Each human being has two biological parents. Consequently, he has four grandparents, eight great-grandparents, sixteen great-great grandparents etc.
Tracing back for 30 generations, one has 2^30, or slightly more than one billion ancestors (at that generational level). The average generational gap is something like twenty years, so those ancestors lived about 600 years ago, in the Middle Ages perhaps. The population of the entire world breached one billion only in the 19th century. This suggests that some inbreeding had gone on, probably unwittingly. To avoid this controversy, one could argue that the one billion ancestors were not all alive simultaneously. But like compound interest, we can see that this exponential growth quickly takes us into perilous territory.
A conservative estimate for the total number of humans who have ever lived is about 100 billion. Over 37 generations, one would have had more ancestors than the number of humans who had ever been alive! But perhaps the models by the historians and anthropologists are unreliable, so let's jack it up to 50 generations, so that each person has more than one quadrillion ancestors. Hardly enough room (or carbon) on earth for that many people! All this without even breaking into the BC era.
Whether or not we evolved from more primitive lifeforms, we can make some conclusions from these considerations. To curb this exponential growth, it seems like we have to either truncate the backward projection (i.e. invoke some sort of "creation"), or accept that the calculated number of ancestors does not represent unique individuals. Unwitting incest becomes exponentially (I think) more likely as we go back in time, so I suppose it acts as a nice counterbalance.
Let's consider a bolder claim: Not too long ago, a woman walked the face of the earth, whose genetic content is in every single person alive today.
I did not make this up. It's actually a widely-accepted claim, and that woman even has the pompous name of Mitochondrial Eve. She was supposed to have lived about 200,000 years ago. Naturally, creationists would be tempted to see this as scientific vindication. The idea of a common ancestor to all living humans intrigued me enough, that I paused to think why this had to be the case. In the end, I was only able to conclude that it could have been the case, so I looked to the literature for a convincing argument.
First of all, we should remind ourselves why this is of any scientific interest. Apparently, each of us has mitochondrial DNA (mtDNA) which is inherited only from the mother. DNA carries our genetic information, which is supposed to give us our characteristics. Mitochondrial Eve, if she had existed, would thus be the Great Grand-mother of humanity today --- her extremely diluted blood would literally be coursing through every human vein today. (But see the wikipedia article for common misconceptions. I'm also not sure whether blood and mtDNA are related.)
How do we know she existed? According to my quick and probably careless research, it is not merely a theory dreamt up by geneticists, but even a simple mathematical fact. This got alarm bells in my head ringing, so I proceeded to look for a proof. It is stunningly elegant. The first thing to note is that each person has only one mother. Consider the set of mothers of all the people living today. This set is smaller than the number of people alive today. Now consider the set of mothers of mothers. This is a smaller set than the previous one. Then consider their mothers, and their mothers' mothers. We arrive at a sequence of sets of decreasing size, which eventually becomes a set with one member --- Mitochondrial Eve herself!
I found a number of problems with this supposed "proof". First of all, the sequence of sets is not required to decrease strictly. It only has to be non-increasing, in which case, we cannot conclude that it will eventually decrease to a singleton set. I've seen a slightly weakened claim in response to this: With near certainty, Mitochondrial Eve did exist. The "proof" of this assumes that there is a non-negligible probability that a mother has more than one daughter (which is probably true). In this case, the sequence of sets has to decrease in size eventually. (But why must it decrease to one? Why not zero???? Or two? Or 1 million???)
Of course, this line of reasoning doesn't explain where Mitochondrial Eve came from. We have nothing to worry about if we believe that she was simply put there by a deity of some sort. Otherwise, we would have to continue this ancestry chasing indefinitely. Dangerous territory. Also, note that there were other women alive alongside Mitochondrial Eve, but their line of daughters didn't manage to persist to the present day. Which prompts two questions, (i) Who was their Mitochondrial Eve? (ii) How likely is it that all of Mitochondrial Eve's contemporaries failed to leave behind a line of daughters over 200,000 years? Despite the fact that Mitochondrial Eve did? (Warning: anthropic reasoning imminent...)
Actually, I discovered that the proof was wrong. It leads to an absurd conclusion. Suppose we arrived at Mitochondrial Eve at the N-th step. That would mean that she is precisely the N-th maternal ancestor of all people alive today. Yes, that means you, your children, and your great-grandparents, (if they are still alive), have the same N-th maternal ancestor.
We abuse the the word "proof" in everyday language to prove all manner of things, which is fine. But the claimant of a mathematical proof ought to bear the full burden of proof.
