Re: Turing vs math

From: Juergen Schmidhuber <>
Date: Thu, 28 Oct 1999 12:37:26 +0200


> I don't really know what you mean, but it sounds like you're
> saying, you don't think real-valued quantities can exist because real
> #'s can't be described with a finite # of bits.
> But as you admit, *sets* of real #'s can easily be described by
> us.

Even the set of all real #'s is not formally describable. You cannot
write a program that lists all reals. In infinite but countable time
you can write down a particular computable real, but not all reals.

You can indeed write down rules for manipulating symbols and generating
proofs. But a symbol doesn't care for whether you think it stands for,
say, ``all reals''. The symbol string ``all reals'' is just another
symbol string. Your mental representation of ``all reals'' is describable
by another finite string, according to UTM theory. There is no compelling
reason to believe in some sort of non-describable ``continuous reality''.


>Let me point out that according to the current state of physics, the world as
>we see it appears to be quantized, however, the superposition of states in QM
>appears to be continuous. This continuity is an indication that the number of
>worlds in the MW has the cardinality of C. This property provide quantum
>computers with the "unthinkable" ability to "compute" in the continuum. In
>this light, Jurgen's comment do not make sense.

The UTM theory predicts that everything including QM superposition
is quantizable. According to it there is nothing like Super-Turing
computability in our universe. Justification: at the moment there is
no data that forces us to believe in continua. Recurring question: why
assume more than necessary?

>Imagine Jurgen arguing with a being capable of quantum computational
>thoughts...The being would just look at Jurgen with ineffable pity and smile.

Many seem to carry a wish for superior beings defying all formal

Received on Thu Oct 28 1999 - 03:40:07 PDT

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