Thursday, October 14, 2010

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.


drransom said...

But what makes you so sure the world is coherent? Dreams always seem coherent when you're having them; it's only when you wake up that you realize how incoherent they were. (Or at least that's how my dreams are, maybe yours are different.)

In other words, P(world seems coherent|world is a dream) ≈ 1, or at least it's high. So the fact that the world seems coherent doesn't do much as evidence that the world is not a dream.

If I suddenly woke up and was like "oh, that was a dream" that would verify that the world we exist in now is a dream. [1] So I'd count "the world is a dream" as a statement that can be verified, but not falsified (just as existential propositions are generally easy to verify but difficult to falsify).

I think the space of possible dreams is at least uncountable. Consider any dream D in which an integer n makes an appearance. Then for every real number r there is a possible dream D' that is like D but where n is replaced with r. The set of all the D''s is uncountable.

[1] Of course, that leaves the question of whether that world is also a dream, but we're talking about this world, not that one.

miller said...

Of course, I'm considering an abstract concept of "dream", a philosophical dream. Philosophical dreams have about as much in common with dreams as philosophical zombies have with zombies.

But let's say that this philosophical dream is incoherent, but it also puts us in a state of mind which is unable to recognize it as such. I'm... uh... not really sure what predictions we can derive from this. I guess we can't derive anything, since it would lead us to distrust the very process by which we derive things.

DeralterChemiker said...

What is it that drives first year graduate students into such bizarre philosophical discussions? I remember my own discussions at that time. Those concerns disappeared in my thirties as reality closed in.

Larry Hamelin said...

As a "scientist", I of course agree with you that the statement, "I might be living (or living 'in') a coherent dream," is uninteresting.

However, as a philosopher, I find the statement, "The statement, 'I might be living a coherent dream,' is uninteresting," to be very interesting indeed.

That's the real value of philosophy, I think: can you give a good, compelling and interesting account of why the supposed difference between "dream" and "reality" is itself uninteresting?

Larry Hamelin said...

Those concerns disappeared in my thirties as reality closed in.

I'm sorry for you. I think the willingness to consider "bizarre" ideas has kept me young, at least at heart, well into my late forties.

drransom said...

Do you have a link to a description of philosophical dreams? I'm familiar with philosophical zombies but not with this sort of philosophical dream.

miller said...

Dr Ransom, that's because I made it up. :P

I mean, when I first heard the question, I interpreted it as a life-long dream, perhaps dreamt by a brain in a jar. Perhaps this brain in a jar lives in a very different kind of universe, though apparently not so different that dreams don't exist.

I did not interpret the question as asking whether I'm currently in the same kind of dream that I have every night, and if I'll wake up within a few hours. That's just a different question entirely. And it doesn't have as good a lead-in to cosmology.

DeralterChemiker said...

Nobels are won for physics, and other real-world achievements, not for interpreting dreams.

drransom said...

I didn't interpret it that way either! But I don't think much hinges on that issue: the key point is that the assumption that an incoherent dream would be identifiable as incoherent from the perspective of a person within the dream is unwarranted. In which case (apparent) coherence is not much by way of evidence against the dream hypothesis.