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Author
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Topic: Is 2nd Law a special case of 4th Law?
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Christopher D. Beling
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posted 27. July 2006 05:40
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Is 2nd Law a special case of 4th Law?
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No, but almost. Dembski, said it better:
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the second law is subject to the Law of Conservation of Information [4th Law]
Hi Salvador, This is indeed the central issue that we need to discuss - thanks for bringing the discussion back on track. I do not have Dembski's "No Free Lunch" with me at present - is it possible for you to fill me and others in with Dembski's meaning and reasoning?
It does not seem to me that you are changing your position with regard to the 2nd - only changing its location from "special case" to "being subject to". I.E. in both cases you draw a big circle for phenomenon described by the regularity (law)we refer to as the 4th - then within this you put a smaller circle (the 2nd law) that governs a subset of phenonenon. I'm not sure I agree about this.
For me I see one big circle - labelled information theory - and within this big circle two smaller circles (i) the circle of phenomenon dealing with Shannon Entropy and its increase (2nd law) and (ii) the circle of phenomenon dealing with CSI and its decrease (or conservation) which is the 4th law.
It would be very helpful if you could give some examples of why you see the 2nd being a subset of lawas encapsulated by the 4th. Chris
P.S. With regard to mereology - from my own experience of having been to some extent in charge of constructing a piece of scientific equimpment over the last 20 years - I do understand that the CSI describing "the system" - does include information (instructions) on how all the pieces fit together. This seems to be related to IC. However, it also includes instructions to th apparatus builder on how the various components are to be fitted together to make the whole.
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William Brookfield
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posted 12. August 2006 12:20
Hi Chris,
I clearly have a different model of "information" than you (and possibly Shannon). Perhaps a different model would help move this thread along (to grand unification). I would like to refer to your earlier post from page 7 of this thread where I feel the difference is most pronounced...
Chris posted 28. November 2005 20:26
quote:
Quote
#A. [CSI>=00011110111001111001101110001111011100111100110111
and
#B. [CI>=00110100100101011111000001100011011011011000101100
"The first of these strings is the output from the weather station in Seattle (i.e. is CSI), - the second string is just random noise (generated in this instance by my tossing a coin) - (i.e. it is only CI)...."
The second string does not carry any information IMO. Notice that the word "form" is part of the word "'in-FORM-ation" and that "form" is the opposite of "random noise"
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...I would strongly argue that it does mean "disorder". Indeed Shannon entropy (information) is a way of measuring (quantifying) the disorder. Look, I know that sounds an oxymoron - i.e. that Shannon information equates with disorder - but by definition it is such. Perhaps the reason that so many folk are confused is because this does sound so weird (information=disorder)."
I am afraid I disagree with your position here Chris -- IE ("information=disorder"). The following is my model of information, order and disorder. In my model "information" is a complex form of "order" and a divergence from randomness the opposite of order...
#1. (Weather) in-FORM-ation[CSI>=00011110111001111001101110001111011100111100110111
#2 Order (mild in-FORM-ation) > =010101010101010101010101010101010101010101010101010
#3. Random coin tosses (no FORM)> =00110100100101011111000001100011011011011000101100
-- #3a Pure random coin toss (corrected)>= (000000000000000000000000000000000000000000000000000) +
(111111111111111111111111111111111111111111111111111) -- simultaneous superpostionality of 0 AND 1.
.. The last display #3a reveals the underlying superpositional (and thus uniform) distribution of pure randomness. The K-complexity in example #1 therefore has a different source than the K-complexity in example #3. In the first case (example #1) K-complexity arises from the complexity of the many informational triggers being sent. In the the second case (example #3.) K-complexity arises from the failure of the binary system to express randomness. Example #3 is a but a string of errors (divergences from pure randomness #3a). "Randomness" can be defined as "absence of specificity." Both #1 and #2 being specified, must be constantly defended from errors #3 and superpositional (#3a) spreading (specificity loss). Error checking such as checksums are therefore needed in order to maintain the integrity/specificity of #1 and #2. This is not true for #3 which is but a long string of errors -- in which random changes (more errors) do not matter. Complexity notwithstanding, movement from #2 to #3 does not represent information gain but instead represents information loss (loss of specificity/information/order).
