Freethought & Rationalism Archive

Principia · 11-14-2002, 08:55 PM

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Topics addressed in the field of philosophy fall into two categories. In the first category are topics that have not (yet) been subjected to a broad yet rigorous mathematical formalization. Accordingly, they are "just word arguments", and have not benefitted from the clarity and power that mathematical precision affords. Examples of topics in this first category are philosophies of art, music, and literature, as well as much of ethics, and other parts of the humanities. By contrast, topics in the second category have been formalized, in a form generally perceived as capturing much of their essence. Such topics include much of what several centuries ago was called "natural philosophy" and is now collectively known as "science". This category also includes those issues in epistemology that were addressed by G�del's incompleteness theorem and related uncomputability results.

In the past several years the issue of whether "inductive inference can justify inductive inference", puzzled over since at least the time of Hume, has migrated from the first category to the second. First in the context of supervised learning (D. H. Wolpert, Neural Comput. (1996), 7:1341; Neural Comput. (1996),7:1391) (what in statistics is called "regression" or "classification"), and later in the context of search algorithms (D. H. Wolpert and W. G. Macready, IEEE Trans. Evol. Comput. 1 (1997),1:67), a body of results has been developed that quantify exactly how and when such induction-justifies-induction can(not) hold. Moreover, this formalization has generated results extending far beyond the original philosophical topic that formed its seed (just as happens with any other formalization of a philosophical topic). These results can be viewed as an extension of traditional Bayesian analysis, into a fully model-independent "geometry of induction". Once factors like the precise inductive algorithm to be used, and the prior probabilities and associated likelihood functions of the problem at hand are specified, the theorems of this geometry tell us what the associated performance of that algorithm is, and how it relates to performance levels that accompany different settings of those factors.

In this book, Dembski attempts to turn this category-change trick for the quasi-philosophical topic of whether "intelligent design" is a legitimate alternative to neo-Darwinism. Central to his approach is an attempt to leverage the recent formalization of the induction-justifies-induction topic. In particular, he relies on some of the "No-Free-Lunch (NFL) theorems" of the geometry of induction. These theorems, loosely speaking, say that the performance-weighted measure of domains in which some search algorithm A beats some contender algorithm B exactly equals the measure of domains for which the reverse is true. So, for example, in attempting to find a high point on a surface, a hill-ascending algorithm will perform no better than random search, and in fact no better than a hill-descending algorithm, over the space of all surfaces one might search. In short, according to these theorems there is no free lunch; without tailoring one's algorithm to the domain at hand, one has no assurances that that algorithm will perform well on that domain.

I say Dembski "attempts to" turn this trick because despite his invoking the NFL theorems, his arguments are fatally informal and imprecise. Like monographs on any philosophical topic in the first category, Dembski's is written in jello. There simply is not enough that is firm in his text, not sufficient precision of formulation, to allow one to declare unambiguously `right' or `wrong' when reading through the argument. All one can do is squint, furrow one's brows, and then shrug.

Nonetheless, there are several points intimately related to Dembski's work that bear emphasizing. First, biologists in particular and scientists in general are horribly confused defenders of their field. When responding to attacks from non-scientists, rather than attempt the rigor that the geometry of induction and similar bodies of statistics provide, they fall back on Popperian incantations, trying to browbeat their opponents into acceding to the homily that if one follows certain magic rituals---the vaunted "scientific method"---then one is rewarded with The Truth. No mathematically precise derivation of these rituals from first principles is provided. The "scientific method" is treated as a first-category topic, opening it up to all kinds of attack. In particular, in defending neo-Darwinism, no admission is allowed that different scientific disciplines simply cannot reach the same level of certainty in their conclusions due to intrinsic differences in the accessibility of the domains they study.

This intrinsic lower certainty of neo-Darwinism than (for example) that of quantum electrodynamics means that there is legitimate room for disputation concerning the history of biology on Earth. So if Dembski had managed to use the geometry of induction properly to quantify that some search algorithm occurring in the biological world had, somehow, worked better than all but the fraction 10^-50 (say) of alternative algorithms, then there would be a major mystery concerning the modern biological mantra. This would be true regardless of whether neo-Darwinists had performed the proper rituals in settling on that mantra.

However, Dembski does not do this. The values of the factors arising in the NFL theorems are never properly specified in his analysis. More generally, no consideration is given to whether some of the free lunches in the geometry of induction might be more relevant than the NFL theorems (e.g., those free lunches concerning "head-to-head minimax" distinctions that concern pairs of algorithms considered together rather than single algorithms considered in isolation).

