think of something you've tried to do or learn before and found pretty difficult, especially something from when you were younger. if you try doing or learning it now, there's a decent chance you will still struggle with it... but a surprisingly high one that it'll somehow be really easy suddenly because you've picked up some orthogonal skill or knowledge that inexplicably changed your brain to a subtly different and better brain without you noticing

in my case, i think i learn almost entirely by example, so when i don't understand something, i just need to see more examples of it usually. sometimes i walk away from something in disgust at not being able to 'get' it, and then spend a few years passively absorbing examples of it by accident, and then come back to it and i'm like "oh why was that so difficult to understand? its just one of Those Things ive seen a million times"

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@jk whenever i don't understand something i just wait a couple months for the Brain Fairy to come and replace my brain with a new one while i'm asleep

@jk this is exactly what happened with me when learning to drive (something I had tried a number of times without success when younger and finally did it last year - although it took me a great deal of time to get my head round the concept of spiral roundabouts (I still don't particularly like them, but mostly because the lane markings are worn away on many round here)

@jk this happens to me frequently and I do not care for it

@jk the effort:output relationship is not so much nonlinear as completely nondeterministic

@jk I've been reading Ultralearning and that jives.


Your assertion applies perfectly for my understanding of algebra.

As a 14 year old, it was "impossible".

At 25, in graduate school, after years of math avoidance, I was faced with a "pass this algebra class or you can't complete this degree".

My brain had matured in ways I cannot describe. The pathways which did not exist at 14 clicked into view and I took the final exam without actually completing the whole class.

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