RE: Implementation

From: Marchal <marchal.domain.name.hidden>
Date: Thu Aug 5 12:49:48 1999

Gilles wrote:

>> Bruno:
>>I agree. I take that for a difficult problem for those who still want to
>>link
>>consciousness'flux with physical phenomenon.
>>I just do not attribute consciousness to an implementation, but to a
>>person;
>>...whatever implements that person. If at some stage her behavior is
>>'buggy', I
>>will be disappointed whatever causes the buggy behavior (n-truncatedness
>>with
>>n little, 'lost of the Klaras in a new situation' or cerebral tumor,
>>Alzeimer, etc.).
>>
>
> Gilles:
>hmm...the failure of analogic systems does not look like the failure of
>digital ones ( compare an old analogic vinyl disk with a modern defectuous
>CD...) Alzheimer and tumoral diseases are the results of normal physical
>laws, with the consequences of gradually fading capacities like expected
>for analogic devices.
>i think that an incomplete or bugged HLUT or TM would produce suddenly
>totally erratic and incomprehensible outputs.


hmm... I see that you believe in the continuum. I agree there
is a sense in which the continuum is more 'primitive'
than the discrete. According to a theorem proved by Tarski
you can have a complete first order theory for the reals.
For exemple 'fermat theorem' is trivially true when the
quantifier'scope is the set of reals. In such a theory you
cannot express the 'real' Fermat theorem (if not arithmetic
would be complete). You cannot even define the notion of
'natural numbers' and that is the problem with taking the
continuum as the only primitive.

Moreover I can imagine that the continuum is a 'creation' of the
extrapolating universal machine facing probable big (very
big !) numbers. I can in some sense justify why UTMs will
believe in the continuum and in analogical phenomena.

Also, I don't pretend that analogical things don't exist, but
I have more than one conception of the continuum and I
don't take it for granted.
There exist recursive approach to the continuum which makes
appear interesting relations between the continuum and the
computable.

I think that vast and redondant discrete systems, having a
most probable deep history, like a brain (with comp), can
fade as well as any analogical system.
Any ? Well, with an ad hoc notion of 'computable reals' and
with an ad hoc analogical system based on that notion of
'computable reals', you can refute me without convincing me.


>If you still believe that we
>could be the result of a discrete computation, it must be absolutely
>perfect and bugfree. This may be a problem if you think like Schmidhuber
>that "real" computations can do that, since any physical system is subject
>to thermal and quantum noise...


I tend to belief that (at least) Aritmetical Truth is absolutely
perfect and bugfree.

It is easy (but not so easy!) to write a correct (bugfree)
program for a universal dovetailer algorithm.
Of course it will generate all program's executions including
all bugfull one. But UD* itself is bugfree.

Tell me what is a physical system please. What do you mean
by "real" computation ?

What you call quantum noise I take it to be a first person
(of the plurial! the bank is multiplied) description of a deep
self-dovetailing on the reals or the complex. (Not unrelated to
Deutch's Qunatum-Depth, I guess).

Thermal matter? Difficult. It probably relies on information/computation
relations, and deviation between relative compressibilities,
or something similar where there are fractal everywhere ..., and
also fixed points, invariants etc. It is also part of number theory.


I am not sure there is a Universe, Gilles, nor any form of
Actual Continuum.

And, even WITHOUT comp, I cannot deny the arithmetical existence
of an incredibily more vast web of 'dreams' !

I am not even sure Cantor Paradise is vast enough for describing
all those dreams (just to tell you how vast that web is).

Don't confuse the web with UD*. Dreams are 'stories' told by UTMs,
and the 'consciousness' which makes the 'stuff' of the dreams
relies (supervenes) on the whole UD*. (cf the PE-omega experiment,
or if you prefer: the Relative Strong Self-Sampling Assumption on UD*).

Thinking about it PE-OMEGA is simply SSA on UD*. The relative and strong
aspect seems derivable ... mmh ... I must think ...

Anyway thanks for your comments :-)

Bruno
Received on Thu Aug 05 1999 - 12:49:48 PDT