My current beliefs say that there is a Tegmark 4 (or larger) multiverse, but there is no meaningful “reality fluid” or “probability” measure on it. We are all in this infinite multiverse, but there is no sense in which some parts of it exist more or are more likely than any other part. I have tried to illustrate these beliefs as an imaginary conversation between two people. My goal is to either share this belief, or more likely to get help from you in understanding why it is completely wrong.
A: Do you know what the game of life is?
B: Yes, of course, it is a cellular automaton. You start with a configuration of cells, and they update following a simple deterministic rule. It is a simple kind of simulated universe.
A: Did you know that when you run the game of life on an initial condition of a 2791 by 2791 square of live cells, and run it for long enough, creatures start to evolve. (Not true)
B: No. That’s amazing!
A: Yeah, these creatures have developed language and civilization. Time step 1,578,891,000,000,000 seems like it is a very important era for them, They have developed much technology, and it someone has developed the theory of a doomsday device that will kill everyone in their universe, and replace the entire thing with emptyness, but at the same time, many people are working hard on developing a way to stop him.
B:How do you know all this?
A: We have been simulating them on our computers. We have simulated up to that crucial time.
B: Wow, let me know what happens. I hope they find a way to stop him
A: Actually, the whole project is top secret now. The simulation will still be run, but nobody will ever know what happens.
B: Thats too bad. I was curious, but I still hope the creatures live long, happy, interesting lives.
A: What? Why do you hope that? It will never have any effect over you.
B: My utility function includes preferences between different universes even if I never get to know the result.
A: Oh, wait, I was wrong. It says here the whole project is canceled, and they have stopped simulating.
B: That is to bad, but I still hope they survive.
A: They won’t survive, we are not simulating them any more.
B: No, I am not talking about the simulation, I am talking about the simple set of mathematical laws that determine their world. I hope that those mathematical laws if run long enough do interesting things.
A: Even though you will never know, and it will never even be run in the real universe.
B: Yeah. It would still be beautiful if it never gets run and no one ever sees it.
A: Oh, wait. I missed something. It is not actually the game of life. It is a different cellular automaton they used. It says here that it is like the game of life, but the actual rules are really complicated, and take millions of bits to describe.
B: That is too bad. I still hope they survive, but not nearly as much.
A: Why not?
B: I think information theoretically simpler things are more important and more beautiful. It is a personal preference. It is much more desirable to me to have a complex interesting world come from simple initial conditions.
A: What if I told you I lied, and none of these simulations were run at all and never would be run. Would you have a preference over whether the simple configuration or the complex configuration had the life?
B: Yes, I would prefer if the simple configuration to have the life.
A: Is this some sort of Solomonoff probability measure thing?
B: No actually. It is independent of that. If the only existing things were this universe, I would still want laws of math to have creatures with long happy interesting lives arise from simple initial conditions.
A: Hmm, I guess I want that too. However, that is negligible compared to my preferences about things that really do exist.
B: That statement doesn’t mean much to me, because I don’t think this existence you are talking about is a real thing.
A: What? That doesn’t make any sense.
B: Actually, it all adds up to normality.
A: I see why you can still have preferences without existence, but what about beliefs?
B: What do you mean?
A: Without a concept of existence, you cannot have Solomonoff induction to tell you how likely different worlds are to exist.
B: I do not need it. I said I care more about simple universes than complicated ones, so I already make my decisions to maximize utility weighted by simplicity. It comes out exactly the same, I do not need to believe simple things exist more, because I already believe simple things matter more.
A: But then you don’t actually anticipate that you will observe simple things rather than complicated things.
B: I care about my actions more in the cases where I observe simple things, so I prepare for simple things to happen. What is the difference between that and anticipation?
A: I feel like there is something different, but I can’t quite put my finger on it. Do you care more about this world than that game of life world?
B: Well, I am not sure which one is simpler, so I don’t know, but it doesn’t matter. It is a lot easier for me to change our world than it is for me to change the game of life world. I therefore will make choices that roughly maximizes preferences about the future of this world in the simplest models.
A: Wait, if simplicity changes preferences, but does not change the level of existence, how do you explain the fact that we appear to be in a world that is simple? Isn’t that a priori extremely unlikely?
B: This is where it gets a little bit fuzzy, but I do not think that question makes sense. Unlikely by what measure? You are presupposing an existence measure on the collection of theoretical worlds just to ask that question.
A: Okay, it seems plausible, but kind of depressing to think that we do not exist.
B: Oh, I disagree! I am still a mind with free will, and I have the power to use that will to change my own little piece of mathematics — the output of my decision procedure. To me that feels incredibly beautiful, eternal, and important.