How, Mathematically, We’re Fucked

Exponential growth on a finite planet does not end well, whatever form it takes

Midjourney imagining “The Vizier Sessi asked the Rajah for a boon. He asked for one grain of rice to be placed on a chessboard and doubled every square --ar 16:9”

I have spoken about the physics and finances of how we’re fucked. Now let’s talk about the math. It’s the reason for both.

To start, let me tell you about the Chessboard Problem. Once, long ago, when the game was young and novel, the Rajah of Somewheristan was so impressed by the game that he offered the Minister Sessi a boon for introducing him to chess. Boons are a serious thing in India and Sessi thought he’d teach the king a lesson. Sessi asked for something very small. He asked for one grain of rice to be placed on a chessboard and doubled every square. The king granted it laughingly, but things got out of control fast.

|  Square  |  Grains Of Rice              | How Many That Is        |
| ------------------------------------------------------------------|
|  8       |  256                         | a few spoons            |
|  16      |  65,536                      | 10 cups                 |
|  24      |  16,777,216                  | 8 sacks (50kg each)     |
|  32      |  4,294,967,296               | 2,000 sacks             |
|  40      |  1,099,511,627,776           | 550,000 sacks           |
|  48      |  281,474,976,710,656         | 23 container ships      |
|  56      |…