Indeed, throughout there is a marked elision of the formal details of the biological processes under consideration. Perhaps the most glaring example of this is that neo-Darwinian evolution of ecosystems does not involve a set of genomes all searching the same, fixed fitness function, the situation considered by the NFL theorems. Rather it is a co-evolutionary process. Roughly speaking, as each genome changes from one generation to the next, it modifies the surfaces that the other genomes are searching. And recent results indicate that NFL results do not hold in co-evolution.

It may well be that there is a major mystery underlying the performance of some search processes that one might impute to the historical transformations of ecosystems. But Dembski has not established this, not by a long shot.

-David Wolpert

Link: <a href="http://www.ams.org/msnmain?fmt=doc&fn=105&id=188409411&l=100&pg3=ICN& r=1&s3=dembski" target="_blank">http://www.ams.org/msnmain?fmt=doc&fn=105&id=188409411&l=100&pg3=ICN& r=1&s3=dembski</a>
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[ November 14, 2002: Message edited by: Principia ]

lpetrich · 11-14-2002, 10:04 PM

Interesting comments. And as one critic notes, real-world fitness functions are not an absolutely random selection of possible fitness functions. It would be interesting to work out mathematically the range of possible shapes of fitness functions; that would likely be easiest with biochemical ones like enzyme-performance functions.

Also, Dembski does not seem to have applied his theorizing very much; he's mentioned bacterial flagella and beaver dam-building, but that's about it.

Principia · 11-15-2002, 07:38 AM

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Also, Dembski does not seem to have applied his theorizing very much; he's mentioned bacterial flagella and beaver dam-building, but that's about it.

Dembski continues his cowardly retreat. It is becoming rapidly clear to me that he uses "his great mass of words," much like Philip Johnson would, to obscure his absolute ignorance of evolutionary biology. For instance, if his argument is neither mathematically formal, nor correctly applies Wolpert's NFL theorems, what else does his Explanatory Filter stand on besides an argument from ignorance? Taking a look at his website, I can't help but notice that the only things going for him are his prolific writings that polemicize Darwinian evolution.

From Dembski, <a href="http://www.arn.org/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=13;t=000428" target="_blank">here</a>:

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Perhaps it's not surprising that critics see my book as depending crucially on the NFL theorems (given my title it might seem the theorems have to be right and applicable across all of biology for my conclusions to hold). But in fact, my key point concerns displacement (the shifting of specified complexity from one place to another -- in the case of evolutionary theorists like Tom Schneider usually unwittingly), and the NFL theorems simply exemplify one instance (not the general case). Indeed, the core idea of chapter 4 of NFL was in my head before I had even heard of the NFL theorems.

And then from Dembski, <a href="http://www.designinference.com/documents/2002.08.Erik_Response.htm" target="_blank">here</a>:

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Erik's biggest mistake, and one responsible for many of his more particular mistakes, is trying to cast my project as one of pure mathematics. It's not and never was intended to be. That's why I write about making an "in-principle mathematical argument" about the inability of material mechanisms to generate specified complexity rather than about a "strict mathematical proof." That's also why Erik constantly has to use scare quotes and qualifiers (he particularly likes the mitigating prefix "quasi-") in describing the mathematical aspects of my work. Thus Erik characterizes my project in No Free Lunch as providing "a subjective quasi-mathematical 'formalization'" and then applying "this 'formalization'" to biology (note the scare quotes around "formalization").

I'm not and never have been in the business of offering a strict mathematical proof for the inability of material mechanisms to generate specified complexity in the same way that no physicist is in the business of offering a strict mathematical proof for the conservation of energy. Mathematics certainly comes into the picture in both instances and is crucial in justifying these claims, but there are empirical and nonmathematical considerations that come into play as well and that make strict mathematical proof not feasible (and perhaps not even desirable).

EDIT: I will be waiting for Dembski's response which I am sure will be great material for another thread about ID whining.

[ November 15, 2002: Message edited by: Principia ]

KC · 11-15-2002, 08:06 AM

Quote:

Originally posted by Principia:


EDIT: I will be waiting for Dembski's response which I am sure will be great material for another thread about ID whining.

[ November 15, 2002: Message edited by: Principia ]

"I'm afraid on this one I'm going to trust the math over the biology" --William Dembski

Cheers,

KC

Principia · 11-15-2002, 02:27 PM

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"I'm afraid on this one I'm going to trust the math over the biology" --William Dembski

Hey, I've been trying to hunt down the source of that Dembski quote. Does anybody have it?

Thanks!

Uzzah · 11-15-2002, 08:45 PM

I have a question as a non-science type of guy. Where's the football?

Uzzah

theyeti · 11-16-2002, 10:27 AM

Quote:

Originally posted by Principia:


Hey, I've been trying to hunt down the source of that Dembski quote. Does anybody have it?