Tracing back for 30 generations, one has 2^30, or slightly more than one billion ancestors (at that generational level). The average generational gap is something like twenty years, so those ancestors lived about 600 years ago, in the Middle Ages perhaps. The population of the entire world breached one billion only in the 19th century. This suggests that some inbreeding had gone on, probably unwittingly. To avoid this controversy, one could argue that the one billion ancestors were not all alive simultaneously. But like compound interest, we can see that this exponential growth quickly takes us into perilous territory.
A conservative estimate for the total number of humans who have ever lived is about 100 billion. Over 37 generations, one would have had more ancestors than the number of humans who had ever been alive! But perhaps the models by the historians and anthropologists are unreliable, so let's jack it up to 50 generations, so that each person has more than one quadrillion ancestors. Hardly enough room (or carbon) on earth for that many people! All this without even breaking into the BC era.
Whether or not we evolved from more primitive lifeforms, we can make some conclusions from these considerations. To curb this exponential growth, it seems like we have to either truncate the backward projection (i.e. invoke some sort of "creation"), or accept that the calculated number of ancestors does not represent unique individuals. Unwitting incest becomes exponentially (I think) more likely as we go back in time, so I suppose it acts as a nice counterbalance.
Let's consider a bolder claim: Not too long ago, a woman walked the face of the earth, whose genetic content is in every single person alive today.
I did not make this up. It's actually a widely-accepted claim, and that woman even has the pompous name of Mitochondrial Eve. She was supposed to have lived about 200,000 years ago. Naturally, creationists would be tempted to see this as scientific vindication. The idea of a common ancestor to all living humans intrigued me enough, that I paused to think why this had to be the case. In the end, I was only able to conclude that it could have been the case, so I looked to the literature for a convincing argument.
First of all, we should remind ourselves why this is of any scientific interest. Apparently, each of us has mitochondrial DNA (mtDNA) which is inherited only from the mother. DNA carries our genetic information, which is supposed to give us our characteristics. Mitochondrial Eve, if she had existed, would thus be the Great Grand-mother of humanity today --- her extremely diluted blood would literally be coursing through every human vein today. (But see the wikipedia article for common misconceptions. I'm also not sure whether blood and mtDNA are related.)
How do we know she existed? According to my quick and probably careless research, it is not merely a theory dreamt up by geneticists, but even a simple mathematical fact. This got alarm bells in my head ringing, so I proceeded to look for a proof. It is stunningly elegant. The first thing to note is that each person has only one mother. Consider the set of mothers of all the people living today. This set is smaller than the number of people alive today. Now consider the set of mothers of mothers. This is a smaller set than the previous one. Then consider their mothers, and their mothers' mothers. We arrive at a sequence of sets of decreasing size, which eventually becomes a set with one member --- Mitochondrial Eve herself!
I found a number of problems with this supposed "proof". First of all, the sequence of sets is not required to decrease strictly. It only has to be non-increasing, in which case, we cannot conclude that it will eventually decrease to a singleton set. I've seen a slightly weakened claim in response to this: With near certainty, Mitochondrial Eve did exist. The "proof" of this assumes that there is a non-negligible probability that a mother has more than one daughter (which is probably true). In this case, the sequence of sets has to decrease in size eventually. (But why must it decrease to one? Why not zero???? Or two? Or 1 million???)
Of course, this line of reasoning doesn't explain where Mitochondrial Eve came from. We have nothing to worry about if we believe that she was simply put there by a deity of some sort. Otherwise, we would have to continue this ancestry chasing indefinitely. Dangerous territory. Also, note that there were other women alive alongside Mitochondrial Eve, but their line of daughters didn't manage to persist to the present day. Which prompts two questions, (i) Who was their Mitochondrial Eve? (ii) How likely is it that all of Mitochondrial Eve's contemporaries failed to leave behind a line of daughters over 200,000 years? Despite the fact that Mitochondrial Eve did? (Warning: anthropic reasoning imminent...)
Actually, I discovered that the proof was wrong. It leads to an absurd conclusion. Suppose we arrived at Mitochondrial Eve at the N-th step. That would mean that she is precisely the N-th maternal ancestor of all people alive today. Yes, that means you, your children, and your great-grandparents, (if they are still alive), have the same N-th maternal ancestor.
We abuse the the word "proof" in everyday language to prove all manner of things, which is fine. But the claimant of a mathematical proof ought to bear the full burden of proof.
