On 19/08/2011 11:23 PM, Patrick Elliott wrote:
> You do realize that about half the people here, including me, read this
> and thought, "Man I really hate this guy for being able to do that
> shit!", right? lol No wonder I can't even figure out some "basic" stuff
> I need for some 3D math. The most I ever derived was some non-standard
> way of multiplying two, two digit, numbers, so it wasn't necessary to do
> all the complicatedly silly stuff the teacher insisted we screw with. :p

Uh, *which* newsgroup am I in? :-?

Seriously though. I was awful at maths when I was at school. Then again, 
when I was at school, "maths" consisted of doing endless arithmetic. In 
class, you would have a textbook the size of a small hardback 
dictionary. Most pages contained 40 questions. For example, you might 
have a page containing 40 sums, another page containing 40 
multiplications, another contained 40 long-divisions, and so on.

At the start of the book, you get to do really easy stuff like 3+7. They 
would have several pages of adding, and then a few pages of subtracting, 
then a few pages explaining how multiplication works, and then some 
pages of multiplication, then how long multiplication works, and then 
several pages of progressively harder long multiplication questions. 
Then they might get you to do sums involving multiple numbers of 
increasing size. Then they have a couple of pages explaining about 
negative numbers, then you do progressively more complicated sums 
involving multiple negative and positive quantities. Then they might 
talk about long division, and get you to do a few hundred of those. And 
then division and multiplication with negative quantities as well. Then 
maybe they start talking about fractions...

Can you imagine anything more MIND-NUMBINGLY BORING than staring at a 
sheet of 40 long division problems? YES, I GET IT! I KNOW HOW LONG 
DIVISION WORKS! STOP BUGGING ME ALREADY! >_<

Seriously. If you know how it works, do you really need to do it 200 
times over just to *prove* that you know how it works? It's not even 
like it's particularly important to be able to *do* long division; it 
isn't something you're going to need to do every day of your adult life. 
You just need to have a firm grasp of /how/ it works and /why/ it works. 
Once you've got that, practising it on endless question sheets is just 
an utter waste of time.

I was always quite bad at arithmetic. I still am. The difference is that 
today, I use a frigging *computer* to do the work for me. :-P My job is 
to figure out what the actual calculation is; the computer does the 
mundane work of actually *running* it.

It wasn't until I got to college that I discovered, mainly due to DKJ, 
that "mathematics" consists of something other than just doing hundreds 
of identical long division calculations over and over again. Mathematics 
provides a systematic way of solving puzzles and problems. It lets you 
manipulate and analyse hypothetical entities who's identity (or, indeed, 
existence) is as-yet unknown. Through tools like FractInt, I discovered 
that mathematics can be beautiful. I spent almost all of my time at 
college sat in the library, absorbing everything I could lay my hands on.

At school, fractions were about the most sophisticated topic we came 
into contact with. Oh, and drawing graphs on graph paper. We a little 
bit of that too. But at college, I learned how to do algebra. I learned 
about complex numbers, vectors and matricies, polynomials, solving 
equations, differential and integral calculus, cryptography, and so on.

By the way, it's not always easy to learn this kind of stuff from books. 
You may not realise, but mathematics is a *very* old subject. It abounds 
with strange vocabulary and archaic turns of phrase. For example, 
instead of a third-order polymonial, a book might talk about a 
polynomial "of order three". On top of that, the books frequently assume 
prior knowledge that I don't have. If you're smart you can sometimes 
figure out the missing pieces for yourself. But sometimes it's really 
hard to follow what's happening. To this day, I /still/ can't figure out 
most logic textbooks. And I guess that's simply because I have nobody to 
ask.

There's some really interesting stuff out there. Like, group theory, 
where you *make up* new kinds of entities which you can "add" and 
"subtract" in a mannar similar to ordinary numbers. How neat is that? Or 
matrix algebra, where you gain the tools necessary for doing crazy 3D 
work. Complex numbers, like normal numbers but with added superpowers. 
Cryptology, a battle of whits between code-maker and code-breaker. I 
could go on and on.

Most people I know seem to be "afraid" of mathematics. Like "oh man, 
there's no way I could ever understand that stuff". Without even 
actually trying. I'm stupid, and I managed it, so how hard can it 
possibly be?

I suspect it's some combination of math being taught badly, a cultural 
expectation that math is impossible to understand, and a society where 
stupidity is seen as desirable.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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