Abstract: If we assume that any universe can be modeled as a computer program which has been running for finitely many steps, then we can assign a multiverse-address to every event by combining its world-program with the number of steps into the world-program where it occurs. We define a probability distribution over multiverse-addresses called a Finite Occamian Multiverse (FOM). FOMs assign negligible probability mass to being a Boltzmann brain or to being in a universes that implements the Many Worlds Interpretation of quantum mechanics.

One explanation of existence is the Tegmark level 4 multiverse, the idea that all coherent mathematical structures exist, and our universe is one of them. To make this meaningful, we must add a probability distribution over mathematical structures, effectively assigning each a degree of existence. Assume that the universe we live in can be fully modeled as a computer program, and that that program, and the number of steps it's been running for, are both finite. (Note that it's not clear whether our universe is finite or infinite; our universe is either spatially infinite, or expanding outwards at a rate greater than or equal to the speed of light, but there's no observation we could make inside the universe that would distinguish these two possibilities.) Call the program that implements our universe a world-program, W.  This could be implemented in any programming language - it doesn't really matter which, since we can translate between languages by prepending some stuff to translate.

Now, suppose we choose a particular event in the universe - an atom emitting a photon, say - and we want to find a corresponding operation in the world-program. We could, in principle, run W until it starts working on the part of spacetime we care about, and count the steps. Call the number of steps leading up to this event T. Taken together, the pair (W,T) uniquely identifies a place, not just in the universe, but in the space of all possible universes. Call any such pair (W,T) a multiverse-address.

Now, suppose we observe an event. What should be our prior probability distribution over multiverse-addresses for that event? That is, for a given event (W,T), what is P(W=X and T=Y)?

Preceded by:  There just has to be something more, you know?  Followed by:  Physicalism: consciousness as the last sense.

Contents:  1. An epistemic difficulty  2. How and why to be a materialist

An epistemic difficulty

Like many readers of this blog, I am a materialist.  Like many still, I was not always.  Long ago, the now-rhetorical ponderings in the preceding post in fact delivered the fatal blow to my nagging suspicion that somehow, materialism just isn't enough.

By materialism, I mean the belief that the world and people are composed entirely of something called matter (a.k.a.  energy), which physics currently best understands as consisting of particles (a.k.a.  waves).  If physics reformulates these notions, materialism can adjust with it, leading some to prefer the term "physicalism".

Now, I encounter people all the time who, because of education or disillusionment, have abandoned most aspects of religion, yet still believe in more than one than one kind of reality.  It's often called "being spiritual".  People often think it feels better than the alternative (see Joy in the merely real), but it also persists for what people experience as an epistemic concern:

The inability to reconcile the "experiencing self" concept with one's notion of physical reality.

A non-materialist thought experiment.

Okay, so you don't exactly believe in the God of the Abrahamic scriptures verbatim who punishes and sets things on fire and lives in the sky.  But still, there just has to be something more than just matter and energy, doesn't there?  You just feel it.  If you don't, try to remember when you did, or at least empathize with someone you know who does.  After all, you have a mind, you think, you feel — you feel for crying out loud — and you must realize that can't be made entirely of things like carbon and hydrogen atoms, which are basically just dots with other dots swirling around them.  Okay, maybe they're waves, but at least sometimes they act like dots.  Start with a few swirling dots… now add more… keep going, until it equals love.  It just doesn't seem to capture it.

In fact, now that you think about it, you know your mind exists.  It's right there: it's you.  Your "experiencing self".  Maybe you call it a spirit or soul; I don't want to fix too rigid a description in case it wouldn't quite match your own.  But cogito-ergo-sum, it's definitely there!  By contrast, this particle business is just a mathematical concept — a very smart one, of course — thought of by scientists to explain and predict a bunch of carefully designed and important measurements.  Yes, it does that extremely well, and you're not downplaying that.  But that doesn't explain how you see blue, or taste strawberry — something you have direct access to.  Particles might not even exist, if that means anything to say.  It might just be that observation itself follows a mathematical pattern that we can understand better by visualizing dots and waves.  They might not be real.

So actually, your mind or spirit — that thing you feel, that you — is much more certain an extant than scientific "matter".  That must be something very important to understand!  Certainly you can tell your mind has different parts to it: hearing, seeing, reasoning, moving, remembering, empathizing, picturing, yearning… When you think of all the things you can remember alone — or could remember — the complexity of all that data is mindbogglingly vast.  Imagine the task of actually having to take it all apart and describe it completely… it could take aeons…