Are We Living in a Simulation? (Column 751)

With God's help

Not infrequently in the past I was asked what I would answer to the question whether we are living in a simulation. A strange question, and on its face an entirely silly one. Not because the answer to it is this or that, but because on its face it makes no sense at all. Just a passing thought: semantically it may perhaps have some kind of meaning, roughly like "Is this triangle round?", "What is the sum of the angles of this sphere?", "Are the waters of the sea kindhearted?", or "Is virtue triangular?". This is unlike "What is the difference between a rabbit?" (answer: "that both its ears are three times longer than each other").

What made me think about it again (actually: for the first time) was an article I saw not long ago on Ynet about some academic paper that is apparently causing a stir (see also here). The article on Ynet bears the title: "Scientists proved mathematically: it is impossible for the universe to be a computerized simulation" (see here for a question I received on the site about this research). On its face, this is a strange and illogical article about a strange and illogical topic, and it led me to wonder which of the silly things that appear in the article are found in the research it describes, and which are the journalist's "value added" (Yogev Israeli). Skimming the paper itself made it clear to me that quite a bit of this is found in the original as well (though in a somewhat more sensible and better-defined form).

In the opening of the article, the following quote from Elon Musk is cited:

Several years ago, Elon Musk declared that, in his opinion, there is a high probability that the reality we live in is nothing more than a computerized simulation.

It turns out that quite a few intelligent people are occupied with this nonsense. (Admit it: we have heard of quite a few people stupider than Elon Musk. He may be a fool, but he is certainly not an idiot.) So I again wondered whether some meaning can nevertheless be found in this strange question. And of course after that we must ask whether it really can be "proved mathematically" that this is not the case.

The Fundamental Problem

There are two questions here: A. The question of idealism: are we existent entities or imaginary ones? B. And if not, then what are we? Are we creatures who live and act within a simulation (run by someone or something)? The fundamental problem with both these questions, as noted, is that their meaning is unclear (even if semantically there is some meaning). If I do not exist but merely constitute a creature in someone else's simulation, then who is conducting this very discussion? The owner of the simulation? This takes us into Descartes' cogito argument (see about it in column 363). Descartes argued that when I myself say or think that I do not exist, this is a self-contradictory statement, since the one who says it certainly exists. Even if I say that I do not exist, the very fact that I say something means that I exist (and therefore what I said is false). I will not go into the question here whether this conclusion is the result of what was later called (by Kant) an 'ontological argument'—that is, a conclusion that follows from conceptual and logical analysis alone, without any assumptions—as Descartes believed. In that column I pointed out that this is not the case. Still, the argument obviously seems correct, and its conclusion obviously correct. I cannot discuss the question whether I myself exist or not.

As for question B, what does it mean that the whole world is a simulation? Presumably they mean to claim that in fact all of us are creations of someone else's mind, and that we are merely objects (which he observes) and not subjects (possessing consciousness and thought). Is this a simulation of some computer, or is it merely a metaphor? If it is a computer simulation, then there are rules for how a computer works and how simulations proceed (they are supposed to be 'computational', for example). The discussion in the paper enters into this, and therefore it seems clear that this is indeed how they see the matter. But on its face this is nonsense. If we do not exist, then who is it that "says" this? Moreover, how can we say anything about the "computer" within which the simulation of which we are a part is taking place? Whence the presumption to say anything about that system? How can we even assume that it is a computational system or a non-computational one? And what importance is there to the question whether the thing within which our fiction exists (that is, we) is a computer or something else? Or to the question whether it is of a computational type or not?

If the basic claim is that we are not really existent entities, the discussion ought to stop here. Everything said beyond that is mere empty chatter. And if we do exist, then the meaning of existing (as a subject; one may discuss whether Bugs Bunny exists) is precisely not being part of a simulation.

When I say that someone else is a creature in a simulation, what I have really said is that he does not exist, and that only I as observer imagine him, perhaps watching him as one watches a film or reads a book. I experience/see some virtual creature, and that is all. There is no meaning whatsoever to discussing whether that creature has consciousness, whether it perceives itself, or how it perceives itself. After all, it does not exist at all. It is only a (virtual) object and not a subject. This is roughly like asking what was really going through Raskolnikov's mind (the hero of Dostoevsky's Crime and Punishment) when he murdered his victim. A meaningless question. He does not exist, and therefore nothing went through his mind. One may of course ask what the author wanted us to think about what would have gone through Raskolnikov's mind had he existed. But that is an entirely different question. That question assumes that we exist, without reference to the existence of the creature that is the object of our thoughts (Raskolnikov). One might ask whether there is someone who watches us although we do not exist, and in whose mind thoughts pass about what passes in our minds (in the literary sense: that is, what would have been supposed to pass through our minds if we really existed). But the discussion whether we are creatures within a simulation is a discussion that we ourselves are conducting, not someone else. Such a discussion has no meaning whatsoever.

