A coherent dream

One of my friends asked me what I think of the idea that we're just living in a coherent dream.

There are two different responses to this claim.  The first is to say that it's uninteresting, because it makes no predictions which diverge from a more typical view.  So why should we care?

However, I would take a different tack.  I think that this claim is uninteresting, because it does make predictions, and those predictions are perpetually falsified.  A false claim is not very interesting, and this one appears to be fantastically false.

This seems like a rather pointless philosophical exercise, but I want to go through the reasoning because as I will explain in a later post, it's relevant to theoretical physics!

Let's take the assumption that all the world is a dream.  There are all sorts of dreams it could be.  Relatively few of these dreams will be coherent; the vast majority will be incoherent.  However, as I can see around me, the dream has been at least coherent for the duration of my life.  So I can eliminate a lot of possible dreams that the world could be.

Of all the possibilities left over, a few will be coherent, but the vast majority are only briefly coherent during my life so far.  So given that the world is a dream, I predict that the dream will descend into incoherence in the next instant.

Hypothesis: The world is a dream.
Prediction: The future will be incoherent.
Results: It still looks coherent to me.
Conclusion: The world is not a dream.

If you were paying close attention, you might have noticed that I snuck in an extra assumption there.  I was implicitly assuming that all possible dreams are equally likely.  How do we even enumerate dreams?  It's not clear to me that the set of all possible dreams is a countable set.  Furthermore, even if we did enumerate them, why should we believe each one equally likely?  This is not true of real dreams.  We have semi-coherent dreams all the time, even though there are a lot more ways for dreams to be completely incoherent.

Another one of my friends objected to the very idea of assigning probabilities to the different possibilities.  Probabilities apply to ensembles, and all we have is the one universe.  He's arguing from a frequentist interpretation of probabilities, while I very consciously apply a Bayesian interpretation.  From a Bayesian perspective, we need to start with some prior probabilities of the different dream possibilities, and from these we make our predictions.  From a frequentist perspective, probabilities apply only to ensembles, so prior probabilities are invalid.

I'm extremely partial to Bayesian statistics, but a good Bayesian knows that you should vary the prior probabilities to see if the conclusion is robust.

So... if all possible dream are equally likely, then we predict that the future is almost certainly incoherent.  This prediction is false, so the claim is false, and therefore uninteresting.

On the other hand, let's say that not all possible dreams are equally likely.  Let's say that the dream will most certainly be coherent.  Then the claim is uninteresting because it makes no predictions.

So either way, we conclude that the claim is uninteresting.  One wonders why I ever blogged about it.  As we'll soon see, very similar reasoning can actually be fruitful when applied in cosmology.