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Author
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Topic: Granville Sewell and the Second Law of Thermodynamics
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The Pixie
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Member # 548
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posted 16. November 2002 18:29
Granville Sewell
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When matter condenses under the influence of gravity to form a planet, or ice crystals form when heat is removed, it is not because Nature can do extremely improbable things; what is happening is exactly what the laws of probability predict, when everything acting on the system is taken into account.
This is correct. But the important point is that you must take everything into account. Entropy does this because it measures the distribution of energy across energy levels. Water condenses from steam because energy is released, and can be distributed around the system, but conversely, water can turn to steam, even though it requires energy to be absorbed (concentrated in the water molecules), as the steam (being a gas) has more available energy levels to distribute that energy around.
Simplistically, there are two competing processes - energetic entropy and structural entropy - but it is vital to realise that they are two aspects of the same thing. This is why you cannot just consider the "carbon order".
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There is a widespread belief that, since order can increase in open systems, the second law must allow extremely improbable things (read: "macroscopically describable things which are extremely improbable from the microscopic point of view") to happen in open systems. My article was supposed to show that is not the case: everywhere else in Nature, whether in an open or closed system, what happens is governed by the laws of probability.
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If an increase in order is extremely improbable when a system is closed, it is still extremely improbable when the system is open, unless something is entering which makes it NOT extremely improbable.
The Gibb's free energy is a useful equation as it extends SLOT to open systems (if the pressure is constant). If you like, the Gibb's free energy indicates whether a process in an open system is improbable, in the same way that straight entropy does for a closed system. The salient equation is:
deltaG = deltaH - TdeltaS
... where deltaG is the change in the Gibb's free energy, and must be negative for a spontaneous process (or positive if the process is improbable). T is the temperature, deltaS the change in entropy and deltaH the change in enthalty (energy released). If you require it I can show you a derivation of the equation, but it is a basic part of thermodynamics.
Rearranging:
-deltaG/T = deltaS - deltaH/T
Now we can say that (-deltaG/T) must be positive for a spontaneous process (a not improbable one). Note that for a closed system deltaH is zero, so the equation collapses to deltaS must be positive, i.e. SLOT.
Overall, the point is that is that putting energy into any system (i.e., making deltaH large and negative) can force it to have -deltaG/T positive, turning it into a probable event (in a thermodynamics sense). So yes, something is entering the system that makes the process "NOT extremely improbable".
Any process, if you pile in the energy, the entropy increases and you can get it to go (but just because it is thermodynamically allowed does not mean it will happen, but that is another argument).
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If you are willing to argue that it only SEEMS extremely improbable, but really isn't, that the four known forces of Nature could create spaceships capable of travelling to the moon and back safely, and computers and the Internet, then you can argue that the underlying principle behind the second law has not been violated here, nothing I have said can counter that.
Are you really claiming that when man built moon rockets, computers and the internet he was violating SLOT? Or are you saying that man operates outside the four known forces of nature? Could you elucidate please?
It is my personal belief that the laws of nature apply equally to man as to planets and plant and stuff. I think chemists will be unable to get carbon condensing out of CO2 in a test tube at room temperature because it violates SLOT. I think physicists will be unable to make an iron block float, defying gravity. I further think moon rockets were built without violating SLOT, and got to the moon and back without defying any of the forces of nature.
Frances
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An increase in order in a closed system is extremely improbable for the simple reason that the law of entropy does not allow this to happen.
I am with GS on this. The reason the law of entropy does not allow it to happpen is that it is improbable, not the other way around. A low entropy, ordered system is less probable than a high entropy disordered system, because the latter has more possible combinations/arrangements of energy.
Pixie
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Elend
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posted 17. November 2002 04:12
I am still surprised whenever someone takes order for entropy and the other way around.
from www.entropylaw.com:
The classical statement of the second law says that entropy will be maximized, or potentials minimized, but it does not ask or answer the question of which out of available paths a system will take to accomplish this end. The answer to the question is that the system will select the path or assembly of paths out of otherwise available paths that minimizes the potential or maximizes the entropy at the fastest rate given the constraints.
