I find it interesting that we can think about [simple and complex] mathematical structures. How did we get the ability to do so and why we can do so?
I distinguish between mathematical structures and "reality". From my perspective, mathematical structures are being used provide succinct description of the perceptible portion of "reality", the Universe as we say. Need all mathematical structures exist?
What can we say about [biological, AI, or even theoretical] systems that can deal with abstract mathematical structures: to be able to construct, modify, specialise or generalise such structures in a extra-computable manner?
>How did we get the ability to do so and why we can do so?
By having to predict or own futures?
When we're deciding which tree to climb for the most fruit and balancing our choice against the one that attracts the least predators we are taking a lot of complex concepts in a very fuzzy manner. The threat we imagine may not be real. The rewards we imagine may not pan out.
This reality simulator we made to survive happened to also work very well when we extend it into maths, which if math is reality would make sense.
I distinguish between mathematical structures and "reality". From my perspective, mathematical structures are being used provide succinct description of the perceptible portion of "reality", the Universe as we say. Need all mathematical structures exist?
What can we say about [biological, AI, or even theoretical] systems that can deal with abstract mathematical structures: to be able to construct, modify, specialise or generalise such structures in a extra-computable manner?