Spiral Pi
The park is a serene place; a creek flows downhill from the central lake. It's actually a small pond, but it's large enough and stocked so that there are fishermen and -women with their lines stretching out into it. An imitation grassy woodland; enough greenery to convince the humans who play there that they are at one with nature, but not so much to overwhelm them with reality.

Lorrie and Cam follow the creek as it bubbles under a bridge, past picnic tables and down the hill. They argue over, er, discuss everything from consciousness to quantum mechanics and sometimes even quantum consciousness. They are like brother and sister or close cousins who grew up next to each other. Both middle class, but he's from the upper middle side of the creek and she's from the lower middle.

The creek runs past a playground before it goes underground to be pumped back up into the lake. There's a jungle gym, a slide and a merry go round in the playground.

Lorrie- Get on.

Cam - What?

Lorrie - Get on, I'll push

Cam - Uh, okay

He gets on the merry go round. Lorrie pushes it and hops on next to him.

Lorrie - I couldn't sleep last night

Cam - Neither could I. I was thinking about circles

Lorrie - Like the way we talk?

Cam - Which led me to thinking about pi. You know, pi isn't rational,

Lorrie - Of course; it's an irrational.

Cam - Irrational! It's completely illogical! You can't remember it, you can't multiply it, you can't even divide it easily into seven pieces!

Lorrie - why seven?

Cam - You, me, your two brothers, my sister, and then there's lah and Widget,

Widget and lah are, well, lets call them imaginary companions, of Cam and Lorrie. They will not figure in this story beyond serving the need to cut pi into sevenths - a nice prime number. The entirety of their vocabulary is one word each. lah says "iamlah" and Widget says "widget". Somehow this is enough to be understood by the other members of the quartet. Widget is green. Both lah and Widget like pie.

Cam - So I decided to design a rational pi.

Lorrie - Um, okay. What would make your pi be rational?

Cam - I've already mentioned calculation. It should be easy to remember, no more than three digits

Lorrie - Twenty two sevenths is rational. And three digits.

Cam - It should be easily determined from first principles

Lorrie - Isn't the ratio of circumference to ...

Cam - Way too complicated, for one thing it involves division ...

Lorrie - Speaking of complicated, I never did like long division. All that guessing about what might be the correct digit then multiplying and subtracting only to find that you've gone too far or not far enough and have to erase it and try again.

Cam - That's because you were an Art major

Lorrie - Philosophy, the queen of Academia.

Cam - Math, queen of the sciences.

Lorrie - Masters degree.

Cam - Bachelors, but Godel proved logic incomplete, so...

Lorrie - So you didn't have trouble with division?

Cam - It was addition that bothered me,

Lorrie - Addition? That’s so basic. Why?

Cam - Why learn the addition tables when theoretically they just summarize counting? I had trouble with 8 + 5.

Lorrie - Why?

Cam begins counting on his fingers,

Cam - … ten, eleven, twelve, thirteen. That's it, thirteen. Thirteen is just a weird result. It's correct but it looks and sounds weird.

Lorrie - Okay, okay. Uh, you were talking about the problem with circles: a ratio is too complicated because division and...

Cam - It also means you have to find a circle to measure.

Lorrie - That's easy you just take two sticks and a piece of string...

Cam turns sideways with one leg off the merry go round and gives it another push. He pulls his foot back up and continues,

Cam - No, that's using the thing you want to prove to prove the thing you want to prove: circular logic, a logical error of the first rank. Even the Greeks knew that.

Lorrie - Plus it's measurement, not logic

Cam - Yes. Now, three is a nice number; I might even accept your twenty two sevenths, but ...

Lorrie - There's always a complication when we're going around like this.

Cam - Anything other than pi itself gives me a spiral.

Lorrie - What?

Cam - A spiral, you know like a circle but it never closes, just keeps getting smaller or larger depending on whether it spirals in or out.

Lorrie - I know what a spiral is, dummy, how?

Cam - It goes in if I go clockwise, and out if I go widdershins. That's if my pi is less than pi and contrariwise if it's greater.

Lorrie - Are you sure you're not using a string and winding it around the stick? No, that can't be; to spiral out, you'd have to unwind it.

Cam - I told you, I'm working from first principles; no string, no stick. Pure mind.

Lorrie - Pure mental it sounds like. But x and y are just r sine or cosine theta and if r is constant you should just get a smaller circle. Or larger.

Cam - changing pi changes trigonometry. The sine and cosine functions are different, you see.

Lorrie - But if r is constant...

Cam - It is, but the angle keeps on growing. The sine of 360 is less than the sine of zero. Or larger depending on whether my pi is smaller or larger than pi and whether we're going clockwise or widdershins.

Lorrie - I feel a headache coming on. We're still talking plane geometry?

Cam - And plain trigonometry, but we have to go through topological calculus to get there.

Lorrie - as long as it doesn't leave the ground; I guess I'm okay with it.

Cam - Your turn.

Lorrie – Huh?

The merry go round has stopped.

Cam - Your turn to push.

Lorrie - Oh.

She gets off the merry go round and stands beside it. Across the street is, you guessed it, a Polly's

Lorrie - I think it's time to test your theory.

Cam - Are you buying?

Lorrie - It's your theory; you’re buying.