The Presumptuous Philosopher’s Presumptuous Friend

One day, you and the pre­sump­tu­ous philoso­pher are walk­ing along, ar­gu­ing about the size of the uni­verse, when sud­denly Omega jumps out from be­hind a bush and knocks you both out with a crow­bar. While you’re un­con­scious, she builds two ho­tels, one with a mil­lion rooms, and one with just one room. Then she makes a mil­lion copies of both of you, sticks them all in rooms, and de­stroys the origi­nals.

You wake up in a ho­tel room, in bed with the pre­sump­tu­ous philoso­pher, with a note on the table from Omega, ex­plain­ing what she’s done.

“Which ho­tel are we in, I won­der?” you ask.

“The big one, ob­vi­ously” says the pre­sump­tu­ous philoso­pher. “Be­cause of an­thropic rea­son­ing and all that. Million to one odds.”

“Rub­bish!” you scream. “Rub­bish and pop­py­cock! We’re just as likely to be in any ho­tel omega builds, re­gard­less of the num­ber of ob­servers in that ho­tel.”

“Un­less there are no ob­servers, I as­sume you mean” says the pre­sump­tu­ous philoso­pher.

“Right, that’s a spe­cial case where the num­ber of ob­servers in the ho­tel mat­ters. But ex­cept for that it’s to­tally ir­rele­vant!”

“In that case,” says the pre­sump­tu­ous philoso­pher, “I’ll make a deal with you. We’ll go out­side and check, and if we’re at the small ho­tel I’ll give you ten bucks. If we’re at the big ho­tel, I’ll just smile smugly.”

“Hah!” you say. “You just lost an ex­pected five bucks, sucker!”

You run out of the room to find your­self in a huge, ten thou­sand story at­trium, filled with throngs of your­selves and smug look­ing pre­sump­tu­ous philoso­phers.