Mutable Levels Are Path-Dependent

XFrequentist

Cyan and I had a good discussion (several, actually) on our long recent drive. Among diverse topics, he explained something that lead to a confusion-reducing revelation.

On meeting Eliezer, Cyan wished to engage him on Measure Theory. Cyan felt that it might be a useful tool for Eliezer's fAI work. The conversation was interesting (I'll leave it to someone more mathematically competent to summarize), but what I remarked on was how it started.

Cyan began, "Eliezer, I'd say you're at least 3 levels above me, but I thought I could offer some advice on Measure Theory..."

I took this to be (needless) status-lowering behavior, and mentioned this in later conversation. However, it came out that this wasn't so, and there was original thinking behind the number "3".

Cyan's formalization of "levels" involved the creation of useful new concepts. Someone a single level above you can create concepts that you can understand, but could not generate on your own.

Cyan felt that Average Physicists were a level above him, Elite Physicists a level higher, and estimated that Eliezer was a level beyond that. Eliezer's original concept of Levels seems to imply that one's level is biologically determined and immutable, and so a single "EY-level" is probably akin to the highest possible "Cyan-level". I will therefore refer to Mutable (Cyan-levels) and Immutable (EY-levels) Levels to distinguish the two. The former is the attainment of one's greatest potential, the latter describes this potential.

I thought that this was a useful way to think about levels and "leveling up", but not completely right. I didn't think that levels were generalizable. Alice, Bob, and Cheryl might form a natural chain in which each was one Mutable Level above the previous person in the chain, but this chain could be very different with different players. Alice, Zorba, Xeno, Yudkowsky, and Cheryl could form an equally logical chain with each person being one Mutable Level above the previous person, so it doesn't make sense to refer to someone as X levels above you.

Cyan and I eventually agreed that this makes more sense, and had the additional benefit providing a useful way to guide seeking out mentors.

Therefore I make several claims I'd like the group's thoughts on:

A useful way to think about "Levels" is as describing increasing ability to produce concepts of greater explanatory power or insight.
It is useful to think of someone as a level above you if they can generate novel ideas that you can only understand, but could not have produced from scratch.
Levels can be usefully thought of as Mutable (if they are amenable to improvement through study or holistic self improvement), or Immutable (if they are biologically - or otherwise - determined and fixed).
One's maximally attainable Mutable Level is equivalent to one's Immutable Level; the latter describes potential, while the former describes the attainment of that potential.
Mutable Levels are path dependent; it makes no sense to talk about levels abstractly, only in relation to specific individuals (or specific groups whose members have very similar abilities in the domain of interest).

Cyan and I had a good discussion (several, actually) on our long recent drive. Among diverse topics, he explained something that lead to a confusion-reducing revelation.

Cyan began, "Eliezer, I'd say you're at least 3 levels above me, but I thought I could offer some advice on Measure Theory..."

I took this to be (needless) status-lowering behavior, and mentioned this in later conversation. However, it came out that this wasn't so, and there was original thinking behind the number "3".

Cyan's formalization of "levels" involved the creation of useful new concepts. Someone a single level above you can create concepts that you can understand, but could not generate on your own.

Cyan and I eventually agreed that this makes more sense, and had the additional benefit providing a useful way to guide seeking out mentors.

Therefore I make several claims I'd like the group's thoughts on:

A useful way to think about "Levels" is as describing increasing ability to produce concepts of greater explanatory power or insight.
It is useful to think of someone as a level above you if they can generate novel ideas that you can only understand, but could not have produced from scratch.
Levels can be usefully thought of as Mutable (if they are amenable to improvement through study or holistic self improvement), or Immutable (if they are biologically - or otherwise - determined and fixed).
One's maximally attainable Mutable Level is equivalent to one's Immutable Level; the latter describes potential, while the former describes the attainment of that potential.
Mutable Levels are path dependent; it makes no sense to talk about levels abstractly, only in relation to specific individuals (or specific groups whose members have very similar abilities in the domain of interest).

I see a few comments focusing on the metric as a valuation of understanding, I suppose a few people may have missed this:

It is useful to think of someone as a level above you if they can generate novel ideas that you can only understand, but could not have produced from scratch.

Bearing this portion of the claim in mind, here are my initial thoughts:

It seems a bit (only a very, very little bit) better to me than simply understanding an idea, but this whole 'levels' business seems far too vague to be useful, especially if we don't have any sort of objective metric for determining exactly how difficult a novel idea is to generate.

Intuitively it seems like the task of creating such a metric would require an understanding of all (or at least most) of the (cognitive and extra-cognitive) factors that play into idea generation, which makes it a very non-trivial task.

On top of the issue of having an objective metric for idea evaluation, we have to determine a valid metric for idea generation potential, because as it stands it appears to me that all we have to go on is the feeling that something is too hard to do, which does not seem even remotely reliable.

Further still, if we want to distinguish between "mutable" and "immutable" levels, it seems that we would have to determine what factors that go into idea generation can be effectively hacked in a reasonable period of time, which is yet another highly non-trivial problem. Bearing in mind these issues, it seems that the "levels" would almost certainly need to be significantly more gradated than this Level += 1, Mutable/Immutable structure.

In addition, even taking into account the reductionist concerns pointed out by komonisto, it seems very likely that bottom-level cognitive features would play into idea generation in various ways such that even if individual tasks were not level-separable (in the sense that gjm is talking about), some sets of tasks likely would be (or at least very nearly be, even if the division isn't always totally clean).