[FOM] The irrelevance or its relevance

José Félix Costa fgc at math.ist.utl.pt
Fri Feb 3 13:28:56 EST 2006

Fomers say (as starting point of discussion)

«I believe this is an interesting point. So why do physicists think of R as
an adequate model for "real" space geometry at all? Is it just an accident
of history or do they seriously believe that unmeasurable things exist?»

Why do physicists believe on R? (In what sense? In the sense they use it in
everyday scientific life?)

They got well known predictive theories. Physical theories synthesize
knowledge and are predictive. Verifiable predictions allow the
«belief-in-science», technology, and the atomic-bomb.

Give us an example of a discrete physical theory (in practice). E.g.,
quantum mechanics describe discrete entities using differential equations.

Once we accept «R» and «abstract R» we can go into higher levels, e.g., the
level of distribution theory that explains Dirac's delta in a solid basis.

I don't believe in incomensurable numbers...

But why is the belief in R more subtle than the current belief that «space»
has eleventh dimensions? Why the belief that unmeasurable things exist is
less surprising than the existence of a parallel universe at 1 mm distance
to me in hyperspace? Today's Physics is a eleventh dimension supertheory.
Physicist seem to be very happy. And they seem to belief in all these

Even if the universe is discrete it can be described in R.
Turing machines can be replaced by differential equations: the transition
function is described by a system of very simple differential equations and
the iteration of the transition function by another.

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

J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc at math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm

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