Hi Glen,
>
> I believe it's also called a "wedge product".  Mike Spivak's tiny but frustrating but elegant book Calculus on Manifolds, if I remember correctly, defines these things and explains what they mean in geometric terms.
>
> Eric
>
>
>
>
>
> On Jul 13, 2010, at 7:30 PM, glen e. p. ropella wrote:
>
>>
>> So, Verlinde lost me in section 4.  But I usually try to continue reading even if I don't understand (just like I continue talking about stuff I don't understand ;-).  And equation 5.35 (attached) had a surprise for me.  What is that ^ symbol between dx^a and dx^b?
>>
>> --
>> glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com
>>
>> <eq-5.35.png>============================================================
>> FRIAM Applied Complexity Group listserv
>> Meets Fridays 9a-11:30 at cafe at St. John's College
>> lectures, archives, unsubscribe, maps at http://www.friam.org
>
>
> ============================================================
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> Meets Fridays 9a-11:30 at cafe at St. John's College
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>

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Re: Gravity as an emergent phenomenon

glen e. p. ropella-2
In reply to this post by Grant Holland
Did Verlinde draw the scrabble metaphor?  Or was it just Overbye, the
NYT author?

 From the paper, it's not clear to me that Verlinde was implying that
the straightened out (minimum entropy config?) polymer molecule was
special in any anthropomorphic sense, just that it was special in the
sense of the elastic force.

I have two questions about your distinction between "absence of
arrangement" and "uncertainty".  Isn't all uncertainty evaluated in the
context of a particular conceptual target?  Similarly, wouldn't any
judgment of arrangement or absence thereof be obtained in the context of
a particular conceptual target?  E.g. Bob can estimate his uncertainty
of guessing the arrangement of scrabble chips, as arranged by Joe in
another room.  And that estimation, were Bob rational and if he thought
Joe were rational, would involve some consideration of the physical
characteristics of the scrabble chips (tiled plane vs. tiled line,
characters upside right vs. upside down or sideways, etc.)?

And, if so, then regardless of _which_ particular target configuration
(of polymers or scrabble chips) has the [at|in]tention of the predictor,
we can estimate the uncertainty associated with each configuration based
on its probability of obtaining, including all factors, some purely
physical, some psychological, etc?

These are rhetorical questions; but I wouldn't mind answers to them
anyway because I'm not convinced of my own conclusion that, although
arrangement and uncertainty _can_ be distinguished they are not independent.


Grant Holland wrote circa 10-07-14 04:38 AM:

>   Verlinde makes the same unfortunate argument that is made by scores of
> scientists - even noted thermodynamicsists - about so-called "disorder":
> namely that certain permutations are "disordered", while other
> permutations are not. To wit:
>
> "Think of the universe as a box of scrabble letters. There is only one
> way to have the letters arranged to spell out the Gettysburg Address,
> but an astronomical number of ways to have them spell nonsense. Shake
> the box and it will tend toward nonsense, disorder will increase and
> information will be lost as the letters shuffle toward their most
> probable configurations. Could this be gravity?"
>
> I find this argument specious.
>
> Just because, from an anthropomorphic, English-speaking bias, he finds
> the Gettysburg address "more ordered" than any other permutation of the
> same length - it is not. They are all permutation of the same number of
> letters. Each is as well-defined, and well-ordered, as the other.
>
> Anyway, "order" is an ill-defined, conflated term within the discussion
> of thermodynamics. It enjoys two distinct usages that get oft-conflated
> in the conversation regarding entropy. One usage is that it means
> "disorganization", "absence of arrangement", "dispersed", etc. This is
> approximately the meaning had originally by R. Clausius. The other usage
> is that of "uncertainty" or "unpredictability". This is the meaning had
> by Shannon. "Disorganized" and "uncertain" do not mean the same thing. I
> can prove this because they can vary independently - and, the same
> phenomenon can exhibit one without the other - the Organized state can
> sometimes be Uncertain...
>
> In between the meanings of Clausius and Shannon are the meanings of
> entropy put forth by Boltzmann and Gibbs. Those meanings are often taken
> to be about "disorganization", but they are actually about
> "uncertainty". They involve probabilities. So, there is much confusion
> within statistical thermodynamics about "entropy", because the
> conversation often assumes that "disorder" is about "disorganization",
> when it is actually about "unpredictability". Certainly, it is confusing
> since Clausius was all about "dispersion", "disorganization", while
> these other two physicists, Boltzmann and Gibbs, were actually about
> "uncertainty".
>
> On the other hand, Shannon was not behaving as a physicist, when he
> "borrowed" the word "entropy" (upon the insistence of von Neumann) for
> his measure of uncertainty. Indeed, he even "borrowed" most of his
> formula from Gibbs. However, with his definition of entropy, Gibbs ( and
> Boltzmann before him) was doing physics - he was describing a specific
> physical phenomenon.
>
> On the other hand, Shannon was not doing physics. Rather he was doing
> mathematical statistics. His definition of entropy is a mathematical
> function whose domain space is probability distributions (to use the
> term loosely). With Shannon's entropy, any probability distribution now
> has a "measure of unpredictability". Some PDFs have more
> unpredictability built into them than others, and he measures it.
>
> Harold Morowitz also makes this point:
>
> [Shannon’s entropy] is a meaningful measure over any probability
> distribution, while [Gibb’s thermodynamic entropy] has meaning only if
> the p_i are the probabilities of a system being in the i^th quantum
> state when the system is at equilibrium, as rigorously defined for
> thermodynamics….[Shannon’s entropy] is a measure on a probability
> distribution; it is not a physical quantity.” [Morowitz 1992]
>
> This is obviously a pet peeve of mine. Welcome any comments!
>
> Grant


