The Call of the Open Sidewalk : /politics/math.html

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?

Addition and scaling.
Cartesian coordinates.
Distances in 3D Cartesian space.
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 | Comments (1)

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Posted by John Vukelic at Wed Apr 20 07:07:31 2011

Computer are tools but so are the programs that run on computers. I think there are software packages that would do what you describe.

Addition and scaling, Cartesian coordinates, Simple iterative optimization.
MATLAB or MATCAD, even an EXCEL spreadsheet

Distances in 3D Cartesian space.
A good CAD program like AutoCAD would let you dimension off of 3D shapes

But if someone doesn't have these "software" tools then yes the fall back is to have the skills to use the computer to solve these problems.

If someone doesn't have a computer then next fall back ismathematical modelling with pen and paper. (before 1985 I think most engineering was done with pen and paper. Citation required)

If someone doesn't know the math background then next fall back is to work off of physical models and actually build the stuff by hand.

If you don't have the tools to build models then you use your imagination to come up with the solution (Einstein used a thought experiment to come up with relativity...that worked out pretty good)

There is always a way of solving a problem.

Engineering should be a time when you are taught how to use "all" the tools available for solving problems.

The Call of the Open Sidewalk

From a place slightly to the side of the more popular path

Wed, 13 Apr 2011

Math Curriculum