Does Your Existence Tell Us Anything About the Universe?

In a Nutshell

Ok, let’s toss a coin. Why not?

If it lands Heads, World A is created. A world containing a single person, with a black beard.

If it lands Tails, World B is created. This has two people. A black beard and a brown beard.

You wake up in complete darkness. You can’t see the colour of your beard. So what’s the chance you’re in World B?

At first sight, 1/2 seems the obvious answer. Heads and Tails are equally likely and you have nothing else to go on. But hold on a bit — there’s only one person in World A and two in World B.

So perhaps the probability that you are in World B isn’t 1/2 after all. Perhaps it’s 2/3.

This is essentially the intuition behind what philosophers call the Self-Indication Assumption, or SIA. Other things equal, you are more likely to live in the world containing more observers. Seems obvious. But is it really as obvious as it seems? To find out, let’s turn on the light.

Now, what colour is your beard? It’s black! But a black beard is certain in World A and only a 50-50 chance in World B.

The new information therefore favours World A.

Now look at it another way.

Before the light came on, World B was twice as likely because it had two people in it, not one. But only one of the two has a black beard. So the chance that we’re in World A is the same as that we’re in World B.

We are back to 50-50.

Same experiment. Same coin. Same black beard.

Different answers.

How come?

The disagreement comes from what we thought our own existence told us before the light was switched on. Is a world more probable simply because it contains more opportunities for someone like you to exist or to observe it? The Self-Indication Assumption says Yes. The alternative view, called the Self-Sampling Assumption (SSA), says No. We should take things at face value.

And that brings us to a fascinating thought experiment known as the Presumptuous Philosopher.

Imagine you are a physicist considering two theories of the universe. Both on the face of it seem equally plausible.

There is just one difference.

Theory A predicts a universe containing an enormous number of people like us, while Theory B predicts a universe containing far fewer. If we apply SIA straightforwardly, the fact that we exist appears to provide evidence for Theory A, for the simple reason that there are so many more people like us in that view of the universe. Our presumptuous philosopher declares, therefore, that we need not wait for any more experiments. He can settle the matter right away. How? Because he points out that he exists, you exist, we all exist, and that’s much more likely to be the case in the massively populated universe that Theory A envisages.

But suppose now that exciting new evidence from a particle accelerator starts strongly favouring Theory B. How strong would that evidence have to become before it overcame the enormous advantage Theory A acquired merely by predicting vastly more observers?

I don’t think intuition gives us an easy way out.

Should the fact that I exist really make me favour a universe containing the hugely greater number of observers even if the evidence of the experiments points heavily the other way? SIA suggests that it should. But do we really want to be like the Presumptuous Philosopher who says that experiments make Theory B 100 times more likely than Theory A but let’s ignore that — because there are 1,000 times more people in a universe where Theory A is true.

So which assumption is right, the SIA or the SSA?

I’m simply not sure, but I’m willing to be persuaded.

But perhaps that is the most interesting thing about these puzzles. We started with a fair coin and asked whether it landed Heads or Tails. We ended up asking whether the mere fact that we are here should count as evidence about the sort of universe we live in.

That’s quite a lot to get from the toss of a coin.