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What is "intelligence?" Can we separate it from society's conception of it? Can we state a computational definition rather than a definition in terms of satisfaction of cultural standards? We undervalue a lot of mental attributes - consistency of thought, sensitivity to subtle differences in concepts, patience, self-reflection, the ability to "go meta" etc. which cannot be detected by the rough and rigid abstract problem solving required by low-level Math (e.g. the Math problems which would qualify prodigies).

I am highly turned off by the idea that we can't "become smart" after an early age. I feel like I "got smart" after I started playing go, I feel like I "got smart" after I learned category theory. I feel like every year I get smarter - and not smarter in the sense of "having more knowledge" but smarter in the sense of being able to solve larger classes of problems, and more complicated problems.

and c.

I am highly turned off by the idea that we can't "become smart" after an early age.

I find this notion rather peculiar. Do people get "highly turned off" that they can't "get tall"? I've known for my entire life that I could never become a professional athlete -- I simply don't have the physique.

What is it about intelligence which makes people get so much more upset than they get about physical attributes?

I don't have an answer to this question, but this seems to be the same attitude that got Lawrence Summers into trouble!

My guess is that "intelligence" can be largely hidden, whereas your physique is immediately apparent even if you just sit and do nothing. That it is hidden then, gives it a mysterious feeling of potential, and nobody wants that put in a box. I think it is a cultural phenomenon that necessitates something like unconditional encouragement.

Intelligence hits closer to home because intelligence is more fundamental to who you are. Children who want to insult each other rarely say "You're weak!" They're more likely to say "You're stupid!"

Would you rather be a brain without a body or a body without a brain?

For a heartrending story about the role intelligence plays in shaping personality, read Flowers for Algernon by Daniel Keyes.

I think you're being presumptuous. I'm not saying that I'm "turned off" by the -fact- that I can't get tall(1). I'm saying that this is not a -fact- at all. Even if it -is- a fact, it certainly is much more uncertain/open for debate than the question of whether you can get tall at a late age. I'm saying that the fact that you -claim it is a fact- is what turns me off. Perhaps I was slightly imprecise. I should have said "I am highly turned off by assertions to the effect that we can't become smart after an early age." This turns me off because belief/assertion creates cultural structure, and cultural structure changes the world. This point is too complex to go into here, sorry.

My claim is even slightly deeper/more provocative than that - I don't think that efforts by a lot of academics (including a lot of my friends) to propagate an idea of "general intelligence" which solidifies at a young age are entirely benign. I think that they are largely founded in worry and attempts to create an elite academic class. Once you're in, you're in (since getting in means that you have a "good" brain which is not really subject to change). It's self-reinforcing and (in my experience) always based in self-doubt.


As an aside, the idea that "people get so much more upset" about the intellectual than the physical is completely absurd. I know a ton of people (girls and guys) who freak out constantly about their appearance. I know like 3 guys (including myself) who are the least bit worried about our intellects. Admittedly, most of my friends are academics, but my interactions with people outside this sphere indicate that the trend is not peculiar to my social group (and is probably even more physical-attribute oriented, in general). Seriously, I can't believe that you wrote this. This isn't meant to be mean or like ad hominem - but seriously? Do you actually believe what you wrote? Do you know anyone who isn't an academic?

To answer what I think you might have meant (namely: why do _I_ get much more freaked out about my intelligence than my physical attributes - which is also presumptuous because you have -no- idea how much I care about my physical attributes) I would like to observe that in modern western society "we are our minds." Your mind is essentially the limit of your capabilities in the sort of world I'm sure both you and I live in (the quote unquote information world). The mind is connected with the ability to create beauty (art), the ability to connect with other human beings (sex), the ability to experience spirituality (love), etc. In the academic world, at least, our physical bodies are a burden. They wear out. They get cancer. They die.

Did you seriously ask this? Were you being rhetorical? I can't tell. I don't mean to be mean, but sheesh.

(1) and I accuse you of attempting to employ an underhanding rhetorical trick in making this implicit comparison, I might add.

There are basically 3 requirements for intelligence that surpass the basic need to survive:

DNA, Diet, and Stimulus.

DNA limits what structures can develop which is the basic foundation of intelligence.

Diet provides the raw materials to crate the structures that DNA is trying to build. Poor diet causes DNA to sacrifice specific objectives to insure survival. Specific toxins like lead also limit the body's ability to create structures. At the same time short term diet inhibits performance.

