Thought experiment 14: The box that can change the past

Newcomb’s Box is a paradox that divides opinion – and casts doubt on our usual understanding of cause and effect.

Illustration by Marie Montocchio / Ikon Images

In front of you are two boxes. In the first, Box A, there is £1,000. The box is transparent. You can see the money. The second box, Box B, is opaque and may or may not contain £1,000,000. You have a choice. You can either take Box B (and Box B only), or you can take both boxes. Whatever money is in the boxes is yours. But here’s the catch: you have been told that there is a very good predictor, let’s call her Meg, who is almost always right. And if Meg predicted that you’d take both boxes, she’ll have left Box B empty. If she predicted you’d only take Box B, she’ll have stuffed it with that million quid.

So, what would you do? Take one box or two?

I’ve long been a two-boxer. But the puzzle divides people. Back in 2016, Brexit referendum year, I debated it in the pages of the Guardian with a one-boxer, the Cambridge philosopher Arif Ahmed. Since then, he’s been appointed free speech tsar for the Office for Students (the higher education regulator), and has declared that university education should be “the intellectual equivalent of stepping into a boxing ring”.

But from boxing rings back to boxes. The Guardian ran a poll and 31,854 readers voted. I moaned at the time that, as with Brexit, a slight majority (in this case, 53.5 per cent) had got it badly wrong – ie they were one-boxers and sided with Arif.

I’d failed to convince readers with the following argument: by the time you’re faced with the choice, Meg has already made her prediction. You cannot influence a decision made in the past by making a decision in the present. Meg has either put £1m into Box B or she has not. So you have nothing to lose by taking both boxes. Think of it this way. Imagine that Box B has transparent glass on the far side – the side you can’t see. Suppose a friend on this far side, looking into Box B, was permitted to communicate with you. What would their advice be? Surely to take both boxes. If the £1m is there, and you choose both boxes, it won’t disappear in a puff of smoke. It is irrational to take only Box B, because, in comparison, taking both boxes will always enrich you by an extra £1,000.

On the other hand, if Meg foresees that you’ll take both boxes, it appears you’ll miss out on a financial bonanza. If the choice is between being rational and being rich, Arif wrote, “I’ll take the money every time.”

Newcomb’s paradox, just described, is named after William Newcomb, an American theoretical physicist who devised the problem in 1960. But it only gathered prominence when the Harvard professor Robert Nozick resurrected it in an article in 1969. Nozick had heard about it at a party – “the most consequential party I have attended”. Over the years, he posed the problem to many people. “To almost everyone it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost equally on the problem, with large numbers thinking that the opposing half is just being silly.”

We don’t face Newcomb’s paradoxes in real life. But it has a similar structure to a more familiar problem in theology. The 16th-century pastor John Calvin thought that God has predetermined who would and who would not ascend to heaven. There’s nothing any of us can do about this. But Calvin also maintained that the best predictor of whether you’re to be saved is that you live an honourable, virtuous life. So, how to conduct yourself? On the one hand, if you don’t live your life in a righteous manner, it is almost certain you won’t be saved. On the other hand, since either you’re saved or you’re not, there isn’t much incentive to behave. In the year Nozick was writing about Newcomb’s paradox, the Northern Ireland footballer George Best trialled behavioural restraint. “In 1969 I gave up women and alcohol”, he said. “It was the worst 20 minutes of my life.” For two-boxer Calvinists, George Best’s approach to life might make sense.

In fact, through conversations with the Australian philosopher Huw Price, I’ve had a rethink. My key assumption was that cause has to precede effect. You can cause things to happen in the future, but not the past. However (and mind-bending though this idea is), it turns out that our best understanding of quantum mechanics requires, or is at least compatible with, backwards causation, with things in the past being altered by things in the present or future.

If that’s right, the paradox dissolves. “Everyone agrees that if we can affect what the predictor did, we should one-box,” says Price. As for the charge that causation can only work forwards: “To an old pragmatist like me, causes are just means to ends. If you want B, and doing A gets you B, then A counts as a cause of B. I want the predictor to put the £1m in the opaque box, and one-boxing gets me that. So it counts as a cause!”

I could never have predicted it, but I’ve changed my mind about Newcomb’s Box. Haven’t changed my mind about Brexit, though.