[nitrogen]

"Perfect knowledge" in this case is probably an assumption as part of a mathematical definition. E.g. "Assume a hypothetical time-varying universe U exists, and the current time state and all previous states of the universe are perfectly known. Iff the following state of U is unpredictable even with this knowledge, U is defined to be truly random."

The idea that randomness has to "come from" somewhere is a different idea, and the question of whether randomness or order is the fundamental state, and the other an emergent property, is an interesting question indeed.

> I'm just honest enough to admit that I don't know, whereas it seems most academics at least are convinced that they do know.

If you don't know, how can you be sure they don't either?

[h1karu]

To posit such a thing as "all previous states" implies that a universe is a finite state machine whereas for all we know the universe could be infinite in which case the value "all previous states" becomes a mathematical impossibility.

> If you don't know, how can you be sure they don't either?

I don't mean to assert any claim about individuals and their personal knowledge I'm merely suggesting that in my opinion the global community of scientists as represented in academia, scientific journals, and in popular literature hasn't made a compelling case for having met it's own scientific burden of evidence (scientific method) to be able to say that "science knows".

In the past that burden of evidence was lower because we had reason to believe that the universe was a much smaller place and that we could measure a much larger percentage of it, but given what we know today that burden of evidence has grown tremendously to the point where any serious scientist should admit to himself that science doesn't know.

[nitrogen]

Regarding infinite states, let's assume infinite storage capacity and a time step approaching 0 (in the limit sense:. It's not science, it's math.

Regarding science, the point is not knowing. Science isn't just answers, it's a process for finding new questions to answer. Something could always come along that radically changes our understanding of some aspect of the universe, but that doesn't necessarily mean what we knew before was wrong, just incomplete. If an old theory explains everything measured up to a point, the old theory is still "right" within the context of those measurements. A new measurement that invalidates the theory doesn't invalidate the previous measurements in almost every case.

It's also important to distinguish between math and science. Mathematicians can make definite claims to correctness because they study "universes" of their own creation. Science only claims correctness in light of current knowledge, within certain error bars. Ignore sociology.

[h1karu]

> Science only claims correctness in light of current knowledge, within certain error bars.

I concur, but my point is that with regard to the mechanics and composition of the universe in which we live it would seem that the more we measure the larger those error bars appear to be. Every once in a while measurements come along which multiply the size of those error bars exponentially and once that happens scientists should take note to adjust the English language they use in characterizing the limitations of their own knowledge. Modern scientists seem to be notoriously slow at this and my suspicion is that this is because it would give the impression that certain fields of science are becoming less knowledgeable as time goes on, and that's not good PR. In other words my only complaint here is related to sociology, the use of language.

Thank you for prompting me to refresh my memory on the differences between mathematics and scientific inquery because in so doing I ran across a quote having to do with the role of the theorist (my favorite) who is caught between the two worlds:

"Before an experiment can be performed, it must be planned — the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted - nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit." — Max Planck

'The Meaning and Limits of Exact Science', Science (30 Sep 1949), 110, No. 2857, 325. Advance reprinting of chapter from book Max Planck, Scientific Autobiography (1949), 110.