[FOM] The irrelevance or its relevance

[Eray Ozkural]

Dear José,

On 2/3/06, José Félix Costa <fgc at math.ist.utl.pt> wrote:
> Even if the universe is discrete it can be described in R.

Yes, certainly. I had wished to allude to Occam's razor, which
suggests us not to multiply entities unnecessarily. In that post,
I also wished to draw attention to the concept of measurability
which seems to play an important role in physics work.

As an example, by Occam's razor, we conclude that Einstein's
theory of gravity entails that there is no such thing as aether. Similar
inductive reasoning has been traditionally employed to show the
non-existence of hypothesized entities (a common example is
phlogiston).

Thus, if the physical space can be modelled by a simpler geometry than
those with uncountable sets, I would tend to think that a model using
R would be false, because it would contain unnecessary entities.

In addition, it may be conceived that if a physical theory posits entities that
can never be measured, even in principle, then this would raise
suspicion. I would also ask the following common questions that
physicists seem to avoid: do we have any direct observation
of a point location? The location of a particle seems to be modelled
as point, is the particle a point, does the point location physically exist
in any way?

Or as you imply, is it better to treat this as "just a model", an idealization
of physical reality, but not a perfect model? Does the Dirac delta
function describe a physical event accurately?

I think that to answer such questions, empirical work is necessary,
but my particular worry here is whether all logical explanations have
been sought.

However, I did not mean to imply that the space is discrete. There
was a previous reference that quantum mechanics can be derived in
computable mathematics. Maybe, that too is just an idealization.

> Thus, I think that answers to these questions are indeed subtle and can not
> be given in the short future.

I agree that we do not know enough, and the questions are subtle.

Regards,

--
Eray Ozkural (exa), PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo  Malfunct: http://www.malfunct.com
http://groups.yahoo.com/group/ai-philosophy
Pardus: www.uludag.org.tr   KDE Project: http://www.kde.org