" Dick is doing applied math and the rules of application are different than just doing math."
how so Harv?
" Dick goes further. He makes the assumption that mathematics is the attempt to map the real universe. Note his text (I'll also quote Dick since he likes to be quoted): "the reason mathematics is so important to science is that we are attempting to map the real universe". This assumption is a huge unwarranted assumption, and shouldn't be part of any pure mathematical work. It is applied mathematics gone headstrong into metaphysics, and that's a major reason why Dick's paper shouldn't be considered with any significant merit. "
is this really so bad? does his paper hinge on this statement? the statement is an argument for using mathematics. Dick's paper is not a pure mathematical work. i wondered about the statement myself, but while i don't believe it is an accurate summation of mathematics i do think it has some rational basis behind it particuarly in light of what his paper is about. certainly mathematics relates to the physical world in many ways as abstractions of features of the world such as quantities, symmetrys, spatial features and operational behaviors.
"This is just blatantly untrue Tim. Science uses mathematics to construct models because they are successful doing it. If science were successful using Alan's fly-by-the-seat-of-your-pants-make-comments-along-the-way type of investigation, then I imagine that Alan would be in large company. Unfortunately, scientific progress isn't achieved in such a loose and capricious fashion (otherwise I might take up physics for a profession...). Science has discovered that mathematics is helpful for developing models that have predictions that match our observations and that provide good explanations, and therefore science uses it. The philosophy behind mathematics is very contentious and divided. Even scientists disagree what mathematics is exactly, and no one has any supportable answer to the question. It can't just be definitions that should concern us, but the whole assumption that we are saying something about reality with our current understanding of math."
Harv, this is almost laughable. a scientist can use mathematics any way he sees fit. and scientific progress has often been achieved in loose and capricious fashion. an example would be how the structure of benzene was discovered. it was discovered by a chemist dreaming of snakes swallowing their tales. the structure of DNA would be another example, a series of trials and errors. our antibiotics were discovered by a gross error of a scientist leaving unwashed petry dishs in a sink when he went on vacation.
so not everyone is on the same page when it comes to ones opinion about what mathematics is. we all still use it and if it is used intelligently the results are often magical they are so successful. again one can embark on what ever scientific enquiry one desires and mathematics will not mind one iota if one uses it.
"The term 'our science' is imprecise. Dick's model has little or no theoretical physics beyond 1950's from what I can tell. Nothing about the physics that was developed using internal symmetries, just the external symmetry physics. It seems strange and coincidental that this is the case since he actually uses external symmetry arguments, but lacks internal symmetry arguments, don't you think so? "
i wouldn't be able to comment on this. i'm still reviewing the first chapter and have only skimmed the whole paper.