p.s. Please excuse the top-posting and full quote... I had some trouble
discretizing your post.

--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com


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Re: Gravity as an emergent phenomenon

Merle Lefkoff
In reply to this post by lrudolph
[hidden email] wrote:
> Glen Ropella asked:
>  
>> What is that ^ symbol between dx^a and dx^b?
>>    
>
>  
Merle Lefkoff writes:

I thought a tensor is a description of a multi-dimensional space, like
stress and strain (what I'm going through right now).


> Roger Critchlow writes:
>  
>> Working from the context, I'd guess: the tensor
>> product between the components <i>dx<sup>a</sup></i>
>> and <i>dx<sup>b</sup></i>of the stress energy tensor
>> <i>T<sub>ab</sub></i>, but I've never been too sure '
>> about tensors.
>>    
>
> I haven't read the Verlinde paper (and don't intend
> to; I find that treating string theoretical physicists
> as ignorable crackpots who, alas, have immense institutional
> power makes my life much simpler), but my guess about
> the "^" symbol is that it's meant to be the "wedge
> product" or "exterior product" rather than the general
> tensor product--in other words, it's skew-symmetric.
> As an example, in old fashioned terms, the tensor
> product of two vectors in R3, a = a1x1+a2x2+a3x3
> and b = b1x1+b2x2+b3x3, where you can make the indices
> of ai and bj be lower and those on x be upper if you
> like, is the "dyad" ab = a1b1x1x1+a1b2x1x2+...+a3b3x3x3,
> which skew-symmetrizes to a^b = (a1b2-a2b1)x1^x2 +
> (a1b3-a3b1)x1^x3 + (a2b3-a3b2)x2^x3 (or maybe, depending
> on taste, to that divided by 2 or 3 factorial).  
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>
>  


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Re: Gravity as an emergent phenomenon

Vladimyr Burachynsky
In reply to this post by Russ Abbott

Russ,

 

I am just catching up on this but first the analogy to gas distribution is not accurate, or at least I question it from my work in solid state diffusion i.e alloys etc.

 

There is a dynamic that ultimate results in lower energy states  Interacting atoms seem to adopt a kind of  neighborliness. They try and balance their energy state to accommodate the neighbor, of course this is not perfect. Since the energy levels are structurally different. For mixtures of similar species my impression is that they just wander about randomly trying to avoid getting excited.  This tendency to go low results in the diffused state. Or crystalline system??? Emergence again Perhaps??

 

Now I can see diffusion as an emergent behavior directly resulting from atoms preferring lower excitement states. But the connection to gravity eludes me. AS it seems to be counter entropic.

 

Just from a quick reading I was surprised how I thought diffusion was being misunderstood and yet now I am thinking that diffusion may be more likely emergent than the previous link to gravity. How curious.  When I was working on the diffusion issue I adopted an approach where dissimilar species were forced to be neighbours and I ran loops for each species trying to adapt to the other and see if there was a stable point between them when they were “Happy” with eachother. I was in hind sight trying to treat each atom as an autonomous agent In a sense without ever having heard the concept.  My assumption was that they were only able to adjust electrons but that was very simplistic. The atomic diameter of an atom can change radically depending on how much energy is involved in the electron distributing pattern. Roughly more electrons, smaller diameter and higher energy states. Dumping photons lowers the energy state. Too bad I wrote this stuff so long ago. I almost forgot that in the misty past. So in brief the atoms are struggling to accommodate eachother and constantly altering their diameter and that seems to push them away from eachother hence the emergence of diffusion.

 

Turns out that there are other mechanics involved. But curious how Emergence shows up in unexpected places. I will read the mail and try and figure out a more refined response.

 

 

Vladimyr Ivan Burachynsky

Ph.D.(Civil Eng.), M.Sc.(Mech.Eng.), M.Sc.(Biology)

 

120-1053 Beaverhill Blvd.

