On Sat, May 9, 2015 at 10:41 PM, LizR <[email protected]> wrote: Before I get started I want to remind people that I'm playing devil's advocate here, maybe mathematics really is more fundamental than physics but I've been taking the opposite stance in the last few posts because nearly everybody on this list assumes the question is settled, and it isn't. A strong case (but falling short of a proof) can be made that physics is the more fundamental.
> > Since computation is allegedly implied by number theory [...] > And whoever makes that allegation is talking nonsense. Nobody can add 1+1 with number theory, you need matter and the laws of physics. > > claiming it isn't an abstract process is the same as denying the > objective existence to number theory > The quantity of computation can be objectively measured and the amount of energy and time used and entropy produced can be precisely predicted for and given calculation, and how long it will take to transmit the results of a calculation over a wire of a given diameter can also be predicted. You can't do any of that with abstract things like love or beauty or justice, but you can do it for calculation. > > or, in an nutshell, denying that 2+2=4 independently of anyone knowing > that it does > By saying "anyone" you're implying the existence of physics and at least one physical thing, but as I said before if not even one thing existed, much less 4, it is not at all obvious that 2+2=4 would have any meaning. > > To prove your point you need to explain why maths is so "unreasonably > effective in the physical sciences" > I can't prove my point and you can't prove yours unless you can explain why a computer made of matter that obeys the laws of physics can determine that 2^57,885,161 − 1, a number with 17,425,170 digits, is prime. I don't have a proof but I can speculate that both the physicist and the mathematician try to make laws that are free from self contradictions, so when a physicist describes nature it will be consistent with one of those mathematical laws. But there are large areas of mathematics, especially modern mathematics, that don't seem to correspond with anything physical. Maybe physicists just haven't found them yet but if such correspondences don't exist would that mean much of modern mathematics has no more reality than a Harry Potter novel? And then there is the question of axioms. J K Rowling made a entertaining and largely plot hole free series of books starting with the assumption (axiom) that magic exists, suppose a mathematician started with the assumption (axiom) that the Goldbach's conjecture was true and went on from there using impeccable logic to write thousands of pages of mathematics and proved hundreds of unusual theorems. But then one day a computer made of matter and obeying the laws of physics found an even integer that was NOT the sum of two prime numbers. Would there be any fundamental difference between what the mathematician did and what Rowling did? Mathematicians often say that mathematics is a language, it that's true then the big question is what is that language talking about? If it isn't something physical then what is it? John K Clark > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
