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
