obnoxio@BRAHMS.BERKELEY.EDU (Obnoxious Math Grad Student) (06/06/87)
[From some comments on a new argument by design based on moonshine etc:] In article <633@uwm-cs.UUCP>, litow@uwm-cs (Dr. B. Litow) writes: >I think that there may be a fly in the ointment. The appearance of ever >larger 'special' symmetries in the differential dynamics of field physics >e.g. the MONSTER and its related lattices may be a symptom of a deep >deficiency in physics. To a rank dilettante much of the last 100 years >of physics looks like an enormous chapter on 'how to get around integrating >the equations of motion' while still obtaining some information by >studying symmetries or using perturbation techniques that are (so it >seems to this reporter) largely based upon saving the appearances. But if one does not *know* the `equations of motion' in the first place, it is essentially impossible to integrate them. This "some information" you mention has been a valuable clue towards discovering just what they are. Mathematically, it is often better to not integrate the equations in the first place--the real information *is* in the symmetries and the like, and not particular trajectories. Consider, for example, the relation- ship between thermodynamics and statistical mechanics. Solving Newton's equations for 10^25 particles tells us very very little. >I even maintain that this is so in the case of that shining night (sic) QED. You maintain so incorrectly. A common source of misinterpretation of all quantum phenomena is to insist that something classical is there and is still to be solved for. Saying that they can't solve for "X", when "X" doesn't exist in the first place, is not a legitimate complaint. (Before we leave talk.religion.misc for good, let me say that that last sentence seems apropos to far too many talk.religion.misc arguments.) (And if you were maintaining something more sophisticated than I've given you credit for, let me know.) >As a computer scientist interested in the exact structure of Turing machine >computations (yes that dull tool) I have lately become disturbed by the >prospect that any kind of a priori approximation method for the equations >of motion in newer theories may have to be noneffective. That possibility always exists, of course, but the newer theories are not heading that way. Rather, the mathematics involved has gotten much more sophisticated. Recent developments in algebraic geometry, for example, have been connected to the vanishing of the cosmological constant to 20 orders in string theories. It is the existence of those rich symmetries that you poohpoohed above which has *enabled* appropriate computations to be done, both theoretic- ally and numerically. "The most incomprehensible thing about the world is that it is compre- hensible." --Albert Einstein > That means that >any attempt to get quantitative details from such theories would depend >on a series of ever more demanding tours de force quickly outstripping >human intellect combined with an appeal to the data that was called long >ago 'saving the appearances'. No one knows if mathematics will ever outstrip the human intellect. My own guess is no, but I am biased. But if superstrings are indeed a theory of everything, there's a good possibility that physics will not outstrip our collective intellects. Just what do you mean by quantitative details? A TOE that correctly pre- dicts the various particle masses, the gravitational radiation background, etc, and proves that it reduces to known physics elsewhere is as good as they come, even in principle. Or are you saying that a TOE is "ineffective" because no one can use it to compute a baseball trajectory? On the contrary, such TOEs show that "in the baseball limit, Newton's laws are valid", *providing* one with an ef- fective computation. (I mean, what *is* a baseball? I can't agree to identifying it with the world-lines of all its constituent atoms.) Or are you saying something subtler yet? > I can to some extent put my money where my >mouth is in this matter. I'd like to see it--that's what this group is for. >[a simpler argument by design:] >*** so loved the world populated by us dunces that *** caused the primes >to be distributed with O(1/log(n)) density. Good enough to allow >almost certain PTIME Monte Carlo sieving for primes. *** did this just >in case we turned out to be too stupid not to need Monte Carlo methods >to do combinatorial optimization. The above is not an argument by design--at least not yet. First such has to refer to physical reality. (As a veteran of the pi-wars, I will leave the details of the rest of my argument to the interested reader.) (It might fit in as an argument from goodness, though.) But you are right about one thing--it is perhaps silly focussing on the Monster and the like when there is already amazing stuff right under our noses. But somehow it and company are so much more astonishing. > But then I do not 'buy' proof by >design. And what is *** ? What? Me Worry? Ditto. But what about too much/good design? ucbvax!brahms!weemba Matthew P Wiener/Brahms Gang/Berkeley CA 94720 "What really interests me is whether God had any choice in the creation of the world." --Albert Einstein