Maybe the problem with intuition is that we misplace our wonder.
Intuition usually works like this:
(Magic) → Behavior → Proof of success
For example:
(Magic) → Run and hold up your glove → Feel the ball land in your glove
(Magic) → Guess that 8 * 5 = 40 → Observe that your final calculation is correct
(Magic) → Guess that the conjecture is true → Create a proof that other mathematicians agree is sound
We find it magical that we can’t observe the background thinking. “Wow, how is it possible that I knew the answer and can’t explain why?”
But it makes more sense to me that conscious thought is magical. The fact that we can observe our own thoughts and behavior depends on mental faculties beyond what lets us accomplish those thoughts and behaviors in the first place. An eagle can fly, but we wouldn’t be surprised to learn that it doesn’t know how.
If Ramanujan could explain his own intuitions about his conjectures, that would be even more wondrous than the fact that he could generate his conjectures without any explanation. Ditto if a baseball player could explain exactly how they knew how to catch a particular pop fly.
Calculators can compute arithmetic. It would take a lot of extra work for them to also produce an explanation for how they computed each specific answer. Likewise, it’s far easier to create a neural network that can classify images than to get that neural network to “explain itself.”
So the magic isn’t that we don’t understand how our brain produces knowledge. The real magic is that we have any access to or executive control over our own thoughts at all.
Of course, being able to extend that account of where our thoughts come from, as you are trying to do, is also part of the real magic.
Maybe the problem with intuition is that we misplace our wonder.
Intuition usually works like this:
(Magic) → Behavior → Proof of success
For example:
(Magic) → Run and hold up your glove → Feel the ball land in your glove
(Magic) → Guess that 8 * 5 = 40 → Observe that your final calculation is correct
(Magic) → Guess that the conjecture is true → Create a proof that other mathematicians agree is sound
We find it magical that we can’t observe the background thinking. “Wow, how is it possible that I knew the answer and can’t explain why?”
But it makes more sense to me that conscious thought is magical. The fact that we can observe our own thoughts and behavior depends on mental faculties beyond what lets us accomplish those thoughts and behaviors in the first place. An eagle can fly, but we wouldn’t be surprised to learn that it doesn’t know how.
If Ramanujan could explain his own intuitions about his conjectures, that would be even more wondrous than the fact that he could generate his conjectures without any explanation. Ditto if a baseball player could explain exactly how they knew how to catch a particular pop fly.
Calculators can compute arithmetic. It would take a lot of extra work for them to also produce an explanation for how they computed each specific answer. Likewise, it’s far easier to create a neural network that can classify images than to get that neural network to “explain itself.”
So the magic isn’t that we don’t understand how our brain produces knowledge. The real magic is that we have any access to or executive control over our own thoughts at all.
Of course, being able to extend that account of where our thoughts come from, as you are trying to do, is also part of the real magic.