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One of the most important philosophical ideas of the 21st century is The Simulation Argument, laid out by Oxford philosopher Nick Bostrom. While some might dismiss it as silly, this would be a mistake. It deserves serious consideration.

While I won't delve into the in-depth mathematics of the argument, it essentially presents us with a three-way disjunct. Roughly, that disjunct is:

Either

1. The chance of a given advanced civilization either destroying itself or getting destroyed before reaching a stage of technological development capable of running simulated consciousness is very close to unity (almost certain in non-math-speak).

2. The proportion of advanced civilizations interested in running simulated consciousness/actually pursuing simulated consciousness is very close to 0.

or

3. We are very likely living in a computer simulation.

It is worth noting that accepting this disjunct is technically all that's required for one to consider the Simulation Argument valid, because all the basic argument seeks to do is establish this disjunct. The Simulation Hypothesis is the idea that 3 is more likely than 1 or 2. I'm not sure I even accept the Simulation Argument, due to some issues I have with how Bostrom arrives at 3. For this reason, we shall start by examining 3 in and of itself.

The reason Bostrom considers 3 to be likely in the case of rejecting 1 and 2 comes from the notion of nested simulations - the idea that sim-worlds could themselves construct computers capable of running sim-worlds, creating another universe at another level of abstraction. The reason that this is important is that if nested simulations were commonplace, as they would be in Bostrom's universe, the number of simulated people would vastly outnumber the number of people in the base-level universe, and sheer probability would favor us being a sim.

Even if we accept Bostrom's disjunct, I still think we have many reasons to believe that 2 is far more likely than 1 or 3. The actual possibility of such simulations is highly suspect, or at least creating such simulations and hiding the fact that they're simulated from the program. The reason for this leads us into theoretical computer science - specifically, the Law of Leaky Abstractions. When I responded to the actual PerC thread about the Simulation Argument, the Law of Leaky Abstractions is the first objection that came to mind. Formally, the law states:

Any non-trivial abstraction is, to some extent, leaky.

Which in layman's terms means there's no way to completely isolate a simulation from its simulator. The implication here is that if we were living in a simulation, physics would probably show it. Specifically, I think we'd find an underlying pattern to quantum mechanics that has not yet been found (if they were being simulated - if our universe/multiverse is base-level, then they would not need an underlying pattern of this sort) and does not look likely given the Bell inequalities. The only assumption this objection rests on is the computability of experiences/laws of physics/whatever, which is necessary for the Simulation Argument in the first place.

Then there are motivation arguments. Supporters of the Simulation Hypothesis have suggested that advanced simulations would run sims for research purposes. However, imagine the effort involved. You'd have to overcome potential ethical opposition in your own civilization, and then once running the simulation constantly keep track of it to make sure the sims don't figure out too much. What would be the motivation for any civilization to create something that is clearly very difficult (if possible at all) to create, where they would constantly have to battle their own creation. If so much effort had to be put in to avoid the sims figuring out their situation, then would the research benefit be worth it? And then there are the economics of such simulations. This is not to say it's inconceivable that a civilization would either overcome or not face these obstacle, but it seems to me that the chance of any given civilization created simulations is actually close to 0.

My last, and perhaps most forceful argument, is a presuppositionalist one - that the Simulation Hypothesis epistemically undermines itself, as do all suggestions of a "transcendent" reality. All our reasoning, the basic cores of our thought and language, is built on the nature of our world. The entire Simulation Argument is constructed under the assumptions of our world. We cannot use our reasoning to posit the existence of something beyond our reasoning - this is invalid. To put it in simpler form, if we assume that we are living in a computer simulation, we are assuming that we can't assume we are living in a computer simulation. This of course is inconsistent with my earlier arguments, but the purpose of those is to illustrate that even if we suspend our epistemological concerns the Simulation Hypothesis is unlikely, in order to build a cumulative case against it.

I think together these constitute a good, rough cumulative argument against considering the Simulation Hypothesis remotely likely.

NOTE: Originally I has also incorporated a very long information-theoretic argument against the Simulation Hypothesis, but Bostrom has addressed this in his 2011 "Patch for the Simulation Argument."
 

