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>> Solomonoff Induction has shown that Bayesian inference will reproduce any underlying computable function given a suitable prior. Btw, when we talk of "func

>> Solomonoff Induction has shown that Bayesian inference will reproduce any underlying computable function given a suitable prior. Btw, when we talk of "functions" we mean a mapping between elements of two or more sets. A "system" is not a function. I don't know a formal definition of a system, but if you're talking about whatever the human brain is doing that's likely to be more easily modelled as a Turing machine. And a Turing machine is not, in itself, a function. It is a computational device that can calculate the result of some set of calculable functions. You can model a Turing machine as a function, e.g. by mapping some set of programs to the set of inputs and outputs of those programs, or something scary like that, but once again this mapping will tell you nothing about the internal operation of any specific Turing machine. If, by any chance, you think of the brain as a universal Turing machine (UTM), then I'd really like to see the function you come up with to represent its behaviour; and let's see how much this function tells you about the internal structure of the brain-UTM.

YeGoblynQueenne 3y ago
Further to all this I must assure you that all of the above is not some attempt at sophistry or trying to score internet points: what we discuss here goes right at the heart of my doctoral research. You can get some background on the problems I've dealt with if you search online for Inductive Logic Programming and Statistical Relational Learning. People in my research community have grappled with these questions for a long time and tried to put together the pieces of the puzzle: relations, functions, algorithms, programs, logic, probabilities, statistics, learning, reasoning... the human mind. They have consistently failed because the pieces of the puzzle don't fit. I think in modern machine learning people have simply given up on trying to make any coherent image out of the puzzle pieces and just bashed them until they yielded and are now wedged together in incongruous patterns that sort of show some kind of image, there. But the incongruities are still felt, like nails on a blackboard.

YeGoblynQueenne 3y ago

Further to all this I must assure you that all of the above is not some attempt at sophistry or trying to score internet points: what we discuss here goes right at the heart of my doctoral research. You can get some background on the problems I've dealt with if you search online for Inductive Logic Programming and Statistical Relational Learning. People in my research community have grappled with these questions for a long time and tried to put together the pieces of the puzzle: relations, functions, algorithms, programs, logic, probabilities, statistics, learning, reasoning... the human mind. They have consistently failed because the pieces of the puzzle don't fit. I think in modern machine learning people have simply given up on trying to make any coherent image out of the puzzle pieces and just bashed them until they yielded and are now wedged together in incongruous patterns that sort of show some kind of image, there. But the incongruities are still felt, like nails on a blackboard.