How, Mathematically, We’re Fucked
Exponential growth on a finite planet does not end well, whatever form it takes
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 | 72,057,594,037,927,900 | 50% of world rice |
| 64 | 18,446,744,073,709,600,000 | 12,000 worlds of rice |At the end of one row, the rice was spilling off the board. By the end of the third row, it was spilling out of sacks. By the fifth row, it was more than the king had in his storehouses. By the penultimate row (the second to last) the king owed 50% of current global rice production (about 45m tons). By the last square, he owed the production of 12 worlds. Which he didn’t have. Which no one has. The king would be ruined by exponential growth. That was the lesson he learned. We ignore this parable at our peril.
Exponential growth is absurd and we have based our entire civilization on this absurdity. Modern society—unlike the ancients—requires exponential growth for social stability. It is a belief we all generally share, and it is this belief that is killing us. Climate change and resource collapse are just symptoms of believing…
