Re: Determinism in the case of bifurcations and symmetry breaking
Let us take Benard cells for example. It is a good idea. I guess that in this case the incompressible Navier-Stokes equations with the Boussinesq approximation for free convection should suffer. If I understand correctly, bifurcation in this case arises when we increase the temperature difference between two plates. That is, if we consider the stationary Navier-Stokes equations on the top of thermal gradient Del T in the system, there is a critical Del T after that we have several solutions. To be back to my question. One could construct a system of equations from the stationary Navier-Stokes equations + Del T(time). In this case we have a problem that at some time when we reach a critical Del T, the system of equation has suddenly several solution and the question would be which one will be chosen. On the other hand, one could use the transient Navier-Stokes equations directly and it seems that in this case the problem of bifurcation will not arise as such. Well, in this case there are numerical problems. My question would be if physical laws allow for the first situation when at some point during transient solution a mathematical model has several solutions. If yes, then I do not understand how physics chose the one of possible solutions. Evgenii On 25.03.2012 05:50 Russell Standish said the following: Look up the literature on catastrophe theory. There were many examples of just these phenomena cooked up (particularly by Zimmerman IIRC) some good, many not so good. I'm sure you should be able to find something appropriate - maybe the appearance of Benard cells for instance. Cheers On Sat, Mar 24, 2012 at 10:05:00PM +0100, Evgenii Rudnyi wrote: Hi Stephen, I am not sure if I completely understand you. My question was rather what happens in Nature if we assume that its mathematical model includes bifurcations and/or symmetry breaking. Do you know a simple mathematical model with bifurcations and/or symmetry breaking? It might be good to consider this on a simple example. Say, I do not understand how do you apply statistics in this case. Either it is unclear to me how infinite computational power will help. Evgenii -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Determinism in the case of bifurcations and symmetry breaking
I have found Logistic Map http://mathworld.wolfram.com/LogisticMap.html Here the system has very different outcomes depending from initial conditions (now I understand your use of statistics). Yet, each trajectory is deterministic. Hence, this was not my question. Sorry for being unclear. Bifurcations in Logistic Map is a result of uncertainty in initial conditions. I was thinking more in terms of Transient Equation of Everything. Does it allow for multiple solutions at some times or not? In this case, Wolfram seems to support determinism: http://www.stephenwolfram.com/publications/recent/ultimateknowledge/ It looks probabilistic because there is a lot of complicated stuff going on that we’re not seeing–notably in the very structure and connectivity of space and time. But really it’s all completely deterministic. «That somehow knowing the laws of the universe would tell us how humans would act–and give us a way to compute and predict human behavior.» «Of course, to many people this always seemed implausible–because we feel that we have some form of free will.» «And now, with computational irreducibility, we can see how this can still be consistent with deterministic underlying laws.» Evgenii On 25.03.2012 06:23 Stephen P. King said the following: Hi Evgenii, You might also find Stephen Wolfram's work with cellular automate replete with examples of bifurcations and symmetry breaking. My thought was considering how to construct models of the behavior of bifurcating and symmetry breaking systems. I was thinking in second-order terms, as it where... Thus the use of statistics... Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: For Evgenii: the-unavoidable-cost-of-computation-revealed
On 14.03.2012 19:58 meekerdb said the following: On 3/14/2012 11:51 AM, Evgenii Rudnyi wrote: ... Then the thermodynamic entropy is subjective. Try to convince in this engineers who develop engines, or chemists who compute equilibria, and see what happens. It is relative not just to the information but the use of that information. Even if you told an engineer designing a steam turbine the position and momentum of each molecule of steam he would ignore it because he has no practical way of using it to take advantage of the lower entropy that is in principle available. He has no way to flex and deform the turbine blades billions of times per second in order to get more power from the steam. The experiment I linked to is extremely simple so that it is possible to use the information. Brent I have looked the paper that you have linked On 13.03.2012 20:09 meekerdb said the following: On 3/13/2012 10:28 AM, Evgenii Rudnyi wrote: ... Could you please give one example from physics (yet please not a thought experiment) where information allows us to reduce entropy? http://www.nature.com/news/2010/101114/full/news.2010.606.html Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality Shoichi Toyabe, Takahiro Sagawa, Masahito Ueda, Eiro Muneyuki Masaki Sano Nature Physics, Volume: 6, Pages: 988–992 (2010) I should say that I am not impressed. One can make a feedback mechanism indeed (by the way, it is quite common in engineering), but then in my view we should consider the whole system at once. What is the