# Are we living in a Simulation?

The short answer is NO WE ARE NOT. You can stop reading here if your curiosity has been satisfied. If you are one of the increasingly scarce people in the world who still insist on thinking for themselves I will devote the rest of this blog to supporting my contention. I never felt compelled to think about this question until I recently realized that many of my “intelligent” friends have taken the musings of various famous futurists to heart and decided that this is a serious physics question. At first I thought they had just watched too many reruns of The Matrix but then I started hearing it in the popular press from luminaries like Elon Musk;

https://www.theguardian.com/technology/2016/oct/11/simulated-world-elon-musk-the-matrix

http://www.space.com/32543-universe-a-simulation-asimov-debate.html

The first problem with providing a rational answer to this question is that it really can’t be formulated as a rational question. What do you mean by living in a simulation?

- There is another universe with physical laws identical to our own which is running a computer that is based on a Turing design that is simulating us?
- There is another universe beyond ours with magical new incomprehensible physics laws that make it possible for a non-Turing based computer to be simulating us but the word “simulation” still means the same thing?

There are many others but let’s just examine these two to see if we can grapple with the questions they present before introducing more. One is easy to address… our universe cannot be simulated with a Turing like computer… or we wouldn’t think Quantum computers were an exciting idea. A Turing based computer cannot compute the physics we experience so we are definitively NOT living in a simulation running inside any kind of computer design that the human race has yet conceived of. This observation is the basis of my related contention that we CANNOT simulate a living organism or a brain with a man-made computer nor will we be uploading our souls to one anytime soon. Our computers simply do not have the capacity to compute the kind of physics that makes life and thought possible. If they could… we would be able to simulate a quantum computer with a Turing computer and we can’t do that either! So question one is silly because any competent computational physicist can decisively observe that we can’t compute real-physics with our toy computers. Making them faster with more bits doesn’t change that problem either, ever.

Now let’s tackle number two… what if magic is allowed? Can there be some external Universe governed by different or better laws than our own that make simulating THIS Universe possible for some other kind of computer design that is NOT like a Turing machine? Fortunately we can answer this question EVEN with “magic” allowed. The math physicists use to describe the relationships between the forces of nature are the same in ALL possible Universes. Physics fails in EVERY universe in which Pi is not exactly Pi. In other words, even God couldn’t change the value of Pi if he wanted to. So if we ARE living inside a simulation, it is a simulation that is robust enough to allow us to employ mathematical tools that tell us about the properties of any possible EXTERNAL host universe. However the fact that Pi has the same value in any universe also tells us that irrational numbers and infinitesimal numbers that we only know how to compute with infinitely iterated recursive functions also have to be computable to unlimited precision instantly by any host universe. How much energy does it take to instantly compute an infinite number series? It takes an INFINITE amount of energy. Can we or any advanced civilization make a computer that can harness an infinite amount of energy? Not that we can conceive of at the moment (without requiring MAGIC) so no.

Humans have derived some amazing mathematics over the past 120 years that describe our universe with remarkable mathematical precision. That math also tells us a great deal about the limits of any new answers we may find to the remaining unanswered questions of physics. Until the era of string-theory in the 1980’s it appeared that our universe was <almost> fully described by just two primary theories. Quantum Mechanics and Relativity. These theories had their aesthetic flaws but their powers for describing the observable properties of our universe where indisputable. The aesthetic flaws however were impossible to ignore;

- The Universe seemed to require the EXACT cancellation of infinitesimal values to compute correctly
- The Universe seemed to require of a few magical constants that were essential to physics working for no explicable reason
- The two theories couldn’t agree on how gravity worked
- The most interesting math that seems to describe physics is beyond our capacity to compute

String theory, culminating in M-theory, blossomed in the 1990’s and seemed to provide answers to these fundamental questions while generating many more. We had discovered exotic new math that seemed to enable us to compute the fundamental particles and constants of physics and provided tools for canceling some of the massive infinities that arose from trying to analyse even the simplest physical systems. String theory even gave us answers to what happens inside singularities and what was the universe before the Big-Bang. Unfortunately many of those answers were hauntingly unsatisfying, because more often than not, string theory told us a lot about the limits of what we know how to compute. Suffice it to say that M-theory provides answers to some of the apparent flaws in classical physics that may have appeared to make the universe look computationally manageable when in fact it was not.

https://en.wikipedia.org/wiki/String_theory

The short of it is that the universe we live in appears to compute infinitesimal values with infinite precision instantly. That takes infinite energy to compute, which means we probably aren’t living inside an advanced alien civilization teenagers gaming PC as a simulation because their PC would need to consume all of the energy in their universe to function, which would cause their parents to unplug the sim when they received their infinite power bill.

