Anthropics in a Tegmark Multiverse

Best explanation by what standard? By the standard where you rank universes from least complex to most complex! You cannot do two different rankings simultaneously.

So then, are you saying that you do not think that a simplicity prior on your brain is a good idea?

How do you describe your thoughts all by themselves?

By describing the abstract structure of that 'network of causal relationships' you were talking about?

Look, there's a Massive Philosophical Problem here which is "what do you take your thoughts to be?" But whatever answer you give, other than just "a universe plus a pointer" I can carry on repeating my trick.

It sounds as though you want to give the answer "an equivalence class of universes-plus-pointers, where (W1, P1) ~ (W2, P2) iff the being at P1 'has the same thoughts' as the being at P2". But this is no good if we don't know what "thoughts" are yet.

ETA: Just wanted to say that the post was very interesting, regardless of whether I think I can refute it, and I hope LW will continue to see discussions like this.

Putting probability distributions over observer moments is a critical first step in this program.

There are some problems with the notion of 'observer moments'. I'm inclined to think they are unresolvable, but perhaps you have some ideas for how to tackle them.

I've already mentioned the problem of the 'boundary' of a subjective state. For instance, consider an old memory which it would take you a long time to 'dredge up'. How is that different in principle from having some information written down somewhere in a notebook in front of you? Is that old memory part of your 'observer moment'? (But then how about a slightly fresher memory)? Is the notebook? (But then how about that thick reference book on your shelf)? It seems obvious to me that there's no principled line to be drawn here.

Then there's the problem of whether a given system is an observer or not. For instance, Dennett is notorious for (correctly!) attributing 'intentional states' to a thermostat: you can view it as an agent who believes the temperature is x and wants it to be y. But is a thermostat an observer? Presumably not, but again it seems that there's no principled line to be drawn between thermostats and people.

And then there's the problem of 'how many observers'. E.g. Is a split-brain patient two observers or one? How about an ordinary person? How much of the corpus callosum needs to be severed to get two observers?

Finally, if A is much much cleverer, more alert, and knowledgeable than B then A ought to have a greater density of 'observer moments' than B? But exactly how much greater? The idea that there's a principled way of determining this seems overoptimistic.

(Going a little off topic: I've actually been thinking along vaguely similar lines to you just lately. I've been trying to devise an approach to the mind-body problem in terms of "perspectives". My overall goal was to try to 'do justice to' the common intuition that a subjective point of view must be determinate and cannot only half-exist, while maintaining the substance of Dennett's position which implies that there may be no fact of the matter as to whether a person is conscious and what they're conscious of. My key idea is that (a) there exist genuine facts of the form "From perspective P, such-and-such would be consciously experienced" but (b) the perspectives themselves do not exist - they're not part of the "state of the world". (Instead, they're "perspectives from which the state of the world manifests itself"). An analogy would be how, in mathematical logic, we have this duality between theories and models, or more broadly, between syntax and semantics. The "syntax side" enables you to state and prove things about stuff that exists, but the syntax itself doesn't exist. (In the same way that there's no such set as ZFC.)

My 'perspectives' are essentially the same as your 'pointers-to-observers'. However, I'd want to stress the fact that perspectives are ubiquitous - e.g. you can take the perspective of a rock, or a thermostat. And you can take the perspective of a person in many different ways, with no fact of the matter about which is right, or even whether it's right to take one. (But from any given perspective, all the subjective facts are nice and 'determinate'.)

It never occurred to me to try to consider the Kolmogorov complexities of perspectives. It's an interesting idea, but it's hard to wrap one's head around given that there are an unlimited number of ways of defining the same person's perspective.)

I believe my only preferences are over experiences. I care nothing about a world without observers, and I care about our world exactly insofar as the world has an effect on the experiences of certain observers.

How do you know this? (What do you think you know, how do you think you know it?) Your brain might contain this belief. Should you draw a conclusion from this fact that what the belief claims is true? Presumably, if your brain contained a belief that 15+23=36, you'll have a process that would not stop at accepting this claim just because your brain claimed it's so, you'll be able to do better. There is no magical truth-machine in your mind, everything should be suspect, understood and believed stronger only when further reflection permits.

What "certain observers"? You were talking only about your own experiences. How do you take into account experiences of other agents? (Or even yourself at other moments, or given alternative observations, imperfect copies.)