On Tue, Sep 27, 2011 at 10:44 PM, Pierz <pier...@gmail.com> wrote:

> OK, well I think this and the other responses (notably Jason's) have
> brought me a lot closer to grasping the essence of this argument. I
> can see that the set of integers is also the set of all possible
> information states, and that the difference between that and the UD is
> the element of sequential computation. I can also see that my
> objection to infinite computational resources and state memory comes
> from the 1-p perspective. For me, in the "physical" universe, any
> computation is restricted by the laws of matter and must be embedded
> in that matter. Now one of the fascinating revelations of the
> computational approach to physics is the fact that a quantity such as
> position can only be defined to a certain level of precision by the
> universe itself because the universe has finite informational
> resources at its disposal. This was my objection to the UD. But I can
> see that this restriction need not necessarily apply at the 'higher' 3-
> p level of the UD's computations. What interests me is the question:
> does UDA predict that the 1-p observer will see a universe with such
> restrictions? If it explains why the 1-p observer seems to exist in a
> world where there is only a finite number of bits available, despite
> existing in a machine with an infinite level of bit resolution, then
> that would be a most interesting result. Otherwise, it seems to me to
> remain a problem for the theory, or at least a question in need of an
> answer, like dark matter in cosmology.
>
> I am going to have to meditate further on arithmetical realism.


Nice.


> I
> don't believe in objective matter either (it seems refuted by Bell's
> Theorem anyway),


Do you agree that at least something has to be primitively real?


> but a chasm seems to lie between the statement  "17
> is prime" and "the UDA (Robinson arithmetic) executes all possible
> programs". The problem is one of instantiation. I can conceive of a
> universe - a singularity perhaps, with only one bit of information -
> in which the statement "17 is prime" can never be made. To formulate,
> ie instantiate, 17, requires a certain amount of information.


True, a certain amount of information is required to realize or represent
certain mathematical truths.  Our universe may be large, but there are
numbers so big we cannot represent them either.  My opinion is that this
practical restriction placed on us does not mean such mathematical truth is
non-existent, only inaccessible.  In the same sense that before there were
high-powered computers, finding large Mersenne primes was beyond our
capacity, but that did not mean they were not already there waiting to be
found.


> To say
> that a program executes, as opposed to saying it merely is implied by
> a set of theoretical axioms, requires the instantiation of that
> algorithm. I suppose this is a restatement of the problem above.
> Arithemetical realism then would be the postulate that everything
> implied in arithmetic is actually instantiated. It seems to me I can
> grant 17 is prime, without granting this instantiation of everything.
>
>
At what point does mathematical truth stop?  It seems to be the existence of
some would imply the existence of all.  If you think Pi has an objective
value, then you should also accept that Chaitin's constant (
http://mathworld.wolfram.com/ChaitinsConstant.html ) has a certain value.
 If it does, it requires the platonic execution of all programs.


>
>
> Sadly when you start to talk about the difficulty of proving that our
> histories in the UD are more random than the actual histories we
> observe, I can't follow you any more - too much theory I'm unfamiliar
> with. I can see however that many (nearly all) of the infinite
> computations passing through our aware states will destroy us, as it
> were, so we can never exist in those computations (sort of anthropic
> principle). This also suggests a kind of immortality, the same kind as
> I propose in a blog post I wrote called the 'cryogenic paradox' in
> which I argue that there can only be a single observer, a single locus
> of consciousness underlying all apparently separate consciousnesses,
> which would really be just different perspectives of this one
> observer. It seems irresistible as a conclusion (from philosophical
> arguments quite different to the UDA), and yet also kind of horrific.
> Only a sort of state-bound recall barrier prevents us from being aware
> that we suffer every fate possible.
>

We also are aware of every possible goodness or blessing.  At a minimum,
this realization should compel us to treat each other better.  In the end,
the conclusion is little different from the golden rule or the concept of
karma.  All the good things we do are experienced by others (ourselves),
same with all the bad things.  In a sense this thought is scary, but it is
also can be unifying and fill us with awe at the infinite possibility and
experience that awaits us.

Jason

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