symmetry breaking

[Nick Thompson]

In an offline conversation about my “open letter”, somebody asked me what symmetry breaking was; Here was my answer.  

 

Symmetry breaking is Guerin/Kaufman talk.  Something like this: Just before Benard cells form, the fluid is symmetrical horizontally (Kaufman/Guerin talk for “uniform”), although there is a gradient of warmth from low to high.  When the gradient reaches a certain intensity, the Benard cell structure is formed and that horizontal uniformity is replaced by upward and downward moving columns of liquid.  The original uniformity (aka symmetry) is broken and (on Steve’s account) energy now moves faster from the warm plate at the bottom to the cold plate at the top because of that symmetry breaking.  I hope I have this right. 

 

Since nobody is answering my question about sink vortices being a case of an anti-dissipative structure, let me attempt my own answer.

 

Nick, you old goose.  You are really confused.  It’s an energy gradient that is being defused, not a water gradient.  The very inefficiency of the sink vortex for moving water is what makes it into an efficient dissipative structure. 

 

n

 

 

 

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

http://www.cusf.org

 

 

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[David Eric Smith]

Nick, hi,

This time I really, really am under the gun and have no business
answering.  But you are not being foolish.  You are pushing correctly
on a set of statements that are not a principle.  As Steve and Peter
and others have said, the only way to properly handle this is actually
to work out a full solution, and then figure out what global
properties the particular solution is expressing, and I haven't done
that, so I can't provide anything that counts as an adequate answer.
But a couple of points that I think are relevant.

The intuition you are pushing:  Water up high has gravitational
potential energy.  That by itself doesn't get turned into heat, so it
doesn't directly dissipate.  If the water can fall, the potential can
be converted to kinetic energy, and from there, various frictional
effects can indeed convert the bulk-motion of the water to thermal
motion.  This is why you would be looking for phenomena that both
speed the rate of fall, but then afterward also speed the slowing of
average motion through frictions to disorderly motion.  Internal
turbulence etc. are all good pathways through which that can happen.

On use of dissipation:  I think that, to the extent that it ever means
anything in these conversations, "dissipation" means the conversion of
energy from a mechanical form into a thermal form that goes into the
entropy.  I will say in a moment why that usage in most conversations
from Schroedinger and Brillouin onward, through Prigogine, are not
reliable.  But at least that statement is precise enough that it can
be falsified.  And sometimes it is okay; it's just that those
sometimes are case-dependent.

On other factors such as constraints:  Yes, all the conversation about
stirring has to do with the role of angular momentum, as well as
potential energy, as a constraint on the configurations available to
the system, and to the processes through which they can dissipate or
do anything else.  Any relaxation process, however described, will be
constrained by whatever factors are put into its initial conditions,
so inequivalent initial conditions need not lead to directly
comparable downstream phenomena.  Angular momentum that you put in by
initial stirring must be transferred to the sink or the air, before
the fluid can slow enough to reach the drain, and that takes time,
because the transfer of angular momentum is mediated by boundary-layer
dynamics, sink-shape effects, etc., just like everything else.

On the reason the standard use of "dissipation" doesn't get you to
principles:  When people say "the entropy", they usually mean the
function which -- IN AN EQUILIBRIUM ENSEMBLE -- would be the proper
measure of uncertainty or distribution of energy among degrees of
freedom.  All these flow problems that we talk about are not described
by equilibrium ensembles; they are ensembles of processes.  Of course,
everybody says that, but apparently most of the time people don't act
as if saying that should then carry meaning for what they think
afterward.  (Like other mantras, its function appears to be to
suppress pre-frontal cortex activity.)  A processes with states and
flows has more that you can know about it than a process with the same
states but without flows.  This means that its uncertainty or
distribution are more constrained -- because they are constrained by
additional quantities -- than the equilibrium counterparts.
Therefore, the function that is the entropy for an equilibrium
ensemble will no longer generally be the correct measure of
uncertainty or distribution for an ensemble of processes.  The CONCEPT
of entropy is still fine, and even the Shannon/Boltzmann definition in
terms of probabilities can still be fine.  But the probabilities come
to be defined on spaces of histories rather than merely of states.
The entropy function that then results from the Shannon/Boltzmann
construction is then not generally the same function that would arise
for any equilibrium ensemble.  Likewise, the ways that constraints act
over the course of histories, and the expression of that action in
terms of _functional_ gradients of this new entropy function, will
generally be new functional forms.  In a limited set of cases, the
starting- and ending-condition equilibrium ensemles are restrictive
enough that one can get away without an explicit model of the
dynamics, and then "dissipation" expressed in terms of the equilibrium
entropy may predict correct descriptions.  But in other cases, while
the asymptotic beginning and ending configurations will continue to
place bounds on what can happen, those bounds may be so loose that
they are not directly informative, and one will be forced to go to an
entropy function that is influenced by the dynamics, to identify what
the true constraints are.  To my knowledge, no systematic prescription
exists to determine which systems will require a proper treatment, and
which will be tractable with the "entropy-production" approximations a
la Prigogine.  But I do find it a shame that the relentless publicity
machines have so taken over the world that everyone seems to follow
Prigogine-speak (which was also Schroedinger-speak and Brillouin-speak
and Henry-Quastler-speak, etc.), when the use of entropies on
histories is common in the Markov chain literature, and was thoroughly
(terrifyingly) understood by Kolmogorov and his students in the 1950s,
and re-iterated by E. T. Jaynes in the 1980s and later (though I am
not sure how much on Caliber is in Jaynes's textbook).  However, since
you originally sent the Ken Dill et al. papers on using Caliber for
the two-state system, I know you have good sources that go back to the
originals.

