Orchid XP v8 wrote:
> anybody studies them - set theory, number theory, category theory, etc.)

Set theory is how you prove arithmetic works. Prove 2+3=5.

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

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On 11/12/2010 03:08 PM, Darren New wrote:
> Orchid XP v8 wrote:
>> anybody studies them - set theory, number theory, category theory, etc.)
>
> Set theory is how you prove arithmetic works. Prove 2+3=5.

I didn't say that set theory is not *important*. I said it is not 
*interesting*. Certainly not to me, anyway. The obvious stuff is 
obvious, and the non-obvious stuff is all tedious riddle-like splitting 
of hairs rather than interesting insights.

Also, several sources state that set theory is the fundamental basis of 
all of modern mathematics, but not one single one makes any attempt to 
explain this sweeping statement. Your assertion that set theory somehow 
has something vaguely to do with arithmetic is typical of this type of 
statement. If there *is* some kind of connection between set theory and 
arithmetic, it is highly non-obvious.

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

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Orchid XP v8 wrote:
> I didn't say that set theory is not *important*. I said it is not 
> *interesting*. 

It's interesting if you want to know whether arithmetic is complete and 
consistent, for example.  Godel's theorem certainly is an interesting insight.

> Also, several sources state that set theory is the fundamental basis of 
> all of modern mathematics, but not one single one makes any attempt to 
> explain this sweeping statement. Your assertion that set theory somehow 
> has something vaguely to do with arithmetic is typical of this type of 
> statement. If there *is* some kind of connection between set theory and 
> arithmetic, it is highly non-obvious.

And *that* is what makes it interesting!  Set theory is like the lambda 
calculus - it's tiny and trivial, but you can prove anything with it.

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

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Am 11.12.2010 12:26, schrieb Orchid XP v8:

> In spite of the insane popularity of her books, there are apparently a
> significant number of people who assert that they aren't very good. (And
> not just the radical Christian sects who assert that any magic without
> reference to God is the work of Satan...)

I've never read them (nor did I see any of the movies). I too heard tell 
that the books were rather bad, but my father insists that while the 
German translation sucks, the English original is actually quite good 
(he's a retired English teacher, and none too easily impressed by any 
"hype", so he may be a comparatively credible witness after all).

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On 12/9/2010 1:04 PM, Mike Raiford wrote:
>
>
> http://www.maa.org/devlin/LockhartsLament.pdf

It's an interesting picture of an establishment.  You get accepted as an 
expert by agreeing with the experts.

Regards,
John

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Am 11.12.2010 13:14, schrieb Orchid XP v8:

> By contrast, this paper seems to assert that mathematics is about
> constructing abstractions and building theories out of them as a matter
> of creativity. Obviously I've never seen any cutting-edge mathematics
> (and I never will), but I've always thought of mathematics looking at
> interesting systems and discovering their properties, out of simple
> human curiosity. Certainly that's why *I* explore mathematics; it's the
> desire to know everything about everything.

... despite there existing proof that this desire is insatisifiable 
(which I find an interesting thing to know, too) - and not only in this 
world, but also in any imaginable one (another interesting thing) except 
for pretty boring worlds.

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Am 11.12.2010 14:46, schrieb Orchid XP v8:

> 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.)

Hehe - when I was a teenager, I wrote a raytracer, too - without even 
knowing POV-Ray; all I had was a few printed b/w chrome spheres on 
checkered planes, the desire to do the same, Snell's law, and a 
classmate who took over the task of developing UI components for the 
interface (we didn't have a library for that either) :-P

Needless to say that the thing was awfully simple, and did not even work 
properly - it got the normals of non-uniformly scaled spheres wrong - 
but hey, you can't do everything right all the time, can you ;-)

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Am 11.12.2010 14:48, schrieb Orchid XP v8:
> On 11/12/2010 12:14 PM, Orchid XP v8 wrote:
>
>> By contrast, this paper seems to assert that mathematics is about
>> constructing abstractions and building theories out of them as a matter
>> of creativity. Obviously I've never seen any cutting-edge mathematics
>> (and I never will), but I've always thought of mathematics looking at
>> interesting systems and discovering their properties, out of simple
>> human curiosity. Certainly that's why *I* explore mathematics; it's the
>> desire to know everything about everything.
>
> Thinking about it... No, I'm not very good at math. I never bother
> proving things.
>
> According to the paper, the proof is far more important than the result
> (at least as far as mathematicians are concerned). I always considered
> the proof to be the most boring part.

You don't need unshakable solid proof for conjectures, so maybe you 
should stick to those. In my eyes that's mathematical enough.

I guess more often than not, proving a good conjecture boils down to the 
mere applying of rules again. Sure, there are famous conjectures out 
there that seem to defy any attempt to prove them, but you don't hear 
about the conjectures that are easy to prove. And after all, /every/ 
proof starts off as a conjecture.

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Am 11.12.2010 06:37, schrieb Slime:
>  > 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.

Yup ;-)

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Orchid XP v8 <voi### [at] devnull> wrote:
> On 11/12/2010 03:08 PM, Darren New wrote:
> > Orchid XP v8 wrote:
> >> anybody studies them - set theory, number theory, category theory, etc.)
> >
> > Set theory is how you prove arithmetic works. Prove 2+3=5.
>
> I didn't say that set theory is not *important*. I said it is not
> *interesting*. Certainly not to me, anyway. The obvious stuff is
> obvious, and the non-obvious stuff is all tedious riddle-like splitting
> of hairs rather than interesting insights.
>
> Also, several sources state that set theory is the fundamental basis of
> all of modern mathematics, but not one single one makes any attempt to
> explain this sweeping statement. Your assertion that set theory somehow
> has something vaguely to do with arithmetic is typical of this type of
> statement. If there *is* some kind of connection between set theory and
> arithmetic, it is highly non-obvious.

suppose you have a set of 2 things and a set of 3 things.  How many things you
have in total?  Is that not how you even learn basic arithmetic?

functions?  a formula mapping things from a set to things from another set?

yeah, set theory is fucking huge.

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