In short, a priori, even before I read a single word of the research and the article describing it, it is clear that this entire discussion is one great heap of nonsense, on both levels: 1. There is no meaning to the discussion whether we exist. 2. Even if there were meaning to that discussion, our own discussion whether we operate within a simulation is senseless. All that remains now is for me to wonder whether this nonsense is the journalist's invention (as often happens when significant scientific results are taken and populist conclusions are drawn from them, sometimes silly ones and perhaps ones with no meaning at all, in order to increase ratings and interest), or whether the researchers themselves fell into this pit of nonsense.

Before I continue, a brief reminder of an earlier discussion, which will illuminate this nonsense from another angle.

A Reminder from Column 158: The Detachment Transformation

At the end of the previous section, the question under discussion was whether human beings are part of a simulation. But before that I touched on a slightly different question: I myself ask whether I live and act in a simulation. About the first question I showed that it has a straightforward meaning (and also a straightforward answer: no). But the second question is already downright senseless and especially ridiculous.

In the series of columns devoted to defining philosophy (155 – 160), among other things I discussed a critique of Ron Aharoni's critique of philosophy. His main thesis is that when a person observes himself and identifies the observer (the subject) with the object of observation (the object), a difficulty is created, and that this is the kind of difficulty with which philosophy deals (he shows there that all philosophical issues are examples of this mistake). According to Aharoni, this is an illusory difficulty, because when a person looks at himself he should see the object he is observing (himself) as an entity separate from the subject observing it (him). I also dealt with this distinction in column 81. From this Aharoni proposes a technique that he calls the 'detachment transformation' in order to diagnose a philosophical issue and show that it is the result of an error. Suppose there is a philosophical issue in which Reuven looks at himself and a difficulty arises. Put another person in place of the object (the one being looked at), and think of it as though Reuven were observing Shimon, and you will immediately see that the difficulty disappears. This is an indication that the difficulty is illusory, since even when Reuven observes himself, this is not essentially different from his observing Shimon.

After explaining his thesis, he goes on to demonstrate how it empties all philosophical questions of content. He goes through the central philosophical issues and shows that once one insists on this distinction (and uses the detachment procedure), the issue evaporates. In one of the chapters of the book he deals with the question of idealism-solipsism. Does what I know indeed exist somewhere out there, or is it a hallucination or a dream that exists only within me (within my consciousness)? Let me say in advance that in my view this is a classic philosophical question, because it is not accessible to the tools of scientific observation, and therefore it does not deal with a description of simple physical reality as I perceive it, but with the question about that very reality. Hence it can be answered only by means of intuition and not by scientific tools, and therefore according to my definition (in the two columns that preceded that one) this is a philosophical question.

Let me sharpen the point: this is not to say that I am troubled by it. Not at all. But I am not troubled because my intuition tells me that the world indeed exists (my senses seem reliable to me), that is, because I found an answer, and not because the question is flawed by definition. This also explains the feeling many people have that this is a stupid, detached question, with no feet on the ground, and that nobody seriously thinks the world is an illusion or a dream. All this is true, but not because the question is undefined or contains a contradiction, circularity, or conceptual confusion, but because in our opinion we have an answer to it. Exactly as nobody today is troubled by the question whether gravity exists. That is an excellent question, but we are not troubled by it because we already have a satisfactory answer to it. But that is when I am dealing with the world or with people outside me. When I am dealing with myself, Aharoni is right that the question truly becomes senseless.

But here we are dealing with an even more bizarre version of this question: am I part of someone else's dream (and not whether someone else is part of my dream, which is what we have been discussing until now and have seen does have meaning, even if the answer to it is simple). I now return to Aharoni's discussion.

The question with which this philosophical issue is concerned is: is the world my dream and therefore not really existent? Aharoni writes there about this question as follows:

This question depends entirely on the fact that a person asks it about himself. Detachment turns it into a ridiculous one: 'Is the whole world Reuven's dream?' is a meaningless question. In this case, detachment not only removes the feeling of philosophy, but the entire problem. This means that the problem has no real content and no existence of its own. It is nothing but the presentation of the circular structure and a declaration about the paradox produced by it.

