Ramble, Part 9: A Matter of Magnitude
Dec. 19th, 2006 02:38 pmI'm not going to say very much about mathematics in the Muslim and Hindu civilizations, mostly because I really don't know as much about them as I should. However, there are a few items that I'd like to point out before going on to postclassical Western mathematics; those will be the subjects of the next two or three posts.
As I understand it, one lesson that people in the hard sciences learn early on is the necessity of keeping track of units. You don't add areas to masses, and if you divide a length by a time you get a speed1. I'd like to devote a little time to a related problem in mathematics, which arises when algebra is conceived of in geometric terms.
( Homogeneity )
Ramble Contents
1. I do mean speed - possibly signed - and not velocity, which is, after all, a vector rather than a scalar.
As I understand it, one lesson that people in the hard sciences learn early on is the necessity of keeping track of units. You don't add areas to masses, and if you divide a length by a time you get a speed1. I'd like to devote a little time to a related problem in mathematics, which arises when algebra is conceived of in geometric terms.
( Homogeneity )
Ramble Contents
1. I do mean speed - possibly signed - and not velocity, which is, after all, a vector rather than a scalar.