On Jun 3, 3:15 pm, Shmuel (Seymour J.) Metz <spamt...@library.lspace.org.invalid> wrote: > In <dknqt.14105$Ju6....@newsfe22.iad>, on 06/01/2013 > at 08:13 AM, Nam Nguyen <namducngu...@shaw.ca> said: > > >Agree. Mathematics is just a language, > > So far, so good. > > >a description, of physics, > > No, any more than English is a description of Physics. Mathematics is > a language that is not about Physics, even if physicists find it > useful. In fact, part of its utility is its generality. > > -- > Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel> > > Unsolicited bulk E-mail subject to legal action. I reserve the > right to publicly post or ridicule any abusive E-mail. Reply to > domain Patriot dot net user shmuel+news to contact me. Do not > reply to spamt...@library.lspace.org
It's so that mathematics is a tool for the sciences, and that only what we can express in natural language is in our (or the, or a) language of mathematics. What is beyond natural language is beyond what we can construct as a symbolic language. (It's fair to say that there are infinitely complex objects of the mathematical universe, in terms of their notation in symbolic language, obviously with a natural read-out).
Then, the point as above was that true _features_ and _effects_ in the numbers, would be directly evidenced in physical effect, where the objects of physics behave according to mathematical laws (as they do, whatever they are, else there would not be causality, generally, which there is).
Then, for the plainly logical, with geometry and mathematics and category as to theories of geometry, numbers, and here sets: then the total reduction and as well the implications of a reduction that is total may well be seen as truly fundamental, for each of those and then all else they describe. Then, the reduction or reductio may well have that there are structural features, instead of a lack thereof, in reducing to the origin and reducing to the universe, and necessarily addressing the duality or generally plurality, of implication, of the the most basic principles in symmetry and conservation: here of theories, theoretical-theoretical.
From an axiomless system of natural deduction, here as simply logical and as the only theory without non-logical axioms, a unique logical and uniquely logical theory, there is the void: and all.
Then, for application, for continuum mechanics: there is an entire field of mathematics yet to be discovered, in the polydimensional, for the natural in the uniform, and the continuous, and the discrete. The continuous/discrete distinction, and where it's resolved, has much more in it, for the discovery of features in numbers, as it has been so ignored, then as to where it's a or the primary subject of research in mathematics of the infinitesimals: and infinity.