So what if you harnessed the apparently infinite computing resources of physics to simulate another world? Then it wouldn’t be a “simulation”, it would be the real universes’s physics computing us. Inversely, we can’t make a Turing computer that simulates a quantum computer… if we could we wouldn’t need quantum computers… If we built a super fast quantum computer using qbits to simulate it, that computer would NOT be able to simulate quantum computing because the act of reading a qbit destroys its quantum state. We would therefore need an infinite number of qbits to simulate a qbit… whoops… Since we live inside a universe that can perform quantum calculations… we’re once again… not living in a simulation. If we were living inside a simulation that could simulate quantum mechanics then we would not be INSIDE the sim unless you got really creative at contriving a definition of “simulation” that was indistinguishable from being made out of the same physics as the ones employed by the host universe?

The circularity of the last point also suggests that the idea of a “simulation” is a purely human contrivance based on the false assumption that it is even possible to compute us with a finite machine. So let’s summarize where we are at before we proceed;

- Our universe appears to require infinite energy to compute. No finite, bounded machine, however large can encompass such a calculation.
- We know that a Turing computer can’t compute our universe… so it can probably also never simulate life or download our minds either.
- A quantum computer can’t simulate a quantum computer. The act of reading a qbit destroys it’s “quantumy” properties, sending us back to needing infinite energy again even if our world was a simulation running inside a quantum computer.
- God can’t change the value of Pi or any other infinitesimal numbers physics requires, so there can be no external universe that obeys new mathematical laws we can’t fathom from here.

So we almost certainly live in the root universe. We may occupy an extremely tiny isolated atoll of The Universe that is uniquely qualified to support life as we know it. We MAY be cut off from physical visibility into The Universe beyond the boundaries that enable our survival but if physics has taught us anything it is that we have been very successful at employing the powers of mathematics to infer information far beyond the confines of our own local environment.

If the answer is relatively straight forward why are great minds debating it? One answer is it’s just a new version of the God debate we’ve been having for centuries. A more interesting answer is that we DO live inside a simulation but not one of any grand scale. The simulation we live inside is between our ears. As much as we like to think of human intelligence, a human brain is really pretty constrained by its limited computing resources. In order to “place” itself in reality the human brain, comprised of about a grapefruit volumes worth of cells and consuming roughly 25 Watts of power has to fabricate a model of the world it is trying to survive in. Our minds cut a LOT of corners in order to hallucinate a model of reality that is complex enough to give us an edge on survival but simple enough to run in real-time so that we can make snap life-or-death survival decisions without needing hours to analyse our survival options when say, we are attacked by a shark. That said the human mind is a remarkable learning machine, it constantly strives to understand and invent models of natural forces that it can use to predict future events based on current circumstances. What does the human mind substitute for a problem it can’t solve or hasn’t solved yet? It may put a TBD marker on the question so that when we have an unresolved thought like, “I wonder why something exists instead of nothing” the brain, which has no way to answer the question, just substitutes an intelligent entity like itself that has or will eventually find the answer to that question. “How does a jet engine work?” Somebody smarter than me figured it out! “How do Amoeba’s work?” Somebody smarter than me made them! Makes perfect sense, right?

So we do live in a crude simulation fabricated by our minds which vastly over-simplifies many things in order to always operate in real-time. The bad simulation of reality is easily breached and we do it often when we analyze the world rationally and use the tools of mathematics and scientific method to carefully define the boundary between how we imagine The Universe works and how it can be PROVEN to actually work. Our minds impose a primitive, instinctual survival filter in front of the real properties of The Universe we inhabit causing us to view it irrationally. Rational thinking is slow, demanding, not suitable for immediate survival and often unrewarding. It requires a great deal of discipline to adhere to while our instincts constantly try to steer us towards believing quicker more appealing ideas that require less work to comprehend and simulate. We crave trite answers to incomprehensible problems. Our minds would not be able to function in a real-time world if we were not constantly forced to surrender to the constraints of our limited computing resources by frequently embracing simplicity over reality, or instinct over reason. This is the intellectual paradox of being human that results in seemingly brilliant scientific minds claiming that they are using computers to model human minds, the climate, creating artificial intelligence or are on the brink of finally getting the Start Menu right in Windows 11.

Conclusion:

- We don’t live in a sim
- We CAN’T live in a sim so we can never be uploaded to a computer
- The universe can’t be simulated but our brains are stupid and easily fooled so there is hope for virtual reality
- Because we are stupid we can IMAGINE that we live in a simulation and something as dumb as we are that is NOT us might be possible to simulate on a computer.
- ergo, there will be no “Artificial Intelligence” like us simulated by a computer there will only be real-intelligence. The are no ACTUAL advances in “Artificial Intelligence” taking place, just advances in computing.