bwt, I owe you a debt of thanks for the Dill papers.  I have a review
out recently in Reports of Progress in Physics, entitled
Large-deviations principles, ... path entropies ..., which only treats
the discrete two-state system, but at least addresses some of these
points, and shows how they all fit together.  Your raising the Dill
papers prompted me to write this, so I could understand the relations.
It's all meant as review material and doesn't contain anything deep or
new, but perhaps does better faith to giving an answer than this email
did.  

If I had the possibility to analyse this system, which I have wanted
to do for many years, I would try to form the full path ensemble,
calculate its entropy, and see whether it decomposes into anything
simpler.  For now, the complexity of fluid dynamics and measures on
continuous spaces has put me off, and I have stayed with simpler
discrete-state, discrete-time processes, where one can learn what
these ideas look like, with minimal overhead making sure that the
measures have been correctly constructed.  

Of course, this is not an answer, but I hope it contributes something
to comfort in putting the question.  

All best,

Eric


============================================================
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

[Nick Thompson]

Thanks, Eric, for taking the question seriously.  I will study your answer
with care.

All the best,

Nick

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf
Of Eric Smith
Sent: Thursday, June 30, 2011 8:35 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] symmetry breaking

Nick, hi,

This time I really, really am under the gun and have no business answering.
But you are not being foolish.  You are pushing correctly on a set of
statements that are not a principle.  As Steve and Peter and others have
said, the only way to properly handle this is actually to work out a full
solution, and then figure out what global properties the particular solution
is expressing, and I haven't done that, so I can't provide anything that
counts as an adequate answer.
But a couple of points that I think are relevant.

The intuition you are pushing:  Water up high has gravitational potential
energy.  That by itself doesn't get turned into heat, so it doesn't directly
dissipate.  If the water can fall, the potential can be converted to kinetic
energy, and from there, various frictional effects can indeed convert the
bulk-motion of the water to thermal motion.  This is why you would be
looking for phenomena that both speed the rate of fall, but then afterward
also speed the slowing of average motion through frictions to disorderly
motion.  Internal turbulence etc. are all good pathways through which that
can happen.

On use of dissipation:  I think that, to the extent that it ever means
anything in these conversations, "dissipation" means the conversion of
energy from a mechanical form into a thermal form that goes into the
entropy.  I will say in a moment why that usage in most conversations from
Schroedinger and Brillouin onward, through Prigogine, are not reliable.  But
at least that statement is precise enough that it can be falsified.  And
sometimes it is okay; it's just that those sometimes are case-dependent.

On other factors such as constraints:  Yes, all the conversation about
stirring has to do with the role of angular momentum, as well as potential
energy, as a constraint on the configurations available to the system, and
to the processes through which they can dissipate or do anything else.  Any
relaxation process, however described, will be constrained by whatever
factors are put into its initial conditions, so inequivalent initial
conditions need not lead to directly comparable downstream phenomena.
Angular momentum that you put in by initial stirring must be transferred to
the sink or the air, before the fluid can slow enough to reach the drain,
and that takes time, because the transfer of angular momentum is mediated by
boundary-layer dynamics, sink-shape effects, etc., just like everything
else.

