On 09/12/2010 06:04 PM, Mike Raiford wrote:
> http://www.maa.org/devlin/LockhartsLament.pdf

Now they need to make a film about a society where musicians are taught 
without being allowed to play or listen to music. And then a renegade 
faction breaks off and starts teaching people by, you know, *playing 
music*. Possibly lead by Robin Williams. That would probably work quite 
well.

Oh, wait a second... I just described the Dead Poets Society, didn't I?



As some of you may recall, I went to a school for stupid people. Perhaps 
unsurprisingly, our "maths lessons" consisted *only* of filling out 
countless billions of long-division sheets.

I mean, seriously. Knowing how to add, subtract, multiply and divide 
(not to mention *estimate*!) is important. But dividing 6-digit numbers 
giving an exact result and a remainder? When the **** am I *ever* likely 
to need to do /that/? And *if* I do, I'll use a calculator. Obviously.

I understand that people need to know how to do division. I have no idea 
why they need to practise double-sized sheets with 40 quotients per side 
featuring 6-figure numbers. Hell, even NASA used a slide rule instead of 
pencil and paper! WTF?

Still, I guess it keeps the demented kids quiet for a while...



It wasn't until nearly the end of my time at school that I discovered 
that "mathematics" was something *other than* arithmetic. There's 
actually more to it than that.

That's actually kinda shocking, when you think about it. It's like 
saying that being an author is about good spelling and grammar. Oh, 
sure, that's *part of* being a good author. A pretty friggin' /tiny/ 
part, though. JKR didn't get to where she is today by using punctuation 
correctly. She got there by convincing Warner Brothers to make her books 
into big-budget films. Oh, wait...

I think, for me, the turning point was where I read an issue of the 
Guinness Book of Records. On one page, it had an image of the Mandelbrot 
set, "the worlds most complex mathematical object". It all went downhill 
from there, really. I discovered complex numbers, and algebra, and I got 
books from the library and read them end to end, trying to discover what 
commands I needed to type into my computer to make it produce these 
amazing fractal patterns. (Usually this was an entirely futile pursuit; 
such books like to include pretty pictures and fail to explain how they 
are made.)

Then I went to college, and I met a man named DKJ. Brilliant 
mathematician. Utterly incapable of comprehending the real world. Quite 
strange. Welsh. Anyway, I spent 2 years camped in the college library, 
absorbing just about every textbook that wasn't so far advanced that I 
couldn't even understand what it was talking about.

At uni, they didn't have any maths books. (Or, they did, but they were 
all at the Leicester branch. I'd have to wait a week to get them before 
I could find out if they were actually worth reading.) They did have GP 
though. More of a programming buff than a maths nut, but all the same... 
Nice sandals, BTW. :-P



This paper seems like a pretty accurate description of everything that 
is wrong with mathematical teaching, and society at large. People seem 
to think that mathematics is about moving symbols around on a sheet of 
paper according to a set of complex and technical rules. Which is a bit 
like saying that writing a best-selling novel is about arranging special 
blobs of black ink in the correct sequence according to a set of rules. 
Strictly speaking, that's what writing a book *is*. But no sane person 
actually thinks about it in those terms.

I've recently seen a few interesting programs on TV about mathematics. 
One featured some guy who's apparently a mathematical genius and another 
who's a comedian, and general hilarity ensued. But I doubt the viewing 
public got much out of it.

Another featured a guy explaining the history of mathematics. 
(Apparently India and China between then invented most if not all of 
modern-day mathematics.) The trouble is, every concept they explained 
had to be watered down so much that even I, as a person who knows the 
underlying mathematics, would be hard-pressed to figure out what they're 
getting at.

The fact that you can compute the result of an infinite sum in a finite 
number of steps is amazing and almost unbelievable. But I'm not sure 
that some computer graphics of a boat sailing forwards and backwards 
adds anything to the understanding of /how/ such a feat is possible.

The whole attitude of society seems to be like "oh, mathematics. Yeah, 
it's *so complicated* that you can't possibly understand it. Better not 
even try. They have *other* people to sort that out anyway. So long as 
you can count, who needs to know more than that?" It's almost like it's 
not "mathematics" if it doesn't look cryptic and incomprehensible.



Some while ago, I read a (fictional) quote that I thought hit the mark 
quite accurately: "You're not a director. You know what the problem with 
people like you is? You don't have anything to say, you just want to BE 
A DIRECTOR."

Well, now suddenly I feel like I have something to say...

Now, if only I didn't completely suck at POV-Ray, I could go make an 
animated short, now that I have found my muse. ;-)

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Warp wrote:
>   I'm not so sure I would call, for example, the problem "is this point
> inside this polygon?" a problem of physics. It sounds mostly a problem
> of pure mathematics.

That's a fair point.  I hadn't really been thinking along those particular 
lines.

>> None of those 
>> apply to programming a board game, for example.
> 
>   If you need to program an AI opponent for such a board game, it certainly
> requires knowledge on several sub-branches of mathematics. 

True, true.  But only "mathematics" because that's what we call things like 
alpha-beta pruning and graph running and so on, if you see what I mean. Lots 
of the stuff that AI does isn't what I'd call "mathematical" even tho you 
use math to describe it. It's just algorithms that the inventors happened to 
describe as math first, I'd say.