Here he applies the transformation of separation/detachment and redirects the question from himself to Reuven. Now the question really does become ridiculous. Why? Because it is clear to me that the world I observe is not Reuven's dream, for several reasons: first, someone else's dreams are not accessible to me, and that option does not exist. Moreover, if the whole world is Reuven's dream, then I too am part of that. If so, who is the person discussing the issue? Who is it that is supposed to determine whether the world is Reuven's dream? Reuven himself? Then where am I in this whole story? Is Reuven the one speaking here, or am I? It is easy to see that if the question is redirected to another person, the problem simply evaporates. All the more so when I discuss the question whether I myself am a character in Reuven's dream. I showed above the absurdity of that.

There I presented a critique of Aharoni's thesis itself, and also of his treatment of this particular philosophical issue. I showed there several of his analytical mistakes. But all this concerns his move from the ridiculousness of the question whether I am Reuven's dream, to the claim that the question whether Reuven is my dream (or perhaps whether I am my own dream) lacks philosophical content. Here our concern is only with his initial assumption: that if one redirects the question by means of the detachment transformation to the question whether I am Reuven's dream, one gets something patently absurd. I completely agree that this is an absurd and senseless claim (but, as noted, not with the consequences he derives from this regarding the nature of philosophical problems). Notice that this claim is entirely equivalent to the claim that we live in a simulation. Instead of a simulation performed on a computer, one posits a dream taking place in a person's consciousness. The ridiculousness of these two claims is of course identical as well.

Is the Universe Computational

The paper's abstract contains its main claim. Here is its translation:

Nevertheless, Gödel's incompleteness theorems, Tarski's undefinability theorem, and Chaitin's information-theoretic incompleteness establish fundamental limits on any such algorithmic program. Taken together, these results suggest that a fully algorithmic "theory of everything" is impossible: certain aspects of reality will remain computationally undecidable and can be approached only through non-algorithmic understanding. We formalize this by constructing a "meta-theory of everything" based on non-algorithmic understanding, showing how it can explain undecidable phenomena and demonstrating that the breakdown of computational descriptions of nature does not entail the collapse of science. Since any putative simulation of the universe would itself be algorithmic, this framework also suggests that the universe cannot be a simulation.

In other words, the authors claim to have proved that the theory of everything cannot be computational. I am not entering into the claim itself, since it rests on quite a bit of knowledge in various fields, and our discussion does not require that. Here I will touch only on the final conclusion: the universe cannot be a simulation.

What is the meaning of that claim? It says only that the theory describing the universe cannot be equivalent to some computer program. There is no algorithm (of the type familiar to us) that describes the laws of nature, that is, they are not computational. This has nothing whatsoever to do with idealist philosophical claims or with ontology in general. It does not deal with what exists and what does not exist, and in fact does not even deal with the world, but with the character of the laws of nature that describe it. The claim is that the laws of nature cannot be implemented by means of computer software. So what? What does this have to do with the metaphysics of a cosmic computer or divine algorithms?

Presenting this conclusion in the form that we are not a simulation is nothing but nonsense. What they proved is not a claim about the world (that is, not an ontological claim), but about the character of the laws of nature that describe it for us (an epistemological claim). Instead of saying that we have reached the conclusion that these laws have a certain property (that they are non-computational), for some reason they prefer to speak the language of science fiction, bring in cosmic computers within which we are all virtual creatures, and make claims about them instead of about us. This is roughly like expressing the fact that there is a law of conservation of energy by claiming that the supercomputer of which we are all a part is borne on the wings of three angels and two fairies, but those angels do not know how to produce energy. And since, as everyone knows, angels do know how to produce energy, apparently there are no such angels and therefore no computer borne by them either.

Sharpening the Distinction: Does Water Solve Equations?

To clarify further the distinction I made between the world and the laws that describe it, I will return to the example I presented in columns 35 and 591. The equations that govern the dynamics of fluids (such as water) are called the Navier–Stokes equations. These are very complicated equations that no mathematician or physicist knows how to solve except in a few especially simple cases. At the same time, the water itself does not find this very difficult. It flows exactly in accordance with those equations in every situation, however complex. Its motion constitutes a solution to the equations in every state in which it is found. Is it correct to say that water solves those equations? Of course not. Just as migratory birds do not solve differential equations when they navigate over enormous distances. The mathematical abilities of birds or of water simply do not exist.

The reason is that the motion of the water follows from its nature. Water does not solve equations; it simply flows. The equations serve human beings who try to describe the movement of water. Human beings who want to know what water will do in a given situation need to solve those equations, but the water simply flows in that situation without solving any equations. Suppose that this equation were non-computational in the sense discussed in the aforementioned paper (that is not the case, but I am using it as an example). Would that say anything about the world? Absolutely not. The water would continue to flow according to its nature. The only thing that would happen is that we could not use a computer or some algorithm to describe the motion of the water. This is mainly a claim about us and not really about the world.

