In terms of how intelligence is distributed across
the nation, people often assume a normal distribution - the familiar Gaussian
bell curve of intelligence - because that’s the shape used in IQ scoring. But
that curve is constructed, not discovered. IQ tests are norm‑referenced: the
scoring system forces the results into a bell curve so that 68% fall within one
standard deviation of the mean, 95% within two, and 99.7% within three. That’s
a property of the measurement, not necessarily of the underlying phenomenon.
If instead we look not at measured cognitive ability but at applied intelligence - the extent to which people actually use their cognitive potential - the distribution across the UK seems to me far more skewed. In fact, it resembles something closer to an exponentially decaying curve. Not a literal Boltzmann distribution (which applies to particles in thermal equilibrium), but a curve with the same shape: heavily weighted toward the lower end, with a long, thin tail of high performers.
The analogy is this: if the y‑axis is number of people and the x‑axis is degree of applied intelligence, then very few people sit at the extreme high end, a moderate number occupy the middle, and a very large proportion cluster toward the lower end. Replace particles with people and energy with cognitive engagement, and I think you get a surprisingly good metaphor for everyday experience.
So, for example, on a scale of 1–100, where 1 is very low applied intelligence and 100 represents the most brilliant minds, my experience suggests that the vast majority of the UK population sits below 50, with a very large proportion below 25. Roughly - and these figures may need slight adjustment, but not much - the distribution might look like this:
1–25 (50%)
26–50 (30%)
51–75 (15%)
76–100 (5%)
This is not a bell curve. Compare it to height or weight. Height is approximately Gaussian because most adults fall between 4ft 9 and 6ft 7, with relatively few outliers. Weight is more skewed, but still clusters around a central tendency. Applied intelligence, however, does not seem to follow the same pattern. And although democratic and egalitarian instincts encourage people to believe otherwise, everyday observation suggests a very different landscape.
What makes this even more interesting is that many skewed, exponentially decaying distributions in human behaviour arise from biased random walks. A random walk occurs when outcomes are shaped by many small, independent influences. For example, take nightclub attendance in Norwich city centre in 2016. Suppose there is a group that regularly parties down Prince of Wales Road, averaging to some value n.
Over a month - say July - each member may or may not go out. If someone goes out, that’s a step to the right (+1). If they stay home, that’s a step to the left (-1). Over time, these independent decisions produce something resembling a random walk. But because exogenous factors exist - post‑Christmas fatigue, hot summer weekends, bank holidays, major events - the walk becomes biased. The result is a distribution that may look bell‑shaped but is not perfectly symmetrical.
Applied intelligence behaves similarly. It is influenced by countless factors: motivation, environment, education, culture, opportunity, personality, stress, health, and so on. These influences do not push equally in both directions. They bias the walk toward lower engagement. And unlike height or weight, there is no natural “restoring force” pulling people toward the mean.
This is why applied intelligence ends up looking like a skewed distribution rather than a Gaussian one. Not because intelligence itself obeys thermodynamic laws - it doesn’t, of course - but because human behaviour often follows power‑law or Pareto‑like patterns, where a small minority produce most of the high‑end output. The curve is steep on the left and thin on the right because cognitive engagement is limited, unevenly distributed, and subject to many downward‑pulling influences.
The upshot is, measured intelligence is Gaussian because the scoring system enforces it. But applied intelligence - the degree to which people use their cognitive potential - is not. It is heavily skewed toward the low end, shaped by biased behavioural dynamics, and resembles an exponentially decaying curve far more than a bell curve.