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Author
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Topic: Is 2nd Law a special case of 4th Law?
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Melvin H. Fox
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Member # 1684
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posted 20. October 2006 08:33
I am in complete agreement with William when he writes:
quote:
I personally see statistical mechanics as a good working tool for the analysis of thermodynamics and information theory, but there is a problem here. A statistical law is an uncertain law and "uncertain law" is a contradiction in terms. Statistically speaking, the 2nd "law" works because of overwhelming probability, not certainty... I am convinced however that the 2nd law is a real law and that the statistical formulation is problematic.
-Mel
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Richard Oldani
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posted 20. October 2006 10:58
William,
You can't expect me to justify my arguments using terminology you have defined If you start with some recognized rational basis such as Darwin's theory, The Mystery of LIfe's Origins", etc. I can comment on it.
You threw me a bit when you said that Darwinists have claimed their theory to be bottom up. Is this true? To me it seemed obvious that Darwin's theory uses top down logic. Anyway since top down and bottom are recognized logical methods I was able to locate a formal definition It states in part,
quote:
Even though a particular study may look like it's purely deductive (e.g., an experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the project. In fact, it doesn't take a rocket scientist to see that we could assemble the two graphs above into a single circular one that continually cycles from theories down to observations and back up again to theories.
Now I can see why a misunderstanding could occur. Darwin uses top down logic to trace the fossil record to its "origins" in single celled organisms. He then uses bottom up logic to formulate his hypothesis based on natural selection. Thus both types of logic are used and his logic is circular. However, because the logic of Darwin's hypothesis is circular (the life forms that are "fit" are the ones that survive), no predictions are possible. A reason can be found for anything. This is not true in my own theory which uses only bottom up logic and two clear tests are possible:
1. It takes longer for a polyatomic solution to return to equilibrium than it does to heat up.
2, The time of energy absorption in a species (stasis) is inversely proportional to the time of saltation.
You are forcing me to justify my arguments and that is good.
I said, quote:
Configurational entropy and CSI, Complex Specified Information, do not have a statistical basis.
Darwinists would certainly say that configurational entropy is being formulated continuously, but I think that the existence of saltations indicates that it is not. If you take it a step further to the physical level than configuration is referred to as dissipative structure and is clearly not continuous. Are we on the same wavelength here?? I too am having a problem with how to respond to Chris's complex arguments. Chris do your arguments have application to evolution? If so, how? In fact an example of any type would help.
Richard
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Christopher D. Beling
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posted 20. October 2006 20:10
Mel and Richard - quote:
... but there is a problem here. A statistical law is an uncertain law and "uncertain law" is a contradiction in terms. Statistically speaking, the 2nd "law" works because of overwhelming probability, not certainty... I am convinced however that the 2nd law is a real law and that the statistical formulation is problematic.
If I could comment. I totally agree with you both that the 2nd law is statistical in its origins which works well because of "overwhelming probability". This can be seen in the fact that for small systems and short times-scales the 2nd law can be violated. Such 2nd law violation was shown to be possible by Evans and Searles and Cohen in the 90s Phys.Rev.E 71 (1993) 2401 Phys.Rev.E 50 (1994) 1645 . They called such entropy decreasing fluctuations - the Fluctuation Theorem (FT). The predictions of Evans et.al. were experimentally confirmed in 2004 when Evans and Searles teamed up with experimentalists Wang et.al. Phys.Rev.Lett 89 (2002) 50601
Phys.Rev.Lett. 92 (2004) 140601 - who held a small colloidal particle in an optical trap and observed entropy decreases over short times scales. In the 2004 paper they make this interesting comment:
quote:
However, several systems of current interest, such as nanomachines and protein motors, operate at length and time scales where the system cannot be considered infinite. At the nano - and microscales the thermal energy available per degree of freedom can be compariable to the work performed by the system. Classical thermodynamics does not apply to these small systems
It seems kind of intuitive that for a system with few particles that they can sometimes scatter into a microstate of higher probability (lower entropy). With regard to DNA we might also think on this. It is a large molecular system which normally mutates to higher "genetic entropy" (functional entropy Hfc) states. However sometimes - very occasionally, reverse mutations do occur bringing back the lost fitness. With DNA time scales I think should be considered short, because one is working with generation times - not seconds?