Experience refines specific structural elements. Without early experience in specific areas it becomes harder to develop efficient systems for dealing with those situations. It's not impossible to learn French at 50 if you only know Spanish, but it's far easer to learn it at 5 than 50. Part of this has to due with the brain ignoring sounds that it finds unimportant.

All of the above statements are well supported by a huge body of research being annoyed by them is like getting pissed off at gravity while building rockets.

"Intelligence" is a hidden variable g, which comes out of statistical tests of various mental examinations. Basically, give a bunch of people a french test, a math test, a physics test, a driving test, etc.

Run statistical tests for hidden variables, and you will discover this mysterious hidden variable 'g'. It is relatively independent of cultural knowledge: i.e., french is nearly independent of g (1), while physics, plumbing and loading irregularly sized boxes into a truck are highly correlated to g. This all comes out of the statistical analysis, and is not assumed apriori.

Then look for correlations between g and career outcome (and other such things), you'll discover strong correlations there as well. Physicists tend to have high g, janitors low g, etc. For instance, I've never met a math/physics/eng faculty member with an IQ below 120 (though mine is below 100).

So this statistical measure g fits very closely with the intuitive picture of intelligence. It's not cultural, but we don't know what it means computationally either.

(1) Amoung frenchies, people with higher 'g' will score better on french tests. But a low g frenchy will beat a high g brit.

I've never met a math/physics/eng faculty member with an IQ below 120 (though mine is below 100).

Yummy, you have to be kidding us. Either that, or you were drunk when you took the test, or we really need to rethink what the tests are measuring. There is no way somebody with subnormal intelligence is involved in exchanges like this:


Apparently someone decided the score a bunch of the Caltech faculty on an IQ test, and a surprising number of them turned up with scores < 100. This doesn't prove that the concept is untenable, but clearly some of our tests are missing things.

That's interesting... any source?

I'm afraid not -- it was just an anecdote circulating around the astro department at Princeton. Feynman was known to have an IQ of 125, and I met a grad student there who admitted to an IQ of around 80 -- a perfectly bright person, to be sure. Again, I don't have the ability to prove these things to you, but I think we should recognize that, occasionally, our methods for measuring intelligence are very very broken.

>Feynman was known to have an IQ of 125

That's still more than 1.5 standard deviations above average. If Feynman's IQ was exactly 125, he would be ahead of "only" 95% of the population.

I agree with this point, but I think that what you run into is that there are certain important cross-cultural trends which might cause g to be pertinent. What I mean is that perhaps the set of tasks which we "regularly perform" are governed by g - these tasks usually involving "problem solving" of the you-give-me-a-well-defined-problem-and-I'll-solve-it variety. It's a kind of reciprocal process - society will produce lots of jobs/roles which fit mass statistics it can determine, and it will also screen for that mass statistic.

What interests me, and what I'm worried that focus on this sort of gross statistic deprives us from thinking about, is the non-regular. I'm interested in the philosophical, the revolutionary, the artistic. I'm interested in what made Einstein Einstein. I don't think it's "g."

Slightly more abstractly/hypothetically: The way I kind of see intelligence is that we can function within contexts (e.g. functioning within the "Math context" would be doing math problems) and "g" corresponds to our ability to manipulate symbols generally, so that we are generally good at working within contexts. This is a really abstract way of saying g corresponds to our ability to solve problems. However, I don't think g says anything about long-term problem solving (involving abstraction, self-reflection), novel content creation (involving cross-context thinking), etc.

Does this make sense?

You are aware that Einstein's brain had some very unusual features, right? I don't pay much attention to this, but I remember it is unusual enough that it is safe to say most people's brains don't have those features.

Relativity was not a well-defined problem when Einstein came up with it. You can analyze this intelligence in however many ways, but it is highly possible that "quantum leaps" in scientific advancement come from unusual thinkers -- unusual in a way that you can't just train very hard in and attain.

"When I use a word, it means exactly what I mean it to mean, no more and no less." -- Humpty Dumpty

"Intelligence is what intelligence tests measure." -- Edward Boring

I'm actually surprised by how few comments have been made regarding the actual nature of intelligence in this thread. yummyfajitas' parent comment is one of those few, and he equates intelligence as we understand it with g, the hypothesized general intelligence posited by psychometricians.

y.f. makes the same two arguments that psychometricians make for the validity of g as a representation of human intelligence,[1] which are supposed to demonstrate g's "internal validity" and "external validity". The former refers to the positive correlations between various (supposed) intelligence tests (described in the jargon as the "positive manifold"), and the latter to the positive correlations between g and supposed success in life. Broadly, the internal validity argument proves the "general" in "general intelligence", whereas the external validity argument proves the "intelligence".