information then and what is its relationship with the entropy of the whole system? By the way the information about the position of the bead have nothing to do with its entropy. This is exactly what happens in any feedback systems. One can introduce information, especially with digital control, but it has nothing to do with the thermodynamic entropy. Then I like In microscopic systems, thermodynamic quantities such as work, heat and internal energy do not remain constant. The authors seem to forget that work and heat are not state functions. How work and heat could remain constant even in a macroscopic systems? I also find the assumption at the beginning of the paper Note that, in the ideal case, energy to place the block can be negligible; this implies that the particle can obtain free energy without any direct energy injection. funny. After block is there, the particle will jump in the direction of the block and it will interact with the block. This interaction will force the particle to jump in the other direction and I would say the energy is there. The authors should have defined better what they mean by direct energy injection. In essence, in my view the title information-to-energy conversion is some word game. It could work when instead of considering the whole system in question, one concentrates on a small subsystem. Say if I consider a thermostat then I could also say that information about the current temperature is transformed to the heater and thus to energy. I am not sure if this makes sense though. Evgenii -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: For Evgenii: the-unavoidable-cost-of-computation-revealed
On 15.03.2012 22:58 Russell Standish said the following: On Thu, Mar 15, 2012 at 07:25:01PM +0100, Evgenii Rudnyi wrote: On 14.03.2012 23:34 Russell Standish said the following: On Wed, Mar 14, 2012 at 07:51:13PM +0100, Evgenii Rudnyi wrote: Then the thermodynamic entropy is subjective. Try to convince in this engineers who develop engines, or chemists who compute equilibria, and see what happens. I take Denbigh Denbigh's position that entropy is not subjective, but rather fixed by convention. Conventions can be entirely objective. This should assuage those engineers you speak of. Could you please explain a bit more what you mean? What does it mean to fix something by convention? Evgenii We take certain macro variables as thermodynamic state variables, rather than others. A Laplace daemon would not agree with that. Its better explained in Denbigh Denbigh, but Brent Meeker has also been making the same point. Cheers Do you mean that the Laplace deamon would not agree with the Second Law? Evgenii -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Determinism in the case of bifurcations and symmetry breaking
On 3/25/2012 2:43 AM, Evgenii Rudnyi wrote: Let us take Benard cells for example. It is a good idea. I guess that in this case the incompressible Navier-Stokes equations with the Boussinesq approximation for free convection should suffer. If I understand correctly, bifurcation in this case arises when we increase the temperature difference between two plates. That is, if we consider the stationary Navier-Stokes equations on the top of thermal gradient Del T in the system, there is a critical Del T after that we have several solutions. To be back to my question. One could construct a system of equations from the stationary Navier-Stokes equations + Del T(time). In this case we have a problem that at some time when we reach a critical Del T, the system of equation has suddenly several solution and the question would be which one will be chosen. On the other hand, one could use the transient Navier-Stokes equations directly and it seems that in this case the problem of bifurcation will not arise as such. Well, in this case there are numerical problems. And then one could use molecular dynamics directly - but this raises a different kind of numerical problem: how to put in the initial conditions for 1e28 molecules. But nature manages. Brent My question would be if physical laws allow for the first situation when at some point during transient solution a mathematical model has several solutions. If yes, then I do not understand how physics chose the one of possible solutions. Evgenii On 25.03.2012 05:50 Russell Standish said the following: Look up the literature on catastrophe theory. There were many examples of just these phenomena cooked up (particularly by Zimmerman IIRC) some good, many not so good. I'm sure you should be able to find something appropriate - maybe the appearance of Benard cells for instance. Cheers On Sat, Mar 24, 2012 at 10:05:00PM +0100, Evgenii Rudnyi wrote: Hi Stephen, I am not sure if I completely understand you. My question was rather what happens in Nature if we assume that its mathematical model includes bifurcations and/or symmetry breaking. Do you know a simple mathematical model with bifurcations and/or symmetry breaking? It might be good to consider this on a simple example. Say, I do not understand how do you apply statistics in this case. Either it is unclear to me how infinite computational power will help. Evgenii -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Theology or not theology (Re: COMP theology)
On Mar 24, 3:58 pm, Bruno Marchal marc...@ulb.ac.be wrote:
OK, nice. Many confuse comp (I am a machine) and digital physics
(reality is a machine), but comp makes reality, whatever it can be,
being NOT a machine, nor the output of a machine. It is more a
perspective effect on infinities of computations.
