Hacker News Reader

Reading the original article further I understand more of what the author meant -- and I agree with him more.

What he means by "statistical myth", I think, is that you can throw any number of measurements into a big bag, even weakly correlated, and you'll always be able to find a general macro-factor that is correlated with all of them and therefore seems to "describe the bag" pretty well... even if the bag itself is absolutely meaningless.

For example, one could throw into the bag height, sexiness, feet length, and BMI, which are all somewhat correlated with one another and with "IQ".

There is a macro factor describing such a bag; but would you call it "general intelligence"?

The fact that we talk about g is because we consider a priori that there actually is such a thing as "general intelligence" and that we are measuring elements of it. Maybe we are, maybe we're not; correlations alone tell us nothing about it.

The analogy with physics, be it temperature or pressure or what have you, is in my opinion quite flawed, because in the case of those entities we know that the elementary events / forces are linked by way of causality with the macro factor, and we know that for reasons other than mere correlation.

In the case of g, on the contrary, the only link between the different elements is the correlation itself. And it gets worse: to be included as a relevant IQ test, a new test has to be correlated with g. To quote from the article:

"By this point, I'd guess it's impossible for something to become accepted as an "intelligence test" if it doesn't correlate well with the Weschler and its kin, no matter how much intelligence, in the ordinary sense, it requires. (...) This is circular and self-confirming, and the real surprise is that it doesn't work better."

So g is at the same time what we're looking for and what we're building upon, having decided it's there already.

This looks much more like religion than science.

Yes! This is what I am trying to say but in a much more muddled and round about way.

For example, one could throw into the bag height, sexiness, feet length, and BMI, which are all somewhat correlated with one another and with "IQ".

The point is that if those phenomena are all correlated with one another, there is likely to be an underlying reason for that. Maybe it's not general intelligence, but there is something.

Suppose you threw a different set of things into the bag: phase of the moon at birth, whether you were bitten by a wolf, and how good you are with computers. These things almost certainly will not be correlated, because there is indeed no relationship between them. The only reason the author discovered a large principal component in all his models is because he explicitly built one in!

Now, my analogy with physics is not to the physics of today. Rather, it's to physics pre-Boltzman. Before that, we didn't really know how the atomic theory of physics was related to thermodynamics. All we really had were correlations - boiling is correlated with burning, with faster chemical reactions, expansion of solids, with the human perception of warmth, etc. We observed they all occurred together, and postulated an underlying variable T which correlated well with all of them. We then exploited the correlation between this hidden variable T and thermal expansion to design a specific test to measure it (thermometers).

Pre-Boltzman, all we had were correlations between fundamentally different physical phenomena. We had various incorrect theories about why some of them occurred together, but that's about it.

Now suppose Boltzman comes along. He says "what you call a single variable T, I can explain with the sum of many variables." Does that mean it's reasonable to conclude T is a "statistical myth"?

See, the article is not arguing that. The article has nothing against latent variable(s) to account for what we observe as intelligence. What it is against is, misapplication of methodology. The myth is not in a latent variable summarizing intelligence, that may very well exists as admitted by the author. The myth is that g is derived in a meaningful way and explains the correlations in data instead of being a by product of the fact that the data is made to correlate (these days) and is just a measure of the correlation of the tests (now made to correlate). Again, I remain sceptical you read the article in full.

g is not as useful as T, since its ability as an explanatory variable and verification in experimental settings are sorely lacking.

Also, even if a valid concept of a single explanatory variable for intelligence were created, I personally, remain sceptical of the scope of its usefulness considering the space of complexity at hand (humans, genes, environment,...) and likely a lot less profound and far reaching as the insights of Boltzmann. And on the political side, the capacity for damage it would entail could be large - many people's lives could be impacted negatively. So it would have to be wielded carefully, one eugenics movement is enough.

What it is against is, misapplication of methodology.

Yes, and the author rightly points out that latent variables do not exclude the possibility of microstructure. That doesn't mean the use of the latent variables is a "statistical myth", unless you define the term "statistical myth" so broadly as to include temperature and pressure.

g is not as useful as T, since its ability as an explanatory variable and verification in experimental settings are sorely lacking.

