Commenter Race Realist claimed in the comment section that IQ and many other physiological traits do not form bell curves.

A bell curve is just a distribution of scores where most people score around average, and as scores move further from the average in either direction, the number of people very gradually decreases (forming the shape of a bell).

As Arthur Jensen noted in his book, Bias in Mental Testing, many physical traits roughly form a bell curve, for example, height:

Birth weight:

Brain weight:

The reason for this, as Jensen brilliantly understood even back in the early 1970s, is these are complex polygenetic traits caused by a great many uncorrelated genetic and micro-environmental effects, and thus their distribution should resemble the flipping of thousands of coins, giving you either bad or good genetic (and environmental) luck:

While it’s true that modern IQ test results are forced to fit a bell curve, this is not necessarily because cognition doesn’t naturally form a bell curve, but rather it’s because in order for test results to naturally form a bell curve, you need what’s called an interval scale: A scale where items increase in difficulty at equal intervals.

But because it can be tricky and tedious to judge whether a certain IQ test item is 10% more difficult than another one, or 30% more difficult,  IQ tests often contain abrupt jumps in difficulty, making them ordinal scales, not interval scales, which prevent the distribution of scores from being smooth and continuous.  As a result scores wont always naturally fit a bell curve, they must be forced to.

However as Arthur Jensen noted in  Bias in Mental Testing, some psychometric tests are based on interval scales.  For example the original Binet scale used the concept of age.  Since the difference between a six-year-old and a five-year-old is theoretically the same as the difference between a ten-year-old and a nine-year-old (one year), this is an interval scale, and so IQs calculated from the ratio of a child’s mental age to his chronological age closely approximated a bell curve for the middle 99% of the population:

As Jensen explained, the departure from normality at the lower extreme is caused by major disorders that override normal polygenetic variation such as mutations of large effect, chromosomal abnormalities, birth trauma and the like.  The surplus of scores at the high extreme is less pronounced and harder to explain.

One of the best measures of IQ is Vocabulary.  Most vocabulary tests are not true interval scales because psychologists arbitrarily pick words for people to define, and these may increase in difficulty in a non-linear way,  however as Jensen noted, some Vocabulary tests are based on selecting words from the dictionary at random, and when this is done, the total number of random words kids can correctly define, approximates a bell curve:

Another example of an interval scale is Digit Span, because Digit spans gradually increase in difficulty one digit at a time, with multiple trials at each difficulty level.  When this was scored such that each digit correctly recalled in the right order scored a point, the scores of 5,539 Navy recruits approximated a bell curve:

Of course I’m not suggesting that all cognitive abilities form a bell curve.  Indeed a member of Prometheus once claimed that because the human mind works in parallel, complex problem solving speed actually doubles every 5 IQ points, which is about as far from a normal distribution as you can get.

An interesting question is why do some forms of cognition (including some very g loaded abilities like Vocabulary) form a bell curve, while spatial and math talent may form an exponential curve, and does this imply math and spatial geniuses are vastly more intelligent than verbal geniuses, since the latter are at most only about 100% verbally smarter than average, while the former are many orders of magnitude spatially or mathematically smarter?