wasn’t sure what she had expected of Eschatology. Maybe a trailer home in Nevada, the walls coated with tabloid newspaper cuttings, the interior crammed with cameras and listening gear. Or perhaps the opposite extreme: an ultramodern facility with a giant virtual representation of the organization’s Mister Big beamed down from orbit, no doubt stroking his white cat.
But this office, here in the heart of Manhattan, was none of that. It was essentially ordinary. That made it all the more scary, of course.
Malenfant said now, ‘So tell me how you know we only have two hundred years.’
Cornelius smiled. ‘We’re going to play a game.’
Malenfant glared.
Cornelius reached under the table and produced a wooden box, sealed up. It had a single grooved outlet, with a wooden lever alongside. ‘In this box there are a number of balls. One of them has your name on it, Malenfant; the rest are blank. If you press the lever you will retrieve the balls one at a time, and you may inspect them. The retrieval will be truly random.
‘I won’t tell you how many balls the box contains. I won’t give you the opportunity to inspect the box, save to draw out the balls with the lever. But I promise you there are either ten balls in here – or a thousand. Now. Would you hazard which is the true number, ten or a thousand?’
‘Nope. Not without evidence.’
‘Very wise. Please, pull the lever.’
Malenfant drummed his fingers on the table top. Then he pressed the lever.
A small black marble popped into the slot. Malenfant inspected it; it was blank. Emma could see there was easily room for a thousand such balls in the box, if need be.
Malenfant scowled and pressed the lever again.
His name was on the third ball he produced.
‘There are ten balls in the box,’ said Malenfant immediately.
‘Why do you say that?’
‘Because if there was a thousand in there it’s not likely I’d reach myself so quickly.’
Cornelius nodded. ‘Your intuition is sound. This is an example of Bayes’s rule, which is a technique for assigning probabilities to competing hypotheses with only limited information. In fact –’ he hesitated, calculating ‘– the probability that you’re right is now two-thirds, on the basis of your ball being third out.’
Emma tried to figure that for herself. But, like most probability problems, the answer was counter-intuitive.
‘What’s your point, Cornelius?’
‘Let’s think about the future.’ Cornelius tapped the softscreen embedded in the tabletop before him. The small monitor before Emma lit up, and a schematic graph drew itself elegantly on the screen. It was a simple exponential curve, she recognized, a growth rising slowly at first, steepening up to a point labelled ‘now’. Cornelius said, ‘Here is a picture of the growth of the human population over time. You can see the steep rise in recent centuries. It is a remarkable fact that ten per cent of all the humans who have ever existed are alive now. More than five per cent of all humans, Malenfant, were born after you were …
‘But that is the past. Let’s imagine how the future might develop. Here are three possibilities.’ The curve continued to climb, steepening as it did so, climbing out of Emma’s frame. ‘This,’ said Cornelius, ‘is the scenario most of us would like to see. A continued expansion of human numbers. Presumably this would require a move off-planet.
‘Another possibility is this.’ A second curve extrapolated itself from the ‘now’ point, a smooth tip over to a flat horizontal line. ‘Perhaps our numbers will stabilize. We may settle for the resources of the Earth, find a way to manage our numbers and our planet indefinitely. A bucolic and unexciting picture, but perhaps it is acceptable.
‘But there is a third possibility.’ A third curve climbed a little way past the ‘now’ marker – then fell spectacularly to zero.
‘Jesus,’ said Malenfant. ‘A crash.’
‘Yes. Studies of the population numbers of other creatures, lower animals and insects, often show this sort of shape. Plague, famine, that sort of thing. For us, the end of the world, soon.
‘Now. You can see that in the first two cases, the vast majority of humans are yet to be born. Even if we stay on Earth, we estimate we have a billion years ahead of us before changes in the sun will render Earth’s biosphere unviable. Even in this restricted case we would have far more future than past.
‘And if we expand off-planet, if we achieve the kind of future you’re working for, Malenfant, the possibilities are much greater. Suppose we – or our engineered descendants – colonize the Galaxy. There are four hundred billion stars in the Galaxy, many of which will provide habitable environments for far longer than a mere billion years. Then the total human population, over time, might reach trillions of times its present number.’
‘… Oh. And that’s the problem,’ Malenfant said heavily.
‘You’re starting to see the argument,’ Cornelius said, approving.
‘I’m not,’ said Emma.
Malenfant said, ‘Remember his game with the balls and the box. Why are we here now? If we really are going on to the stars, you have to believe that you were born in the first one-billionth part of the total human population. And how likely is that? Don’t you get it, Emma? It’s as if I drew out my ball third out of a thousand –’
‘Far more unlikely than that, in fact,’ said Cornelius.
Malenfant got up and began to pace the room, excited. ‘Emma, I don’t know statistics from my elbow. But I used to think like this as a kid. Why am I alive now? Suppose we do go on to colonize the Galaxy. Then most of the humans who ever live will be vacuum-sucking cyborgs in some huge interstellar empire. And it’s far more likely that I’d be one of them than what I am. In fact the only pop curve where it’s reasonably likely that we’d find ourselves here, now, is –’
‘The crash,’ said Emma.
‘Yes,’ Cornelius said sombrely. ‘If there is a near-future extinction, it is overwhelmingly likely that we find ourselves alive within a few centuries of the present day. Simply because that is the period when most humans who ever lived, or who will ever live, will have been alive. Ourselves among them.’
‘I don’t believe this for a second,’ Emma said flatly.
‘It is impossible to prove, but hard to refute,’ said Cornelius. ‘Put it this way. Suppose I tell you the world will end tomorrow. You might think yourself unlucky that your natural life span has been cut short. But in fact, one in ten of all humans – that is, the people alive now – would be in the same boat as you.’ He smiled. ‘You work in Las Vegas. Ask around. Losing out to one in ten odds is unlucky, but not drastically so.’
Emma said, ‘You can’t argue from analogy like this. There are a fixed number of balls in that box. But the total number of possible humans depends on the undetermined
