RE: Doomsday and computational irreducibility

From: Jonathan Colvin <jcolvin.domain.name.hidden>
Date: Tue, 21 Jun 2005 21:06:22 -0700

Russell Standish 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.

Are you familiar with Wolframian CI systems? The idea of CI is that while
the system evolves deterministically, it is impossible (even in principle)
to determine or predict the outcome without actually performing the
iterations. I'm not at all sure that the idea of block representation works
in this case.


>> 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 :)

I'm thinking of Wolframian CI. There seem to be no short-cuts under that
assumption (ie. No simpler model possible).

>
>
>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).

I don't see that causal structure is key. My understanding of the standard
DA is that the system (universe) itself has knowledge of its future that the
observer lacks (sort of bird's eye vs. frog's eye situation), which avoids
the reverse -causation problem. Wolframian CI seems like it might be
problematic for that account.

Jonathan Colvin
Received on Wed Jun 22 2005 - 00:08:11 PDT