The first wrinkle in these arguments is the claim that all human intelligence tests positively correlate with each other to give a universal intelligence factor. This is false; there exist demographics where g is _not_ the predominant factor explaining inter-demographic test score differences.[2]

Here is another problem. Psychometricians tend to decide whether some test metric measures intelligence by how well it correlates with existing "intelligence tests" that're g-associated. y.f. does this in his comment: "It is relatively independent of cultural knowledge: i.e., french is nearly independent of g (1), while physics, plumbing and loading irregularly sized boxes into a truck are highly correlated to g". (I.e., French tests can't be real tests of intelligence, since they don't correlate with g, but physics, plumbing, and bin packing must be, because they do.) But this renders the internal validity argument circular: its two prongs now become: (1) g must exist because intelligence tests correlate positively, and (2) and intelligence tests are those tests that correlate positively with g. The circle closes.

The external validity argument supposedly rescues the g concept from this trap, by demonstrating that g correlates vaguely with real-life behaviours. Unfortunately, the correlations are nowhere near perfect, that g correlates with success doesn't suffice to show causality, and pointing out the correlations does not eliminate the underlying circularity in g's definition. All in all, the evidence is inadequate to reject the null hypothesis that there is no causal link between g and life success.

[1] Well, I say "human intelligence", but if I recall correctly, at least one psychometrician even tried to argue that g might well be a cross-species phenomenon!

[2] Dolan, C.V. Roorda, W., and Wicherts, J. M. (2004). "Two failures of Spearman's hypothesis: The GATB in Holland and the JAT in South Africa", Intelligence, vol. 32, p. 155-173.

You seem to misunderstand the definition of g, as g is not defined in terms of intelligence tests.

Take as your statistic the result of many tests: physics, box loading, french, basketball, etc, and then do a PCA or similar test. One of the principal components will be g, provided you have enough data. This is what defines g.

Intelligence tests are simply tests designed to be more highly correlated with g. If we discarded intelligence tests, we could recreate them (or equivalent tests) based on statistical analysis of the other test data. They are certainly not arbitrary measures.

The external argument doesn't rescue g; g is quite safe. The external argument merely claims that 'g' and 'intelligence' are the same thing, or very close. g exists regardless of what you want to call it.

As for the paper you cite, I skimmed it. Unless I misunderstood it horribly, it merely claims that particular IQ tests don't effectively measure g across different groups. That doesn't mean g doesn't exist as a hidden variable, merely that a particular test is poorly correlated with it for some population.

I've posted this at least three times on Hacker News, but I'm just shocked people haven't read it:


This guy is a statistics professor, and has a lot to say about exactly what "g" is. He even runs experiments! I know the article is a bit long but I promise it's worth reading.

Well, I admit, I just skimmed it, I'll try to read the whole thing later. But near as I can tell, he isn't addressing the validity of g at all, merely claiming it is unproven that genetic differences between population groups is due to genetics or other factors (a claim I don't disagree with).

You're right; sorry, wrong essay. The other one, by the same guy, addressing that point:


Are there any studies showing that basketball performance, French fluency, bin packing, and physics knowledge, all taken together, will produce a meaningfully large general factor? Intuitively it seems unlikely, and it doesn't jibe with what I understand g's definition to be based on the comments of people like Eysenck and Jensen, who justified g on the basis of intelligence test correlations, and only later tried to tie it to biological functions (evoked brain signal potential in Eysenck's case, reaction time in Jensen's) and metrics of social, sports, and job performance.

Regardless, I agree that g exists in at least a limited sense, but I maintain that there is insufficient evidence to demonstrate that it emerges from innate, immutable physical properties of the brain, and you still can't attribute life success to it.

>I am highly turned off by the idea that we can't "become smart" after an early age. I feel like I "got smart" after I started playing go, I feel like I "got smart" after I learned category theory.

The percentage of the population that can participate in the two activities you mentioned is probably less than 1%. You probably were smart at an early age.

You're justifying a hypothesis circularly.

I was somewhat gifted at an early age, but I consider my intellectual growth over the past 5 years (17-22) to vastly outstrip my growth before that.

