One little, two little, three little Indians....

Senator Elizabeth Warren (D-MA, which means Democrat from Massachusetts), whose picture I am not going to show -- you can look it up for yourself -- finally underwent DNA testing to prove once and for all that she is of Native American heritage. She said she was Native American on an application to be a professor at the Harvard Law School a couple of decades ago, and Harvard, eager to comply with the desire of the U.S. Federal Government that there be minorities on their faculty, hired her. It may not have happened in just that way or for just those reasons, but that is how it looked from 50,000 feet to the casual observer in the general populace.

This week the Boston Globe reported the results of Senator Warren's DNA testing, then issued a correction, then issued another correction. It first said that Senator Elizabeth Warren was between 1/32nd and 1/64th Native American, then said she was between 1/32nd and 1/1024th Native American, then said she was between 1/64th and 1/1024th Native American.

As the parole board told Nicholas Cage in Raising Arizona, "Well, okay then."

This is very confusing to the casual observer, and even to the observer who is not so casual.

Senator Warren now feels exonerated and is demanding that President Trump pay up on his offer to donate a million dollars to a charity of her choice if she is Native American. He denies making such an offer, but even if he did, wouldn't it be fairer if he donated 1/1024th of a million dollars ($974.56) instead?

Here's an interesting footnote. An expert (some people say an expert is anyone more than 50 miles from home carrying a briefcase; others break the word down into its component parts, saying "ex" is a has-been and "spurt" is a drip under pressure) has determined that Senator Warren is 0.09% Native American, slightly less than one-tenth of one percent. He also says that the average European-American is 0.18% Native American, or slightly less than two-tenths of one percent. Here's another interesting footnote. Leaders of the Cherokee Nation, whose politics I am not aware of, said yesterday that the amount of Native American blood Senator Warren has does not qualify her for membership in their tribe.

That is all backdrop and prelude to the real subject of this post, which is:

Genealogy is fascinating, but it also can be very confusing.

For example, what does all that stuff mean, 1/32nd, 1/64th, 1/1024th, and how do they know, and where do they come up with those strange numbers?

I will tell you.

It's really simple.

It all has to do with the fact that everyone has two parents, a father and a mother. You would not be here if you didn't have two parents. I could go into more detail and speak at length of XX and XY chromosomes, but I will not. The very astute among you may also note that you have (or had) four grandparents because your father had two parents and your mother had two parents.

It has to do with powers of 2. Yes, math. Sorry.

If you think of your parents as being one generation back from you (because they are), and your grandparents as being two generations back from you (because they are), and your great-grandparents as being three generations back from you (because they are) -- you can carry this on as far back as you can find names and data -- you can determine the number of direct ancestors you have in each generation by thinking of the powers of 2. That is:

2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, and so on. If math makes your eyes cross and your head hurt, I'll put it into words. Two squared (2 x 2) is four, two cubed (2 x 2 x 2) is eight, two to the fourth power (2 x 2 x 2 x 2) is 16, and so on. Let's fill out that table a little more fully:

2¹ = 2
2² = 4
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512
2¹⁰ = 1024

and so on and so forth. If your eyes are glazing over, hang in there just a little longer. It will be over soon.

Simply substitute the phrase "In the xth generation before me, I have y direct ancestors" where x is the ordinal number instead of the cardinal number of the power of 2 and y is the number after the equal sign. That is:

In the first generation before me, I have 2 direct ancestors (my parents).
In the second generation before me, I have 4 direct ancestors (my grandparents).
In the third generation before me, I have 8 direct ancestors (my great-grandparents).
In the fourth generation before me, I have 16 direct ancestors (my great-great-grandparents).
In the fifth generation before me, I have 32 direct ancestors.
In the sixth generation before me, I have 64 direct ancestors.
In the seventh generation before me, I have 128 direct ancestors.
In the eighth generation before me, I have 256 direct ancestors.
In the ninth generation before me, I have 512 direct ancestors.
In the tenth generation before me, I have 1,024 direct ancestors.

I have used American-style nomenclature here. It is my understanding that in the U.K. what we call great-grandparents are called grand grandparents, and the greats are one off after that. Continental differences cannot be helped in this post.

So if one, count 'em, one of Elizabeth Warren's 1,024 ancestors in the tenth generation before her was a Native American, she is claiming to be Native American for purposes of Harvard Law School being able to report to the U.S. Federal Government that their faculty included a minority.

I think the Boston Globe waffled in order for Senator Warren to save face, for she had always said that either her 3rd or 4th great-grandmother was Native American. If that were so, she would be 1/32nd or 1/64th Native American, the numbers used in the Boston Globe's original story. To be 1/1024th Native American, the ancestor would be her 8th great-grandmother, several generations earlier.

The total number of direct ancestors you have to the tenth generation before you is cumulative: 2+4+8+16+32+64+128+256+512+1024 and that's a lot of direct ancestors.

Maybe next time we'll explore Fibonacci numbers and the "golden spiral". Then again, maybe we won't.