Re: Turing Machines Have no Real Time Clock (Was The Game of Life)
Hal Finney writes: > Russell Standish, <[EMAIL PROTECTED]>, writes: > > Why do you think the only possibilities are that the universe is > > either discrete or continuous? For example, the space Q^4 (4-D space > > built from rational numbers) is neither. > > Rational numbers are continuous, by the typical definition. Between > any two rational numbers there is another (and therefore, an infinite > number of others). Hunh? This is certainly true, but on the other hand between any two rational numbers there are also an infinite number of irrationals. But even if this were not the case, the fact that any two rationals have other rationals in between would not make Hal's claim of continuity true; rather it would prove the opposite, discontinuity. Seems to me we have here a demonstration that, as in physical reality, continuity cannot exist. What could it possibly mean? -dlj.
Re: The Game of Life
Hal Finney writes: > It has been found that "Life is Universal", meaning that you can > construct a Universal Turing Machine out of the Life rules. It would > then be possible to program it to simulate any mathematical or logical > system, hence SAS's should be possible. But only if the outside world supplies the necessaries. I don't insist on John Horton Conway, or even Hal Finney, but I do insist that the machine be plugged into the wall. It's really a pissoff to see people writing about these patterns being "self-organizing." They're organized by the throughput from the power company. -dlj.
Re: White Rabbits and QM
Christopher Maloney <[EMAIL PROTECTED]> posted: To: everything-list <[EMAIL PROTECTED]> Sent: Saturday, November 13, 1999 10:25 PM Subject: Re: White Rabbits and QM > Russell Standish wrote: > > Introduction > > Wigner[8] once remarked on ``the unreasonable effectiveness of > > mathematics'', encapsulating in one phrase the mystery of why the > > scientific enterprise is so successful. There is an aesthetic > > principle at large, whereby scientific theories are chosen according > > to their beauty, or simplicity. These then must be tested by > > experiment -- the surprising thing is that the aesthetic quality of a > > theory is often a good predictor of that theory's explanatory and > > predictive power. > > I would go so far as to say that it is a good predictor of a theory's > validity, or truth. Explanatory or predictive power is not dependent > on simplicity. It always seemed to me that Eugene Wigner's epigram was made possible only by ignoring the effect of Darwinian selection. We should recall that the famous formula n(n+1)/2 for the area of a circle with radius n has fallen into total disuse, not because of its lack of elegance but because it is ridiculously inaccurate. For exactly the same reason, nobody any more uses the slick p*r^2 to sum the numbers from p to r. It's a nice looking expression, catchy even, but it gives wrong answers. This is why the Platonic mood of so many math aficionados strikes me as odd. The correspondence between mathematical structures and the real world -- or anything else -- is utterly of our choosing, it seems to me. Cheers, -dlj.
