If we treat the priors as hypotheses about the distribution of events in the world, then past data can provide evidence about which one is right, and (the principle of) Will’s prior would have given excessively low credence to humanity’s first million years being the million years when life traveled to the Moon, humanity becoming such a large share of biomass, the first 10,000 years of agriculture leading to the modern world, and so forth.
On the other hand, the kinds of priors Toby suggests would also typically give excessively low credence to these events taking so long. So the data doesn’t seem to provide much active support for the proposed alternative either.
It also seems to me like different kinds of priors are probably warranted for predictions about when a given kind of event will happen for the first time (e.g. the first year in which someone is named Steve) and predictions about when a given property will achieve its maximum value (e.g. the year with the most Steves). It can therefore be consistent to expect the kinds of “firsts” you list to be relatively bunched up near the start of human history, while also expecting relevant “mosts” (such as the most hingey year) to be relatively spread out.
That being said, I find it intuitive that periods with lots of “firsts” should tend to be disproportionately hingey. I think this intuition could be used to construct a model in which early periods are especially likely to be hingey.
On the other hand, the kinds of priors Toby suggests would also typically give excessively low credence to these events taking so long. So the data doesn’t seem to provide much active support for the proposed alternative either.
It also seems to me like different kinds of priors are probably warranted for predictions about when a given kind of event will happen for the first time (e.g. the first year in which someone is named Steve) and predictions about when a given property will achieve its maximum value (e.g. the year with the most Steves). It can therefore be consistent to expect the kinds of “firsts” you list to be relatively bunched up near the start of human history, while also expecting relevant “mosts” (such as the most hingey year) to be relatively spread out.
That being said, I find it intuitive that periods with lots of “firsts” should tend to be disproportionately hingey. I think this intuition could be used to construct a model in which early periods are especially likely to be hingey.