Human intelligence: spiky or smooth?

Jul 2, 2026

Humans have various strengths and weaknesses which are relevant to knowledge work. For example, according to Managing Oneself by Peter Drucker, some practical career-oriented questions to ask yourself are:

• Are you a reader or a listener?
• Do you work best alone or in a team?
• Are you a decision-maker or an adviser?

But the far more interesting (and likely more important) question is: which cognitive tasks is your brain best suited for? When it comes to knowledge work, the classic split which comes to mind is between the STEM people and the social sciences people. It seems generally accepted that someone can be great at reading comprehension but bad at math, or a great coder but a terrible writer.

Because of this, I wanted to know if it’s possible to get an accurate cognitive profile, through some sort of testing, which measures a human’s fundamental cognitive strengths and weaknesses, such that you can predict that human’s performance in various domains. But before I started researching, I wanted to confirm that this idea of strengths and weaknesses is even valid — perhaps, instead of a jagged profile, individuals just have a certain level of general intelligence, and that’s what determines their performance across all the tasks. So, which one is it: jagged, or general?

Correlation

In a famous research paper published in 1904, English psychologist Charles Spearman observed that children’s performance across seemingly unrelated school subjects were positively correlated — for every single test pairing, performance on one test was positively correlated with performance on the other. In the century since, the result had been replicated by studies with such consistency that it has been described as “arguably the most replicated result in all psychology”.

The intuitive response to this is that there is actually some kind of general intelligence, or “g” for short, which determines how a human will perform on a cognitive task. But before settling for that answer, it’s important to understand how researchers actually arrive at the concept of g, and what the evidence shows.

First, researchers find the correlation coefficient for a pair of tests. They repeat this for every possible pair from a test battery (a group of tests). By laying all these correlations out in a grid, with each test being both a row and a column, you get a correlation matrix.

Once we have a correlation matrix, the question becomes: which factors caused these correlations to emerge? For example, it could be one general factor, or several smaller factors. To figure out the answer, researchers use factor analysis: a statistical tool which takes a correlation matrix and tries to reverse-engineer the factors underlying the results. Using linear algebra, it outputs a table: the rows are the variables (test scores), the columns are the factors, and the cells contain the factors’ correlations with the variables such that they would reproduce the original correlation matrix.

With our all-positive correlation matrix as the input, factor analysis outputs one factor. This factor is known as the “g-factor”. Given that, it’s easy to think: “all-positive correlation matrix —> one underlying factor —> that factor is general intelligence —> one general intelligence ‘knob’ in the brain determines performance across all cognitive domains”. But the question isn’t settled yet.

As argued by Cosma Shalizi, an associate professor of statistics at CMU, this chain of reasoning is invalid. To understand why, suppose that there’s actually no “master engine”, and that each person instead has lots of small, independent cognitive abilities. We can call them “tools” and number them 1-100. Different tests might recruit different tools — for example, let’s say:

• Vocabulary test recruits tools {7, 8, 25}
• Arithmetic test recruits {7, 12, 22}
• Matrix pattern test recruits {3, 22, 45}

We can actually get the same all-positive correlation matrix with these several tools correlating to our test scores, rather than just one. Thus, while factor analysis is a useful statistical tool, its output here cannot be relied upon to definitively show that there is only one factor driving the test scores. From what we know so far, we actually have three options:

1. There is one universal factor driving the test scores.
2. There are multiple tools impacting test scores but they’re all correlated.
3. There are multiple tools impacting test scores, the tools are independent (not correlated), and each test pair shares at least one tool (this could be a different tool for each pair).

Option 3 is non-obvious; here’s why it can reproduce our correlation matrix:

• The tools are independent, meaning that any given pair of tools does not correlate. A person strong in one tool isn’t more or less likely to be strong in another tool.
• Take a pair of tests. Test 1 recruits 100 tools, and Test 2 recruits 99 other tools, plus one shared tool with Test 1.
• Because of our independence condition, we can imagine that a tool’s strength is just a random value between -100 and 100. Furthermore, let a person’s test score just equal the sum of the strengths of the tools it recruits.
• If you sum the strengths of the 99 non-shared tools for both tests, they more or less cancel out to a number near 0.
• Let s represent the strength of the single tool recruited by both tests. Then we have:
• Score on test 1 = s + ~0
• Score on test 2 = s + ~0
• Both scores mostly reflect the strength of the shared tool. Across a population, people who score strongly on Test 1 tend to also score strongly on Test 2, producing a positive correlation. Thus, our all-positive matrix is also possible under Option 3.

So, we’ve confirmed that we have three potential options. Does this mean we can’t definitively answer our question?

Before we can say that, there’s another key piece of evidence we need to look at.

The g-score

Remember the factor analysis table?

We already know what it tells us: one hidden factor explains the correlation matrix (even if that’s not necessarily true). And, as we can see in the table above, it also tells us how strongly each test correlates with that factor. This number is known as “g-loading”. Here’s what we can do with this:

1. Take a person’s scores on each of the tests in the battery.
2. Standardize and sum the scores, weighing each score by the g-loading of its corresponding test (the number we get is called a “g-score”),
3. Rank the test-takers by their g-score.
4. Repeat this process for different test batteries.
5. Compare the rankings of test-takers across different test batteries. How well do they match up?

A famous study published in 2004 analyzed the results of that exact process, and the findings were profound: the g-score rankings, which were produced using three different test batteries, are correlated with coefficients 0.99, 0.99, and 1.00. Over four-hundred participants were ranked in almost exactly the same order.

But there is a major, major caveat. If you take a look at the three batteries, they are actually quite similar in the abilities they test. They’re all mainly pen-and-paper, and they all test categories like vocab, memory, and spatial/numerical/inductive reasoning. Rather than showing that a broad variety of cognitive tasks recruit the same tool(s), the study shows that similar cognitive tasks recruit the same tool(s). Thus, this finding isn’t helpful in answering our original question about general intelligence.

Where that leaves us, for now

Ultimately, we haven’t been able to eliminate any of our three options:

1. There is one universal factor driving the test scores
2. There are multiple tools impacting test scores but they’re all correlated.
3. There are multiple tools impacting test scores, the tools are independent (not correlated), and each test pair shares at least one tool (this could be a different tool for each pair).

The conclusion is that it’s inconclusive. Based on what we’ve explored so far, we can’t definitively determine which is correct. Using common sense, it’s pretty obvious that option 3, at least in its most extreme form (1 shared tool, no tool is shared by a pair more than once) is not indicative of the truth. When you sit down to do any kind of paper test, you at least have to read what’s on the paper. So every paper test, to some extent, taps the “tool” of reading comprehension. Yet this doesn’t mean that option 3 in a more relaxed form isn’t true, because it’s not required that each shared tool is different. In fact, it’s more intuitive that we’d get an all-positive correlation matrix if there is overlap.

Thus, all three options survive, and I’m not able to provide an answer to the question (yet). It feels like performance in cognitive domains is likely driven by a mix of general and jagged intelligence, among other factors, but “feels like” isn’t a satisfying answer. I will continue to explore this topic in the hopes of finding one.