Power of Two

I was playing Akinator when someone I know popped up on screen.

It asks yes-or-no questions and narrows down the person you're thinking of. Five questions cover 2 to the 5th — 32 patterns. Twenty questions, over a million. Binary choices compound exponentially, shrinking the space faster than intuition can follow.

There's a scam that exploits this same scale. Stock prediction spam.

One day an email arrives. Tomorrow's market will go up. The next day, it did. Another email. This time it says down. Right again. Three in a row. Then the fourth email lands. Want the next prediction? Pay up.

Here's how it works. Start by sending emails to a huge list. Half get "up," half get "down." Next day, send only to the group that got the right answer. Split again. After three rounds, one-eighth of the original list has received three correct predictions in a row from a "prophet." Sell them a product. The prediction ability is zero. They just walked a binary tree.

For engineers, powers of two are familiar territory. Binary search halves the space every step. Twenty comparisons find a value in a sorted array of a million entries. Just keep splitting in two, and the space narrows at logarithmic speed.

Akinator's questions, binary search, stock prediction spam — they're all doing the same thing. Repeating a binary choice. The difference is what you put at the end.

When my acquaintance's name appeared on screen, I laughed. Thirty-three binary choices to reach one person out of eight billion. Just thirty-three. Powers of two look like magic when used right.