
On Aug 11, 2009, at 2:47 PM, Hal Finney wrote: physics, not just in mathematics. True, the nature of such results are a bit different, since all our current physical theories might turn out to be wrong. But, hey, maybe our understanding of computation or even mathematics has some fundamental flaw, too. The estimate on the limits to brute-force search are mine, based on a *very* rough estimate that draws on the results in the following paper: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-46X8Y6W-1&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=976695769&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=d98e72ef5fe3301fead2dbc93c2885e4 (I haven't actually read the paper; my analysis was based on an article I can't find that discussed the implications of this one.) The basic summary of the author's result is: "[T]he total number of bits and number of operations for the universe does not exceed O(10^123)." I guessed about how this value scales (as the cube of the time - one factor for time, two for the size of the light sphere you can reach in that time; not 3 because the information content of space goes up as the area, *not* the volume - a very weird but by now standard result). Now, my scaling technique may be completely flawed, or my computations may be wrong. Or the paper could be wrong. (I wouldn't bet on it.) Or the physics may be wrong. (I *really* wouldn't bet on that.) But the fact that there are other bounds around that are not as tight, or that one can describe a machine that would do better if there were a way to realize it, aren't evidence for any of these. Bounds can be improved, and a description isn't a working machine. In fact, the whole point of the article that I *did* read is that this result should make use re-examine the whole notion of a "possible" computation. It's easy to describe a computation that would take more than 10^123 steps. Ackerman's function exceeds that for pretty small input values. We've traditionally said that a computation is "possible" if we can describe it fully. But if it couldn't be realized by the entire universe - is that really a *useful* notion of "possible"? -- Jerry --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to majordomo@metzdowd.com ----- End forwarded message ----- -- Eugen* Leitl <a href="http://leitl.org">leitl</a> http://leitl.org ______________________________________________________________ ICBM: 48.07100, 11.36820 http://www.ativel.com http://postbiota.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE
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Jerry Leichter