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Author
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Topic: Is 2nd Law a special case of 4th Law?
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2ndclass
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Member # 1979
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posted 24. August 2006 13:34
Salvador:
quote:
There are situations where CSI may be k-simple, not k-complex.
Which is why your doubt about "whether selection favors CSI over simplicity" doesn't make much sense.
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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 begin studied is par for modern physics, especially quantum theory.
The behavior of quantum-level processes is dependent on how those processes are measured, but the results are still objective, i.e. it doesn't matter who performs the measurement. So I don't see how quantum mechanics mitigates CSI's subjectivity problem.
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In otherwords, CSI which can constrain 2nd laws are deeply tied to specifications which come so naturally to humans.
I don't know what it means for a law to constrain another law. Is it a meta-law, or do you mean that Dembski's 4th Law places more constraints on physical events than the 2nd Law?
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That may be true from some other perspectives of information, but I don't think that is constent with the formulation of CSI.
Actually, copying strings usually generates more information in the CSI approach than it does in the algorithmic information approach. Consider that if Nicholas Caputo had repeated the same sequence several times, then that would represent a large increase in the amount of CSI, but only a slight increase in the amount of algorithmic information.
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2ndclass
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posted 24. August 2006 19:06
Christopher:
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you seem to be implicitly saying that CSI#1 does have the property of “randomness”
Actually, it wasn't a question of whether CSI#1 is random, it was a question of whether the statement "CSI#1 is random" describes CSI#1 independently of its context, or describes the combination of CSI#1 and its context. Sorry I wasn't clear on that.
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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.]
Good points. I take it we're in agreement that [open,open,open> is compressible since it's a 120 bit string that contains little more than 40 bits of algorithmic information. Regardless of whether the 120 bit string is found in the real world, its compressibility indicates that its components are interdependent, and that's what we're testing for when we mentally concatenate the strings.
(Algorithmic compressibility is an all-purpose test for interdependence, but it's obviously overkill in most cases. We don't need algorithmic compressibility to figure out that exact copies of a complicated string are related to each other. But I don't know of any other approach that works in all cases.)
W.R.T. randomness, suppose we're given a long, incompressible string. Under the algorithmic information definition of randomness, we can immediately label the string "random". But under the intuitive definition (which is the one you're advocating), we can label it random only if:
a) we happen to know that it was generated by an irreducibly random (i.e. quantum) process, or
b) we happen to know that no equivalent pattern exists in the universe.
The problem is that the intuitive definition depicts randomness as a property not only of the string itself, but also of its causal story. But often we're checking for randomness in order to determine the causal story of the string. In that case, we have to look for external patterns that match, but how do we know when to stop looking?
Similar problems are found in Dembski's terms. For example, is the following string complex, using Dembski's definition?
1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
Is the following string specified?
1001011110001110110110001100111110010001001001000101110111100011010111000011010110111100011010001101000011000
Neither of those questions can be answered without looking at additional relevant data, and we have no way of know whether we've taken into account all of the relevant data.
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Salvador T. Cordova
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posted 24. August 2006 21:44
quote:
2ndclass wrote:
Actually, copying strings usually generates more information in the CSI approach than it does in the algorithmic information approach. Consider that if Nicholas Caputo had repeated the same sequence several times, then that would represent a large increase in the amount of CSI, but only a slight increase in the amount of algorithmic information.
I think this is incorrect because in the case of Caputo one is increasing the space of possible outcomes by having a longer string.
CSI increase assumes one is dealing with the same size space of possible outcomes, not a changing size of space. If a changing space is involved, to apply conservation of CSI one has to use Cartesian Products to define the space of possiblities. I have not yet spent time to analyze such a situation.
Shallit and Elsberry change the space of possibilities on the fly in their TSPGRID program and thus do exactly what should not be done in measuring CSI. They effectively compare apples and oranges. For similar reasons, the following statement is in error: "if Nicholas Caputo had repeated the same sequence several times, then that would represent a large increase in the amount of CSI."
If one is going to be changing the size of the space Omega on the fly, one needs a specialized technique to deal with that possibility. I'm not versant yet in how to do that, except to say Caputo copying strings is an inappropriate way of viewing increase in CSI unless the copied string and the originals are considered part of the space omega of possible outcomes.
[ 25. August 2006, 00:06: Message edited by: Salvador T. Cordova ]
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Salvador T. Cordova
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posted 24. August 2006 21:55
quote:
2ndclass wrote:
Salvador:
quote:
There are situations where CSI may be k-simple, not k-complex.
Which is why your doubt about "whether selection favors CSI over simplicity" doesn't make much sense.
In my post at Uncommon Descent which you quote, the simplicity I was referring to was probabilistic simplicity, NOT k-simplicity. With that in mind, I think my comment will make more sense: natural selection should favor a low CSI state. I have not made any statement whether Natural Selection will favor a k-simple state.