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Out of interest, what was the information-theoretic argument that you say Bostrom addressed in his paper on a 'Patch for the Simulation Argument'? In my opinion that paper doesn't actually address adequately the flaw it points out. The problem with his formula is that he assumes that post-human and non post-human civilizations in the root reality have the same number of individuals, thus Bostrom's disjunction might be true or it might not, but this is all we can say, no other statement may be made without knowledge of the root reality.

His first patch asks us to accept the assumption that any disparity between the average number of individuals per real post-human civilization and the average number of individuals per real civilization, whether post-human or not, is of an order much less than the number of simulations that are theoretically possible. I emphatically do not accept this assumption, we cannot know that this is or is even at all likely to be the case without some knowledge of the root reality. To be rigorous Bostrom needs to restate this mathematically as, A/(BF) << N, where A is the average number of individuals per real civilization, post-human and non post-human, B is the average number of individuals per real post-human civilization, F is the fraction of real civilizations that have run simulations in the time over which averages A and B have been determined, and N is the average number of ancestor simulations run by such civilizations. To obtain Bostrom's assumption we require that either A ~ BF (since N is assumed to be large) or A < BF, but we cannot estimate A with even a minimum of reliability without full knowledge of the root reality.

In his second patch he asks us to assume that the period in any non post-human civilizations history that matches our experience is of a similar length to the same period in any post-human civilizations history. Again, I emphatically do not accept this, Bostrom cannot state that this is a reasonable assumption without some knowledge of the root reality. For instance, we might entertain the possibility that non post-human civilizations in the root reality might never have gone post-human due to a simple stagnation of technological advance rather than some form of extinction, extending greatly the period in a civilizations history in which individuals with experiences like ours exist. Bostrom is trying to assume a uniformity of history between post-human and non post-human civilizations to bolster his argument, which he can't do with any honesty, it's simply pretending to have knowledge of the root reality, whatever that may be.

It is interesting to note that in Bostrom's argument he presents us with a formula that purports to represent the probability that we are ourselves simulated. What this means is that the variables in this formula must necessarily represent their corresponding values for the entire simulation hierarchy, else the fraction derived thus does not represent the probability that the world, as observed by an individual selected at random from the entire hierarchy, is simulated. Instead it would represent the probability, from the perspective of individuals in the highest level of a subset of the hierarchy, that an individual selected at random from within this closed subset is simulated (note that this is not equivalent to the probability of being simulated for an individual who questions whether they are themselves a simulation). This distinction points to an problem not discussed in Bostrom's argument, that of observer dependence on any estimation of probability within the hierarchy. If we are to estimate the fraction of simulated individuals by extrapolating values for F, B and N from present empirical observation, then the resulting fraction corresponds to the probability for a subset of the hierarchy as mentioned above, unless we assume that our reality is a perfect mirror of those higher up in the hierarchy, a nonsensical proposition even if we were to accept a strict adherence to running ancestor simulations only, as any level in the hierarchy could never have sure knowledge of any civilizations, other than their own, that were ever present in the root reality and thus entire possible branches of the simulation hierarchy would be utterly unknown to them. What this amounts to is that we cannot make assumptions from our own experience about a possible root reality at a level higher than ours in any possible simulation hierarchy, we cannot know the history of civilization in the root reality with even a minimum of certainty even if we could be reasonably certain about a hypothetical civilization that is simulating us by disregarding the possibility of anything other than ancestor simulations. Extrapolating from a sample of one is deeply unwise, but Bostrom attempts to do this anyway; why would other civilizations in the root reality have histories that mirror our own? It is also important to repeat that any probability derived in the way of Bostrom's simulation argument does not correspond to the probability that any given individual and their respective world is a simulation. The correct interpretation is that it gives a probability that a randomly selected individual, from an estimated list of simulated and non-simulated individuals, is simulated from the perspective of the person who compiled the list, not the perspective of the individual under scrutiny. Our position in the hierarchy gives an estimated list of individuals that is not necessarily the same as that of any level at the same depth in the hierarchy and is certainly not the same as that of higher levels, since unknown civilizations may abound in higher levels of the hierarchy. In this same way, we are not a randomly sampled civilization from the simulation hierarchy and as such, any probability we estimate does not apply to us.

Note: Updated to correct some slightly erroneous terminology, restate patch one in a more rigorous manner and append the final paragraph relating to observer dependence and probability.
 
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