[ 22. October 2006, 21:07: Message edited by: Christopher D. Beling ]
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Christopher D. Beling
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posted 20. October 2006 20:19
Richard- quote:
Chris do your arguments have application to evolution? If so, how? In fact an example of any type would help.
Thanks for asking! Yes my arguments are very much connected with evolution. If the 4th law is correct then CSI (biological genetic information) is either conserved or it is decreasing. This would correspond to what I call (4th#1 and 4th#2)in my diagram on page 15 of this thread (3 Oct). This is highly pertinent to evolution, because Darwinists hold the view that bioinformation is on a monotonic increase - right from the time of the first primitive cell! [Although they would probably say that extinctions suddenly wiped out some bioinformation - they certainly believe that between extinctions a monotonic increase in bioinformation - due to natural selection and neutral drift - took place]. Unequivocally demonstrating the 4th law would be extremely strong evidence against the validity of the Darwinian theory of macroevolution. quote:
Darwinists would certainly say that configurational entropy is being formulated continuously, but I think that the existence of saltations indicates that it is not.
Couldn't agree more. The increase in configurational entropy - equates with an increase in Omega space, i.e. an increase in the length of coded DNA. Darwinists normally believe that this is the product of gene duplication followed by adaptation - and other modes of novel gene production. This in violation of the 4th and I just don't buy it for that reason which is connected to the improbability of randomly walking from one functional gene into another. Yes, Saltations are a support - if you look at my diagram of Oct 3 you will see that for #1 and #2 - CS information has sudden onsets (which I believe are due to inputs from outside the natural realm).
An other area is intraspecies variations. Here one sees a decrease of available information. Different human races now exist - but we all came from the same original stock. It impossible to now put all that bio-information back into one human. I believe this tendency is information loss, but I dont know how to formulate this. - Chris
[ 20. October 2006, 21:10: Message edited by: Christopher D. Beling ]
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Richard Oldani
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posted 21. October 2006 12:41
Chris, you give the following quote,
quote:
However, several systems of current interest, such as nanomachines and protein motors, operate at length and time scales where the system cannot be considered infinite. At the nano - and microscales the thermal energy available per degree of freedom can be compariable to the work performed by the system. Classical thermodynamics does not apply to these small systems
but then you completely misinterpret what they said when you say,
quote:
It seems kind of intuitive that for a system with few particles that they can sometimes scatter into a microstate of higher probability (lower entropy).
The quote did not refer to a multiparticle system, but rather to a single nanomachine or protein motor. They are not talking about intermolecular motions relative to a laboratory reference system, but rather intra molecular motions with motion relative to the nanomachine itself. IOW, "classical thermodynamics does not apply to these small systems" because this is not a kinetic system. The "thermal energy available per degree of freedom" refers to the bond energy, vibrational and rotational, of nanomachines and protein motors. The study you speak of equates entropy with energy flow, and disorder with energy dissipation. IOW a switch is made from a particle interpretation to an energy interpretation. I see it as a huge source of confusion in chemical and biological thermodynamics which I have spoken of in previous posts.
I think a comment on the origin of the second law is appropriate here. The second law was first formulated around 1850 and took its present form in 1860. http://www.wolframscience.com/reference/notes/1019b
These first studies involved steam engines with temperature differences of hundreds of degrees and corresponding heat flows. They were based on molecular models that had no internal structure so that collisions are reversible. On the other hand, studies of nano machines, protein motors, and life involve highly complex molecular chains which cannot even correctly be referred to as molecules and temperature differences that are certainly less than 1 degree. So the reason the second law is not valid for these systems is because they have internal structure.
