Introduction

Most people on less wrong seem to be some kind of hedonic consequentialist.   They think states with less suffering and more joy are better.  Moreover, it is intuitive that if you can cause some improvement in human well-being to be achieved then (other things being equal) it is better to realize that improvement as soon as possible.  Also, most people on this site seem to be realists about special relativity.  That is they assume that any inertial reference frame is an equally valid point from which to describe reality rather than believing there is one true reference which offers a preferred description of reality.  I will point out that these beliefs (plus some innocuous assumptions) lead quickly to paradox.

Relativity Realism

Before I continue I want to point out that empirical observations really are agnostic about the existence of a preferred reference frame.  Indeed, it's a consequence of the theory of relativity itself that it's predictions are equally well explained by postulating a single true inertial reference frame and simply using the Lorentz contraction and time dilation equations to compute behavior for all moving objects.  To see that this must be true not that if we take relativity seriously the laws of physics must work correctly in any reference frame.  In particular, if we imagine designating one reference frame to be the true reference frame then, relativity itself, tells us that applying the laws of physics in that reference frame has to give us the correct results.  

In other words once we accept Einstein's equations for length contraction and time dilation with velocity we can interpret those equations as either undermining the idea of a fixed ether against which objects move (any reference frame is equally valid) or that there really is a fixed ether but objects in motion behave in such a manner that we can't empirically distinguish what is at rest.

At first blush this second result seems so jury rigged that surely the simpler assumption is that there is no preferred reference frame.  This relies on a false description of the situation.  The question isn't, "do we assign a low prior probability to the laws of physics conspiring to hide the true rest frame from us?"  Presumably we do.  The question should be, "given that the laws of physics do conspire to make a special rest frame empirically indistinguishable from any other inertial frames what probability do we assign to such a frame existing?"  After all it is a mathematical truth that the time dilation and length contraction do perfectly conspire to prevent us from measuring motion relative to some true rest frame (if it existed) so in deciding whether to believe in a preferred rest frame we aren't deciding between laws that would and wouldn't hide such a frame from us.  We are only deciding whether, given we have such laws, whether we think such an undetectable true rest frame exists.

To make it even more plausible that there is some true rest frame I will remark (but not argue) that relativity is a pretty general phenomena that can be derived from any model that conserves momentum, where the forces obey the inverse square law and all propagate at a constant speed relative to some fixed background, matter is held together in equilibrium states of these forces and time is implicitly measured via the rate it takes these forces to propagate.  In other words if you have atoms held together by EM forces and the time it takes physical processes to happen is governed by the time it takes either forces or matter to cross certain distances then relativity comes for free.  So it isn't amazing that we might have a true prefered reference frame and yet it be impossible to experimentally determine that frame.

(As an aside this interpretation of relativity, fully consistent with all observables so far, makes for much better scifi since FTL travel doesn't allow anyone to go back in time). 

A Paradox Resulting From Relativity Realism

Suppose we have two different brain implants that will be implanted in two different conscious but coma bound individuals.  After a delay of 10 minutes after implantation the first device delivers an instantaneous burst of euphoria every second.  The other delivers an instantaneous burst of discomfort every second.  I assume we would all agree that (with sufficient additional assumptions) the world is a better place if we implant just a device of the euphoria inducing kind and a worse place if we just implant a device of the second kind.  So assume the devices are appropriately calibrated so that the effect of implanting both is neutral (or very very nearly so).  So far so good.

I think we can all agree that the world would be better off if we delayed implanting the discomforting device by 10 minutes (or equivalently implanted the pleasurable device 10 minutes earlier).  If you dispute this conclusion then you get absurd results if you even admit the possibility of a universe that exists forever as in such a universe it is no better to permanently increase human welfare now than to delay that increase by 10 minutes or 10 centuries.

Now assume that the two individuals receiving the transplants are actually on spaceships moving in opposite directions at high rates of speed and the implantation is done at the instant they pass by each other.  For simplicity we assume everyone else dies at this instant (or add an irrelevance of identical outcomes assumption and note that the two ships are moving at the same velocity relative to everyone else).  

From the reference frame of the individual who received the beneficial implant we can analyze the situation as follows.  Without loss of generality we can assume the ships are traveling at an appropriate speed so that for every second that pases in our reference frame only 1/2 a second passes on the other ship.  Thus in this reference frame the first experience of discomfort is delayed by 10 minutes and then only occurs every other second.  Now surely the world is no worse off because the discomfort occurs less frequently.  But ignoring the fact that the discomforting device fires less frequently this is exactly equivalent to implanting the desirable device 10 minutes before the undesirable one.  Thus, since implanting both in the same reference frame was neutral, it is actually favorable (better than not implanting them) to do so when the recipients are in fast moving reference frames moving in opposite directions.  Note the same result holds if we assume the device only creates discomfort or euphoria a single time with the minor assumption that if two worlds only differ in events before time t then what happens after time t is irrelevant to which one is preferable.