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If the world selects those dynamics that minimize potentials at the fastest rate given the constraints, and if ordered flow is more efficient at reducing potentials than disordered flow, then the world will select order whenever it gets the chance. Theworld is in the order production business because ordered flow produces entropy faster than disordered flow (Swenson, 1988, 1991, 1992, 1995; Swenson & Turvey, 1991)
So, if order means faster entropy increase, why cannot order appear from disorder?
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Daniel Edington
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posted 17. November 2002 11:16
I get the impression from reading the posts on this topic that many people have the idea that change in entropy by itself is enough to determine if a process is thermodynamically favorable. Also it seems to be a common thought that if a process results in a negative entropy change that the process is somehow prohitied. neither of these ideas are correct.
Think about this one:
What is the entropy change for the combustion of hydrogen gas with oxygen gas?
Its a simple reaction and we know it is a spontaneous process.
Dan
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Frances
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Member # 169
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posted 17. November 2002 15:20
I would like to look in more details at the concept of entropy as used in information. Finley has published a paper: Complex Specification (CS) — A New Proposal For Identifying Intelligence which has some interesting as well as troublesome concepts.
The reason I call the concepts troublesome is because Finley seems to have redefined the concept of Shannon information. Finley for instance considers the 5 letter words in English. 5 letter words would require 23 bits to represent them but English words only require 13 bits. Finley names the remaining 10 bits to be specification but in fact the 'remaining' 10 bits are more properly called information.
Lucent labs have an excellent overview of Shannon and his contributions
Shannon's famous paper on information can be found Here
Tom Schneider has an excellent introduction to Shannon entropy which starts with a Glossary and includes a Primer on information
So what is information: It's the decrease in uncertainty of a receiver before and after receiving the message. From Schneider's primer"
Information R=Hbefore - Hafter
In Finleys example Hbefore is 23 bits, Hafter is 13 bits thus the information is 10 bits. Finley however refers to this as specification and to the 13 bits as information, this seems to be the inverse of how information is commonly defined.
My suggestion to Finley is to use the common definitions for information and entropy which means switching the terms information and specification in his paper.
In fact the amount of information that can be expressed by English would be 10 bits not 13 bits. This is easy to see if we were to assume that English allows for all combinations thus 23 bits of 'information'? But there would be no information in these 23 bits, all characters are equiprobable. The concept of information is indeed a tricky one.
The concept of specification or 'overhead' is an interesting one but I would propose that there would be no limitation of overhead to the 10/13 bits remaining. In fact one may envision shorter or longer error correction bits.
Thus information is Hmax-Hobs and specification is Hobs. But how would be the entropy of a system be considered 'specification'?
Schneider describes some common Pitfalls with Shannon information
Now I would like to tie this in with non-equilibrium thermodynamics.
First of all lets look at the theory of non-equilibrium thermodynamics and 'dissipative structures'
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How are biological organisms able to self-organize and maintain their life processes far from equilibrium? The answer to this essential question is found in the theory of ‘dissipative structures’ (Capra, 1996). Dissipative structures are open systems, they need a continual input of free energy from the environment in order to maintain the capacity to do ‘work’. It is this continual flux of energy, into and out of a dissipative structure, which leads towards self-organization and ultimately the ability to function at a state of non-equilibrium.
Source
Stephanie also looks at the entropy Hmax and Hobs. Hmax is the maximum entropy (equiprobable distribution) and Hobs is the observed entropy. She calls Hmax-Hobs the organizaiton and Hobs the entropy.
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Non-equilibrium thermodynamics is a special case of the second law of thermodynamics that is used to explain the existence of self-replicating dissipative structures. It describes how biological systems become more complex and organized through time as the result of, not at the expense of, increasing entropy. More specifically, non-equilibrium thermodynamics applies the concept of entropy to the formation of informational complexity and describes how it is shaped or organized by historical, developmental, and environmental constraints.
It seems that according to the theory of dissipative structures and non-equilibrium thermodynamics, order and complexity arise almost inevitably.
In biology experiments by Schneider and Adami have shown indeed how information and complexity of the genome can increase due to the 'Maxwell demon'-like actions of selection, with the difference that the information increase is more than compensated for thus not violating any thermodynamic laws.
I found the following Paper on information and entropy to be quite useful.
[ 17. November 2002, 15:39: Message edited by: Frances ]
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The Pixie
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posted 17. November 2002 17:17
Daniel Edington
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Also it seems to be a common thought that if a process results in a negative entropy change that the process is somehow prohitied.
