Appendix C. Vectors and matrices (linear algebra fundamentals)

Vectors and numbers are the language of machine thought. Bits are the most fundamental “number” that machine computation is based on, a little like letters (characters) are the most fundamental, irreducible part of words, the language of thought for humans. All mathematical operations can be reduced to a few logical operations on sequences of bits. Sequences of characters are processed by human brains when we read in an analogous way. So if we want to teach machines about our words, the first challenge is to come up with vectors to represent characters, words, sentences, and intermediate concepts that the machine will need to work with to produce seemingly intelligent behavior.