Häggström: Uniform distribution is a model assumption

The obvious interpretation of “no free lunch” is that no optimizer is faster, in general, than any other. This misses some very important aspects of the result, however. One might conclude that all of the optimizers are slow, because none is faster than enumeration. And one might also conclude that the unavoidable slowness derives from the perverse difficulty of the uniform distribution of test functions. Both of these conclusions would be wrong. If the distribution of functions is uniform, the optimizer’s best-so-far value is the maximum of n realizations of a uniform random variable. The probability that all n values are in the lower q fraction of the codomain is p = q^n. Exploring n = log2 p points makes the probability p that all values are in the lower q fraction. Table 1 shows n for several values of q and p. It is astonishing that in 99.99% of trials a value better than 99.999% of those in the codomain is obtained with fewer than one million evaluations. This is an average over all functions, of course. It bears mention that one of them has only the worst codomain value in its range, and another has only the best codomain value in its range.

The reader has surely realized where this is leading: the universal Pure Noise assumption implies that there is no structure at all in the universe. The question of why there is such structure, together with the closely entangled questions "Why are the laws of nature what they are?" and the deeply frightening "Why is there something rather nothing?", take us into the deepest realms of metaphysics and cosmology. But this is where we end up, given the general character of Dembski's arguments. I warmly welcome Dembski to pursue these deep and difficult questions.9 But they have little or nothing to do with the details of evolutionary biology (no more, it appears, than with, say, the Newtonian theory of gravity; cf. the elegant satire in [21]). So my final piece of advice to Dembski is that he quits pestering the biologists.

Inferring design from the presence of "active information" directly contradicts Dembski's previous paradigm. The Explanatory Filter attributes deterministic events to "necessity" rather than design, but his new approach attributes them to design. (Deterministic processes are chock full of active information -- they always hit their target with a probability of 1.)

The only null hypothesis that Dembski has ever considered in practice is uniform chance. With the "active information" approach, he gives up the pretense that other hypotheses should be considered. His previously de facto dichotomy of pure chance vs. design has now become official.

Has Häggström said where this has been submitted? I'm curious because (a) it's a reply to an unpublished manuscript, and (b) what journal wouldn't want a paper containing reference [21]?

Bob

secondclass: Inferring design from the presence of "active information" directly contradicts Dembski's previous paradigm. The Explanatory Filter attributes deterministic events to "necessity" rather than design, but his new approach attributes them to design. {snip}

Do we really need a whole paper to sum this up? I think three paragraphs would be enough.

No Free Lunch - without knowledge of the problem, then on average any search is no better than a random one.

Dembski and Marks - since it does not have intelligence (knowledge), then natural selection and mutation (search) is no better than a purely random one. A simply calculation of possible DNA shows that a random method would not result in a complex subject like a human in anywhere near a realistic timescale; hence an intelligent mechanism must be involved.

Reality - A random combination of DNA would likely not result in a viable life-form, much less one which could survive in the given environment. Mutation is very likely to result in a life-form which is similar to its parent and probably able to survive. This equates to "knowledge" of the problem in the sense of No Free Lunch, so the theory does not equate natural selection and mutation to a random method, and calculations about random methods have no relevance.

We all forget the important point that Laws Require a LawGiver.

Hasn't the entire history of science been a journey away from that presumption?

We all forget the important point that Laws Require a LawGiver.

Before I tear into the papers with some relish based on my dislike for Dembski and newfound liking for Häggström [the double ¨aut;-man :-)], I must make the following neutral observations:

- Marks is a coauthor (claims Dembski) and the D&M paper is trivially misleading of Häggströms and others models. If the authorship is real, I fear that Marks may be heading the Behe way. Pity, since he has produced a lot of research.

- Häggström makes NFL not only simple but trivial (as he notes), and his responses efficient, which is why I like his work. OTOH he inserts more of the same pseudoscience bashing in his reply that he had to take out of the original, so while I like his style as well, I can't call it efficient.

- Häggström has published his original paper and has the reply in review. Meanwhile I doubt Dembski has gotten his original published, and it seems it is the coauthorship that has gotten the reply in review.

FWIW, this is my take on the papers after quick browsing:

Häggströms papers are good, so there isn't much to discuss. He shows why a probabilistic interpretation of NFL is natural and simple. He also shows why closeness in fitness space, with few catastrophes, are natural and simple too, and how it refutes Dembski's abuse of NFL.

News for me is that one can place time changing or coevolving fitness spaces in NFL scope. Also, I hadn't appreciated how ill suited uniform probability priors are for inferences such as bayesian on large sets.