That is what the second law says, actually...
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Think about this one:
What is the entropy change for the combustion of hydrogen gas with oxygen gas?
Hydrogen has an entropy of 114.6 J/mol/K, oxygen has an entropy of 204.9 J/mol/K, water has an entropy of 70.0 J/mol/K (at 25degC). The reaction is:
2H2 + O2 --> 2H2O
So the entropy change (deltaS) is apparently 2x70.0 - 2 * 114.6 - 204.9 = -294.1 J/mol/K
But, there is an energy release, a big energy release (deltaH) of 241800 J/mol. If we are looking at a closed system, then the water produced will be very hot and gaseous, its entropy much higher than 70.0 J/mol/K (I do not have figures to cope weith that). In an open system, we can assume all the energy released goes into the surroundings, and the water, eventually, is a liquid at 25degC. We can now use the Gibb's equation (T is the temperature in K).
deltaG = deltaH - TdeltaS
deltaG = -241800 - 298x(-294.1)
deltaG = -154158.2
deltaG negative indicates entropy (of the system plus the surroundings) is increasing, so the process is thermodynamically allowed.
Frances
My impression is that Shannon is talking about a specific form of data transmission where the ideal is that the data is transmitted as an exact copy. Therefore the received version cannot be better than the original by definition, and so it is trivially true that informational entropy cannot decrease.
While this is true in just about all technological applications, it is not true in biology. I am not supposed to be a copy of my parents; information entropy could be increasing or decreasing. Consider also the sum of human knowledge; clearly information entropy is at an all time low in this system.
Pixie
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Frances
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posted 17. November 2002 19:37
Frances
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My impression is that Shannon is talking about a specific form of data transmission where the ideal is that the data is transmitted as an exact copy. Therefore the received version cannot be better than the original by definition, and so it is trivially true that informational entropy cannot decrease.
That's not what Shannon is arguing , in fact Shannon argues that entropy can decrease and the decrease is commonly refered to as information. A totally randomized message would have maximum entropy while a message which has non-uniform probability distributions has a decreased informational entropy.
While entropy can never be larger than the maximum entropy, it surely can decrease and increase. In fact Shannon does talk extensively about noisy channels
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Janitor@MIT
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Member # 125
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posted 18. November 2002 13:46
Sometime ago I read an article by Walter Fontana in which he opened with the statement that biology lacks a theory of the possible because it lacks a theory of organization. Interesting how he relates the two things, possibility and organization, in his own mind… Also strange that biology, the study of living organisms—an organism being definitively an organized thing—lacks a theory of organization. (Maybe I’m just confused here, but Fontana might be called to account—I thought evolutionary theory was our theory of biological organization?)
Finley might have taken advantage of a considerable body of Kolmogorov complexity theory. I’m not that familiar with the subject, so please indulge me, but it appears as if Finley’s information/specification has an analog there in prefix(-free) coding. The basic idea can be found in Fano and (independently) Shannon and is usually referred to as Shannon-Fano coding. A simple case is “goedelizing” binary strings by assigning to each a natural number. In Shannon-Fano coding it is an ordering of an ensemble of possible messages according to relative probability measures, and in K-complexity it is an ordering of the (compressed) strings according to the length in bits. (Notice also how closely related specifying is to comparing.)
What we have done is specify how an ordering or organizing of some set of (pre-specified) data is to be done. This ordering or organizing can be done arbitrarily. The more difficult task is to find the “natural” order. So the relation of specification to order and organization is at least implicit in everything we have had to say. The relation between specificity and order/organization holds for thermodynamics as well. The reason why entropy is so strongly identified with uncertainty is exactly because entropy is deficient in this specificity. Specificity is not absent altogether here. Instead a maxent state is definitively specified as that which lacks any further specification, or is minimally specified. I.e., there is no further order, organization, or information that we can extract from the system. We have discovered a limit, and the relation of order, organization, and specificity to limits, as in Fontana’s intuit about what is “possible,” might be interesting to explore.
