We are probably living in a simulation, here's why

'Many works of science fiction as well as some forecasts by serious technologists and futurologists predict that enormous amounts of computing power will be available in the future. Let us suppose for a moment that these predictions are correct. One thing that later generations might do with their super-powerful computers is run detailed simulations of their forebears or of people like their forebears. Because their computers would be so powerful, they could run a great many such simulations. Suppose that these simulated people are conscious (as they would be if the simulations were sufficiently fine-grained and if a certain quite widely accepted position in the philosophy of mind is correct). Then it could be the case that the vast majority of minds like ours do not belong to the original race but rather to people simulated by the advanced descendants of an original race. It is then possible to argue that, if this were the case, we would be rational to think that we are likely among the simulated minds rather than among the original biological ones. Therefore, if we don't think that we are currently living in a computer simulation, we are not entitled to believe that we will have descendants who will run lots of such simulations of their forebears.' - Nick Bostrom

In his classic rendering of the simulation argument, Bostrom posits that one of the following trilemma must be true:

1. The fraction of human-level civilisations that reach a post human stage (one capable of running high-fidelity ancestor simulations indistinguishable from reality) is very close to zero
2. The fraction of post-human civilisations that are interested in running ancestor simulations is very close to zero
3. The fraction of all people with our kind of experiences that are living in a simulation is very close to one

So, to frame this by the assumptions it makes, if we assume the following:

1. It is possible for a civilisation to reach a post-human level of technological advancement (and doesn't self-destruct first)
2. And that with a sufficient level of technological advancement, it is possible to create simulations that would be indistinguishable from reality
3. And that post-human civilisations with that level of technology would actually be interested in running ancestor simulations
4. And that given the likely amount of computing power involved it would be possible for such a civilisation to create many millions of simulations with a negligible proportion of their computing power

Then it must follow that there are many more simulated realities than the one true base reality (possibly reaching ratios of millions or even billions to one). Therefore, for any conscious being, the probability they can assign to themselves being in base reality is 1/N.
(Where N=the number of simulated realities there are and is highly likely to be > millions)

Therefore the probability we are in a simulated reality is very close to 1.

Now let's look at some of these assumptions in more detail and see if the argument still holds.

Is it possible for a civilisation to reach a post-human level of technological advancement?
This is actually one of the least certain of all of the assumptions in my opinion. Humanity sits very precariously on the brink of self-annihilation, but we have to hope that it is possible for a society (even just one, out of all post-human civilisations) to collaborate enough not to destroy themselves with nuclear warfare, superintelligent AI, superbug pandemics or catastrophic climate change.

Is it actually theoretically possible to create a simulation indistinguishable from reality?
This question essentially boils down to whether we would have enough computing power to do so. Well, physicists in Oxford have recently claimed, that to accurately model quantum phenomena, we would need prohibitive levels of computing power. For example, to store the information on a few hundred electrons would require more atoms than is available in the universe. However, as we will discuss, a full simulation of quantum systems is not necessary for a simulated reality so I don't think this really challenges the simulation theory.

Bostrom argues that if technology continues to progress at any rate, then it will be possible, whether that be in a few decades or hundreds of thousands of years. It's extremely difficult to put an upper bound estimate on what level of computing power is possible, as we cannot imagine what future technology will look like. If you told someone 100 years ago that they could have a match box sized object that contained access to all of the world's knowledge and information, they would have laughed at you.

However, we can put some lower bound estimates based on what we currently know about the laws of physics and computing. Eric Drexler has calculated a physical limit of 10^21 operations/second for a sugar cube sized computer. Robert Bradbury has written about the Matryoshka brain which is a computer with a mass on the order of a planet that would be able to achieve 10^42 operations/second. And Seth Lloyd has calculated the physical limit to computing power to be 5x10^50 operations/second carried out on 10^31 bits by an object with volume 1L and mass 1Kg in his seminal Nature paper.

