Montreal by night. (c) Jan Haugland

No, we probably don’t live in a simulation

Elon Musk, everybody’s favorite entrepreneur and all-around genius, stated some time ago that he believes we all live in a computer simulation. The chance that we are as real as we like to believe, the argument goes, is only one to “billions” against.

Musk restated a well-known and often discussed paper by Nick Boström, titled Are you living in a computer simulation? This paper makes the following quite convincing argument, saying one and only one of the following must be true:

(1) the human species is very likely to go extinct before reaching a “posthuman” stage;
(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
(3) we are almost certainly living in a computer simulation.

Unlike Musk, who is convinced that (3) must be the correct option, Boström himself is cautious and says that absent any actual evidence either way, we should conclude that any of the three are equally likely. The probability that we live in a computer simulation would then be a still substantial ~33 %.

Who could have known that Plato’s cave was just a piece of computer software ?

The “simulation argument” is not the only argument along this line. It is a relative to the so-called Doomsday argument, which also uses statistical thinking to draw conclusions that are not reliant on an empirical investigation.

The Doomsday argument, most famously proposed by astrophysicist Brandon Carter in 1983, goes roughly as follows: If we place all humans who were ever born and who will ever be born on a long line, chances are that any specific human (say, you or I) would be placed somewhere in the middle, not at the very start and not at the very end of human history.

If 60 billion humans have been born so far, then there is a 95% chance that the total number of humans that ever will exist is no more than 20 × 60 billion = 1.2 trillion. So, depending on how childbirths and the population size evolves, there is a certain time-span until humanity with a 95% certainty will be extinct. Our fate is entirely independent of nuclear weapons, super-volcanoes or killer meteorites: humanity will 19 times out of 20 be wiped out by a statistical argument. The dinosaurs got off easily.

Many dismiss this argument out of hand as silly, but refuting it is a lot harder. It is, after all, founded on a statistical method that boasts significant success from World War II intelligence: The German Tank problem. Faced with estimating the number of the feared heavy German Panzer V (Panther) tanks being produced, the allies used the serial numbers on captured and destroyed vehicles to estimate the total number of tanks.

German Panzer V assembly line. By Bundesarchiv, Bild 183-H26258 / CC-BY-SA 3.0, CC BY-SA 3.0 de, Picture from Wikipedia.

Using Bayes’ theorem, this method yielded an estimate of 270 tanks produced in February 1944, more than conventional intelligence suggested. After the war, German records revealed the correct number to be 276. Not bad!

Quite a few assumptions had to be correct for this analysis to work. The Germans had to be their typical meticulous selves and use serial numbers in the form 1, 2, 3 and so on. If they had used random numbers, or used a formula that yields a ridiculously high numbers (like Elon Musk’s Tesla cars), this method would not work.

So, does it work with humans?

The simulation paper and the Doomsday arguments both rely on a purely statistical argument to create conclusions ex nihilo, from no observed facts. The Doomsday argument makes explicit what is not clearly stated in the simulation paper: we have to assume that we are typical.

This line of reasoning has a peculiar theory of origins, that humans in one paper or intelligent civilizations in the other paper are produced from an assembly line, or, if you will, are randomly sprinkled across the landscape and fall down at a random place with a certain distribution and probability. We could be tempted to call it the Statistical Stork Theory of Origins.

This Stork theory has its advantages. We no longer need advanced telescopes or a space program, we only need a good understanding of statistics, including Bayes’ theorem, to know how the universe works and what our fate is.

For example, we could investigate whether we are alone in the universe. First, we can start with a more modest question, are we the only intelligent species in our solar system? This is the example James B. Hartle and Mark Srednicki used in their 2007 paper Are We Typical? Perhaps surprisingly, it was not written to counter either the Doomsday nor the simulation argument, but just as well could be. Cosmologist Sean Carroll did actually briefly touch on these theories in a lecture where he summarized Hartle and Srednicki’s paper.

Jupiter with its major moons in the foreground. Picture by NASA.

Imagine that we have a theory concerning our solar system, that there are trillions of intelligent gasbags floating around in the atmosphere of Jupiter.

Theory A predicts that there are likely to be intelligent beings living in the atmosphere of Jupiter; theory B predicts that there are no such beings. Because Jupiter is much larger than the Earth, theory A predicts that there are today many more jovians than humans.

Following the statistical arguments outlined earlier, we can save ourselves the work of going to Jupiter to check. You see, if there are trillions of jovians in our solar system, then it follows that jovians, not humans, are the typical intelligent beings in our solar system. We are typical, we are clearly not jovians, so jovians with overwhelming probability do not exist.

As Hartle and Srednicki states, it would seem absurd to reject the theory that jovians exist on the basis that humans must be typical. We have to look and find out!

We simply have no right to assume we are typical; that is a theory we have to substantiate separately.

We can also move it down to Earth, as it were. Unbeknownst to history, one hunter-gatherer philosopher 10,000 years ago invented statistics and presented this argument to his tribe of a few hundred people: there is a theory that there are millions of foreigners all around the world. They are all barbarians. But we are typical people, and we are not barbarians, so foreigners with overwhelming probability do not exist.

The problem these arguments suffer is that we have no right to assume we are typical members of any set we haven’t even investigated, we have no right to create conclusions out of thin air, but we have to go out there in the world and look.

This certainly applies to the (hypothetical) human-jovian argument, and you probably agree that it applies to the Doomsday argument. But what about its relative, Boström’s computer simulation argument, the one we are actually discussing?

The two arguments may appear different, but in this respect they are similar: they both assume we are typical.

The hidden assumption in the computer simulation argument is that every civilization has a sort-of metaphysical ideal existence, and our cosmic stork spreads all of them across the entire cosmic landscape, consisting of both real, physical civilizations and computer simulated worlds. The simulations are, if Musk is correct, overwhelmingly more common, so we most likely were dropped by the stork into one of them.

This is obviously not our actual origins. Whether or not we live in a simulation must be determined based on empirical research and physical evidence, not blind statistical arguments. Whether our world is real or simulated, our history is our own, and we don’t know whether we are typical representatives of either. We don’t know about even one extraterrestrial civilization, we aren’t even close to accurately simulating a cubed millimeter of our universe, we don’t know if the term “posthuman” even makes sense, so producing a statistical argument based on these ideas are statistical overreach.

The simulation argument can also be used against itself. Obviously, it would take enormous computing power to generate the universe down to its deepest levels, even if the simulation was smart enough to only simulate the parts that a conscious agent was actually investigating or exposed to. It follows that long before these superhumans ever created a perfect simulation that our most advanced experiments could not detect, there were a long line of faulty but gradually improving simulations. There were obviously many, many bad simulations before anyone managed to create really good ones. So, if we live in a simulation, we almost certainly live in a bad one, one which fails to perfectly simulate the quantum effects of light from supernovae or the details of the Large Hadron Collider experiments. In that case, we would already have detected that something was weird. Once you begin to argue that these data could have been forged, made up or fudged, you are on a slippery slope to claiming that no other intelligent beings than yourself actually exist (see solipsism).

The bottom line is that both the evidence and logic suggests we are denizens of a real universe, and debates about a simulation, while very entertaining, have no force to put us into the matrix.

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