A lot of it is the difference between learning practically and learning theoretically. You don’t have to understand the underlying mechanics in practice to know how to keep getting the same result. Your brain doesn’t have to be doing any math, it just has to have shaken a bottle enough times to have a good comparative basis formed.

Learning to calculate the current remaining volume in a container when observing someone else shake it… that would use all that theoretical knowledge and math.

It’s like knowing how hard you have to throw an egg at a wall for it to break instead of bounce off. You do it 100 times, you just get a good feel for it. Doing all the math, and then trying to learn it practically is barely gonna affect how quickly you learn it in practice. But if you wanted to make a robot that throws it exactly hard enough without wasting any energy, practical knowledge will have almost no value, and theory and math will be incredibly valuable.