Determinism from the Perspective of the Simulation Argument

It’s been almost two years since I last wrote about Free Will vs Determinism. The argument is the standard one, that since everything in the universe is governed by physical laws, it is completely deterministic. However, because it is not possible to to simulate the entire universe, it is at the same time unpredictable, so we should act as if there is free will.

However, one obstacle stood in the way of that argument: Quantum randomness.

With true randomness, we cannot say that the universe is deterministic. But with the basis that everything is governed by natural laws, it makes equally no sense to assert the existence of free will. Because, if all the same random events occurred the same way, another “run” of the universe would have the exact same result.

Even when you are thinking in your head at this very moment that you have free will, what is really most likely happening is that chemical processes in your brain have led your conscience to make that decision. If the entire universe “restarted” with the exact same sequence of random events, you would make the exact same decision again.

The Simulation Argument.

This is where the argument gets interesting. There is a very scary paper written by philosopher Nick Bostrom called, “Are You Living in a Computer Simulation?” It is scary because the implication, given a couple of premises, is that we are almost certainly living in a computer simulation. Not only that, but the argument posits that our simulators are themselves extremely likely to be in a simulation, and those simulators are likely too to be in a simulation, etc.

With the near certainty that we are in a simulation, determinism can only become stronger. You have probably heard of things called random number generators. A lot of these work by taking a seed number, and then running it through a specialized function over and over again, resulting in what is known as pseudorandom. These generating sequences that seem random but are completely deterministic, if you know where it started, i.e., the seed number and the algorithm.

This means that, providing our simulation ancestors, the beings who simulated our universe, are using similar ideas of random number generation, all the “random” quantum events we measure in our universe could actually be a completely determined sequence, perhaps by an algorithm so complex that it would be physically impossible to calculate from within this universe.

Of course, this is provided two premises:

  1. We are in a simulation.
  2. Our simulation could use pseudorandom number generation.

Premise 1 is actually very likely, from sheer numbers in the argument. It is Step 2 that is undecidable and for us to choose. If we accept it, this would imply our entire universe, including quantum events, is completely determined. And if we reject it, it would not rule out the possibility of total determinism either.


Given some invented definitions, here are the levels for free will vs determinism in the simulation framework:

  1. Total Free Will: Consciousness is special, i.e. not bound by physical laws. Free will comes from a higher source. (Question: What if this higher source is bound by physical laws in its universe?)
  2. Weak (Random) Free Will: Consciousness is not special, i.e. it is bound by physical laws. However, there are events in the universe that exhibit true randomness, so it is not fully deterministic.
  3. Weak (Random) Determinism: True randomness exists. However, given a specific set of outcomes of random events, the universe runs the same way.
  4. Total Determinism: True randomness does not exist, only pseudorandom exists. Thus, our universe will always run the same way under the same starting conditions.

Philosophy of The Matrix (Part 2)

Part 2 deals with the philosophy of prophecy. Part 1 discussed the philosophy of existence and simulated realities. Later parts may cover cycles of existence, morality and ethics, and computer intelligence.

The Oracle: Prophecy

The Oracle is a sentient program who knows, or at least gives the appearance of knowing, future states of the world. First we have the intriguing self-fulfilling prophecy effect in which knowledge of a future event causes the event to happen. The question is: Would the event have occurred if the subject did not know it would occur? The following scene in the first movie is truly amazing:


			I'd ask you to sit down, but
			you're not going to anyway.  And
			don't worry about the vase.

			What vase?

	He turns to look around and his elbow knocks a VASE from
	the table.  It BREAKS against the linoleum floor.

			The vase.

			Shit, I'm sorry.

	She pulls out a tray of chocolate chip cookies and turns.
	She is an older woman, wearing big oven mitts,
	comfortable slacks and a print blouse.  She looks like
	someone's grandma.

			I said don't worry about it.  I'll
			get one of my kids to fix it.

			How did you know...?

	She sets the cookie tray on a wooden hot-pad.

			What's really going to bake your
			noodle later on is, would you
			still have broken it if I hadn't
			said anything.

	Smiling, she lights a cigarette.


