## Archive for January 19, 2013

### Once Removed, Twice Shy

Family relations are hard.

A man is holding a photograph of another man and says, “Brothers and sisters I  have none, but this man’s father is my father’s son.” Who is the man in the photo?

But you don’t need riddles to make confusing situations. Real life is difficult enough.

When Lynne Cheney was doing genealogy research for Blue Skies, No Fences, a memoir about growing up in Wyoming, she discovered an interesting tidbit: Barack Obama and Dick Cheney are cousins. In particular, both are descendants of Mareen Duvall, a Huguenot who immigrated from France and settled in Anne Arundel County, Maryland.

Based on her homework, Lynne Cheney claimed that they were eighth cousins. The Chicago Sun-Times, however, reported that they were ninth cousins once removed.

If either Cheney or the Sun-Times got it wrong, well, who could blame them? This whole business of nth cousins p times removed is a bit overwhelming.

The holiday season is a good time to review the rules for consanguinity. (Consanguinity, from the Latin consanguinitas, means “blood relation.” The first two syllables lead to the modern term cousin.) At holiday gatherings, it is not uncommon for discussions like the following to occur:

“Hey, who was that on the phone?”

“That was Johnny. You remember him, Uncle Lenny’s brother’s kid?”

“Oh, yeah! What is he, my third cousin?”

“Actually, he’s your first cousin once removed.”

“No, he’s not! He’s your great nephew!”

“????????”

It wasn’t until a recent family gathering that I realized (a) I ought to learn these rules about consanguinity so I could avoid these ridiculous conversations and (b) there’s got to be a simple mathematical formula to figure out the relationship between two people.

As it turns out, once I found the solution to (b), then (a) was pretty easy.

Figuring out the relationship between two people can be accomplished with the following algorithm.

1. Make an ascent list for each person. An ascent list is a list of ancestors proceeding from each person to their parents, to their grandparents, to their great-grandparents, and so on.
2. Determine the first ancestor common to both ascent lists.
3. Express the common ancestor in the form GxP and GyP for each person. Then, the two people are nth cousins p times removed, based on the following:
$R(x,y) = \min(x,y), |x-y| = n, p$

• The values of x and y depend on how many G’s appear in the relationship. For instance, a grandparent would be G1P, but a great-great-great-grandparent would be G4P.
• The algorithm works for x = 0 or y = 0, either of which would indicate a parent.
• If n = 0, the relationship between the two people is sibling (p = 0), niece/nephew (p = 1), great niece/nephew (p = 2), and so on.

As an example, let’s say that you and Johnny are trying to figure out how you’re related. Your great-great-grandmother (G3P) is Johnny’s grandmother (G1P), so x = 3 and y = 1. Then

$n = \min(3, 1) = 1$

and

$p = |3 - 1| = 2$

which means that Johnny is your first cousin twice removed.

According to geni.com, Barack Obama is the 9th great grandson of Mareen Duvall and Dick Cheney is the 8th great grandson of Mareen Duvall. If that’s correct, then x = 9, y = 8, and Obama and Cheney are eighth cousins once removed.

And if that’s the case, then neither the Chicago Sun-Times nor Lynne Cheney got it correct. (See, I told you this sh*t was hard.)

If you really want to geek out on the mathematics of consanguinity, check out http://www.knotsystem.dk/TheKnotSystem.pdf.

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

## MJ4MF (offline version)

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