Relative Math: How Many Descendants?

Arresting a Witch

Illustration by Howard Pyle (7) 

...there is an ancient Bedouin Arab saying, “I against my brother, my brothers and me against my cousins, then my cousins and I against strangers," which nicely illustrates the philosophy of caring most for those who are genetically closest to us. (6)

When I first found that some of my ancestors had been accused of being witches, I was surprised at how hard it hit me. It's one thing to read historical accounts of the witch craze that hit New England in 1692, but it's a deeply emotional experience to realize that those were my relatives in the history books.

Of course, that's one of the big lessons learned from family history research--the history books are filled with our own relatives. After a couple of days of thinking about these Massachusetts ancestors, I began to wonder just how many other people might be descended from accused "witches." Is my family unusual, or are there a lot of us?

That brought me to something else (somewhat related) that I've always wondered: Just how many pilgrims were on board the Mayflower if so many people claim to be descendants? Was the little ship bigger than we thought? Let's take a little detour and look at the Mayflower issue first.

Here is what I found: "Of the 102 passengers of the Mayflower, 24 males produced children to carry on their surnames. And although approximately half of the Mayflower passengers died at the plantation during the harsh winter of 1620-21 (one passenger had died at sea while another was born before landing), today a staggering 35 million people claim an ancestral lineage that runs all the way back - sometimes through fifteen generations - to the original 24 males. That number represents 12 percent of the American population." (1)

If you'd like to figure out if you are one of the 35 million Mayflower descendants, you might start here. (2)

Now, back to the witches. Of the three accused witches I have found so far in my mother's family tree, two are 7th great aunts (that's just a short way to say my great, great, great, great, great, great, great aunts), and one is related by marriage, being the second wife of my 9th great grandfather. Since I believe that figuring out how many 7th great aunts I might have would be impossible because each family has a different number of children, it might be easier to take a look at that 9th great grandfather to get an idea how many others share a relationship with him.

According to a chart I found, I should have a total of 2,048 9th great grandparents, and so do you. Sounds like a lot, right? Considering we each have four grandparents, 8 great grandparents, 16 great great grandparents, you can count up by generation and see just how it happens. (3)

I'm pretty sure that means that my 9th great grandfather and his wife are related to a whole lot of other people and their families.

Looking at another chart that shows potential descendants (allowing all hypothetical families just three children), if I'm interpreting correctly my 9th great grandfather would have something like 236,196 living descendants. So I'm guessing that, just like in the Mayflower example above, it's not that unusual for modern-day Americans to find that they are descended from either accusers or accused at the witch trials. (4)

If you'd like to find out if you are related to any of the "witches," this site gives a list of those arrested for witchcraft, those found guilty and executed, the one who refused to enter a plea and was tortured to death, those who were pardoned, those who escaped from prison, and a great deal more. (5)

If you'd like to dig a little deeper into family tree math and even find out about "relatedness coefficients" you're going to love this article by Jeffrey Rosenthal. The Bedouin quote at the beginning of this post came from that article. I think it perfectly explains why I cried and had nightmares when I found out about my relatives being accused of witchcraft. (6)

Next: Two Sarahs and Mary, Accused as Witches

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Sources

1. How Many People Are Descended From the Mayflower Passengers? History News Network, http://historynewsnetwork.org/blog/7360 

2. Are You One of 35 Million Mayflower Descendants? Here's How to Find Out. Family History Daily, http://familyhistorydaily.com/genealogy-help-and-how-to/are-you-one-of-35-million-mayflower-descendants-heres-how-to-find-out/

3. Number of Persons in Your Ancestry. The Cajuns.com: Genealogy, History, and Culture. http://www.thecajuns.com/ancestry.htm

4. How Big is Your Family Tree? Mon Valley History, by Mike Donaldson. Hosted by Rootsweb. http://freepages.genealogy.rootsweb.ancestry.com/~pamonval/howbig.html

5. The Salem Witch Trials Victims: Who Were They? By Rebecca Beatrice Brooks, History of Massachusetts Blog. http://historyofmassachusetts.org/salem-witch-trials-victims/

6. The Mathematics of Your Next Family Reunion, by Jeffrey Rosenthal. +Plus Magazine; Living Mathematics. https://plus.maths.org/content/mathematics-your-next-family-reunion.

7. Arresting a Witch, illustration by Howard Pyle to accompany "The Second Generation of Englishmen in America," by T. W. Higginson, Harper's New Monthly Magazine, Vol. 67, (June - November), 1883: 221. From Wikimedia Commons. 
https://commons.wikimedia.org/wiki/Howard_Pyle#/media/File:ArrestingAWitch-Pyle.jpg