Ant, Horse, Ian, EVERYONE please go read this, its like our cousins over in physics are the belatedly arriving cavalry.
Some further quotes from the NS article: "A set is just a collection of objects, anything from the infinite set of prime numbers to the set of all mammals" "TOPOI share one key feature; each gives rise to its own variety of logic" "Now they could see boolean algebra for what it was, merely the most familiar of many possible types of algebra" "Does this mean we must acept a universe that is real but about which any question will recieve myriad answers all of them true" Am I experiencing "cleveland harbour" rit large? > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] Behalf Of Ron Kulp > Sent: 18 April 2007 18:06 > To: [email protected] > Subject: Re: [MD] TOPOS > > > JOS, > Thanks again for the link! This ties in directly about what > I'm saying about classical > generalised assumptions And why it does not serve us at the > quantum level. > > "In regard to the three conditions listed above for a > ‘realist’ interpretation, our > scheme has the following ingredients: > 1. The concept of the ‘value of a physical quantity’ is > meaningful, although this > ‘value’ is associated with an object in the topos that may > not be the real-number > object. With that caveat, the concept of a ‘property of the > system’ is also meaningful. > 2. Propositions about a system are representable by a Heyting > algebra associated > with the topos. A Heyting algebra is a distributive lattice > that differs from a > Boolean algebra only in so far as the law of excluded middle > need not hold, > i.e., > ∨ ¬ > 1. A Boolean algebra is a Heyting algebra with strict equality: > > ∨ ¬ > = 1. > 3. There is a ‘state object’ in the topos. However, generally > speaking, there will > not be enough ‘microstates’ to determine this. Nevertheless, > truth values can be > assigned to propositions with the aid of a ‘truth object’. > These truth values lie > in another Heyting algebra. > This new approach affords a way in which it becomes feasible > to generalise quantum > theory without any fundamental reference to Hilbert spaces, > path integrals, etc.; in > particular, there is no prima facie reason for introducing > continuum quantities. As we > have emphasised, this is our main motivation for developing > the topos approach. We > shall say more about this later. > From a conceptual perspective, a central feature of our > scheme is the ‘neo-realist6’ > structure reflected in the three statements above. This > neo-realism is the conceptual > fruit of the mathematical fact that a physical theory > expressed in a topos ‘looks’ very > much like classical physics. > This fundamental feature stems from (and, indeed, is defined > by) the existence of > two special objects in the topos: the ‘state object’7, , > mentioned above, and the > ‘quantity-value object’," > > > I love it...topos comes very close to my line of thinking on > the subject. > -Ron > moq_discuss mailing list > Listinfo, Unsubscribing etc. > http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org > Archives: > http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ > http://moq.org.uk/pipermail/moq_discuss_archive/ > > This email was received from the INTERNET and scanned by the > Government Secure Intranet Anti-Virus service supplied by > Cable&Wireless in partnership with MessageLabs. (CCTM > Certificate Number 2006/04/0007.) 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