|
![](/i/fill.gif) |
>> Although it did leave me wondering for a moment: Am I actually "good at
>> math"? Or am I just good at following directions?
>
> Perhaps it could be compared to computer algorithms: If you are given
> a computational problem for which you need to create an efficient algorithm,
> how good are you at coming up with such an algorithm?
To be honest, I've yet to discover a computational problem which hasn't
already been solved 25 different ways (usually before I was even born).
The art of writing efficient computer programs appears to be the art of
figuring out where the **** all these algorithms are written down.
Because, let's face it, any algorithm that I can invent will be several
complexity classes worse than what the greatest minds of the 20th
century could think up.
> If you routinely can devise efficient algorithms for given computational
> problems, then one could say that you are good at algorithmic programming.
> Likewise I'd say that if you routinely can solve mathematical problems,
> devise mathematical formulas to describe things and so on, you are good
> at math.
Well, when I was a teenager I wrote my first ray tracer. Which doesn't
sound that impressive, until you realise that I have to figure out how a
ray tracer actually *works* in the first place, using nothing other than
the documentation for POV-Ray. (This is *before* Warp added the SDL ray
tracer, I should point out... That would have made it significantly
easier, obviously.)
In short, I had to deduce that you perform ray intersection tests by
solving simultaneous equations. (Usually if you want to draw a shape,
you want a parametric representation of it. But POV-Ray seems to talk a
lot about equations rather than formulas, which was a big tip-off.) And
then I had to work out how you actually solve simeltaneous (non-linear)
equations. (No, I didn't know how to do that.) And then I had to shift a
bunch of algebra around to make it happen. (That, arguably, is just
blindly applying rules. Mathematica(tm) could have done it just as
capably as me.)
FWIW, I was utterly astonished when I ran the program and it actually
freaking *worked*!
> Anybody can calculate 2+2 or even solve an equation, in the same way
> as anybody can write a "hello world" program or a program which calculates
> the sum of a list of numbers, but that doesn't make that someone *good* at
> math/programming.
Actually, I suck at arithmetic. (Fortunately, I have a computer to do
that for me...) What I consider myself to be modestly good at is
mathematical reasoning.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
![](/i/fill.gif) |