On 27 Jul 2014, at 19:46, Jesse Mazer wrote:
On Sun, Jul 27, 2014 at 1:13 PM, David Nyman <[email protected]>
wrote:
On 27 July 2014 17:27, Jesse Mazer <[email protected]> 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.
At step 1-6. OK.
But this is why there is step 7 and 8. At step six, you are still at
the middle of the argument.
At step seven, you can still save physicalism by assuming a unique
small primitive physical universe. Small really means here FPI immune.
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.
CTM = Comp (to use with moderation when tired of the sound of comp).
BTW, I suggested an ontology in the earlier comment to Bruno at http://www.mail-archive.com/[email protected]/msg16244.html
-- 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.
Any sigma_1 complete theory, on arithmetic, or any other inductive
collection of finite entities, will do.
But such system can be extended in much more powerful (in terms of
proving large set of arithmetical, or theoretical computer science) by
admitting stronger induction axioms.
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?
The UD is just the base. The simplest basic ontology. With such thesis
it defines effectively what is computable, and it defines the relative
measures, which will not depend on which UD you start with.
But the view from inside are constrained by the self-reference, which
associate canonical structure on the possible consistent extensions.
The atomic propositions are the sigma_1 sentences, and observable with
probability one is defined by true in all consistent extensions in
case there is such a consistent extension. ([]p & <>t). It is a bit of
"help your self in case you can".
It might work because we get logics which are "quantum "enough" to
provide a quantization, and hopefully the quantum type of measure.
The universal wave, or the universal matrix aspect should normally be
part of the core physics of the average universal machine, and Löbian
machine should known, and seems to know. (In sense definable in
computer science).
This relies on Church thesis, Kleene, Gödel, Löb. Comp makes easier,
(mathematical), to handle the pieces of the puzzle.
A special program can win the physical observable, but that is what we
need to derive from the (Turing) universal view.
Bruno
Jesse
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