From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4839 Path: news.gmane.org!not-for-mail From: Greg Meredith Newsgroups: gmane.science.mathematics.categories Subject: Re: Axioms of elementary probability Date: Fri, 15 May 2009 12:35:43 -0700 Message-ID: <5de3f5ca0905151235l29a483c4sa7184bd4e06073ad@mail.gmail.com> Reply-To: Greg Meredith NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1242593332 7690 80.91.229.12 (17 May 2009 20:48:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 17 May 2009 20:48:52 +0000 (UTC) To: Jeff Egger , Original-X-From: categories@mta.ca Sun May 17 22:48:45 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1M5nHp-0000Tv-CD for gsmc-categories@m.gmane.org; Sun, 17 May 2009 22:48:45 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1M5mZb-0002sz-Sv for categories-list@mta.ca; Sun, 17 May 2009 17:03:04 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4839 Archived-At: David, Here 's an arXiv reference for the "cottage industry" i was referring to. Best wishes, --greg On Wed, May 13, 2009 at 12:59 PM, Greg Meredith < lgreg.meredith@biosimilarity.com> wrote: > David, > > To my mind there are three presentations of a "theory" of probability. Two > arrive at essentially the same theory by somewhat different means; these are > frequentist and Bayesian presentations of "standard" probability theory. The > third comes from a completely different direction: quantum mechanics. i > remember when i first encountered the Dirac presentation of QM and the > interpretation of as a probability amplitude. My first thought was > -- hang on, doesn't that come with an obligation to prove that this aligns > with (satisfies the axioms of) a theory of probability. In attempting to > work that out for myself, i realized that it didn't; discovered a whole > cottage industry of people who had made a similar observation; and argued to > myself that of the various notions of probability put forward, this one > enjoyed being rigourously employed in physical calculations verified to many > decimal places. > > Best wishes, >