A computer's 1p reality would be digital physics though. If I am Super
Mario, my universe is a digital reality. It seems that you say comp
says that Super Mario will doubt his reality is digital, which I would
agree with if I believed comp. Super Mario's reality could be a
machine or not a machine but his 1p of it is digital because I, as
programmer, have 3p views of its digits.
Of course, I say there is more to it than that: In fact Super Mario
has no 1p at all, and is only a 3p avatar simulating our own 1p world
semiotics. Our own 1p actually permeates 3p because sensemaking is
grounded in the unity of singularity as a natural self dividing into
multiplicity rather than aggregates of data imitating the 3p functions
of a self.
UDA explains
why the contrary occurs, through the first person indeterminacy
bearing on a very huge and complex arithmetical reality.
Why does hugeness, complexity, first person, or indeterminacy affect
whether something is digital or not?
Because there is a continuum of computational histories
(computations)
going through your state in arithmetic, or in the UD.
There are histories. OK. Why does that make them digital or not?
I assume I am a machine. Then the first person notion are NOT
machine, they are NOT digitalisable for the first person point of view.
Does that mean that the only justification for saying they are not
digital is because our experience is not digital and you assume that
machines are like us?
The rest follows
from the 1-indeterminacy and its invariance for the huge delays in
the
UD virtual reconstitutions. Ask more if this is unclear, but you are
supposed to have study the UDA.
Yes, I don't really get where 'delays' come from.
This is explained already in step 2, and then in the fact that the
Universal Dovetailer dovetails. It run all computations, but some are
infinite, so it runs them little pieces by little pieces, and
introduce vast and many delays in all computations.
I have a similar view but don't limit it to computation. The cosmos is
a process of nesting frames of experience, creating a concrete
interior semiotic medium of nested frequencies ('time') and an
abstract exterior semiotic medium of nested scales ('space'). The
process is computational, but what is being computed is sense and
motive.
Does the UDA exist
in 'time'? Is time an inevitable epi- of +, *, and n?
I guess you mean the UD. UDA is for the 8 step UD *Argument*.
Yes, comp makes all notions of time phenomenological, except the UD
time steps, which are based on the successor relation s(x) = s(x) + 1.
But physical time and subjective duration needs longer explanations,
and are mainly indexical first person (plural, singular) notions.
Time then exists as a consequence of UD, not a primitive within which
UD computes and wouldn't have any 'delays'.
Still not seeing
a connection with whether something is digital or not.
If we are digital, our experience bears on an infinite set of
computations, and the result is not digital. I let you study a bit
more the UDA.
Yeah, I don't understand. Does Super Mario's experience bear on an
infinite set of computations?
Second, the first person impression of the machine might be (and is
necessarily, once you accept Theaetetus' insight) a non
digitalizable
truth, from the machine point of view.
Which of Theaetetus' insight do you mean?
The definition of knowledge by true belief. Kp = Bp p.
I think I know what that is, but since Google shows nothing at all for
it, please spell it out for me one more time.
Google on theaetetus.