Dembski & Marks reply is remarkable however. It is based on open misdirection instead of the weasel wording used in their ev paper.

They claim that Häggström assume closeness for fitness. He is of course studying the specific process in question, and uses a trivial observation of it.

Further they claim that algorithms such as Dawkins WEASEL or Avida are based on immediate success or failure. "With no metric to determine nearness, the search landscape for such searches is binary†- either success or failure. There are no sloped hills to climb."

But it is simple to see that these algorithms use a range of fitness. For example the WEASEL fixes one letter at a time by selection, until final success. If that isn't hill climbing, what is? And what does Marks know of search algorithms?

In passing the usual and weary argument of a selected target is mentioned, easily fixed by random selection over a set of letters.

Notable is that Dembski now concedes the efficiency of selection in evolution. His analysis of WEASEL makes him conclude that "... the random search is 2.9387x10⁴¹ per cent worse than partitioned search. Partitioned search contributes an enormous amount of information."

I say again, Dembski says that the natural process of selection results in an enormous improvement in efficiency! I hope he makes that clear to his creationist supplicants.

Of course, using a new and ill formed concept of "active information" (based the same uniform prior Häggström rejects on these problems) D & M claims that Häggström supplies information.

But what they try to show is what all biologists already know about existing processes - that selection is a hill climber (and enormously efficient compared to random search) and that mutations are mostly neutral.

They will probably continue in their efforts to prove evolution's efficiency, and maybe they can find priors that works for their measure. But I must conclude as Häggström that they should quit pestering biologists and let those who have known this for 150 years continue to study new stuff instead.

Hi, I have one question. Is Tom English working for Dembski thus defending his work?

Toni,

Short answer: No. Tom told me that affiliating himself with the EIL does not constitute an endorsement of their work so far.

Torbjörn, what reply of Marks & Dembski are you referring to when you say "Dembski & Marks reply is remarkable however. It is based on open misdirection instead of the weasel wording used in their ev paper." Got a URL? Thanks!

RBH

secondclass
Thanks, he seems reasonable and unlike Dembski, he can actually discuss potential pitfalls of his work. I first noticed him over at Mark Chu-Carrol's blog.

Anyway, I've read Häggström's paper and something puzzles me: is Dembski reaching for dichotomy? Like, pure noise vs. design? He can place deist god at the beginning of the universe who set's up the rule but doesn't this mean that since universe is obviously not pure noised regardless of its origin (natural or deistic) we can't really see the different between apparent and real CSI.

Which basicly flushes CSI argument down the toilet.

They deduce, from the absence of Pure Noise, the existence of an intelligent designer, but this requires a dogmatic belief in the idea that without the latter, everything must be uniformly distributed [page 5]

Rather, his position, for the best of my attempts to make sense of it, is that in the absence of an intelligent designer, we should expect to find Pure Noise wherever we look. [page 8]

RBH, sorry for late response.

You can find Marks' and Dembski's reply from Perakh's link to Häggström's page. He is linking to Dembski's home page.

The paper in question is "Active Information in Evolutionary Search. [posted 5jun07] Paper currently under review on the mathematical foundations of intelligent design coauthored with Robert J. Marks II. This paper critiques Olle Häggström’s 2007 article in Biology and Philosophy titled “Intelligent Design and the NFL Theorems.”"

If you by any chance meant their ev paper, it has been retracted from the EIL web site. Maybe the wayback machine can help you.

TomS:

It is true that ID (at least in Dembski's latest version) is asking how the world would look without physical laws. It is equivalent to asking "why does the universe exist" because it is outside the distribution that we can observe and/or model.

According to cosmologist Sean Carroll such a question is meaningless. And philosophically it isn't more informative than asking "why not".

bump

We all forget the important point that Laws Require a LawGiver.

It is true that ID (at least in Dembski’s latest version) is asking how the world would look without physical laws.

I warmly welcome Dembski to pursue these deep and difficult questions. But they have nothing t do with the details of evolutionary biology ...

I don’t know whether the question is “tautological”

Whether or not the question is tautological, I have no opinion, and I don't want to discuss it much. However, because I did raise the point, perhaps it is only fair to say a word why I have doubts about your argument: "I am" can only be said if I am, but it doesn't seem to me to be tautological. "This is an English sentence" is true only if it is an English sentence, but that sentence isn't tautological. "This is a response", "I'm here", ... and so on.

“I am” can only be said if I am, but it doesn’t seem to me to be tautological.

