|
Author
|
Topic: Searching Large Spaces
|
|
|
Salvador T. Cordova
Member
Member # 959
|
posted 09. March 2005 15:56
Bill,
Although I know you know this and you covered it in your books, and you are aware of Yockey and Axe's, just for your protection, the example target of 20^100 for a protein might get some criticism.
The rejection region for the functional protein occupies a larger target than just one sequence in most proteins. The rejection region may occupy thousands if not millions of sequences.
We do know it is small relative to the entire space, and I'm aware that your other works account for this. The number of functional sequences for a protein of length 100 is not 1 sequence but some number much larger. You actually accounted for that in Section 5.10 of you book "No Free Lunch", and perhaps phrasing it in those terms (as you did in your book) for a protein of length say 300 and then accounting for the improbability of a functional sequence will get you the numbers you are looking for.
Notwithstanding that, I just don't want critics having an opportunity to get a cheap shot on your first paragraph. Perhaps a little rewording can buy you a little insurance from such attacks.
Congratulations by the way on the Trotter prize.
Salvador
[ 09. March 2005, 16:03: Message edited by: Salvador T. Cordova ]
IP: Logged
|
|
Salvador T. Cordova
Member
Member # 959
|
posted 09. March 2005 16:34
Bill,
With respect to the uniform random sampling, you pointed this out:
quote:
Do any of these higherlevel
probabilities induce the nonuniform probability that characterizes effective
search of the original search space? What stochastic mechanisms might induce
such higher-level probabilities?
For any interesting instances of biological evolution, we don’t know the answer
to these questions. But suppose we could answer these questions. As
soon as we could, the No Free Lunch Regress would kick in, applying to the
larger environment once its probabilistic structure becomes evident. And so,
this probabilistic structure would itself require explanation in terms of stochastic
mechanisms. On the other hand, lacking answers to these questions, we
lack a stochastic mechanism to explain the nonuniform probabilities (and corresponding
assisted searches) that the larger environment is supposed to induce
and that makes effective search of the original space possible. In either case,
the No Free Lunch Regress blocks our attempts to account for assisted searches
in terms of stochastic mechanisms.
The degree that non-uniformity in sampling improves the search is correlated to the coincidental information in the non-uniform sampling strategy. Meaning, a uniform sampling strategy has low information content. A non-uniform sampling strategy has higher information content.
One may complain the uniform sampling as helping your case, but I think your counter is to show that the degree of correlation between the search improvement and the sampling strategy is the degree of informaton (complexity) in the sampling strategy. That in itself is a form of information displacement and results also in a regress problem (what caused the non-uniform sampling strategy?).
Dean Kenyon actually hope for something similar with Bio-Chemical Predestination, where the search was improved somehow by physical law. If such a law had existed, that would have constituted displacement, not to mention, as Bradley, Thaxton, and Olsen pointed out in their book Mystery of Life's Origin, it would negate the information bearing capacity of the polymers, the polymers would be like salt crystals. In essense Kenyon was hoping the structure of the space of possibilites Omega, was really smaller than all the combinatorial possibilities, because of physical law. If that were the case however, physical law would have been information rich, and as Chaitin has shown independently, it is not.
One way also to negate such complaints is to extend by way of analogy the example of a long string of coins:
quote:
H T H H H T T H T H H T T T T H T H H H....
If the string, the target is Kolmogorov Complex, that the distribution of coins is 50 head and 50% tails, then it can be shown any non uniform probability such as an unfair coin of say 70% head and 30% tails does not help the probability of hitting the target string.
By way of extentsion (and I'm only giving the sketchiest of details), one can see that if the targets are K-complex in a certain way, then the uniform distribution is the optimal, best case, distribution. And thus your conclusions hold for such cases without much further argument.
I know I'm not being tremendously clear, but I hope the gist of what I'm saying might be useful at some later date. My contribution here is just a drop in the bucket to the fine and substantive work your paper offers.
Salvador
[ 09. March 2005, 17:50: Message edited by: Salvador T. Cordova ]
IP: Logged
|
|
William A. Dembski
Member
Member # 7
|
posted 09. March 2005 21:35
Thanks Sal. I'm planning a follow-up paper on nonuniformity, specification, and Bayesian displacement. I expect your concerns will be addressed in it. --Bill
IP: Logged
|
|
David L. Hagen
Member
Member # 323
|
posted 14. March 2005 22:13
On the other side of Sal's comments, may I suggest adding a caveat noting that you are only addressing the relatively small "small" simple probabilities of the amino acid sequences, and not the greater probabilities and vastly more complex real life issue of protein folding. e.g., see:
http://folding.stanford.edu/papers/Nina-MSM-JCP-2004.pdf
Some sequences of folds self assemble into larger structures (crystal like). Conversely, one or more misfolds can cause numerous diseases such as "Alzheimer's, Mad Cow (BSE), CJD, ALS, Huntington's, and Parkinson's disease." See http://folding.stanford.edu/
"Normal" real life proteins must be found within a very complex protein folding space, some of which self assemble, some of which do not, and some 'misfolds' which seriously degrade or destroy functionality or host viability and must be excluded (or they are "selected" out.)
IP: Logged
|
|
Art
Member
Member # 179
|
posted 14. March 2005 22:47
With respect to David's remarks, issues discussed in the OP of this thread on ISCID bring to the picture a fascinating Darwinian, low-information approach to the "problems" that are mentioned.