The following is the examples listed in order of specificity;
#1. Information (K-complex -- highest specificity)
#2. Order (moderately K-simple)
#3. Complex Pseudo randomness (statistically K-simple)
#3a. Real randomness (K-simple -- lowest specificity)
The order continuum listed in terms of Order Magnitude;
#1. Information (residual machine order {binary} plus high in-form-ation {CSI})
#2. Order (residual machine order {binary} plus low information)
#3. "Randomness" (binary residual machine order only)
#3a Pure randomness (no order of any kind -- superpositionality)
William Brookfield
[ 12. August 2006, 12:27: Message edited by: William Brookfield ]
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Salvador T. Cordova
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posted 14. August 2006 19:54
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Hi Salvador, This is indeed the central issue that we need to discuss - thanks for bringing the discussion back on track. I do not have Dembski's "No Free Lunch" with me at present - is it possible for you to fill me and others in with Dembski's meaning and reasoning?
Chris,
(Please forgive my delay. )
Regarding what Bill wrote in No Free Lunch, I can only reference it in passing, and I'm not competent at this time to argue his position effectively, even though, by and large, I think he is on the right track.
There is hypothetically an extremely rare situation where Maxwell's demon could conceivably succeed. In such case it would be becuase the system contained a high degree of CSI that allowed this little "magic" trick to occur.
We can see something of an approximation of this with random number generators. The statistics look very noisy, much like the maximum entropy of a system. If however, one had an exact copy of the mechanics of the random number generator, one could write an algorithm which would negate the entropy. See Anti-Noise system to get an idea of what I mean.
Thus if Maxwell's demon had CSI describing the behavior of the noise, it could control the dynamics of the system because it can create an anti-entropy algorithm. Thus the amount of CSI (and appropriate coupling devices) constrains the behavior in terms of the 2nd law.
Such a system would require a degree of omniscience to create Maxwell's demon (so it could anticipate molecular trajectories), but in principal the availabiltiy of such CSI constrains 2nd laws behavior.
There is actually a real world parallel to this issue. It seems that proteins are able to move somewhat exploiting Maxwell's demon.
Protein folding and evolution are driven by the Maxwell Demon activity of proteins.
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In this paper we propose a theoretical model of protein folding and protein evolution in which a polypeptide (sequence/structure) is assumed to behave as a Maxwell Demon or Information Gathering and Using System (IGUS) that performs measurements aiming at the construction of the native structure.
And one that was really interesting:
Molecular Motors at the Limits of Nanotechnology
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Macro-scale thermodynamic engines convert the random motion of fuel-produced heat into directed motion. Such engines cannot be downsized to the nanometre scale, because thermodynamics does not apply to single atoms or molecules, only large assemblies of them. A great challenge for the field of nanotechnology is the design and construction of microscopic motors that can transform input energy into directed motion and perform useful functions such as transporting of cargo. Today’s nanotechnologists can only look in envy at the biological world, where molecular motors of various kinds (linear, rotary) are very common and fulfil essential roles.
Inspired by the fascinating mechanism by which proteins move in the presence of thermal noise, many physicists have been trying to establish novel concepts and strategies that might lead to the construction of man-made motors and machines on mesoscopic to molecular scales. Operating far from thermal equilibrium, molecular motors successfully combine noise and space-time asymmetry to generate useful functions such as transport, pumping, separation or segregation of particles. Such man-made molecular machinery, when realized, will not only be able to perform useful tasks on the atomic and molecular scales, but will also provide fundamentally new ways to manipulate molecules and nanoscale objects. Various mechanisms suitable for converting supplied energy into directed motion are discussed in this special issue. An important problem that has been raised in this issue, and has still to be resolved, concerns the possibility of controlling induced motion. In particular, a major problem is that of resolving the contradiction between the fascinating idea of feeding the energy by a driving random motion, and yet being able to control that motion; for example: starting the motion, stopping it, changing the velocity, and so on.
