# MugaSofer comments on Pascal’s Mugging: Tiny Probabilities of Vast Utilities

• What is the mere Earth at stake, com­pared to a tiny prob­a­bil­ity of 3^^^^3 lives?

Do you re­ally think this would be clearer or more rigor­ous if writ­ten in math­e­mat­i­cal no­ta­tion?

Any­way, that’s an in­ter­est­ing ques­tion, and, if it turns out that the Solomonoff prior is in­deed heavy-tailed w.r.t. any rele­vant state vari­able, it would seem to me as a good rea­son not to use Solomonoff in­duc­tion.

Isn’t that kinda the point?

[edit: these are not rhetor­i­cal ques­tions.]

• What is the mere Earth at stake, com­pared to a tiny prob­a­bil­ity of 3^^^^3 lives? Do you re­ally think this would be clearer or more rigor­ous if writ­ten in math­e­mat­i­cal no­ta­tion?

The prob­lem is that Solomonoff in­duc­tion is an es­sen­tially opaque model.

Think of it as a black box: you put in a string of bits rep­re­sent­ing your past ob­ser­va­tions and it gives you a prob­a­bil­ity dis­tri­bu­tion on string of bits rep­re­sent­ing your pos­si­ble fu­ture ob­ser­va­tions. If you open the lid of the box, you will see many (ideally in­finitely many) com­puter pro­grams with ar­bi­trary struc­ture. There is no easy way to map that model to a prob­a­bil­ity dis­tri­bu­tion on non-di­rectly ob­serv­able world state vari­ables such as “the num­ber of peo­ple al­ive”.

Isn’t that kinda the point?

My in­ter­pre­ta­tion is that Yud­kowsky as­sumes Solomonoff in­duc­tion es­sen­tially a pri­ori and thus is puz­zled by the dilemma it allegedly yields. My point is that:

• It’s not ob­vi­ous that Solomonoff in­duc­tion ac­tu­ally yeilds that dilemma.

• If it does, then this would be a good rea­son to re­ject it.

• My point is that:

It’s not ob­vi­ous that Solomonoff in­duc­tion ac­tu­ally yeilds that dilemma. If it does, then this would be a good rea­son to re­ject it.

And my point is that:

• It seems like it should; the ar­ti­cle ex­plic­itly asks the reader to try and dis­prove this.

• That’s kinda the point of the ar­ti­cle.

It ap­pears we all agree. I think.