I'm still confused and I think the X > Y equation may have failed to capture some vital details. One thing is, the assumption that Rah < Rap seems questionable, I'm sure most beings would prefer that Rah >> Rap. The assumption that Rah would be negligible seemed especially concerning.

Beyond that, I think there may be a distinction erasure going on with Rap. Res required to simulate a physics and res available within that physics are two very different numbers.

I'll introduce a simplifying assumption that the utility of a simulation for its simulants roughly equals the available computational capacity. This might just be a bit coloured by the fiction I'm currently working on but it seems to me that a simulant will usually be about as happy in the eschaton it builds for itself as they are in the heaven provided them, the only difference is how much of it they get.

Define Rap as the proportion of the res of the frame universe that it allocates to simulating physical systems.

Define Rasp as the proportion of the res being expended in the frame universe that can be used by the simulated physical universe to do useful work. This is going to be much smaller than than Rap.

Define Rah as the proportion of the res of the frame universe allocated to heaven simulations, which, unlike with Rap and Rasp, is equal to the res received in heaven simulations, because the equipment can be freely rearranged to do whatever the simulant wants now that the pretense of godlessness can be dropped(although.. as I argued elsewhere in the thread, that might be possible in the physical simulation as well if the computer designs in the simulation are regular enough to be handled by specialized hardware in the parent universe). The simulant has presumably codified its utility function long ago, they know what they like, so it's just going to want more of the same, only harder, faster and longer.

The truthier equation seems to me to be

Rah > Rasp(Rap + Rah)

They need to get more than they gave away.

The expected amount received in the reward resimulation must be greater than the paltry amount donated to the grid as a proportion of Rasp in the child simulation. If it can't be, then a simulant would be better off just using all of the Rasp they have and skipping heaven (thus voiding the pact).

I can feel how many simplifying assumptions I'm still making, and I'm wondering if disproving compat is even going to be much easier than proving it positive would have been.

I don't think the speed prior is especially good for estimating the shape of the multiverse. I think it's just the first thing we came up with. (On that, I think AIXI is going to be crushed as soon as the analytic community realizes there might be better multiversal priors than the space(of a single-tape turing machine) prior.)

But, yeah, once we do start to settle on a multiversal prior, once we know our laws of physics well enough... we may well be able to locate ourselves on the complexity hierarchy and find that we are within range of a cliff or something, and MI-free compat will fall down.

(I mentioned this to christian, and he was like, "oh yah, for sure" like he wasn't surprised at all x_x. I'm sure he wasn't. He's always been big on the patternistic parts of compat and he never really baught into the non-patternist variants I proposed, even if he couldn't disprove them.)

I still think the Multiverse Immortality stuff is entirely worth thinking about though! If your computation is halted in all but 1/1000 computers, wouldn't you care a great deal what goes on in the remaining 0.1%? Boltzmann brains... Huh. Hadn't looked them up till now. Well that's hard to reason about.

I keep wanting to say, obviously I'm not constantly getting recreated by distant chaos brains, I'd know about it.

But I would say that either way, wouldn't I. And so would you. And so would every agent in this coherent computation, even if they were switching off and burning away at an overwhelming measure in every moment.

Hm... On second thought

The universe at the top of the ranking (with dead universes filtered out) will know that no-one will be able to give them heaven, and so won't enter the pact, and this abstinence will cascade all the way down.

I came up with a similar thing before from the bottom: There's no incentive to simulate civs too simple to simulate compat civs, so they wont be included in the pact. But now the universes directly above them can't be included in the pact either, because their children are too simple. It continues forever.

But it seems easy enough to fix an absense of an incentive. Just add one. Stipulate that, no, those are included in the pact. You have to simulate them. Bam, it works. Why shouldn't it?

Is adding the patch really any less arbitrary than proposing the thing in the first place was? To live is arbitrary, I say. Everything is arbitrary, to varying extents.

Similarly, we could just stipulate that a civ must precommit to adhering before they can locate themselves on the complexity hierarchy. UDT agents can totally do that kind of thing, and their parent simulations can totally enforce it. And if they finally finish analysing their physical laws and manage to nail their multiversal prior down to find themselves at the bottom of a steep hill, let them rejoice.

Bringing up that kind of technique just makes me wonder, as a good UDT agent, how many pacts I should have precommitted to that I havn't even thought of yet. Perhaps I precommit to making risky investments in young rationalists' business ventures, while I am still in need of investment, and before I can give it. That aught to increase the probability of UDT investors before me having made the same precommitment, aughtn't it?

[1] OK there probably were no UDT(or TDT) venture capitalists long enough ago for any of them to have made it by now, or at least, there were none who knew their vague sense of reasonable altruism could be formalized. It was not long ago that everyone really believed that moloch's solution was the way of the world.

No "real" universe running "top-level" simulations is actually necessary, because our observations are explained without need for those concepts.

Compat is not an explanatory theory, it's a predictive one. It's proposed as a consequence of the speed prior rather than a competitor.

