In Favor of Narrower Conclusions

Also, somehow, an article about unsupervised learning

This article has sat in the drafts folder for a couple of months. I couldn’t come to a conclusion in the initial version, so I’ve decided to revive it with a different point. The article will therefore contain a sort of “plot twist” mid-way through.

Is Automobile Fanciness Real?

When I read debates about IQ and intelligence, I’m struck by two opposing claims that both seem false.

1. g, a statistical feature found via feature reduction is real and the same thing as intelligence

2. g is an arbitrary social construct and therefore not real

I’ll start by trying to explain where g comes from. I’m not an expert on factor analysis, but I’m familiar with other unsupervised learning algorithms. These algorithms take large amounts of data and reduce it to a digestible form. In some algorithms, the result takes the form of latent “components” or “factors” that make intuitive sense but defy simple quantification. The Big Five personality model provides the best example of factor analysis. Users complete a personality test with hundreds of questions, and a model reduces these to five readable digestible variables.

Below, you can see a factor analysis concerning the attributes of cars. The user takes multivariate data on the automobile’s speed, weight, engine type, acceleration, speed, and other info and organizes them into two latent components. Component 2 (the y-axis) looks like “sportiness” while component 1 (the x-axis) seems to represent something like “luxuriousness” or “fanciness.” The fancy sports cars sit in the top right while the boring normie cars reside in the bottom left. Remember, no one told the model to look for sportiness or fanciness. The model found it via correlations of observable variables.

Source: https://rpubs.com/sid9715/581026

How, though, do we know to choose two factors? Why not one dual measure of sportiness/fanciness? Why not opt for five latent features, like personality? With unsupervised learning algorithms, there’s no perfect rule for determining the number of features. We do have a graph, though, that can give us a good hint.

Same source as above

Imagine a 100-variable dataset. We can reduce this dataset to a smaller number of latent features (aka components), but doing so will lose some of the information of the original dataset. We could settle on 99 latent features. This would minimize the information loss, but it wouldn’t help us understand the data. We could also reduce the whole dataset to one latent feature. This maximizes interpretability, but we risk losing a ton of info. The graph above helps us thread the needle. Wikipedia calls it a “Scree Plot,” but, the cool kids call it the “elbow graph.” Think of the y-axis as the amount of information captured. The actual value isn’t important here, just the size of it relative to the other dots. The first latent feature captures a whole lot of information, as it always does. The second latent feature captures some more info, though not as much as latent feature #1.

After that, the drop-off flattens. We obtain a bit of info from feature 3, but there’s little movement from #3 to #4. After 4, the y-values barely budge. In other words, selecting 5 features barely captured any more info than selecting 4 features. This produces an “elbow” or a point in which the y-values start to flatten. From the graph above, I’d say the “elbow” occurs at either 2 or 3.

Smarter people use more sophisticated methods, but they all amount to finding where the information loss stops. Personality seems to reduce to five factors. Those cars above seem to reduce to two factors. Human intelligence seems to reduce to one factor, and researchers call this factor g.

Realness

Consider the two positions:

1. Automobile sportiness is real. It is an objective scientific discovery, no different from Newtonian mechanics or the germ theory of disease.

2. Automobile sportiness is an arbitrary social construct that doesn’t represent anything real about the world

Do either seem right to you? Now let’s take this back to IQ

From Russell T. Warne’s In the Know: Debunking 35 Myths about Human Intelligence:

IQ, or an IQ score, is not the same as intelligence or g. Instead, IQ is a measure of general intelligence. To use an analogy, just as kilograms and pounds are a measure of weight, IQ is a measure of intelligence. IQ is not intelligence itself any more than the number on a scale is a person’s weight. In both cases, the number is a measurement and not real topic of interest

On the contrary, here’s a one-star review of In the Know from Amazon:

Warne’s wish to assimilate psychology to physics is understandable because the kind of intelligence tapped by IQ tests—the kind that is emphasized in the Western educational system in which IQ tests were developed—is one that aims at rational control of the material and social world. This kind of intelligence is, of course, valuable—indeed, our very survival can depend on it—but it represents just one region of the intelligence spectrum, a region that can be sampled in discrete tasks that can be unambiguously assessed and scored.

[…]

Since g is defined by purely mathematical operations, it is not clear just what it represents in the real world, if anything.

The Warne quote seems odd. Weight and mass don’t refer to nuanced concepts. Intelligence is a lot more nebulous. I don’t think most people conceptualize a one-dimensional scale when speaking about intelligence.

