What Do You Think You Are The Science of What Makes You You - Brian Clegg Page 0,4
scary, as it’s only little old 2 that is being multiplied by itself. But to put it another way, that is 18.5 billion billion (if you want to be precise, it’s 18,446,744,073,709, 551,615 grains). A whole lot of rice. Very roughly it’s about 300 billion tonnes of the stuff – the amount the world would currently consume in 600 years.
The sheer volume of rice involved is fascinating – but what has this to do with genealogy? Exponential doubling also comes into a family tree due to a simple fact that we’re all aware of, even though we tend not to think through the consequences. Each individual person on a family tree – you, for instance – will have exactly two biological parents. This means that if we ignore siblings (we will come back to them) and simply trace back an individual’s tree into history, the number of people in each preceding generation doubles. In your tree you will have two parents, four grandparents, eight great grandparents and so on.‡
Linear versus exponential growth: the linear line goes up one each time, the exponential line doubles each time.
Just like the chessboard rice grains, these numbers do not initially seem to be very extreme, until we start to combine them with a realistic count of generations going back in time. For convenience, generations used to be treated as 25 years, because it’s easy to do the maths and it was a reasonable approximation for the average age at which people became parents. These days, 30 is more like a sensible average, but for most of history the value tended to be lower, so 25 may be the best number. We’ll try both.
Just like the chessboard, the count of your directly linked ancestors goes through exponential doubling – in this case doubling with every generation, rather than with every square on the board. There’s one of you, three people with your two parents, seven people with your four grandparents and so on – that familiar series of 1, 3, 7, 15… So, looking back n generations in your past, we get to a total of 2n–1 people, in a tree stretching back into history from you as the root. And this is true for every one of the near 8 billion people alive today (which brings in siblings). Each individual has a tree stretching back in history the same way.
THE MISSING BILLIONS
Now for the big reveal. It has been estimated that around 110 billion people have lived since Homo sapiens came into existence a couple of hundred thousand years ago. That’s obviously a guestimate, but not a bad one. The figure that is most often quoted is 108 billion, based on a calculation by a group called PRB. I’ve made it 110 billion, partly because 108 billion gives a spurious feeling of accuracy and partly because one of their assumptions, that Homo sapiens has been around for 50,000 years, is a significant underestimate based on current data.
So, how many generations does that 110 billion represent? Just using your personal tree, we would need to go back around 37 generations. This is because 236 is around 68 billion and 237 is around 137 billion. If there were a totally separate tree for each person alive today, we would only need about 34 generations. Clearly that’s a reduction too far, as siblings will share the same tree – so it would be realistic to go for, say, 36 generations.
If we use 25-year generations that takes us back just 900 years into the past, or with 30-year generations we get back 1,080 years. Using this simplistic calculation, humans should have only been around for 900 to 1,000 years. In reality, though, we know that history goes back several thousand years further and archaeologically and palaeontologically speaking we can say that Homo sapiens has been in existence as a species for perhaps 200,000 years. Being generous and using the longer figure of 30 years for a generation, that’s 6,666 generations. Which would mean 26666 people in the single family tree starting from you, a phenomenally large number. It’s approximately 4 × 102006. To put that number into context, the number of atoms in the universe is often estimated to be around 1080.
Clearly, something has gone horribly wrong with this calculation. What these numbers reflect is that the nice well-ordered family tree we get from genealogists has been pruned incredibly tightly. We don’t have neat, spreading trees, but complex tangles. Go back a few generations and you will find