Somewhere else you said that human intelligence can’t be replicated because we can’t replicate a brain on a subatomic level. Still is this level of fidelity really required? MAME emulates tons of old arcade games but it doesn’t need to emulate the behavior of electrons inside the chips.

Couldn’t we even emulate our world with enough fidelity without the need to replicate its quantum behaviors?

Two good questions. Turing machines can perfectly emulate Turing machines with finite energy. Quantum computers can’t emulate quantum computers perfectly with finite energy. So your question boils down to this “does life REQUIRE more than a Turing machine to simulate it?” The answer to your question is very probably YES life requires more than a Turing machine to emulate. I’ve written several articles in previous blogs about why this is likely to be the case. That’s not the same as saying that artificial life is not possible with a Turing machine, it just won’t be like ours. I got into 3D graphics in the 1980’s because I was interested in using computers to simulate quantum interactions between Kilgore and matter. That was how I came to learn about ray tracing. Ray tracing is the modern technique we use to make movie effects look real. I can’t even spot some cgi effects anymore they’ve gotten so good. That doesn’t mean we’ve actually mastered light simulation, we’ve just mastered fooling our own eyes. We may yet master fooling our minds into thinking we’ve mastered AI, that’s a lot easier to accomplish than actually doing it.

Facebook reminded me of an old article I posted a year ago that I was going to write a blog about how MIT just proved that neural networks are actually NOTHING like the way humans think… They’re NOT a simulation of intelligence, they’re just something WE invented that seems to think. So we’re really making progress at finding ways to rationalise that we are making progress.

“The short of it is that the universe we live in appears to compute infinitesimal values with infinite precision instantly.”

I don’t believe a live computer-generated simulation would necessarily need to compute an infinitesimal number of values to an infinite level of precision instantly. For example, while we could definitely point to transcendental numbers (e.g. pi and e) as being infinitely precise (and therefore requiring an infinite amount of resources to compute to their exact values), their real-world values MUST be far less precise due to absolute constraints on what constitutes reality; items like distance and causality (i.e. change over time).

Only a simulation would allow for the possibility of a length shorter than that of the Planck length (i.e. approximately 1.616199×10^−35 m), or of causal interaction over a moment shorter than the speed of light over a distance of the Planck length (i.e. Planck time, which is approximately 5.391×10^-44 s). When factoring these limitations in, the real-world values of pi and e are functionally finite (even though their respective “simulated” values are exact, but non-terminating).

“If we were living inside a simulation that could simulate quantum mechanics then we would not be INSIDE the sim unless you got really creative at contriving a definition of “simulation” that was indistinguishable from being made out of the same physics as the ones employed by the host universe?”

Absolutely. I don’t think a real-time, computer-driven simulation would be possible for the reasons outlined in your article. The definition of “simulation” would most definitely need to be stretched.

The only kind of “simulation” I see as viable would be a sort-of “seeded simulation”. A finite amount of energy could be used to seed this universe, and it could even be deployed in such a way to ensure that a certain interactions would be guaranteed to occur over a given amount of causal propagation. However, I think a “seeded simulation” would be far more limited for the observing universe, since: 1) the amount of energy needed to correctly seed the simulated universe so that causal propagation occurred as they intended would need to increase the farther that causal propagation was desired (which would mean finite energy for finite causal propagation, and 2) limited ability to observe the changes within the simulated universe (analogous to our limited abilities in external observations of black holes (Hawking radiation, no-hair theorem, etc)).

“Our minds cut a LOT of corners in order to hallucinate a model of reality that is complex enough to give us an edge on survival but simple enough to run in real-time so that we can make snap life-or-death survival decisions without needing hours to analyse our survival options when say, we are attacked by a shark”

I suppose this is the closest we’ll get (in our lifetimes at least) to a so-called “simulated” existence. While we often purport that we are capable of impossible feats and a seemingly boundless capacity for learning, in the end, we are really only electro-chemical state machines with all-too-real physical limitations. If we replace a global simulation for a large number of individual simulations, then our interpretation of “reality” would be (as Morpheus of the Matrix trilogy put it) “[nothing more than] electrical signals interpreted by your brain”.

“This is the intellectual paradox of being human that results in seemingly brilliant scientific minds claiming that they are using computers to model human minds, the climate, creating artificial intelligence or are on the brink of finally getting the Start Menu right in Windows 11”

You just couldn’t resist, could you?

Good discussion Jonathan, you’ve actually given me material to tackle the same position from a very different angle. The key assumption underlying your premise is;

“I don’t believe a live computer-generated simulation would necessarily need to compute an infinitesimal number of values to an infinite level of precision instantly.”