In the context of the environment, it seems very doubtful that Neo would have broken the vase had the Oracle not told him to not worry about it. The scene illustrates the limitations of free will via prophecy. The realizations are quite scary. We know that the Oracle is a computer program in the matrix. Back to simulated realities for a moment, it is physically possible, because the program is running in some place outside the simulation, for the Oracle to know the future, if and only if events are deterministic. By deterministic, I mean lacking randomness or free will. This concept is more understandable built bottom-up.

Consider a universe with 100 particles moving around. Someone from another universe with more resources could theoretically create a computer simulation of those 100 particles. Now suppose the 100 particles existed only in a simulation. The scale of time in that universe is both arbitrary and meaningless. We could stop the simulation for 10 years of our time, resume the simulation, and in the point of view of the simulation, not a beat would have been skipped.

We now add one layer of complexity to the situation. Instead of the program simulating 100 particles, it is now simulating sentient beings. Those beings would have no awareness of the universe surrounding them, and hence, to them, time is relative. Now suppose the simulation is fully deterministic. It should then be theoretically possible to create a second simulation, starting with the exact same states. We may then speed up one of the simulations, or slow/pause the other, causing the faster one to surpass the other in time. Then we could technically observe what happens in the faster simulation and relate to the beings in the slower simulation what will happen in the future.

But, by telling them what will happen, we are interfering with the simulation. If in the faster simulation, a certain character, say Bob, is supposed to be involved in a car accident, but we tell the other simulation’s Bob that he is going to have a car accident, then the second Bob could theoretically avoid the accident. Therefore, the second simulation is not deterministic because an unpredictable, outside entity interfered with it.

Let us first look at two other cases of self-fulfilling prophecy, both in self-contained, deterministic worlds. For this purpose, we exit the Matrix temporarily. Consider Shakespeare’s Macbeth. If you are not familiar with the plot of this play, then look up the summary on Wikipedia or skip this paragraph if you do not want spoilers. Now, in the play, Macbeth learns from three witches that he is to be the future king of Scotland. Acting on this knowledge, he then lays a trap, murdering the current king and then proclaiming himself king. Had he not known the witches’ prophecy, he would most likely not have murdered the king and become king himself. Philosophically, this plot is deterministic. Since it is entirely possible that the witches merely made a random guess, there is no outside force influencing the plot (the visions and ghosts later on can be physically interpreted as hallucinations.) So, if you ran the universe again, the same thing would have happened.

One more example is Premonition (2007). If you actually want to see this movie (despite that it had mostly negative reviews as a film, it has a very thought-provoking plot), go ahead and skip this paragraph. Otherwise, continue. In the movie, Linda experiences non-chronological order, waking up on Thursday, then Monday, then Saturday, etc. (because of this, the movie is somewhat confusing the first time). She learns on Thursday from a sheriff that her husband Jim died on Wednesday in a car accident, and that it happened at the main road’s “Mile 220” sign. She later wakes up on Wednesday. Jim is still alive. She tries to “save” him, but ends up getting Jim to be at the “Mile 220” road. A speeding car comes by and narrowly misses Jim’s car. Although Jim survives and Linda is relieved that the accident was “avoided,” Jim’s car fails to start, and he is stuck in the middle of the road. A large truck full of gasoline approaches and cannot stop in time, exploding on impact and causing Jim’s car to explode as well. What is fascinating, however, is that had Linda not had the premonition, Jim would not have been killed.

Now, the fundamental difference between these two cases and the one in The Matrix is that in the last case, the world is not deterministic. Hence the real question is, How did the Oracle know? A computer cannot simulate something more complex than itself, that is, the total number of things to simulate cannot exceed the limits by the computer’s processing power. (A counter-argument is that the computer can run a more complex simulation at a slower rate, but the Matrix is a real-time simulation, so the counterclaim is invalid here.) In order for the Oracle program to predict what will happen in an interaction between itself and a human, it will need to be able to fully simulate both the human and itself because there is mutual interaction. But hold on a second, a computer cannot simulate itself plus something else! It is analogous to fitting the space of  a larger box completely inside a smaller one; it cannot be done.

