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@ -60,7 +60,7 @@ Consider circumnavigating the Earth, that is, travelling in the same direction u
The precise magnitude of these discontinuities depends on whether we measure time, or its logarithm. In both cases, we get very large discontinuities, plausibly of more than 100 years. However, our estimates are inexact. In particular, our data only shines in the period 1870 - 1961, and thus we are most confident in the discontinuity created by the first circumnavigation by plane (as opposed to by ship & train). This happened in 1931 and our two estimates of the magnitude of that discontinuity are 11 and 40.5 years.
According to the first measure, *the first cosmonaut wasn't really a discontinuity* (a deviation of 1 year from the predicted value). Furthtermore, if we estimate the next data point extrapolating the previous progress *linearly*, we get four-ish discontinuities. But as the graphs below show, the natural fit is not linear, it's hyperbolic / exponential-ish. So here definitions also get in the way, because whether any point is a discontinuity depends on which model we use to extrapolate from past data.
According to the first model, *the first cosmonaut wasn't really a discontinuity* (a deviation of 1 year from the predicted value. But note that this model would have predicted negative times after a while). Furthermore, if we estimate the next data point extrapolating the previous progress *linearly*, we get four-ish discontinuities. But as the graphs below show, the natural fit is not linear, it's hyperbolic / exponential-ish. So here definitions also get in the way, because whether any point is a discontinuity depends on which model we use to extrapolate from past data.
Throughout the 19th century, we see ships develop into faster and faster ships, and then give way to planes, which in turn gain in speed, until they're all overtaken by Yuri Gagarin in a rocket. This repeated upmanship is what's downstream of the exponential shape, and you couldn't have predicted that by extrapolating the very real gains in ship speed at the beginning of the century; you couldn't have predicted rockets. As for the implications for AI scenarios, this example may serve to ilustrate the mechanics of how very fast progress can look like on the inside, and adds another datapoint for AI Impact's base rate estimation.