[ 24. August 2006, 21:56: Message edited by: Salvador T. Cordova ]
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2ndclass
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posted 25. August 2006 11:25
Salvador:
quote:
I think this is incorrect because in the case of Caputo one is increasing the space of possible outcomes by having a longer string.
CSI increase assumes one is dealing with the same size space of possible outcomes, not a changing size of space. If a changing space is involved, to apply conservation of CSI one has to use Cartesian Products to define the space of possiblities.
Conservation of CSI isn't the issue. Obviously it's not conserved in the Caputo case since Caputo is an intelligent agent. The fact is that the more times Caputo cheats, the more CSI he generates. You seem to be saying that we shouldn't call this an increase in CSI, even though it obviously is.
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In my post at Uncommon Descent which you quote, the simplicity I was referring to was probabilistic simplicity, NOT k-simplicity.
So when you said "simplicity" you meant "high probability"? I've never seen the word used that way before. Have you?
Regardless, your statement still doesn't make sense. It's not doubtful that improbable selections are favored over highly probable selections; rather, it's false by definition.
[ 25. August 2006, 14:27: Message edited by: 2ndclass ]
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Salvador T. Cordova
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posted 25. August 2006 20:41
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So when you said "simplicity" you meant "high probability"?
exactly
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I've never seen the word used that way before. Have you?
Dembski uses the phrase, probabilistic complexity. See : Design by Elimination vs. Design by Comparison. When I said probabilistic simplicity that means low probabilistic complexity, and I used the phrase to help you understand what I meant. I tried to use the phrase probabilistic simplicity to help you understand the sense of simplicity being used.
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Regardless, your statement still doesn't make sense. It's not doubtful that improbable selections are favored over highly probable selections; rather, it's false by definition.
Probabilistic simplicity referred to the probability of the configuration, not the probability of selection. Selection will tend to favor low CSI states because low CSI states should be more frequent and there is less metabolic load and there is less purifying seleciton to be done. The fundamental point however, is that it has not been theoretically demonstrated selection will favor complex states. There is some evidence of the opposite.
Honestly, 2ndclass this sort of nitpicking of what I said on another forum and throwing it into this discussion on thermodynamics is derailing the conversation. I don't appreciate having to defend something I said on another forum in this thread on thermodynamics. If you feel you need to alert the readers of something I said that was wrong you're welcome to put it on another thread.
I feel I've made a good faith effort to respond to your questions even though they were off topic, but I would rather you ask such questions regarding what I said in another forum on another thread unless of course I explcitly quote from that other forum, in which case I'm the one introducing the material. I don't recall that I brought up the issue of natural selection in this thread, or that it was the focus of interest.
[ 26. August 2006, 00:54: Message edited by: Salvador T. Cordova ]
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Salvador T. Cordova
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posted 25. August 2006 21:18
quote:
2mdclass wrote:
Conservation of CSI isn't the issue. Obviously it's not conserved in the Caputo case since Caputo is an intelligent agent. The fact is that the more times Caputo cheats, the more CSI he generates. You seem to be saying that we shouldn't call this an increase in CSI, even though it obviously is.
It is exactly the issue when one says one is "increasing CSI". The phrase has a definite meaning in Dembski's literature. For example, there may be two systems: system A composed of a 2-coins string and system B composed of a 500-coin string. Increasing CSI does NOT mean going from the 2-coin string to the 500-coin string, even though the 500-coin string might have more CSI.
Caputo "copying a string" is not even the correct description of what happened in the context of ID literature. A copy of somehting suggests that we have two systems A and B with the same capacity (identical spaces of outcomes Omega). Copying A to B means making the B conform to the pattern in A. But the space Omega with regard to Caputo is treating all his trials as one complete system, and CSI is judged for that entire system.
And beyond that, the sum total of his actions evidenced high CSI, it is inappropriate to say he increased CSI.
Thus when you said:
quote:
Actually, N copies of a string has at least log2(N) bits more information than the string itself.
is not sufficiently descriptive to make statements about CSI. In ID literature, if one is talking about copies, each copy presumes to have the same space omega as the next. Thus if one has 10 500-coin strings and each string is identical and has CSI, then the CSI in each string is 500 bits. If I know in advace A = B = C = D = E = F = G = H = I = J, then if I know A, there is no uncertainty in B,C,D,E,F,G,H,I,J thus because there is no uncertainty, there can neither be a reduction of uncertainty, therefore I(B|A) = 0.
The information of A&B = I(A&B) = I(A) + I(B|A) = I(A)
Thus, in ID literature the following claim would only lead to confusion:
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N copies of a string has at least log2(N) bits more information than the string itself.
Thus the information for N copies of string A if the other strings are conditionally dependent on A is I(A), not I(A) + lgon2(N) + x, where x is some number. See No Free Lunch pages 127 and beyond.
