Humans do something other than follow algorithms: An algorithm has 1) an input, and 2) an output that's related to the input in a prescribable way (i.e. it has to halt—Turing) Creativity can't be an algorithm, because one can't specify criteria for what the output would be.
Well… I can’t actually give you two numbers. I can only perform physical actions, such as writing a numeral on a piece of paper. Then we can agree that the number represents a non-physical thing; but no one has been able to coherently explain what “represents” means.
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You can perform the addition and tell me the answer, and it may be right or wrong, and this is obviously extremely useful, but it is not at all clear how exactly it relates to the formal theory of computation.
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This *could*, in principle, just be philosophical nitpicking: but Part III of The Eggplan, which I’m currently attempting to write, explains that it has substantive implications for how we can be use formal rationality in the physical world.
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Sorry, “numeral” not “number” here!
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You could say that about computers, too. We press their buttons and they blink their lights at us, based on circuits and voltages. Haven't you defined algorithms out of existence? There are actions both computers and people can do that we describe as "following an algorithm."
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