Confused about information theory
If I understand information theory right, then, given "Socrates is human" and "all humans are mortals", there is no information in "Socrates is mortal", as it can be derived from the given statements. But what about the computational cost of deriving conclusions from statements? Does information not capture or consider that at all?
Aquinas said that angels immediately know all the consequences of their knowledge. But humans do not.
Just to give an obvious example, in cryptography, the public key is known. The private key is derivable from the public key, but the computational cost is so hight that it seems obvious that the private key is information, and in fact quite valuable information.
So it seems that between information and compute there should be some theory that connects them, but I can't remember having come across anything like that? What am I missing?
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