Oct 23, JDN 2457685

Every subculture of humans has words, attitudes, and ideas that hold it together. The obvious example is religions, but the same is true of sports fandoms, towns, and even scientific disciplines. (I would estimate that 40-60% of scientific jargon, depending on discipline, is not actually useful, but simply a way of exhibiting membership in the tribe. Even physicists do this: “quantum entanglement” is useful jargon, but “p-brane” surely isn’t. Statisticians too: Why say the clear and understandable “unequal variance” when you could show off by saying “heteroskedasticity”? In certain disciplines of the humanities this figure can rise as high as 90%: “imaginary” as a noun leaps to mind.)

One particularly odd idea that seems to define certain subcultures of very intelligent and rational people is the Simulation Argument, originally (and probably best) propounded by Nick Bostrom:

This paper argues that at least one of the following propositions is 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.

In this original formulation by Bostrom, the argument actually makes some sense. It can be escaped, because it makes some subtle anthropic assumptions that need to be considered more carefully (in short, there could be ancestor-simulations but we could still know we aren’t in one); but it deserves to be taken seriously. Indeed, I think proposition (2) is almost certainly true, and proposition (1) might be as well; thus I have no problem accepting the disjunction.

Of course, the typical form of the argument isn’t nearly so cogent. In popular outlets as prestigious as the New York Times, Scientific American and the New Yorker, the idea is simply presented as “We are living in a simulation.” The only major outlet I could find that properly presented Bostrom’s disjunction was PBS. Indeed, there are now some Silicon Valley billionaires who believe the argument, or at least think it merits enough attention to be worth funding research into how we might escape the simulation we are in. (Frankly, even if we were inside a simulation, it’s not clear that “escaping” would be something worthwhile or even possible.)

Yet most people, when presented with this idea, think it is profoundly silly and a waste of time.

I believe this is the correct response. I am 99.9% sure we are not living in a simulation.

But it’s one thing to know that an argument is wrong, and quite another to actually show why; in that respect the Simulation Argument is a lot like the Ontological Argument for God:

However, as Bertrand Russell observed, it is much easier to be persuaded that ontological arguments are no good than it is to say exactly what is wrong with them.

To resolve this problem, I am writing this post (at the behest of my Patreons) to provide you now with a concise and persuasive argument directly against the Simulation Argument. No longer will you have to rely on your intuition that it can’t be right; you actually will have compelling logical reasons to reject it.

Note that I will not deny the core principle of cognitive science that minds are computational and therefore in principle could be simulated in such a way that the “simulations” would be actual minds. That’s usually what defenders of the Simulation Argument assume you’re denying, and perhaps in many cases it is; but that’s not what I’m denying. Yeah, sure, minds are computational (probably). There’s still no reason to think we’re living in a simulation.

To make this refutation, I should definitely address the strongest form of the argument, which is Nick Bostrom’s original disjunction. As I already noted, I believe that the disjunction is in fact true; at least one of those propositions is almost certainly correct, and perhaps two of them.

Indeed, I can tell you which one: Proposition (2). That is, I see no reason whatsoever why an advanced “posthuman” species would want to create simulated universes remotely resembling our own.

First of all, let’s assume that we do make it that far and posthumans do come into existence. I really don’t have sufficient evidence to say this is so, and the combination of millions of racists and thousands of nuclear weapons does not bode particularly well for that probability. But I think there is at least some good chance that this will happen—perhaps 10%?—so, let’s concede that point for now, and say that yes, posthumans will one day exist.

To be fair, I am not a posthuman, and cannot say for certain what beings of vastly greater intelligence and knowledge than I might choose to do. But since we are assuming that they exist as the result of our descendants more or less achieving everything we ever hoped for—peace, prosperity, immortality, vast knowledge—one thing I think I can safely extrapolate is that they will be moral. They will have a sense of ethics and morality not too dissimilar from our own. It will probably not agree in every detail—certainly not with what ordinary people believe, but very likely not with what even our greatest philosophers believe. It will most likely be better than our current best morality—closer to the objective moral truth that underlies reality.

