Humans are computationally bounded, Bayes is not. In an ideal Bayesian perspective:
Your prior must include all possible theories a priori. Before you opened your eyes as a baby, you put some probability of being in a universe with Quantum Field Theory with SU(3)×SU(2)×U(1) gauge symmetry and updated from there.
Your update with unbounded computation. There’s not such thing as proofs, since all poofs are tautological.
Humans are computationally bounded and can’t think this way.
(riffing)
“Ideas” find paradigms for modeling the universe that may be profitable to track under limited computation. Maybe you could understand fluid behavior better if you kept track of temperature, or understand biology better if you keep track of vital force. With a bayesian-lite perspective, they kinda give you a prior and places to look where your beliefs are “mailable”.
“Proofs” (and evidence) are the justifications for answers. With a bayesian-lite perspective, they kinda give you conditional probabilities.
“Answers” are useful because they can become precomputed, reified, cached beliefs with high credence inertial you can treat as approximately atomic. In a tabletop physics experiment, you can ignore how your apparatus will gravitationally move the earth (and the details of the composition of the earth). Similarly, you can ignore how the tabletop physics experiment will move you belief about the conservation of energy (and the details of why your credences about the conservation of energy are what they are).
Yes, I also realized that “ideas” being a thing is due to bounded rationality—specifically they are the outputs of AI search. “Proofs” are weirder though, and I haven’t seen them distinguished very often. I wonder if this is a reasonable analogy to make:
I think only particular reward functions, such as in multi-agent/co-operative environments (agents can include humans, like in RLHF) or in actually interactive proving environments?
Humans are computationally bounded, Bayes is not. In an ideal Bayesian perspective:
Your prior must include all possible theories a priori. Before you opened your eyes as a baby, you put some probability of being in a universe with Quantum Field Theory with SU(3)×SU(2)×U(1) gauge symmetry and updated from there.
Your update with unbounded computation. There’s not such thing as proofs, since all poofs are tautological.
Humans are computationally bounded and can’t think this way.
(riffing)
“Ideas” find paradigms for modeling the universe that may be profitable to track under limited computation. Maybe you could understand fluid behavior better if you kept track of temperature, or understand biology better if you keep track of vital force. With a bayesian-lite perspective, they kinda give you a prior and places to look where your beliefs are “mailable”.
“Proofs” (and evidence) are the justifications for answers. With a bayesian-lite perspective, they kinda give you conditional probabilities.
“Answers” are useful because they can become precomputed, reified, cached beliefs with high credence inertial you can treat as approximately atomic. In a tabletop physics experiment, you can ignore how your apparatus will gravitationally move the earth (and the details of the composition of the earth). Similarly, you can ignore how the tabletop physics experiment will move you belief about the conservation of energy (and the details of why your credences about the conservation of energy are what they are).
Yes, I also realized that “ideas” being a thing is due to bounded rationality—specifically they are the outputs of AI search. “Proofs” are weirder though, and I haven’t seen them distinguished very often. I wonder if this is a reasonable analogy to make:
Ideas : search
Answers : inference
Proofs: alignment
Ideas come from unsupervised training, answers from supervised training and proofs from RL on a specified reward function.
I think only particular reward functions, such as in multi-agent/co-operative environments (agents can include humans, like in RLHF) or in actually interactive proving environments?