On Mon, May 15, 2006 at 03:51:56PM +0200, Bruno Marchal wrote:
>
>
> Le 15-mai-06, à 13:59, Russell Standish a écrit :
>
> >> OK, why not taking that difference [description/computation] 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.
>
>
> You do? See below.
>
>
>
> >
> >>
> >>
> >>
> >>> 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?
>
>
>
> I think it is a third person description.
>
That's what I suspect most people think. My point is that it needn't
be, and it is in fact inherently first person. I make this point in
many different papers, as well as my book.
In the fairness of scientific discussion, I am willing to be shown
wrong, of course :)
> >
> > 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,
>
>
> ? The UD has neither inputs nor outputs. (like any "universe" or
> "everything", note)
>
>
Perhaps I'm being a little casual in my terminology. What I'm
referring to is UD*.
>
>
> > to
> > the space of meanings.
>
>
> Which space is it? What do you mean (here) by "meanings"?
An observer attaches a meaning to the data e observes. The set of all
such meanings is semantic space or "meaning space". I believe this is
necessarily a discrete set (but not necessarily finite).
> If it is a
> mathematical semantics then which one, if not, I don't understand. I
> already ask you similar question after my first reading of your Occam).
>
>
>
>
> > 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.
>
>
> Note that this approach is non constructive (and thus cannot be first
> person, at least as I use it and modelize it). I have already argued
> that it can be refined through the notion of depth (a la Bennett),
> which takes a notion of "long" computation into account; but it is
> still incomplete relatively to the first person indeterminacy problem
> (pertaining on the set of *all* (relative) computations, and not at all
> on the set of descriptions).
> The non-constructibility is a problem here, given the goal of deducing
> physical laws or principles "without physics".
>
And now I don't understand you. Why does constructibility, or
otherwise have anything to do with the 1/3 person distinction?
>
> If you have succeed in eliminating all the "many person pov" - white
> rabbits, then publish!
Well, I have! One thing you can't accuse me of is not publishing my
ideas.
>
> Frankly it seems to me you don't really address the first person issue
> (and thus the mind/body issue).
Yes - you've said that before, and its a point I've never understood.
> For example, what is your theory of
> mind? In particular, do you say yes to the comp doctor?
Pretty much everything thing I've done summarises the theory of the
mind by the function O(x). It maps descriptions (aka bitstrings) to
meaning. I do make use of a robustness property, which essentially is
that O^{-1}(y) is not of measure zero, but that is about it.
In particular, none of my results depend on whether I would say yes to
the comp doctor or not.
> I think that eventually, we have to limit ourself to the discourses
> that a self-referentially correct machine (or entity, or growing
> entities of such lobian kind) can have about herself and her
> possibilities.
And I think you could be right, or even approximately right. At this
stage, we need to explore.
>
> I am not saying your argument is wrong, just that is incomplete (and
> unclear, but this could be my incompetence).
>
> Bruno
>
Well, of course it is incomplete if you're looking for a TOE. For the
White Rabbit issue, the argument is quite simple. I have conceived of
the White Rabbit problem in a certain way: the unreasonable
effectiveness of mathematics, the (non-)failure of induction. It
certainly appears to me that the argument addresses this conclusively,
from a first person point of view, however, there is always room for
doubt that I have overlooked some nuance.
I am willing to concede that there is possibly more to the WR problem,
but I have yet to see it expressed in a manner I can understand :).
Where I suspect most people might come unstuck is justifying why
formula (1) from "On Complexity and Emergence" should be called
complexity. The reason comes down its connection with Kolmogorov
complexity - it is the obvious generalisation of complexity to 1st
person and non-computationalist scenarios.
--
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