Winnipeg, Manitoba

CANADA R2J 3R2 

(204) 2548321  Phone/Fax

[hidden email] 

 

 

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of Russ Abbott
Sent: July 13, 2010 1:01 PM
To: [hidden email]; The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Gravity as an emergent phenomenon

 

I always find myself confused about how to think about entropy. The article says that gravity is an entropic force. I understand that to mean that it not reducible to lower level forces but to be reducible (if that term applies) to statistical thermodynamics. 

Just as there are a lot more ways that a gas can be more or less uniformly distributed in a closed area than the ways it could be bunched up in a corner -- and hence we tend to find it more or less uniformly distributed -- gravity according to this analysis is like the universe in a more uniformly distributed state rather than a more unusual state.

There is no force that causes it. It is a statistical phenomenon. In other words, gravitational attraction is like whatever it is that pushes a gas bunched up in a corner to become more uniformly distributed.  But the whatever-it-is in the case of a gas is nothing but statistical phenomena. There are no forces involved even though from a naive point of view it may appear that there is a force that is pushing the gas to be spread out.


-- Russ


On Tue, Jul 13, 2010 at 10:36 AM, Nicholas Thompson <[hidden email]> wrote:

Pamela,

I got all ready to be huffy about the article, but then found it really
interesting.  At risk of going all professorial on you, I want to examine
your expression, "no more than a".   The most important phenomena that we
experience are all emergents.  If you hit me with a rock, the hardness  and
edginess of the rock that collapses my skull, are all emergents.

So, then what the dickens is meant by "no more than"?  I think it means
SOMETHING and would like to explore it further with you (and others on the
list.)  "Reduction" means to some to account for a phenomenon n terms of
events or objects that are smaller than the phenomenon itself.  Reduction
is always to break a process or an object into its parts.  To others,
"reduction" means to explain a phenomenon by reference to a more familiar
or well understood phenomenon.  This latter understanding of reduction
opens the possibility for a reduction to refer to a process that is larger
or more inclusive than the process it reduces, what I would call an
up-reduction, to distinguish it from the "breaking-into-parts" sort of
reduction.  It sounds to me that the account of gravity being offered in
this article is a case of up reduction in that sense.

I hope others will read the article and comment, because i wasnt sure I
understood it.

All the best,

Nick



Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]




> [Original Message]
> From: Pamela McCorduck <[hidden email]>
> To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
> Date: 7/13/2010 12:39:41 PM
> Subject: [FRIAM] Gravity as an emergent phenomenon

>
> Great food for thought. Gravity might be no more than an emergent
phenomenon:
>
>
>
http://www.nytimes.com/2010/07/13/science/13gravity.html?_r=1&partner=rss&em
c=rss

>
>
>
>
>
> "God keep me from ever completing anything. This whole book is but a
draft--nay, but the draft of a draft. Oh, Time, Strength, Cash, and
Patience!"
>
>                       Melville, "Moby Dick"
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org



============================================================
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entropic force (was Gravity as an emergent phenomenon)

glen e. p. ropella-2
In reply to this post by Roger Critchlow-2
Roger Critchlow wrote circa 10-07-13 09:07 PM:
> The proposition of entropy causing action at a distance reminded me of a
> notorious demonstration.  A beaker of water and a beaker of sugar
> dissolved in water are sealed together inside a bell jar.  Over time the
> level of liquid in the beaker of water will drop and the level of liquid
> in the beaker of sugar water will rise.

For better or worse, I can't stop thinking about this concept that
gravity is an entropic force... perhaps especially because I'm lacking a
good (any?) understanding of the physics and math.

It seems to me that entropic forces can be described as the tendency of
systems to move toward, stay in, and return to densely populated regions
of configuration space.  I.e. if there's a (small/sparse set of)
configuration(s) that's isolated (in some sense) from larger, denser
sets of configurations, then saying "entropic force" is just a term
expressing that the system is more likely to be found in and move toward
those larger, denser sets.

And then if gravity were such an entropic force, I would be forced to
think that, somehow, the close proximity of any two bits (pun intended)
of matter allows more configurations than if those two bits are far
apart.  That would be why gravity is attractive.  There are more ways
for the bits to interact if they're closer together.

I'm not sure why, but this seems counter intuitive to me.  I just
naively assumed that it doesn't matter how far apart two bits of matter
are, the measure of the configurations of the system they constitute is
constant.... like two entangled photons at opposite sides of the universe.

I suppose my fundamental confusion could be caused by the unnaturalness
of cosmic time scales, quantum entanglement, and action at a distance.
But it seems inverted for me.  I suppose having worked in simulation for
so long has brainwashed me.  E.g. parallelism can be simulated by
serialism, time can be compressed to make slow interactions equivalent
to fast interactions, occluded interactions can be ignored as long as
there are no side effects of the hidden events, etc.  I suppose I've
come to think that the universe really does submit/adhere to the
closures we stamp onto various sub-systems (holons).  But if that were
the case, then gravity as an entropic force would not make sense because
the configuration space has a constant size no matter how close any bits
of matter are.

So my question to y'all is: Am I interpreting "entropic force"
correctly?  What have I misunderstood?

