Earlier quoted context omitted.
One of the reasons you can’t get good at riding a bike by reading about it is that we literally don’t understand the mechanics of bike riding. It’s a currently unsolved problem in physics. Google it if you do t believe me! So I get what you’re saying, but it is maybe not the optimal example.
https://royalsocietypublishing.org/doi/10.1098/rspa.2007.185...
I always adore the split between how my brain does things instinctually, but making it arbitrary completely demolishes the 'natural' flow of it. Same with complex ball throwing / bouncing trajectory calculations.
It also immediately makes me angry about how we teach math. When you learn about powers (squares, cubes, roots, etc), these things are just written out as arbitrary concepts instead of displaying them geometrically.
Hell, when I was first taught the Pythagorean theorem, it was just explained by drawing a triangle with A² + B² = C², without also drawing out the related squares of each side. Immediately doing that would instill so much more intuition into the math. In general, mathematical concepts gain so much clarity by doing them geometrically.