June Writealong: Day 1

[carrieironhorse]

This is totally a spur-of-the-moment thing, but since rii_dono  was saying she needed to finish her story, and I need to finish the first half of my draft (it's a good thing my self-imposed deadline is generous, but I HAVE been sticking to it fairly well), I figured we could do a June Writealong! Anyone is welcome to join in.

Here's how it's going to work:

Comments

Oooh, ooh, can I play?

[mathwiz1123]

This is Tyler (in case you two couldn't guess from the math themed name...) and I'm a hobo ninja mathemagician who happens to enjoy writing.

My goal is to complete two short stories (I'm thinking in the neighborhood of 10k words each) by the end of the month.

I would offer some of my artwork as a prize, but it is considered a weapon of mass distuction in 14 states and 11 contries...

Maybe I could offer mathematical wisdom such as e^(pi*i)=-1.... oh darn it...

Re: Oooh, ooh, can I play?

[carrieironhorse]

:D Of course you can play! That's a great goal. You don't have to offer prizes, it's sorta my responsibility, so don't worry about it. (As for e^(pi*i), well, http://xkcd.com/179/ sums up how I feel about that.)

Re: Oooh, ooh, can I play?

[mathwiz1123]

I could explain to you why this is so (for the longest time I thought it was just a bunch of malarky as well), but it would involve calculus, which I know you are averse to.

Re: Oooh, ooh, can I play?

[carrieironhorse]

Hey I like calculus! I wrote a whole story about a world where they use calculus as magic. (It already is magic, but, you know, more magic.)

Re: Oooh, ooh, can I play?

[mathwiz1123]

But would you really like me to explain it to you?

Re: Oooh, ooh, can I play?

[carrieironhorse]

If you can make it make sense, sure! Or you don't have to. I am content with not knowing.

Re: Oooh, ooh, can I play?

[mathwiz1123]

Let's see if I can make this make sense: The first critical piece of the proof is Taylor Series. The theory behind Taylor Series is that, given a function f(x), the expansion f(b)+f'(b)(x-b)+f''(b)(x-b)^2/2!+f'''(b)(x-b)^3/3!+...+f^(n)(b)(x-b)^n/n!+...=f(x) for x sufficiently close to b, where ' denotes derivative.
The Taylor Series expansion of f(x)=e^x with b=0 is 1+x+x^2/2+x^3/6+x^4/24+... This Taylor Series is valid for all values of x.
If you plug in k*i, where k is any real number, you get e^(k*i)= 1+k*i-k^2/2-k^3*i/6+k^4/24+k^5*i/120-...
Separating the terms with and without i's gives 1-k^2/2+k^4/24-... and i*(k-k^3/6+k^5/120-...) The first of the two groups is the Taylor series expansion of cos(k) and the second is i times the Taylor series expansion of sin(k).
So, putting it together, e^(k*i)=cos(k)+i*sin(k)
So e^(pi*i)=cos(pi)+i*sin(pi)=-1+i*0=-1

Re: Oooh, ooh, can I play?

[rii_dono]

AAAAH CARRIE WHAT HAVE YOU DONE!? ANOTHER ONE OF MY EVIL OVERLORD BRETHREN (WHOM I DON'T ACTUALLY CARE ABOUT AND I'M GLAD THEY'RE DEAD) GONE, GONE! ALL TO HAVE TYLER EXPLAIN SOMETHING THAT WILL NEVER, EVER MAKE SENSE TO ME! AAAGH WHY!? WHY!? THE EQUATION BUUUURNS!

Re: Oooh, ooh, can I play?

[mathwiz1123]

Don't sell yourself short, Leigh. I'm sure if you had the desire to you could eventually understand it.

As for the equation burning: no pain, no gain. :)

Re: Oooh, ooh, can I play?

[rii_dono]

...
Wherever you're going for the next two years, be glad it isn't here where I could just wring your little neck, my friend.

Re: Oooh, ooh, can I play?

[carrieironhorse]

LOL.

Re: Oooh, ooh, can I play?

[carrieironhorse]

You lost me at cos(k) and sin(k), but I'm glad that someone understands it, at least. (Also, I am too lazy to apply my brain any further. :D )