a tale of sampling from a uniform distribution on the unit interval
When the day of the lottery came, we all thronged in excitement. It was the densest crowd you’ve ever seen, packed so tight we made neutron stars look like loose and spacious assemblages.
We all wanted to win.
We all knew we had no chance.
I say “no chance” literally. They were sampling uniformly from the unit interval. Each of us had the same probability of victory: zero. Yet (and I know I was not alone in this) I was sure that I would triumph. In an irrational space of my mind, lower than logic and deeper than thought, I non-reasoned thus:
There are infinite numbers among us.
Each of us has equal odds; a chance of precisely zero.
Repeat the lottery every second for an eternity, and my name would never come up, not once.
Every one of my neighbors and companions faces the same impossible odds.
And yet someone will win the lottery. Someone must. Someone will receive impossible grace, incalculable salvation.
And then the crowning thought:
Why not me?
Every number on the interval was thinking along the same lines. Lunatic hope abounded.
Why not me?
Why not me?
Why not me?
At last, they began to read the digits, in rapid-fire succession. The first digit was a 7, meaning that the number was between 0.7 and 0.8.
In an instant, 90% of the numbers collapsed in defeat. The sting was all the sharper because the hope had been so foolish, so preventable. They knew they could not win, yet they had not believed what they knew, had not known what they believed.
The next digit was a 1. The winner would be between 0.71 and 0.72.
Again 90% of the remaining numbers–all those beginning 0.70 or 0.73 or 0.79–felt the same gnawing stupidity, the shame of shattered hope. They should have known better. They did know better. But hope knows only hope–until it knows disappointment.
The digits rattled on. Three, six, zero, two… and on, and on, and on. Soon we knew that the winner would be between 0.713602343995 and 0.713602343996. Still, infinite numbers remained in contention. Infinite creatures held hope in the hearts.
The longer they lasted–now a dozen, now a hundred, now a thousand digits deep–the more certain of destiny they became, the higher their anticipation crested…
…and the more devastating was their eventual elimination.
Even now, the digits rattle on. The overwhelming majority of numbers sit dejected, all hope extinguished. Yet I am not among them.
I am in that tiny sliver, still clinging to possibility, ten thousand digits into the lottery.
I am ecstatic with the sense of destiny. My victory is certain.
And I know, deep down, that my chances are no better than when the lottery first began.
