Simulation Relationship To Parent

Various candidate rules that govern a simulation's relationship to its "parent", that is the outside world that runs it.

Ability Leakage - The simulated universe cannot violate the rules of the parent's universe in the parent's universe. For example, time flowing backward in the simulation cannot make time flow backward in the parent universe if the parent does not already have such a feature.
Law Independence - The simulated universe's rules can be more restrictive or less restrictive than the parent's. There is no cross-universe subset enforcement as long as features don't cross between (above).
Internal Consistency - A given simulation must still follow its own laws. It cannot violate/contradict the "laws of math" that govern it, at least not without "crashing" the model. For example, the model does not define ("handle") what happens when something is divided by zero, yet during the course of the simulation, such an event does occur. We've "popped" out model.

More to come...

--top

I'm wondering whether we could create a simulation that violates these rules (i.e., a simulation within a simulation could break the simulation's reality). If so, these rules would only be only applicable to our very own level of the chain: not applicable to the children, not applicable to the parent (if any).

In other words, could I create a virtual universe whose rules are "if this virtual universe creates a simulation, this simulation will manage to break the universe's reality"? Why not? -- PhilippeDetournay

If we could observe this simulation within a simulation and thereby obtain any results from it - even a single number or letter or character or bit - it would violate Ability Leakage, as we would have obtained results by means of violating the laws of our universe. OTOH, if you can't obtain any results from it, then supposedly anything is possible... OTOH it would be really difficult to assert or prove a simulation within the simulation ever happened, much less assert it violated the laws of our universe. In truth, all this also applies to first-level simulations. What Top means by Law Independence seems to be: you can simulate some laws distinct from those we observe in our universe (though the simulation-software can't violate any laws - thus the other two points).

This is not exactly my point. We are in universe U0. In there, we create simulated universe U1, that itself simulates universe U2. I created U1 so that it could create U2 such as U1 can obtain, through U2, values that it shouldn't be possible to obtain directly. In other words, U1 violates Ability Leakage.

The question is: would such a U1 exist? I can think of a couple of programs that would qualify. But then, if I can create U1 and U1::U2 such as U2 violates U1's laws, one could consider U2 as a some kind of magic wand from U1's perspective, effectively extending U1's laws to encompass U2. This way, U1 doesn't violate Ability Leakage anymore. Back to square one... This seems a reasoned conclusion.

In any case, the title of the page is misleading: this should be ParentRelationshipToSimulation?, as U2 can infer absolutely nothing about U1. From our point of view, our parent universe might not need to implement these three relationships. This is how I refute the SimulationArgument: who said our parent universe had to implement the laws of logic?

Proposed axioms of logic are accepted based on their proven ability to lead one to accurate predictions and prevent demonstrably inaccurate conclusions... much the same as any other theory or law. If we were to make observations in our 'parent' universe (presuming such a thing exists) we would not necessarily come to accept the same axioms of logic as 'laws'. Actually, if we were to observe more of our universe than just a tiny fraction of a little blue ball on the outer spiral arm of one medium-sized galaxy (out of millions of billions) we also might need to discard some of what we consider 'laws' today. But looking into invented universes is still cheaper than thoroughly exploring our own.

One of the more interesting things to consider: if you can't observe a simulation, then there is (by nature) no risk whatsoever of ability leakage. Of course, you're also stuck in the awkward postion of being completely unable to prove you've even got a 'simulation'. But considering this, it is possible that a universe within a universe have a completely different set of physical laws... e.g. if (as some scientists speculate) 'black holes' actually tear through to expand internal dimensions and essentially a 'big bang' within another 'universe', then that universe could have a completely different set of natural laws than our own. We'd never know, of course, which is why we can only speculate.

In other words, if we were able to observe, through a simulation, things that violate the law of our Universe, that would mean that these laws are not what we thought they were. Hence, if laws of logic are true, Ability Leakage is true by construction. And if laws of logic don't apply (this sentence cannot be terminated)

If we can't observe something, directly or indirectly, to any large definition of observation, then from my point of view this something doesn't exist (it can't have any impact of me). It can therefore have any property it wishes. Of course, some would consider that thinking about something brings it into existence (since it had an impact of me).

I suspect that the Law Independence rule is rather vacuous in the sense that "as long as features don't cross between" keeps the law from applying for pretty much everything of interest. It seems the 'laws of a simulation' as you describe them above would correspond to the laws experienced by an agent living within the simulation and observing it from the inside, complete with us tweaking its brain with universal 'undos' and all that jazz.

Suppose, for a moment, that as god-programmers of a simulation we were in a position to observe the simulation (as we are wont to do - a simulation isn't much good if you have no means to observe it). In that case, we'd be able to learn any information that one can could learn within any such simulation. As a consequence, it is immediately clear that all rules guiding information in our universe also apply in the simulated universe, lest there be 'Ability Leakage'. There is no violating information theory and entropy, halting problem, bypassing NP-completeness, goedel's incompleteness theorem, etc.

Those are mathematical models, not physical models. They may have consequences in the physical world, but that is not necessarily the reason they cannot be "bypassed". I never claimed simulations could break math models. If one models a different physical universe, the model still needs to be internally consistent, at least if you don't want to blue-screen your subjects. Perhaps this should be added to the "rule list". --top

Now consider 'time'. Time as we understand it in our universe is literally a partial-ordering of observations (which is why time is relative), and we keep 'accurate' time by focusing on 'regular' observations (daily cycle of sunrise/sunset, moon going round sun, hands going round clock, vibrations of a cesium atom under pressure of a laser beam, etc.) So, what would it take to make time move backwards in a software simulation? We could take a simulation that has moved forward and attempt to 'rewind' it, but that would be our experience, not that of the agent within the simulation (who has, at the end, no experience of time going backwards). Time going backwards would, for the agent, would require the agent be able to observe and react to events and observations that haven't happened yet, resulting in effects that happen prior to their cause. To make this happen in the simulation, we'd need to deliver the effects before cause to the agent... which would leak into our universe as the ability to determine and observe the effects before the cause (i.e. the ability to receive a message before it has been sent). So, again, this is no-go.

Extracted discussion about NonChronologicalSimulations into separate page.

We're certainly free to mess around with some rules of a simulation (e.g. we can tweak gravity in a world-sim). But what we can't do is write software that breaks any natural laws of our universe, which means we can't, in software, take advantage of any 'laws' in a simulation that aren't compatible with our own. Software must obey every natural law of our universe (in addition to arbitrary limitations from the machine).

What keeps us from changing the speed of light in a simulated universe? Or making a universe that follows Newton's laws to a T, ignoring relativity and quantum mechanics? --top

The original claim that sparked this whole debate wasn't about 'simulations', but 'software'. Most physical simulations - even those with alternative physics that tweak Newtons Laws or add properties like anti-friction - don't require software that violates laws of our universe. But 'Law Independence' certainly implies one could write simulations that do require software that violates the laws of this universe (because any other possibility strongly implies Law Dependence). Perhaps I'm objecting to your 'Law Independence' claim because I'm reading it more liberally than you intended when you wrote it.