Imagine you had a random sample of 16 white men with the following heights measured without shoes on:

Todd: 75 inches

Dave: 74 inches

Bill: 72 inches

Tim: 72 inches

Ted: 71 inches

Mike: 70 inches

Joe: 70 inches

Ed: 70 inches

Rick: 70 inches

Henry:68 inches

Ian: 68 inches

Andy: 68 inches

Don: 68 inches

Steve:67 inches

Eric: 67 inches

The average raw height of these men is about 70 inches and the standard deviation is about 2.4 inches. Now if we wanted to express these heights on the same scale as IQ, where the white mean is set at 100 and the white standard deviation is set at 15, instead of calling it IQ (Intelligence Quotient) we would call it HQ (Height Quotient). In order to convert the heights to HQ, we would use the following formula:

HQ = [(Height – 70 inches)/2.4](15) + 100

When this is done, the men have the following HQs:

Todd: 131

Dave: 125

Bill: 113

Tim: 113

Ted: 106

Mike: 100

Joe: 100

Ed: 100

Rick: 100

Henry:88

Ian: 88

Andy: 88

Don: 88

Steve:81

Eric: 81

We would call the HQs listed above fluid HQs, because they were taken without shoes and thus measured the raw physical height, uncontaminated by the socioeconomic opportunity to buy better shoes.

Now imagine we asked all the men to put their shoes on and found the following heights measured with shoes:

Todd: 77 inches

Dave: 76 inches

Bill: 74 inches

Tim: 74 inches

Ted: 72 inches

Mike: 71 inches

Joe: 71 inches

Ed: 71 inches

Rick: 71 inches

Henry:68 inches

Ian: 68 inches

Andy: 68 inches

Don: 68 inches

Steve:67 inches

Eric: 67 inches

Now the mean height has risen from about 70 inches to about 71 inches, and the standard deviation has risen from about 2.4 inches to about 3.13 inches. So the shoes have not only increased the average height of the men, but increased the differences between them. Why? Because the short men were unable to find employment, and thus couldn’t afford to buy shoes at all. This is analogous to how people with low fluid IQ are denied access to more education to prop up their crystallized IQ.

By contrast, the men who were at least 70 inches tall could afford to buy shoes which increased their height one inch, and the men who were at least 72 inches tall could afford to buy shoes that increased their height by two inches. This is analogous to how people with high natural IQs get full academic scholarships, and thus can afford graduate school with greatly increases their crystallized IQ.

So let’s call HQ measured with shoes on (if you even have shoes), crystallized HQ, because it reflects both the raw biological trait, and the cultural perks that trait allows you to acquire (in this case of HQ, shoes. In the case of IQ, schooling). In order to calculate the crystallized HQs that are also scaled to have a mean and SD of 100 and 15 respectively, we invoke the same formula used above, except we amend it to reflect the new distribution of heights:

HQ = [(Height – 71 inches)/3.13](15) + 100

With the above formula, the men in whatever shoes they have, get the following crystallized HQs:

Todd: 129

Dave: 124

Bill: 114

Tim: 114

Ted: 105

Mike: 100

Joe: 100

Ed: 100

Rick: 100

Henry:86

Ian: 86

Andy: 86

Don: 86

Steve:81

Eric: 81

Notice how the HQs of the men calculated with whatever shoes they have, are virtually identical to their HQs measured without shoes on. So even though an environmental intervention (buying shoes) greatly increased the absolute difference in height between men, measured in inches, it did nothing to increase the *relative* difference between men, measured in HQs, which by definition have a standard deviation of 15.

Analogously, even though factors like education, parenting, studying, etc, greatly increase performance on crystallized IQ tests like vocabulary and the SAT, they have little effect on the *relative* difference between people, as measured by the IQ scale. This is why both HBD extremists and extreme HBD deniers can both be right simultaneously; because culture has large effects on absolute differences while biology determines relative differences.

It’s only when you get environmental effects that are uncorrelated with individual differences in biology (i.e. 20th century increase in schooling partly responsible for the Flynn effect), that the effect of culture becomes unmasked.