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them as our clocks. For example, if a fossil is in a sediment with 120-million-year-old igneous rock above it and 130-million-year-old igneous rock below it, you know the fossil dates from somewhere between 120 million and 130 million years ago. That’s how all the dates I mention in this chapter are arrived at. They are all approximate dates, not to be taken as too precise.
    Uranium-238 is not the only radioactive isotope we can use as a clock. There are plenty of others, with a wonderfully wide spread of half-lives. For example, carbon-14 has a half-life of only 5,730 years, which makes it useful for archaeologists looking at human history. It is a beautiful fact that many of the different radioactive clocks have overlapping timescales, so we can use them to check up on each other. And they always agree.
    The carbon-14 clock works in a different way from the others. It doesn’t involve igneous rocks but uses the remains of living bodies themselves, for example old wood. It is one of the fastest of our radioactive clocks, but 5,730 years is still much longer than a human lifetime, so you might ask how we know it is the half-life of carbon-14, let alone how we know that 4.5 billion years is the half-life of uranium-238! The answer is easy. We don’t have to wait for half of the atoms to decay. We can measure the rate of decay of only a tiny fraction of the atoms, and work out the half-life (quarter-life, hundredth-life, etc.) from that.
    A ride back in time
    Let’s do another thought experiment. Take a few companions and get in a time machine. Fire up the engine and zoom back ten thousand years. Open the door and have a look at the people you meet. If you happen to land in what is now Iraq, they’ll be in the process of inventing agriculture. In most other places they’ll be ‘hunter-gatherers’, moving from place to place, hunting wild animals and gathering wild berries, nuts and roots. You won’t be able to understand what they say and they will be wearing very different clothes (if any). Nevertheless, if you dress them in modern clothes and give them modern haircuts, they will be indistinguishable from modern people (or no more different from some modern people than people are different from one another today). And they will be fully capable of breeding with any of the modern people on board your time machine.
    Now, take one volunteer from among them (perhaps your 400-greats-grandfather, because this is approximately the time when he might have lived) and set off again in your time machine, back another ten thousand years: to twenty thousand years ago, where you have a chance to meet your 800-greats-grandparents. This time the people you see will all be hunter-gatherers but, once again, their bodies will be those of fully modern humans and, once again, they will be perfectly capable of interbreeding with modern people and producing fertile offspring. Take one of them with you in the time machine, and set off another ten thousand years into the past. Keep on doing this, hopping back in steps of ten thousand years, at each stop picking up a new passenger and taking him or her back to the past.
    The point is that eventually, after a lot of ten-thousand-year hops, perhaps when you’ve gone a million years into the past, you’ll begin to notice that the people you meet when you emerge from the time machine are definitely different from us, and can’t interbreed with the people who boarded with you at the start of its journey. But they will be capable of breeding with the latest additions to the passenger list , who are almost as ancient as they are themselves.
    I’m just making the same point as I made before – about gradual change being imperceptible, like the moving hour hand of a watch – but using a different thought experiment. It’s worth saying in two different ways, because it is so important and yet – quite understandably – so hard for some people to appreciate.
    Let’s resume our journey into the