Are you interested in elegance given physical relevance? For instance, Maxwell’s equations aren’t anything all that special in themselves, but when you discover that they explain approximately all of electricity, magnetism and light it’s a different matter.
I didn’t think about this part, because originally I was only thinking about math. Thank you for giving specific examples, so I can test my intuition to them.
Uhm… I’d say that “Δ . B = 0” doesn’t trigger my feeling of awesomeness, however important it may be. Even “E = m * c^2″ doesn’t, and that has a lot of applause light connected with it. They are just too simple; they feel like “a + b = c”.
On the other hand, I realized that if I don’t know what the equation means, I can’t decide whether it is good enough. So the meaning is a part of the utility function, but mathematical elegance is another part (the feeling of “oh, this is really equal to that?” like when the pieces of puzzle suddenly fit together) -- and I want the equations that satisfy both criteria.
Squark’s examples are already great enough and probably all I need, so if you had some specific examples in mind, please post them here, but otherwise I already have what I wanted.
Are you interested in elegance given physical relevance? For instance, Maxwell’s equations aren’t anything all that special in themselves, but when you discover that they explain approximately all of electricity, magnetism and light it’s a different matter.
I didn’t think about this part, because originally I was only thinking about math. Thank you for giving specific examples, so I can test my intuition to them.
Uhm… I’d say that “Δ . B = 0” doesn’t trigger my feeling of awesomeness, however important it may be. Even “E = m * c^2″ doesn’t, and that has a lot of applause light connected with it. They are just too simple; they feel like “a + b = c”.
On the other hand, I realized that if I don’t know what the equation means, I can’t decide whether it is good enough. So the meaning is a part of the utility function, but mathematical elegance is another part (the feeling of “oh, this is really equal to that?” like when the pieces of puzzle suddenly fit together) -- and I want the equations that satisfy both criteria.
Squark’s examples are already great enough and probably all I need, so if you had some specific examples in mind, please post them here, but otherwise I already have what I wanted.