Pretty amazing!
[ 14. August 2006, 19:56: Message edited by: Salvador T. Cordova ]
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Christopher D. Beling
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posted 15. August 2006 09:44
Salvador, Thats a very interesting post and I begin to see where you and Bill are coming from with regard to the Maxwell demon and the IGUS - hope to make further comment after some thought.
William, I do agree with you in your critique of the earlier post. My usage of the word "disorder" was wrong but forgivable perhaps since other people use the words "disorder" (and "random") to mean "complex". A complex string is one with a high Shannon Entropy (no. of bits greater than 50 or 150 - depending on where you take the upper complexity bound). Thus I agree it is wrong (i.e. as in being unhelpful and confusing) to refer to a "complex" string as being "random" or "disordered" just because the string satisfies all the tests of statistical randomness - the reason is that there may well be semantic information present on the string (agree?).
We perhaps need to be strict on this point because there is confusion in the literature - for example in Paul Davies book "The Fifth Miracle" - that deals with origin of life - I read (p117)
quote:
Chaitin proposes a definition of a random sequence as one that cannot be algorithmically compressed; the shortest description of a random sequence is simply the sequence itself
He then suggests that the virus MS2 with portion
[MS2portion> = 0100011101110100100111001101011010111011
(where A==00.U=11,G=01,C=10) is "random". We seem to agree that we should not bow to such usage. This string is "complex" (yes), it has the property of satisfying the test of statistical randomness (yes), and is probably algorithimically incompressable (yes) - however the sequence carries functional information (it is an element of CSI - ie.with specification) - and thus to call it "random" gives a wrong impression and we should not do this - for the word "random" (or disordered) indicates lack of meaning.
I looked up the etymological root of the word "random": quote:
"having no definite aim or purpose" (1655), "produced at great speed - ie. carelessly and haphazardly" - from Frankish (Old French) word "rant" meaning "rush, disorder, impetious"
The meaning of "random" is thus quite clear - and a "complex" bit string carrying semantic or functional information should not be referred to as "random".
Thanks for getting us to reflect on the meaning of the word "information" = IN - FORM ation. A complex string carrying information from the Seattle weather station -IN FORMs a picture on a television set and an observers mind. The complex string carrying the MS2 virus IN FORMs certain behavior (forms) on an invaded cell.
The case of the pure random toss #3; Is inspired from quantum mechanics? i.e. the idea that a pure quantum state can collapse to spin up or spin down in a completely ontic random way?
Thanks for putting me right - Chris
[ 15. August 2006, 09:48: Message edited by: Christopher D. Beling ]
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2ndclass
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posted 15. August 2006 18:48
Christopher: quote:
We seem to agree that we should not bow to such usage. This string is "complex" (yes), it has the property of satisfying the test of statistical randomness (yes), and is probably algorithimically incompressable (yes) - however the sequence carries functional information (it is an element of CSI - ie.with specification) - and thus to call it "random" gives a wrong impression and we should not do this - for the word "random" (or disordered) indicates lack of meaning.
Given an incompressible string and nothing else, it makes no sense to say that the string is specified or meaningful. It is only in combination with other data that the string can have semantic significance. If we explicitly, rather than implicitly, combine all of the relevant data, then the algorithmic compressibility of the total data set will indicate that the data is not random. Thus, Chaitin's randomness test is appropriate even in the case of semantic meaning.
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William Brookfield
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posted 18. August 2006 21:00
Christopher,
Thank you for your thoughts on this.
It seems to me, the connection between thermodynamics and information theory arises because there is but a single info-order-disorder continuum -- to which the math globally applies. Orthodox thermodynamics however seems to apply it in upside down fashion tracking "entropy" instead of its opposite "order" or "information."