This is both undisputed, and unrelated to the author's argument. The difference between our pre-Boltzman understanding of T and our contemporary understanding of g is one of precision. The author's argument was independent of precision, so invoking precision to protect his argument is disingenuous.

You might want to criticize the confidence levels of g. That's a perfectly legitimate thing to do. But that's not what I'm responding to.

So it would have to be wielded carefully, one eugenics movement is enough.

Not sure about that. The Dor Yesherim organization does such a great job of eugenics, I'd love to see further eugenics movements in other genetically isolated groups.

The authors viewpoint seems to be that things that can be directly measured do exist. So I would think that the author would be find with talking about temperature the same way he's ok with talking about IQ ("That thing that IQ tests measure").

I would agree with you personally, and say that really any measurement involves some implicit figuring so there really isn't any difference between IQ and T.

A flaw with your argument is that biology is harder than physics. That is, the interactions of the elementary constituents of biology are many orders of magnitude vastly more complex than those of the point particles found in newtonian physics. Which makes sense considering the compositional hierarchy involved from atom -> cells -> humans. Hence reductionists statistical methods are likely to be far less useful/meaningful than in thermodynamics.

I do not care about the downvoting. But I am guessing it is due to my saying that biology is harder than physics [1]. Perhaps I should clarify to say that a broad mathematical understanding of biology is a harder problem than doing so for your typical system studied in physics. In biology, systems can only be modeled and not understood or derived from fundemental principles, as the interactions of the basic entities are too complex. Or consider: Quantum mechanics, it is a straight forward linear theory (just conceptually difficult) while much of biology is analytically and computationally hard, often involving things like non-linear dynamical systems. A further difficulty here is that the behaviour of the whole of the things studied in biology cannot be inferred by studying its constituents - due to feedback-dissipation processes leading to self organization.

While I am clarifying, I might as well point out that while I personally believe that the usefulness for looking for broad general factors is meaningless considering the dimensions in consideration, there might be some use for them in aggregrate. However, these should not be taken for more than they are. Statistics. Furthermore, You, yummyfajitas, argue agianst a strawman. Did you read the article? Because if you did you would have seen:

I don't want to be mis-understood as being on some positivist-behaviorist crusade against inferences to latent mental variables or structures. As I said, my deepest research interest is, exactly, how to reconstruct hidden causal structures from data.

...

Similarly, pointing out that factor analysis and related techniques are unreliable guides to causal structure does not establish the non-existence of a one-dimensional latent variable driving the success of almost all human mental performance. It's possible that there is such a thing. But the major supposed evidence for it is irrelevant, and it accords very badly with what we actually know about the functioning of the brain and the mind.

Which leads me to the fact that Shalizi has no qualm against dimensionality reduction. Instead he is against the methodologies used and how the conclusions are drawn:

1) g is almost a tautology. It is due to the correlations in the tests which are made to correlate. When performing such factor analysis on these variables a dominating factor which most explains their variance must appear due to algebraic reasons.

2) No one has tried to explained g directly, experimentally or otherwise. Instead they still argue in terms of correlations.

3) They still use simple correlation matrices - linear models from yestercentury. Other more appropriate or robust methods such as non-parametric statistics have since been refined or developed.

[1] http://metabolism.math.duke.edu/docs/04whyams.pdf

The downvoting (not by me, BTW) is probably because you didn't understand the math and simply appealed to complexity. Your appeal to complexity was both incorrect (pressure = sum of hidden variables, g = sum of hidden variables, complexity is equal) and also irrelevant (Shalizi's argument is against statistical reductions and is independent of complexity).

My objection is not to the fact that Shalizi is hypothesizing a microstructure to g. Here is what I had to say about that part of the article: "It's a great article... Thompson's model makes a specific prediction about g - it should be normally distributed. So overall, I agree with the author's scientific argument: g is very likely to be decomposable into subfactors."

