[xiaoma]

> "I think that if you see a complex equation, you should be able to roughly imagine it in your head."

This breaks down in many cases. What if your equation involves complex numbers for each component? What if it's an eight dimensional space or perhaps a multi-hundred dimensional space for recommender system?

At some point, you have to be comfortable with more abstract representations.

[adamnemecek]

I think of complex numbers as just points/vectors.

As for multidimensional spaces, you might not be able to visualize all the dimensions at once but by doing them three dimensions at a time, you can go Pretty far.

You should check that the abstract representations still make sense intuitively.