I should perhaps point out that by positing two possible sources of K-complexity (#1 and #3) I am challenging the comprehensive validity of the Chatin/Kolmogrov definition of "randomness."
Chris;
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"We perhaps need to be strict on this point because there is confusion in the literature.."
It certainly looks that way to me.
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"We seem to agree that we should not bow to such usage."
Yes Indeed.
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"--the sequence carries functional information (it is an element of CSI - ie. with specification) -"
Knowing (as we do) that this string carries specified functional information (for Davies has told us -- and we know this as general fact about DNA), it cannot be logically referred to as "random." It is a specifically structured (ordered) part of a structure (order). According to Davies this string is a crucial and specific component of an orderly structure. Randomness, being the opposite of order (and the opposite of information) is a destroyer of information.
One can freely randomize and re-randomize your random coin toss example (#3) and it will still function as a valid example of a random coin toss. This is not true for DNA information which functionally specific and is destroyed by randomization. One can scramble and re-scramble ones eggs and still enjoy scrambled eggs but if one is hoping to hatch a live chicken one had better not scramble the egg (order/form) the chicken (order/form), nor the DNA sequence (order/form) that codes (informs) for both.
Order that is K-complex and functionally specific (such as information) therefore stands in stark contrast to randomness that is (pseudo) K-complex and functionally spread (unspecific). For Davies to maintain that this string is both "random" (pseudo k-complex & unspecified) while telling us that it is also "information rich" (K-complex & specified) is to maintain a contradiction. You are therefore correct IMO that Davies should be using the words "complex" or "K-complex" throughout instead of the word "random."
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The case of the pure random toss #3[a]; Is inspired from quantum mechanics?
Yes indeed and from General Relativity -- spacetime-mass superpositionality at the core of a black hole singularity. It is also inspired from following the orthodox definition of "randomness" through to its logical conclusion.
Hi 2ndClass quote:
2nd Class
"Given an incompressible string and nothing else, it makes no sense to say that the string is specified or meaningful.
Luckily we have not been given "an incompressible string and nothing else." See Davies "The Fifth Miracle" page 117 through 119.
quote:
It is only in combination with other data that the string can have semantic significance. If we explicitly, rather than implicitly, combine all of the relevant data, then the algorithmic compressibility of the total data set will indicate that the data is not random. Thus, Chaitin's randomness test is appropriate even in the case of semantic meaning."
I am afraid that I do not the follow the logic of your last sentence. A compressed skeletal form is still a form (order).
With regard to information being transmitted through a binary system Chatin's randomness test appears inappropriate as directly applied -- but does appear appropriate in inverted form, as an order/information test. As more and more redundancy is removed from a data-stream the result is very dense stream of info-nuggets and the maximum info-per-bit, given the system's resolution. While the string of info-triggers would appear random (to a naive casual observer) we are not at this time naive about DNA and its crucial mapping to organism form and function. The specific DNA sequence is not only part of the organismal form but is indeed a crucial part. The DNA sequence is complex, non-random and information rich (IMO).
[ 18. August 2006, 21:03: Message edited by: William Brookfield ]
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2ndclass
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posted 21. August 2006 15:20
William, thank you for the Davies reference.
Davies's synonymization of random with information-rich is standard usage in information theory. Davies shows that randomness is a function of algorithmic compressibility, and he also introduces a metric for differentiating quality random strings from gobbledygook random strings, namely specificity. Says Davies:
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A functional genome is both random and highly specific -- properties that seem almost contradictory.
To see why they are not contradictory, we should note that randomness is an intrinsic property of the string, but specificity is not (at least not in the case of random strings). In other words, specificity is not a function of the string alone, but rather of the relationship between the string and something else.
I submit that randomness and specificity are both measures of algorithmic compressibility, the only difference being the scope in which they're applied. Randomness indicates the degree to which the string by itself is compressible. Specificity indicates the compressibility of the string combined with something else.