“This is an English sentence” is true only if it is an English sentence

P.S. If you consider "I am" under the condition that it is stated by the entity to which "I" refers, it is tautological and parallel to "there is something", and further illustrates the silliness of the "deep" question. Consider asking "Why do I exist rather than not exist?". It's true analytically, since "I" is indexical and is meaningless if there's nothing for it to refer to. It's similar to "Why did I have my parents and not some other parents?" or "Why am I me and not you?" It helps to remember that, like "I" and "you", "something" is a pronoun, not a definite indicator.

“I’m here”

Popper's Ghost: Why is there something rather than nothing? Because it's tautological -- the question can only be asked if something exists, so the answer to the question "Does something exist" is necessarily "yes". Talk about nothingness being "more likely", even if coherent, would be mistaken in that it doesn't take conditional probability into account -- nothingness has 0 probability if something is posing the question. People talk about the Anthropic Principle as if it were something deep and special (more capitalization), but it's really a trivial tautology. There are deep questions that can be asked, such as why the universe we live in can be characterized by such a small number of relational invariants, but "why is there something rather than nothing" is not one of those deep questions.

While I appreciate your desire to quickly dismiss the deeply disturbing question of why there is something rather than nothing,

Let me point out a fatal flaw in your argument:

In particular, your argument presupposes that with positive probability, there exists something. (*)

You talk about conditioning on the event that someone asks the question. To even talk about such conditioning, we need to assume that the universe is generated by a random mechanism that places positive probability on the event that someone asks the question.

To even talk about such conditioning, we need to assume that the universe is generated by a random mechanism that places positive probability on the event that someone asks the question.

From the above, the "why is there something rather than nothing" question can be bypassed with this explanation: The set of universes is the set of possible universes; there's nothing else that "the set of universes" could sensibly mean. Since this universe is possible, it's among the set of universes (i.e., it "exists"). The only question left to answer is why we're in this universe rather than some other, or why this universe is the way it is, and we know that is answered directly by the Anthropic Principle.

But the arguments by "Heja Elfsborg" are valid. Popper's Ghost needs to catch up on some basic probability and learn what "conditional probability" means.

Regrettably, I was forced to delete the latest comment by "Popper's Ghost," posted as a reply to comment 131746, because "Popper's Ghost" resorted to a profanity in his addressing the commenter who used the moniker "Elfsborg stinks."

Thanks you Mr Perakh for keeping it clean! I suppose profanity is the only resort for somebody who throws out "conditional probability" and gets called on its definition.

Popper's Ghost -- Although you do not seem to be the kind of person who will get around to explicitly admitting error, it nevertheless seems to me that my comment to you has not been in vain, because in your later postings you have backed off from all use of probabilistic language in your argument. That is an improvement.

But your argument still has serious shortcomings. A very useful device for judging the validity of a philosophical argument is to apply it to a more familiar situation and see where it leads. In that spirit, consider the following three exchanges:

Q1: Why was John F Kennedy killed?
A1: If he hadn't been killed, you would never have thought of asking this question, so the mere fact that you're asking it shows that he was killed, and there is nothing more to say about this issue.

Q2: Why did the dinosaurs go extinct?
A2: Well, if they hadn't, then you wouldn't have asked. This shows that the dinosuars did go extinct, thus answering your question fully.

Q3: Why is there something rather than nothing?
A3: If there was nothing, then in particular you would not have been around to ask the question. Hence, there exists something. This simple deduction settles the matter, and nothing more needs to be said.

I am sure you agree that answers A1 and A2 are highly unsatisfactory. But answer A3 uses the exact same kind of reasoning, so we must conclude that also A3 is unsatisfactory.

[A possible attempt at this point to distinguish Q3 from Q1 and Q2 would be to note that that me may still conceive of a situation where questions Q1 and Q2 are asked in spite of both JFK and dinosaurs still being alive, while if nothing exists there is absolutely no way that that Q3 can be asked. To counter this objection, let me replace "ask" by "askh" in the above exchanges, where "askh" is defined to mean "pose a meaningful question". Then the discrepancy between Q1/Q2 and Q3 disappears. Also, it seems to me unlikely that replacing "ask" by "askh" in your argument would change its validity, because it would be extraordinarily surprising if it turned out that our capacity to ask meaningsless questions turned out relevant to deep metaphysical issues.]

It seems to me that the mistake you make is a misunderstanding of what the word "why" means. Suppose we observe an event B, and ask "why B?". What we mean by this is that we want an explanation for how B came about from circumstances not including B. If the explanation involves "because of B" or "because we observed B", then it is circular, and not a valid answer to the "why" question.

Specifically, let B be the event that something exists. In the later version of your argument, where you replaced probability by possibility, a key step was your claim that B is possible. But your argument for why B is possible is that we have observed the event B. This is very much the same kind of circularity as in your earlier, probabilistic, version of your argument.