Do we live in a computer simulation?

Some days I can almost get myself to believe that we live in a computer simulation, that all we see around us is a façade designed to mislead us. There would finally be a reason for all this, for the meaningless struggles, the injustice, for life, and death, and for Justin Bieber. There would even be a reason for dark matter and dark energy, though that reason might just be some alien’s bizarre sense of humor.
It seems perfectly possible to me to trick a conscious mind, at the level of that of humans, into believing a made-up reality. Ask the guy sitting on the sidewalk talking to the trash bin. Sure, we are presently far from creating artificial intelligence, but I do not see anything fundamental that stands in way of such creation. Let it be a thousand years or ten thousand years, eventually we’ll get there. And once you believe that it will one day be possible for us to build a supercomputer that hosts intelligent minds in a world whose laws of nature are our invention, you also have to ask yourself whether the laws of nature that we ourselves have found are somebody else’s invention.

If you just assume the simulation that we might live in has us perfectly fooled and we can never find out if there is any deeper level of reality, it becomes rather pointless to even think about it. In this case the belief in “somebody else” who has created our world and has the power to manipulate it at his or her will differs from belief in an omniscient god only by terminology. The relevant question though is whether it is possible to fool us entirely.

Nick Bostrum has a simulation argument that is neatly minimalistic, though he is guilty of using words that end on ism. He is saying basically that if there are many civilizations running simulations with many artificial intelligences, then you are more likely to be simulated than not. So either you live in a simulation, or our universe (multiverse, if you must) never goes on to produce many civilizations capable of running these simulations for one reason or the other. Pick your poison. I think I prefer the simulation.

Math-me has a general issue with these kinds of probability arguments (same as with the Doomsday argument) because they implicitly assume that the probability distribution of lives lived over time is uncorrelated, which is clearly not the case since our time-evolution is causal. But this is not what I want to get into today because there is something else about Bostrum’s argument that has been bugging Physics-me.

For his argument, Bostrum needs a way to estimate how much computing power is necessary to simulate something like the human mind perceiving something like the human environment. And in his estimate he assumes, crucially, that it is possible to significantly compress the information of our environment. Physics-me has been chewing on this point for some while. The relevant paragraphs are:

“If the environment is included in the simulation, this will require additional computing power – how much depends on the scope and granularity of the simulation. Simulating the entire universe down to the quantum level is obviously infeasible, unless radically new physics is discovered. But in order to get a realistic simulation of human experience, much less is needed – only whatever is required to ensure that the simulated humans, interacting in normal human ways with their simulated environment, don’t notice any irregularities.

The microscopic structure of the inside of the Earth can be safely omitted. Distant astronomical objects can have highly compressed representations: verisimilitude need extend to the narrow band of properties that we can observe from our planet or solar system spacecraft. On the surface of Earth, macroscopic objects in inhabited areas may need to be continuously simulated, but microscopic phenomena could likely be filled in ad hoc. What you see through an electron microscope needs to look unsuspicious, but you usually have no way of confirming its coherence with unobserved parts of the microscopic world.

Exceptions arise when we deliberately design systems to harness unobserved microscopic phenomena that operate in accordance with known principles to get results that we are able to independently verify. The paradigmatic case of this is a computer. The simulation may therefore need to include a continuous representation of computers down to the level of individual logic elements. This presents no problem, since our current computing power is negligible by posthuman standards.”

This assumption is immediately problematic because it isn’t as easy as saying that whenever a human wants to drill a hole into the Earth you quickly go and compute what he has to find there. You would have to track what all these simulated humans are doing to know whenever that becomes necessary. And then you’d have to make sure that this never leads to any inconsistencies. Or else, if it does, you’d have to remove the inconsistency, which will add even more computing power. To avoid the inconsistencies, you’ll have to carry on all results for all future measurements that humans could possibly make, the problem being you don’t know which measurements they will make because you haven’t yet done the simulation. Dizzy? Don’t leave, I’m not going to dwell on this.

The key observation that I want to pick on here is that there will be instances in which The Programmer really has to ramp up the resolution to avoid us from finding out we’re in a simulation. Let me refer to what we perceive as reality as level zero, and a possible reality of somebody running our simulation as level 1. There could be infinitely many levels in each direction, depending on how many simulators simulate simulations.

This idea that structures depend on the scale at which they are tested and that at low energies you’re not testing all that much detail is basically what effective field theories are all about. Indeed, as Bostrom asserts, for much of our daily life the single motion of each and every quark is unnecessary information, atoms or molecules are enough. This is all fine by Physics-me.

Then these humans they go and build the LHC and whenever the beams collide the simulation suddenly needs a considerably finer mesh, or else the humans will notice there is something funny with their laws of nature.

Now you might think of blasting the simulation by just demanding so much fine-structure information all at once that the computer running our simulation cannot deliver. In this case the LHC would serve to test the simulation hypothesis. But there is really no good reason why the LHC should just be the thing to reach whatever computation limit exists at level 1.

But there is a better way to test whether we live in a simulation: Build simulations ourselves, the more the better. The reason is that you can’t compress what is already maximally compressed. So if the level 1 computation wants to prevent us from finding out that we live in a simulation by creating simulations ourselves, they’ll have to ramp up computational efficiency for that part of our level 0 simulation that is going to inhabit our simulation at level -1.

Now we try to create simulations that will create a simulation will create a simulation and so on. Eventually, the level 1 simulation will not be able to deliver any more, regardless of how good their computer is, and the then lowest level will find some strange artifacts. Something that is clearly not compatible with the laws of nature they have found so far and believed to be correct. This breakdown gets read out by the computer one level above, and so on, until it reaches us and then whatever is the uppermost level (if there is one).

Unless you want to believe that I’m an exceptional anomaly in the multiverse, every reasonably intelligent species should have somebody who will come up with this sooner or later. Then they’ll set out to create simulations that will create a simulation. If one of their simulations doesn’t develop into the direction of creating more simulations, they’ll scrap it and try a different one because otherwise it’s not helpful to their end.

This leads to a situation much like Lee Smolin’s Cosmological Natural Selection in which black holes create new universes that create black holes create new universes and so on. The whole population of universes then is dominated by those universes that lead to the largest numbers of black holes - that have the most “offspring.” In Cosmological Natural Selection we are most likely to find ourselves in a universe that optimizes the number of black holes.

In the scenario I discussed above the reproduction doesn’t happen by black holes but by building computer simulations. In this case then anybody living in a simulation is most likely to be living in a simulation that will go on to create another simulation. Or, to look at this from a slightly different perspective, if you want our species to continue thriving and avoid that The Programmer pulls the plug, you better work on creating artificial intelligence because this is why we’re here. You asked what’s the purpose of life? There it is. You’re welcome.

This also means you could try to test the probability of the simulation hypothesis being correct by seeing whether our universe does indeed have the optimal conditions for the creation of computer simulations.

Brain hurting? Don’t worry, it’s probably not real.