The Call of the Open Sidewalk

I recently had to design a reflector for a light fixture. After I was done I ended up with two dimensions that depended on one another. After some thought I had a true mathematical insight. The solution to my problem was the same as the solution to the intersection of a line and a cone. After futzing with the rotations (nothing was at right angles) I would of ended up with two equations in two unknowns. Using the more or less mechanical process of algebra I could of solved those equations.

My abstraction led to algebra. That is because I spent a lot of time as an undergraduate in the faculty of engineering. As a result the fact that I have access to a computer did not really help that much.

So what would I of had to know to be comfortable in solving this problem by programming?

1. Addition and scaling.
2. Cartesian coordinates.
3. Distances in 3D Cartesian space.
4. Simple iterative optimization.

That is pretty much it. I didn't even have to know about real numbers if I knew anything about scaling integers. Note the absence of geometry or algebra.

My point is that if we want to teach people how to solve problems with computers we still have to teach them math. But it would be different math. That is more or less the dilemma we face.

Anyway, in the end I solved the problem with some stiff cardboard and scissors. I learned how to do this quickly and accurately from my father. I guess there is some sort of moral here too...

posted at: 08:15 | path: /politics | permanent link to this entry