However, the same analysis done in the reference frame of the unpleasant implant gives the exact opposite conclusion.

Avoiding the Paradox

Perhaps one might try and avoid the paradox by insisting that no experience truly occurs instantaneously.  However, this is easily seen to be futile.

Assume that each device inflicts pleasure or discomfort for duration epsilon << 1 second.  If you assume that the total badness of the uncomfortable experience is somehow mediated by changes in neurochemistry or other physical properties you are lead to the assumption that even described from the reference frame of the desirable implant the experience of 2*epsilon seconds of discomfort by the time dilated individual is really no worse than the experience of epsilon seconds of discomfort would be for someone with that implant in your reference frame.  In other words when time is dilated the experience of pain per unit time is diluted.  This leads to the exact same result as above.

On the other hand if we really do increase the weight we give to pain experienced by those undergoing time dilation an even simpler set of implants leads to paradox.  These implants start working immediately, one generating a pleasant experience for 5 minutes the other an unpleasant experience for 5 minutes again calibrated so that installing both is overall neutral.  Now by assumption from the reference frame of the beneficial implant things are overall worse (the longer duration of discomfort experienced by the other individual is overall worse than someone in the same reference frame getting the undesirable implant) and vice versa from the other reference frame.

The use of instantaneous experiences was merely a way to simplify the example but irrelevant to the underlying inequalities.  Those inequalities are a result of the implicit time discounting forced by the assumption that other things being equal it is better for improvements to occur now rather than later combined with the fact that realism about relativity renders facts about simultaneity incoherent.

Personally, I think the only decent way of avoiding this paradox is to deny realism about relativity.  Sure, it's a radical move.  However, it's also a radical move to say it's not true that it's better to cure cancer now than in 10 centuries even if the human race will continue to exist forever.  Indeed, even if you don't assume literally infinite duration of effects even an unbounded potential length of effect with probabilities that decrease sufficiently slowly is equally problematic.

Responses

I've deliberately avoided phrasing this dilemma in terms of a formal paradox and listing the assumptions necessary to generate the paradox.  Partly this is laziness but it's also a desire to see how people are inclined to respond before I attempt to draw up formal conditions.  After all I ultimately want to capture common views in the assumptions and if I don't know what people's reactions are I can't pick the right assumptions.

The recent article on overcomingbias suggesting the Fermi paradox might be evidence our universe is indeed a simulation prompted me to wonder how one would go about gathering evidence for or against the hypothesis that we are living in a simulation.  The Fermi paradox isn't very good evidence but there are much more promising places to look for this kind of evidence.  Of course there is no sure fire way to learn that one isn't in a simulation, nothing prevents a simulation from being able to perfectly simulate a non-simulation universe, but there are certainly features of the universe that seem more likely if the universe was simulated and their presence or absence thus gives us evidence about whether we are in a simulation.

In particular, the strategy suggested here is to consider the kind of fingerprints we might leave if we were writing a massive simulation.  Of course the simulating creatures/processes may not labor under the same kind of restrictions we do in writing simulations (their laws of physics might support fundamentally different computational devices and any intelligence behind such a simulation might be totally alien).  However, it's certainly reasonable to think we might be simulated by creatures like us so it's worth checking for the kinds of fingerprints we might leave in a simulation.

Computational Fingerprints

Simulations we write face several limitations on the computational power they can bring to bear on the problem and these limitations give rise to mitigation strategies we might observe in our own universe.  These limitations include the following:

1. Lack of access to non-computable oracles (except perhaps physical randomness).
   
   While theoretically nothing prevents the laws of physics from providing non-computable oracles, e.g., some experiment one could perform that discerns whether a given Turing machine halts (halting problem = 0') all indications suggest our universe does not provide such oracles.  Thus our simulations are limited to modeling computable behavior.  We would have no way to simulate a universe that had non-computable fundamental laws of physics (except perhaps randomness).
   
   It's tempting to conclude that the fact that our universe apparently follows computable laws of physics modulo randomness provides evidence for us being a simulation but this isn't entirely clear.  After all had our laws of physics provided access to non-computable oracles we would presumably not expect simulations to be so limited either.  Still, this is probably weak evidence for simulation as such non-computable behavior might well exist in the simulating universe but be practically infeasable to consult in computer hardware.  Thus our probability for seeing non-computable behavior should be higher conditional on not being a simulation than conditional on being a simulation.
2. Limited ability to access true random sources.
   
   The most compelling evidence we could discover of simulation would be the signature of a psuedo-random number generator in the outcomes of `random' QM events.  Of course, as above, the simulating computers might have easy access to truly random number generators but it's also reasonable they lack practical access to true random numbers at a sufficient rate.
3. Limited computational resources. 
   
