Популярно о конечной математике и ее интересных применениях в квантовой теории

About FOM

FOM is an automated e-mail list for discussing foundations of mathematics. It is a closed, moderated list, subscriptions and postings must be approved by the moderator, currently Martin Davis. Approval of a posting does not imply agreement with the views expressed in the posting. FOM subscribers typically have advanced training in mathematics, philosophy, computer science or related fields, and either have professional activity in one of these directions or are preparing for such a career. The FOM list is intended to provide a venue for discussing the provocative, sometimes controversial, ideas which drive contemporary research in foundations of mathematics and which often do not find their way into journal articles. FOM postings must be highly relevant to issues and programs in foundations of mathematics. They should reflect high intellectual and scholarly standards. However, FOM is not a venue for papers that should be submitted to journals. Generally, detailed proofs and technical details are not welcome. Of course, pointers to more extensive accounts, published in print or on the Web are welcome. Postings should be thoughtful, well-reasoned, and lively. Although controversy is both expected and desired, personal invective and other irrelevant discussions will not be permitted. Quotation from previous postings should be limited to what is absolutely needed for understanding, and quotations within quotations are particularly to be avoided. All postings are available in full on the archive. FOM postings must consist of single-spaced, plain text and have an informative subject line in the e-mail header. Extended quotes from other FOM postings should be avoided.

Postings to FOM (by subscribers only) should be addressed to fom@cs.nyu.edu

The FOM Editorial Board currently consists of:

Stephen Simpson

Harvey Friedman

Martin Davis

Andreas Blass

William Tait

John Baldwin

Alasdair Urquhart

Т.е., опять произносятся очень хорошие слова о том, что разные подходы приветствуются, даже “the provocative, sometimes controversial, ideas which drive contemporary research in foundations of mathematics and which often do not find their way into journal articles.” Эти слова похожи на те, которые произносятся в editorial policy of Foundations of Physics и от них тоже дух захватывает. FOM – это не журнал, а форум для обсуждения разных идей, поэтому политика FOM выглядит очень привлекательно. Большинство начальников FOM против стандартной математики и за так наз. finitism, т.е., подход когда нет бесконечностей. Но, с другой стороны, в той математике, которую они пропагандируют нет и операций по модулю числа. Так происходит, например в Robinson arithmetic и Peano arithmetic. Эти арифметики считаются неполными и в приложениях не применяются. Но в целом мне казалось, что то что я пытаюсь делать они должны приветствовать. Ясно, что когда я узнал про FOM, то сразу захотел в нем участвовать. Но – это не открытый форум, и вначале надо, чтобы начальники FOM одобрили твое участие. Т.е., проблема типа arxiv-vixra.

Я послал в FOM такой application: