On Monday, April 22, 2002, at 11:23 PM, Joseph Ashwood wrote: > > From: <[EMAIL PROTECTED]> >> If a RNG runs off Johnson noise, then the ability to predict its >> output would imply the ability to violate the second law of >> thermodynamics. If it runs off shot noise, then the ability to >> predict its output would disprove quantum mechanics. > > Actually there are models that fit the universe that are entirely > deterministic.
Could you mention what they are? Boehm's "hidden variables" model is generally discredited (some would say "disproved"). Alternatives to the Copenhagen Interpretation, notably EWG/"many worlds," Hartle's "consistent histories," and Cramer's transactional model, are still not deterministic, in that the world an observer is in ("finds himself in") is still not predictable in advance. Operationally, all interpretations give the same results, i.e., the Uncertainty Principle. (Which is why I mentioned "hidden variables," the only alternative theory which _might_ have restored classical Lagrange/Laplace predictability, in theory.) And even if the world were Newtonian, in a classical billiard ball sense, with Planck's constant precisely equal to zero, predictability is a chimera. Consider a game of billiards, with perfectly spherical billiard balls, a perfectly flat table, etc. Trajectories depend on angles to a precision that keeps going deeper and deeper into the decimals. For example, predicting the table state after, say, 3 seconds, might require knowing positions, speeds, and angles (in other words, the vectors) to a precision of one part in a thousand. Doable, one might say. But after 30 seconds, any "errors" that are greater than one part in a billion would lead to "substantially different" table states. Fail to know the mass or position or elasticity or whatever of just one of the billiard balls to one part in a billion and the outcome is no longer "predictable." After a couple of minutes, the table positions are different if anything is not known to one part in, say, 10^50. Even talk of a "sufficiently powerful computer" is meaningless when the dimensions of objects must be known to better than the Planck-Wheeler scale (even ignoring issues of whether there's a quantum foam at these dimensions). I feel strongly about this issue, and have thought about it for many years. The whole "in principle the Universe can be calculated" was a foray down a doomed path WHETHER OR NOT quantum mechanics ever came out. The modern name for this outlook is "chaos theory," but I believe "chaos" gives almost mystical associations to something which is really quite understandable: divergences in decimal expansions. Discrepancies come marching in, fairly rapidly, from "out there in the expansion." Another way of looking at unpredictabality is to say that real objects in real space and subject to real forces from many other real objects are in the world of the "real numbers" and any representation of a real number as a 25-digit number (diameter of the solar system to within 1 centimeter) or even as a 100-digit number (utterly beyond all hope of meaurement!) is just not enough. (Obscure aside: What if Wheeler and others are right in some of their speculations that the universe is ultimately quantized, a la "It from Bit"? Notwithstanding that we're now back into quantum realms and theories, even if the universe were quantized at Planck-scale levels, e.g., at 10^-33 cm levels, the gravitational pull of a distant galaxy would be out somewhere at the several hundredth decimal place, as a wild guess. The point being, even a grid-based positional system would yield the same "real number" issues.) In short, predictability is a physical and computational chimera: it does not, and cannot, exist. > Admittedly the current line of thinking is that entropy > exists, but there we still have not proven that it must exist. Just as no sequence can ever be proved to be "random," so, too, one can never prove that entropy "exists" except in the definition sense. Our best definition of what we mean by random is that of a thing (sequence, for example) with no shorter description than itself. This is the Kolmogorov-Chaitin definition. Much more is available on the Web about this, which is generally known as "algorithmic information theory." --Tim May