In the case for Caputo, each pull of the arm was a priori presumed to be conditionally indepenedent, and the word copy has very strong connotations that can confuse the issue.
[ 25. August 2006, 21:28: Message edited by: Salvador T. Cordova ]
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2ndclass
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Member # 1979
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posted 28. August 2006 11:24
Salvador:
quote:
Probabilistic simplicity referred to the probability of the configuration, not the probability of selection.
The probability of the configuration is, in large part, the probability of selection, as the configuration was selected over many generations. But you're right that this is off-topic, and I apologize for the derailment.
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Increasing CSI does NOT mean going from the 2-coin string to the 500-coin string, even though the 500-coin string might have more CSI.
If "increasing CSI" has special meaning in Dembski's work, then I'll avoid the word "increasing". I think we would all agree that a 500-coin string of all heads has more CSI than a 2-coin string of all heads, and that's exactly my point. Thank you.
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Salvador T. Cordova
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posted 29. August 2006 22:42
quote:
Salvador:
quote:
Probabilistic simplicity referred to the probability of the configuration, not the probability of selection.
The probability of the configuration is, in large part, the probability of selection, as the configuration was selected over many generations. But you're right that this is off-topic, and I apologize for the derailment.
I've opened another thread on that issue, because I that is not consistent with my interpretation of what CSI is. The matter can be taken up at : Probability of configuration is not the same as the probability of selection
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Christopher D. Beling
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Member # 723
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posted 31. August 2006 04:33
Well gents let me try and get the discussion back on track by focusing in again on the meaning of randomness and CSI - I believe we need to do this to nail the 4th. Quoting 2nd class:
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W.R.T. randomness, suppose we're given a long, incompressible string. Under the algorithmic information definition of randomness, we can immediately label the string "random". But under the intuitive definition (which is the one you're advocating), we can label it random only if:
a) we happen to know that it was generated by an irreducibly random (i.e. quantum) process, or
b) we happen to know that no equivalent pattern exists in the universe.
It seems that in the posts I have been more concerned about whether a non-compressible (K-complex) string is CSI (and hence non-random + non ordered), whereas 2nd class has been more concerned about whether the non-compressible (K-complex) string is random.
I have made the above logic diagram (I am a kind of visual person – apologies) which I hope might stimulate more discussion. It really shows that both our positions (i.e. looking for CSI or randomness) are one and the same thing; since by logic a K-complex string can only be either random or CSI (and not both). Thus I express total agreement with the above quote.
Salvador
quote:
There are situations where CSI may be k-simple, not k-complex.
I fully agree and this is expressed in the above diagram where CSI spans both k-simple and k-complex. An example of k-simple CSI is:
[pi> = 11001001000011111101101010100010001000010110100011..
The first 50 bits of pi=3.14 etc as derived by a simple computer algorithm (5th miracle, Davies, p117): On the other hand an example of k-complex CSI is:
[MS2> = 010001110111010010011100110101101011101110101000010
50 bits from a portion of virus MS2 RNA. This hits a “functional life” target of making the virus “work”. I know 2nd class will not be too happy with defining specification via “functional life” – but are we agreed on the remainder? Apologies if all this is old hat or obvious. Christopher
[P.S. Incidentally for completeness sake let me offer two other strings for the above categories–
[Ordered>=10101010101010101010101010101010101010101010101010
i.e. perhaps the first 50 surface atoms of a NaC crystal, Na=1, Cl=0 (5th miracle p116) This string and others relating to physical regularities are K-simple
[Random>= 11000011010110001101111111010001100011011001110111
the sequence of 50 coin throws by Bill (p59 No Free Lunch). Since the causal events in Bill’s brain and hands when throwing were so complex (and unknown to both Bill and us) – we refer quite rightly to the sequence being haphazard and/or epistemically random]
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2ndclass
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posted 31. August 2006 14:18
Christopher, I think your diagram is right on the money, given your definition of random. And I even agree with the part about the "functional life" target.
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Christopher D. Beling
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posted 31. August 2006 21:24
Thanks, 2ndclass: I am glad we are on track together, even surprisingly on CSI being defined through “functionality”. I think I understand you. Earlier you made the statement:
quote:
In my mind, CSI entails dependencies , not necessarily usefulness.
and have always talked about a necessary (but not perhaps sufficient) qualifying condition of CSI as being its context, i.e. that “some other equivalent pattern exists in the universe”.
To clarify then take a sender “S”, a CSI package, and a receiver “R”. In cellular biology contest S=DNA, CSI=mRNA, and R=protein. Notably S and R are at different locations in the universe and CSI can be too. Your necessary condition on the CSI will be met: namely that the CSI code will find an equivalent pattern in S, and in R (after decoding). Am I on track? I am interested - as to whether you see your “contextual= found elsewhere” condition as a necessary condition for CSI or a sufficient condition? Christopher.
