sorry Harv comparing the statements below i don't see contradiction. i see agreement.
Dr. Dick says:
"the reason mathematics is so important to science is that we are attempting to map the real universe".
Harv says:
"If thought in terms of math education, then abstractions should be thought of as independent of 'real' things, however in the context of how mathematics is discussed here (i.e., in epistemological terms), then you are quite right that mathematics is about reality since what else could it be about? There is a whole history that can trace how things become abstract and that this forms a chain of references that ultimately reduce any abstract thing to a particular thing."
with regard to further issues that you've raised.
i agree with your assertion that mathematics is not done in a complete vacuum from the world in which we live. There are traces of the world that find their way into mathematics. It happens in the manner in what axioms we consider important, what we generally mean by those axioms and 'undefined terms', etc.
nor do i have a problem with your assertion that mathematics is not a physical science concerned with making accurate statements about the universe. but this is not to say that it doesn't draw it's essence from reality, nor does it say that the abstractions it contains are not a part of reality.
i've not seen any indication in Dr. Dick's paper that he has implied that his work must be true simply because he has used mathematics in the creation of it. more so he points out that for the attack he is making on reality it is perhaps the best tool to use.
your assertion that Dr. Dick assumes that because he has used mathematics as his basis and he has matched the laws of physics that somehow he has escaped the requirements to produce new observables seems odd to me. if he has truly matched the laws of physics which have already produced observables why should Dick's work be expected to produce new observables?
regards, tim
