open problems
The Singularity Has No Date
The 1960 Science essay 'Doomsday' fit two millennia of world population growth to a formula and the formula ran to a single point: Friday, November 13, 2026. Sixty-six years later, two of the most powerful men in technology started talking about exactly such a date. This piece takes the word singularity back to its mathematical root, the point where 1 divided by x breaks at zero, and separates two curves that look alike from a distance: exponential growth, which always has a computable value, and hyperbolic growth, 1 over (T minus t), which tears at a fixed calendar date T. Five people tried to define a technological singularity: von Neumann, Good, Vinge, Kurzweil, Solomonoff. Only Solomonoff wrote equations you can test. His test says watch whether the doubling time between major AI capability leaps is itself shrinking. The best data we have, from METR, says it is: from 196 days across the full series, to 130 days for models since 2023, to 88 days for 2024 models, each step roughly two-thirds of the last. The condition looks met. It also looks untrustworthy: the task set changed, a calculation error was corrected by up to twenty percent, and the ceiling above sixteen hours is admitted unreliable. Then the 1960 paper itself returns as the precedent: the population curve that held for two thousand years simply bent, because its assumption broke against reality. Singularities in data do not end the world; they announce a regime change. The real singularity has no date. It is the moment your personal re-adaptation time becomes longer than the doubling time outside, and you start chasing a state that is already obsolete when you reach it. We are having an End of the World party on Friday the thirteenth, knowing it goes on after.
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