--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com


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Re: entropic force (was Gravity as an emergent phenomenon)

Nick Thompson
Glen,  

You and Grant are starting to make my poor=old rejected  english major's
brain spin:  I think I have finally seen the point of this whole discussion
about gravity.  Let it be the case that everything in the universe is in
one spot .... that is low entropy right?  And we all agree that the world
tends to high entropy.  So, what's with this gravity thing, which will,
eventually, if allowed to play out, bring everything together in a single
lump.

Nick  

Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]




> [Original Message]
> From: glen e. p. ropella <[hidden email]>
> To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
> Date: 7/16/2010 12:34:15 PM
> Subject: [FRIAM] entropic force (was Gravity as an emergent phenomenon)
>
> Roger Critchlow wrote circa 10-07-13 09:07 PM:
> > The proposition of entropy causing action at a distance reminded me of a
> > notorious demonstration.  A beaker of water and a beaker of sugar
> > dissolved in water are sealed together inside a bell jar.  Over time the
> > level of liquid in the beaker of water will drop and the level of liquid
> > in the beaker of sugar water will rise.
>
> For better or worse, I can't stop thinking about this concept that
> gravity is an entropic force... perhaps especially because I'm lacking a
> good (any?) understanding of the physics and math.
>
> It seems to me that entropic forces can be described as the tendency of
> systems to move toward, stay in, and return to densely populated regions
> of configuration space.  I.e. if there's a (small/sparse set of)
> configuration(s) that's isolated (in some sense) from larger, denser
> sets of configurations, then saying "entropic force" is just a term
> expressing that the system is more likely to be found in and move toward
> those larger, denser sets.
>
> And then if gravity were such an entropic force, I would be forced to
> think that, somehow, the close proximity of any two bits (pun intended)
> of matter allows more configurations than if those two bits are far
> apart.  That would be why gravity is attractive.  There are more ways
> for the bits to interact if they're closer together.
>
> I'm not sure why, but this seems counter intuitive to me.  I just
> naively assumed that it doesn't matter how far apart two bits of matter
> are, the measure of the configurations of the system they constitute is
> constant.... like two entangled photons at opposite sides of the universe.
>
> I suppose my fundamental confusion could be caused by the unnaturalness
> of cosmic time scales, quantum entanglement, and action at a distance.
> But it seems inverted for me.  I suppose having worked in simulation for
> so long has brainwashed me.  E.g. parallelism can be simulated by
> serialism, time can be compressed to make slow interactions equivalent
> to fast interactions, occluded interactions can be ignored as long as
> there are no side effects of the hidden events, etc.  I suppose I've
> come to think that the universe really does submit/adhere to the
> closures we stamp onto various sub-systems (holons).  But if that were
> the case, then gravity as an entropic force would not make sense because
> the configuration space has a constant size no matter how close any bits
> of matter are.
>
> So my question to y'all is: Am I interpreting "entropic force"
> correctly?  What have I misunderstood?
>
> --
> glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org



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Re: entropic force (was Gravity as an emergent phenomenon)

Vladimyr Burachynsky
Nick Glen Grant,

Another confused old guy, But there was something called Planck's Distance
that said that two atoms could not get any closer under normal circumstances
without enormous forces yet Bose condensates are literally superimposed
indistinguishable atoms albeit identical. From my meager metallurgy days.

So there seems to be some kind of stand off between the two.
Lets really bend the rules here and speculate that all that we have defined
is a figment of our biological failures. We are always making assumptions
that we can think, when we might just be spinning old neurons that make us
feel good about ourselves. Kind of like a little too much beer and the girls
start looking better and better as the night proceeds. With Much regret in
the mornings. Perhaps our intelligence is much less than claimed and not
even an emergent phenomenon at all. While everything else is.

I don't like where this is leading... I have had enough trouble
understanding economic theorems now this tsunami of an idea spooks me. I
guess it is like Freeman Dyson's one electron universe. It can be everywhere
and everywhen to satisfy infinite expectations.

 
 
Vladimyr Ivan Burachynsky
Ph.D.(Civil Eng.), M.Sc.(Mech.Eng.), M.Sc.(Biology)
 
120-1053 Beaverhill Blvd.
Winnipeg, Manitoba
CANADA R2J 3R2
(204) 2548321  Phone/Fax
[hidden email]
 
 

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf
Of Nicholas Thompson
Sent: July 16, 2010 4:00 PM
To: [hidden email]
Subject: Re: [FRIAM] entropic force (was Gravity as an emergent phenomenon)

Glen,  

You and Grant are starting to make my poor=old rejected  english major's
brain spin:  I think I have finally seen the point of this whole discussion
about gravity.  Let it be the case that everything in the universe is in
one spot .... that is low entropy right?  And we all agree that the world
tends to high entropy.  So, what's with this gravity thing, which will,
eventually, if allowed to play out, bring everything together in a single
lump.

