/sci/ - Science & Math

>>14725528
John, quick question: I have heard the book you use as a reference is your 40-year-old high school physics textbook. Why use such an obviously elementary and unsuitable book as a reference? It's quite clear that nobody in the field uses this as a reference. Why not use something like Landau and Lifshitz's Course of Theoretical Physics? I can assure you, it's far more often used as a reference.

I've been thinking about this lately. Do you think geniuses like John von Neumann seriously questioned the information they absorbed? Quotes like pic rel make it seem like what these geniuses have in common is ridiculous memorization skills

scientifically speaking

"It is very hard for any mathematician to believe that mathematics is a purely empirical science or that all mathematical ideas originate in empirical subjects. Let me consider the second half of the statement first. There are various important parts of modern mathematics in which the empirical origin is untraceable or if traceable so remote that it is clear that the subject has undergone a complete metamorphosis since it was cut off from its empirical roots. The symbolism of algebra was invented for domestic, mathematical use, but it may be reasonably asserted that it had strong empirical ties. However, modem, "abstract" algebra has more and more developed into directions which have even fewer empirical connections. The same may be said about topology. And in all these fields the mathematician's subjective criterion of success, of the worth-whileness of his effort is very much self-contained and aesthetical and free (or nearly free) of empirical connections. In set theory this is still clearer. The power and the ordering of an infinite set may be the generalizations of finite numerical concepts, but in their infinite form (especially power) they have hardly any relation to this world. If I did not wish to avoid technicalities, I could document this with numerous set theoretical examples-the problem of the "axiom of choice," the "comparability" of infinite "powers," the "continuum problem". The same remarks apply to much of real function theory and real point-set theory. Two strange examples are given by differential geometry and by group theory: they were certainly conceived as abstract non-applied disciplines and almost always cultivated in this spirit. After a decade in one case and a century in the other, they turned out to be very useful in physics. And they are still mostly pursued in the indicated, abstract, non-applied spirit. What is the mathematician's normal relationship to his subject? What influences, what considerations, control and direct his effort?"

>>12479806
A/s/l
Physicist here

>>12474941
>Relational Quantum Mechanics
Do you have a good reference for that OP (or someone else here)?

I've already had many courses in QM and the Italian guy gave a talk (that I couldn't attend) at my uni, but otherwise I'm rather blank on the subject - but interested
Thanks.

>>11895840
Jech is a book in the field of Set Theory. It's about transfinite induction, V=L and large cardinals and such. It states UFC axioms on page one and then makes 5 pages of comments on classes and well ordering. You don't learn what you mean by set theory in that - for that you want an intro to logic book.