-- 
Darren New, San Diego CA, USA (PST)
   Serving Suggestion:
     "Don't serve this any more. It's awful."

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Am 10.12.2010 14:39, schrieb Invisible:

> As some of you may recall, I went to a school for stupid people. Perhaps
> unsurprisingly, our "maths lessons" consisted *only* of filling out
> countless billions of long-division sheets.
>
> I mean, seriously. Knowing how to add, subtract, multiply and divide
> (not to mention *estimate*!) is important. But dividing 6-digit numbers
> giving an exact result and a remainder? When the **** am I *ever* likely
> to need to do /that/? And *if* I do, I'll use a calculator. Obviously.
>
> I understand that people need to know how to do division. I have no idea
> why they need to practise double-sized sheets with 40 quotients per side
> featuring 6-figure numbers. Hell, even NASA used a slide rule instead of
> pencil and paper! WTF?

Hollywood lied to you about the moment in the Apollo 13 mission when the 
astronauts asked the ground grew to double-check their maths: They did 
/not/ use slide rules in that situation, but indeed pen & paper, because 
slide rules don't help with simple addition of numbers.

As for divisions, AFAIK slide rules weren't used back then except for 
quick estimates. Precise calculations would either be done by a single 
computer requiring huge amounts of electricity, or by a room full of 
computers requiring huge amounts of coffee.

Back then, computer was an actual job, requiring highly trained people. 
After division, they would have learned how to interpolate using 
logarithmic and trigonometric tables and stuff.

I'd also say it was good for our generation to know how to add, 
subtract, multiply and divide without a pocket calculator, because you'd 
probably not carry one around with you all the time back then. Remember, 
we didn't have cell phones with pocket calculator apps in our pocketses 
wherever we went.

> That's actually kinda shocking, when you think about it. It's like
> saying that being an author is about good spelling and grammar. Oh,
> sure, that's *part of* being a good author. A pretty friggin' /tiny/
> part, though. JKR didn't get to where she is today by using punctuation
> correctly. She got there by convincing Warner Brothers to make her books
> into big-budget films. Oh, wait...

Not really. The books were amazingly popular before the movies. I'm 
pretty sure JKR didn't have to beg - if anyone did any begging, it was 
most likely Warner Brothers.

Post a reply to this message

Invisible escreveu:
> At this point DKJ peered over my shoulder, and pointed out that what I 
> had just done was "integral calculus", and some guy called Laplace had 
> invented it 200 years ago. He showed me the general formula for 
> integrating a polynomial. I was kind of suspicious at the exact integral 
> coefficients; of all the possible real numbers in existence, that seems 
> like a rather large coincidence. None the less, I went home and managed 
> to find my dad's old calculus book.
> 
> Now it actually made perfect sense. :-P

You should really have gone to a special school of another kind.  Your 
parents didn't realize your math brain was running faster than those of 
other kids of your age...

calculus is tough for anyone.  I wouldn't ever be able to grasp it while 
a teen...

-- 
a game sig: http://tinyurl.com/d3rxz9

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On 12/9/2010 3:57 PM, Warp wrote:

>>> And while I took and understood a great deal of math, it wasn't until
>>> physics class that I suddenly said "Oh, *that* is what an integral is for!"
>>>
>> or trigonometry after encountering POVray
>
>    Geometry, trigonometry and in some cases even calculus has been quite
> useful in graphical-heavy and game programming.
>

Or when dealing with writing software for industrial equipment. I can't 
believe how much trig I actually used when working on machinery. It was 
necessary, some of the stuff I was dealing with were circles that had to 
line up tangent to a board, etc..

-- 
~Mike

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clipka wrote:
> Not really. The books were amazingly popular before the movies. 

My theory is that she discovered how to do *actual* magic, and used it to 
make tons of money and fame by writing best-selling books about fake magic, 
just to distract the masses.

-- 
Darren New, San Diego CA, USA (PST)
   Serving Suggestion:
     "Don't serve this any more. It's awful."

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Am 10.12.2010 22:08, schrieb Darren New:
> clipka wrote:
>> Not really. The books were amazingly popular before the movies.
>
> My theory is that she discovered how to do *actual* magic, and used it
> to make tons of money and fame by writing best-selling books about fake
> magic, just to distract the masses.

Nice one ;-)

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> Geometry, trigonometry and in some cases even calculus has been quite
 > useful in graphical-heavy and game programming.

Graphical and game programming has been quite useful in learning 
geometry, trigonometry, and in some cases even calculus.

  - Slime

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Slime <pov### [at] slimelandcom> wrote:
>  > Geometry, trigonometry and in some cases even calculus has been quite
>  > useful in graphical-heavy and game programming.

> Graphical and game programming has been quite useful in learning 
> geometry, trigonometry, and in some cases even calculus.

  Or perhaps more like: Programming has been a good incentive to learn math?

-- 
                                                          - Warp

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Darren New <dne### [at] sanrrcom> wrote:
> clipka wrote:
> > Not really. The books were amazingly popular before the movies. 

> My theory is that she discovered how to do *actual* magic, and used it to 
> make tons of money and fame by writing best-selling books about fake magic, 
> just to distract the masses.

  It reminds me of the "corollary" to Clarke's third law of prediction:

  "Any sufficiently advanced magic is indistinguishable from technology."

-- 
                                                          - Warp

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