I think on a strict interpretation of Christiano’s definition, we’re almost right on the bubble. Suppose we were to take something like Nvidia’s market cap as a very loose proxy for overall growth in accumulated global wealth due to AI. If it keeps doubling or tripling annually, but the return on that capital stays around 4-5% (aka if we assume the market prices things mostly correctly), then there would be a 4 year doubling just before the first 1 year doubling. But if it quadruples or faster annually, there won’t be. Note: my math is probably wrong here, and the metric I’m suggesting is definitely wrong, but I don’t think that affects my thinking on this in principle. I’m sure with some more work I could figure out the exact rate at which the exponent of an exponential can linearly increase while still technically complying with Christiano’s definition.
But really, I don’t think this kind of fine splitting rolls with the underlying differences that distinguish fast and slow takeoff as their definers originally intended. I suspect if we do have a classically-defined “fast” takeoff it’ll never be reflected in GDP or asset market price statistics at all, because the metric will be obsolete before the data is collected.
Note: I don’t actually have a strong opinion or clear preference on whether takeoff will remain smooth or become sharp in this sense.
I think on a strict interpretation of Christiano’s definition, we’re almost right on the bubble. Suppose we were to take something like Nvidia’s market cap as a very loose proxy for overall growth in accumulated global wealth due to AI. If it keeps doubling or tripling annually, but the return on that capital stays around 4-5% (aka if we assume the market prices things mostly correctly), then there would be a 4 year doubling just before the first 1 year doubling. But if it quadruples or faster annually, there won’t be. Note: my math is probably wrong here, and the metric I’m suggesting is definitely wrong, but I don’t think that affects my thinking on this in principle. I’m sure with some more work I could figure out the exact rate at which the exponent of an exponential can linearly increase while still technically complying with Christiano’s definition.
But really, I don’t think this kind of fine splitting rolls with the underlying differences that distinguish fast and slow takeoff as their definers originally intended. I suspect if we do have a classically-defined “fast” takeoff it’ll never be reflected in GDP or asset market price statistics at all, because the metric will be obsolete before the data is collected.
Note: I don’t actually have a strong opinion or clear preference on whether takeoff will remain smooth or become sharp in this sense.