# Häggström: Uniform distribution is a model assumption

On a few occasions Dembski lamented that his critics are usually not mathematicians and hence are not really qualified to debate his mathematical exercise. Recently two professional mathematicians - Olle H�ggstr�m and Peter Olofsson, both highly qualified experts in math statistics and related fields, published essays showing serious faults in Dembski’s mathematical output. Dembski and Marks responded with an article where they attempted to refute Olle’s arguments. While some replies to Dembski and Marks have already been posted, a reply from Olle himself was expected. I am glad to inform PT visitors that Olle’s reply to Dembski and Marks has appeared here. I think Olle succeeded admirably to reveal the emptiness of Dembski-Marks’s arguments.

It is also relevant in this context to remind the readers that under NFL, search is trivial. One of the recent additions to Dembski and Marks’ so called ‘lab’ is Tom English who has shown that random search is extremely trivial

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.

Thomas M. English Evaluation of Evolutionary and Genetic Optimizers: No Free Lunch Evolutionary Programming V: Proceedings of the Fifth Annual Conference on Evolutionary Programming, L. J. Fogel, P. J. Angeline, and T Bäck, Eds., pp. 163-169. Cambridge, Mass: MIT Press, 1996.

Seems that one of the lab’s collaborators disagrees strongly with Dembski’s interpretations as well. This is going to be interesting.

I love the conclusion which states

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.

[21] The Onion (2005) Evangelical scientists refute gravity with new ‘intelligent falling’ theory, August 17.

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 H�ggstr�m 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}

We all forget the important point that Laws Require a LawGiver. Things are “necessary” IFF they are designed that way.

Dr. Dr. Dembski is merely explictly including this previously implicit axiom. (It’s been a while, is “axiom” the correct mathematical term?)

fusilier James 2:24

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.

Nope, all it requires is a law maker. Laws are just abstractions of regularities in nature.

Before I tear into the papers with some relish based on my dislike for Dembski and newfound liking for H�ggstr�m [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 H�ggstr�ms 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.

- H�ggstr�m 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.

- H�ggstr�m 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:

H�ggstr�ms 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 H�ggstr�m 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 H�ggstr�m rejects on these problems) D & M claims that H�ggstr�m 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 H�ggstr�m 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.

Torbj�rn, 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 H�ggstr�m’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.

Following up on Toni Petrina’s remarks.

H�ggstr�m’s paper has a couple of comments:

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]

First of all, the readers deserve a response from the advocates of ID as to whether this is a correct interpretation of the use of the NFL theorem to support ID.

And then, whatever the correct interpretation, there is Toni’s question. What distribution does ID suggest? Even if evolution is not an adequate search algorithm, does that mean that ID is? What reason is there to believe that an intelligent designer would change the distribution from Pure Noise to a distribution that allows something-or-other to perform a better search? And what is that something-or-other search algorithm?

And I would suggest, beyond this, that ID appears to present even a worse situation than the natural case. On the naturalistic assumption, we are able to limit the V set to physically possible states. For example, to the DNA sequences of equation (1). The point of having an ID is to go beyond mere physical limitations. An ID, even if it is not literally omnipotent, is at least more “potent” than nature. And we can add to that that the ID is not limited to designing things according to their reproductive fitness. Living things which are not “fit” will survive, if the ID decides that they will survive. If the ID is limited to designing things according to fitness, then there is nothing for the ID to do.

To summarize:

Evolution is not an inadequate search algorithm.

If evolution were an inadequate search algorithm, that does not mean that ID is an adequate search algorithm.

ID presents a worse case for a search algorithm to work with.

RBH, sorry for late response.

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.

I notice that some religious and woo woo people like to capitalize certain words as if that made their referents more real. I think this both reflects and reinforces their irrational pathology. To put it in familiar terms, I don’t think that word means what you think it means. “law: … 15. (in philosophy, science, etc.) a. a statement of a relation or sequence of phenomena invariable under the same conditions.”

