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
> 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.