Measuring Fractal Dimension ?

[greg]

Paul Rubin wrote:
> Steven D'Aprano <steve at REMOVE-THIS-cybersource.com.au> writes:
> 
>>But that depends on what you call "things"... if electron shells are real 
>>(and they seem to be) and discontinuous, and the shells are predicted/
>>specified by eigenvalues of some continuous function, is the continuous 
>>function part of nature or just a theoretical abstraction?

Another thing to think about: If you put the atom in a
magnetic field, the energy levels of the electrons get
shifted slightly. To the extent that you can vary the
magnetic field continuously, you can continuously
adjust the energy levels.

This of course raises the question of whether it's
really possible to continuously adjust a magnetic field.
But it's at least possible to do so with much finer
granularity than the differences between energy levels
in an atom.

So if there is a fundamentally discrete model
underlying everything, it must be at a much finer
granularity than anything we've so far observed, and
the discrete things that we have observed probably
aren't direct reflections of it.

-- 
Greg