Socrates asked to Theaetetus to define knowledge. Theatetus gives
many definitions that Socrates critizes/refutes, each of them. One of
them consists in defining knowledge by belief, in modern time the
mental state, or the computational state of the belief and the
knowledge is the same, and a belief becomes a knowledge only when it
is (whatever the reason or absence of reason) true. Another one is the
justified true belief, which is the one which you can translate in
arithmetic with Gödel's predicate. You can read Bp p by I can
justify p from my previous beliefs AND it is the case that p. To give
you an example, if the snow was blue, a machine asserting snow is
blue can be said to know that snow is blue. Indeed, the machine
asserts the snow is blue, and it is the case that snow is blue
(given the assumption).
The problem (for some) with that theory is that it entails that,
when awake, we cannot know if we are dreaming or not, although in
dream we can know that we are dreaming, the same for being not
correct. It is
Re: Determinism in the case of bifurcations and symmetry breaking
On 3/25/2012 2:46 PM, meekerdb wrote: On 3/25/2012 2:43 AM, Evgenii Rudnyi wrote: Let us take Benard cells for example. It is a good idea. I guess that in this case the incompressible Navier-Stokes equations with the Boussinesq approximation for free convection should suffer. If I understand correctly, bifurcation in this case arises when we increase the temperature difference between two plates. That is, if we consider the stationary Navier-Stokes equations on the top of thermal gradient Del T in the system, there is a critical Del T after that we have several solutions. To be back to my question. One could construct a system of equations from the stationary Navier-Stokes equations + Del T(time). In this case we have a problem that at some time when we reach a critical Del T, the system of equation has suddenly several solution and the question would be which one will be chosen. On the other hand, one could use the transient Navier-Stokes equations directly and it seems that in this case the problem of bifurcation will not arise as such. Well, in this case there are numerical problems. And then one could use molecular dynamics directly - but this raises a different kind of numerical problem: how to put in the initial conditions for 1e28 molecules. But nature manages. Brent Dear Brent and Evgenii, Nature computes itself by evolving in time. The universe is not a program running somewhere else. It is a universal computer, and there is nothing outside of it. ~David Deutsch A possible easy answer as to how Nature manages to put in the initial conditions is to consider that the actual evolution physical system of those 1e28 molecules, etc. is the actual computation of its behavior, as Stephen Wolfram has already pointed out. This makes sense once we cast aside the idea that computations are somehow objectively alienated from the physical world. When and if we consider that the evolution of each and every physical system is its own computation of itself and that computational universality is more or less just a mapping of the functions involved and not some crypto-substance dualism that completely separates the computations from the physical systems, then the difficulties of measures and so forth vanish. We no more need to invoke immaterial programs than we need to conjure immaterial spirits to explain these things and trying in vain to eliminate that which is so obviously real, our subjective consciousness, as at best an illusion, is equally a fools game. Dualism will work iff used correctly. In a sense, we might think of all of the functionally equivalent computations of the behavior of a system define transformations (endomorphism?) on a space whose fixed point is identified with the actual physical system itself. Dually we can say that all of the physical dynamics of a system define a logical algebra whose (Kleene)fixed point http://en.wikipedia.org/wiki/Knaster%E2%80%93Tarski_theorem is the semantics of the computation. Abstract and concrete aspects touch in the actual objects themselves. IMHO, it is what Hegel and Marx tried to explain with their theories of alienation http://answers.yahoo.com/question/index?qid=20110402044539AAlw9hI that is the error. There is no actual dichotomy between mind and body or particular from Totality, there is only a problem of how to explain how bodies interact with bodies and how to minds interact with minds. We have most of the solutions to these problems already outlined before us in QM, GR and the work of Marchal, Turing, Barwise, Kleene, Wolfram, etc. What we actually struggle for is our individual understanding of these principles. When we are trying to built predictive models of physical phenomena to control aspects of them, we are not capable of creating simulations that are more faithful to the systems themselves and so have to use approximations and other devices to overcome this shortcoming. Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: For Evgenii: the-unavoidable-cost-of-computation-revealed
