Just A Random Question

I was reading one of the latest issues of New Scientist when I encountered an interesting question by a reader:

We all have two parents, four greatparents, eight great-greatgrandparents, sixteen great-great-greadgrandparents and so on and so forth. So if I want to draw a family tree up to 10 generations, I would have 1024 ancestors above me. Now, if I reseach my family tree for up to 40 generations, I would have 2⁴⁰ (which is about 10¹²) ancestors out there. This is clearly more than all the human being that have ever lived on Earth (approximately 10¹¹). Of course, I wouldn't have more ancestors than all the people that have ever lived, but what is wrong with my reasoning? Doesn't everyone have two parents?

p/s: The question is paraphrased to avoid copyright infringement.

This is something to ponder about. To be frank I haven't really figured it out thoroughly, but I will work hard this weekend. :)


Update: Haha, got it when I was on the way back from school (posted this one in the school computer lab). But obviously Shou Farn beat me to it, and his explanation is great!

*** Spoiler ***

Actually, the flaw in the argument is that, not all of our ancestors are unique / different. In other words, as you draw the family tree up many generations, you will eventually realize that some of the people will play many different roles in the family tree. For example, your mother's mother's father's mother's mother's father may be the same person as your father's mother's father's father's mother's father.

In fact, following the same line of thought, we can see that inbreeding must be happening in some way among human beings. By inbreeding I don't mean one person mating with his or her siblings (that would be disgusting). Instead, inbreeding can be understood as "the reunion of gene as it is passed down through different routes of family tree".

Let's just set up an example... Let's say Kenny is my daughter's son's son's son's daughter's son, and Maria is my son's son's daughter's daughter's daughter. Next, suppose I have this hypothetical, unique gene AB which is always passed down from one generation to another generation. Firstly, note that if no inbreeding has occured, the unique gene AB is only found in my direct offsprings. My daughter will have AB, my son will have AB, Kenny would have AB, Maria would have AB too. If a random person does not have AB, then he is not my offspring. However, AB is also remarkable in that it is a "marker" for the occurence of inbreeding - in a mating couple, if both persons have gene AB in their DNA, both of them must be my offsprings. In the case of Kenny and Maria, if they fall in love with each other and mate together, they are considered inbreeding. Or to use my earlier definition, the union of Kenny and Maria is the union of my AB gene.

Hope that I haven't bored you to death. :) But to me, this kind of thing is more interesting than the neural system.