I’ll take that statement as a challenge to attempt to refute your assumption. I get why this seems like a reasonable assumption, we don’t need all that precision to get life, at some scale a rounding error will be fine. I assert that IF that were true and we were a sim we would observe mathematical moire patterns in infinitesimal numbers which would make them cryptographically vulnerable. Tests on quantum number generators appear to show no statistical moire patterns that would suggest truncation or rounding of their values in this Universe. If we found them… cryptography might not work. Our statistical tools for analyzing extremely big numbers are very powerful and so far the Universe’s quantum random number generator appears to be moire free. BUT your assumption was not about whether or not we are in a sim, you simply asserted that you think it is likely we could compute some reasonable facsimile of life in a Turning machine that tolerated such rounding errors. Here’s why I think there is a good chance you are actually mistaken and a second argument for why we are probably not a sim. First read my blog article titled “Life Needs Noise” as a basis for this point. In that article I observe that the way life is computed is completely different from the way a Turing machine computes.

Life appears to rely on the Universe’s random number generator to compute correctly. Does it REQUIRE the full precision of the Universe’s random number generator?

Physicists like to confuse interesting philosophical discussions about the structure of life with equations that nobody but they understand. If we agree that life requires NOISE to compute and if we agree that quantum noise appears to have infinite precision (No truncation patterns that would we should be able to easily observe) then what is the magical pure SOURCE of the Universe’s random number generator? There are several quotes about the properties of quantum mechanics from the great minds of physics that might give us a clue.

“What really interests me, is whether God had any choice in the creation of the world.”

-Albert Einstein

“God does not play dice with the Universe.”

-Albert Einstein

“A key feature of quantum theory [is that] it deals with probabilities rather than certainties, not because we lack absolute knowledge, but because some aspects of Nature are, at their very heart, governed by the laws of chance.”

“Everything that can happen does happen”

-Brian Cox

“Though we talk of the universe “splitting,” this isn’t precisely true. From a mathematical standpoint, there’s only one wavefunction, and it evolves over time. The superpositions of different universes all coexist simultaneously in the same infinite-dimensional Hilbert space. These separate, coexisting universes interfere with each other, yielding the bizarre quantum behaviors.”

In Dublin in 1952, Erwin Schrödinger gave a lecture in which he jocularly warned his audience that what he was about to say might “seem lunatic.” He said that, when his Nobel equations seemed to describe several different histories, these were “not alternatives, but all really happen simultaneously.” This is the earliest known reference to the multiverse.[1]

Let’s put these thoughts together into another interpretation or perspective on what they imply. The Universe is described by a wavefunction which exists in a Hilbert Space of all possible states it can occupy. If Hilbert space is NOT real then we have no explanation for how the apparent random properties of the Universe seemingly emerge from nothing… however if ALL possible Hilbert spaces are real then we DO have an answer. Wavefunctions are described by continuous functions, if all of them exist at once and we only live in one of them then we can only observe the quantum state of the one we live in which will generally conform to a flawless Gaussian distribution of probabilities occurring for all events. Hence the Universe can appear to have a flawless random number generator from our point of view, while still being perfectly described by a continuous wave function. The finite number of quantum states that the Universe can physically occupy may be incomputably huge but finite none-the-less. But wait… if the quantum states are finite then the Universe must have a precision limit right? Probably not, quantum mechanics breaks down at the Planck Length where we are then forced to resort to the more exotic mathematics of String Theory to again find a seemingly continuous Universe. The implications of this are interesting… if the Universe has unlimited precision then it is effectively cryptographically isolated from other Universes. The boundary between our world and the others is defined by flawless entropy and it’s impenetrable. If the Universe has a precision limit, then the boundary between our world and others may be “crackable” in the sense that it may be possible for us to simulate one of the others with a quantum computer. The source of our apparent perfect randomness is the anthropomorphic principal itself, the only Universe possible for life to observe will appear to be made of perfect Gaussian probability distributions at the quantum level.

Back to the original question… is there a digital precision limit sufficient for usefully simulating life and quantum mechanics? Maybe but I would predict that we might encounter the problem we encounter now with digital physics simulations and neural networks. They get “stuck” in local minima’s where they oscillate forever without escaping. The missing precision in a calculation causes them to never compute a value that would bump them out of a trapped quantum state such that the physics simulation eventually collapses into regularity. It is the infinite, instant continuousness of physics that appears to prevent us all from dying quickly by collapsing into stasis. To keep a finite precision simulation of life alive, I predict that you would find that you needed to constantly pump quantum noise into the simulation from the Universe to keep it unstable…. and once you inject quantum noise from reality into the sim that way… is it still a sim?

In other words, it seems LIKELY to me that the quantum property of a particle having some probability, however remote, of teleporting instantly to any position in the entire Universe is essential to simulating life and intelligence. I assert that quantum tunneling may be the source of “creation”, “innovation”, “evolution” or “creativity” in physics.