Conscious beings can infer the physical contents and laws of their world in various ways - instinct that then fails to be contradicted by experience, trial and error, theory. But as Descartes noted, self-awareness logically necessitates at least one epistemic belief - the belief in the self.

Physics could in principle exist without consciousness - and many physics in Greater Reality, doubtless do exist unobserved by any local consciousnesses. The converse is not obviously true: it's not clear how a consciousness could exist without being embedded in some local physics. Much has been made about how physics is logically prior to consciousness, and perhaps the foregoing is why.

Nevertheless, conscious programs [by which I mean programs that more or less continuously notice that they exist] genuinely have a special kind of a priori knowledge of their own existence. In all counterfactuals of their own observation that can be ranked by these programs as "simple" or "likely" by these programs, one fact remains invariant: the fact of their own existence to observe that counterfactual. Utterly fantastic [/foreign/alien; our physics may be fantastic to some metaphysical foreigner] physics may be difficult for some such conscious programs to imagine; nevertheless it is conceivable. Not so with their own non-presence.

In this sense, it doesn't make sense to say that physics is logically prior to consciousness [ also known in this context as existence, sentience, self-awareness . . . ] - at least, not for conscious beings reasoning anthropically. When so reasoning, a conscious program must indeed take itself as the most prior invariant, with physics absolutely constrained exactly insofar as the self necessarily constrains it.

In what sense, then, do I claim the worlds in Greater Reality unobserved by any local consciousnesses can exist? They certainly can't interact with ours via local physics. My answer: It's not clear to me that all beings which have values or pursue things rationally or intelligently must do so consciously. It seems quite plausible to me that worlds in Greater Reality containing no consciousnesses local to themselves can logically interact with us when non-conscious beings in them acausally trade with our universe [equivalently, when our universe acausally trades with theirs].

So now we have two anthropic questions to answer:

1] Who else could we have been, and why are we these people?

and

2] Who and what is out there for us to trade with?

I'm going to put the second question aside for a moment, and take a closer look at the first one.

Who is "we"? Whatever is your opinion about the rank of the sentient population of Earth - whether it includes shrimp and beetles, or just magpies, chimps, and humans, or just adult humans - its exact number and character seems as arbitrary as physics itself. When reasoning about who "we" could have been, as soon as you bring in mere physical counterfactuals, that seems to provide an allowance for a rock falling on a young woman's head in a counterfactual world, eliminating her [ real in this world ] progeny. You might seek to leave this problem aside, when reasoning about who you could have been born as, among an invariant "us" - but physical reductionism implies that, in order for you to have been born as someone of the opposite sex and two towns over, something about that person's brain must have been different - implying that some differential must exist between this world and that counterfactual world, either in the laws of physics, or in the universe's initial conditions. Certainly my individual soul can be abstracted from this physics somewhat [or physics from it] - or I wouldn't be able to do ordinary physical-counterfactual reasoning, let alone anthropics. But there's no particular reason to think that local reality's popular collective of souls is, by default, uniquely enumerated-and-characterized as a set, separately from local reality's physics.

So we find that question [1] was misphrased. The first, simplest, foundational question I ask should not be "Who could we have been and why are we these people?". Is it, then "Who could I have been and why am I this person?" I don't think so; if it's me thinking, as Descartes said, well, it must be me existing. In «subjective anthropics» [ := anthropics done by a conscious being ], I'm the invariant. What changes is other things about my reality. So the proper question [or at least the most proper question I can think of, so far] is finally "What worlds could I have found myself in, and why do I find myself in this world?"

How can I [begin to] answer this question? And how can we answer question [2] above?

Beyond "apply a good algorithmic measure of complexity in the asubjective case, and in the subjective case, apply some measure of algorithmic complexity while keeping the self invariant", I don't know yet.

But I can give an example of how not to.

There is an idea going around - I'm honestly not sure exactly where it originated, but an example can be found in this post by searching on 'hottest' - that physically hotter worlds are more anthropically frequent, by virtue of having higher entropy [= lower information content], and thus, being "easier to point to". This idea doesn't make any sense to me. If you believe that probabilistic Shannon entropy is the best way to characterize simplicity, then probably the crux for you will be that I think Kolmogorov's model of information content, while not perfect, strictly supersedes Shannon's model.

Physically hotter worlds are harder to logically point to.

The reasons for this:

1. Worlds containing N+1 atoms-as-identified-by-thermodynamics contain at least one more free parameter that must be simulated, when compared to worlds containing N atoms-as-defined-by-thermodynamics.

2. Worlds where the fastest atom is moving with speed x/t-1, must progress physics at minimum every [t-1] time units, while worlds where the fastest atom is moving with speed x/t, must only progress physics at minimum every [t] time units. [ And more generally, worlds where the ith atom is moving at x/t-1 as compared to x/t must progress local physics around that atom a minimum of every [t-1] time units as compared to every [t] time units. ]

So "physically hotter worlds are simpler and therefore higher in reality-measure" doesn't map on to a good algorithmic concept of world-simplicity/world-plausibility.

Also, if anyone would be interested in my solutions to Carlsmith's various thought experiments [to which Carlsmith [and Yudkowsky for reposting the jackets thought experiment back in March] I am deeply indebted! h/ts!], including God's extreme coin toss with jackets and my own extra-extreme variant, I could publish those sometime.