FINAL DRAFT: for PHILOSOPHICAL BOOKS

to Gregory Mulhauser's review of DARWIN'S DANGEROUS IDEA

It is a pleasure to respond to such clear, constructive criticism. I will comment on five minor points raised by Mulhauser, and then turn to his major criticisms.

(1) I am grateful for the information about von Schilcher and Tennant's book, which unaccountably had not crossed my path before. I am not the only author to have overlooked it, and a cursory reading shows that it does anticipate points in many more recent books, including my own. And Mulhauser is right that Sampson and Montague would have been valuable allies had I developed my critique of Chomsky further--but that is a tangential issue in an overlong book.

(2) Do Skinnerian creatures "contemplate" their past errors? Only, as Mulhauser says, "on a very broad meaning," which is all that I intended: there must be some surviving trace of any past error so that the system has something relevant to adjust. The way I put it was indeed misleading, and I have taken steps to clarify the issue in my new book, Kinds of Minds (Basic Books and Weidenfeld and Nicholson, 1996), in which I also have more to say about the coevolution of memes and minds.

(3) My understanding of "algorithm" is not, I think, shifting but fixed throughout the book: the set of all Turing machines. Mulhauser suggests that this cannot be my meaning, since I say we can "treat any physical process at the abstract level as an algorithmic process." I don't see the conflict, since even if we grant for the sake of argument that there are physical processes the fine details of which are non-computable, this does not preclude their being treated at some more molar level as algorithmic, which is all that I was claiming. Mulhauser, however, says there is a more radical challenge arising from very recent work by Siegelmann and himself. I was wrong, he claims, to draw the crane/skyhook boundary at Turing computability, since there turn out to be chaotic neural networks with analogue components whose powers reach beyond Turing-computability and whose means cannot be "accurately" modeled by any Turing algorithm. I recommended that we consider the attractive prospect that the physical universe is Turing-computable, but I certainly didn't claim to offer a proof. Mulhauser offers grounds for any who wish to resist this assumption, even as a working hypothesis, and we shall see. If this new result stands up to scrutiny (of a sort beyond my own competence to conduct), and if it turns out moreover that these chaotic neural networks are a discernible part of our universe--the physical universe, not just the mathematician's universe of logical possibility, I will be obliged to move the boundary, as he notes. But recall all the hapless attempts to brandish Gödel's Theorem as a disproof of materialism about the mind. Until we are given an argument that shows in detail why we must model some portion of the physical world as a chaotic neural net (on pain of manifest inability to predict and explain), we do well to drag our feet on the issue. Mathematical proofs about what is possible or impossible in these areas sometimes hinge on assumptions that make them less interesting and important than they first appear.

(4) I am way out of my depth when the topic turns to the computability of physics, and if I fall for the "common mistake" of assuming that all standard physics is computable, it is Roger Penrose who has led me astray, since I took the point from him. (It turns out that I also (mis-)took a point from Richard Feynman. I quoted with approval (p.360) his rhapsodic commentary on potassium in the brain, but it is based on an elementary mistake, according to a recent letter to Nature. That's the risk I run when I rely on experts in other fields, as I often do.)

(5) I think Mulhauser misses my point about the logical problem with an algorithmic process spawning a non-algorithmic sub-process. Mulhauser sees that this is not an inescapable contradiction, since there is no telling what byproducts may happen to be found by--or even created in the course of operations of--any particular concrete instantiation of an algorithm. That was my point: any such non-algorithmic sub-process must be considered something external (even if it is a physical byproduct, somehow, of the larger process), found and then incorporated into the larger process. Otherwise it would be, in effect, a non-algorithmic sub-system of the supersystem, contradicting the premise that the supersystem was algorithmic.

Now to the major issues raised. Mulhauser is not persuaded by my Darwinian deflation of God the Lawgiver as the source of the order needed if evolution by natural selection is to unfold. He is right that Smolin's proposal does not (yet) include any account of heritability, and is, as Smolin himself acknowledges, highly speculative. And yes, the critic of Darwin's universality might indeed hold out for a further explanation of how the rest of the physical laws (the regularities which Smolin's speculations take for granted) came to have their apt values. All I claim to have done is to remove the aura of inescapability from the anti-Darwinian challenge. One is under no pressure to grant that there must be a Lawgiver, since it could all just be the product of random variation over eons (or even eternity, in John Archibald Wheeler's version). Mulhauser's cautionary footnote about Wheeler's untrammeled imagination is well-taken, by the way. My own infrequent conversations with Wheeler have left me gasping at his blithe tolerance of theoretical extravagance, not to say weirdness, but as I point out, there are no humdrum facts of cosmology.

