While my post was pretty misguided (I even wrote an apology for it), your comment looks even more misguided to me. In effect, you’re saying that between Lagrangian and Hamiltonian mechanics, at most one can be “true”. And you’re also saying that which of them is “true” depends on the programming language we use to encode them. Are you sure you want to go there?
In effect, you’re saying that between Lagrangian and Hamiltonian mechanics, at most one can be “true”.
We may even be able to observe which one. Actually, I am pretty sure that if I looked closely at QM and these two formulations, I would go with Hamiltonian mechanics.
Ah, but which Hamiltonian mechanics is the true one: the one that says real numbers are infinite binary expansions, or the one that says real numbers are Dedekind cuts? I dunno, your way of thinking makes me queasy.
That point of view has far-reaching implications that make me uncomfortable. Consider two physical theories that are equivalent in every respect, except they use different definitions of real numbers. So they have a common part C, and theory A is the conjunction of C with “real numbers are Dedekind cuts”, while theory B is the conjunction of C with “real numbers are infinite binary expansions”. According to your and Eliezer’s point of view as I understand it right now, at most one of the two theories can be “true”. So if C (the common part) is “true”, then ordinary logic tells us that at most one definition of the real numbers can be “true”. Are you really, really sure you want to go there?
While my post was pretty misguided (I even wrote an apology for it), your comment looks even more misguided to me. In effect, you’re saying that between Lagrangian and Hamiltonian mechanics, at most one can be “true”. And you’re also saying that which of them is “true” depends on the programming language we use to encode them. Are you sure you want to go there?
We may even be able to observe which one. Actually, I am pretty sure that if I looked closely at QM and these two formulations, I would go with Hamiltonian mechanics.
Ah, but which Hamiltonian mechanics is the true one: the one that says real numbers are infinite binary expansions, or the one that says real numbers are Dedekind cuts? I dunno, your way of thinking makes me queasy.
Sorry—I wrote an incorrect reply and deleted it. Let me think some more.
That point of view has far-reaching implications that make me uncomfortable. Consider two physical theories that are equivalent in every respect, except they use different definitions of real numbers. So they have a common part C, and theory A is the conjunction of C with “real numbers are Dedekind cuts”, while theory B is the conjunction of C with “real numbers are infinite binary expansions”. According to your and Eliezer’s point of view as I understand it right now, at most one of the two theories can be “true”. So if C (the common part) is “true”, then ordinary logic tells us that at most one definition of the real numbers can be “true”. Are you really, really sure you want to go there?