1960: The Year The Singularity Was Cancelled | Slate Star Codex

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Source: 1960: The Year The Singularity Was Cancelled | Slate Star Codex

1960: THE YEAR THE SINGULARITY WAS CANCELLED

[Epistemic status: Very speculative, especially Parts 3 and 4. Like many good things, this post is based on a conversation with Paul Christiano; most of the good ideas are his, any errors are mine.]

I.

In the 1950s, an Austrian scientist discovered a series of equations that he claimed could model history. They matched past data with startling accuracy. But when extended into the future, they predicted the world would end on November 13, 2026.

This sounds like the plot of a sci-fi book. But it’s also the story of Heinz von Foerster, a mid-century physicist, cybernetician, cognitive scientist, and philosopher.

His problems started when he became interested in human population dynamics.

(the rest of this section is loosely adapted from his Science paper “Doomsday: Friday, 13 November, A.D. 2026”)

Assume a perfect paradisiacal Garden of Eden with infinite resources. Start with two people – Adam and Eve – and assume the population doubles every generation. In the second generation there are 4 people; in the third, 8. This is that old riddle about the grains of rice on the chessboard again. By the 64th generation (ie after about 1500 years) there will be 18,446,744,073,709,551,616 people – ie about about a billion times the number of people who have ever lived in all the eons of human history. So one of our assumptions must be wrong. Probably it’s the one about the perfect paradise with unlimited resources.

Okay, new plan. Assume a world with a limited food supply / limited carrying capacity. If you want, imagine it as an island where everyone eats coconuts. But there are only enough coconuts to support 100 people. If the population reproduces beyond 100 people, some of them will starve, until they’re back at 100 people. In the second generation, there are 100 people. In the third generation, still 100 people. And so on to infinity. Here the population never grows at all. But that doesn’t match real life either.

But von Foerster knew that technological advance can change the carrying capacity of an area of land. If our hypothetical islanders discover new coconut-tree-farming techniques, they may be able to get twice as much food, increasing the maximum population to 200. If they learn to fish, they might open up entirely new realms of food production, increasing population into the thousands.

So the rate of population growth is neither the double-per-generation of a perfect paradise, nor the zero-per-generation of a stagnant island. Rather, it depends on the rate of economic and technological growth. In particular, in a closed system that is already at its carrying capacity and with zero marginal return to extra labor, population growth equals productivity growth.

What causes productivity growth? Technological advance. What causes technological advance? Lots of things, but von Foerster’s model reduced it to one: people. Each person has a certain percent chance of coming up with a new discovery that improves the economy, so productivity growth will be a function of population.

So in the model, the first generation will come up with some small number of technological advances. This allows them to spawn a slightly bigger second generation. This new slightly larger population will generate slightly more technological advances. So each generation, the population will grow at a slightly faster rate than the generation before.

This matches reality. The world population barely increased at all in the millennium from 2000 BC to 1000 BC. But it doubled in the fifty years from 1910 to 1960. In fact, using his model, von Foerster was able to come up with an equation that predicted the population near-perfectly from the Stone Age until his own day.

But his equations corresponded to something called hyperbolic growth. In hyperbolic growth, a feedback cycle – in this case population causes technology causes more population causes more technology – leads to growth increasing rapidly and finally shooting to infinity. Imagine a simplified version of Foerster’s system where the world starts with 100 million people in 1 AD and a doubling time of 1000 years, and the doubling time decreases by half after each doubling. It might predict something like this:

1 AD: 100 million people
1000 AD: 200 million people
1500 AD: 400 million people
1750 AD: 800 million people
1875 AD: 1600 million people

…and so on. This system reaches infinite population in finite time (ie before the year 2000). The real model that von Foerster got after analyzing real population growth was pretty similar to this, except that it reached infinite population in 2026, give or take a few years (his pinpointing of Friday November 13 was mostly a joke; the equations were not really that precise).

What went wrong? Two things.

First, as von Foerster knew (again, it

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