How many races are there? Depending on who you ask there are anywhere from only two to over 100. Since many humans are too dumb and too biased to give an objective answer, let’s turn to math.

Perhaps a more objective approach was deployed by Cavalli-Sforza who transformed a genetic distance matrix of 42 ethnic groups into a scatter plot.

Once he had them in a scatter plot, he could do principal component analysis

The first principal component can be thought of as the g factor of race. It is the line that best fits all the races and the primary dimension upon which they can all be ranked. It reflects the great Out of Africa migration and how far from Africa the races were able to travel. Those who stayed in or close to Africa score at one extreme (Europeans and Africans themselves). Those who were able to travel all the way to Australia, Siberia and the Americas score at the opposite extreme (East Asians, Native Americans, Oceanians).

To find the second principal component, you need a variable that is 100% independent of the first variable. Thus you need to draw a line through the scatter plot that in 90 degrees from the first, but not just any 90 degree line, but one that minimizes the distance between the new line and ethnic groups.

The second dimension seems to correlate with skin color. Those who score high on the second Principal Component are white skinned peoples like Northeast Asians & Northwest Europeans. Those who score low have dark skins, like sub-Saharan Africans and Oceanians.

With two components you can crudely organize humanity into 4 major races: sub-Saharan Africans (lower right), Caucasoids (upper right), Northeast Asians & Amerindians (upper left) and Oceanians (bottom left).

However white supremacists might not be happy to be lumped in with commenter “Loaded” in a single Caucasoid race. Perhaps if Cavalli-Sforza had added a third principal component, that separation may have occurred. A third principal component would have to be at 90 degrees of both the first two and thus requires three dimensional space where it would stand like an erect pole.

Cavalli-Sforza never bothered, but using a smaller data-set of 26 populsations, Jensen extracted SIX principal components. He then spun the six components like a spin on Wheel of Fortune. “Varimax rotation maximizes the variance of the
squared loadings of each component, thereby revealing the variables that cluster together most distinctly,” said the brilliant Jensen.

Jensen wrote:

“The population clusters are defined by their largest loadings (shown in boldface type) on one of the components. A population’s
proximity to the central tendency of a cluster is related to the size of its loading in that cluster. Note that some groups have major and minor loadings on different components, which represent not discrete categories, but central tendencies. “

The six rotated components are: (1) Northeast Asians (2) Caucasoids, (3) Southeast Asians & Pacific Islanders, (4) sub-Saharan Africans, (5) North and South Amerindians and Eskimos, (6) aboriginal Australians and Papuan New Guineans.

However Jensen neglected to do a principal component analysis on the rotated principal components themselves or maybe he did but didn’t publish it because the results were unpalatable. You might think that’s not possible because principal components by definition are uncorrelated, however one purpose of rotating them is they become no longer 90 degrees apart and thus are no longer orthogonal.

Had he done such a second order principal component analysis, he may have found second-order factors. Perhaps (1),(3) and (5) would form a second order factor. Perhaps (2) would form another. Perhaps (4) and (6) would form a third. Then we’d have the three main races of the Bible: Mongoloids, Caucasoids and Negroids (not that I believe in the Bible or the Koran or any other holy book).

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