## Friday, November 04, 2011

### Math & Genealogy - it does a family good!

If you were born on this planet, in the last 80,000 +/- a few years, you may not know it, but we are all pretty much the same.   In fact, we are 99.5% genetically the same..  And rather than bore you about the birds and bees, and genetics, let's talk about something really neat - math!   A subject we can all "relate" to in terms of genealogy and families.

Our genes were handed down from our parents and their parents before them.  We also are familiar with the phrase that we refer to based on our ancestral DNA, such as "I am 1/2 French or 1/8 Indian".

Well, my friends, before you move onto the next blog, here is a spoiler - the total accumulation of your ancestors, going back to 100AD or several generations, totals nearly 4.3 billion living at that time!!!   Pretty incredible, and you would think someone should get an award with that many ancestors!  How is that even possible??

Let me show you how I came up with this number, but first, lets start with a simple example.  If your parents were born in France and you were born in the USA, you would be 100% French.   This is because you are 1/2 of each parental blood line.  Now, consider if you were born in the USA, but your mother was 50% French, and your father was 50% German, that would mean you are 25% French and 25% German.

Staying with our French side of the family, lets continue back further in time, to say 1099 AD, and the question is, are these people still French?    Oui, ils sont Français!   Now, if we go further back to 100 AD, then it gets a bit difficult because at that time, they were known as Gauls, and were under Roman rule.     And where did the Gauls come from?  Check out wiki for more details on the history, but I am sure you get the point.

To determine what the TOTAL number of ancestors I have going back to 100AD, I need to make some assumptions and use a little bit of math, using a geometric progression of 2^n or "2 raised to the nth power", where n is the generation in question.  This means that if 2^3, you multiple 2*2*2.

To illustrate further, lets go back 3 generations:
- 1st generation:   parents - 2^1 is 2
- 2nd generation:  grandparents - 2^2 is 4
- 3rd generation:  great-grandparents - 2^3 is 8

To get the total number of ancestors, we sum up all 3 generations to get 2+4+8 or 14.  There is even a  formula for this so we can tackle those bigger numbers, which is 2*(2^n-1), again where n = generations. Again, we find that the total number of ancestors, going back 3 generations would be: 2*(2^3-1) or 2*7=14.

Now we can figure out how many ancestors I have going back to 100AD.  First we need to figure out how many generations.  If we assume that each "generation" is about 20-60 years (I will explain this in another blog), we just need to calculate the number of years passed and divide those by 20 or 60.   This gives us 2011-100 = 1911 years / 60 years, or 32 generations.

Therefore, the total number of people that existed 32 generations ago would be 2^32, or about 4.3 billion!   Just so you know, we recently passed the 7 billion mark on the planet, this year!   To see how many TOTAL ancestors that would be since 100AD, we have about 9  billion!   That's a huge number and I must say, sounds TOO large, considering.   More research will need to be done on this, but for now, lets see what comments are posted and if anyone can find any mistakes in the math or assumptions.

In conclusion, when you consider that the human species on this planet has been around for some time before 100 AD, then one might ask how many humans have really lived since the beginning of "time"?   In addition, one may realize that with this many ancestors, we must have one common to most if not ALL of us, which means, we are all related!

This is really amazing and why, even though I have a heritage from a few different countries, when you start going back further, it starts to blend all together.   That is why I like to consider my origins as planet Earth and I also have a heck of a lot of cousin!   Of course, if you look forward 2000 years, and we spread out into the cosmos, populating other planets like Mars, imagine what they may be calling themselves and us.