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Salvador T. Cordova
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posted 31. August 2006 22:17
Chris,
I think that was an excellen analysis and a good diagram. The distinguishing characteristic of CSI is that it is a binary not unary representation:
quote:
whereas the traditional understanding of information is unary, conceiving of information as a single reduction of possibilities, complex specified information is a binary form of information. Complex specified information , and specified information more generally, depends on a dual reduction of possibilities, namely a conceptual reduction (i.e., conceptual information) combined with a physical reduction (i.e., physical information ).
Unfortunately it is easy to misconstrue Dembski's sense of binary, since computer bits are "binary" but that is not the sense of his meaning of binary above.
What distinguishes CSI complexity is not whether it is k-complex or k-simple, it is whether the configurations in a physical space of possibilities is improbable. A string without at physical context cannot be CSI.
If the space of possibilities caused each outcome to be probabilistically complex, then ordered k-simple patterns would be automatically CSI.
This is where it can get a little peculiar, because, an k-simple patter may not be CSI if the underlying physical space prevented complexity.
I'll write in a subsequent post what I mean.
Salvador
[ 31. August 2006, 22:19: Message edited by: Salvador T. Cordova ]
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Salvador T. Cordova
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posted 31. August 2006 22:29
In a space of outcomes where each outcome is highly probable, one can have:
quote:
1. k-simple patterns (salt-crystal)
2. k-complex patterns??? (I can't think of an example, if any exist)
In either #1 or #2, there is no CSI.
In a highly improbable space of outcomes, where each outcome is improbable one can have:
quote:
3. k-simple patterns (all heads)
4A. k-complex specified patterns
4B. k-complex not-specified patterns
#3 is automatically CSI, #4 depends on whether an independent specification exists. 4A will evidence CSI, 4B does not.
This may seem like a peculiar way of describing the issue, but a way to conceptualize it is that #3 and #4A are (in Dembski's writings) in the same family since both are specified. Unfortunately, the human mind tends to think of #4A and #4B as being "kin" to each other.
Salvador
[ 31. August 2006, 22:31: Message edited by: Salvador T. Cordova ]
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Christopher D. Beling
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posted 01. September 2006 00:19
Salvador, This is not a reply to your above post, but to your earlier one - which I should have responded to - apologies. Let me express some my thoughts: you say:
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What is challenging with the 4th law is that specification has dependence on the observer.. .If CSI is tied to a human observers repertoire of specifications . .
Can't really agree – I am sure specification can be put on an objective footing. I have ideas about how this might be done, and as yet I have not had time to read Bill’s paper on specification. I know human CSI is dependent on the observer, but I don’t understand why for natural CSI (i.e. DNA info) this must be so?
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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.
I would really caution on such thinking. This idea of the events in the quantum world being observer dependent are all over the popular literature. To me this has to be one of the biggest hoaxes of modern times. Like Darwinism it is metaphysically driven and stems from the “logical positivism” of the Vienna Circle of the 1920s. The Copenhagen interpretation of quantum mechanics that you seem to be accepting as truth only made ground because of "logical positivism" culture into which it was born and the fact that physicists had generally become disinterested in metaphysics and had more practical concerns. Einstein never believed in the philosophy of logical positivism making him an outcast, along with Kurt Godel and his metamaths , from other great thinkers of the age - remember his famous “God does not play dice”. Believing in metaphysics (on the physics side mind you) also made him something of an outcast in physics circles too. This is one reason why Kurt and Albert were best friends at Princeton - allies in a world gone positivist. I for one tend to agree with Einstein. David Bohm for example follows Einstein to some degree in a “hidden variables” alternative in his book Wholeness and the Implicate Order. You might be interested in the fact that two of my colleagues (of excellent repute in maths) have recently found a deep mathematical set-theoretic fault with the Copenhagen Interpretation.
But to convince you let me ask a question: Before human beings were on the planet earth and there were no human observers – how could the trajectory that led to our present solar system and planet Earth have been directed? Surely all the quantum processes between particles were just happening in one big causal nexus.
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. . . how can it be that CSI also constrains the 2nd law????
I think that CSI (and 4th law) does in a sense constrain the 2nd law – but only in the sense of it being a deeper more comprehensive theory/understanding; There is a sense though in which we human beings do not having access to all CSI governing particle motion –leading us to a theory of entropy (a human construct) and its increase. I would like to develop this concept with you.
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It almost seems the universe and the laws of physics are constrained in some ways to the abilities of human observation.
Surely the simplest understanding of this is that the Great Designer, also designed our minds and that this is where the commonality between human mathematics and physical law derives?
[ 01. September 2006, 02:14: Message edited by: Christopher D. Beling ]
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