Tag Archives: exponents

Math Tricks Prove You Have Famous Ancestors


Everyone’s been fascinated during recent years about delving into their ancestry and family history.

I did a little work on ancestry.com and it wasn’t too hard to trace my ancestry back to some people who fought in the United States Civil War, and then to some who fought in the Revolutionary War, which was pretty cool, since it qualified me to join the Sons of the American Revolution.

But then, I kept going and found that I am, among other things, descended from King Edward III of England and his son, Edward the Black Prince of Wales, and that Geoffrey Chaucer is my 16th great-uncle.

At first, this seemed amazing, and I thought, “Wow! What are the chances of such a thing?”

Actually, using some basic statistics and probability, the chances are very likely that you are related to someone famous from the Middle Ages (about 400 A.D. to 1500 A.D.) or earlier, in whatever region of the world your ancestry comes from. 

As an example, let’s assume you were born in 1980, and that on average, a new generation comes along every 25 years. Then, each of your two ancestors would be descended from two more parents, and so forth. So, a century before, in 1880, that you would have 2 x 2 x 2 x 2 ancestors, or 2 to the 4th power, which would be 16 great-great-grandparents.

Add another hundred years to trace back to 1780, and the number of spots to fill in your family tree would equal 2^8, or 256 potential ancestors.

In 1680, the number of spots to fill would increase to 2^12, or about 4,000 potential ancestors.

In 1580, 2^16 (about 64,000 ancestors)

In 1480, 2^20 (about a million ancestors)

In 1380, 2^24 (about 16 million ancestors)

In 1280, 2^28 (about 250 million ancestors)

Just for fun, go another 50 years to 1230 A.D., making the exponent a nice round 2^30, which is over a billion ancestors.

But in 1230, there were only about 400 million people living on Earth.  What does that mean?

It means that there are LOTS of people over-counted in that family tree, because the lines actually come back together over and over. Not just because second, third, and fourth cousins marry each other — if you go far enough in time, everyone is technically a cousin to everyone else.

So, this means that you are you are descended from a lot of different people by a lot of different lines of inheritance — lots of VERY DISTANT cousins marrying each other — no matter what your ethnic background is.  There are a billion slots that have to be filled in on the ancestral tree, and only 400 million people to put in them, so a lot of people have to be filling multiple slots on your ancestral tree.

Does this mean you are descended from every person who was alive in 1230 A.D.?  No — depending on your ethnic background, your ancestry could be focused on groups in the Americas, or south Africa, or southeast Asia, China, Japan, and so forth, since those groups did not largely mix with other groups worldwide until later in history; and plus, there were many people alive in 1230 A.D. who don’t have living descendants today.

But if you know some of your ancestors were from Europe or around the Mediterranean, then the odds are that anyone who was alive in 1230 A.D., lived in Europe or around the Mediterranean, and has living descendants, is likely one of your ancestors, including all of the Holy Roman Emperors, and the peasants they ruled; William the Conqueror and many of his knights; Lady Godiva; Pope Innocent III; and so on.  Basically, everyone you read about in the history books; the conquerors and the conquered, the famous and the unknown — if they had descendants, there’s a pretty good chance they’re one of your ancestors.

Pretty cool, huh?

Math tricks like this are fun to play with. If you enjoy learning things like this, you might enjoy taking the GMAT or the GRE. Contact me anytime to discuss options for test prep and tutoring on the SAT, ACT, LSAT, GMAT, GRE, and MCAT!