Re: what relation do mathematical models have with reality?
Forwarded on behalf of Brent Meeker:
> On 24-Jul-05, you wrote:
>
> > Brent Meeker writes:
> >> 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.
> >
> > This makes sense but you need another element as well. This shows up
> > most explicitly in Bayesian reasoning models, but it is implicit in
> > others as well. That is the assumption of priors.
> >
> > When you observe evidence and construct your models, you need some
> > basis for choosing one model over another. In general, you can create
> > an infinite number of possible models to match any finite amount of
> > evidence. It's even worse when you consider that the evidence is noisy
> > and ambiguous. This choice requires prior assumptions, independent of the
> > evidence, about which models are inherently more likely to be true or not.
>
> In practice we use coherence with other theories to guide out choice. With
> that kind of constraint we may have trouble finding even one candidate
> theory. We begin with an intuitive physics that is hardwired into us by
> evolution. And that includes mathematics and logic. Ther's an excellent
> little book on this, "The Evolution of Reason" by Cooper.
>
>
> >
> > This implies that at some level, mathematics and logic has to come before
> > reality. That is the only way we can have prior beliefs about the models.
> > Whether it is the specific Universal Priori (1/2^n) that I have been
> > describing or some other one, you can't get away without having one.
> >
> >> 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.
> >
> > I don't think this works, for the reasons I have just explained.
> > Mathematics and logic are more than models of reality. They are
> > pre-existent and guide us in evaluating the many possible models of
> > reality which exist.
>
> I'd say they are *less* than models of reality. They are just consistency
> conditions on our models of reality. They are attempts to avoid talking
> nonsense. But note that not too long ago all the weirdness of quantum
> mechanics and relativity would have been regarded as contrary to logic.
>
>
> Brent Meeker
Received on Sun Jul 24 2005 - 22:29:59 PDT
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