From another angle: after all, the world exists and proceeds as it proceeds. That is, there is such behavior in actuality. Water moves as it moves, trees grow, and birds navigate. Therefore there cannot be any obstacle to there being a "computer" that simulates this behavior. If someone were to build an analog system corresponding to everything that happens in the world, it would certainly do it. Remember that water is itself an analog computer that solves the Navier–Stokes equations.

Of course, the following can be construed as a claim about the world: the world is built in such a way that human beings have no algorithmic way of describing it. But on the ontic plane this is not a particularly interesting claim. It belongs to the epistemic plane (= the cognitive plane; epistemology is the theory of knowledge, and it deals with human knowledge of the world), because the main interest in it lies in what it says about us and about the descriptions we can (or cannot) find for the world. In other words, it speaks about science and not about the world. In column 687 I described Norton's dome, which gives us a not-bad example of the limitations of our descriptions of the world, limitations that do not necessarily exist in the world itself.

For us, the term simulation is connected to algorithms (or Turing machines), that is, to the language by means of which we perform calculations and describe and model the world. When the authors spoke about simulation, that is what they meant. But if we broaden this term to include all possibilities of modeling the world (beyond the Turing machines they were talking about, and probably also beyond the limits of Gödel's theorem on which they relied), it seems to me that there can be no obstacle to the existence of such a model. As noted, the world itself is such a model. Bottom line: if the computer engineer who built the "computer" within which our simulation runs does not suffer from human limitations (he works like the water itself and not like human beings who describe it), then there is no obstacle at all to all of us being a simulation in his "computer." There are the philosophical and conceptual considerations I discussed above, which tell us that the metaphysical-ontic question is senseless. But that has no connection whatsoever to the mathematical proofs discussed in the aforementioned paper, and certainly not to quantum theory, relativity, and information theory. At most, these can address the question of the character of our descriptions of the world (the laws of nature), which I do not see as a particularly interesting philosophical issue, and in any case not a metaphysical-ontic one.

The authors themselves speak about the need for a non-algorithmic addition to the theory of everything, that is, they too understand that their claim concerns only questions of Turing computability and not of modeling in general. They too understand that there may be a model that describes the world if we add to the algorithmic part another non-algorithmic layer (whether to call that a "computer" or not is merely a semantic question). This of course sharpens my claim that their implied transition to metaphysical questions is completely unfounded.

A Note on Popular Science

The articles that report these findings present them as a philosophical revolution. By their very nature as popular-science articles, their emphasis is on the issue of computerized simulation and less on the technical considerations and matters in the research. Reading these reports can lead the reader to conclusions as though findings of decisive philosophical importance have been discovered here, whereas to the best of my understanding that is simply not the case. The conclusion they reached, if it is correct (as noted, I am a bit doubtful about it a priori), is certainly significant for scientists, but it has no great philosophical significance, nor is it of major interest to the average popular reader. And even if one wants to present these conclusions to the public, they could have said it in less pictorial language: the scientific description of nature is not Turing-computable. Sounds a bit dry, does it not? No wonder they prefer to speak about cosmic computers, people, and universes as simulations, even though all these are terms that belong to the realm of fantasy and science fiction, and have no connection whatsoever to the research findings.

I must say that phenomena of this kind are very common in the literature of popular science. The presentation of a scientific finding is greatly amplified and shown in a populist and pompous way, with the significance of the findings inflated and stretched in multidisciplinary and philosophical directions, quite without justification. There are mainly two reasons for this on the journalists' side, and one additional reason on the scientists' side.

From the writers' side, they of course do not always specialize in the field they are covering, and so they latch onto the populist aspects of the scientific research. Another reason is ratings. Which of the readers of Yediot or Maariv is interested in a report about some technical scientific finding? But the scientists themselves also tend to reinforce this trend, because they have an interest in presenting their research as momentous and as important beyond the technical issue and the specific field in which they work. Anyone familiar with this world knows that sometimes a report in the daily press (here we jokingly called it "Scientific Maariv") is perceived as more significant than the scientific publication itself (every article published in the daily press was posted on the bulletin board of the physics department, but nobody posted there anything from the professional literature). The reason is that the popular press reports only on findings that have broad and fundamental significance, and rightly so. Because of the readers' lack of interest, you will not find there reports on specific technical and professional findings. But for that very reason scientists have an interest in appearing there, because it means that their research has broad and fundamental importance. They therefore tend to present their research as having such meanings in order to gain reports in the daily press. Thus the academy's public-relations people try to promote such publications, and certainly when researchers themselves are interviewed, they too tend to present things in a populist (and not merely popular) manner. I should note that this paper is somewhat unusual in this respect, because my impression is that the pomposity and populism are already present in the scientific paper itself and not only in the popular reports about it.