Unless, of course, there are two layers of simulation, not one. Suppose the Earth combined with its Matrix program are being simulated in a more “real” universe. Then because the more real beings do not have to interact with our universe, our universe would be deterministic, along with everything within it. So, in the outer-universe, programmers could have run two simulations of us, and fed in information from one simulation into the Oracle program-within-a-program in the other simulation. However, there is another way to explain how the Oracle knows: the Oracle is using knowledge from previous existences.


Script of The Matrix: (Accessed 11/24/09) <>.

Philosophy of The Matrix (Part 1)

Part 1 deals with the philosophy of existence and simulated realities. Later parts may cover prophecy and cycles of existence, morality and ethics, and computer intelligence.

Imagine you are running an advanced simulation of the world. The simulated people would go about their normal daily routines, until one day, a glitch in the software occurs, and certain things within the program begin to go berserk. No problem, for you simply manifest yourself in the program, fix the glitch, and continue on the simulation. That is, until the world you live in, your world, begins to glitch. Then suddenly, you observe actions that defy the laws of physics. In almost no time, the problem is fixed. What just happened? Are you yourself living in a simulation, and did a more “real” being just fix a glitch in your simulation?

The Matrix Scrolling
The Scrolling Matrix Code

Welcome to the world of simulated reality. The most famous exposition of this realm of philosophy today lies in The Matrix (1999), a film in which the vast majority of people exist as simulated beings and are unaware that the world they are living in is not real. A small number of humans become aware that they are in a simulation and actually exit the Matrix and enter the real world, but this raises many questions. Besides the epic bullet-time and combat scenes, the movie prompts some interesting philosophical thoughts about reality, and what exactly is reality.

Just as the beings in the Matrix existed in a simulation, do we too exist in a simulation? Dr. Nick Bostrom, philosopher at the University of Oxford, says very likely. Bostrom (2003) states in his abstract

[A]t 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. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation.

The main point of the paper is to demonstrate this trichotomy, especially showing why (3) is true given that civilization advances past (1) and (2). Basically, if it is possible that some race achieves the ability to create advanced simulations on a massive scale, e.g. trillions of simulations, then are we more likely to be the one designer race in the real universe, or a simulated race in one of the trillions of simulated ones? The infinitesimal chance of the former scenario becomes even more nonexistent if one considers that even a designer race might itself be a simulation, etc. If each of the trillion simulations creates a trillion simulations, then we are most likely in a simulation within a simulation; because of the exponential nature of these numbers, chances are we are in the lowest chain of the simulation pyramid.

Wikipedia, a very strong source in philosophy, has a nice comprehensive and thought-provoking article on simulated reality (see References). It is especially interesting in the discussion of computational aspects of massive simulations for the designer end, and it covers just as well the philosophical end.

By this point, you should have a basic understanding of the Matrix and simulated realities. Read on if you want my own spin on the topic.

The idea that we may be living in a simulation seems at first to be absurd. After all, you can see and feel objects around yourself, and even more, as shown by your reading this article on philosophy, you are capable of thought. Remembering Descartes’ famous line, “I think, therefore I am,” you can confidently reason, “I exist.” But existence on what level?

In The Sims, a video game that is also a life simulation, one could argue both sides of existence for the characters in the game by using different levels of perception. In the level of the simulation, the character obviously exists. If it did not, there would be no game. The virtual data that comprise the character are just as real as the atoms comprising us. But what about in the level of our reality? In that case, the character would not physically exist. Sure, the virtual data has to be stored by something physical, e.g. a silicon chip, but can the underlying form of the character actually be considered real? In our own bodies, the quarks and leptons (the fundamental building blocks of matter, or at least with current-day physics) directly comprise our existence. In the silicon chip, the particles are merely ways to represent virtual data, which are then processed by a program, which then creates image and audio, which we then perceive with our senses to build a picture of the character, but only in our minds. To be sure, direct sensory perception will always require some construct of the individual mind, but in this case, the character has a very different type of existence, if it considered to be existing at all.

