How to imagine compounding growth?

Most people have heard the mythical story about the invention of chess:

When the game was presented to a king, the fascinated monarch offered its creator to choose his own reward. The inventor, a brilliant and cunning mathematician, asked for a single grain of rice to be placed on the first square, two grains on the second, four on the third, and so on, doubling on each square of the chess board.

The King accepted without imagining the implications. Exponential growth across the 64 squares meant the total grains of rice would exceed the entirety of the world’s historical production of rice.

That’s the story that most know. This is the ending most books left out: Upon realizing he had been fooled, the king came up with an ingenious response. He committed to paying but demanded the inventor stay next to the board to count each grain of rice and make sure he was properly rewarded. And of course, the inventor was condemned to never leave.

When trying to understand the effect of compounding AI growth, we should expand the limits of our imagination until we can picture the most extreme future we estimate could be realistic… And at that moment we must imagine once again. Rinse and repeat.