"You are wrong about many Puerto Ricans being racially mixed. I once visited Puerto Rico. I saw no mixed-race people there. Everyone I saw was either Black or White." My thesis advisor, a kindly man who encouraged my interest in the history of the "race" notion, replied thus to something I had said.

"This is probably a semantic problem," I tried to explain. "Some people whom you see as White or Black might call themselves mixed."

"They cannot call themselves something that does not exist," my advisor insisted. "You cannot be a little bit Black, any more than you can be a little bit pregnant or a little bit dead. You are either Black or not. There is no in-between. I should know."

Now folks, we all should know better than to debate semantics. Some readers see that different people can use words differently. They realize that arguing over the "correct" meaning of words like Black or White is pointless because such discussion is sterile and never-ending. But others, sad to say, simply cannot grasp that a word can mean one thing to Johnny but something else entirely to Sally. They will argue forever that Johnny or Sally is just being stubborn.

Oddly, such blindness to semantics is not cured by education. My advisor is a respected historian, a Ph.D. who has published definitive work on U.S. political history. Also, it does not seem to depend on smarts. The most brilliant Black historian publishing today insists that the dictionaries are wrong -- that only White people can be "racist" since "racism" depends on power. Perhaps it depends on fluency in several languages and consequent mental agility regarding word meaning. I do not know. All I know for sure is that some of us see the silliness in semantic arguments, while others do not.

Nevertheless, set aside my professor's bizarre theory that no mixed-race people can possibly exist. Despite his ill-advised choice of expression, a kernel of honest doubt lurks at the heart of his argument. It is not due to semantic confusion, and it can be cured with education.

What was bothering him is this: if Puerto Ricans have been totally intermarrying (with just as many interracial couples as same-race couples) for at least six generations, why is not everyone light brown? It is true that many Puerto Ricans are light brown. But many are as fair-skinned as any Norwegian and others are as dark as any Nigerian. According to my professor, if mixing had been complete and constant since the PR census of 1850, which recorded a 50-50 Black/White population, then everyone should look blended.

Like most of us, my professor fails to remember his high-school biology. Like most of us, he has forgotten the tale of nineteenth century monk Gregor Mendel's (1822-1884) wrinkled peas and smooth peas. Elementary genetics shows that no large intermarrying 50-50 biracial population will ever blend completely, but will continue to produce about one genetically European child in every eight and one genetically African child in every eight forever. Another way of saying this is that, although most children seem to "blend" their parents' features, if both parents are mixed then one child in four will always be darker than both parents and one in four will always be lighter than both parents.

This phenomenon is neither due to "race" nor to any unique property of melanin heredity. It is independent of how many genes govern complexion. Indeed, it has nothing to do with human beings and applies equally to plants. It has to do with sex, nothing more. It is the inevitable consequence of two basic facts: First, every sexually reproducing organism has two parents. Second, life's DNA is digitally encoded; it is not analog. Hence, every trait is governed by two copies, not one, of the controlling set of genes. One copy inside every cell nucleus came from each parent.

Imagine if complexion were governed by a single gene. (In fact, at least three genes affect complexion, but we shall come back to this in a moment.) In this case, the offspring of a Nigerian and a Norwegian would look in-between (Arab or Berber, say) since the child would have one copy for dark complexion and one for fair. But the child's genes are just as strong as in her parents. They do not dilute. The child's digitally encoded dark gene is just as strong as the Nigerian mother's, and her fair gene is just as strong as that of her Norwegian father. Her blended appearance is not due to any dilution or blending of the parents' genes. It is due to the action of two pure, strong, unblended genes working at cross-purposes.

Assume now that this child grows up and marries a similarly mixed person. Their offspring will inherit one gene copy from the mixed mother (either pure Nigerian or pure Norwegian, at random) and one from the mixed father (again, either pure Nigerian or pure Norwegian). Work out the probabilities. Out of every four babies in this third generation, two will come out with in-between appearance (like their parents). But one will come out pure Norwegian and one will come out pure Nigerian, like their grandparents. Those who recall high school biology will recognize Mendel's experiments.