My interpretation of all this is that the fourth law talks about bond energy while the second law talks about kinetic energy and they have to be clearly distinguished from each other in order to avoid confusion. I think that 90% of the confusion about thermodynamics as applied to life arises due to attempts to lump all entropy, all disorder into a single variable or mental concept.
Regards, Richard
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Richard Oldani
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posted 22. October 2006 12:43
Chris, can you post links to the Phys Rev Letter articles or do you have email copies? If you have them available I would greatly appreciate getting them. I can use interlibrary loan, but it would take at least two weeks. (disorder should read order in the last sentence) RO
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Christopher D. Beling
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Member # 723
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posted 22. October 2006 21:14
Richard, I have put in the links to those papers. I can see we do have some differences, you dealing more with energy - myself more with entropy. I am reading your paper and find it interesting but with some concepts that are difficult to understand - and I want to. Sadly pressures of work mean that I have to sign off this thread for a while - until January DV. In the mean time I hope I have time to reflect on your paper. Its been great dialoging with you recently. Regards. Chris
[ 25. October 2006, 02:31: Message edited by: Christopher D. Beling ]
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Christopher D. Beling
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posted 23. October 2006 01:12
Sal - I do not wish to mess with the line of discussion presently ongoing in this thread. But since I have to sign off for a while, I just wanted to give some thoughts on your major question. quote:
It is still my feeling MIND and information somehow constrains behavior of the 2nd law.
This a complex issue that needs more unpacking. However,you give this quote of Harold Morowitz:
quote:
First the human mind, including consciousness and reflective thought, can be explained by activities of the central nervous system, which in turn, can be reduced to the biological structure and function of that physiological system. Second, biological phenomena at all levels can be totally understood in terms of atomic physics, that is, through the action and interaction of the component atoms of carbon, nitrogen, oxygen, and so forth. Third and last, atomic physics, which is now understood most fully by means of quantum mechanics, must be formulated with the mind as a primitive component of the system.......We have thus, in separte steps, gone around an epistemological circle--from the mind, back to the mind. The results of this chain of reasoning will probably lend more aid and comfort to Eastern mystics than to neurophysiologists and molecular biologists...
This Immanentist or Emergentist idea meshes easily with the monist materialist perspective of the west where life is seen as crawling out of the primeval soup via totally naturalistic processes. As Morowitz points out, however, it also meshes well with eastern religions where time is seen to be circular and reality is subjective. Both western and eastern forms of monism deny transcendence. Students today don't even get a chance of thinking about trascendence - it is not talked about - and often what is not said is more powerful than that which is.
I draw 2 diagrams beneath. The RHS diagram shows the "epistemological circle" of Morowitz. (I hope I am portaying his ideas correctly?). The LHS diagram I believe portrays the state of affairs and is what I would thin more ID compatible. This is a model that does not rule out transcendence. Here Mind with a capital M is that from which all information derives. Time flows in but one direction. This model obeys the 4th law (types #1,#2). 
I fear that theories that are supported by monistic world views should be dealt with on an equal footing to those underpinned by dualism, as far as this humanly possible. We all strive for metaphysical neutrality - but think about the resistance to the Big Bang!
Sal; you say
quote:
von Neumann was able to demonstrate 2nd law purely from quantum principles and some little trick with matrices.
If you could find time to find a reference to this work it would be appreciated. I know that von Neumann introduced entropy into quantum theory, but I didn't know he had tackled the 2nd law. Regards - Chris
[ 24. October 2006, 00:39: Message edited by: Christopher D. Beling ]
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Christopher D. Beling
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posted 23. October 2006 12:15
Mel - you ask
quote:
Is entropy withdrawn from the universe because the input of chemical energy is directed or would this same effect be present where the input is undirected?
I think perhaps my last answer was not totally correct. Consider photosynthesis - energy is input from photons from the Sun. They are picked up by Chlorophyll molecules. These complex molecules did not come together by chance - they are "tuned in" to a broad spectrum of light from the Sun. In this sense one could say that there was some "directing" - but via the DNA that coded for the Chlorophyll.