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2ndclass
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posted 21. August 2006 22:42
My previous post is pretty vague, so I'll give some examples.
A simple example is found on page 13 of Dembski's latest specification paper. Dembski points out that flipping a coin 100 times results in a random, unspecified sequence. But what if someone claims to have flipped the exact same sequence yesterday? In that case, the sequence is specified. Note that the specification is found not in the sequence itself, but in its relationship with yesterday's sequence. The combination of the two sequences is compressible.
Similar to this is Dembski's example of rocks on the ground forming a pattern that exactly matches a constellation. Neither the rocks nor the constellation is specified by itself, but the fact that they match entails a specification.
For a less obvious example, consider an English word, say, "mayonnaise". The word by itself is incompressible, but if we compare it to the English lexicon, we find a match. So the word/lexicon combination has a redundancy, which entails compressibility, thus specification. But the word without the lexicon is unspecified.
Finally, a genome describes tissues, organs, and an organism that are somewhat information-rich, but also contain redundancies. I submit that if we compress a genome completely, then the result is unspecified. The information describing the functional relationships between tissues and between organs gets eliminated when the genome is compressed. The only specificity left is found in the relationship between the organism and its environment.
I'm not expressing this idea very well, but hopefully it makes some sense.
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Christopher D. Beling
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posted 22. August 2006 00:38
Hi 2nd class; you are certainly bringing up some interesting ideas. They seem mainly to deal with concept/quantity of CSI. If possible let us get these ironed out - so that we might operate as a team speaking the same language (same meanings of words) - and I hope that Salvador will be patient ![[Smile]](smile.gif) CSI is so central to the 4th law.
quote:
Given an incompressible string and nothing else, it makes no sense to say that the string is specified or meaningful. It is only in combination with other data that the string can have semantic significance. If we explicitly, rather than implicitly, combine all of the relevant data, then the algorithmic compressibility of the total data set will indicate that the data is not random. Thus, Chaitin's randomness test is appropriate even in the case of semantic meaning.
Consider the case of a sender of information "S" and a receiver "R". "S" sends CSI#1 to "R" along some communication channel. If CSI#1 has semantic content then it will trigger some functional action at "R" (action that would not have accured by the laws of physics alone). I understand that what you are saying is that there is operational code in "S" and "R" as well as CSI#1, and that when you concatenate all this code it will become Chaitin-Kalmogorov compressible (am I right?), and it is this compressibility of the concatenated string that tells us that CSI#1 is infact carrying semantic information (right?). I think it is a neat idea - for example one expects the information on a gene to be there on the m-RNA (CSI package) and likewise on the proteins. BUT does this idea really work?
What if a dud-gene was transcripted and then transcribed into a protein - the protein would be a useless protein with no cellular function. In this case can we refer to the m-RNA carrying CSI?
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Note that the specification is found not in the sequence itself, but in its relationship with yesterday's sequence. The combination of the two sequences is compressible.
Here I accept the first sentence - although I do think we must always be aware of the analogical restrictions that might imply when we are dealing with humanly generated CSI. The second sentence concerns me though, because any string of characters if replicated and concatenated will never have more information than the original string. Seep p129 of No Free Lunch wgere I quote:
quote:
--there is no more information in two copies of Shakespeare's Hamlet than in a single copy
Thanks for the reference to Bill's latest paper - which I eagerly look forard to reading. Christopher
[ 22. August 2006, 09:01: Message edited by: Christopher D. Beling ]
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2ndclass
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posted 22. August 2006 12:35
Christopher, thank you for your thoughtful response.
quote:
I understand that what you are saying is that there is operational code in "S" and "R" as well as CSI#1, and that when you concatenate all this code it will become Chaitin-Kalmogorov compressible (am I right?), and it is this compressibility of the concatenated string that tells us that CSI#1 is infact carrying semantic information (right?).
