Gravity in a Nutshell is too chatty, would like something else

[vanhees71]

I took the table rather as what math is applied in which subarea of (theoretical) physics. I've also no idea, where number-theoretical methods are used in physics, but one should never think one doesn't need a specific mathematical subject ever in physics. Usually it's according to Murphy's Law: Whenever you hit a problem in theoretical physics you exactly need math you don't know about ;-)). That's why it is so important to have a good education in mathematical methods to be able to learn the math you may need in some problem but you don't know yet.

 

[Demystifier]

But there is geometry in classical mechanics, and analysis/PDE in relativity and functional analysis in QM.

Just as there is analysis in differential geometry/topology, or algebra in algebraic geometry/topology, or relativity in QM, or ... Nobody said that there is no overlap between different branches. The analogies should correspond to the typical styles of thinking within certain branches. For instance, I matched interpretations of QM with logic and set theory because those are the most philosophical branches of physics/mathematics.

Personally, I find it most difficult to think like a number theorist, which may be related to the fact that it is hard to associate it with anything in physics.

 

[vanhees71]

I'd match "interpretations of QM" with esoterics and non-scientific approaches to realtity. SCNR.

 

[Daverz]

I lost my copy of Weinberg in a move. Were there more insights and better exposition that in any texts written in the 45 years since? Wondering if I should look for a new copy.

 

[Demystifier]

I'd match "interpretations of QM" with esoterics and non-scientific approaches to realtity. SCNR.

Well, perhaps some mathematicians have similar feelings about set theory. If you have ever been reading about the theory of infinite ordinal numbers, you will probably know what I am talking about.
Indeed, the famous mathematician Poincare considered such mathematical constructs totally meaningless.

 

[vanhees71]

I see, so each science has its dead bodies in the basement ;-)). Anyway, math can be very weird, particularly in view of Goedel's results, which has killed Hilbert's hope for a fully self-consistent axiomatic approach in the sense that you cannot prove the consistency of any sufficiently interesting axiomatic system within this system itself.

 

[Demystifier]

I see, so each science has its dead bodies in the basement ;-)).

Yes, except that I would put it differently. I would say than any science XYZ has questions about XYZ which cannot be answered within XYZ, leading to a need for philosophy of XYZ.

 

[vanhees71]

Hm, but than it's not science anymore. A real paradox, after all!

 

[Demystifier]

Hm, but than it's not science anymore. A real paradox, after all!

The real paradox is that there is no strict boundary between science and philosophy, yet most scientists think they know exactly where the boundary is.

 

[martinbn]

The real paradox is that there is no strict boundary between science and philosophy, yet most scientists think they now exactly where the boundary is.

Many, if not most, would say that the boundary is precisely where the boundary of their interests is. If they are doing it, it is real science, if they are not interested, then it is useless philosophy.

 

[vanhees71]

The real paradox is that there is no strict boundary between science and philosophy, yet most scientists think they know exactly where the boundary is.

I don't know it, but I clearly feel when science becomes philosophical, when I see it ;-)).

 

[vanhees71]

Many, if not most, would say that the boundary is precisely where the boundary of their interests is. If they are doing it, it is real science, if they are not interested, then it is useless philosophy.

Or the other way: Philosophers often are interested in philosophy only and don't care about the science. What I dislike is that nevertheless they make "philosophy of science" about the science they are not intersted in! SCNR.