Is this enough to create a simulated reality?
In short, yes. To create a simulated reality, the main computing cost would be the simulated minds within it. This is because it is simply not necessary to simulate the entire universe to a quantum level. One also does not need to fill in detail on unobserved regions such as the far reaches of the universe, the earth's core or the atomic structure of most things etc. Because a simulator would have access to the belief states of their simulated minds and could fill in detail on an ad-hoc basis as and when needed e.g. only when someone decides to look down an electron microscope does some of the atomic structure actually need to be in place. Even if an error does occur, the simulator could just edit the brains of the simulated minds or skip back a few seconds and re-run the simulation.

So, the computing power required for everything other than the simulated minds themselves is negligible, but would it be feasible to simulate minds? To do so it has been estimated that we would need no more than about 10^14 10^17 operations/second. RAM requirements of a human brain are about 10^8 bits/second, so negligible. As a highly conservative upper bound estimate then:

100 billion humans X 50 years per human X 30 million seconds per year X 10^14-17 = 10^33-36 operations/second.

So a single matryoshka brain (of which a highly advanced society would likely have many) can achieve 10^42 operations/second, and would thus be able to simulate the entire mental history of humanity with less than 1 millionth of its processing power for 1 second.

Would our simulated minds have a conscious experience of reality like we do?
This is naturally a difficult question. I do think however, that it would be naïve to assume that consciousness is substrate dependent and that an essential property of it is that it is implemented on carbon-based biological neural networks housed in a cranium. I don't see any reason that a silicon-based system in a computer couldn't also work.

Would a post-human civilisation actually want to create simulated realities?
Some have argued that the scientific value of ancestor simulated minds to post-human civilisations is negligible and that they may have decided that recreational activities are a very inefficient means of attaining pleasure, which is much more easily obtained from direct stimulation of the brain's reward centres. Personally, I don't buy this, there would have to be an extremely strong convergence amongst all possible post-human civilisations towards not wanting to create them, even at a negligible computing power cost.

Given all of the above, I'm of the opinion that there is a non-negligible (and in fact highly probable) chance that we are indeed living in a simulation. Now let's turn to some of the consequences of this:

1. Maybe there is a god and maybe we do need to please someone to reach an afterlife (re-simulation as the same consciousness). But how? Maybe simulated beings should strive to be as interesting as possible to avoid not being switched off? Maybe we should endeavour to forget the idea that we might be living in a simulation because surely that invalidates the whole simulation for the simulator and they might switch us off? Does this mean nothing matters or that we have no reason to behave morally towards each other? No, I don't think so, because the simulated beings are conscious nonetheless and thus still morally relevant.
2. If we follow the above assumptions, then it must follow that those simulating us are also in a simulation and that this can go up multiple levels (with a physical limit to the number of levels governed by the exponential increases in computing power).
3. If we ourselves manage to create a simulated reality, then that disproves the first two of Bostrom's scenarios (inability to create and unwillingness to create) and thus the only possibility left is that we are in a simulation. If we do manage to create a simulated reality however, this would start to dramatically increase the amount of computing power for our simulators (especially those at the very top of the multiple levels simulations) and so we must hope that we or our simulators are not switched off at this point.
4. The universe that we observe may only be a very tiny piece of reality and the laws of physics we perceive may be entirely different to those of base reality. I can't even begin to think what these might actually entail.
5. We cannot get proof that we aren't in a simulation because any proof that we do get, could itself be simulated.
6. The simulated world could contain many shadow people in which only one or a few people are actually conscious and the others are essentially zombies who are just rendered at a sufficiently high resolution so as to not appear different to the conscious simulated mind.

Thinking we might be in a simulation is not even that much of a fringe, niche idea either. Neil de Grasse Tyson has put the odds of us being in a simulation at 50%, Max Tegmark at 17% and David Chalmers at 42%. Elon Musk is famed for stating his belief that there is a 1/billions chance that we are not in simulation. The physicist James Gates has even found error correcting codes (computer code used in the creation of web browsers) in the physical laws governing quarks, electrons and supersymmetry and Ray Kurzweil (Google's AI expert & famous futurist) is also a key proponent.