The problem with making distinctions between “specification” and “information” is that even unspecified information (whatever you want to call it) is specified as being “unspecified.” LOL Of course, “unspecified” information isn’t much information at all! This is a problem in information theory: specification precedes all other information-theoretic operations we perform. Specification is indeed the more elementary concept than information. Information is not the primitive term in the theory—specification is. W/o it we have no information. It’s difficult to imagine how it could be otherwise! E.g., first Finley specifies that we will be treating five-letter strings drawn from the English alphabet. He then proceeds to make further specifications, etc.
Specificity is the missing (implicit?) term in information theory. It is almost but not quite synonymous with information, as specification must precede information. It is not information that reduces uncertainty, it is a property possessed by information that reduces uncertainty: specification. (And "specificity" is a central principle in biology. Has been since the late 19th century. Its more modern incarnation is the sequence hypothesis.)
Now Dr. Dembski has made, I believe, an important contribution to information theory here, by focusing on the specification of information. Its one of those slap your head and say, “Damn! It’s so obvious! Wish I’d thought of it!” sort of things. However, begging his forgiveness, his work is virtually unknown to the community of theorists, scientists, and engineers who deal routinely with information theory.
http://www.ieee.org/organizations/pubs/transactions/information.htm
(LOL No pressure. Just trying to be helpful.)
Frances, how does Shannon measure the noise in a channel?
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Mark Szlazak
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posted 18. November 2002 15:02
As an aside, I'd just like to add a little reference page that talks about the second law of thermodynamics and various concepts of entropy.
There are various disconnects between information and energy.
The Second Law Of Thermodynamics
Others not mentioned in this page are found within quantum theory. It looks like non-locality is real and if this is the case then another interesting disconnect exists between energy and information.
Matter/energy transport/teleportation and signaling can't be superluminal, but causation and information transmission (excluding the part that would complete the signalling) can. Furthermore, this information transmission capacity is huge if not infinite. Apparently this is the case because the relative polarization angle can be set to any value along the continuum between polarizers in opposite wings of an Aspect-like EPR experiment.
[ 19. November 2002, 10:43: Message edited by: Mark Szlazak ]
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The Pixie
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posted 19. November 2002 11:08
Frances
I am unclear how informational entropy relates to thermodynamics entropy (as I said earlier in the thread), and having read the paper by Stephanie E. Pierce (and briefly the others) that you quoted am no clearer.
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If biological organisms were not historical slaves, character distribution would be random, maximum entropy would be realized, and biological systems would succumb to equilibrium.
I think this phrase sums up my problems. This is my interpretation:
Hmax seems to be all possible genetic codes (or the number thereof), while Hobs seems to be those genetic codes that result in the organism in question. So Hobs is the information and (Hmax - Hobs) is the specification. Biological entities are restricted to Hobs genetic codes because of their genetic history (i.e. they inherit characteristics). If they did not inherit information, each organism would have a random genetic code, and Hobs would equal Hmax. This is all true, but so what?
Then she further claims that if organisms did not inherit, and so Hobs=Hmax, the organism will "succumb to equilibrium". This seems to be a jump to thermodynamic entropy, and made without any justification. I am not too sure what she envisages the organism (or system?) will actually do.
I would be interested to see what Wiley and Brook said in the papers Pierce draws mostly on.
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The answer to this essential question is found in the theory of ‘dissipative structures’ (Capra, 1996). Dissipative structures are open systems, they need a continual input of free energy from the environment in order to maintain the capacity to do ‘work’. It is this continual flux of energy, into and out of a dissipative structure, which leads towards self-organization and ultimately the ability to function at a state of non-equilibrium. A famous example of a self-organizing, dissipative structure is the spontaneous organization of water due to convection.
What is the big deal with "non-equilibrium thermodynamics" and "dissipative structures". Which out of a man, a refrigerator, a car (automobile) and a star would be included in the definitions. All of them need energy from the environment (food, electricity, petrol (gas) and matter respectively) to do work. All of them have a heat output. In two cases this situation does not lead to self-organisation, in the other two cases self-organisation is present, but I would hesitate to say that self-organisation follows. Is self-organising a pre-requisite of a dissipative structure or a consequence of it or independent of it? Also, all four function at non-equilibrium; this is a direct consequence of the original stement that they are all getting an energy input.
Thanks for any insight.
Pixie
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Mark Szlazak
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posted 19. November 2002 15:13
Hi Pixie.
