[Resolved] Is the SIA doomsday argument wrong?

[EDIT: I think the SIA dooms­day ar­gu­ment works af­ter all, and my ob­jec­tion to it was based on fram­ing the prob­lem in a mis­guided way. Feel free to ig­nore this post or skip to the re­s­olu­tion at the end.]

ORIGINAL POST:

Katja Grace has de­vel­oped a kind of dooms­day ar­gu­ment from SIA com­bined with the Great Filter. It has been dis­cussed by Robin Han­son, Carl Shul­man, and Nick Bostrom. The ba­sic idea is that if the filter comes late, there are more civ­i­liza­tions with or­ganisms like us than if the filter comes early, and more or­ganisms in po­si­tions like ours means a higher ex­pected num­ber of (non-fake) ex­pe­riences that match ours. (I’ll ig­nore simu­la­tion-ar­gu­ment pos­si­bil­ities in this post.)

I used to agree with this rea­son­ing. But now I’m not sure, and here’s why. Your sub­jec­tive ex­pe­rience, broadly con­strued, in­cludes knowl­edge of a lot of Earth’s his­tory and cur­rent state, in­clud­ing when life evolved, which crea­tures evolved, the Earth’s mass and dis­tance from the sun, the chem­i­cal com­po­si­tion of the soil and at­mo­sphere, and so on. The in­for­ma­tion that you know about your planet is suffi­cient to uniquely lo­cate you within the ob­serv­able uni­verse. Sure, there might be ex­act copies of you in vastly dis­tant Hub­ble vol­umes, and there might be many ap­prox­i­mate copies of Earth in some­what nearer Hub­ble vol­umes. But within any rea­son­able ra­dius, prob­a­bly what you know about Earth re­quires that your sub­jec­tive ex­pe­riences (if veridi­cal) could only take place on Earth, not on any other planet in our Hub­ble vol­ume.

If so, then whether there are lots of hu­man-level ex­trater­res­tri­als (ETs) or none doesn’t mat­ter an­throp­i­cally, be­cause none of those ETs within any rea­son­able ra­dius could con­tain your ex­act ex­pe­riences. No mat­ter how hard or easy the emer­gence of hu­man-like life is in gen­eral, it can hap­pen on Earth, and your sub­jec­tive ex­pe­riences can only ex­ist on Earth (or some planet al­most iden­ti­cal to Earth).

A bet­ter way to think about SIA is that it fa­vors hy­pothe­ses con­tain­ing more copies of our Hub­ble vol­ume within the larger uni­verse. Within a given Hub­ble vol­ume, there can be at most one lo­ca­tion where or­ganisms veridi­cally per­ceive what we per­ceive.

Katja’s blog post on the SIA dooms­day draws or­ange boxes with hu­mans wav­ing their hands. She has us up­date on know­ing we’re in the hu­man-level stage, i.e., that we’re one of those or­ange boxes. But we know much more: We know that we’re a par­tic­u­lar one of those boxes, which is eas­ily dis­t­in­guished from the oth­ers based on what we ob­serve about the world. So any hy­poth­e­sis that con­tains us at all will have the same num­ber of boxes con­tain­ing us (namely, just one box). Hence, no an­thropic up­date.

Am I miss­ing some­thing? :)

RESOLUTION:

The prob­lem with my ar­gu­ment was that I com­pared the hy­poth­e­sis “filter is early and you ex­ist on Earth” against “filter is late and you ex­ist on Earth”. If the hy­pothe­ses already say that you ex­ist on Earth, then there’s no more an­thropic work to be done. But the heart of the an­thropic ques­tion is whether an early or late filter pre­dicts that you ex­ist on Earth at all.

Here’s an over­sim­plified ex­am­ple. Sup­pose that the hy­poth­e­sis of “early filter” tells us that there are four planets, ex­actly one of which con­tains life. “Late filter” says there are four planets, all of which con­tain life. Sup­pose for con­ve­nience that if life ex­ists on Earth at all, you will ex­ist on Earth. Then P(you ex­ist | early filter) = 14 while P(you ex­ist | late filter) = 1. This is where the dooms­day up­date comes from.