Nick  

Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]




> [Original Message]
> From: glen e. p. ropella <[hidden email]>
> To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
> Date: 7/16/2010 12:34:15 PM
> Subject: [FRIAM] entropic force (was Gravity as an emergent phenomenon)
>
> Roger Critchlow wrote circa 10-07-13 09:07 PM:
> > The proposition of entropy causing action at a distance reminded me of a
> > notorious demonstration.  A beaker of water and a beaker of sugar
> > dissolved in water are sealed together inside a bell jar.  Over time the
> > level of liquid in the beaker of water will drop and the level of liquid
> > in the beaker of sugar water will rise.
>
> For better or worse, I can't stop thinking about this concept that
> gravity is an entropic force... perhaps especially because I'm lacking a
> good (any?) understanding of the physics and math.
>
> It seems to me that entropic forces can be described as the tendency of
> systems to move toward, stay in, and return to densely populated regions
> of configuration space.  I.e. if there's a (small/sparse set of)
> configuration(s) that's isolated (in some sense) from larger, denser
> sets of configurations, then saying "entropic force" is just a term
> expressing that the system is more likely to be found in and move toward
> those larger, denser sets.
>
> And then if gravity were such an entropic force, I would be forced to
> think that, somehow, the close proximity of any two bits (pun intended)
> of matter allows more configurations than if those two bits are far
> apart.  That would be why gravity is attractive.  There are more ways
> for the bits to interact if they're closer together.
>
> I'm not sure why, but this seems counter intuitive to me.  I just
> naively assumed that it doesn't matter how far apart two bits of matter
> are, the measure of the configurations of the system they constitute is
> constant.... like two entangled photons at opposite sides of the universe.
>
> I suppose my fundamental confusion could be caused by the unnaturalness
> of cosmic time scales, quantum entanglement, and action at a distance.
> But it seems inverted for me.  I suppose having worked in simulation for
> so long has brainwashed me.  E.g. parallelism can be simulated by
> serialism, time can be compressed to make slow interactions equivalent
> to fast interactions, occluded interactions can be ignored as long as
> there are no side effects of the hidden events, etc.  I suppose I've
> come to think that the universe really does submit/adhere to the
> closures we stamp onto various sub-systems (holons).  But if that were
> the case, then gravity as an entropic force would not make sense because
> the configuration space has a constant size no matter how close any bits
> of matter are.
>
> So my question to y'all is: Am I interpreting "entropic force"
> correctly?  What have I misunderstood?
>
> --
> glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org



============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org


============================================================
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Re: entropic force (was Gravity as an emergent phenomenon)

glen e. p. ropella-2
Vladimyr Ivan Burachynsky wrote circa 10-07-16 06:53 PM:
> Another confused old guy, But there was something called Planck's Distance
> that said that two atoms could not get any closer under normal circumstances
> without enormous forces yet Bose condensates are literally superimposed
> indistinguishable atoms albeit identical. From my meager metallurgy days.
>
> So there seems to be some kind of stand off between the two.

Right.  I think the admission of an "entropic force" (distinct from the
non-causal measurement problem pointed out by Russ in the other thread)
as a force says something about the _agility_, instability, or
sensitivity to perturbation of the system being studied.

A completely "disordered" heat death (I assume) is a completely stable,
robust equilibrium.  So, although we'd say it has maximum entropy, it's
actually quite orderly, as it were.

On the other hand, as Nick put it, all the matter in the universe lumped
into a singularity, which (again, I assume) would mean minimum entropy,
is also quite orderly.

So, I suppose it's important to remember that entropy is _purely_ a
relative term... a way of relating one system to another (or two systems
to the third they become when mixed).  If there's only a single system,
then the term "entropy" is meaningless.

If all this rhetoric flows well, then an entropic force is a statement
about the difference between the degrees of freedom (wiggle room)
between two sets of configurations, _assuming_ some/any microscopic
force doing the wiggling (brownian motion, heat, diffusion,
particle-mediated fields, ... whatever).  In particular, it shows up
when the space of configurations is not totally well-mixed.  I.e. when
some regions of the configuration space have lots of well-connected
"points" and other regions are isolated in whatever sense that matters
to the hypothetical/unspecified microscopic force.

This would all make the conclusion that black holes are _not_
singularities perfectly reasonable.  The death of a black hole would
just be the system walking that rare/difficult path away from the
well-connected region of configuration space out to the ill-connected
region of the configuration space of normal space-time.  That rare path
could happen by a vanishingly rare chance (assuming the
hypothetical/unspecified microscopic force is stochastic at all) or due
to a bias in the microscopic force that makes the path more likely (e.g.
more heat, more mass, more energy, whatever).