On the other hand, none of that implies that IQ represents nothing in the real world. The book cites correlations between different types of cognitive tests (including verbal and mathematical), school performance, job performance, musical ability, and even military ability. Warne also notes that IQ correlates with greater brain size and brain organization. As such, IQ seems to represent something about the real world. It seems unlikely that vocabulary tests, math tests, playing the violin, and aerial combat just happened to all test the same skill. Furthermore, the types of tasks associated with g seem to fit an intuitive definition of intelligence. As Warne puts it:

…g is a general mental ability that is related to every other mental ability; that it helps individuals create and execute plans, engage in reasoning, and learn… To me, this sounds a great deal like intelligence.

The point about g resulting from “purely mathematical operation” makes some sense, though. Of course, I won’t take that phrase literally. Sums and ratios result from mathematical operations, while few deny those constructs. Still, there’s a choose-your-own-adventure aspect to factor analysis that makes me hesitant to put in the same “realness” league as cell membranes and protons. I don’t really know if g is “real” or if it’s “really intelligence” or how I’d attempt to answer those questions. More importantly, I don’t think anyone needs to argue for these propositions. If I wrote a book about IQ, I’d probably start it with someone like this:

I know that IQ predicts various life outcomes and that it correlates with certain positive qualities in the brain. I also know that that it measures something that looks an awful lot like what we call “intelligence” in English. I’ll leave the “Is IQ real?” or “Does IQ measure intelligence?” questions to the linguists in philosophers. If I say “IQ measures intelligence,” I mean it as a less-wordy shorthand for “IQ is correlated with abilities that look a lot the things we refer to as intelligence in English.”

The Five-Ton Purple Ball Argument

When I started this article, I intended to provide some insight into the “What is intelligence?” question. I soon realized that I don’t know how to figure that out, and I’m not sure what value the answer would provide. Instead, I’ll focus on the idea of “over-arguing.”

Imagine that someone proposes a plan, and this plan involves dropping five-ton purple balls onto people’s heads. You might think, “hey, that would kill people. I’m against that.” The planner then points to evidence showing no damage when people had one-ounce purple balls dropped on their heads. You have a couple of options here. You could say, well, duh, not all purple balls will kill people; I’m just worried about the five-ton ones. There’s another option though. You can concede no ground. You can insist that all purple balls kill people by employing some bizarre definition of “purple” or “kill”. You can scour the literature for methodological flaws that you’d ignore in other contexts. You can dismiss all human observations as the product of sinister power dynamics.

I understand this is a silly example, but I see it in non-silly circumstances. I’ve entered unfortunate conversions with both pure Anarchists and pure Libertarians that reject exceptions to their viewpoints. I don’t want to delve into current events, but I also recall comparable instances on both sides of almost all hot-button issues: COVID, Ukraine, police reform, etc. Still, my best example comes from a long-dormant debate.

I started college at the end of the New Atheism era. By this time, New Atheists somewhat split into two groups: the chill ones and the angsty ones. I joined a Team Chill club. Every once in a while, an un-chill atheist would attend a meeting. I recall one such attendee arguing that the world would have been better off without religion. We believed in God just as little as he did, but that claim seems almost impossible to judge. Sure, there are no crusades without religion. There are also none of the social circumstances that would lead to you condemning them in a university meeting room. There’s no anything that we know about the present without religion. The “no religion” counterfactual involves a different world with different countries inhabited by different people. One can dig even deeper into the complexities of this claim. In the no-religion universe, do the Bible and Greek Mythology still exist as literature? What about Japanese Yokai? Do we still have yoga and meditation? Given its near universality, humans probably contain some genetic proclivity towards religion. So, do our genes change in this counterfactual?

No one can determine the truth value of “religion has a been a net negative for humanity,” and no one needs to! The overall net negativity of religion is not what brought people to New Atheism. These atheists never spent much time mulling over the consequences of Zoroastrianism flourishing in Iran 2600 years ago. Rather, the new atheists cared about specific certain theocratic overreaches in the present day. These issues included bans on abortion and gay marriage in the United States alongside repression of women and same-sex couples around the globe. It’s much easier to make the case for freedom of and from religion than to craft a broad historical analysis of religion’s impact. I don’t need to consider a re-drawn globe or a rewritten human genome if I want to support gay marriage.

In short, there’s no reason to make the harder case when you can get by with the easier one. I’m not saying no one should debate difficult topics. Someone can parse whether IQ measures intelligence or whether religion has benefitted humanity, but that person doesn’t have to be you. If your conclusion rests on simple premises, push the murky stuff aside.