It's probably best to think of the matter of protein functionality as a convergence of two different aspects of polypeptides - attaining a survivable fold (governed by molecular Darwinian processes) and acquiring specific functionality (via specific, albeit rather small, sequence motifs). Rather than the 20 amino acid alphabet, it would be interesting to try and think in terms of functional elements (folds, motifs, etc).
IP: Logged
|
|
Salvador T. Cordova
Member
Member # 959
|
posted 15. March 2005 14:04
I have yet to hear any criticisms of the mathemtical derivations. ![[Wink]](wink.gif)
I will await the helpful work of math professors to iron out any possible kinks in the execution of the math, but I'm confident, however the final results are materially correct.
The Fundamental Theorem of Calculus was in use for 200-300 years before Riemann proved it rigorously, I see the same situation for the Fundamental Theorem of Intelligent Design.
I have seen the theorem play out in specific instances, but the task of formally generalizing the results was obviously a huge undertaking as is demonstrated by some 90 pages of spread out to 3 papers, with this being the 3rd.
One consequence of the Fundamental Theorem is not readily obvious.
If natural selection infuses biotic reality with CSI, the selection pressures and "random variations" must also contain CSI.
For example, when you hear the "hiss" of white noise, is it really noise or is it information (like that found in the "hiss" of and encoded in a modem or fax signal)?? It is sufficient to say the supposed "white noise" is actually informational when one sees the final result, such as a successful fax transmission. If you can take this "white noise" and with a simple transformation, demonstrate it contains data then one realizes it is not noise, but information. The supposed stochastic entity is not a random process after all, but a carefully crafted one. Yet superficially the two entities seem indistinguishable, save for the fact one can be decoded.
One realizes that for natural selection to create biotic reality, it would have to be extra-ordinarily fine tuned, that the appearance of non-design in the selection forces is an illuion, much like hearing a modem signal gives the illusion of white noise. So Darwinism is refuted at least in the sense that if natural selection acting on "random variation" would have to be fine tuned, not to mention the "random variation" would also have to be fine tuned (in the sense that it only appears to be "white noise" but is in fact a well-crafted signal).
But then again, perhaps neither are fine tuned, and both are actually noise.
Thus, in either case, intelligence is at least an adequate explanation, though many reject that because they don't believe such an intelligence could possibly exist. From a scientific standpoint, I offer it as a hypothesis that an Intelligence was responsible for life.
It shows, as Barrow demonstrated for Quantum Mechanics at the cosmological scale, that there is also an information regress to an intelligence at the biological scale.
It was hard actually to look at a biological system like say the transcription mechanisms in eukaryotes and be able to declare formally whether it is designed, just by lookiing at it's arrangement, not knowing what the exact details of it's origin are. The theorem makes the analysis very easy and leads us to realize if natural selection and random variation were involved, they would have to be extremely well coordinated.
However, we can hypothesize that they are not coordinated, that they are indeed stochastically random signals. This leads to the empirically falsifiable claim that CSI will be steadily deteriorating in biotic reality. Creating metrics to establish this will be challenging, but a rote obvservation of the number of extinctions and the rise of genetic deterioration is consistent with that claim.
Salvador
[ 16. March 2005, 11:58: Message edited by: Salvador T. Cordova ]
IP: Logged
|
|
Salvador T. Cordova
Member
Member # 959
|
posted 21. March 2005 20:23
Bill,
quote:
You wrote:
Note that by a stochastic mechanism, here,
I mean any causal process governed exclusively by the interplay between chance
and necessity and characterized by unbroken deterministic and nondeterministic
laws.
Minor, minor point which I offer as a point of clairfication to pre-empt your less friendly critics from pretending they found a counter example to your work.
Your work is fine, but I think it would help if you address this at least somewhere in your writings.
If a polymer of the form S, where S is like the polymer of the dimensions you describe in your first paragraph where it's improbability is 1/20^100, in a sense, if we find a string say SS, the improbability is 1 / 20^(100*2), and the improbility of SSS is 1/20^(100*3) etc...
Clearly, your calculations would hold for a purely stochastic process. My concern is your critics will claim then a mix of simple deterministic process (Elsberry and Shallit use the phrase "simple computational process") and a stochastic process will account for very large improbailities of the form 1/20^(100*N) for N repeats, and they might claim the supposedly found a counter example to your work. In fact I can hear, Elsberry and Shallit saying their old SAI examples serve as counter examples to your theorem. I clearly see that such examples would not be a counter example because your paper deals with stochastic processes, not algorithmic or deterministic processes...
However, the forseen problems are easily remedied by saying if a combination of an algorithmic and stochastic process is suspected to be at work creating large alogrithmically compressible strings, one only need consider the number of bits in smallest compressed string. Or, also, physical objects may not achieve function if they are not in a digitally uncompressed state (i.e. certain numbers of repeats in DNA control regions, etc.).
There are other ways we can deal with such complaints, but I thought I would bring it to your attention first. I'm confident your work still stands, but in the spirit of brainstorms, I think this is possible kink we need to iron out.
Salvador
[ 21. March 2005, 21:04: Message edited by: Salvador T. Cordova ]
IP: Logged
|
|
William A. Dembski
Member
Member # 7
|
posted 21. March 2005 21:58
Dear Salvador,
Stochastic processes (which I am using interchangeably with stochastic mechanisms) constitute a very general mathematical object and subsume computational processes. Indeed, any deterministic process, nondeterministic process, or mix of the two, insofar as these can be captured mathematically at all, are captured by stochastic processes. Have a look, for instance, at the two volumes on stochastic processes by Karlin and Taylor.
Best regards,
Bill
IP: Logged
|
|
|
Printer-friendly view of this topic