My objection is simply to the term "statistical myth". By Shalizi's argument, macroscale variables which abstract away an ensemble of microscale variables are a "statistical myth". Depending on your philosophical axioms, that's a fine thing to believe - but we should acknowledge that if you believe this, then you also believe pressure is also a statistical myth.

As for the new points you raise:

1) G is a tautology if you deliberately posit a family of normally distributed variables with positive correlations. In fact, it's a tautology if you posit a family of strongly correlated normally distributed variables of any sort (the factors might just have negative components).

This does not, however, explain why performance on various tests is correlated. G and multifactor models are an attempt at explaining this. Thompson's model (which has g built in) is another.

2) Indeed, we don't really understand it. For a long time we didn't understand pressure or temperature either - all we understood was the macroscopic effects. So what?

3) You are clearly speaking about something you don't know much about. If you want to argue that linear models don't work because the data is nonlinear, do it. You haven't. Neither did the author.

Complexity is not equal because the hidden variables of g (I will use it as you do for now) is not equal to the hidden variables of pressure.

The term statistical myth is appropriate because g is a myth. It is not backed by any direct experimental evidence but arises due to manipulations of statistical techniques. The Gas Law you cite was derived from experiments not from muddled manufacturings of statistics. And the tests correleate because they are made to correlate - it is all quite circular. Your post misrepresents Shalizi. Shalizi's argument is not "macroscale variables which abstract away an ensemble of microscale variables are a 'statistical myth'". Rather, it is that the way in which the latent variable g is first arrived at and then subsequently used to drive conclusions is invalid and meaningless:

But now new tests are validated by showing that they are highly correlated with the common factor, and the validity of g is confirmed by pointing to how well intelligence tests correlate with one another and how much of the inter-test correlations g accounts for. (That is, to the extent construct validity is worried about at all, which, as Borsboom explains, is not as much as it should be. There are better ideas about validity, but they drive us back to problems of causal inference.) By this point, I'd guess it's impossible for something to become accepted as an "intelligence test" if it doesn't correlate well with the Weschler and its kin, no matter how much intelligence, in the ordinary sense, it requires, but, as we saw with the first simulated factor analysis example, that makes it inevitable that the leading factor fits well. [13] This is circular and self-confirming, and the real surprise is that it doesn't work better.

As I quoted Shalizi prior: 'I don't want to be mis-understood as being on some positivist-behaviorist crusade against inferences to latent mental variables or structures. As I said, my deepest research interest is, exactly, how to reconstruct hidden causal structures from data.'

I also do not understand how you use g, as explained it is not composed of factors. It is the dominating factor. While I do not know about Intelligence tests I did follow the mathematics he gives and have applied similar in machine learning contexts. And Considering the wide variety of data linear models fail to properly capture my intuition is that yes, linear methods and assumptions of a Gaussian is overly simplistic without a solid backing argument, which has been unable to be given for near on a century now.

p.s. you are right, my original post was orthogonal to what Shalizi had to say. This was just my argument agains't yours in that I don't feel generalizing to one factor for a system as complex as human intelligence will produce as meaningful results as generalizing to a simple law for a collection of atoms/ a gas did.

I think what the author means is that g is a statistical necessity, and that being such, doesn't imply that it's an actual reality.

What you seem to be saying is that, in any case, g is a useful proxy for a reality that is difficult to know in detail. This doesn't contradict the author's thesis.

The question remains, does g exist beyond arithmetics, is there such a thing as "general intelligence". Maybe it's a useless question, in that we don't need to know whether g "exists": we only need to know that it works.

But there is a big difference between intelligence and thermodynamics: policies are implemented that impact the lives of millions of people based on an understanding of g that may be completely false. If g is only a statistical artifact and nothing more, then it's still useful for statisticians, but for policy makers, the underlying factors need to be identified and understood.

That's why I object to the term "statistical myth" - it implies the measure is not useful in cases when it is. If g is a useful proxy, it's useful for policy makers. All they need to know is that low T implies dead homeless, and low g implies a higher probability of unskilled employment.

The fact that g is actually a sum of independent variables, or T is a sum of squares of velocities of particles is irrelevant to them.