In Defense of IQ
What Scalar Metrics Can Mean About Intelligence
1. Orientation
A recent exchange framed IQ as a scalar projection from a high-dimensional cognitive space, emphasizing that such projections are inherently lossy and sensitive to the choice of linear form. The implication was that mid-range IQ scores largely reflect geometric concentration rather than substantive differences in intelligence, and that the measure itself therefore carries limited explanatory weight.
The mathematical premises of that framing are sound. Cognitive abilities plausibly span many dimensions, and any attempt to summarize performance compresses that space. What remains open is the interpretive step: what follows from those facts about dimensionality and projection.
This essay approaches that question from a prior commitment developed elsewhere: intelligence is effectiveness within a game. A game, in this sense, is any strategic interaction defined by goals, constraints, and choices among alternatives. Intelligence becomes meaningful only relative to such contexts, and measurement becomes meaningful only once the relevant game is made explicit.
From this perspective, the issue shifts. The question is not whether IQ captures intelligence in general, but whether it measures effectiveness within a particular family of strategic contexts, and whether scalar compression is appropriate within that domain.
2. Intelligence as Game-Relative Effectiveness
Intelligence admits of definition only relative to structure. Strategy presupposes goals, constraints, and alternatives, and intelligence names the effectiveness with which an agent navigates that structure. Outside a game, intelligence collapses into an undifferentiated abstraction.
Different games reward different competencies. Social coordination emphasizes signaling and norm navigation. Scientific inquiry emphasizes hypothesis testing and error correction. Economic competition emphasizes prediction and optimization under scarcity. Each domain supports its own intelligences, shaped by the strategic environment in which success is evaluated.
This framing carries an immediate implication: every intelligence measure is implicitly indexed to a game. Disputes arise primarily when that index remains unarticulated.
3. The Game IQ Measures
IQ measures performance within a recognizable family of games. These games share structural features:
abstract rule systems
symbolic manipulation
time-bounded decision making
transfer across formally similar problems
Success within this family depends on rapid pattern extraction, generalization, and error correction under cognitive load. These competencies matter in environments organized around formal rules and compressed information flows, including modern educational systems, technical disciplines, and bureaucratic institutions.
It is often noted that these institutions resemble the structure of IQ tests themselves. This reflects historical path dependence rather than circular invalidation. Games select for the skills that sustain them. Once stabilized, performance within the game remains meaningfully rankable, even when the game’s dominance is contingent rather than inevitable.
Once the game is specified, the use of a scalar measure follows naturally. Games generate scores.
4. Scalar Measurement Within a Game
Scalar measurement is a routine feature of games. Scores compress performance into a form that supports comparison, prediction, and coordination under shared rules. Their legitimacy depends on whether they track success in the game rather than on whether they capture every trait of the players.
IQ functions in the same way. It summarizes effectiveness across many instantiations of the same game structure. Information is lost in compression, yet relevance is preserved when the summary retains variance that predicts future performance within that domain.
Controversy emerges primarily when scalar scores are treated as if they applied outside the game they summarize.
5. Empirical Constraint and Shared Variance
IQ emerged from the observation that performance across many abstract cognitive tasks covaries. Test construction follows this signal by retaining tasks that load strongly on shared variance and discarding those that do not.
This process constrains the measurement. Variants that drift away from the underlying structure lose predictive power. Stability across test batteries, populations, and time reflects anchoring to a real pattern rather than freedom of representation.
Within the game it measures, IQ behaves like a calibrated score rather than an arbitrary projection.
6. Bounded Variation, Biology, and Distribution Shape
Human cognitive performance develops within biological and environmental limits. Neural architecture, developmental pathways, and energetic constraints bound variance long before formal testing occurs. Aggregation across bounded traits produces familiar distributions.
Biology bounds the space of possible cognitive strategies, while games determine which regions of that space are amplified, rewarded, or ignored. The resulting bell-shaped curves reflect the structure of the underlying system rather than an artifact of projection geometry alone. Their persistence across contexts follows from the stability of the game’s constraints.
7. Generality, Transfer, and g
General intelligence does not require universality across all games. It requires transfer across a broad class of games that share deep structural features. Abstract reasoning, symbolic manipulation, and error correction recur across many strategic environments, enabling competence in one to support competence in others.
IQ tracks effectiveness across this equivalence class. This explains both its transferability and its limits. It is neither a game-free essence nor a narrow parochial skill, but a measure of performance across a structurally related family of games.
8. Predictive Reach
Within its domain, IQ associates reliably with learning rate, symbolic reasoning, and performance in cognitively dense institutions. These associations operate probabilistically and admit wide individual variation.
Predictive reach justifies measurement. Interpretation requires additional premises that lie outside the game itself.
9. Measurement, Status, and Misuse
Scalar scores influence coordination and status. That influence often generates discomfort, which becomes misdirected toward the measurement rather than toward the uses to which it is put.
The game-relative framing separates description from valuation. IQ describes effectiveness within a defined strategic context. Social and political decisions require further criteria.
Questions about why modern societies reward this particular game more than others concern political economy rather than measurement validity. Conflating the two obscures both.
Postscript
IQ is best understood as a game-relative scalar: a compressed summary of effectiveness within a particular strategic domain. Its legitimacy arises from empirical constraint, stability, and predictive relevance. Its limits arise from the same source.
Intelligence remains plural. Games remain diverse. Measurement remains essential wherever coordination and prediction matter.
Defending IQ in this sense amounts to defending disciplined abstraction—bounded by context, anchored in structure, and evaluated by what it enables rather than by what it excludes.