4 ms·

As far as I remember probability distributions were clearly used all over the course but were introduced in a "probability light" manner (which probably made se

As far as I remember probability distributions were clearly used all over the course but were introduced in a "probability light" manner (which probably made sense for people studying physics but not so much for me).

ur-whale 2y ago
This is exactly what I remember from every physics course I took in my life: many physicists use math as a blunt tool rarely even bothering explaining them, and almost never justifying why the tool is actually applicable to the problem at hand (e.g. by simply stating that the axioms of the math seem to align with physical observations at all times, thereby very much justifying the use of the mathematical framework). Far worse, many a physic teacher doesn't even understand the tools they're using from math: they're just parroting and regurgitating from memory a combo of the textbook and what they've been told all the way to grad school, and if you happen to manage to corner them after class to dig a little, you quickly discover how shallow their understanding of the math actually is. Both Thermodynamics and Electromagnetism were initially hell on earth for me for this very reason: the profs were both incapable of explaining what the tools were and did, how they worked and why they were applicable. All they wanted was for you to absorb and memorize the formulas and stop asking all these stupid questions about the math. When I finally understood the math tools underlying the two subjects, both thermo and electromagnetism became crystal clear, but boy was the initial exposure an effing headache. A very good example of this is the famous book "div, grad, curl and all that" that many people hail as excellent. Well, I strongly disagree. It was written by a physicist, and the whole book is laden with references to either fluid mechanics or electromagnetism. It never is capable of explain things without making reference to physics when the tools are in fact completely independent of it.
kgwgk 2y ago
Somehow Gibbs managed to write his “Elementary Principles in Statistical Mechanics” before Kolmogorov was even born (a few days before Gibbs’ death).
- 331c8c71 2y ago
  Sure, half of the math (if not more) was done in the same way e.g. by using tools or concepts informally before they were defined rigorously.
  - kgwgk 2y ago
    To the extent that one doesn’t need measure theory to do statistical mechanics there is no need to teach measure theory in a statistical mechanics course. “If anyone wants to concentrate his attention on infinite sets, measure theory, and mathematical pathology in general, he has every right to do so. And he need not justify this by pointing to useful applications or apologize for the lack of them; as was noted long ago, abstract mathematics is worth knowing for its own sake. But others in turn have equal rights. If we choose to concentrate on those aspects of mathematics which are useful in real problems and which enable us to carry out the important substantive calculations correctly – but which the mathematical pathologists never get around to – we feel free to do so without apology.” [Jaynes 2003, p. 673] By the way, rigour and generality are different things.
    - 331c8c71 2y ago
      > To the extent that one doesn’t need measure theory to do statistical mechanics there is no need to teach measure theory in a statistical mechanics course. I never assumed otherwise. That being said, I couldn't be bothered to memorize and reproduce the handwavy exposition that made sense to a particular physicist. And it's not that I was there to prove a point - I was asked about the basic constructions like probability distributions, densities etc. > infinite sets, measure theory, and mathematical pathology > By the way, rigour and generality are different things. Measure theory and Kolmogorov axiomatization addressed very real problems like Bertrand's paradox plaguing classical probabilit to the point that it was often seen as a black art rather than science. Moreover, stochastic processes in continuous time are not very intuitive and a sound theory would be next to impossible to develop without solid foundations.
      - kgwgk 2y ago

ur-whale 2y ago

This is exactly what I remember from every physics course I took in my life: many physicists use math as a blunt tool rarely even bothering explaining them, and almost never justifying why the tool is actually applicable to the problem at hand (e.g. by simply stating that the axioms of the math seem to align with physical observations at all times, thereby very much justifying the use of the mathematical framework). Far worse, many a physic teacher doesn't even understand the tools they're using from math: they're just parroting and regurgitating from memory a combo of the textbook and what they've been told all the way to grad school, and if you happen to manage to corner them after class to dig a little, you quickly discover how shallow their understanding of the math actually is. Both Thermodynamics and Electromagnetism were initially hell on earth for me for this very reason: the profs were both incapable of explaining what the tools were and did, how they worked and why they were applicable. All they wanted was for you to absorb and memorize the formulas and stop asking all these stupid questions about the math. When I finally understood the math tools underlying the two subjects, both thermo and electromagnetism became crystal clear, but boy was the initial exposure an effing headache. A very good example of this is the famous book "div, grad, curl and all that" that many people hail as excellent. Well, I strongly disagree. It was written by a physicist, and the whole book is laden with references to either fluid mechanics or electromagnetism. It never is capable of explain things without making reference to physics when the tools are in fact completely independent of it.

kgwgk 2y ago

Somehow Gibbs managed to write his “Elementary Principles in Statistical Mechanics” before Kolmogorov was even born (a few days before Gibbs’ death).

331c8c71 2y ago
Sure, half of the math (if not more) was done in the same way e.g. by using tools or concepts informally before they were defined rigorously.
- kgwgk 2y ago
  To the extent that one doesn’t need measure theory to do statistical mechanics there is no need to teach measure theory in a statistical mechanics course. “If anyone wants to concentrate his attention on infinite sets, measure theory, and mathematical pathology in general, he has every right to do so. And he need not justify this by pointing to useful applications or apologize for the lack of them; as was noted long ago, abstract mathematics is worth knowing for its own sake. But others in turn have equal rights. If we choose to concentrate on those aspects of mathematics which are useful in real problems and which enable us to carry out the important substantive calculations correctly – but which the mathematical pathologists never get around to – we feel free to do so without apology.” [Jaynes 2003, p. 673] By the way, rigour and generality are different things.
  - 331c8c71 2y ago
    > To the extent that one doesn’t need measure theory to do statistical mechanics there is no need to teach measure theory in a statistical mechanics course. I never assumed otherwise. That being said, I couldn't be bothered to memorize and reproduce the handwavy exposition that made sense to a particular physicist. And it's not that I was there to prove a point - I was asked about the basic constructions like probability distributions, densities etc. > infinite sets, measure theory, and mathematical pathology > By the way, rigour and generality are different things. Measure theory and Kolmogorov axiomatization addressed very real problems like Bertrand's paradox plaguing classical probabilit to the point that it was often seen as a black art rather than science. Moreover, stochastic processes in continuous time are not very intuitive and a sound theory would be next to impossible to develop without solid foundations.
    - kgwgk 2y ago