[UhUhUhUh]

A problem is that the reverse is also true. Simple example: stretch a rope around the earth that fits tightly and add 1 m to the length. Can a cat go under the rope (it's always a cat). Intuitively that seems like a "No". The simplest of formulae says "Yes" ( 1m/2pis = +/- 15 cm). Here, pretty much everyone has to resist intuition and trust numbers. I think the best way to conceptualize intuition is some sort of unconscious sub-process carried out by the brain at all times that has to be shut down or de-prioritized most of the time to allow for hard, "empirically-validated", processes to dominate the global activity (similar to early life "pruning"). As all neuronal processes, these need to be activated to remain available.

[harperlee]

Intuitively it can also be answered: suppose you pinch the rope, so it is tight (you step on it and pull from between your two feet, for example). You'd have a handle for the earth that will go to about just above your knee. A cat fits!

[UhUhUhUh]

Good point. That's the power of thought-experiments! It's about stimulating intuition.

[laxatives]

Maybe youre right, but your example is not a good one. Your problem reduces to, does 1m of rope provide enough to cover a cat? You actually have greater than 1m of rope since the cat has width.

Maybe a better example is, what is the best way to accelerate a ball horizontally from a fixed height? IE how can we most efficiently translate potential energy to kinetic energy in the horizontal direction?