All this would mean is that a mostly ill-connected universe, sparsely
populated by (dynamically evolving) gravity wells keeps the universe in
a dynamic equilibrium somewhere between heat death (chaos) and one big
lump of condensate (order).  (Sorry... I've been brainwashed by Langton. ;-)

> Lets really bend the rules here and speculate that all that we have defined
> is a figment of our biological failures. We are always making assumptions
> that we can think, when we might just be spinning old neurons that make us
> feel good about ourselves. Kind of like a little too much beer and the girls
> start looking better and better as the night proceeds. With Much regret in
> the mornings. Perhaps our intelligence is much less than claimed and not
> even an emergent phenomenon at all. While everything else is.

Heh, all I can say to that is "So what?"  ;-)  I already _know_ that all
my thoughts are flawed and, likely, mere self-gratification.  And, being
the self-centered bastard that I am, I tend to think that other people
are like me and that all their thoughts are flawed and, likely, just
their own self-gratification.  (That's why the myth of the free market
is so attractive to me.)

But you can choose to play the particular game.  Or you can choose to
hang out on the balcony smoking cigars with the misfits while others
play the game at the kitchen table.  I'm just making a small attempt to
play the game... or perhaps learn enough about the game to know I
wouldn't have any fun playing it.  When I get tired, bored, or lazy,
I'll quit.

--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com


============================================================
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Re: entropic force (was Gravity as an emergent phenomenon)

Russ Abbott
Under the information-based view of entropy a heat death universe would have high entropy because it would take a large amount of information--a great many bits--to capture it.  One would have to say where each bit of material is. Since each bit is more or less randomly located, there is no way to compress that information. On the other hand, if all matter were compressed into a single point, it would take very little--very few bits--to record that state of the universe.

-- Russ



On Mon, Jul 19, 2010 at 3:41 PM, glen e. p. ropella <[hidden email]> wrote:
Vladimyr Ivan Burachynsky wrote circa 10-07-16 06:53 PM:
Another confused old guy, But there was something called Planck's Distance
that said that two atoms could not get any closer under normal circumstances
without enormous forces yet Bose condensates are literally superimposed
indistinguishable atoms albeit identical. From my meager metallurgy days.

So there seems to be some kind of stand off between the two.

Right.  I think the admission of an "entropic force" (distinct from the non-causal measurement problem pointed out by Russ in the other thread) as a force says something about the _agility_, instability, or sensitivity to perturbation of the system being studied.

A completely "disordered" heat death (I assume) is a completely stable, robust equilibrium.  So, although we'd say it has maximum entropy, it's actually quite orderly, as it were.

On the other hand, as Nick put it, all the matter in the universe lumped into a singularity, which (again, I assume) would mean minimum entropy, is also quite orderly.

So, I suppose it's important to remember that entropy is _purely_ a relative term... a way of relating one system to another (or two systems to the third they become when mixed).  If there's only a single system, then the term "entropy" is meaningless.

If all this rhetoric flows well, then an entropic force is a statement about the difference between the degrees of freedom (wiggle room) between two sets of configurations, _assuming_ some/any microscopic force doing the wiggling (brownian motion, heat, diffusion, particle-mediated fields, ... whatever).  In particular, it shows up when the space of configurations is not totally well-mixed.  I.e. when some regions of the configuration space have lots of well-connected "points" and other regions are isolated in whatever sense that matters to the hypothetical/unspecified microscopic force.

This would all make the conclusion that black holes are _not_ singularities perfectly reasonable.  The death of a black hole would just be the system walking that rare/difficult path away from the well-connected region of configuration space out to the ill-connected region of the configuration space of normal space-time.  That rare path could happen by a vanishingly rare chance (assuming the hypothetical/unspecified microscopic force is stochastic at all) or due to a bias in the microscopic force that makes the path more likely (e.g. more heat, more mass, more energy, whatever).

All this would mean is that a mostly ill-connected universe, sparsely populated by (dynamically evolving) gravity wells keeps the universe in a dynamic equilibrium somewhere between heat death (chaos) and one big lump of condensate (order).  (Sorry... I've been brainwashed by Langton. ;-)

Lets really bend the rules here and speculate that all that we have defined
is a figment of our biological failures. We are always making assumptions
that we can think, when we might just be spinning old neurons that make us
feel good about ourselves. Kind of like a little too much beer and the girls
start looking better and better as the night proceeds. With Much regret in
the mornings. Perhaps our intelligence is much less than claimed and not
even an emergent phenomenon at all. While everything else is.

Heh, all I can say to that is "So what?"  ;-)  I already _know_ that all my thoughts are flawed and, likely, mere self-gratification.  And, being the self-centered bastard that I am, I tend to think that other people are like me and that all their thoughts are flawed and, likely, just their own self-gratification.  (That's why the myth of the free market is so attractive to me.)

But you can choose to play the particular game.  Or you can choose to hang out on the balcony smoking cigars with the misfits while others play the game at the kitchen table.  I'm just making a small attempt to play the game... or perhaps learn enough about the game to know I wouldn't have any fun playing it.  When I get tired, bored, or lazy, I'll quit.

