On 23-Jul-05, you wrote: > Hi Brent, > ----- Original Message ----- > From: "Brent Meeker" <[EMAIL PROTECTED]> > To: <email@example.com> > Sent: Friday, July 22, 2005 8:31 PM "Michael Godfrey" <[EMAIL PROTECTED]> Date > Subject: Re: what relation do mathematical models have with reality? > > >> On 22-Jul-05,Stephen P. King wrote: >> >>> Hi Brent, >>> >>> Ok, I am rapidly loosing the connection that abstract models >>> have with the physical world, at least in the case of >>> computations. If there is no constraint on what we can >>> conjecture, other than what is required by one's choice of logic >>> and set theory, what relation do mathematical models have with >>> reality? >>> >>> Is this not as obvious as it appears? >> [BM] >> Here's my $0.02. We can only base our knowledge on our experience >> and we don't experience *reality*, we just have certain >> experiences and we create a model that describes them and >> predicts them. Using this model to predict or describe usually >> involves some calculations and interpretation of the calculation >> in terms of the model. The relation of the model to reality, if >> it's a good one, is it gives us the right answer, i.e. it >> predicts accurately. Their are other criteria for a good model >> too, such as fitting in with other models we have; but prediction >> is the main standard. So in my view, mathematics and theorems >> about computer science are just models too, albeit more abstract >> ones. Persis Diaconsis says, "Statistics is just the physics of >> numbers." I have a similar view of all mathematics, e.g. >> arithmetic is just the physics of counting. > > [SPK] > > Ok, I would agree completely with you if we are using Kant's > definition of *reality*- Dasein: existence in itself, but I was trying to > be point out that we must have some kind of connection between the > abstract and the concrete. > One thing that I hope we all can agree upon about *reality* is that > what ever it is, its properties are invariant with respect to > transformations from one point of view to any other. It is this trait that > makes it "independent", but the problems with realism seem to arise when > we consider whether or not this *reality* has some set of properties to > the exclusion of any others independent of some observational context. > QM demands that we not treat objects as having some sharp set of > properties independent of context and thus the main source of > counterintuitive aspects that make QM so difficult to deal with when we > approach the subject of Realism. OTOH, we have to come up with an > explanation of how it is that our individual experiences of a world seem > to be confined to sharp valuations and the appearance of property > definiteness. Everett and others gave us the solution to this conundrum > with the MWI.
MWI is *a* solution. But it is also possible to regard QM as a theory of what we know or can say about a system. Have you read Bohm's interpretation of QM? MWI seemed very promising when it seemed to solve the Born problem. But since it has been shown that the Born postulate is independent, then one might as well postulate that only one thing happens - as in consistent histories, or Bohm's intepretation. >Any given object has eigenstates (?) that have eigenvalues > (?) that are sharp and definite relative to some other set of eigenstates, > but as a whole a state/wave function is a superposition of all possible.I I'm not sure what you mean by "object". In general an object, such as an electron, has different eigenvalues depending on how it is prepared/measured. So they are not necessarily properties of the object alone. > So, what does this mean? We are to take the a priori and context > independent aspect of *reality* as not having any one set of sharp and > definite properties, it has a superposition of all possible. That's not how I'd take it. >The trick is > to figure out a reason why we have one basis and not some other, one > partitioning of the eigenstates and not some other. That's the decoherence program of Zeh, Zurek, Joos, Schlosshauer, et al. > > What does this have to do with mathematics and models? If we are going > to create/discover models of what we can all agree is sharp and definite- > our physical world, we must be sure that our models agree with each other. > This, of course, assumes that there is some connection between abstract > and concrete aspect of *reality*. Or that we pick out those parts of our experience which we can describe by models indpendent of viewpoint. The rest we call subjective experience. Brent Meeker