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> it is quite surprising that these two sets of axioms that look nothing alike produce the same self-consistent physics Why is that surprising? This sort of t
by lisper 3y ago
> it is quite surprising that these two sets of axioms that look nothing alike produce the same self-consistent physics
Why is that surprising? This sort of thing seems to be ubiquitous in our universe. F=ma is equivalent to the principle of least action. Turing machines are equivalent to the lambda calculus. Electrodynamics is equivalent to the existence of a finite reference velocity.
Also:
> You need to define temperature as an associative observable
Did you mean transitive? My understanding is that the required axiom is that if system A is in thermal equilibrium with system B, and B is in equilibrium with C, then A will be in equilibrium with C. That's transitivity, not associativity.
- krastanov 3y agoIndeed, this type of "surprises" is how you know you are probably on the right track with your choice of abstraction. But I still find the word "surprise" reasonable for the emotion I feel when I observe something like that. Very pleasing reassuring intellectually satisfying surprise. A "sufficiently smart armchair theorist" might discover these "surprises" in advance simply from consistency and beauty and simplicity considerations, but these armchair theorists are usually just a made up thing we imagine when teaching. I corrected the wrong use of the word associative, thanks!