--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com


============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org


============================================================
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Re: entropic force (was Gravity as an emergent phenomenon)

glen e. p. ropella-2
Russ Abbott wrote circa 10-07-19 03:54 PM:
>   Under the information-based view of entropy a heat death universe
> would have high entropy because it would take a large amount of
> information--a great many bits--to capture it.  One would have to say
> where each bit of material is. Since each bit is more or less randomly
> located, there is no way to compress that information. On the other
> hand, if all matter were compressed into a single point, it would take
> very little--very few bits--to record that state of the universe.

You seem to be repeating things I just said. ;-)

But that's not the interesting part of what I said.  The interesting
part is that no work can be done in either case.  In fact, neither end
of the spectrum is interesting at all.  Interestingness lies between
heat death and singularity.

A further interesting thing (perhaps only to my self-gratifying
thoughts) is that the maximal entropy heat death actually _can_ be
described with very little information.  All it takes is a uniform RNG
distribution.  I can write that program in... 5 minutes! ;-)

Seriously though, it all depends on what layer, stance, or aspect taken
by the observer.  And if the universe is in a state of heat death, there
is no observer.  So, again, the concept of "entropy" becomes meaningless
in heat death.  Entropy is only meaningful in between the heat death and
the singularity.  I.e. it's only a relative term.  It's degenerate in
any absolute/universal context.

--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com


============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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Re: entropic force (was Gravity as an emergent phenomenon)

Russ Abbott
On Mon, Jul 19, 2010 at 4:13 PM, glen e. p. ropella <[hidden email]> wrote:
A further interesting thing (perhaps only to my self-gratifying thoughts) is that the maximal entropy heat death actually _can_ be described with very little information.  All it takes is a uniform RNG distribution.  I can write that program in... 5 minutes! ;-)

I guess that's a joke. But to be overly literal minded, one random distribution of elements is not the same as another random distribution any more than one string of random digits is the same as another string of random digits--unless of course they just happen to be identical. Of course they have a lot of properties in common, but one might just happen to be the first n digits of pi, whereas the other might not be.

Seriously though, it all depends on what layer, stance, or aspect taken by the observer.  And if the universe is in a state of heat death, there is no observer.

As I said, I struggle with the notion of entropy, but as I understand it no observer is needed. I think it's well defined in both the information and thermodynamics senses without relying on an observer.  Why do you say it relies on an observer?

-- Russ




On Mon, Jul 19, 2010 at 4:13 PM, glen e. p. ropella <[hidden email]> wrote:
Russ Abbott wrote circa 10-07-19 03:54 PM:

 Under the information-based view of entropy a heat death universe
would have high entropy because it would take a large amount of
information--a great many bits--to capture it.  One would have to say
where each bit of material is. Since each bit is more or less randomly
located, there is no way to compress that information. On the other
hand, if all matter were compressed into a single point, it would take
very little--very few bits--to record that state of the universe.

You seem to be repeating things I just said. ;-)

But that's not the interesting part of what I said.  The interesting part is that no work can be done in either case.  In fact, neither end of the spectrum is interesting at all.  Interestingness lies between heat death and singularity.

A further interesting thing (perhaps only to my self-gratifying thoughts) is that the maximal entropy heat death actually _can_ be described with very little information.  All it takes is a uniform RNG distribution.  I can write that program in... 5 minutes! ;-)

Seriously though, it all depends on what layer, stance, or aspect taken by the observer.  And if the universe is in a state of heat death, there is no observer.  So, again, the concept of "entropy" becomes meaningless in heat death.  Entropy is only meaningful in between the heat death and the singularity.  I.e. it's only a relative term.  It's degenerate in any absolute/universal context.


--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com


============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org


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Re: entropic force (was Gravity as an emergent phenomenon)

glen e. p. ropella-2
Russ Abbott wrote  circa 07/19/2010 05:06 PM:

> On Mon, Jul 19, 2010 at 4:13 PM, glen e. p. ropella
> <[hidden email] <mailto:[hidden email]>>
> wrote:
>
> I guess that's a joke. But to be overly literal minded, one random
> distribution of elements is not the same as another random distribution
> any more than one string of random digits is the same as another string
> of random digits--unless of course they just happen to be identical. Of
> course they have a lot of properties in common, but one might just
> happen to be the first n digits of pi, whereas the other might not be.

Yeah, sorry.  I never learned to tell jokes.  Yes, I agree that it's not
as simple as a distribution of an RNG.  It would have to be a real RNG,
anyway, I suspect.  And that would imply more than 1 system: the one
being described and the one generating the random numbers for the
description.  But my underlying point still stands: that when
characterizing a physical system (with concepts like entropy and
thermodynamics as a whole), one has to choose the layers or aspects they
want to pay attention to.  If the characterization is intended to
capture the details of every particular element (boson, lepton, virtual
particle pair, etc. in its position, velocity, spin, etc.), then the
description _would_ be as large as the universe, itself.  There could be
no abstraction in such a characterization, making it useless as a model.

