a superintelligent alien may not understand what we call mathematics. the mathematical tools we use may be built-in to their brains/bodies so they don't need to externalize ideas like prime numbers
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@2ck Can you give any example in humans where we instinctively understand a concept but not consciously so?
@admin @freemo @aetios I guess color is another example. After thinking about it more, being more intelligent than a human isn't necessary. probably even orthogonal. the interface that we have with the world biases the things we think are basic and natural. an alien may be capable of understanding, but their perceptions may make our presentation of mathematics deeply unintuitive
I'd say most people do not understand color, instinctually or otherwise. we have labels for colors that are completely arbitrary but we fail pretty badly at being able to objectively categorize color, in fact our physical limitations make it harder to understand than it otherwise would.
Take for example distinguishing between pure green and a composite green (made of blue and yellow). to a human they would look indistinguishable when in fact they arent even related colors in any way. You'd insist two colors with no similarity were the same to someone who actually understood the colors being presented.
@freemo @admin @aetios that's kinda what I was getting at, that we don't have to understand color. I admit it's not a great analogy in the context of my OP: I have a hard time extending it. My main theme though is that natural evolution could make weird creatures that don't calculate like we do because they don't need to. limitations in my knowledge of mathematics, evolution, and physics prevent me from taking that thought much further
Yea but my point is without understanding color we as humans have very poor instinctual understanding of it.
Presumably the alien you refer to would not understand prime numbers but still be able to look at a number and know if its prime or not, even if it has no idea what being prime means.
But I cant think of any analogy like that in humans. For example color, humans **cant** identify colors without understanding. If shown a bunch of colors and told to match of the colors that were the same, we wouldnt be able to do it.
You and I **think** we have some automatic understanding of color only because you and I have the same instinctual system that agrees. So we assume if everyone agrees there must be some "truth" to it. But the fact is its just that we all have the same preprogramed fantasy as to what we think colors are and it doesnt match reality.
@freemo @admin @aetios I get your point. I don't know a solid example of a natural perception of a formal mathematical concept.