I’d be very interested in a concrete construction of a (mathematical) universe in which, in some reasonable sense that remains to be made precise, two ‘orthogonal pattern-universes’ (preferably each containing ‘agents’ or ‘sophisticated computational systems’) live on ‘the same fundamental substrate’. One of the many reasons I’m struggling to make this precise is that I want there to be some condition which meaningfully rules out trivial constructions in which the low-level specification of such a universe can be decomposed into a pair (s1,s2) such that s1 and s2 are ‘independent’, everything in the first pattern-universe is a function only of s1, and everything in the second pattern-universe is a function only of s2. (Of course, I’d also be happy with an explanation why this is a bad question :).)
The way I was thinking about it, the mathematical toy model would literally have the structure of microstates and macrostates. What we need is a set of (lawfully, deterministically) evolving microstates in which certain macrostate partitions (macroscopic regularities, like pressure) are statistically maintained throughout the evolution. And then, for my point, we’d need two different macrostate partitions (or sets of macrostate partitions) such that each one is statistically preserved. That is, complex macroscopic patterns it self-replicate (a human tends to stay in the macrostate partition of “the human being alive”). And they are mostly independent (humans can’t easily learn about the completely different partition, otherwise they’d already be in the same partition).
In the direction of “not making it trivial”, I think there’s an irresolvable tension. If by “not making it trivial” you mean “s1 and s2 don’t obviously look independent to us”, then we can get this, but it’s pretty arbitrary. I think the true name of “whether s1 and s2 are independent” is “statistical mutual information (of the macrostates)”. And then, them being independent is exactly what we’re searching for. That is, it wouldn’t make sense to ask for “independent pattern-universes coexisting on the same substrate”, while at the same time for “the pattern-universes (macrostate partitions) not to be truly independent”.
I think this successfully captures the fact that my point/realization is, at its heart, trivial. And still, possibly deconfusing about the observer-dependence of world-modelling.
I’d be very interested in a concrete construction of a (mathematical) universe in which, in some reasonable sense that remains to be made precise, two ‘orthogonal pattern-universes’ (preferably each containing ‘agents’ or ‘sophisticated computational systems’) live on ‘the same fundamental substrate’. One of the many reasons I’m struggling to make this precise is that I want there to be some condition which meaningfully rules out trivial constructions in which the low-level specification of such a universe can be decomposed into a pair (s1,s2) such that s1 and s2 are ‘independent’, everything in the first pattern-universe is a function only of s1, and everything in the second pattern-universe is a function only of s2. (Of course, I’d also be happy with an explanation why this is a bad question :).)
I think that’s the right next question!
The way I was thinking about it, the mathematical toy model would literally have the structure of microstates and macrostates. What we need is a set of (lawfully, deterministically) evolving microstates in which certain macrostate partitions (macroscopic regularities, like pressure) are statistically maintained throughout the evolution. And then, for my point, we’d need two different macrostate partitions (or sets of macrostate partitions) such that each one is statistically preserved. That is, complex macroscopic patterns it self-replicate (a human tends to stay in the macrostate partition of “the human being alive”). And they are mostly independent (humans can’t easily learn about the completely different partition, otherwise they’d already be in the same partition).
In the direction of “not making it trivial”, I think there’s an irresolvable tension. If by “not making it trivial” you mean “s1 and s2 don’t obviously look independent to us”, then we can get this, but it’s pretty arbitrary. I think the true name of “whether s1 and s2 are independent” is “statistical mutual information (of the macrostates)”. And then, them being independent is exactly what we’re searching for. That is, it wouldn’t make sense to ask for “independent pattern-universes coexisting on the same substrate”, while at the same time for “the pattern-universes (macrostate partitions) not to be truly independent”.
I think this successfully captures the fact that my point/realization is, at its heart, trivial. And still, possibly deconfusing about the observer-dependence of world-modelling.