I think that's the main point where we disagree. I think there's a hell of a lot more to it.
I remember noticing when I was in school that while I could learn a variety of things, there were definitely subjects that were a lot easier for me and others in which I'd struggle no matter how hard I worked. I also observed other people with very different profiles of easy and hard subjects.
I barely passed organic chemistry. I studied hard, but it just would not "take." I had a friend who breezed through it. Anything that involved writing though? I'd breeze through it. I could get As in any class that involved understanding concepts and writing about them with almost no effort. This same friend struggled to write an essay.
I actually dropped out of vertebrate anatomy. Tons and tons of clades and names for discrete things. I found a way to adjust my major requirements to avoid taking it. Otherwise I would have had to switch majors. There is no way I could have passed that class with any amount of tutoring.
It's like I have a photographic memory for concepts, but can't recall discrete facts. I kept looking for the underlying patterns in organic chemistry but it turns out we don't understand it well enough to have those... we just know a ton of reactions that do things. I flounder badly in subjects whose facts can't be attached to an abstract conceptual framework, but I can read about a concept once and I understand it forever.
As a programmer I really love IDEs with "code insight" and other features that basically consult the documentation for you in real time. I get everything about the concepts and algorithms but can never remember the order of arguments on memcpy() even after using it for 20 years. I know memcpy() is there and what it does conceptually though, so it's fine since the IDE will show me which argument goes first.
My point is that different people who are "smart" can differ radically in their ability profile.
'g' is a scalar that tries to measure the relatively large chunk of correlation that tends to show up on aptitude tests.
On average, individuals who do well on one type of intellectual task tend to do well on most other types of intellectual tasks. Maybe someone is good at all forms of pattern recognition but just can't manage 3d-rotation tasks. It happens.
So an IQ test isn't perfect. There isn't one true value that exists in the world that is 'g'. Many tests now break out 'verbal' and 'mathematical' IQ, but I suspect even those have a correlation > 0.5
Take someone like John Von Neumann. One of the greatest mathematicians of the 20th century (and perhaps all time), he could also converse in a multitude of languages (native Hungarian, English, French, German, Italian, Ancient Greek). He was also an avid history buff, reading through Wilhelm Oncken's 46-volume Allgemeine Geschichte in Einzeldarstellungen at the age of 8 [1].
Later, he studied and became a chemical engineer while at the same time studying for his Ph.D in mathematics at the age of 20!
there is only one single gene that gives rise to all of the variance in intelligence among humans.
This does not follow. The claim is that some brains are better at learning than others. This means they can model and describe the complex relationship between ideas across a multitude of subject domains. It doesn't say anything about a single gene being responsible.
[1] https://en.wikipedia.org/wiki/John_von_Neumann#Child_prodigy
Yeah a zero cost sum model is totally wrong. As are models which assume that everyone is born equally smart and all differences just come from training or whatever. Some people have better abilities and it doesn't imply that they are worse in other areas. But they might only have extraordinary performance in specific tasks. And others, like I've mentioned above, have golden hands, von Neumann being an example.
I've done some searching and the model of intelligence seems to be an open area of debate, but it seems that research has moved on from the "not much more than g" era. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6526477/
> For several decades, the question of whether measures of specific cognitive ability contributed anything meaningful to the prediction of performance on the job or performance in training once measures of general mental ability were taken into account appeared to be settled, and a consensus developed that there was little value in using specific ability measures in contexts where more general measures were available. It now appears that this consensus was premature, and that measures of specific abilities can make important contributions even if general measures are taken into account.
See also https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6480721/ and https://doi.org/10.1111/j.1744-6570.2010.01182.x
There is a nice paper on this topic.
On the Measure of Intelligence - François Chollet https://arxiv.org/abs/1911.01547
I believe generality in human intelligence is overrated. We can't do large multiplication in our heads, we can't solve the Salesman problem in our heads, and many other things we can't do because our intelligence is not in fact general. It has a set of skills and can combine them in many ways.
Whatever that special thing is, once you see it in action you realise it's a genuine facet of something. You may not want to call it an intelligence, but I'm ok with doing so. It wasn't a physical thing, they weren't physically special, ergo it was a mental thing. "Intelligence" covers that quite well, I think.
Burmese pythons are way stronger than humans yet I doubt anyone would call them more intelligent. Mantis shrimp have way faster reflexes and their vision is way more sophisticated than ours yet they're not more intelligent as well.
There is a lot of debate over the definition of intelligence but one thing most definitions have in common is that it is general. A human being can play the piano, solve an integral, write a novel, compose a photograph, and many many more things. We do all of these things using the same "muscle", our brain. It turns out that some people's brains are faster at being able to learn all of these myriad tasks. That's all there is to it.