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).
I'm sure there aren't specific mathematics and programming modules in the brain. There certainly are different kinds of functionality in the brain (how helpful it is to think of it as divided into modules is debatable) and some of it is more useful for doing mathematics or programming or whatever than other parts.
(Camera A may be better than camera B for landscape photography and camera B better than camera A for taking pictures at rock concerts. That doesn't require that the cameras have landscape-specific modules. All it needs is that, e.g., A has better optics and a higher-resolution sensor, while B has better autofocus and less noise when its sensitivity is cranked way up.)
So, if it sometimes happens that (1) two people's natural mental faculties differ drastically in their "distribution of power" and (2) there's a substantial difference in how useful the bits where they differ are for two different kinds of thinking, then there will be subject-specific "immutable levels".
Prima facie it seems that both #1 and #2 do happen. Of course it might turn out that #2 doesn't really, because (a) differences in intellectual power are all malleable, so that no kinds of "immutable levels" are real, or (b) differences in mental power are concentrated in some universal "g-factor" that affects all kinds of thinking equally, or (c) it just so happens that more specific variations always more or less cancel out overall (it's hard to see how that would work, but who knows?).
I'd be interested to see evidence for any of those, or for any other good reason to reject #1 and #2. So far, though, they look pretty plausible, and I don't see where I've failed at reductionism any further than we all have to on account of not actually knowing very much about how intelligence works.
It's also worth noting that "immutable" means something like "largely fixed from adulthood on" rather than "largely determined by one's genes", and whatever there may have been in our ancestral environments there are all kinds of interesting things in our early environments when our brains are most malleable that might correlate with later ability in fields like number theory, psychology, AI programming, music, etc.
(Examples, in case they're needed, of mental faculties that seem like reasonable candidates for varying differently in different people, and that could be of varying importance across different fields: Visual imagination. Short-term memory. Modelling of other people's likely feelings, thoughts, and behaviour. Language acquisition. Visual pattern-spotting. Auditory pattern-spotting.)