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Author
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Topic: Probability of configuration not the same as probability of selection
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Salvador T. Cordova
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Member # 959
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posted 29. August 2006 22:39
This thread is a spin off of a discussion starting at Is the 2nd Law a Special Case of the 4th Law? Post 120
and ending
Post 127
The issue was whether the definition of CSI explicitly states the probabilty of selection. I argue that it does not. CSI is defined soley by the chance hypothesis of a simple distribution. The likelihood of selection (natural or otherwise) acting on it is not inherent in the definition of CSI's metrics.
What Bill Dembski argues however, is that the simple distribution probability can be used to estimate the the likelihood a uninformed selective agency can exist to create CSI. That is the fundamental thesis of his renderings of No Free Lunch and the displacement theorem.
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2ndclass
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Member # 1979
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posted 30. August 2006 11:08
Salvador, I assume that by "simple distribution" you mean uniform, though I note that a singleton, which is the opposite entropic extreme, is also simple.
Under this assumption, I have several responses, which I'll post serially as I have time.
Response #1: Dembski takes Darwinian mechanisms into account when calculating complexity.
In his recent specification paper, Dembski describes the chance hypothesis of the bacterial flagellum:
quote:
Moreover, H, here, is the relevant chance hypothesis that takes into account Darwinian and other material mechanisms.
and
quote:
...where H, as we noted in section 6, is an evolutionary chance hypothesis that takes into account Darwinian and other material mechanisms...
Why would he take into account Darwinian mechanisms, which presumably include selection, if a uniform distribution hypothesis is sufficient?
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2ndclass
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Member # 1979
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posted 30. August 2006 11:24
Response #2: If a uniform distribution is sufficient, then complexity is ubiquitous.
Suppose we periodically observe a coin on the ground. Every time we observe it, it's heads. Under a uniform distribution, 500 such observations entail 500 bits of complexity. And since a sequence of all heads is simply described, it's specified. Thus the state of the coin over the 500 observations is designed, even though nobody has touched it.
Furthermore, why should we restrict our Omega to heads and tails? The coin could also be standing on edge, or it could have disintegrated, or turned into a leprechaun. Under a uniform distribution, all of the possibilities we can think of are equally probable, so we can attribute arbitrarily high complexity to a single observation.
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2ndclass
Member
Member # 1979
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posted 30. August 2006 12:36
Response #3: The displacement theorem assumes that the search is probabilistically independent of the target, which is usually not the case.
Suppose we stretch out a large rubber sheet over a large horizontal frame, and specify a target by placing a weight at an arbitrary location. If we place a marble on the sheet, it will quickly find the target.
The effectiveness of this search is attributable to two facts: (1) Gravity pulls stuff down, and (2) rubber bends smoothly when pressure is applied. The amount of information in these two facts is a constant, while the amount of information in the target is a function of the size of the sheet. Thus, for a large enough sheet, the amount of information in the target is greater than the amount of information that renders the search effective.
To understand how we got around the displacement problem, notice that when we specified the target, we also shaped the sheet. The fitness function (the shape of the sheet) is wholly determined by location of the target and the two facts stated above. Dembski, on the other hand, assumes that the fitness function is probabilistically independent of the location of the target. As he says in Searching Large Spaces:
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First off, it should be clear that an assisted search needs to input a substantial amount of novel information to make the search successful.
This is true, except that the information need not be novel -- it can come indirectly from the target itself.
This dependency also holds for optimization algorithms such as RM+NS, although the causal direction is opposite that of the rubber sheet example. For optimization algorithms, the fitness function, along with a threshold value, determines the target. Thus a probabilistic dependency between target and search, thus shared information.
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2ndclass
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Member # 1979
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posted 30. August 2006 13:38
Response #4: Dembski's Conservation of Information Theorem, as stated in his latest paper, applies only to Dembski's ad hoc definition of information.
In the paper referenced above, Dembski starts out by defining the information associated with a search as the surprisal associated with succeeding. Under this definition, information decreases as the effectiveness of the search increases. Noting that this is counterintuitive, Dembski then defines a different information measure, "added information", by relativizing the first measure to a baseline and negating it. Because of this negation, the new information measure increases with search effectiveness.
But what does this measure of information correspond to in the real world? Certainly not standard notions of information. For example, consider that an fitness function that is randomly selected from a uniform distribution of functions is information-rich (using standard Shannon or algorithmic definitions of information), and yet such a function will not lend itself to effective optimization searches. On the other hand, a smooth unimodal fitness function is comparatively information-poor, and yet it facilitates very effective optimization.
In order to claim conservation of information, Dembski defined information in a way that runs counter to his original definition and to standard definitions. Given such latitude to redefine terms, we could claim that anything is conserved.
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Poul Willy Eriksen
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Member # 1976
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posted 27. November 2006 10:37
2ndclass wrote:
quote:
In order to claim conservation of information, Dembski defined information in a way that runs counter to his original definition and to standard definitions. Given such latitude to redefine terms, we could claim that anything is conserved.
Hi 2ndclass;
I have been looking at the paper, and while I may agree with you, I don't think the problem so much is the chosen definition of information.
The point in Dembski's argumentation is that information should increase with sample size, and basically any monotonous transformation would do the trick.
The problem is rather, how relevant the 4th law is. Is there more information in the universe today than 13 billion years ago? There is more variation today, arrangements of atoms that didn't exist back then. In that sense, information has increased, but what has that to do with search strategies? It is assuming that the universe was some kind of search. The search for intelligent life? Since the universe is still running, apparently the search has been in vain this far ![[Big Grin]](biggrin.gif)
- pwe
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2ndclass
Member
Member # 1979
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posted 06. December 2006 09:59
pwe, you're right. Besides the fact that Dembski changed the sign on his definition of information, a more fundamental issue is his defining it in terms of a search in the first place. The problem is that he gives us no principled way to determine what processes can or cannot be modeled as searches.
Take the trajectory of the moon, for example. Given all the places in the universe that the moon could be, isn't it amazing that it occasionally ends up in a place that provides us with an eclipse? If we model the moon's motion as a search, then it's obvious that it isn't blindly sampling random locations throughout the universe. So it's an assisted search, and is therefore, according to Dembski, intelligently designed.
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GSchultz
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Member # 1953
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posted 17. December 2006 23:42
quote:
Response #2: If a uniform distribution is sufficient, then complexity is ubiquitous.
Suppose we periodically observe a coin on the ground. Every time we observe it, it's heads. Under a uniform distribution, 500 such observations entail 500 bits of complexity. And since a sequence of all heads is simply described, it's specified. Thus the state of the coin over the 500 observations is designed, even though nobody has touched it.
If we are told a priori that nobody has touched it, then we are not making 500 independent observations from any distribution; rather we are intentionally replicating one observation 500 times. That wouldn't be 500 bits of complexity. 500 separate coins on the sidewalk, all showing heads would be a different story.
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2ndclass
Member
Member # 1979
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posted 18. December 2006 13:20
GShultz: quote:
If we are told a priori that nobody has touched it, then we are not making 500 independent observations from any distribution
That's exactly my point. According to Salvador, the uniform distribution is universally applicable, which would mean that we could consider each observation to be sampled from a uniform distribution. As you point out, that doesn't make sense.
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