Categories: Genealogy, Technologies

Genealogy is an educational and empowering endeavor. What usually starts out as mere curiosity can grow into a hobby and then into a full blown obsession. There are numerous pathways to take as one begins to explore a particular line, and the discoveries are as exciting as finding buried treasure. When tracing one’s own genealogy, it can be truly inspiring — indeed, researching your own family has the capacity to change your perspective about yourself, your family, and even strangers around you.

Regions long settled by people of a specific culture are particularly interesting to explore, genealogically speaking. In our own south Louisiana, family ties criss cross in hatch patterns that would make a patchwork quilt look like a straight line. After 20 years of my own genealogical exploration, I can attest to the simply joy of wonder and amazement that comes when I learn of a new ancestor in my tree.

There’s also an analytical side to genealogy. As a mathematician and computer scientist, I enjoy bringing that perspective to various interests of mine; it’s a fun way to describe my interests and hobbies. The relationships in genealogy most certainly lend themselves to certain mathematical principles, and I’d like to explore those here. If you are timid about math, I will do my utmost to explain things in detail, and I hope you come out with a better understanding and appreciation of the discipline of genealogy.

Quantifying Identity

Our identity is often tied to some outstanding characteristic that we possess. For many of us, our family name provides us with a foundation of how we see ourselves. It is also the most common starting point for someone who is taking their first steps in genealogy — we start with our father and then go to his father, and so on and so on.

Other characteristics reinforce our identity, including aspects of our physicality. Skin tone and color, facial features, and other constructs like build and height reveal insights into our family and the genetics that we have inherited from them. Yet in today’s busy and absorbed world, complexity is eschewed; the abridged and summarized view of things is always preferable. Yet is identity really that simple? By looking at these factors alone, are we grossly simplifying our true identity and missing out on the bigger picture? What if we could see ourselves and others around us in a richer, more analytical light than merely their last names or what they look like?

One of the challenges of genealogy is to comprehend the true nature of who we are and from whom we are descended. We often think of ourselves as a product of our parents, and them as a product of theirs. Beyond two or three generations, we are completely removed from personally knowing our ancestors due to the limits of human lifespan. If our family is fortunate enough to have old photographs or tintypes, we can get a glimpse into how they looked, but those opportunities tend to be more rare than not.

Un Parmi Plein d’Autres Mondes

I propose a different way of looking at your identity: the concept of “Un Parmi Plein d’Autres Mondes” (one of many others). This view is based on the precepts of reproductive biology which dictate that a male and a female come together in a union, combining their respective reproductive contributions to form an offspring. While it is true that science and technology are pushing these boundaries today through multi-party fertilization and other interesting techniques, I will maintain focus on the binary relationship of the natural order of reproduction which has been the model of creating offspring since time immemorial.

This model yields a “tree” that can be navigated as it grows in the number of “leaves.” To illustrate how this tree grows, I suggest a simple exercise. To start, get a pencil and a sheet of paper. The, at the bottom of the sheet, draw a single small circle and put your initials in it. This circle represents you. Now, draw two circles above your circle —be sure to draw these two circles next to each other, but not too close. These are your parents. Put their respective initials in their circles, then connect them to your circle by drawing a line from each. I’ve shown my own drawing below, along with some helpful annotations.

Your drawing shows the relationship between you and your parents. Both of them have contributed their respective genetics to you; hence, you are 50% your father and 50% your mother. You have two parents, so you can say that you are composed of 2 people of the 1st generation above you.

Now, above your father’s circle, draw two circles side by side. These are his parents. If you know their initials, put them there, and draw the lines to connect those circles to your father’s circle. Do the same for your mother’s parents. Follow the steps correctly and you will have six circles on the page (not counting your own): your two parents, and their two parents, respectively. This shows that you are now composed of 6 people up to 2 generations above you (your grandparents are one generation 2, and your parents are generation 1).

If you continue this exercise into the 3rd generation, you will add eight more circles (two circles for each of your grandparents), and there will be a total of 8 + 4 + 2 = 14 circles (again, do not count your own circle). In that state of the diagram, you are composed of 14 individuals.

The truth of the matter is that you the sum of many, many people, and the true scope is impossible to obtain because genealogies only go so far. However, this exercise is not meant to give an actual number; it’s sole purpose is to demonstrate the scale of growth as you add generation after generation to your illustration.

Exploring The Math

Just within a few more steps, you will begin to see a pattern emerging: each new generation that you add appears to double the number of people who become part of your overall makeup. In mathematics, this type of problem can be expressed succinctly in a function which is the summation of an exponent:

The result of this equation is the number of people who are part of your ancestry within a variable number of generations we will denote as x. Don’t let the mathematical notation or formula intimidate you. It’s merely a compact, concise notation that I’ll break down.

If we plug in different numbers for x (the number of generations we’re interested in examining), we’ll get the following results:

• 1 generation up: f(1) = 2¹ = 2 individuals
• 2 generations up: f(2) = 2¹ + 2² = 6 individuals
• 3 generations up: f(3) = 2¹ + 2² + 2³ = 14 individuals
• 4 generations up: f(4) = 2¹ + 2² + 2³ + 2⁴ = 30 individuals
• 5 generations up: f(5) = 2¹ + 2² + 2³ + 2⁴ + 2⁵ = 62 individuals
• 6 generations up: f(6) = 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ = 126 individuals
• 7 generations up: f(7) = 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ = 254 individuals
• 8 generations up: f(8) = 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ + 2⁸ = 510 individuals

As you can see above, each additional generation more than doubles the number of individuals from the previous generation.

It turns out that we can conveniently express this relationship in a more compact notation that doesn’t require the summation. We simply add one to the exponent and subtract 2 from that value to get the result:

where x is the number of generations we are interested in. This new formula applied with the values of x in the above table will yield the same results. For each higher generation we consider, the number of individuals contributing to our genetic makeup and hence, our identity, more than doubles. To verify this, we can use a principle from calculus by taking the limit of the number of people in generation x+1 divided by the number of people in generation x.

The limit is 2. This simply means that we can be assured that the number of individuals that are added we consider another generation is at least two times the previous amount (it is actually double the number of the previous generation plus 2). This confirms that after a just a few generations, it can become quite unwieldy to determine our entire ancestor profile.

Examining Assumptions

While I’ve derived a simple formula for determining your ancestor count up to a specific generation, there is an underlying assumption that must be made to ensure the answer is accurate: no two members of the same generation can share the same parent. If that were the case, then the true number would be less than the one provided by the formula. In nature, this exception would only occur if either a full or half-brother and sister produced an offspring together. While not likely, it is important nonetheless to view the result of the equation as a maximum if not equal number of ancestors up to that generation.

Summary

The Greek aphorism “Know Thyself” is very much apropos. Your identity is yours to project and advertise however you desire. You may choose to emphasize your Acadian, African, Creole, German, Irish, or other identity — I respect this is as a personal choice. Always bear in mind, though, that you are a composite of many, many people who have contributed to your genetic makeup. We are all truly Un Parmi Plein d’Autres Mondes. Being aware of this fact (and the mathematics behind it), along with the continual building of your ancestral tree will bring continuing levity and balance to your self identification, as well as an appreciation of your fellow Louisiana kinsmen.

— Boisy Pitre