I say this because this is the pattern that has emerged throughout the advancement of civilization thus far, and the whole reason we’re assuming posthumans might exist is that we are projecting this advancement further into the future. Humans have, on average, in the long run, become more intelligent, more rational, more compassionate. We have given up entirely on ancient moral concepts that we now recognize to be fundamentally defective, such as “witchcraft” and “heresy”; we are in the process of abandoning others for which some of us see the flaws but others don’t, such as “blasphemy” and “apostasy”. We have dramatically expanded the rights of women and various minority groups. Indeed, we have expanded our concept of which beings are morally relevant, our “circle of concern”, from only those in our tribe on outward to whole nations, whole races of people—and for some of us, as far as all humans or even all vertebrates. Therefore I expect us to continue to expand this moral circle, until it encompasses all sentient beings in the universe. Indeed, on some level I already believe that, though I know I don’t actually live in accordance with that theory—blame me if you will for my weakness of will, but can you really doubt the theory? Does it not seem likely that this it the theory to which our posthuman descendants will ultimately converge?

If that is the case, then posthumans would never make a simulation remotely resembling the universe I live in.

Maybe not me in particular, for I live relatively well—though I must ask why the migraines were really necessary. But among humans in general, there are many millions who live in conditions of such abject squalor and suffering that to create a universe containing them can only be counted as the gravest of crimes, morally akin to the Holocaust.

Indeed, creating this universe must, by construction, literally include the Holocaust. Because the Holocaust happened in this universe, you know.

So unless you think that our posthuman descendants are monsters—demons really, immortal beings of vast knowledge and power who thrive on the death and suffering of other sentient beings, you cannot think that they would create our universe. They might create a universe of some sort—but they would not create this one. You may consider this a corollary of the Problem of Evil, which has always been one of the (many) knockdown arguments against the existence of God as depicted in any major religion.

To deny this, you must twist the simulation argument quite substantially, and say that only some of us are actual people, sentient beings instantiated by the simulation, while the vast majority are, for lack of a better word, NPCs. The millions of children starving in southeast Asia and central Africa aren’t real, they’re just simulated, so that the handful of us who are real have a convincing environment for the purposes of this experiment. Even then, it seems monstrous to deceive us in this way, to make us think that millions of children are starving just to see if we’ll try to save them.

Bostrom presents it as obvious that any species of posthumans would want to create ancestor-simulations, and to make this seem plausible he compares to the many simulations we already create with our current technology, which we call “video games”. But this is such a severe equivocation on the word “simulation” that it frankly seems disingenuous (or for the pun perhaps I should say dissimulation).

This universe can’t possibly be a simulation in the sense that Halo 4 is a simulation. Indeed, this is something that I know with near-perfect certainty, for I am a sentient being (“Cogito ergo sum” and all that). There is at least one actual sentient person here—me—and based on my observations of your behavior, I know with quite high probability that there are many others as well—all of you.

Whereas, if I thought for even a moment there was even a slight probability that Halo 4 contains actual sentient beings that I am murdering, I would never play the game again; indeed I think I would smash the machine, and launch upon a global argumentative crusade to convince everyone to stop playing violent video games forevermore. If I thought that these video game characters that I explode with virtual plasma grenades were actual sentient people—or even had a non-negligible chance of being such—then what I am doing would be literally murder.

So whatever else the posthumans would be doing by creating our universe inside some vast computer, it is not “simulation” in the sense of a video game. If they are doing this for amusement, they are monsters. Even if they are doing it for some higher purpose such as scientific research, I strongly doubt that it can be justified; and I even more strongly doubt that it could be justified frequently. Perhaps once or twice in the whole history of the civilization, as a last resort to achieve some vital scientific objective when all other methods have been thoroughly exhausted. Furthermore it would have to be toward some truly cosmic objective, such as forestalling the heat death of the universe. Anything less would not justify literally replicating thousands of genocides.

But the way Bostrom generates a nontrivial probability of us living in a simulation is by assuming that each posthuman civilization will create many simulations similar to our own, so that the prior probability of being in a simulation is so high that it overwhelms the much higher likelihood that we are in the real universe. (This a deeply Bayesian argument; of that part, I approve. In Bayesian reasoning, the likelihood is the probability that we would observe the evidence we do given that the theory is true, while the prior is the probability that the theory is true, before we’ve seen any evidence. The probability of the theory actually being true is proportional to the likelihood multiplied by the prior.) But if the Foundation IRB will only approve the construction of a Synthetic Universe in order to achieve some cosmic objective, then the prior probability is something like 2/3, or 9/10; and thus it is no match whatsoever for the some 10^12 evidence in favor of this being actual reality.

Just what is this so compelling likelihood? That brings me to my next point, which is a bit more technical, but important because it’s really where the Simulation Argument truly collapses.

How do I know we aren’t in a simulation?

The fundamental equations of the laws of nature do not have closed-form solutions.

