On Sat, Oct 15, 2011 at 06:53:59PM +0200, Bruno Marchal wrote:
>
> On 15 Oct 2011, at 02:50, Russell Standish wrote:
>
> >On Fri, Oct 14, 2011 at 05:01:26PM +0200, Bruno Marchal wrote:
> >>
> >>On 13 Oct 2011, at 23:50, Russell Standish wrote:
> >>>I don't see why Bayes' theorem assumes a physical universe.
> >>
> >>
> >>Bayes' theorem does not assume a physical universe. But some use of
> >>bayes theorem to justify the laws of physics, presuppose that a
> >>physical universe is an object (may be mathematical, like in
> >>Tegmark) among other objects.
> >
> >Then why couldn't the physical universe be a trace (aka history)
> >of UD*?
>
> Because the UDA show it to be a sum of infinitely many computations.
> Even 2^(aleph_0) due to the dovetailing of the real (and complex
> ...) inputs of the program generated and executed by the UD. This
> cannot be generated by any programs. It can only be lived or
> inferred by the internal observers experimenting their golabl (on
> UD*) first person indeterminacies.
>
Fair point. Let me rephrase: Why couldn't the physical universe be a
set of computations, all giving rise to the same experienced history.
>
> >
> >>
> >>
> >>>All it
> >>>assumes is a prior probability distribution. Something like the
> >>>universal prior of Solomonoff-Levin, or the distribution of observer
> >>>moments within UD*.
> >>
> >>I don't think such a distribution makes sense. What makes sense is a
> >>computational state, and a distribution of (competing) universal
> >>machines relating that state with other states through the
> >>computations that they emulate.
> >>
> >
> >Whenever an observer interprets multiple different input strings (ie
> >observations) as the same thing, the S-L distribution makes
> >sense. Particularly so if the mapping process is a computation.
>
> I am not sure I understand this.
>
The S-L distribution is defined as the sum over all programs that halt and
produce a given output (x say) of 2^{- length of program expressed as
a bitstring}.
We can replace the Turing machine with any function that takes
bitstrings, and maps them to a countable set of meanings (which can be
identified with N, obviously), provided the map is prefix free (ie if we
read n bits, and decide the meaning is x, we cannot change our mind
after reading n+m bits).
> >
> >The UDA indicates we must be supervenient on all programs passing
> >through our current observer moment.
>
> It makes sense with OM = 3-OM = relative computational state. But
> this is not Bostrom's OM a priori (provably with comp).
>
It seems we've been around the world on this one. There is only one OM
concept, which is defined by the information content of the observer
at a point in time.
But there may be multiple programs instantiating a given observer, so
there will in general be multiple machine states corresponding to a given
OM.
> >
> >I know there are only a countable number of programs. Does this entail
> >only a countable number of histories too? Or a continuum of histories?
> >I did think the latter (and you seemed to agree), but I am partially
> >influenced by the continuum of histories available in the "no
> >information" ensemble (aka "Nothing").
>
> It is a priori a continuum, due to the dovetailing on the infinite
> real input on programs by the UD.
>
IIUC, the programs dovetailed by the UD do not take inputs. You
expanded a bit on this in your response to Brent, but I don't follow, sorry.
>
> >
> >Could it be that there are only a countable number of histories after
> >all, given there are only a countable number of programs. That would
> >be one big difference right there.
>
> We do agree on this. The difference is that the comp statistics is a
> statistics on non-random things, even if those things include
> computations (non random) with random inputs.
>
Are you agreeing there may only be a countable number of histories
after all? Or something different :).
I'm not sure what you mean by random inputs. Surely, if random inputs
were applicable, then the histories will be random things.
> >>Well, because UDA shows that the laws of physics are logico-
> >>arithmetical, and that they take the form of internal
> >>(epistemological) relative statistics on computation.
> >
> >I actually don't get that conclusion from your work, so it might be
> >worth elaborating more.
>
> This already happens in the UDA step 7. We don't need the
> immateriality or the 'arithmeticality'.
Sorry - I think I minsinterpreted what you said previously...
> >The Theatetus definition leading to the AUDA has the feel of something
> >"put in by hand", rather than being a logical consequence of the
> >UDA. Nothing wrong with that, of course, but we should be honest with
> >it, if it is the case.
>
> I agree I am not always clear on that. That is why I try to
> distinguish comp (used in UDA), and comp+theaetetus, used in AUDA.
> But the theaetetus ca be shown to be the unique definition meeting
> the requirement of computer science, provability logic, and the
> usual definition of knowledge (Kp -> p, Kp -> KKp,
> K(p->q)->(Kp->Kq)). It can be motivated, as it is by Socrates in the
> Theaetetus of Plato, by the dream argument, which is basically step
> 6 of UDA.
> How would you define knowledge axiomatically, accepting that you
> want it to apply to an entity (a machine) whose beliefs are
> rational, in the sense of obeying classical logic on the finite
> things?
>
As I said - I don't have an answer to that. I'm not an
epistemologist. All I can say is that your axioms seem to treat
knowledge as rather like how we might know a mathematical fact, rather than
how we know a fact of chemistry, or a fact of human life. So it seems
unsatisfactory to me.
It could be that knowledge resists axiomatisation. It could be that a
different set of axioms is more appropriate - eg incorporating ideas
from evolutionary theory. WRT the latter, I would say that life, and
also evolution has also resisted axiomatisation, in spite of a number
of attempts.
--
----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics hpco...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