Thanks!

It's in NFL. I don't have a copy so I can't say which page number, but it's in the section where he talks about URF-13, which is a functional protein that was recently generated from a random sequence in maize. Dembski is pointing out for us why CSI is nothing but an exercise in question-begging.

See this <a href="http://www.arn.org/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=1;t=001828" target="_blank">ARN thread</a> for some commentary.

theyeti

scigirl · 11-16-2002, 10:48 AM

Quote:

Originally posted by Uzzah:
I have a question as a non-science type of guy. Where's the football?

Uzzah

Haha Uzzah, I think the same thing every time I see an "NFL" thread!

Go Broncos!

scigirl

lpetrich · 11-16-2002, 11:00 AM

I think that anyone discussing the "NFL theorems" ought to mention that these are "No Free Lunch" theorems and not "National Football League" ones.

Principia · 11-16-2002, 02:16 PM

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theyeti: It's in NFL. I don't have a copy so I can't say which page number, but it's in the section where he talks about URF-13, which is a functional protein that was recently generated from a random sequence in maize. Dembski is pointing out for us why CSI is nothing but an exercise in question-begging.

Hey thanks. I found the quote in ARN's archives (there is good stuff in there -- plenty of ammo to use against IDiots). Apparently, the quote came from a personal email from Dembski:

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Thanks for your note. I had been alerted to T-urf13 previously, but it finally became clear just why this is supposed to pose a challenge. The knock out punch is supposed to be this: "The gene that encodes URF13, T-urf13, was produced from recombination of NON-PROTEIN-CODING gene segments only." There's no reason, however, to think that non-protein coding gene segments are truly random. Indeed, a lot of junk DNA probably was at some point coding DNA. It seems to me that T-urf13 is simply CSI that had gone underground and now has been reconstituted. I would need more of the details, but the mathematics behind CSI is clear -- you can't get it via chance and necessity. I'm afraid on this one I'm going to trust the math over the biology.

The link is broken in the ARN thread above (probably a post Ides crash thing). Here it is:
<a href="http://www.arn.org/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=1;t=000066" target="_blank">http://www.arn.org/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=1;t=000066</a>

EDIT: Incidentally, let's compare Dembski's quote above with that of his peer, <a href="http://www.arn.org/ubb/ultimatebb.php?ubb=get_topic;f=13;t=000439;p=1" target="_blank">Mr. Superbrains</a>:

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Langan: For example, in this thread, we have at least a couple of self-avowed scientists, if we may call them that in their glorious defiance of logic, who think that one can pull logic and scientific reality apart and examine them separately. Of course, that�s beyond asinine; because meaningful examination itself requires logic, one can�t examine anything once logic has been excluded from it. As soon as they call themselves "scientists", they sign on the dotted line and indebt themselves to logic in every way, shape and form. But in - you guessed it - glorious defiance of logic, we instead see them claiming, in apparent contempt of biology to boot, that the emergence of chickens had nothing to do with the reproductive DNA of their parents...or at least that one can�t successfully apply this fact to the chicken-or-egg problem even though logic and biology say unequivocally that one can.

Once somebody decides that logic is too heavy a piece of baggage to carry into a battle of ideas, there is no longer any reason to think that he can be reached by rational means. Obviously, this makes it a waste of time to argue with him. Everything comes down to pure negative emotion...e.g. his resentment of theism, his irreverence toward any hint of intellectual authority, or his angry rebellion against the abhorrent necessity of occasionally following orderly rules of thought and discourse.

Math is to Dembski as Logic is to Langan??

[ November 16, 2002: Message edited by: Principia ]

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11-14-2002, 10:04 PM	#2
lpetrich Contributor Join Date: Jul 2000 Location: Lebanon, OR, USA Posts: 16,829	Interesting comments. And as one critic notes, real-world fitness functions are not an absolutely random selection of possible fitness functions. It would be interesting to work out mathematically the range of possible shapes of fitness functions; that would likely be easiest with biochemical ones like enzyme-performance functions. Also, Dembski does not seem to have applied his theorizing very much; he's mentioned bacterial flagella and beaver dam-building, but that's about it.

11-15-2002, 08:45 PM	#6
Uzzah Regular Member Join Date: Oct 2002 Location: Tennessee Posts: 196	I have a question as a non-science type of guy. Where's the football? Uzzah

11-16-2002, 11:00 AM	#9
lpetrich Contributor Join Date: Jul 2000 Location: Lebanon, OR, USA Posts: 16,829	I think that anyone discussing the "NFL theorems" ought to mention that these are "No Free Lunch" theorems and not "National Football League" ones.

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