## Are You Related to Confucius?

I recently read an interesting argument claiming that we are all descendants of Confucius. Basically, the argument goes like this:

No matter who you are, you came from a mother and a father (I won’t go into details). So, in your family tree, the part **behind** **you** has two branches, like this:

The same goes for your mother and father, and their mothers and fathers, and so on. Thus, continuing on back the line, you see a family tree like this

And it just keeps going and going and going. Now, an interesting mathematical feature of this tree is that, as your move backward in time, each generation has **twice as many branches** as the generation that precedes it (roughly speaking). Go back a hundred or so generations to the time of Confucius–that means that the number of branches in your family tree at that time is roughly **2 raised to the 99th power!**

Now, 2^99 = **633825300114114700748351602688 **(thank you, **WolframAlpha!**) A reasonable estimate is that, at the time of Confucius, there were only something like 250000000 (250 million) people **total**. Each of those 2^99 spots in your family tree has to be filled by **someone**, which means, on average, each person in existence at that time had to fill roughly **2535301200456458802993** of the spots in your family tree. It’s virtually a **statistical impossibility** that Confucius wasn’t filling one of those spots.

I guess that makes us cousins?

*Click here to see more in Probability.*

That is very narrow-minded thinking. This argument deliberately forgets several key factors. The first fact missing is that it is not at all entirely impossible for us to share more than one common ancestor. The second is the fact that many of us are the product of the same race repeatedly in-breeding. If this was not true, then there would be only one race and no different physical characteristics. It is possible that we have an ancestor that goes far beyond the years of Confucius, presumably from Africa.

Wouldn’t the fact that Confucius had 2 kids, and given that even one of them had his/her own kids mean that the population in world right now should be around 3.1e29?