As I pointed out in my other [LW(p) · GW(p)] comments [LW(p) · GW(p)], these levels are about potential, not ability. The question are not really about "Can you answer $x$?" They are more along the lines of "Can you easily learn to answer $x$?" I believe this decouples "the crystallized intelligence requirements from the fluid ones".

What about recursion as a concept makes it hard for people to understand?…I'd like to see the article point at the key idea behind recursion that people have trouble grasping.

Recursion requires a person to hold two layers of abstraction in zeir mind simultaneously. This could require twice as much working memory. Working memory, unlike crystallized intelligence, is something we cannot do much to improve.

Is there a 'cannot learn pointers' in chemistry for example?

I have never tutored chemistry. But I have tutored physics for years. I have never run into anything like "cannot learn pointers" in standard undergraduate physics. The only time I encounter anything like "cannot learn pointers" is when I discuss my weird crackpot theories of relational quantum gravity and entropic time.

The ideas involved in undergraduate computer science are simpler than the ideas involved in undergraduate physics. The difference between undergraduate computer science and undergraduate physics is that undergraduate physics is a set of solutions to a set of problems. It requires little creativity. You can (relatively speaking) learn everything by rote. While fluid intelligence helps you learn rote knowledge faster, fluid intelligence tends not to put a hard cap on total rote knowledge acquisition.

On the other hand, computer science requires a person to solve novel (albeit simpler) problems all the time. It makes sense one's ability to do this could be limited by fluid intelligence.

The other difference between computer science and physics is that in physics you never have to hold two layers of abstraction in your head at the same time. It makes sense that holding two layers of abstraction in your head at the same time could be limited by working memory. One's ability to solve novel problems is the definition of fluid intelligence. Fluid intelligence is correlated with working memory.

My brief forays into chemistry suggest chemistry involves more rote knowledge and less "juggling multiple layers of abstraction" than computer science does. Chemistry, like all subjects, is limited by intelligence at some level. But I would expect the floor is lower than physics and computer science.

I'd also be wary of the possibility this entire framework / system looks good because it positions your tribe as superior (computer programmers) and possibly you somewhere comfortably towards the top.

Really? I do not know a single computer programmer who meets #9. I know only one who passes #8. Most of my programmer friends do not even pass #7. This framework puts quants on top. Not computer programmers. I do not think anyone would doubt that quants are smart people—at least in the sense relevant to this post.

Computer programmers tend to be superior at computer programming (and perhaps related fields).

This article triggered me emotionally because I think one of the things that prevents people from learning things is the belief that they can't. I wouldn't want anyone to take away from this article that because they didn't understand pointers or recursion at some point in there life, it was because they are dumb and should stop trying.

Among the most important things I have learned from Less Wrong is the value of epistemic rationality over instrumental rationality. It breaks my heart that certain people seem unable to perform certain tasks I consider trivial. The greater cruelty is blaming someone for their failure to achieve a goal zey lack the potential to accomplish.

I appreciate your genuine attempt to understand this post. Python is indeed a stand-in for any programming language of comparable complexity. Pointers and recursion could indeed be flipped around. I think we are on the same page concerning these details.

You seem to be making a few claims: (1) that these skills require an increasing amount of 1-dimensional intelligence (2) that one cannot do lower-indexed things without doing higher-indexed ones and (3) that there is something fundamental about this.

1. Yes.
2. Not quite. There can be a little slippage between close-together indices, especially #6 & #7. More importantly, this hierarchy is about talent and potential, not ability. If someone could do #5 with a little bit of study then that counts as doing #5. It is easy to imagine a mathematician who understands recursion but has never written a line of computer code. But I would be surprised if such a person could not quickly learn to write simple Python scripts.
3. This is technically an implication, not a claim. But…yeah.

First, what is an abstraction?