On the reason the standard use of "dissipation" doesn't get you to
principles:  When people say "the entropy", they usually mean the function
which -- IN AN EQUILIBRIUM ENSEMBLE -- would be the proper measure of
uncertainty or distribution of energy among degrees of freedom.  All these
flow problems that we talk about are not described by equilibrium ensembles;
they are ensembles of processes.  Of course, everybody says that, but
apparently most of the time people don't act as if saying that should then
carry meaning for what they think afterward.  (Like other mantras, its
function appears to be to suppress pre-frontal cortex activity.)  A
processes with states and flows has more that you can know about it than a
process with the same states but without flows.  This means that its
uncertainty or distribution are more constrained -- because they are
constrained by additional quantities -- than the equilibrium counterparts.
Therefore, the function that is the entropy for an equilibrium ensemble will
no longer generally be the correct measure of uncertainty or distribution
for an ensemble of processes.  The CONCEPT of entropy is still fine, and
even the Shannon/Boltzmann definition in terms of probabilities can still be
fine.  But the probabilities come to be defined on spaces of histories
rather than merely of states.
The entropy function that then results from the Shannon/Boltzmann
construction is then not generally the same function that would arise for
any equilibrium ensemble.  Likewise, the ways that constraints act over the
course of histories, and the expression of that action in terms of
_functional_ gradients of this new entropy function, will generally be new
functional forms.  In a limited set of cases, the
starting- and ending-condition equilibrium ensemles are restrictive enough
that one can get away without an explicit model of the dynamics, and then
"dissipation" expressed in terms of the equilibrium entropy may predict
correct descriptions.  But in other cases, while the asymptotic beginning
and ending configurations will continue to place bounds on what can happen,
those bounds may be so loose that they are not directly informative, and one
will be forced to go to an entropy function that is influenced by the
dynamics, to identify what the true constraints are.  To my knowledge, no
systematic prescription exists to determine which systems will require a
proper treatment, and which will be tractable with the "entropy-production"
approximations a la Prigogine.  But I do find it a shame that the relentless
publicity machines have so taken over the world that everyone seems to
follow Prigogine-speak (which was also Schroedinger-speak and
Brillouin-speak and Henry-Quastler-speak, etc.), when the use of entropies
on histories is common in the Markov chain literature, and was thoroughly
(terrifyingly) understood by Kolmogorov and his students in the 1950s, and
re-iterated by E. T. Jaynes in the 1980s and later (though I am not sure how
much on Caliber is in Jaynes's textbook).  However, since you originally
sent the Ken Dill et al. papers on using Caliber for the two-state system, I
know you have good sources that go back to the originals.

bwt, I owe you a debt of thanks for the Dill papers.  I have a review out
recently in Reports of Progress in Physics, entitled Large-deviations
principles, ... path entropies ..., which only treats the discrete two-state
system, but at least addresses some of these points, and shows how they all
fit together.  Your raising the Dill papers prompted me to write this, so I
could understand the relations.
It's all meant as review material and doesn't contain anything deep or new,
but perhaps does better faith to giving an answer than this email did.  

If I had the possibility to analyse this system, which I have wanted to do
for many years, I would try to form the full path ensemble, calculate its
entropy, and see whether it decomposes into anything simpler.  For now, the
complexity of fluid dynamics and measures on continuous spaces has put me
off, and I have stayed with simpler discrete-state, discrete-time processes,
where one can learn what these ideas look like, with minimal overhead making
sure that the measures have been correctly constructed.  

Of course, this is not an answer, but I hope it contributes something to
comfort in putting the question.  

All best,

Eric


============================================================
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

[David Eric Smith]

Oops! I need to make an emendation:

It was Roger Critchlow who sent all the Dill papers whenever-it-was,
perhaps a year ago.

I remain equally grateful, this time to the right person.

Many thanks,

Eric


============================================================
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

[Steve Smith]

On 6/30/11 8:02 AM, Nicholas Thompson wrote:

Thanks, Eric, for taking the question seriously.  I will study your answer
with care. 

Ask a simple question, and waddya get?
    Another day older and deeper in (conceptual) debt!

Eric says:

" All these
flow problems that we talk about are not described by equilibrium ensembles;
they are ensembles of processes.  Of course, everybody says that, but
apparently most of the time people don't act as if saying that should then
carry meaning for what they think afterward.  (Like other mantras, its
function appears to be to suppress pre-frontal cortex activity.) "

What a great insight!  I wonder how much of our blather here on this list is in fact crafted or selected for it's ability to suppress pre-frontal cortex activity? Wow!  While we *think* we are promoting pre-frontal activity, we may very well be supressing it!  I wonder if there is a simple heuristic for recognizing "mantras" in clear text?

