| What got me for a while was the concept of a tensor: For example: What is a tensor? Wrong way to answer it: Well, the number 5 is a tensor. So's a row vector. So's a column vector. So's the dot product and the cross product. So's a two-dimensional matrix. So's a four-dimensional matrix, just... don't ask me to write one on the board, eh? So's this Greek letter with smaller Greek letters arranged on its top right and bottom right. Literally anything you can think of is a tensor, now... try to find some conceptual unity. Then coordinate-free fanaticism kicked in, robbing the purported explanations of any explanatory power in terms of practical applications of tensors. The only thing they could do was shift indices around. What finally made it stick is decomposing every mathematical concept into three parts: 1. Intuition, or why we have the concept to begin with. 2. Definitions, or the axioms which "are" the concept in some formal sense. 3. Implementations, or how we write specific instances of the concept down, including things like the source code of software which implements the concept. |