Hatto von Aquitanien wrote: > guenther vonKnakspot wrote: > > > the ever more present wrong notion that mathematics is dependent on > > computability and the expanding belief that mathematics is somehow > > subjected to the constrains of physical reality. > > I know this was addressed to someone else, but I would also like to offer my > thoughts on this matter. I contend that mathematics _is_ constrained by > physical reality. The underlying logic which determines mathematics is a > manifestation of physical reality. I believe what you are asserting is That is an issue for Philosophers which I don't believe can be resolved definitely. I do not subscribe to it, but can not refute it either, so let us please agree to exclude it from this particular discussion.This is not howewer the flawed reasoning that I am refering to. I am talking much baser contentions made by the ill educated like denying the existence of certain mathematical objects on the ground that they can not be physically constructed. An example would be the set of Natural Numbers whichs existence is denied because there are not sufficient atoms in the universe to build a tangible physical representation of it, or specific irrational numbers on on the same grounds pertaining to their decimal base representation.
> that mathematics should not be required to produce physically measurable > results as a test of its validity. I really have to wonder if such a > requirement is unrealistic.
If you make such a requirement, then you will not get very far. What is a physically measurable result that gives validity to the number 2 ? Or to the law of distributivity? or to the differentiability of a given function? Mathematical concepts have no consequences in physical reality and the laws of the physical universe have no consequence for mathematical concepts. (as long as we keep to the agreement I requested above).
> It's interesting to observe that some people > are wont to point to the fact that formal proofs can be verified by > computer programs. > > I note that you object to the idea that "mathematics is dependent on > computability". I don't know if you mean that exclusively in terms of > solving equations and/or finding approximate numerical solutions, or if you > also object to the idea the mathematical proofs should be machine > verifiable. I curious to know what you think of this: http://metamath.org/
I agree with the idea that mathematical proofs should be machine verifiable; as long as this is a statement about computer science and not about mathematics. Regards.