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Cantor's Dancing Angels
The angels are dancing tonight. They’re tangoing and swinging and waltzing, whirling up a cloud of dust.
My heart is pounding and I’m giddy and guffawing too loudly and I keep tripping and I think I might be spinning, though I was trying to walk.
He pulls me into him, grabs my hands in his. You need to sit down.
We’re cross-legged on the cold black-and-white tiles, leaning against the bathtub, and he’s twisting a strand of my hair round and round and round his finger.
I’m almost drifting off when his breath is suddenly heavy and warm in my ear, the tinge of alcohol once more engulfing me. What if there was no such thing as time?
I giggle demurely and stroke his leg with the side of my pinky. Well then I guess I’d have to spend the rest of my life here with you.
I mean, try to remove yourself from the constraint of time. What happens?
Okay. I guess everything happens all at once?
All at once and never, all at the same time.
He laughs and takes a swig of his Bud Light. I think I want to puke. I hear him swallow.
We sit quietly, his fingers still playing with my hair.
I turn, trying to look him in the eye, though my world is still twisting back and forth a little in a mildly relaxing way. What about cause and effect?
Cause and effect is simple. You throw a ball, then it goes in the basket.
But what about without time?
Everything still relies on everything else, though it all happens in the very instance it’s thought of.
Who thinks of it? God?
We do. He laughs again.
But if everything is all at once, is it anything? Wouldn’t it be zero?
Squashing infinity into nothingness just by removing one constraint. Interesting. All of existence and time, or lack thereof, like tiny bugs under a magnifying glass on a seemingly benign sunny day.
I was thinking more along the lines of angels.
How so? You wanna burn some angels?
No, I mean if there was no time and space, we could be angels on the head of a pin.
Ooh, yes, space is harder to imagine not being there, but try that, too. No time or space. He tucks the strand behind my ear.
I watch the waltzes and figure eights bundle up a pin in infinity, their wispy spindle fibers more nebulous than smoke, until I laugh at the absurdity
and it’s gone.
He smiles, unfazed. What’s so funny? Never played with infinity and zero before? How about dimensions?
I trace the square tiles on the floor with my finger and realize I’m not quite so dizzy anymore. Well, I know that technically points have no dimension and zero space, but string infinitely many together and you get a line, and string enough lines together and somehow there’s infinite area even though it’s all made of points, nothing.
He rests his hand on mine on the tiles, entwining our fingers. His grin is tantalizing. Not bad.
Keep adding dimensions. Except with universes. Imagine this universe, our universe, which has time and space but is finite, contained in an entire ultra universe. And that in another one.
It’s hard to imagine.
For sure. And what if you start with a universe with infinite time and space? Imagine infinite upon infinite upon infinite, through to infinity, of these universes. Keep going, and you realize that infinite space and time isn't the ultimate form of infinity.
Where would they all fit? I’m lightheaded and giddy, but my thinking feels sharp.
In a dimension far beyond space and time, of course. But you can’t picture it because you exist within the constraints of our known universe. Another brazen grin.
You’re blowing my mind. I rest my head on his shoulder and he wraps his arm around me.
His face is flushed. Great; how about we start with a smaller innermost universe? Think of a simple stream of consciousness existing on a point, as the point. It has no dimensions.
Fine, we could be empty floating souls on our pin instead of angels, if you want.
Sounds good. Now nest the points without increasing the dimension. Don’t let it get “bigger” spacewise. Make it fractal; you get all sorts of neat tricks. Denseless with zero interior but extending infinitely. In-between dimensions. Infinite perimeter around a finite, even zero, area.
If we were in a fractal universe, we could meander around for infinitely long and never have to leave. Instead of angels or souls on a pin, let’s dance in the dust of our own fractal world.
We sit in silence again for a long time, our minds infinitely far away but still together.
He gently squeezes my arm. You know, if these tiles extended on and on, out to infinity, the probability of someone finding our little fractal world here would be zero.
He teases, Would you like to be zero with me? How does being nothing sound?
I’d like to be here forever, but not zero. Hmmm... how ‘bout instead, let’s just pretend to just be two normal buzzed teenagers alone in a bathroom, okay?
Ithaca, New York
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