One-fourth, one-half, one-fourth. That is Mendel's profoundly important lesson about features that seems to "blend." The first generation will be in-betweens. But the second-generation offspring of two in-betweens will be one-fourth pure "A," one-half in-between, and one-fourth pure "B." One-fourth, one-half, one-fourth. ANY feature. ANY organism. That is the central message of genetics. It is what high school biology classes try to impart. How this simple fact later becomes corrupted inside maturing brains into bizarre notions of "dominance" and "blood ratios" is a mystery of pedagogy. One-fourth, one-half, one-fourth. Remember that.

How do multiple complexion genes change things? If two separate genes affect a trait (each with two copies), then more combinations are possible for the third generation. Out of every sixteen babies in the third generation: One will inherit the Norwegian complexion of its grandfather (four European, zero African genes). Four will have a mid-European complexion (three Europe, one Africa). Six will inherit the Mediterranean complexion of their parents (two Europe, two Africa). Four will have an Ethiopian or San complexion (one Europe, three Africa). And one will inherit the Nigerian complexion of its grandmother (zero Europe, four Africa). Since one-in-sixteen is rare it would, in all likelihood, take an additional generation of selective marriage to produce children of pure Norwegian or Nigerian genetic makeup.

Since, in reality, at least three genes affect complexion, then the possible combinations are more numerous and it takes yet another generation of intermarriages before the original types are likely to reemerge.

Three points are important. First, no matter how many genes control complexion, no matter how many possible combinations there are, individuals of pure Norwegian and pure Nigerian appearance will inevitably reemerge in every large 50-50 population. Second, one child in four will always be darker than both parents, half will be in between the parents, and one in four will be lighter than both parents. This is independent of how mixed or unmixed you might think the parents are. Draw a straight line from Norway to Nigeria and you will find that complexion change is gradual throughout its length. There is no break. Everyone along the line is mixed to some extent except at the very ends. Of course, this does not mean that two Norwegian-looking parents can have a Nigerian-looking child. It simply means that two Castilian-looking parents have a 25 percent chance of having a child with a northern Iberian appearance (Asturian, say) and an equally small chance of having an Andalusian-looking child. Such small differences gradually accumulate over generations to produce the line's end-points. Third, in the short term, what you see is what you get. A Norwegian appearance (phenotype) results from Norwegian genes (genotype), a Nigerian phenotype results from a Nigerian genotype. There is no lurking invisible Black or White gene that can suddenly pop out.

What about ratio of Negro blood? Forget it. The most exhaustive study of this topic is Caroline Bond Day and Earnest Albert Hooton, A Study of Some Negro-White Families in the United States (Cambridge MA: Harvard University, 1932). This project studied 350 families comprising more than 2,500 photographed individuals. The author, Caroline Bond Day, classified each subject by fraction of "Negro blood" and arranged their photos in family trees, traced all the way back to the original immigrant ancestors from Africa or Europe. (The photos in this article come from her book.) She found that one person in four with 3/8 to 1/2 "Negro blood" could, as she put it, "pass for white." Every person with 1/4 "Negro blood" could do so if they chose: "I know of no case of a quadroon who could not easily pass for white." And people with 1/8 Negro blood or less are, quite simply, white in every way: "In the few examples of octoroons which I have studied I have been able so far to see no traces whatever of Negro admixture."

The flaw in Ms. Day's analysis was that it was based on the erroneous blending model -- that such terms as "1/2 Negro blood" or "1/4 Negro blood" are meaningful. In fact, as Mendel demonstrated, what matters is not the fraction of "Negro blood," but whether the subject is of the first mixed generation or of a later generation. Fortunately, Ms. Day's misunderstanding was corrected before her book was published. Despite her erroneous hypothesis that fraction of "Negro blood" was significant, Ms. Day had assembled a team of anthropometrists and statisticians (Earnest A. Hooton, Carl Seltzer, Constance Tyler) who measured the facts and reported the rules of thumb given here. They concluded with the following statement: "the evidence here surveyed indicates a Mendelian segregation of skin pigment with multiple factors."

In conclusion, what seemed a paradox to my advisor would be obvious to Gregor Mendel. About one Puerto Rican in eight is as White as any European, both in appearance and in the genes that he or she can bequeath. And about one Puerto Rican in eight is as Black as any African, both in appearance and in the genes that he or she can bequeath. Nevertheless, every Puerto Rican other than recent immigrants has equal numbers of African and European ancestors.

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