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[Sowelu]

Things in the natural world that are totally awesome.

Euler's identify.  e^(i*pi)+1=0.  e and pi are basically the important transcendental numbers, and i is, well, the square root of -1 (which I guess is pretty awesome by itself).

It works because e^(i * A) basically treats A as an angle in radians, and spits out the coordinates one unit length from the origin as a complex number: x + iy.  0 radians corresponds to 'east' or 1 + i*0, therefore pi radians corresponds to 'west', or -1 + i*0.  Output:  -1.

Essentially, it's just a very simple case of a simple formula.  Nothing magic about it.  But...somehow, when you stick the (arguable) five most important constants into one neat little equation, they all add up.  And that's pretty cool.

yes, you can also do something stupid like pi^(0*(e+i))=1, but whatever

[Renault]

Does math really count as "The Natural World?" I always assumed it was a human construction, more akin to a language describing phenomena than an expression of literal nature. I'm not a math student though, and I'll be the first to admit I'd easily be wrong in assuming such.

Incidentally, the simple supply-demand chart is pretty awesome, if less elegant. It has its minor weaknesses, but its essentially the foundation of all economic thought, from monetarists to Marxists. Its rare that human societies have some fundamental, semi-quantifiable relationship that almost everyone can point to as a starting point in explaining anything from international markets to soda sales at a vending machine. In that regard, I think its pretty cool.

[Sowelu]

Math is TOTALLY the natural world.  It's essentially the most natural thing there is.  To a large extent, physics is derived from math instead of the other way around.  Humans give it names, but the formulas are a universal language because they are universal truths.

[DJ]

I still don't know how magnets work

[Jervous]

Fuckin' miracles man

[Vector]

It works because e^(i * A) basically treats A as an angle in radians, and spits out the coordinates one unit length from the origin as a complex number: x + iy.  0 radians corresponds to 'east' or 1 + i*0, therefore pi radians corresponds to 'west', or -1 + i*0.  Output:  -1.

yes, you can also do something stupid like pi^(0*(e+i))=1, but whatever

It works because e^x is actually the limit of a series, and the particular computation sums to -1.

Your explanation states that e^[-1] = -1, which is not true, and pi^(0*(e+i)) is a vacuous formula, which is why mathematicians don't use that one.

Does math really count as "The Natural World?" I always assumed it was a human construction, more akin to a language describing phenomena than an expression of literal nature.

Eh, there's all kinds of arguments about that.  Some people call it an art, some people call it a science.  It doesn't really matter either way.

Math is TOTALLY the natural world.  It's essentially the most natural thing there is.  To a large extent, physics is derived from math instead of the other way around.  Humans give it names, but the formulas are a universal language because they are universal truths.

Actually, this is one of the reasons why mathematicians and physicists argue so much: physicists have knowledge of the physical world from experimentation, and often invent mathematics to make their computations work.  Then the mathematicians go along behind them and prove that their computations play nicely with the rest of their results.

Also, they aren't universal truths.  They're only true within their axiomatic systems, which, despite perhaps appearing self-evident, are not true everywhere.


As for my favorite part of the natural world: symmetry.  All of it.

[Rilder]

The fact that we exist to figure out math and how magnets work is a miracle.

[KaguroDraven]

About 'is math natural or not', math is the same in every language, 1 + 1 always = 2, even if you call the numbers something different it's always there, that has to count for something.

[Vector]

About 'is math natural or not', math is the same in every language, 1 + 1 always = 2, even if you call the numbers something different it's always there, that has to count for something.

That's false.  Think about the number system with only two values, 1 and 0.  Then 1 + 1 = 0, and we aren't just renaming... it's something different.

Similarly, in certain cases you can have a*b= 0, where neither a nor b is zero...

(Hint: it involves matrices)

[Renault]

I did not mean to derail this threat >.< Sorry about that. It is, however, an interesting debate. Maybe this sub-thread needs a sub-thread? heh...

[Vector]

I did not mean to derail this threat >.< Sorry about that.

Hey, I'm always glad for math derails


Erm... other awesome things.  The interactions of plant hormones are really amazing.

[Sowelu]

As a programmer, I object, and state that multiplying matrices is not doing the same as multiplying non-matrices, it's an overloaded operator!

Number systems with only two values horrify me. 

Okay, here's another awesome thing.  It's possible to see the same star in the sky in two different places.  Gravitational lensing!  Let's say you're the @ sign and there's two stars in a straight line from you:
@    *     *
Light from the further star that's passing above the nearer star can be bent by gravity and redirected towards you, so that it looks like the further star is above the nearer star.  It can also be bent from the lower side, so you see that star below the closer one too...  Wacky.

Oh yeah, and for clusters and galaxies and really really big things that are really really far away, scientists actually *don't know* how far away they are.  The scales involved are just so whacked out that, without points of comparison, even playing with redshifting and stuff won't give you an accurate answer.  We have to keep being more and more creative to find stuff out.

[Duke 2.0]

 Have we figured out why magnets work yet anyway? We have mapped their effects, but have we figured out how they actually work?

[Leafsnail]

Have we figured out why magnets work yet anyway? We have mapped their effects, but have we figured out how they actually work?

You mean like... magnets that you can hold in your hand, or going down alllll the way to the fundamental electromagnetic force?

[Sowelu]

Well this is embarassing.  I know them as far as it involves something to do with electrons and spin at the lowest level.  Above that I know that ferromagnets form aligned regions within which everything is pointed the same way, but I don't know what's between those, what actually generates a magnetic field on a macro level.  en.wikipedia is too complex, and simple.wikipedia is too simple.  Anyone else?