Hi Jos, I have this mail "starred" in my inbox to have a good look at - looks very interesting. Just tied up with the day job for a few days .....
Ian On 4/19/07, Laycock, Jos (OSPT) <[EMAIL PROTECTED]> wrote: > > 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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