On the acceleration model, the periods from 1500-2000, 10kBC-1500, and “the beginning of history to 10kBC” are roughly equally important data (and if that hypothesis has higher prior I don’t think you can reject that framing). Changes within 10kBC − 1500 are maybe 1/6th of the evidence, and 1⁄3 of the relevant evidence for comparing “continuous acceleration” to “3 exponentials.” I still think it’s great to dig into one of these periods, but I don’t think it’s misleading to present this period as only 1⁄3 of the data on a graph.
I’m going to try and restate what’s going on here, and I want someone to tell me if it sounds right:
If your prior is that growth rate increases happen on a timescale determined by the current growth rate, e.g. you’re likely to have a substantial increase once every N doublings of output, you care more about later years in history when you have more doublings of output. This is what Paul is advocating for.
If your prior is that growth rate increases happen randomly throughout history, e.g. you’re likely to have a substantial increase at an average rate of once every T years, all the years in history should have the same weight. This is what Ben has done in his regressions.
The more weight you start with on the former prior, the more strongly you should weight later time periods.
In particular: If you start with a lot of weight on the former prior, then T years of non-accelerating data at the beginning of your dataset won’t give you much evidence against it, because it won’t correspond to many doublings. But T years of non-accelerating data at the end of your dataset would correspond to many doublings, so would be more compelling evidence against.
I’m going to try and restate what’s going on here, and I want someone to tell me if it sounds right:
If your prior is that growth rate increases happen on a timescale determined by the current growth rate, e.g. you’re likely to have a substantial increase once every N doublings of output, you care more about later years in history when you have more doublings of output. This is what Paul is advocating for.
If your prior is that growth rate increases happen randomly throughout history, e.g. you’re likely to have a substantial increase at an average rate of once every T years, all the years in history should have the same weight. This is what Ben has done in his regressions.
The more weight you start with on the former prior, the more strongly you should weight later time periods.
In particular: If you start with a lot of weight on the former prior, then T years of non-accelerating data at the beginning of your dataset won’t give you much evidence against it, because it won’t correspond to many doublings. But T years of non-accelerating data at the end of your dataset would correspond to many doublings, so would be more compelling evidence against.