See my post above and look at the link on SLOT for the various types of entropy and how they don't necessarily mean the same thing as thermodynamic entropy or even correlate well with energy (i.e, see cite by Landauer at end of article).
Never the less, here's an intuitive definition of von Neumann entropy which gives the information carried by the information source and is the entropy used in Shannon's theory:
"An information source which has lower entropy occupies fewer states with higher probability. It can be said to be better known, and therefore the appearance of its results will bring less information. In contrast, a source with higher entropy occupies more states with lower probability. Its messages are less expectable, and therefore bring more infomation."
Note that the entropy here is not in pure thermodynamical quantities.
[ 19. November 2002, 16:07: Message edited by: Mark Szlazak ]
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Frances
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posted 19. November 2002 16:05
Pixie,
You raise some very good questions related to information theory and it may be helpful to clarify some of these concepts further since Dembski has unnecessarily complicated matters by defining information as the I(A)=-log(2)P(A) which is a somewhat confusing concept since a better name for this would be Hmax (the max entropy under uniform distribution).
Let me first point you to a Basic introduction to Information theory
Lets define some terms and first show the problem with I(A)
Entropy H, x a discrete variable {1...M}
H = - Sum P(x) log(2) P(x)
Where x is summed over all discrete variable 1..M
The first observation can be made that the more uniform the higher the entropy, additionally H is always greater than or equal to zero.
L the number of bits required to encode x
L(x) = - log(2) P(x)
Now we jump to the following excellent primer
equation (8) is the same as entropy defined above, now look at equation 9 and you will notice that for uniform probability (Hmax) H becomes (with P(x) now 1/M)
H = log M or H = - log(2) P(x)
Here we recover the definition of information as used by Dembski but in fact we notice that it is the entropy under the assumption of uniform probability distribution.
So what then is information?
Information R is Hbefore - Hobs or the reduction in uncertainty
Hobs is the observed entropy and the difference between the two is commonly refered to as information
The reason why biological entities have an observed entropy which is lower than the max entropy is because of the causal history, that is, the action of for instance natural selection and mutation which inserts information into the genome (a concept equivalent to reducing the entropy).
It may also be helpful to understand the connection between informational entropy and thermodynamica entropy
Again the same website provides us with a good paper. Equation 23 captures the link between information and thermodynamical entropy.
Things become a little bit confusing if we start assigning new definitions to these terms. Thus what you define specification is in fact information and what you deine to be information is in fact maximum entropy.
Dissipative structures or non-equilibrium thermodynamics is a whole different ball park than equilibrium thermo. Remember that energy can be exchanged in an equilibrium manner. Perhaps the following paper may be helpful
The concept of thermodynamic equilibrium is explained by the zeroth law of thermo... yes there are in fact already four laws of thermodynamics. The Carnot cycle is an example of a process which is reversible by virtue of being in thermodynamic equilibrium. By virtue of this the entropy remains the same.
In addition to the close to thermodynamic equilibrium, there is a whole new field of non-equilibrium thermodynamics which has a whole range of new features. Such as self organization, dissipative structures etc.
In case of your examples man seems to be the best example of a non-equilibrium structure. Refrigerators are best understood in terms of near-equilibrium thermodynamics (Carnot cycle). I found the following links to be very useful.
I hope that this clarifies the differences between near-equilibrium and far-equilibrium processes.
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Noel Rude
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posted 19. November 2002 16:21
The following in response to the last post above by Janitor@MIT -- though being neither physicist nor mathematician nor biologist it comes with some trepidation -- but wondered ... in linguistics we see language as operating on three levels:
1. The Word with (lexical) meaning -- might this equate in some way with specification? -- words have no information content apart from some larger context. Meaning, in this sense, is -- it is timeless. Animals, certainly never in the wild, know words. Communication for them begins and ends at the next level.
2. The Clause with (propositional) information -- comparable to the proposition in logic and the function in mathematics, is the minimal unit of information in language. Information, in the linguistic sense, is an event -- it happens -- it is not timeless -- information is communicative (whether between minds or machines or in nature?).
3. The Larger Context with (discourse) coherence -- language is negotiated in time clause by clause: each clause relating in some way to what has gone before (and might come after), else we have incoherence, and each clause also advancing with something new, else we have nothing but tautology.
