[FOM] Mumford on the foundations of Mathematics

[Eray Ozkural]

On 8/28/06, Frank Waaldijk <frank.waaldijk at hetnet.nl> wrote:
> i can only hope that this message will get past the moderator, since my
> previous message which was related to this issue (a real statistical
> experiment to test whether our world is deterministic) was blocked
> repeatedly.

While such an experiment would be valuable if it could be
conceived of, I have yet to find means to accomplish it. Our
definitions of randomness hinge on uncomputable values, which
seem to make the aforementioned experiment practically
impossible. However, I feel inclined to repeat a suggestion by
the AI researcher Schmidhuber that perhaps one day a
lucky student will demonstrate a pseudo random number
generator, in the form of a cellular automata etc., that will
precisely reproduce the quantum phenomena which are thought
to be genuinely non-deterministic in some interpretations of
QM. So far, these discussions are highly speculative.

The relevance to FOM: I don't think there is a mathematical
problem with imagining a uniform probability distribution over an
interval of the real number line. The problem that you mention
seem to be philosophical. Some mathematicians have raised
concerns about the reality of the real number line, though:

http://www.cs.auckland.ac.nz/~chaitin/olympia.pdf

In one sense, mathematics is the art of abstraction. However,
not all abstract concepts will be equally useful. For instance, the
concept of set has great many applications, which make it useful.
If it were not possible to find a single real-world application of the
concept of set, then I doubt that it would not even be considered
as mathematics from a mathematical perspective. Thus, I think
one might wish to associate mathematics and physics.

Regards,

-- 
Eray Ozkural (exa), PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo