Yesterday, I wrote a length about pigeonholes and cats. But did I get carried away? Much as I hate to presume that you've read that post - I don't think this is going to make much sense if you haven't...
I'm not the kind of person who lets a blog post fester and evolve before posting; I'm the kind of person who will write a blog post and stick it up immediately. Publish and be damned.
Having read back yesterday's post, I wrote the following:
"Of course, given so many years, the genes of Henry IV will have spread themselves wide throughout the population and so many of us will be distantly related to him. But the only way to prove that would be to take DNA samples."
I got lost in my own words when writing this and there are two distinct problems with that short assertion.
The first is to suggest that DNA samples would prove relationship to Henry IV. I must put my hand up here and admit that I slipped between the idea of mathematic proof and the common meaning of the word without flagging it up. What I meant of course, was that DNA testing would show that it was either very likely or very unlikely that we were related to Henry IV.
DNA testing is an exact science but that shouldn't be taken to mean that the results are definitite in the pure mathematical sense. Say Henry IV had a particular set of mutations in his DNA which also showed up my DNA. Then the overwhelmingly likely reason is that I am descended from him and this mutations have come to me that. Much less likely - but not impossible - is that exactly the same set of mutations has arisen by chance in a completely separate line and I am not related to Henry IV.
The second problem with my assertion is that I said the "only way to prove..." when talking about DNA testing. There is no way to prove in the mathematical sense that I (or anyone else) is related to Henry IV. (That's an argument for another day, although I can make it rigorous, I promise) there is another way which doesn't involve DNA testing, and gives about as much certain and it's very simple.
Evolution tells us that humans evolved from an ape-like ancestor. At some point in the past there must have been a common ancestor from which all humans are descended. Every human is descended from that ancestor, including Henry IV and so we are all related to Henry IV.
So - I hear you not asking - why isn't that rigorous. The chances of evolution happening twice are very slim. Very slim indeed. But they are not zero. So it's theoretically possible that life began twice, completely indedependently, and in both cases, animals identical to humans evolved and Henry IV is one of those lines and I'm in the other.
At this point, please don't mistake me for some kind of nutter. I'm not. Obviously evolution of humans hasn't happened in parallel twice on earth. But the point is that the chances of it happening are not zero, and so we can't say in the mathematical sense that we have proved it didn't happen - even if we have shown beyond reasonable doubt that it didn't. But note that there isn't a pigeonhole - abstract or otherwise - in sight.
One footnote here is to note that we can easily show - beyond reasonable doubt - that we are all related to Henry IV but not that we are descended from him directly.
And that's why I like to write things in Tippex - they correct themselves...