🚀 go-pugleaf

In article <1992Nov10.173302.27756@sun0.urz.uni-heidelberg.de>, gsmith@lauren.iwr.uni-heidelberg.de (Gene W. Smith) writes:
> In article <1992Nov8.154955.15938@prim> dave@prim.demon.co.uk (Dave
> Griffiths) writes:
> 
> >Our current theories say that spacetime is infinitely subdivisable. ...
> ... Occams razor
> >might suggest that there are _no_ continuums out there. We can get by OK
> >without 'em.
> 
> We can also get by with 'em.  If the simplest idea is the best, it
> follows that if continuums are simplest, they are best.
> 
This is the question. Continuous models are the simplest to work with
mathematically, but are the simplest possibility as models of physical
reality? I do not think so. The information content of any finite volume
of space-time with a finite energy appears to be finite. Using continuous
models to build finite structures is extreme overkill of the kind nature
does not seem to use.

There is good reason to suspect that no completed infinite totalities
exist. The continuum that appears in formal mathematical systems is different
then what mathematicians mean by `the continuum'. The latter is a speculative
philosophical idea that cannot be formalized mathematically. For example
the real numbers definable in any consistent formal system are countable.
They are just not countable *within* that system. Some mathematicians
will claim they can formalize the `true continuum' by saying what they mean
by real numbers is *all real numbers* not just those definable in a
particular formal system. Whether *all real numbers* exists or this phrase
has any mathematical meaning is itself a speculative philosophical question.

Paul Budnik