On Tue, Jun 21, 2005 at 03:25:21AM -0700, Jonathan Colvin wrote: > A new (at least I think it is new) objection to the DA just occurred to me > (googling computational + irreducibility +doomsday came up blank). > > This objection (unfortunately) requires a few assumptions: > > 1) No "block" universe (ie. the universe is a process). > > 2) Wolframian computational irreducibility ((2) may be a consequence of (1) > under certain other assumptions)

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Actually, I think that 2) is incompatible with 1). A computational process is deterministic, therefore can be replaced by a "block" representation. > > 3) No backwards causation. > > The key argument is that by 1) and 2), at time T, the state of the universe > at time T+x is in principle un-knowable, even to the universe itself. > > Thus, at this time T (now), nothing, even the universe itself, can know > whether the human race will stop tomorrow, or continue for another billion > years. > In any case, computational irreducibility does not imply that the the state of the universe at T+x is unknowable. In loose terms, computational irreducibility say that no matter what model of the universe you have that is simpler to compute than the real thing, your predictions will ultimately fail to track the universe's behaviour after a finite amount of time. Of course up until that finite time, the universe is highly predictable :) The question is, can we patch up this criticism? What if the universe were completely indeterministic, with no causal dependence from one time step to the next? I think this will expose a few "hidden" assumptions in the DA: 1) I think the DA requires that the population curve is "continuous" in some sense (given that it is a function from R->N, it cannot be strictly continuous). Perhaps the notion of "bounded variation" does the trick. My knowledge is bit patchy here, as I never studied Lebesgue integration, but I think bounded variation is sufficient to guarantee existence of the integral of the population curve. 2) The usual DA requires that the integral of the population curve from -\infty to \infty be finite. I believe this can be extended to certain case where the integral is infinite, however I haven't really given this too much thought. But I don't think anyone else has either... 3) I have reason to believe (hinted at in my "Why Occam's razor" paper) that the measure for the population curve is actually complex when you take the full Multiverse into account. If you thought the DA on unbounded populations was bad - just wait for the complex case. My brain has already short-circuited at the prospect :) In any case, whatever the conditions really turn out to be, there has to be some causal structure linking now with the future. Consequently, this argument would appear to fail. (But interesting argument anyway, if it helps to clarify the assumptions of the DA). -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------

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