Going recursive here, I wonder about the brain-state/chemistry that might be involved in our (my!) propensity for (near) idle speculation about things I know just enough about to be dangerous.  There seems to be something very soothing about this kind of speculation... hmmm?

As for the rest of your (Eric) response!  What a lot to unpack... I mostly get process vs equilibrium ensembles, spaces of histories and and some of the entropy talk, but am lost entirely on the topic of competing definitions of "diffusion" and it's precise relevance to this conversation... I'll give it my best shot though... dig a little deeper.

I believe This is the Dill paper you refer to?  I missed it the first time it was passed around I think. Or with your just-out re-attribution to RC, rather than NT  And here is a lecture by Dill at MIT that might be more accessible by some?

- Steve



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[Roger Critchlow-2]

So here's a vortex game for you all.  

There is a fleet of sail boats racing from Newport, Rhode Island across the Atlantic to the mouth of the English Channel.  If you go to http://www.nyyc.org/transatlantic/ and click on [Tracker] you'll get a map of the North Atlantic with the positions and tracks of the boats marked.  The red line is the great circle from south of Nantucket to the finish, the shortest path.  

Up on the control bar there's a button which will turn on a wind direction/intensity overlay so you can see the low pressure SE of Greenland with an eastern arm that stretches almost to the Azores;  the high pressures centered west of Brest, SW of Greenland, way south of the Great Banks; and the head wind that the fleet is beating into.  There's a slider under the weather button which allows you to step the wind overlay forward in time to the predicted winds at 3hour intervals in the future.

Find the fastest path given where the wind is, how well you can drive the boat, and where you expect you and the wind will be on the next watch.  The wind arrows the map shows are from the freely available NOAA GRIB models, but most of those boats are getting the best weather predictions that money can buy.

Human ingenuity vs fluid dynamics, the state of the art, no doubt getting very wet at the moment.

-- rec --

On Thu, Jun 30, 2011 at 11:13 AM, Roger Critchlow <[hidden email]> wrote:

There are several papers from Ken Dill and students that deal with these approaches.  And i don't think you missed them, they turned up after a discussion on Maximum Entropy Production principles.

-- rec --

On Thu, Jun 30, 2011 at 11:00 AM, Steve Smith <[hidden email]> wrote:

On 6/30/11 8:02 AM, Nicholas Thompson wrote:

Thanks, Eric, for taking the question seriously.  I will study your answer
with care. 

Ask a simple question, and waddya get?
    Another day older and deeper in (conceptual) debt!

Eric says:

" All these
flow problems that we talk about are not described by equilibrium ensembles;
they are ensembles of processes.  Of course, everybody says that, but
apparently most of the time people don't act as if saying that should then
carry meaning for what they think afterward.  (Like other mantras, its
function appears to be to suppress pre-frontal cortex activity.) "

What a great insight!  I wonder how much of our blather here on this list is in fact crafted or selected for it's ability to suppress pre-frontal cortex activity? Wow!  While we *think* we are promoting pre-frontal activity, we may very well be supressing it!  I wonder if there is a simple heuristic for recognizing "mantras" in clear text?

Going recursive here, I wonder about the brain-state/chemistry that might be involved in our (my!) propensity for (near) idle speculation about things I know just enough about to be dangerous.  There seems to be something very soothing about this kind of speculation... hmmm?

As for the rest of your (Eric) response!  What a lot to unpack... I mostly get process vs equilibrium ensembles, spaces of histories and and some of the entropy talk, but am lost entirely on the topic of competing definitions of "diffusion" and it's precise relevance to this conversation... I'll give it my best shot though... dig a little deeper.

I believe This is the Dill paper you refer to?  I missed it the first time it was passed around I think. Or with your just-out re-attribution to RC, rather than NT  And here is a lecture by Dill at MIT that might be more accessible by some?

- Steve

============================================================
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
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[Nick Thompson]

Vladimyr,

 

I love it!  I am going on a trip, so unless my host is particularly forgiving, fear that I wont be able to try it at his house, but I sure will when I get back.  Contrary to Lee, I don’t think, however, that confined water has anything to do with it.  Plumbing systems have pressure release pipes that vent gas upward as water rushes downward from the sink.  But the straw is a nice test of that proposition.  