It seems to me that information science could profit from the insights of linguists. Trouble is, though, linguistics is so fractious these days that I imagine most nonlinguists probably don't know where to start.
[ 19. November 2002, 16:30: Message edited by: Noel Rude ]
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Evan
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posted 19. November 2002 19:32
Frances writes "Here we recover the definition of information as used by Dembski but in fact we notice that it is the entropy under the assumption of uniform probability distribution."
I saw a speech by Vic Stenger in which Vic made this same point, and argued that Dembski's arguments about "no new information" were just another form of the 2nd Law of Thermodynamics objections to evolution that have been around for a long time. Vic also argued, as you might expect if you know Vic, that these arguments were flawed (as is being discussed in a adjacent thread).
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Frances
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posted 19. November 2002 20:59
I assume you are refering to The Emperor's New Designer Clothes? I was not familiar with this one. I have been researching these issues and found A FREE LUNCH IN A MOUSETRAP to be helpful. It is fascinating to me how it seems that the 2nd law can be expressed in so many different ways helping us understand concepts of information, entropy and probability.
A friendly voice whispered in my ear and pointed me towards another resource by Vic Stenger in which many of his arguments seem to be similar to mine.
quote:
Thus H equals the number of bits that are needed to transmit a signal communicating that configuration, irrespective of the content of the message. In the special case where Pn = P for all n, H = - log2P, which is the form Dembski uses for his measure of information.12
I would not want to ignore the critiques of Vic's work either
Of course I would like to point out that starting one's article with
quote:
However, those with deep-seated prejudices are more likely to cloud the discussion with argumentative misconceptions and inaccuracies, either through ignorance or malice. I don’t know Professor Stenger, but his writings lead me to believe the latter.
Seems to be self defeating.
All it all I am excited since it seems that we are getting closer to resolve the (2nd)^2 law of thermodynamics.
[ 19. November 2002, 23:17: Message edited by: Frances ]
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The Pixie
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posted 20. November 2002 08:14
Frances
quote:
Dissipative structures or non-equilibrium thermodynamics is a whole different ball park than equilibrium thermo. Remember that energy can be exchanged in an equilibrium manner. Perhaps the following paper may be helpful.
The concept of thermodynamic equilibrium is explained by the zeroth law of thermo... yes there are in fact already four laws of thermodynamics. The Carnot cycle is an example of a process which is reversible by virtue of being in thermodynamic equilibrium. By virtue of this the entropy remains the same.
I understand what thermodynamic equilibria are, I just do not see why people feel the need to make such a big deal about non-equilibrium thermodynamics. A couple of examples of equilibria are the two halves of a cup of coffee (heat flow from one half to the other is equal to the heat flow in the opposite direction) and a saturated salt solution (salt is dissolving at the same rate it is coming out of solution). The Carnot cycle is not an example of equilibrium; something is changing at each step (though the system does get to equilibrium at the end of each step). The Carnot cycle is reversible by virtue of being an ideal situation; in reality it will require an energy input (hence your refrigerator has a compressor), and is not reversible.
Although the first paper you mention is called "Equilibrium Thermodynamics", the word equilibrium does not appear anywhere else in the paper, and to my mind it is not about equilibrium at all.
All interesting processes are non-equilibrium thermodynamics, because otherwise nothing (on the macroscopic scale) is happening. So why add the "non-equilibrium" qualifier?
quote:
In addition to the close to thermodynamic equilibrium, there is a whole new field of non-equilibrium thermodynamics which has a whole range of new features. Such as self organization, dissipative structures etc.
In case of your examples man seems to be the best example of a non-equilibrium structure. Refrigerators are best understood in terms of near-equilibrium thermodynamics (Carnot cycle). I found the following links to be very useful.
I do not find the distinction between near-equilibrium and far-equilibrium to be useful. For instance, how far is far? And also equilibrium is a relative state, depending on what system and what aspects of it we are looking at (if you include nuclear processes, entropy is maximised by fusion/fission to iron, and most systems are a long way from this equilibrium).
SLOT is universal, both near-equilibrium and far-equilibrium systems are affected by it. Look at this paper, which comments on Prigogine's work (and others too), especially p32-33.
Pixie
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