Thomson’s Sampling Theory of Intelligence: Can g Emerge Without a General Ability?

Godfrey Thomson showed that correlated intelligence-test scores do not logically require one general mental cause. Overlapping samples of many processes can produce a similar pattern. At the beginning of intelligence research, Charles Spearman confronted a striking fact: people who did relatively well on one mental test tended, on average, to do relatively well on others. He proposed that a general factor, g, contributed to performance across diverse tests. Godfrey Thomson saw the same correlations and asked a more unsettling question: what if the pattern could arise without every test drawing on one common mental resource?

His sampling theory—later associated with the “bonds” model—offered an alternative. A cognitive task might recruit a sample from a very large number of mental elements or processes. Different tasks correlate because their samples overlap. The positive manifold can then emerge even if there is no single process that every task shares. That is why Thomson remains important: he separated a statistical observation from one particular causal explanation of it.

Imagine a workshop full of tools

Suppose a workshop contains 1,000 specialized tools. Task A requires 100 of them. Task B requires another 100. Forty happen to overlap. Task C draws a different sample, overlapping partly with A and partly with B. Now imagine people differ in how effectively many of those tools operate. Performance on A and B will be correlated because the tasks depend partly on the same elements. Across many tasks, a broad positive pattern can appear. Nothing in this illustration requires one master tool used by every task. Thomson’s original “bonds” were theoretical elements, not discovered neurons. Historical versions speculated about neural units, but modern readers should not mistake the metaphor for established neurobiology. The enduring idea is overlapping sampling.

Why this was a challenge to Spearman

Spearman’s g has at least two roles that are easy to conflate. Descriptively, a general factor can summarize the covariance among diverse cognitive tests. Causally, one might go further and claim that this factor corresponds to a single general capacity that produces the correlations. Thomson challenged the second step. He did not need to deny that a general factor could be extracted statistically. He showed that the same kind of covariance structure could, in principle, be generated by a very different underlying architecture. Modern reanalyses of Thomson’s bonds model have reinforced the identification problem: covariance data alone may be unable to distinguish a common-cause model from a suitable sampling model.

This is a profound lesson in psychometrics. A factor model can fit the data beautifully without telling us uniquely what mechanism created the factor structure.

Does sampling theory mean g is an illusion?

No. If g is defined psychometrically as a general dimension estimated from the covariance among cognitive measures, the covariance is real whether its cause is one process, many overlapping processes, developmental interactions or some combination. Sampling theory changes the interpretation. It says that a general statistical dimension need not be a literal general mechanism inside the head. The distinction resembles a shadow. The shape of a shadow can be measured precisely. But the shadow alone may not uniquely identify the three-dimensional object that cast it.

From Thomson to modern process theories

The sampling intuition did not disappear. Contemporary theories such as Process Overlap Theory revive a related idea using cognitive processes rather than Thomson’s historical bonds. Complex tasks recruit multiple domain-general and domain-specific processes; overlap among those requirements can help generate positive correlations. The modern theory is not simply Thomson with new vocabulary. It makes different assumptions and attempts a more explicit cognitive account. But the family resemblance is direct enough that Thomson is an important ancestor.

What evidence would decide between explanations?

This is where the theory becomes harder. If competing causal architectures can reproduce similar correlation matrices, factor analysis alone cannot settle the dispute. Researchers need additional constraints: experimental manipulations, process-level measures, developmental evidence, neuroscience, formal models that make different predictions, or interventions that selectively change proposed mechanisms. Even those approaches may support mixtures rather than one winner.

Thomson’s lasting contribution

Sampling theory matters less because psychologists now believe the brain literally contains Thomson’s unspecified “bonds” and more because he exposed a logical gap that intelligence science still confronts. The positive manifold is an observation. g is a powerful statistical representation of common covariance. A single general cause is one possible explanation—not something factor analysis proves by itself. Once that distinction is clear, the century-long debate about intelligence becomes much easier to understand.