Meanwhile, I got a little ticked off in lecture two where he starts talking about the "complex conjugate" of a vector, and how if you multiple a vector by its' complex conjugate, you get it's magnitude. If you are talking about a two dimensional vector, like an arrow drawn on a sheet of graph paper, then the product you get from multiplying these two vectors is the square of the hypotenuse. Shades of Pythagoras!
Then I thought a little more, and began to wonder if maybe I was being unfair. I am partial to terms like "Pythagorean theorem", "hypotenuse" and "Cartesian coordinate system" because those are the terms I learned as a lad. I don't like "complex", "conjugate" and "vector", because, well, because they are new. Are they really any worse than the old terms? Well, maybe. "Complex" implies complicated, and complex numbers are not really complicated, so it's a bad term. "Conjugate" is something you do with words, not numbers, so it's a stupid word, and "vector" can mean either of two things (a list of numbers or an arrow) and you have to figure it out from context. So all you people who say "math is stupid" have some grounds for your complaint.
All this so far has just been an excuse to post this erudite bit of wisdom I found on Look! A Baby Wolf!:
There were three Indian squaws. One slept on a deer skin, one slept on an elk skin, and the third slept on a hippopotamus skin. All three became pregnant. The first two each had a baby boy. The one who slept on the hippopotamus skin had twin boys.This just goes to prove that…. the squaw of the hippopotamus is equal to the sons of the squaws of the other two hides.
And here's the generalisation for you : Pythagoros on a sphere :-
ReplyDeletehttp://www.savory.de/blog_apr_09.htm#20090420
because Pythagoras on a plane is just a special cae (where R is infinite).
The solution to that hippo problem is radius x diameter x radius squared,
ReplyDeleteor
rdr^2
or
rdrr.
(Har de har har!)