Another interesting facet is the very fine tuning that exists between the energy of photons from the sun, and the transparency "window" of the Earth's atmosphere and water. The light wavelengths from the Sun match the earth's "window" perfectly and the window is just-right to cut out the the harmful UV. One may argue that plants' chlorophyll developed through NS to adapt to the Earth's atmosphere, but the problem is one of the fundamental constants of nature. Those constants that give the output frequency of the Sun are of a different set from those that determine chemistry and that make molecules like chlorophyll possible. This interconnectedness (IC ?) is most remarkable. I read about this in the book " Science:Christian Perspectives for the New Millenium " (CLM/RZIM publishers - can't find it on amazon] - article by Walter Bradley (p177). So perhaps one can strongly argue that the process behind the absorption of light is directed. But directed in the sense that there is an Intelligence behind it. Signing off for a while but hoping to hear about the dice experiment sometime! - Chris
William,
I have not had time to question you on your diagram regarding CSI (page 10). There are some aspects of it I do not understand and would like to. I also admit to not fully understanding the difference between "mock" and "nformational" K-complexites. I hope such discussions can take place latter. - Chris
[ 24. October 2006, 01:20: Message edited by: Christopher D. Beling ]
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Richard Oldani
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posted 24. October 2006 21:35
I am dropping out for awhile after a short but very fruitful session. I got several ideas to improve the paper I have posted and was about to contact the editor to see if it was too late to make improvements. At the same time he contacted me to say the abstract was not written in sufficiently good French. Because he had not approved all of it I now have a chance to rewrite the section on thermodynamics.
If anyone has any questions about it you can post them in the archive or email me at oldani@juno.com I will post answers and the changes when finished. Thanks. RO
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William Brookfield
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Member # 565
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posted 25. October 2006 14:52
Hi Richard,
I have surveyed the internet and I it appears that the terms "top down" and "bottom up" can refer to just about anything ![[Eek!]](eek.gif) . Denyse O'leary however has just published an article that explains and then uses these terms in precisely the way that I originally intended. web page
There clearly seems to have been some confusion wrt how our words are being defined. You seem to have maintained that Darwin's theory is "top down" and yet even by the link you provided (regarding inductive&deductive theory building) Darwin's theorizing seems "bottom up" to me. My understanding is that Darwin spent his early life collecting raw data (bottom) and only later did he "allow himself" to make up a theory (top). I am not to saying that your theory is wrong only that there could be communication problems wrt terms in your paper. It would be sad to have a perfectly good theory dismissed -- not because it was wrong -- but because it was misunderstood. At this point I think that both Darwin's theory and your theory are "bottom up" (I.E., matter first) theories. I am happy to see that your paper is now up here at ISCID and I wish you luck with it. My understanding is that it will have its own discussion thread.
Richard
quote:
If you start with some recognized rational basis such as Darwin's theory
Frankly, I am not sure that Darwin's theory actually has a rational basis. As I see it "macro-evolution" is an extrapolation of "micro-evolution." Microevolution in turn, is dependent upon each species' flexibility. Flexibility/adaptability however, is itself a positive design attribute that requires an explanation. Galapagos finches that would immediately choke and die on the first drought-hardened seeds are easy to design compared to finches that can adapt and survive through countless environmental assaults. A computer program that can barely run in a single computer environment is far easier to design than a program that can itself adapt, self correct and thrive in countless computer environments (PC, MAC, Unix, Atari etc.,) If living species were more poorly designed they would immediately drop dead in response to the slightest environmental change -- and there would be no Darwinian "evolution" (macro or micro). The genetic information (for each variant) corresponding to every environmental change has to be in place before any organism can "evolve" in response to selective pressure. Darwinian theory therefore, has no validity of its own IMO and is wholly parasitic upon massively competent design. Adaptable species are exponentially more information-rich than species devoid of genetic contingency plans (the crucial extra information/variants). All of the "evidence of evolution" (peppered moths, bacterial antibiotic resistance etc.) is subsequently evidence for design IMO.