Yes, exactly.
quote:
What if a dud-gene was transcripted and then transcribed into a protein - the protein would be a useless protein with no cellular function. In this case can we refer to the m-RNA carrying CSI?
Good question. I suppose it depends on one's definition of CSI. In my mind, CSI entails dependencies, not necessarily usefulness.
quote:
The second sentence concerns me though, because any string of characters if replicated and concatenated will never have more information than the original string.
Thus the compressibility of the doubled string. (Actually, N copies of a string has at least log2(N) bits more information than the string itself.)
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Christopher D. Beling
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posted 23. August 2006 00:32
2ndclass, I am glad to be understanding you. Indeed I agree with you that "dependence" (as in what happens at "R" being dependent on what was sent out by "S") could be a very neat way of empirically defining the "specificity" part of CSI. Indeed, I think it also neat that the dependency you talk of, could be empirically detected through the K-compressibility of all code found in "S", the CSI and "R".
I would, however, like to address the basic issue of "randomness" (i.e. what we really mean by saying a string of characters is "random") through which we first got onto this subject via William's post. Is it really correct to talk of a CSI package (on route between "S" and "R") as being a "random" character string even if it causes something to happen at "R" that depended on what was sent from "S" [where further, to be precise, this "happening" would not have happened under the action of natural law alone or any string that was significantly distorted from CSI#1]. I still maintain this to be inappropriate usage(and from William's post he agrees), because to say a character string is put together "haphazardly" (i.e. just thrown together anyhow - which is the fundamental meaning of the word random) is to deny the fact that what happens at "R" is dependent on the receipt of the CSI in a special way that requires all the characters to be absorbed (decoded)in "R" in the correct sequence. Thus the characters and their relative positions along the string (taken as a whole entity in itself) cannot be random (in the true sense of the word) since a specific dependent happening at "R" occured (agree?).
Incidentally, a question - on K-compressibility. We have agreed on K-compressibility if "S",the CSI package, and "R" taken as a whole (and that this feature could be a helpful way of detecting specificity), but what about the K-compressibility of the CSI package taken as a thing in itself, if nothing about "R" and "S" is known (other than background knowledge that the CSI is known to be compatible with both "S" and "R"). For example is the virus sequence:
[MS2portion>= 0100011101110100100111001101011010111011
likely to be K-compressible?
quote:
Actually, N copies of a string has at least log2(N) bits more information than the string itself.
Thanks for pointing this out. Christopher
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2ndclass
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posted 23. August 2006 12:16
Christopher, thank you again for your response.
quote:
Thus the characters and their relative positions along the string (taken as a whole entity in itself) cannot be random (in the true sense of the word) since a specific dependent happening at "R" occured (agree?).
The question is whether the "randomness of CSI#1" a property of CSI#1 alone, or is it a property of CSI#1 and its context? The algorithmic information theoretic definition assumes the former, while the more common intuitive definition assumes the latter. Obviously, there's no right or wrong definition as long as we're consistent.
quote:
We have agreed on K-compressibility if "S",the CSI package, and "R" taken as a whole (and that this feature could be a helpful way of detecting specificity), but what about the K-compressibility of the CSI package taken as a thing in itself, if nothing about "R" and "S" is known (other than background knowledge that the CSI is known to be compatible with both "S" and "R"). For example is the virus sequence:
[MS2portion>= 0100011101110100100111001101011010111011
likely to be K-compressible?
The string by itself looks incompressible, but I would think that compatibility, by definition, would mean that it's compressible when combined with S or R.
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Salvador T. Cordova
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posted 23. August 2006 23:03
quote:
William Brookfield wrote:
Davies should be using the words "complex" or "K-complex" throughout instead of the word "random."
Thank you for re-joining the discussion.
I agree with you, and will simply add some extreme care needs to be excercised when discussing Davies and Dembski as each of them have nuanced but significantly different conceptions of specified complexity, with Dembski I think doing a good job of properly overhauling Davies initial ideas.
In Davies literature, K-complex = random.