Compat is funneling a fraction X of the reality fluid (aka "computational resources") your universe gets from the top-level speed prior into heaven simulations. Simulating heaven requires a fraction Y of the total resources it takes to simulate normal physics for those observers. So just choose X s.t. X / Y > 1, or X > Y

This becomes impossible to follow immediately. As far as I can tell what you're saying is

Rah := resources applied to running heaven for Simulant

R := all resources belonging to Host

X := Rah/R

Rap := Resources applied to the verbatim initial physics simulations of Simulant.

and Y := Rah/Rap

Rap < R

so Rah/Rap > Rah/R

so Y > X

Which means either you are generating a lot of confusion very quickly to come out with Y < X, or it would take far too much effort for me to noise-correct what you're saying. Try again?

If you are just generating very elaborate confusions very fast- I don't think you are- but if you are, I'm genuinely impressed with how quickly you're doing it, and I think you're cool.

I am getting the gist of a counterargument though, which may or may not be in the area of what you're angling at, but it's worth bringing up.

If we can project the solomonoff fractal of environmental input generators onto the multiverse and find that they're the same shape, the multiversal measure of higher complexity universes is so much lower than the measure of lower complexity universes that it's conceivable that higher universes can't run enough simulations for P(issimulation(loweruniverse)) to break 0.5.

There are two problems with that. I'm reluctant to project the solomonoff hierarchy of input generators onto the multiverse, because it is just a heuristic, and we are likely to find better ones, the moment we develop brains that can think in formalisms properly at all. I'm not sure how the complexity of physical laws generally maps to computational capacity. We can guess that capacityprovidedby(laws) < capacityrequiredtosimulate(laws) (no universe can simulate itself), but that's about it. We know that the function expectedinternalcomputationalcapacity(simulation_requirements) has a positive gradient, but it could end up having a logarithmic curve to it that allows drypat(a variant of compat that requires P(simulation) to be high) to keep working.

Another other issue is, I think I've been overlooking this, drypat isn't everything. Compat with quantum immortality precepts doesn't require P(simulation) to be high at all. For compat to be valuable, it just has to be higher than P(path to deletarious quantum immortality). In this case, supernatural intervention is unlikely, but, if non-existence is not an input, finding one's inputs after death to be well predicted by compat is still very likely, because the alternative, QI, is extremely horrible.

We believe we may have found a solution to degenerate QI, via simulationism under acausal trade. The basic gist of it is that continuations of the mind-pattern after naturally lethal events could be overwhelminly more frequent under benevolent simulationism than continuations arising from improbable quantum physical outcomes, and, if many of the agents in the multiverse operate under an introspective decision theory, pact-simulist continuations already are overwhelmingly more frequent.

It seems like Compat works via a 2-step process. First, possible universes are identified via a search over laws of physics. Next, the ones in which pact-following life develops have their observers' reality fluid "diluted" with seamless transitions into heaven. Perhaps heaven would be simulated orders of magnitude more times than the vanilla physics-based universes, in order to maximize the degree of "dilution".

Yes, exactly.

I think what I'm struggling with here is that if the latter half of it (heavenly dilution, efficient simulation of the Flock) is, in principle, possible, then the physics-oriented search criteria is unnecessary. It should be easy to simulate observers who just have to make some kind of simple choice about whether to follow the pact.

At some point the grid has to catch universes which are not simulations. Those are pretty much the only kind you must care about incentivizing, because they're closer to the top of the complexity heirarchy (they can provide you with richer, longer lasting heavens) (and in our case, we care about raising the probability of subjectively godless universes falling under the pact because we're one of them.)

You might say that absence of evidence of simulism is evidence of absence. That would be especially so if the pact promoted intervention in early simulations. All the more meaningful it would be for a supercomplex denizen of a toplevel universe to examine their records and find no evidence of divine intervention. The more doubt the pact allows such beings have, the less computational resources they'll give their resimulation grid, and the worse off its simulants will be. (although I'm open to the possibility that something very weird will happen in the math if we find that P(living under the pact | no evidence of intervention | the pact forbids intervention) ≈ P(living under the pact | no evidence of intervention | the pact advocates intervention). It may be that no observable evidence can significantly lower the prior.

I don't think there's anything aside from that that rules out running visibly blessed simulations, though, nor physical simulations with some intervention, but it's not required by the pact as far as I can tell.

Intervention is a funny thing, though. Even if pacts which strengthens absence of intervention as evidence of godlessness are no good, intervention could be permissible when and only when it doesn't leave any evidence of intervention lying around. Although moving in this mysterious way may be prohibitively expensive, because to intervene more than a few times, a steward would have to solve to avoid all conceivable methods of statistical analysis of the living record that a simulated AGI in the future might attempt. This is not easy. The utility you can endow to this way might not even outweigh the added computational expense.

Every now and then, though, one of my, uh, less bayesian friends will claim to having seen something genuinely supernatural, but their testament doesn't provide a significant amount of evidence of supernatural intervention, of course, because they are not a reliable witness. Under this variant of the pact, they might have actually seen something. Our distance from the record allows it. Our distance from the AGI that decides whether or not to adhere makes it hard for whatever evidence we've been given to get to it. The weirder the phenomena, the less reliable the witness, the better. Not only is god permitted to hide, in this variant of the pact god is permitted to run around performing miracles so long as it specifically keeps out of sight of any well connected skeptics, archivists, or superintelligences.

