# Re: Smullyan Shmullyan, give me a real example

On Mon, May 15, 2006 at 11:17:35AM +0200, Bruno Marchal wrote:
>
>
> Le 15-mai-06, à 02:04, Russell Standish a écrit :
>
> >>
> >> I guess it is a delicate point, a key point though, which overlaps the
> >> ASSA/RSSA distinction (that is: the Absolute Self Sampling Assumption
> >> versus the Relative Self Sampling Assumption).
> >>
> >> If you identify a "conscious first person history" with a "third
> >> person
> >> describable computation", it can be argued that an explanation for
> >> physics can be given by Bayesian sort of anthropic reasoning based on
> >> some  universal  probability distribution like Hall Finney's
> >> Kolmogorovian UDist. Note tat this approach relies also on Church
> >> Thesis. Here somehow the TOE will be a winning little program. I agree
> >> that this would hunt away the third person white rabbits.
> >
> > I disagree. The UDist comes from looking at the measure induced on a
> > set of descriptions
>
> OK.
>
>
> > (or computations if your prefer,
>
> It is not the same. It changes the whole problem, especially from the
> Relative SSA (Self-sampling assumption).
>
>
>
> > although the two
> > are not equivalent),
>
>
> OK, why not taking that difference into account. I think it is a
> crucial point.

I do :). However, its makes no difference as far as I can tell to the
Occam's razor issue.

>
>
>
> > given a reference Turing machine U. This appears
> > to be a 3rd person description, but it need not be so.
>
>
> I am not sure I understand.
>

Do you mean you don't think it is a 3rd person description, or do you
mean you don't think it can be anything else?

>
>
> > As I have
> > pointed out (but suspect it hasn't really sunk in yet), U can be
> > taken to be the observer erself.
>
>
> I could agree, but U cannot *know* e is U. Need some bet or act of
> faith.
> In general if U describes the observer, he is a "big" number in need of
> an explanation. I mean, the existence of  "big stable U" is what we try
> to explain.
>

Sure. In fact the argument does not even hinge upon the observer being a
UTM. However, if not, then the distribution is not exactly universal
(hence my quotes below).

>
> > When done this way, there is a 1st
> > person "universal distribution", with a corresponding 1st person Occam
> > razor theorem. And this implies the absence of 1st person white
> > rabbits.
>
>
> I really don't understand.
>
> Bruno
>

The details, of course are in my paper "Why Occams Razor". To
summarise, an observer induces a map O(x) from the space of
descriptions, which is equivalent AFAIK to the output of your UD, to
the space of meanings. For any given meaning y, let omega(y,l) be the
number of equivalent descriptions of length l mapping to y (for
infinite length description we need the length l prefixes). So

omega(y,l) = |{x: O(x)=y & len(x)=l}|

Now P(y) = lim_{l->\infty} omega(y,l)/2^l is a probability
distribution, related to the Solomonoff-Levin universal
distribution.

C(y)=-log_2 P(y)

is a complexity measure related to Kolmogorov Complexity.

Basically this is an Occams Razor theorem - the probability of
observing something decreases dramatically with its observed
complexity. And this is a pure 1st person result. It doesn't get rid
of all white rabbits, but the remaining ones are dealt with the
Malcolm-Standish argument.

>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
--
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