>> Seriously though, it all depends on what layer, stance, or aspect taken
>> by the observer.  And if the universe is in a state of heat death, there
>> is no observer.
>
> As I said, I struggle with the notion of entropy, but as I understand it
> no observer is needed. I think it's well defined in both the information
> and thermodynamics senses without relying on an observer.  Why do you
> say it relies on an observer?

Well, I'm using a rather naive definition of entropy that depends on
there being 2 systems to compare.  The total entropy of one (closed)
system is only useful when comparing it to another (closed) system,
distinct in any variable like space or time.  When talking about an
increase in entropy for a single system, we compare the system at time
t_0 to that same system at time t_1.  Even in that case, entropy is a
measure applied to 2 different systems.  We often choose to call it the
same system and refer to it as changing state; but in practice, it's the
same measure used to compare 2 separate systems (non-causally derived
from measures of heat and causally derived from measures of the states
of its constituents).

The observer is necessary to do the measuring.  If the observer is
_inside_ the system, then that results in an infinite regress.  So, an
observer measuring the entropy of the universe from inside can, at best,
approximate (or show a bound for) the total entropy.  And the only point
in placing the whole universe in that metric space (the entropy
quantity) is to compare it to other systems, subsets of itself or the
whole universe at different times.

--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com


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Re: entropic force (was Gravity as an emergent phenomenon)

Russ Abbott
Please see below.

-- Russ

 
But my underlying point still stands: that when
characterizing a physical system (with concepts like entropy and
thermodynamics as a whole), one has to choose the layers or aspects they
want to pay attention to.  If the characterization is intended to
capture the details of every particular element (boson, lepton, virtual
particle pair, etc. in its position, velocity, spin, etc.), then the
description _would_ be as large as the universe, itself.  There could be
no abstraction in such a characterization, making it useless as a model.

If all the particles were arrayed in a regular lattice, the description could be smaller than the universe itself. I thought that was the point of entropy.
 
When talking about an
increase in entropy for a single system, we compare the system at time
t_0 to that same system at time t_1.  Even in that case, entropy is a
measure applied to 2 different systems.  We often choose to call it the
same system and refer to it as changing state; but in practice, it's the
same measure used to compare 2 separate systems (non-causally derived
from measures of heat and causally derived from measures of the states
of its constituents).

The observer is necessary to do the measuring.  If the observer is
_inside_ the system, then that results in an infinite regress.  So, an
observer measuring the entropy of the universe from inside can, at best,
approximate (or show a bound for) the total entropy.  And the only point
in placing the whole universe in that metric space (the entropy
quantity) is to compare it to other systems, subsets of itself or the
whole universe at different times.

Whether it's one system or two, a messy arrangement takes more work to describe than a neat one. This is a perspective from outside the system, but it would seem to be a perspective in which entropy makes sense without having to say anything special about an observer.  Of course whenever we say anything about anything there is an implied observer, but we don't complain about that in other contexts.
 


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Re: entropic force (was Gravity as an emergent phenomenon)

glen e. p. ropella-2
Russ Abbott wrote  circa 07/20/2010 09:55 PM:
> If all the particles were arrayed in a regular lattice, the description
> could be smaller than the universe itself. I thought that was the point
> of entropy.

Perhaps you're right.  But that is also counter-intuitive to me.  If
entropy really is a measure of "disorder" in any sense, then it's hard
for me to imagine a maximal entropy state as describing a completely
smooth landscape where every element sits on a point in a regular lattice.

But physically, entropy is about the ability to do work.  So, it seems
to me that our understanding of the concept of "heat death" needs a
little more emphasis on "heat", which describes the vibration of
particles and says nothing about any microscopic patterns.  A heat death
doesn't describe particles laid out on a regular lattice.  It's about
not being able to _use_ any of the microscopic activity, whether you
know what that activity is (data about the degrees of freedom for every
particle) or not.

Still, a shortest description of it can be made by uniform RNGs over all
the potential degrees of freedom for elements spread more or less
evenly, though not necessarily _totally_ ... omnisciently, god-like,
regular lattice evenly, through the universe.  In order to get that
short description, though, you have to abstract yourself from the
microscopic detail.  The RNG distribution demarcates the ontological
wall, behind which we're completely ignorant (e.g. "heat").  A fully
concrete, non-abstract model would be the same "size" as the universe
itself, even in heat death.

>  This is a perspective from outside the system,
> but it would seem to be a perspective in which entropy makes sense
> without having to say anything special about an observer.  Of course
> whenever we say anything about anything there is an implied observer,
> but we don't complain about that in other contexts.

I don't see how it's possible to talk about a perspective from outside
the system without talking about an observer, even if that observer is
just another, separate, system.  That was the whole point.  Entropy only
seems like a coherent concept in the context of 2 or more systems,
making either extreme (heat death of the universe or all matter inside a
singularity) degenerate cases.

--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com


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