For this, a little thought experiment shall do. First, imagine a real-world chair. How would you go about making this chair nonexistent? Remember, the goal is not to simply argue over the existence of the chair, but to actually remove it from existence. One idea is to hide it behind another object. Now one cannot see the chair, but another person walking along on the other side of the obstacle will easily see it. That would not work. How about we dig a hole, throw in the chair, and bury it? It would not be seen, but with the right technology, one could deduce the existence of a chair at the spot. Now, the chair would also decompose over time. Hold on, think about the concepts of nonexistence and destruction for a moment. The burying of the chair is actually complicated in that it note only removes the chair from sensory perception, but also removes it from its current form over time. To better understand this, consider a much faster phenomenon, the detonation of an atomic bomb. If the chair were placed at ground zero of such an explosion, it would be disintegrated in a split second. Then to what extent can we say the chair exists? The chair does still exist. The individual quarks and leptons that originally comprised the chair are still moving around, even if they are separated from each other. How can this be philosophically different from a chair decomposing over time? I contend it is not. Even when the chair is left in the open, perceivable to anyone, it is surely losing atoms over time. Basically, in the nuclear explosion, the building blocks of the chair still exist. And since we still call the object a chair when it is losing atoms slowly, in the fast case the chair also exists, for it is well within the laws of physics that—although not likely at all from the second law of thermodynamics—all the fragments of the chair come back together to form a full chair. At this point, can we say it is the same chair? Yes, because it consists of the exact same atoms that it had to start out as. It is thus impossible to make a chair nonexistent, unless, of course, one factors in the fact that modern physics allows for the destruction of quarks and leptons comprising the chair a la matter-antimatter annihilation. But this annihilation does not violate the conservation of mass-energy. The energy released from the explosion could return back into matter and reform the chair or parts of it.

Now imagine a universe that is in every way the same as our own but without the particles composing the chair. If one were to measure the total mass-energy of both universes, one would find that one universe has more than the other; even if the chair were totally annihilated, it would still retain its mass-energy and thus leave some footprint in our universe. (Granted, this mass-energy difference may be extremely hard to measure, perhaps even empirically impossible, but assume it is theoretically possible, for this thought experiment is trying to find a fundamental difference between existence in reality and in simulations, not an empirical one.) In our universe, therefore, a real chair cannot be made nonexistent.

So what separates this real chair from a virtual chair? The difference is that a virtual chair can be made nonexistent. While our universe conserves mass-energy, a simulated universe we create would not have any reason to enforce this law. In fact, even if it did, could we not, as the programmers, simply inject a piece of code that removes all data of the chair? This act would conserve mass-energy in our own universe, but not in the simulated one. Now think of the two-universe distinction again. One universe, or simulation, would never have had the chair to start with, while the other had a chair that was then removed. It is theoretically possible that, from the way the code was written, the two simulations have exactly the same data at this point. Thus the two simulations are at this point in time identical, and since the chair by definition does not currently exist in one simulation, it must not exist in the other simulation either.

A final intricacy of the thought experiment: What if we ourselves are in a simulation? Then, just as we can cause some item in our simulation to cease existence, our simulator race could cause some object in our universe to be removed completely, even its mass-energy. Therefore an object in our universe would cease to exist.

What has the chair experiment taught us in terms of philosophy? That the existence of an object has different levels depending on whether it is simulated, or its level of simulation. This way, a simulated character provably has a lower level of existence than that of a real character. Now, on to the philosophy of The Matrix.

The situation of humans in the Matrix simulation is quite complex, in that the humans have an existence in the real world as well as in the simulated world. Also, some humans only exist in the real world, while anthropomorphic computer programs exist only in the Matrix (with the exception of a particular rogue software). The characters in the Matrix thus have mixed levels of existence.

More interestingly, a certain program openly talks to the humans about existence and the future: the Oracle. How does it know, and why? Part 2 will cover the philosophy of prophecies.


Bostrom, Nick. “Are You Living in a Computer Simulation?” Philosophical Quarterly (2003), Vol. 53, No. 211, pp. 243-255. Can be found online: <>.

Wikipedia. “Simulated Reality.” (Accessed 11/18/2009): <>.