Do We Live In a Computer Simulation?

My reply to Max Tegmark on The Simulation Argument.

Posted Jun 13, 2014

I was invited by the American Humanist Association to present the arguments of my paper “Natural Evil and the Simulation Hypothesis” at the national conference this past weekend. It was fun: I met a lot of interesting people and learned a lot. As far as non-academic conferences go, it was a great success. However, I wanted to take a moment to talk about the Keynote speech by Max Tegmark, author of “Our Mathematical Universe.” As I recall, I had no major objections to his talk (although I did think that he vastly underestimated how common life is in our universe–he seemed to think that we are the only example of life in the entire observable universe). But someone asked him a question about my talk, specifically regarding the simulation hypothesis—the suggestion that we live in a computer generated reality. He claimed that simulation arguments, like Nick Bostrom’s, are fallacious and that, even if it is true that we live in a computer simulation, we should live our life just the same. I wanted to respond.

I should begin by saying that I agree with the latter, as does everyone I know who thinks the simulation argument is sound. Even if we are in a simulation, the people who inhabit that simulation are still conscious beings—and as such, they have rights and obligations thus it is wrong to cause them pain and suffering (this, of course, aligns with the ideals of humanism expressed at the conference). But Tegmark’s claim that the simulation argument is fallacious—specifically, that it is fallacious for the reason he says—is way off the mark. I also read that section of his book in preparation for my talk, and not only are his objections to the argument not convincing, but they seem to indicate that he doesn’t actually understand the simulation argument.

The section of his book on the simulation argument, found in chapter 12, begins with the assumption that Nick Bostrom and the like are arguing that we actually are in a simulation. They are not. Most specifically, Bostrom is simply arguing that we have to either believe that (a) we won’t create a computer simulated universe, (b) that we can’t ever create such simulations, or that (c) we will and thus we are probably in one. But he doesn’t say which option is most likely. More generally, he is suggesting that there is a direct epistemic relation between how likely one thinks it is that we will one day create a simulation, and how likely one should think that we are in one. In short, the argument suggests, the creation of one will make it most likely that the physical universe contains billions; and if there are billions of simulated universes, and only one physical universe (and since you can’t tell from the inside what kind of universe you live in), then most likely ours is one of the simulated ones.  

In his response to the question posed to him after his lecture about my talk, Tegmark suggested that the simulation argument is fallacious because it has to make unwarranted assumptions about whether the physical laws in the physical universe (like the one above ours, if we are simulated) will allow the creation of a simulated universe like ours. But the argument does no such thing. Bostrom is very open to the possibility that simulations are physically impossible; this is one reason that a simulation may never be created and why Bostrom’s conclusion is conditional; only if we do one day create a simulation, will it be likely that we are in a simulation ourselves. But notice that, if one day we do create a simulation, we won’t have to assume that the laws that govern the physical universe allow for the creation of a simulated universe like ours—we will know that they do. Why? If ours is the physical universe, then clearly they do because we just created one; but if ours is a simulated one, we couldn’t be here if they didn’t.

In his book, Tegmark suggests that, if we are in a simulation it is most likely an embedded simulation—e.g., a simulation within a simulation within a simulation.  He takes this to be a reductio ad absurdum; it's such a ridiculous consequence that the original hypothesis must be false. But this consequence is actually something that Bostrom himself realizes and he does not find it absurd at all. Of course, there is a limit to how deep simulations could be stacked, but thinking that the universe in which we are simulated is also simulated is certainly no more absurd than the idea that we are in a computer simulation in the first place. Further, it has nothing to do with Bostrom's modest conditional conclusion that we're most likely in a simulation, if we one day create one.

Those who think about the simulation hypothesis usually envision a simulation being run in a sequence; the computer churns away making the events of the simulation happen one at a time (although this could happen at varying speeds, the inhabitants of a simulated world would all experience the passage of time the same).But since Tegmark thinks our universe can be described completely mathematically, he thinks this is not necessarily so. Simulations might be static. Roughly put, to simulate a universe like ours, one may simply need to describe it mathematically and embed that description on a memory stick. Indeed, study of our universe has suggested that it is static. Simultaneity is relative, so the events of the universe do not happen in a temporal sequence; instead, they bare space-time relations to one another in a static four-dimensional block. So, unless we can establish a preferenced reference frame by which objective simultaneity can be defined—something Einstein denied—our universe cannot be the kind of simulation that the likes of Bostrom usually have in mind.

Notice however that this point does not defeat Bostrom's argument; it really says nothing about the truth of his conditional conclusion. In fact, it makes it more likely that we do live in a simulation. Again, Bostrom is simply arguing that how likely it is that we are in a computer simulation is directly proportional to how likely it is that we will one day create one. By adding yet another way to create a simulation—instead of running it sequentially with a computer program we could simply write it statically on a memory stick—Tagmart makes it even more reasonable to conclude that we will one day create a simulation. Consequently, his argument makes it more likely that we are in one.

In another objection to the simulation argument, Tagmark makes the mistake of equivocating on the word "simulate." He suggests it would be difficult if not impossible to simulate our world because it contains quantum randomness; if we set up a simulation with the same initial conditions as ours, quantum randomness would likely produce a different result. Although likely true, this is irrelevant; it does not make it impossible to create simulated universes. Although exact simulations (that are identical to our world in every way, right down to every event in history) might be useful, they are usually not the kind of simulations that the likes of Bostrom have in mind. They have in mind simulated universes that would be similar to ours, but not exactly the same. In fact, what would make them interesting are their differences. Tagmark is equating exact simulation (replication) with approximate simulation (similarity). The fact that we couldn’t accomplish the former does not entail that we can’t accomplish the latter.

Interestingly, Tagmark’s thesis about the mathematical nature of our universe suggests that—roughly put—the differentiation between physical and simulated universes may be trivial. If I understand him correctly, he thinks that our universe may simply be an abstract mathematical object—an equation, if you will—and such objects exist, regardless. They might be instantiated by a physical universe, run on a program, or written on a memory stick—but even if they are not, they still exist as mathematical objects, and thus still exist. In fact, Tagmark suggests, if they do exist as abstract objects, being instantiated in a physical world or on a computer would seem to make no difference; that would not make them exist any more than they already do.

I’m not a big fan of abstract objects, including mathematical ones; I don’t think they “really” exist. I also am inclined to think that something instantiated in a physical reality (whether it be a computer hard drive or not) has a level of existence it would not have merely as an abstract object. But Tagmark’s thought is still an interesting one. Notice that, if he is right, we need not explain the universe’s existence any more than we need to explain the truth of “1+1=2.” If abstract mathematical objects are an ontological reality, they necessarily exist, so if our universe is a necessary object, it necessarily exists as well. This would deflate the cosmological argument even more than it already has been deflated.

Overall, Tagmark’s talk was interesting and even inspiring in parts. I’m glad to have heard it. I can’t speak to his entire book, as I have not read it. But, unfortunately, he doesn’t fully understand the simulation argument, and that made his comments regarding it unconvincing.