Chris,
quote:
Sadly pressures of work mean that I have to sign of this thread for a while.
It is sad that global society does not see the value of your work here and reward you accordingly. You have made enormous contributions to this thread and to ISCID, IMO. Your scholarship and cordiality has been exemplary. I certainly look forward to your return in January or earlier.
WRT my "{m}K-complexity" and "{i}K-complexity" the former {m} is complexity produced by a conflict or collision of some kind (e.g. car crash/randomness/complex accident scene) whereas the {i} version is functionally-specific information-carrying complexity (DNA code, nanotechnology, CSI).
Mel,
If we all(?) agree that the statistical approach (to info-thermo-dynamics) is useful but flawed then what would we replace it with? I think the solution hinges upon a unified notion of "space" into which specified systems can spread. By "space" I mean "omega space" (information theory) "phase space" (thermodynamics) and "spacetime" (relativity).
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Richard Oldani
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posted 01. November 2006 05:17
William,
Sorry for the delay. I am researching the experiments Chris talked of on the fluctuation theorem. If you are interested you can find links to the original papers on Denis Evans home page. It describes "violations" of the second law when tiny beads are dragged through water by a laser tweezers. Fascinating stuff.
I agree with O'leary that Darwins theory is bottom up. But as I said before his work was top down. That is, he researched the fossil record (top) amd then used it to hypothesize an "origin" of the species (down). Without the top down work there is no bottom up theory. His logic is circular therefore so he can prove anything, going from the general to the specific or the specific to the general. However, because it is circular no predictions are possible other than carefull chreographed ones. quote:
Frankly, I am not sure that Darwin's theory actually has a rational basis.
I agree with you here. I would classify his "theory" as a geneology, a family tree. I don't see anything scientific about it. The science was done later by microbiologists.
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John A. Davison
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posted 01. November 2006 06:57
Darwinism is the most failed hypothesis in tne history of science. It should have died shortly after its inception when it failed the acid test of expermental verification: in other words about the same time that the Ether of Physics and long after the Phlogiston of Chemistry had disappeared for the same reasons. It is neither a theory nor an hypothesis as it has no predictive power.
"A past evolution is undeniable, a present evolution undemonstrable."
John A. Davison
[ 01. November 2006, 07:00: Message edited by: John A. Davison ]
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Poul Willy Eriksen
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posted 04. December 2006 11:01
Ok, the posts in this thread do clear up some of the confusion I have had about what is what; but I have a few questions that I would like to pose here. Then I'll have to see if anybody bothers to response :-)
Salvador Cordova wrote back in May 17 2005:
The 2nd law is a measure of the deterioration of orderliness and increase in K-complexity. Ironically, in this case, an increase in K-complexity is a decrease in specified complexity.
And Mr.Cordova wrote May 18 2005:
Consider the following ordered configuration of coins
H H H H H H ......
It is actually (in ID parlance) considered specified complex, even though from a Kolmogorov view point it is actually K-simple.
When we shake the coins up it becomes K-complex and the specified complexity is blown away, and the configuration reaches entropy very quickly with random amounts of heads and tails....
The coins obey the 4th law. In like manner molecules being heated obey the 4th law going from the specified state of orderliness to disordierliness
Ok, that's more than a year and a half ago, and things may be different today, let's have a look at these statements anyway.
A generic entropy function looks like this:
H = − k ∑ i pi log pi
where pi is the probability that the system will be in the i'th state. The entropy function assumes its maximum, − knp log p, for p = p1 = ... = pn, where n is the number of possible states. The constant k scales between various logarithmic bases. If k = 1, and the logarithmic base is 2, H can be interpreted as a measure of uncertainty regarding the current state, the number of binary questions needed to reduce the uncertainty to 0. The information gained is equivalent to the uncertainty reduced.