   We always want our simulations to run faster and require less resources but we are limited by the power of our hardware.  In response we often resort to less accurate approximations when possible or otherwise engineer our simulation to require less computational resources.  This might appear in a simulated universe in several ways.
   
   • Computationally easy basic laws of physics. For instance the underlying linearity of QM (absent collapse) is evidence we are living in a simulation as such computations have a low computational complexity.  Another interesting piece of evidence would be discovering that an efficient global algorithm could be used that generates/uses collapse to speed computation.
   • Limited detail/minimal feature size.  An efficient simulation would be as course grained as possible while still yielding the desired behavior.  Since we don't know what the desired behavior might be for a universe simulation it's hard to evaluate this criteria but the indications that space is fundamentally quantized (rather than allowing structure at arbitrarily small scales) seems to be evidence for simulation.
   • Substitution of approximate calculations for expensive calculations in certain circumstances.  Weak evidence could be gained here by merely observing that the large scale behavior of the universe admits efficient accurate approximations but the key piece of data to support a simulated universe would be observations revealing that sometimes the universe behaved as if it was following a less accurate approximation rather than behaving as fundamental physics prescribed.  For instance discovering that distant galaxies behave as if they are a classical approximation rather than a quantum system would be extremely strong evidence. 
   • Ability to screen off or delay calculations in regions that aren't of interest.  A simulation would be more efficient if it allowed regions of less interest to go unsimilated or at least to delay that simulation without impacting the regions of greater interest.  While the finite speed of light arguably provides a way to delay simulation of regions of lesser interest QM's preservation of information and space-like quantum correlations may outweigh the finite speed of light on this point tipping it towards non-simulation.
4. Limitations on precision.
   
   Arguably this is just a variant of 3 but it has some different considerations.  As with 3 we would expect a simulation to bottom out and not provide arbitrarily fine grained structure but in simulations precision issues also bring with them questions of stability.  If the law's of physics turn out to be relatively unaffected by tiny computational errors that would push in the direction of simulation but if they are chaotic and quickly spiral out of control in response to these errors it would push against simulation.  Since linear systems are virtually always stable te linearity of QM is yet again evidence for simulation.
5. Limitations on sequential processing power.
   
   We find that finite speed limits on communication and other barriers prevent building arbitrarily fast single core processors.  Thus we would expect a simulation to be more likely to admit highly parallel algorithms.  While the finite speed of light provides some level of parallelizability (don't need to share all info with all processing units immediately) space-like QM correlations push against parallelizability.  However, given the linearity of QM the most efficient parallel algorithms might well be semi-global algorithms like those used for various kinds of matrix manipulation.  It would be most interesting if collapse could be shown to be a requirement/byproduct of such efficient algorithms.
6. Imperfect hardware
   
   Finally there is the hope one might discover something like the Pentium division bug in the behavior of the universe.  Similarly one might hope to discover unexplained correlations in deviations from normal behavior, e.g., correlations that occur at evenly spaced locations relative to some frame of reference, arising from transient errors in certain pieces of hardware.

Software Fingerprints

Another type of fingerprint that might be left are those resulting from the conceptual/organizational difficulties occuring in the software design process.  For instance we might find fingerprints by looking for:

1. Outright errors, particularly hard to spot/identify errors like race conditions or the like.  Such errors might allow spillover information about other parts of the software design that would let us distinguish them from non-simulation physical effects.  For instance, if the error occurs in a pattern that is reminiscent of a loop a simulation might execute but doesn't correspond to any plausible physical law it would be good evidence that it was truly an error.
2. Conceptual simplicity in design.  We might expect (as we apparently see) an easily drawn line between initial conditions and the rules of the simulation rather than physical laws which can't be so easily divided up, e.g., laws that take the form of global constraint satisfaction.  Also relatively short laws rather than a long regress into greater and greater complexity at higher and higher energies would be expected in a simulation (but would be very very weak evidence).
   
3. Evidence of concrete representations.  Even though mathematically relativity favors no reference frame over another often conceptually and computationally it is desierable to compute in a particular reference frame (just as it's often best to do linear algebra on a computer relative to an explicit basis).  One might see evidence for such an effect in differences in the precision of results or rounding artifacts (like those seen in re-sized images).

Design Fingerprints

This category is so difficult I'm not really going to say much about it but I'm including it for completeness.  If our universe is a simulation created by some intentional creature we might expect to see certain features receive more attention than others.  Maybe we would see some really odd jiggering of initial conditions just to make sure some events of interest occurred but without a good idea what is of interest it is hard to see how this could be done.  Another potential way for design fingerprints to show up is in the ease of data collection from the simulation.  One might expect a simulation to make it particularly easy to sift out the interesting information from the rest of the data but again we don't have any idea what interesting might be.

Other Fingerprints

I'm hoping the readers will suggest some interesting new ideas as to what one might look for if one was serious about gathering evidence about whether we are in a simulation or not.