Dear Lev,
You already asked Terry Padden to do so. Are we stupid?
Sept. 20:
*In science, the term 'discrete' means just the negation of 'continuous' and no more*.
-- Mathematics has problems with the notion continuum since Dedekind's "Stetigkeit und Irrationale Zahlen". Numbers are always considered discrete.
So that while all of modern science is based on the formalism that is precise elaboration of the 'continuous',
--Really?
I am convince, we have not had a precise and general elaboration of the 'discrete'.
-- When a child learns to count, it has to grasp discrete entities first.
My essay outlines a formalism addressing the latter issue.
-- Sorry.
Oct.5:
As suggested by Schrödinger (see p. 2 of my essay), when the idea of 'discrete' entered physics at the beginning of the 20th century, it "has been forced upon us very much against our will".
-- Line spectra were known earlier, singularities too.
Now, more than a century later, despite the popularity the term 'discrete' has gained, our understanding of the 'discrete'--as it is present in nature--has not really advanced.
-- Engineers do not have such problems.
As I mentioned in the above post, the reason this situation persists has to do with the lack of any adequate conception of 'discrete'. We still talk of the 'discretizations of space and time' in spite of the fact that such concepts are not formally meaningful: 'discretization' of the continuous model does not produce a 'discrete' model.
-- Let me tell you that I tend to share Schroedinger's imagination of a single particle as a field that extends into space without limit, while I feel in position to change my point of view and consider it as something discrete within the space of wave numbers. Where is the problem? Are engineers more flexible than physicists?
Regards,
Eckard
