Maxwell Tabarrok (maxwell-tabarrok)
Enlightenment Values in a Vulnerable World
Thank you for reading!
There's a great chapter in Deustch's Beginning of Infinity on counterintuitive properties of infinite sets. One of them is relevant to anthropic reasoning type arguments sometimes made by longtermists.
For example, the grabby aliens paper deducing a lot of information based on the fact that human's appearance seems astoundingly early relative to the lifetime of the universe. Or the Doomsday argument which says we should expect the world to end soon as that's the only outcome which would make our presence average rather than being an outlier right at the beginning of human history.
However, as Deustch points out that if you pick any number in an infinite set, it will be astoundingly close to the beginning. More precisely, notions of 'average' or 'common' are not well defined in infinite sets. There are just as many odd integers as odd + even integers. There are just as many integers divisible by a trillion as there are integers. So if the universe is confirmed to be truly infinite then these anthropic reasoning arguments will have to change.