On 22-Jul-05, you 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?
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. Brent Meeker