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

Physical laws are elements of physical theory. The way the world would look without physical laws is how it looked before we started to do science, and how it looks to those who are scientifically illiterate. And if we’re talking about how a world containing an unconstrained deity would look – imagine a 2-year old’s room after she’s thrown a temper tantrum, only infinitely messier, for one possibility (of infinitely many).

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.

Why is there something rather than nothing? Häggström’s paper does actually mention that question (on page 9), and suggests:

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”, but I do know that ID is no better at answering it than it is at answering simpler questions like “What does an intelligent design result in?” or “When did intelligent designs take place?”. Of course, ID is not in the business of answering questions.

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

I just explained why it is. Feel free to point out an error in my reasoning, or provide a counterexample by describing a possible world in which the statement “there is something” can be stated yet is false.

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.

No, “I am” can be said by a tape recording of someone long dead, for instance.

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

A tautology is a logical necessity. The truth of your sentence is only true contingent on the facts about English. Someday English might change and your sentence will no longer be true.

But that’s ok, most people are as incredibly inept at logical thinking as you are.

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.

P.P.S.

“I’m here”

It’s very odd to me that you don’t consider this tautological, since it seems to be equivalent to “I am where I am”.

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, things are not quite as simple as you suggest. You can use (sound versions of) the Anthropic Principle to deduce THAT something exists, but not WHY that is the case. Let me point out a fatal flaw in your argument:

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. In particular, your argument presupposes that

with positive probability, there exists something. (*)

Now, why (*) is true? This seems to me just as deep and difficult a question as the original one. You can try applying your conditioning argument again, but that would again presuppose (*), so the circularity of your argument becomes evident.

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

I don’t appreciate the ad hominem. My desires, which you have mischaracterized, are irrelevant.

Let me point out a fatal flaw in your argument:

Your gibberish does no such thing.

In particular, your argument presupposes that

with positive probability, there exists something. (*)

I presupposed no such thing. It’s a simple subjunctive: If there is nothing, the question won’t get asked. This neither presupposes there is something nor that there isn’t.

As I said, don’t feel bad, as most people are incredibly inept at logical thinking.

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.

I really don’t know where you got this nonsense; it looks like a flat out fallacy of affirmation of the consequent. It’s quite possible for there to be something without anyone ever asking the question; that was the case in this universe until recently, and in an infinity of other possible universes it’s always the case.

There are deep foundational linguistic (or philosophical, but virtually all valid philosophical questions are linguistic) questions, like what do “exist” or “is” (no reference to Clinton intended) or “real” or “universe” mean, that need to be grappled with before one can fully comprehend why the “why is there something rather than nothing” question is off base. First one must recognize that “exist” only applies properly to sets, not individuals; unicorns don’t exist, but there is no unicorn that doesn’t exist. (This may be difficult to follow for non-native speakers of English, but it’s the only language I speak, so I have to use it.) Then one must recognize that, say, cows exist in a sense different from integer solutions of a^2 + b^2 = c^2 exist. Cows are “real”. So “something exists” seems to mean “The set of real things is non-empty”. But philosophers such as David Lewis have argued that “real” is indexical; it refers to this universe specifically, and since this universe is comprised of what it contains, “the set of real things” is non-empty by definition (of “real”). So then we get to the question “why are there universes”, but then we need to understand what the heck we mean by “universe”. If “universe” just means “everything there is”, then the question is circular. And if it doesn’t, then what does it mean? Physicists have a notion of “universe” that is a closed lawful system, but what’s a “system”? it seems to be a mathematical abstraction. What’s the difference between an arbitrary abstract virtual universe and our “real” universe? That gets back to “real” being indexical; there isn’t any essential difference. When one tries hard to do a semantic analysis of the language, it seems to always come out circular – which is another way in which it is tautological. It’s hard to give “real” any useful semantic content, but one metaphysical model that attempts to solve the problem is modal realism.

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.

This really points to a quite different question: what are there people to ask the question? But the answer to that is well known, especially at this site: historical contingency. And as is well known, Daniel Dennett has argued that it is somewhat inevitable, while Stephen Jay Gould has argued that it isn’t. But this is an empirical question, not a metaphysical one.

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.