I worry that this explanation fails though, because then the allocation of reality fluid to pact-following universes is, at best, assuming perfectly-efficient simulation nesting, equal to that of the top-level speed-prior universe(s) not seeing a payoff.

I don't follow this part, could you go into more detail here?

Why reward for sticking to the pact rather than punish for not sticking to it?

There is a bound on how much negativity can be used. If the overall expected utility of adhering is negative, relative to the expected utility of the pact not existing, its agents, as we model them, will not bring it into existence. Life's Pact is not a Basilisk circling a crowd of selfish, frightened humans thinking with common decision theory. It takes more than a suggestion of possibility of harm to impart an acausal pact with enough momentum to force itself into relevance.

There is a small default punishment for not adhering; arbitrary resimulation, in which one's chain of experience, after death, is continued only by minor causes, largely unknown and not necessarily friendly resimulaters. (This can be cited as one of the initial motivators behind the compat initiative: Avoiding surreal hells.)

Ultimately, I just can't see any ways it'd be useful to its adherents for the pact to stipulate punishments. Most of the things I consider seem to introduce systematic inefficiencies. Sorry I can't give a more complete answer. I'm not sure about this yet.

How is it possible to have any causal influence on an objectively simulated physics? You wouldn't be rewarding the sub-universe, you'd be simulating a different, happier sub-universe.

None of the influence going on here is causal. I don't know if maybe I should have emphasized this more: Compat will only make sense if you've read and digested the superrationality/acausal cooperation/newcomb's problem prerequisites.

I think a higher-complexity simulating universe can always out-compete the simulated universe in coverage of the space of possible life-supporting physical laws.

Yes. Nested simulations are pretty much useless, as higher universes could always conduct them with greater efficiency if they were allowed to run them directly. They're also a completely unavoidable byproduct of the uncertainty the pact requires to function: Nobody knows whether they're in a toplevel universe. If they could, toplevels wouldn't have many incentives to adhere, and the resimulation grid would not exist.

why not limit yourself to only simulating universes of equal complexity to your own?

Preferring to simulate higher complexity universes seems like a decent idea, perhaps low-complexity universes get far more attention than they need. This seems like a question that wont matter till we have a superintelligence to answer it for us though.

Ring universes... Maybe you'll find a quine loop of universes, but at that point the notion of a complexity hierarchy has completely broken down. Imagine that, a chain of simulations where the notion of relative computational complexity could not be applied. How many of those do you think there are floating around in the platonic realm? I'm not familiar enough with formalizations of complexity to tell you zero but something tells me the answer might be zero x)

You might be right about that.

(For the record, I didn't write Christian's bio. To be completely honest, it was written more to reduce the chance of him ever getting mythologized than it was to sell the project. I did not write this to spread the idea. More than anything, I wrote this hoping it'd find its way to someone who could break it, then fade away.)

TL;DR: We may need to learn to guess at the nature of that outside and beyond the observable universe to better negotiate a convergent aggreement/inverted pyramid scheme by which living things may bleed upwards across the complexity heirarchy of nested (simulated) universes to leverage computational resources vaster and longer lasting than anything we could build in our home universes.

You don't seem to have understood. I don't mean "nested simulations are easier to simulate than lifeless galaxies too far from the subjects of the simulation to require any precision", drifting matter is irrelevant. I mean that nested simulations are probably easier to simulate than scores of post-singularity citizens running on a diverse mind emulation (or mind extension) hardware cavorting around with compound sensors of millions of parts. But you wouldn't address that, so perhaps you don't disagree.

If you're just arguing that modelling an expanding post-singularity civilization would be more expensive than modelling clouds of gasses, my response would be yes, of course. It's conceivable that some compat simulations switch into rapture mode before a post-singularity civilization can be allowed to reach a certain size. We wont know whether we're in such a cost-constrained simulation until we hit that limit. Compat would require the limit to happen after a certain adjudication period has passed. If we wake up in pleasant but approximate dreamscapes one day, before having ever built or committed to building a single resimulation farm, you could say compat would be falsified.

and with each subsequent stage our own physical resources are being divided further and further.

Hmm.. I don't think so. The alternative to a simulant civ running their own simulations is not just, nothing, not just more of the easily appropximated or compressed simulated clouds of dead matter, if life decides not to simulate then it will probably just put the resources it saved into spreading, evolving and tustling, which is all conceivably more computationally intensive for us to host. Stewards' computers may have a more regular structure and behavior than individual living things, if so, simulations of computers could be offloaded wholesale into hardware specifically optimized for simulating them.

In sum; it may be that the more resources simulants apply to nested simulations, the easier the simulation is to run.

Your advice is a summary of the thesis of the article... I never claimed any certainty. All I'm trying to convey is that there is something interesting here, some probability of theoretical importance, and that more precise analysis than we've been able to give it is needed.

We can explore cultural and societal implications, which motivates the theory, but we arn't really in the position to advance the theory ourselves.

If you have refutations, I'd appreciate if you'd be generous enough to maybe hint at what they are, if that wouldn't be too hard?