Recently, in a conversation with a coworker, I was trying to describe the rate at which time passed subjectively, with a term that distinguished from the usual objective clock speed constrained only by general relativity and generic human psychology. I ended up saying "meta-rate". That bothered me for reasons I couldn't put a finger on until today.

I realized I'd been aiming for Hofstadter's use of the modifier 'meta', and that this seemed to conflict with the LessWrong use of "mesa-".

'Meta' is for when you go outside the system. 'Meta-reasoning'. 'Meta' refers to things that are strictly more powerful than the object-level versions of themselves. 'Meta-cult'. 'Meta-dispute'. 'Meta-currency'.

'Meta' seemed to modify object-level referents to make them more all-inclusive - allowing us to modify an object-level word such as 'cat', to predicate over a sort of ideal or Platonic fusion referent that counterfactually-exists in our preferred, as opposed to the real, social consensus. I'd rather join a meta-cult than a cult, I'd rather win a meta-dispute than a dispute, and I'd rather have 10 meta-dollars than 10 dollars. And I think I'd rather pet a meta-cat, than a cat.

Because "meta-" seemingly modifies object-level referents to be more computationally powerful, and "mesa-" is supposed to be the inverse of "meta-", the locally-colloquial reference to unaligned AI genies [and various other kinds of computations] which are more powerful than their "outer" begettors, as 'mesa-optimizers', has always bothered me.

But today I realized that [I think?] when I try and square the circle of why Hofstadter's meta-genie is 'meta', with the square of why mesa-optimizers are 'mesa-', I'm looking at a subjectivity problem. [Not in the sense of qualia but in the sense of indexical uncertainty - an anthropic problem, though these aren't the typical cases where you bring in "anthropics".]

"Meta-"X is more desirable to me.

"Mesa-"X is more desirable to you - and you are not me, so to me it looks like you're dragging my group's precious social consensus, selfishly closer to yourself. [Which is fine if you're aligned enough with me! In fact, these concepts aren't exactly diametrically opposed - if our world is composed of identical agents, meta-X and mesa-X will be exactly the same for all X.]

Hofstadter's Meta-[...]-Genies, wouldn't make sense, if they didn't jointly compose an aligned optimizer:

Achilles: [...] Tell me, Mr. Genie--what is a meta-wish?

Genie: It is simply a wish about wishes. I am not allowed to grant meta-wishes. It is only within my purview to grant plain ordinary wishes, such as wishing for ten bottles of beer, to have Helen of Troy on a blanket, or to have an all-expenses-paid weekend for two at the Copacabana. You know--simple things like that. But meta-wishes I cannot grant. 

[...] 

Achilles: Oh, I feel so rotten. I was REALLY HOPING to wish for a hundred wishes . . . 

Genie: Gee, I hate to see anybody so disappointed as that. And besides, meta-wishes are my favorite kind of wish. Let me just see if there isn't anything I can do about this. 

[...]

Meta-Genie: I am the meta-Genie. You summoned me, O Genie? What is your wish? 

Genie: I have a special wish to make of you, O Djinn, and of GOD. I wish for permission for temporary suspension of all type-restrictions on wishes, for the duration of one Typeless Wish. Could you please grant this wish for me? 

Meta-Genie: I'll have to send it through Channels, of course. One half a moment, please.

[ subsequently, Achilles's wish is [in 1 meta-moment] passed up the infinite chain to GOD and in the process converted into a meta-wish, a meta-meta-wish [a wish about wishes about wishes], etc. ]

[ --Douglas Hofstadter, Gödel, Escher, Bach ]

"Meta" seems to suggest 'higher' [and the M does a good job of suggesting "mountains", and peaks]. By contrast, "mesa" is the name of a mountain with its top cut off - it suggests flattening and lowering, height being brought further inward.

I'm going to try remembering "meta" as "an idealization of the object-level thing which brings the surface of my utility function further outward", and "mesa" as "an idealization of the object-level thing which, given the opportunity, would slice orthogonally through the mountains of my utility function, cutting them off".

Of course, my meta- is someone else's mesa- - and vice versa. But it hardly makes sense to refer to a generic "mesa-rate", any more than it would make sense to refer to a generic "you", or a generic "antisocial". "Mesa-" is a term that can, to some extent, be used only indexically - only with a concrete referent, that is not-me in some specific, context-given way.