Sunday, July 18, 2010

The Brain sings about the brain

Mouse sing song about brain. Brain and brain! What is brain?

[First person to identify Star Trek reference gets a bottle of Saurian Brandy]

Possible worlds and 'modal realism'

This approximately 6 minute clip does a good job of sketching the notion of possible worlds, first explored in any detail by Leibniz. The basic idea can be described as follows:

Assume that there is a vast library of books. God owns this library. Each volume in the collection is an exhaustive description of a way the universe could have turned out. Now, exactly one of those volumes describes our universe (its title "Kronos"). Imagine that volume is red, while all the others are blue.

If you were to grab any of the blue books and begin reading, you would notice some differences between what it says and what you find described in Kronos. In fact, there are a good many volumes that do not contain chapters describing your life, my life, indeed, the life of planet Earth.
On the other hand, there are certain things you will find in every one of the volumes. For instance, the sections on mathematics will be the same. The various geometries (Euclidean and non-Euclidean) will all be there, with the same truths about triangles for instance. Logical truths are invariant across worlds. In every world, in every volume, if some statement P is true, then P is true.

Now Leibniz did not commit to the reality of these other worlds. Ours is the only actual world. At points he does seem to claim that given enough time, or endless time, all of the possibilities must become actual at some time or another, this full actualization being somehow a manifestation of the perfection of God. So, for instance, granted that it is possible that I quarterback the Tom Landry coached Cowboys, even though it didn't happen this time around, it will..eventually. This is not quite Nietzsche's eternal return of the same, but akin. An eternal return of the very similar. Of course, given enough time, Nietzsche's thesis would also hold. Question: that guy way in the future, quarterbacking the Cowboys, is he really me?

David Lewis, as you can see from the video, took seriously the idea that the possible worlds all those blue volumes describe do exist 'side by side' with our world. This is an idea taken up by some cosmologists as well. According to their view, the reason our world seems so surprisingly fine tuned for life is that our world is one of a perhaps infinite set of universes, each of which bubbles up out of a quantum substrate. Each bubble, when it erupts, sets up, crystallizes, or instantiates one set of possible natural laws. Think of the bubbles as setting parameters, much as you and every other player of some game or sim can set parameters as they play the computer simulation. In neighboring universes, gravitation is stronger, so life as we know it never developed. Ditto for other natural laws and constants. So, it is really not surprising, in fact it is inevitable that life occurred. No miracle, no designer necessary.

Of course, one might suspect that the many worlds hypothesis substitutes one big freaking mystery, with an even larger freaking mystery. Where, before we only had to explain the existence of one universe, and one set of natural laws and constants, now we have to explain the substrate and mechanism that generates a possibly infinite set of universes, each with one set of natural laws and constants. Phew!

Now, getting back to the philosophers; why would Lewis want to postulate possible worlds? It boils down to a view of declarative statements as 'truth bearers'. When I say that Felix is on the mat, that statement is true if the cat I refer to is indeed on the mat at the moment of my utterance. But how can counterfactual claims be true or false, or are they just false, because counterfactual, after all? Well, if you want to call all counterfactuals false, you have to throw quite alot of baby out with the bathwater.

If this keyboard were to right now, fall to earth, it would accelerate at 32 feet per second / per second. At least that is what I believe will happen if my admittedly foggy memory of physics is a reliable guide. Now, that claim is counterfactual, and most of us would say that it is true. Right? Well, if true, what is it describing? Clearly not my keyboard which was at that time squarely and safely planted on my computer desk's leaf. Lewis has an easy answer, modeled on factual statements like 'my keyboard is right now being pounded by my fingers'. In a neighboring possible world, one very much like this one, the keyboard did travel downward at the described acceleration. That is what makes the counterfactual true.

Bizzaro-world I know. Philosophers find the damnedest things to worry about.