It was called the Ulam Spiral, sometimes the Prime Spiral, but the people who thought about it as just about "prime numbers" were missing the point. But of course, none of them had actually been out here, in the endless grey sea where the numbers went on forever. A dark, sometimes choppy, sometimes smooth sea where numbers weren't quantities, but just patterns, and where everything was so still, and so silent. But where there were still patterns. I like to come out here, and travel around the numbers. I don't see the numbers, though, just their patterns.
It was called the prime spiral, because Stanislaw Ulam showed it to Martin Gardner, and if you take 1 as the origin, and you see the numbers spinning off in a spiral like this:
543
612
789
You can see
diagonal lines of primes. But of course, I spent a lot of time here. I saw other things. I looked at squares, cubes, fourth powers and onward. Much onward. I had been here a while. Take a "circle" of numbers with the center being a cube and the radius being a square. How many fifth powers could you find in there? And that is what I considered as I walked far, far out in the grey zone of the spiral. Actually, today, I was back to considering primes: could there be a line on the spiral, an
infinite line, with no prime numbers at all? I had a lot of time to think about it, and I believed there was. I also believed that the next line upward (or downward, or sideways...depending on how you looked at it...) had to contain
twin primes, somewhere in its infinite length.
Twin primes? Of course they are real. I discovered that on my journeys out here. The real question for me was whether there was an infinite amount of twin primes with the number in between having only three prime factors. When I walked across the number line, that is what I looked at: the amount of factors of each number, and those were the waves on the sea, or sometimes the steps. Sometimes I would find a prime number out among numbers with thousands or millions of factors...and slide sleepily down into the shaft. In fact, I was about to do that right now.
Only the bells came, only the lights came. Ringing and flashing, and drawing me inward from the seas of infinity, to the prosaic, normal numbers that could be calculated as quantities, and not as patterns. And then, painfully awake and aware in the dull single digits, and looking at the number "1", I found myself lifted out of the symmetry and peace of the Ulam Spiral all together.
In a basement somewhere.
There is a man tied up below me.
Did I tie him?
I look at my hands, I don't think so. Don't look too agile.
Three fingers on each hand. Don't look good for tying.
The man is also gagged.
Should I feel bad? It smells bad. There is a whine in the air. Something malfunctioning? Or from the man? Both.
High windows with a little bit of light coming in.
The fluorescent lights in here are too bright they hurt my eyes but also so dim I can't really see what is going on.
What am I doing here I want to go home.
The man rolls over and is resting against an old couch. Not much down here. Torn linoleum and a single ratty couch.
The man has a blindfold that has fallen down around the eyes. Should I be here, who is he? My hands feel my face, is this my face?
He whines. And then his eyes open. I realize why the blindfold was there. His eyes. That look. The blindfold was to protect him, because anyone who saw those eyes...
My foot goes out. It is big and solid. Don't know how many toes. My food finds the junction between his arm and his ribs, and I hear a crunching sound. I realize how big my feet are.
Over and over.
I want those eyes to close. I don't want to look at what is in those eyes.
I forget how long it takes, hearing the air leaving his lungs, hearing bones break. The eyes close. I hope they won't open again.
I am back at my home in the spiral. The numbers are boring here, your 65's and 247's. I take a moment to catch my breath. I decide to skip away, I want the calm grey sea of numbers without quantities, just patterns, again. I can take the origin anywhere: I could take it as a transfinite number. The patterns still exist. Transfinite numbers still have to follow some rules: odd, even, odd, even, odd, even. One of those odd numbers out in transfinite territory is divisible by 5. A paradox, or perhaps an antinomy: a number with an infinite quantity can still be divided into infinite sections of five. Imagine a fence that is five bricks tall, and with infinite length. You can of course deconstruct the fence, and with the same quantity of bricks, build a fence that is three units high and goes on forever. And yet, that fence can still be divided into sets of five bricks. Forever. Isn't that obvious?
And out there in the peaceful transfinite numbers, I find some twin primes that are still separated by only a three factor number (all three factors are infinite), and I crawl even further down into the dark shaft, darker and darker, dark beyond mere absence, a comforting dark that insulates me from everything, and close my eyes.