Intelligence comes from the power of discrimination. To a certain extent, I tend to agree that there ought to be some function that should correctly classify. The other aspect of Intelligence is power of interpretation. What mathematical function does that?
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Intelligence is the ability to model. Interpretation of models is done by meta-modeling parts of the intelligent system. The self can even be seen as a tertiary model (the mind looking at how its model of itself deals with with its models of reality).
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A step beyond general intelligence, could a biological entity be considered an universal intelligence?
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We are probably the first, and it required more than a single brain, but our organization into lasting cultural structures in the cumulative service of rationality. But hey, we figured how to do that.
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