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)

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).


-- 
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