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> all this crazy complicated and far-fetched ideas, rather than simple and beautiful principles to understand reality Would you mind giving some examples of wh

by twtw 8y ago

> all this crazy complicated and far-fetched ideas, rather than simple and beautiful principles to understand reality Would you mind giving some examples of what kind of "simple and beautiful principles" you have in mind?

krastanov 8y ago
Depends on the level (and I am just giving some examples): - Advanced high school: You can use conservation of energy or other "conservation laws" as a guiding principle. This lets you solve a problem with just a couple of lines of simple algebra. On the other hand, using the "naive" approach of studying the forces that act on the system would require heavy algebra and some calculus. - College: Instead of calculating the path of a ray of light through some inhomogeneous piece of transparent matter by doing some form of raytracing, you can use Fermat's "minimization principle". They are equivalent, but a rigorous definition of the minimization principle is a single sentence, while the other approach takes a lot of work to express clearly. - Advanced college: Conservation laws are actually consequences of symmetries. Instead of thinking in terms of a complicated expression for energies and momenta, you can say that they are consequences of the fact that the laws of the universe do not change from today to tomorrow. Yes, the more simple and beautiful a principle is, the more abstract it is. However, the simplicity and ease of working with it makes the abstraction worth it. Just like in C you can have your own weird struct that implements objects and higher order functions, but using a functional or object oriented language makes everything safer and easier and more readable.
- SquishyPanda23 8y ago
  > Conservation laws are actually consequences of symmetries. For those unfamiliar, this is essentially the content of Noether's Theorem[0]. One of many beautiful contributions of Emmy Noether. I've heard several physicists describe it as one of the most beautiful theorems in physics. [0] https://en.wikipedia.org/wiki/Noether%27s_theorem https://en.wikipedia.org/wiki/Noether%27s_theorem
everybodyknows 8y ago
Conservation of energy and conservation of vector momentum directly explain the phenomenon of coastal rip currents, a mortal danger to beach-goers. Whereas if you go by the usual public sources, they're as mysterious as sun spots.
Retra 8y ago
Pretty much anything in thermodynamics. Phase changes, energy, entropy, symmetry, action principles, degrees of freedom, fluctuation-dissipation theorem, equipartition theorem, etc..

by twtw 8y ago

krastanov 8y ago

Depends on the level (and I am just giving some examples): - Advanced high school: You can use conservation of energy or other "conservation laws" as a guiding principle. This lets you solve a problem with just a couple of lines of simple algebra. On the other hand, using the "naive" approach of studying the forces that act on the system would require heavy algebra and some calculus. - College: Instead of calculating the path of a ray of light through some inhomogeneous piece of transparent matter by doing some form of raytracing, you can use Fermat's "minimization principle". They are equivalent, but a rigorous definition of the minimization principle is a single sentence, while the other approach takes a lot of work to express clearly. - Advanced college: Conservation laws are actually consequences of symmetries. Instead of thinking in terms of a complicated expression for energies and momenta, you can say that they are consequences of the fact that the laws of the universe do not change from today to tomorrow. Yes, the more simple and beautiful a principle is, the more abstract it is. However, the simplicity and ease of working with it makes the abstraction worth it. Just like in C you can have your own weird struct that implements objects and higher order functions, but using a functional or object oriented language makes everything safer and easier and more readable.

SquishyPanda23 8y ago
> Conservation laws are actually consequences of symmetries. For those unfamiliar, this is essentially the content of Noether's Theorem[0]. One of many beautiful contributions of Emmy Noether. I've heard several physicists describe it as one of the most beautiful theorems in physics. [0] https://en.wikipedia.org/wiki/Noether%27s_theorem https://en.wikipedia.org/wiki/Noether%27s_theorem

everybodyknows 8y ago

Conservation of energy and conservation of vector momentum directly explain the phenomenon of coastal rip currents, a mortal danger to beach-goers. Whereas if you go by the usual public sources, they're as mysterious as sun spots.

Retra 8y ago

Pretty much anything in thermodynamics. Phase changes, energy, entropy, symmetry, action principles, degrees of freedom, fluctuation-dissipation theorem, equipartition theorem, etc..