## Can a Person Be One-Third Black?

The answer is no with a but. A person with full knowledge of his or her genealogy cannot be precisely one-third black. Why not? It has to do with the mathematics underlying family trees. Everyone has two birthparents. Those parents each had two birthparents, and their parents each had two birthparents. The number of ancestors one has can be ascertained by taking increasing powers of 2. One starts with one individual, then two parents, four grandparents, eight great-grandparents and so on.

If one looks at a person’s great-grandparents, it becomes clear that one can be 1/8, ¼, or ½ any given ethnicity. A person who has only one black great-grandparent would be 1/8 black. A person with only two black great-grandparents would be ¼ black. It is not hard to see how a person could be 3/8 or ¾ black.

But what has to happen for a person to be one-third black? In order for this to occur, one would need to have a number of ancestors at some generation to be evenly divisible by three. However, a generation evenly divisible into thirds will never occur. To show why, I must make reference to prime factorizations. A prime factorization of a number lists the combination of the smallest prime factors that multiply up to a number. For instance, the prime factorization of 15 is 3 * 5. The smallest prime factor of 15 is 3 (1 is not prime). Clearly the product of 3 and 5 is 15. Going back to generations, try taking the prime factorization of the total number of ancestors at any generational level. At the great-grandparent level, there are 8 ancestors. The smallest prime factor of 8 is 2. When one divides 8 by 2, one is left with 4. The smallest prime factor of 4 is 2, which leaves 2. The prime factorization of 8 is 2*2*2 or 2^3. Every number has one exclusive prime factorization. There is no alternative prime factorization of 8 other than 2^3. All of a number’s possible factors can be generated from its prime factorization. The factors of 8 are 1, 2, 4, and 8 only. Notice that 3 is not among these factors. For a generation to be evenly divisible by 3, the number of ancestors must have 3 as one of its factors. Yet at any generational level, the number of ancestors will always have a prime factorization of 2^n where n is the number of generations from the individual to the ancestor. At one generation, it will be 2, at two generations it will be 4, at three generations, 8, and so on.

How close can one get to being one-third black? Awfully close. If one goes back 5 generations, one has 32 ancestors. If exactly 11 of these 32 ancestors are black, then the individual would be 34.375% black. If one has 43 out of 128 ancestors who are black, then the individual would be 33.59375% black, less than half of one-percent away from being one-third black. Of course to know one’s ethnic purity to this level of accuracy, one would have to look back seven generations and know the ethnicity of every ancestor at this generational level.

Another way one could be one-third black is if one is missing information about some relatives and then calculates out of known relatives only. For instance, even though one has 4 grandparents, one may only have information regarding 3 of them. If a person has one black grandparent, two white grandparents and one unknown grandparent, he or she might consider himself or herself to be one-third black.

A final scenario I thought of seems to me fairly weak but still plausible. I began with the given that each person has two birthparents. However, what happens when a person is born through a surrogate? If an egg from a mother and a sperm from a father combine to form a zygote which is then implanted in a surrogate mother, can one argue that the resulting child has three parents? There is a case to be made here, but I think most reasonable people would consider the parents of the child to be the egg donor and the sperm donor.

1. #1 by lt786 on April 26, 2009 - 10:10 pm

haha this is one of the most interesting posts I have ever read…

I’m 1/16th black…

2. #2 by How I Lost Thirty Pounds in Thirty Days on May 3, 2009 - 1:28 pm

3. #3 by Kikolani on May 4, 2009 - 7:39 pm

I was thinking that it would have to be an even number part, like 1/2, 1/4, 1/8 and so forth. Unless genetically, some racial characteristics pass more strongly with one gender than another. I’m not sure that works though.

~ Kristi

4. #4 by Maffin on April 23, 2010 - 1:05 am

Allright, I have a few questions here. Let’s say a woman got married to two men. The woman is white; one man is black and the other man is white. The three got together and the wife had a baby. The child can either be 100% white OR 50% black and 50% white.
Now my question is: Could the ancient people have considered that child to be one-third black, regardless of appearance from that threesome? Any historical evidence related to this event? The answer is obvious these days but some people were delusional back then. Crazy (0_0)

And here’s a biological question: Is there or has there been such a natural life form with three biological birthparents?

Also, is there any science fiction movie, TV series or any piece of literature which talk about a species with three birth parents?

5. #5 by asad123 on April 23, 2010 - 7:54 pm

Maffin, you may be interested in this article, http://www.technovelgy.com/ct/Science-Fiction-News.asp?NewsNum=1442, “Three Genetic Parents? How About Seven?” The story, “Venus and the Seven Sexes” by Tenn imagines an organism with seven sexes.

6. #6 by Roof Helmet on December 1, 2010 - 4:33 pm

we always keep track of our family tree because it is exciting to know the family tree `”.