On Sun, Mar 25, 2012 at 03:49:17PM +0200, Evgenii Rudnyi wrote: Do you mean that the Laplace deamon would not agree with the Second Law? Evgenii Yes - there is no second law for the Laplace daemon. Each microstate is distinct and equiprobable. Cheers -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: For Evgenii: the-unavoidable-cost-of-computation-revealed
On 3/25/2012 6:44 AM, Evgenii Rudnyi wrote: On 14.03.2012 19:58 meekerdb said the following: On 3/14/2012 11:51 AM, Evgenii Rudnyi wrote: ... Then the thermodynamic entropy is subjective. Try to convince in this engineers who develop engines, or chemists who compute equilibria, and see what happens. It is relative not just to the information but the use of that information. Even if you told an engineer designing a steam turbine the position and momentum of each molecule of steam he would ignore it because he has no practical way of using it to take advantage of the lower entropy that is in principle available. He has no way to flex and deform the turbine blades billions of times per second in order to get more power from the steam. The experiment I linked to is extremely simple so that it is possible to use the information. Brent I have looked the paper that you have linked On 13.03.2012 20:09 meekerdb said the following: On 3/13/2012 10:28 AM, Evgenii Rudnyi wrote: ... Could you please give one example from physics (yet please not a thought experiment) where information allows us to reduce entropy? http://www.nature.com/news/2010/101114/full/news.2010.606.html Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality Shoichi Toyabe, Takahiro Sagawa, Masahito Ueda, Eiro Muneyuki Masaki Sano Nature Physics, Volume: 6, Pages: 988–992 (2010) I should say that I am not impressed. One can make a feedback mechanism indeed (by the way, it is quite common in engineering), but then in my view we should consider the whole system at once. What is the information then and what is its relationship with the entropy of the whole system? What you asked for was an example of using information to reduce entropy: not obtaining information AND using it to reduce entropy. The experiment does not actually violate the second law of thermodynamics, because in the system as a whole, energy must be consumed by the equipment — and the experimenters — to monitor the bead and switch the voltage as needed. By the way the information about the position of the bead have nothing to do with its entropy. It has to do with the entropy of the system of bead plus medium. The rotating bead could be used to do mechanical work via energy which was extracted from the random motion of the molecules in the medium. This is Gibbs free energy, so the bead plus medium plus information has a lower entropy that just the bead plus medium. This is exactly what happens in any feedback systems. One can introduce information, especially with digital control, but it has nothing to do with the thermodynamic entropy. Because it is not extracting energy from random molecular motion, aka heat. Then I like In microscopic systems, thermodynamic quantities such as work, heat and internal energy do not remain constant. The authors seem to forget that work and heat are not state functions. How work and heat could remain constant even in a macroscopic systems? They don't remain constant, but their statistical fluctuations are very small compared to their absolute value. Of course if you had information about these fluctuations you could use it to extract energy and decrease the entropy of the system. I also find the assumption at the beginning of the paper Note that, in the ideal case, energy to place the block can be negligible; this implies that the particle can obtain free energy without any direct energy injection. funny. After block is there, the particle will jump in the direction of the block and it will interact with the block. This interaction will force the particle to jump in the other direction The molecular motion of the medium forces it to jump one way or the other at random, the information is used to keep it from jumping back. So the work is extracted from the heat energy of the medium, not from the interaction with the blocks. and I would say the energy is there. The authors should have defined better what they mean by direct energy injection. In essence, in my view the title information-to-energy conversion is some word game. It could work when instead of considering the whole system in question, one concentrates on a small subsystem. Any demonstration of the principle is going to concentrate on a small system because it is impossible to use information about 1e26 molecules. And of course it will be a subsystem in the sense that some other device has to be used to get the information and if that device in included as part of a closed system, then the 2nd law will apply - since it applies to closed systems. You seem to be arguing against claims that were not made by saying a laboratory demonstration isn't a practical application. Brent Say if I consider a thermostat then I could also say that information about the current temperature is transformed to the heater and thus to energy. I am not