I in turn am not persuaded by Mulhauser's objection based on the assumption of a mathematically continuous space of physical possibilities, but I am glad he raised it, since it brings into the open an issue I have long been puzzled by. Is nature really continuous? For instance, can we make sense of the idea that the value of some physical variable is actually an irrational number rather than any rational approximation thereof? You can't do physics without using equations that call for real numbers, but so far as I can see, this goes no distance towards establishing Mulhauser's strong thesis of continuity, with its implication of more than countably infinite possible universes to test. Even in the manifestly digital, quantized, and only countably infinite world of Conway's Life, real numbers are needed to express such important constants as the "speed of light"--the fastest velocity of propagation of change across the Life plane--which occurs along the diagonal and hence is faster by a factor of the square root of 2 than any change propagated from cell to cell along rows or columns at maximal speed (if we preserve the standard convention that Life cells are unit squares in a Euclidean space). This geometrical fact obviously carries no implications about continuity of the actual workings of the Life world. Does the mathematics used to describe the physics of the real world have a different status? I don't know. I am not sure what it would mean to say that we need either real numbers or noncomputable functions to describe the world. There may be arguments in theoretical physics that show why the continuities we observe in nature are Real continuities, but I have yet to be introduced to them. I will be very interested to consider any further instruction or argument Mulhauser can offer on this score.

The larger problem he sees with my book is my "mathematically incoherent" representation of a single Design Space. He is right that there are different ways one might try to systematize the ensemble of possibilities I wished to discuss into a multi-dimensional space, and I did not settle on one way and stick to it. Now does this make my account "deeply flawed" or just annoyingly inconstant in its presentation? Some of the problems Mulhauser sees can be brushed aside, I think. I don't claim, as he says, that the LoM contains all possible genomes; I say (in scare-quotes) that it contains "all possible genomes"--alluding by those scare-quotes to the point I had already made about the Library of Babel, which doesn't contain all possible books either (having none in Arabic or Chinese, for instance, but only translations of them), a negligible shortcoming for my purposes. His points about the difference between infinite and merely Vast spaces of possibilities are, so far as I can see, elaborations of points I made, not contradictions thereof. I would say the same thing about his comments on the "open question" of how to organize a space of phenotypes and how to incorporate a fitness dimension into the space; it is for the sorts of reasons he cites that I myself expressed doubts about developing the boundaries between different grades of possibility in any rigorous way (pp 103-7). And he is right that given the various ways I invite my readers to visualize the space, my appeal to Hamming distance as an intuitive measure of difference is out of order, so I should drop it.

His effort to find a consistent interpretation of my remarks on Design Space leads him to an "unremarkable" destination which was indeed, pretty much all that I had in mind for the time being. We agree on the main point. As he puts it, "everything 'designed' is related by descent to some product of natural selection." Provided we understand "descent" in all its varieties to be an unmysterious natural relation, this is not a trivial claim. If one of the fruits on the Tree of Life is the beaver's dam, another is the Aswan Dam, and the processes that led to the design of each are related: the later, more sophisticated phenomena are both descendants of and composed of the very elements that account for the earlier, simpler phenomena.

I proposed Design Space as the single arena in which all this has happened. Mulhauser wishes my vision of Design Space was more mathematically precise and cogent, and so do I. It would be wonderful to have a powerful scientific theory instead of just a philosophical image, but that is beyond me. He points to some of the difficulties that lie in the path of those who (I hope) will try their hands at this difficult set of problems. I welcome attempts like his to push what is impressionistic or metaphorical in my story into either clarity or oblivion. More of the former than the latter, if I'm lucky, but there is still a lot of conceptual work to be done.

1. I am indebted to Seymour Papert for illuminating discussion of Mulhauser's review and my reply.