By "abstraction", I mean a simplification of the universe—a model. By "higher-level abstraction", I mean a model built on top of another model.^[1]

I am not referring to how these models are built upon one another within mathematics. I am trying to organize them based on how they are constructed inside a typical human brain. For example, a human being learns to write before learning arithmetic and learns arithmetic before learning calculus. It is possible to construct calculus from the Peano axioms while skipping over all of arithmetic. But that is not how a human child learns calculus.

To put it another way, a human being learning a complex skill begins by learning to perform the skill consciously. With practice, the skill becomes unconscious. This frees up the conscious mind to think on a higher (what I call more "abstract") level. Rinse and repeat. To use an example from Brandon Sanderson's creative writing lectures, a novice author is worried about how to put words down on a page while a skilled writer is thinking with plot structure. An author cannot afford to think about higher level activities until the lower level activities are automatic.

I hope this clarifies exactly what I mean by "abstraction".

The best I can make of this post is that these tasks have something akin to a hard-floor in g-factor required…

Yes. That is the point of this post.

…which is an extraordinary claim in need of extraordinary evidence.

Really? What makes you think this is an extraordinary claim? My prior is 50%/50% credence without evidence. Here are some observations I have used to subsequently update those priors.

• I am not the first person to point out that there is a hard floor on the intelligence required to understand pointers. Joel Spolsky wrote about the basic idea concerning pointers back in 2005. My college computer science teacher pointed out something similar in 2011.
• On the low end of the spectrum, I have cared for severely retarded adults who appeared to have $g$-related ceilings. This is a sensitive example and I do not want to get too deep into it. But it should be clear that someone without enough $g$ to hold a coherent conversation is unlikely ever to perform arithmetic at the level specified in this post.
• Similarly, an adult who has trouble remembering how to press 3 buttons on a smartphone is unlikely ever to write computer code.
• On the high end of the spectrum, quants are regularly hired from physics departments. These people can apparently pick up finance faster than students trained in economics. The difference seems to be mathematical aptitude. When I talk to quants I can get away with explaining much less than when I talk to, say, a Silicon Valley CTO. At least one friend of mine has confirmed this evaluation.
• I have spent countless hours tutoring physics, computer science and other subjects. The levels in my post comes from my personal experience. When it comes to specific subjects it often feels like there's a block and my interlocutor cannot fit all of the relevant information in zeir head at once.

In the scientific literature it is established that traits like fluid intelligence and working memory are basically capped. If the ability to reason at certain levels of abstraction is capped by fluid intelligence or working memory then that would explain the phenomenon I have observed.

Similar ladders exist in other domains—drawing, for example. But I have not observed such hard ceilings on one's performance in drawing. Effective training seems far more important. The same goes for routine physics, entrepreneurship and foreign languages.

I like where you are going with #10. Perhaps it could condensed into "informatic creativity".

If one person is talking analytically and the other is talking about meaning-making, then you're each trying to have different conversations.  One of you is talking about how to do something and the other is talking about how to motivate people to do something.  If at all possible you should let the first person lead; if they're diligently working on the problem then they're motivated enough.  

To consider your support team example: they seem to be assuming that if their product works well, customers will be satisfied.  That's not a terrible strategy, and it puts the focus on something they can control (the product).  If you could point to something else about the customer experience that's causing customer dissatisfaction, they would probably understand the problem and deal with it.  But if there's nothing specific that needs addressing otherwise, it's probably best just to let them focus on getting the instrument to work as well as possible.

And of course, maximizing customer satisfaction is itself a strategy toward achieving your real goal, which is profit.  Companies don't give their flagship products away for free*, no matter how much it would please the customers.

*With the exception of some loss leaders that are carefully calculated to grow revenues over the long term.

The pointer puzzle was unfair. I have removed it. What quibble do you have with #4?

I have never met someone who took a year to understand recursion. If it is not grasped quickly then the student never reaches mastery at all. Many programmers read this website and so far not a single one has contested this claim.

Incidentally, I bounced off of CS for a couple years after getting a bad grade in my first CS class. But I bounced off because the class was too easy and therefore not worth time. Not because it was too hard.