In Dembski's literature, complex is improbable, and k-complex may or may not be relevant at all.
There are situations where CSI may be k-simple, not k-complex.
What is challenging with the 4th law is that specificaiton has dependence on the observer. This may be disconcerting at first until one realizes, that the observer being part of the system being studied is par for modern physics, especially quantum theory.
There is deep in all of this a very bold claim. If CSI is tied to a human observers repertoire of specifications, how can it be that CSI also constrains the 2nd law???? It almost seems the universe and the laws of physics are constrained in some ways to the abilities of human observation. This is actually somewhat at the heart of the various flavors of the Anthropic Principle and the thesis of Privileged Planet.
I don't mean to derail the discussion with this statement, but at some point someone might recoil and realize the bold claim that is actually being asserted in a very subtle way when we constrain the 2nd law by the 4th law, or talk about the specifications in DNA.
Perhaps the best way to introduce this is Dembski's essay: The Last Magic.
In otherwords, CSI which can constrain 2nd laws are deeply tied to specifications which come so naturally to humans. There may be similar analogs in biology.
Nobel Laureate Wigner also pointed out the rather peculiar relationship between human specificaitons and natural law:
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
quote:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
Salvador
[ 24. August 2006, 21:49: Message edited by: Salvador T. Cordova ]
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Salvador T. Cordova
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posted 23. August 2006 23:08
quote:
2ndclass wrote:
Actually, N copies of a string has at least log2(N) bits more information than the string itself.
That may be true from some other perspectives of information, but I don't think that is constent with the formulation of CSI.
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Christopher D. Beling
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posted 24. August 2006 06:15
2ndclass, thanks for continuing the stimulating exchange. I am, however, still concerned about your usage of the word “random” in conjunction with CSI messages and to know whether you have backed down on your original usage. When you say:
quote:
The question whether the “randomness of CSI#1” is a property of CSI#1 alone or is a property of CSI#1 and its context?
you seem to be implicitly saying that CSI#1 does have the property of “randomness”. Thus you seem to be saying that:
[MS2portion>= 0100011101110100100111001101011010111011
is most likely not K-compressible (lets for sake of argument this is so), while
[MS2portion;S,R>= 0100011101110100100111001101011010111011
(i.e. the RNA portion seen in context) is most likely K-compressible – e.g. perhaps say to
[MS2portion;S,R; K-compressed>= 010001110111010010
and because of this [MS2portion> is not to be classified as "random". This is a neat way of classifying basically all CSI as "non-random" but I have my doubts as to whether this is a valid way of arguing. Let me challenge your schema in the following way:
Joe locks up his bicycle with a 40 bit combination lock, and the semi-CSI (only 40bits) that he chooses (encodes in the lock) for its opening is
[open>=0100011101110100100111001101011010111011
Joe then leaves town, but his friend Fred wants to use his bike in his absence. He has to phone Joe to find the opening combination. Joe sends [open> to Fred on the phone allowing Fred to activate to open the lock. Note the CSI [open> occurs in three places (i) in the encoding and mind of (S=Joe), (ii) along the phone line (channel) and (iii) at the receiver (R=Fred) in the lock opening. The number [open> is exactly the same at all three locations. Concatenating to form [open,open,open> produces really no more information than is present in [open> - it’s the same sequence after all. [it is true that log2(3)=1.6bit, but this is negligible compared to the information in the 40 bit string and of more importance there is no place or time where the entity [open,open,open> in reality exists.]
Thus I am persuaded that CSI [open> is really non K-compressible, and thus will be classified “random” (on the Chaitin-Davies definition) in both "stand alone" and "contextualized" approaches of your schema. Thus I back Salvador in believing that people are nuancing the word “random” to suite their own metaphysics:
quote:
In Davies literature, K-complex = random.
In Dembski's literature, complex is improbable, and k-complex may or may not be relevant at all.
In view of these things can you now agree that one should not refer to a piece of CSI (compressed or otherise) as being “random”? Christopher
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