Take a look at the Schrodinger Equation, the Einstein field equations, the Navier-Stokes Equations, even Maxwell’s Equations (which are relatively well-behaved all things considered). These are second-order partial differential equations all, extremely complex to solve. They are all defined over continuous time and space, which has uncountably many points in every interval (though there are some physicists who believe that spacetime may be discrete on the order of 10^-44 seconds.) Not one of them has a general closed-form solution, by which I mean a formula that you could just plug in numbers for the parameters on one side of the equation and output an answer on the other. (x^3 + y^3 = 3 is not a closed-form solution, but y = (3 – x^3)^(1/3) is.) They have such exact solutions in certain special cases, but in general we can only solve them approximately, if at all.

This is not particularly surprising if you assume we’re in the actual universe. I have no particular reason to think that the fundamental laws underlying reality should be of a form that is exactly solvable to minds like my own, or even solvable at all in any but a trivial sense. (They must be “solvable” in the sense of actually resulting in something in particular happening at any given time, but that’s all.)

But it is extremely surprising if you assume we’re in a universe that is simulated by posthumans. If posthumans are similar to us, but… more so I guess, then when they set about to simulate a universe, they should do so in a fashion not too dissimilar from how we would do it. And how would we do it? We’d code in a bunch of laws into a computer in discrete time (and definitely not with time-steps of 10^-44 seconds either!), and those laws would have to be encoded as functions, not equations. There could be many inputs in many different forms, perhaps even involving mathematical operations we haven’t invented yet—but each configuration of inputs would have to yield precisely one output, if the computer program is to run at all.

Indeed, if they are really like us, then their computers will probably only be capable of one core operation—conditional bit flipping, 1 to 0 or 0 to 1 depending on some state—and the rest will be successive applications of that operation. Bit shifts are many bit flips, addition is many bit shifts, multiplication is many additions, exponentiation is many multiplications. We would therefore expect the fundamental equations of the simulated universe to have an extremely simple functional form, literally something that can be written out as many successive steps of “if A, flip X to 1” and “if B, flip Y to 0”. It could be a lot of such steps mind you—existing programs require billions or trillions of such operations—but one thing it could never be is a partial differential equation that cannot be solved exactly.

What fans of the Simulation Argument seem to forget is that while this simple set of operations is extremely general, capable of generating quite literally any possible computable function (Turing proved that), it is not capable of generating any function that isn’t computable, much less any equation that can’t be solved into a function. So unless the laws of the universe can actually be reduced to computable functions, it’s not even possible for us to be inside a computer simulation.

What is the probability that all the fundamental equations of the universe can be reduced to computable functions? Well, it’s difficult to assign a precise figure of course. I have no idea what new discoveries might be made in science or mathematics in the next thousand years (if I did, I would make a few and win the Nobel Prize). But given that we have been trying to get closed-form solutions for the fundamental equations of the universe and failing miserably since at least Isaac Newton, I think that probability is quite small.

Then there’s the fact that (again unless you believe some humans in our universe are NPCs) there are 7.3 billion minds (and counting) that you have to simulate at once, even assuming that the simulation only includes this planet and yet somehow perfectly generates an apparent cosmos that even behaves as we would expect under things like parallax and redshift. There’s the fact that whenever we try to study the fundamental laws of our universe, we are able to do so, and never run into any problems of insufficient resolution; so apparently at least this planet and its environs are being simulated at the scale of nanometers and femtoseconds. This is a ludicrously huge amount of data, and while I cannot rule out the possibility of some larger universe existing that would allow a computer large enough to contain it, you have a very steep uphill battle if you want to argue that this is somehow what our posthuman descendants will consider the best use of their time and resources. Bostrom uses the video game comparison to make it sound like they are just cranking out copies of Halo 917 (“Plasma rifles? How quaint!”) when in fact it amounts to assuming that our descendants will just casually create universes of 10^50 particles running over space intervals of 10^-9 meters and time-steps of 10^-15 seconds that contain billions of actual sentient beings and thousands of genocides, and furthermore do so in a way that somehow manages to make the apparent fundamental equations inside those universes unsolvable.

Indeed, I think it’s conservative to say that the likelihood ratio is 10^12—observing what we do is a trillion times more likely if this is the real universe than if it’s a simulation. Therefore, unless you believe that our posthuman descendants would have reason to create at least a billion simulations of universes like our own, you can assign a probability that we are in the actual universe of at least 99.9%.

As indeed I do.