On Sun, Jul 27, 2014 at 1:13 PM, David Nyman <da...@davidnyman.com> wrote:

> On 27 July 2014 17:27, Jesse Mazer <laserma...@gmail.com> wrote:
> > I don't see why that should follow at all, as long as there are multiple
> > infinite computations running rather than the UDA being the only one,
> I may be missing some other point you're making, but I think this is
> already dealt with after Step 8 of the UDA (universal dovetailer
> argument). By this point in the argument, we have abandoned the notion
> of a "primitively-physical universe".

But when you say "by this point in the argument", do you mean there was
some earlier step that established some good *reasons* for why we should
abandon the notion of a "primitively-physical universe" (or primitive
universal computation), or is it just something that was posited at some
point for the purposes of exploring the consequences, without any claim
that this posit was implied by earlier steps in the argument? As I said, it
seems that someone could accept everything in steps 1-6 of Bruno's argument
but still posit that the measure of each observer-moment would be
determined by its limit frequency in some unique universe-computation U.

> Given that we are assuming CTM,
> we need some ontology to fix the notion of computation, and
> arithmetical relations suffice for this purpose.

Sorry, what does "CTM" stand for? It doesn't appear anywhere in Bruno's
"Comp (2013)" paper which I'm using for reference.

BTW, I suggested an ontology in the earlier comment to Bruno at
-- basically using an axiomatic system which allows you to deduce the
truth-value of various propositions about a computation, propositions
equivalent to statements like "after N time steps, the read/write head of
the Turing machine moves to space 1185 on the Turing tape, finds a 0 there,
changes its internal state from #5 to #8 and changes the digit there to 1".
Then, a given computation can be defined in terms of the logical relations
between a set of propositions, so one computation A can "contain" an
instance of another computation B if some subset of propositions about A
have an isomorphic structure of logical relations to the logical relations
between propositions about B.

Since the structure of arithmetic can also be defined in terms of a set of
propositions with logical relations between them, and any statement about a
particular computation can be decided by determining the truth-value of a
corresponding statement about arithmetic, it may be that defining
computations in terms of "arithmetical relations" would lead to all the
same conclusions as the definition I suggest above, though I'm not sure.

> Such a  Library must in particular contain "universal dovetailers"
> that themselves generate every possible program and execute each of
> them in sequence by means of dovetailing. This must include
> recursively regenerating themselves in an infinitely "fractal" manner.
> This characteristic implies a quite extraordinarily explosive
> regenerative redundancy. Hence it seems plausible a priori, even
> without a detailed calculus, that the resulting computational
> structure (i.e. the infinite trace of the UD, or UD*) must completely
> dominate any measure competition within the computational landscape
> defined by arithmetical truth (or the small part of it needed for the
> assumption).

That seems very handwavey to me, and while it might seem plausible
initially I think it becomes less so when you think more carefully about
how measure might actually be assigned. Do you disagree that if we use the
particular definition of measure I suggest, in the example I gave with U
and U' (both containing a universal dovetailer alongside a bunch of other
computers churning out endless copies of me in Washington or me in Moscow)
the UD will *not* dominate the "measure competition", in that U and U' will
give very different answers to the relative likelihood that I find myself
in Washington vs. Moscow in Bruno's thought-experiment?


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