Or, you had a certain innate intelligence to begin with, and are only now practicing with it.

At this point it's impossible to know one way or the other. Genetic intelligence versus developed intelligence is something that the top scientists of several fields are still investigating.

I don't think that we can really investigate "genetic intelligence" until we have a definition of intelligence which makes -any sense at all-, which we don't.

I find a lot of the opinions of neuroscientists I've talked to/read articles from to be really dogmatic in their interpretation of intelligence (probably because they aren't regularly faced with Very Hard Problems in the sense that mathematicians/computer scientists are - their conception of intelligence is often a little more superficial - but anyway, I'm massively generalizing).

My entire point is that I don't think it's useful to think about intelligence as a "thing." I think of the brain as a computational structure. At birth, it has certain properties. It changes in certain ways. It can get better or worse at certain tasks. Because Official People have to say Official Things they always treat their own statements about Intelligence as if they're objective and well-informed which, let me tell you, they are not.

Just because people disagree on exactly what constitutes intelligence doesn't exempt the brain from the same general limitations that we see elsewhere in physiology.

Take fast-twitch muscle tissue for one example. Different people have a genetic predisposition towards developing more or less fast-twitch muscle fibers, which gives them the potential to be faster runners or have faster reflexes. Now, that's not to say that someone without that predisposition can't train hard and also be fast; likewise, if someone with that predisposition doesn't make use of it on a regular basis, then they're not likely to be any quicker than anyone else in reasonably good physical condition.

However, assuming the same training regimen, the person with the beneficial genetics will always have an advantage.

There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way. Yes, someone of average intelligence can work very hard and produce the same results as someone who's more intelligent and less motivated. But, you're comparing someone who's operating at their peak potential against someone who isn't.

I think cperciva's original point was merely that due to the nature of the field of mathematics, there's a huge barrier to entry where that genetic advantage becomes necessary. I disagree with that point only a little bit; if I worked really hard at it, I might be able to produce a small handful of exceptions against the very large body of evidence in cperciva's favor.

"There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way."

I agree if what you mean is that there's no reason to believe that there is no fixed, genetically-determined components to intelligence. I disagree if you are making any sorts of claims about what these components are (as I said, I don't even think we can make gross claims like people are born with "good memories").

I also agree with the point that cultures look for certain intellectual traits in young children. I cannot say whether these particular traits are determined genetically because it is highly possible that we learn a great deal (and abstractly) even from the first day of our lives.

The thing is that (as another poster pointed out) there IS a salient statistic (g - for general intelligence) which we can be "better" or "worse" at - but its value in a field like math which requires highly specialized mental strategies is questionable.


I think that you should look at the example of the polgar sisters - they were raised to be grandmasters in chess and 2/3 of them did (the other one become an international master). I think this puts a bullet in at least one interpretation of your theory.

I now think you're allowing your own prejudices on this subject cloud what you're reading, and what you're saying in response. I think I was fairly clear in my position that genetics plays an important role in intelligence, specifically because we have no indication that the brain is exempt from the same physiological rules that the rest of the human body obeys.

| I think that you should look at the example of the polgar sisters...

I specifically covered edge cases in mentioning the impact of training on innate ability.

What does it mean that the brain "obeys the same physiological rules" that the body obeys? This point is incoherent.

My point is that yes, there is a genetic aspect to intelligence (duh), but that doesn't mean that there is a genetic component to how "fast" your brain is or how much "memory" you have. These could be emergent phenomena - not directly determinable.

Please tell me more specifically how my prejudices are clouding what I'm reading/saying. You didn't follow this point up.

I'm not sure that your experience of feeling smarter contradicts cperciva's point about intelligence being determined early in life. I can see that there could be a difference between intelligence as some kind of innate capacity and how that capacity is applied to various tasks.

You can certainly learn more stuff and so be able to do more difficult things, but your ability to learn and apply knowledge may not be changing.

This is a good point. I agree that my feeling smarter does not actually mean that I am smarter. I -do- produce a lot more, but this could be due to other factors.

I think you're hitting very close to the important issue here which is that all of this is very difficult to define/think about without a really good idea of what sorts of computations our brains perform.

My point isn't really so much that I think it can change, even, it's that we should be way more skeptical when it comes to making claims about subtle concepts like these. Usually I find that those who say "we are only really growing intellectually until we're 5" have a very limited and kind of rigid conception of intelligence.

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