 

Nick

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of Vladimyr Burachynsky
Sent: Saturday, July 02, 2011 8:54 PM
To: 'The Friday Morning Applied Complexity Coffee Group'
Subject: Re: [FRIAM] symmetry breaking

 

Hello All,

 

Years ago I ran some funky little tests spinning liquid epoxy on a platter to attempt perfect parabolas.

The equations required angular velocity and viscosity to get the correct equation for curvature.

If your sink is analogous then the swirling motion should leave the water near the drain at the lowest point with the lowest pressure. The surface near or at the margins should contain more water. The surface area has also changed.

 

So now you should get a long soda straw and stick into the drain and see if there is a relationship to the air in the system trying to escape the drain .

 

A suggestion, set up a free Sky Drive account and dump some video with notes and we can all have a look without  the Viagra adverts.

 

Sprinkle some floaters ( rubber duckies) and see how they travel perhaps.

 

Vladimyr Ivan Burachynsky PhD

 

 

[hidden email]

 

 

120-1053 Beaverhill Blvd.

Winnipeg,Manitoba, R2J3R2

Canada

 (204) 2548321 Land

 

 

From: [hidden email] [mailto:[hidden email]] On Behalf Of Roger Critchlow
Sent: June-30-11 1:32 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] symmetry breaking

 

So here's a vortex game for you all.  

 

There is a fleet of sail boats racing from Newport, Rhode Island across the Atlantic to the mouth of the English Channel.  If you go to http://www.nyyc.org/transatlantic/ and click on [Tracker] you'll get a map of the North Atlantic with the positions and tracks of the boats marked.  The red line is the great circle from south of Nantucket to the finish, the shortest path.  

 

Up on the control bar there's a button which will turn on a wind direction/intensity overlay so you can see the low pressure SE of Greenland with an eastern arm that stretches almost to the Azores;  the high pressures centered west of Brest, SW of Greenland, way south of the Great Banks; and the head wind that the fleet is beating into.  There's a slider under the weather button which allows you to step the wind overlay forward in time to the predicted winds at 3hour intervals in the future.

 

Find the fastest path given where the wind is, how well you can drive the boat, and where you expect you and the wind will be on the next watch.  The wind arrows the map shows are from the freely available NOAA GRIB models, but most of those boats are getting the best weather predictions that money can buy.

 

Human ingenuity vs fluid dynamics, the state of the art, no doubt getting very wet at the moment.

 

-- rec --

 

On Thu, Jun 30, 2011 at 11:13 AM, Roger Critchlow <[hidden email]> wrote:

There are several papers from Ken Dill and students that deal with these approaches.  And i don't think you missed them, they turned up after a discussion on Maximum Entropy Production principles.

 

-- rec --

 

On Thu, Jun 30, 2011 at 11:00 AM, Steve Smith <[hidden email]> wrote:

On 6/30/11 8:02 AM, Nicholas Thompson wrote:

Thanks, Eric, for taking the question seriously.  I will study your answer

with care. 

Ask a simple question, and waddya get?
    Another day older and deeper in (conceptual) debt!

Eric says:

" All these

flow problems that we talk about are not described by equilibrium ensembles;

they are ensembles of processes.  Of course, everybody says that, but

apparently most of the time people don't act as if saying that should then

carry meaning for what they think afterward.  (Like other mantras, its

function appears to be to suppress pre-frontal cortex activity.) "

What a great insight!  I wonder how much of our blather here on this list is in fact crafted or selected for it's ability to suppress pre-frontal cortex activity? Wow!  While we *think* we are promoting pre-frontal activity, we may very well be supressing it!  I wonder if there is a simple heuristic for recognizing "mantras" in clear text?

Going recursive here, I wonder about the brain-state/chemistry that might be involved in our (my!) propensity for (near) idle speculation about things I know just enough about to be dangerous.  There seems to be something very soothing about this kind of speculation... hmmm?

As for the rest of your (Eric) response!  What a lot to unpack... I mostly get process vs equilibrium ensembles, spaces of histories and and some of the entropy talk, but am lost entirely on the topic of competing definitions of "diffusion" and it's precise relevance to this conversation... I'll give it my best shot though... dig a little deeper.

I believe This is the Dill paper you refer to?  I missed it the first time it was passed around I think. Or with your just-out re-attribution to RC, rather than NT  And here is a lecture by Dill at MIT that might be more accessible by some?

- Steve

 

============================================================
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