An example: a position on a genome may be in one out of four possible states: A(denine), C(ytosine), T(hymine), and G(uanine). Assuming equiprobability, we have
H1 = − 4/4 * log2 (1/4) = log2 (4) = 2
That is two bits of uncertainty.
Somehow we first detect that the nucleotide is a pyrimidine; that is, either C or T.
Recalculating we get
H2 = − 2/2 * log2 (1/2) = log2 (2) = 1
That is, the information that the nucleotide is a pyrimidine reduced our uncertainty from 2 bits to 1 bit, so we gained 1 bit of information, and have 1 more bit to go.
We now detect that the nucleotide is a C.
Recalculating we get
H3 = − 1/1 * log2 (1/1) = log2 (1) = 0
So, we have again reduced our uncertainty with 1 bit and therefore gained 1 bit of information, and we have no uncertainty left. All in all, our gain in information is our loss in uncertainty: H1 − H3 = 2.
Say we have N coins on a table, all heads up, just as in Mr. Cordova's example. We can now start flipping coins, and some will probably land tails up. Each cell in the state space contains one configuration of the coins, so there are 2N cells in the state space, and they all have exactly the same probability, 2-N, so the entropy is constant. The K-complexity will most likely remain high.
The N coins, all heads up, do not initially represent N bits of information, because we knew that they were all heads up. Once all coins have been flipped at least once, we do have N bits of uncertainty, and we can gain N bits of information from inspecting the coins. This will be the case, everytime we flip all the coins.
The point here is that the system is resampled, each time before we check. Entropy is a property of state, not of causal history. Information, however, is never resampled. A string such as "HHHHH..." representing N heads remains the same; what may change is whether that string represents the current state or not.
You can of course also sample a certain newspaper such as the New York Times, for example read it once a week; but it makes no sense to say that information is lost, because each sample doesn't contain exactly the same articles week after week. Compare this to the different process of keeping a certain copy of a newspaper and check it week after week; it will undergo some physical corruption, but whatever was written in it remains whatever was written in it.
Now, say we have some population of organisms. We pick an organism and look at a particular gene in its genome. What is the information in that gene? To answer that, we need to know the à priori uncertainty. If there are 1,200 nucleotides in the gene, is our uncertainty 41200? It shouldn't be, because we actually first need to know the frequency of each allele. The set of alleles constitutes the state space for the gene. The number of alleles may be as small as 1, and it is certainly much smaller than 41200. If there are two alleles, the maximum uncertainty is 1 bit, namely if they have the same frequency. This is independent of the length of the gene, because the probabilities in the entropy formula depend on the actual state space, not some theoretical state space. What is the K-complexity of the allele? We can't know. If we look at the nucleotides, it may be very high. But maybe the gene controls, say, flower color (assuming our population is from some species of flowering plants), then one allele may give white flowers, and another give red flowers. So we can name the alleles after the flower colors. But names such as "red flowers" and "white flowers" are constants, so the K-complexity of the alleles does not change.
Assume these plants to be diploid and let us say that there are actually ten alleles of this gene. Yet, the two genes in each offspring of a cross between two of the plants are sampled from a state space of at most four different alleles. The difference when compared to the coins example is, of course, that each generation is not made from a complete resampling from the entire state space.
Great care should be exercised, when mixing information theory and thermodynamics, and particularly great care shoul be exercised, when mixing either or both of these with biology.
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Melvin H. Fox
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posted 04. December 2006 21:30
Poul,
You seem to echo William’s question with the added set of alleles state space:
quote:
If we all(?) agree that the statistical approach (to info-thermo-dynamics) is useful but flawed then what would we replace it with? I think the solution hinges upon a unified notion of "space" into which specified systems can spread. By "space" I mean "omega space" (information theory) "phase space" (thermodynamics) and "spacetime" (relativity).
I wonder if it would help if we could show each of theses states to be measurable.
-Mel
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