From: Osher Doctorow [EMAIL PROTECTED], Thurs. Sept. 5, 2002 6:17PM I have now read page 2 of Yurtsever, having previous read page 1, and I must confess that his style does not quite have the clarity of my style - his is more like the clarity of Sigmund Freud's style : > ) However, I am happy to see that he recognized the role of Godel's incompleteness theorem on his page 1.
On page 2, Yurtsever put the cart before the horse in a sense by telling us what would happen if his theory turns out to be correct, but since he plans to prove it in pages 3ff, he can be forgiven for that. I notice in connection with his last 2 paragraphs of page 2, which run over into the first 2 paragraphs of page 3, that he seems to agree with Sir Roger Penrose and me (independently - I have never met Sir Roger) that brain activity cannot be faithfully simulated on a digital computer. Sir Roger, by the way, like me (I have been told) rather dislikes computers and does not (or at least when last I heard about it) even answer email on computers. I am slightly different in that I both write and answer email, but I rather dislike digital computers although I will defend to the death their right to have their own opinions. : > ). I have not yet decided about quantum computers, analog computers, molecular computers, laser/light computers, etc. My argument about brain activity is far simpler than Sir Roger's - I derive it from mathematical fuzzy multivalued logics and their probability-statistics and proximity function-geometry-topology analogs, which does not make use of randomness as incompressibility or even computer randomness at all. Speaking of randomness, I pointed out that incompressibility randomness is only one interpretation of randomness. To those of us who grew up and spent at least half of our lives in the non-computer world (or at least, the not heavily computerized world), probability and statistics vs computer viewpoints are not quite the same thing. When somebody in one of my statistics classes tells me that something is random, I tend to be slightly put off. You see, everything is random in a sense in probability-statistics. Even the non-random world so-called is random, only the probability of the random part is near or at zero - which, strangely enough, does not mean impossible or the null set. Let me clarify the latter. The probability of an impossible event, like the probability of the null set, is zero. But an uncountably number of things have probability zero. In n-dimensional Euclidean space or even spaces that are rather similar to it, any n-k dimensional subset (k = 1, 2, 3, ..., n - 1) has probability zero provided that a continuous random variable has a distribution on that space or on a volume of space containing the events in question. The proof is the same as the corresponding proof for Lebesgue measure. Moreover, the same is true for time, not such space, since an event that occurs at only one point in time has dimension 0 in time, and so has dimension one less than the time dimension of 1, and so the above result holds. So in 3-dimensional Euclidean-like space or 3+1 Euclidean-like spacetime, points, strings, planes, plane figures or their approximations laminae, curves, lines, line segments, curve segments, 2-dimensional surfaces of 3-dimensional objects (e.g., the surface of the human brain, the surface of a human being which is usually skin, the surface of an organ, the surface of the earth, etc.), they all have probability 0 under the rather general assumption that a continuous random variable has a distribution on space(-time), e.g., the Gaussian/normal distribution. The events at or near probability zero, and likewise processes of those characteristics, are RARE EVENTS/PROCESSES (RARE EVENTS for short). Now that I have started elaborating, I will conclude with one other note of caution. In what might look like an Old Testament prohibition, I should say that *ALL IS NOT IN CONCATENATED STRINGS OF SYMBOLS.* In fact, it might be more accurate to say that almost nothing is in strings, but that might be misunderstood, so I restrain myself. In my theory, which I refer to as Rare Event Theory (RET), I distinguish between SYNTAX and SEMANTICS. Of course, computer people do that too, and computational linguists. But when push comes to shove, they mostly regard information as SYNTAX. In order not to confuse myself with computer people or computational linguists, I distinguish between information, which is syntactic, and KNOWLEDGE, which is semantic in the usual dictionary sense of MEANING - what symbols and words and propositions and sentences MEAN. I am not at all sure that incompressibility captures KNOWLEDGE so much as SYNTAX. However, we will let that pass for now, except for the slight detail that Knowledge, Memory, and Rare Events appear to coincide - although part of it is a well-motivated and well-indicated conjecture. In any case, I will continue to the substance of page 3 rather than interrupt myself or you further. For those who are interested, I refer readers to my contributions to superstringtheory.com, my paper in B. N. Kursunuglu et al (2000), to G. 't Hooft's Holographic Principle, and to Statistical Learning Theory by Vapnik (2000) for starters. Osher Doctorow