Math clicks when the shapes stop moving

I understand a new operation faster when I can hold one example still.

For a dot product, that can be as small as:

Suppose the input is:

x = [2, 1]

and the weight vector is:

w = [0.5, -1]

Then the dot product is:

2 * 0.5 + 1 * -1 = 0

Once the example is fixed, I can change one thing at a time. Change the first input and the first term changes. Change the second weight and the second term changes. The equation becomes a small system I can perturb instead of a line of symbols I am trying to memorize.

This is why animated explanations sometimes lose me. Motion is useful for showing a transition, but it can also make the relationship disappear as soon as it appears. Stable notation gives me somewhere to look.

The formula is still important. It just becomes easier to remember after the shape of the operation has stayed still long enough to inspect.