OK, this statement has some exaggeration in it, yet, I really shocked myself how much I depend on having some drawing in front of me (or any kind of visual perception), when somebody explains me math. Hearing just words doesn't work at all.
Even if I analyze the way how I remember math ideas, I get that they are mostly pictures what stays in my head. (Words are just a bonus that can be attached to the necessary picture in my memory.) A rather boring example case analysis follows:
For example even such non-visual theorem like Chernoff bounds: At the first place, there is the Gauss distribution: the famous "hilly curve" that lies on x-axis having the y-axis in the middle. Then there is one more vertical line the right side of the y-axis, quite close to it, which is telling: "although I lie close to y-axis (distance C) only (exponentially in -C squared) small ratio of the mass (of the Gauss distribution) lies on the right side from me". And there is also formula picture (it also has a picture-like nature) where one important place is in the probability brackets (there is the C\sqrt(n)) which influence another place in the exponent of e (after the "<" sign) where is something like C squared times 2.
Recalling some of the experiences from the lectures I recently took, I also have to say, that the teachers are speaking unnecessarily much. Most of the words just flow through my head. Now I believe that what I rather need is pictures (or even animation/movie) on the blackboard that can be additionally accompanied by explanations and important keywords. Do the teachers teach bad in general or am I an E.T. by accident thorwn on the planet Earth? What do you think?By the way, if you accept my first claim of this note, don't you think that from this point of view the glorified LaTeX just sucks?:)
But that is for another chapter.
