Is everything a simulation? Maybe, but not in the way you think.

The most recent episode of Futuristic Now, a podcast by my friend Gray Scott, is about The Simulation Theory: the idea that the entirety of our experience–perhaps our entire universe–may be some form of simulation. Gray goes over some of the ideas people have put forth, and talks about some ways this view could be interpreted. As is always the case with his thought-provoking podcast, he brings up more questions than answers: If we are a simulation, who or what created us? What would the purpose be for creating a simulated universe? Does the mere existence of a simulation even require that there be a “creator” at all?

Simulation–especially computer simulation–is a topic that is very close to my heart. My earliest peer-reviewed published research was on a formal model of the relationship between neurochemical processes and social interaction, and I used a simulation model to show that basic, low-level chemical drivers of behavior are sufficient to give rise to some observed patterns of group behavior. Later, I used neural network models with different designs and architectures to try to understand how our basic processes of attention and decision work.

In both cases, I was using simulation as a way of taking a set of complex assumptions about the way a system works, and basically “running the model” based on those assumptions to see what the consequences would be. This is a pretty common method for exploring the consequences of scientific theories about large and complex dynamic systems. Scientists use simulations to understand everything from climate change to traffic patterns and the spread of disease.

So I have a lot of personal experience with simulations. But even so, when I’m listening to Gray’s podcast and he asks provocative questions about whether the universe itself is a simulation, it makes me realize that when we talk about “big philosophy”, it’s best to begin at the beginning.

What the hell does it mean to call something a “simulation” anyway? Without relying on dictionaries or academic coursebooks, let’s see if we can build a formal definition of “simulation” from scratch.

A (semi-)formal definition of “simulation”

First of all, for something to be a “simulation” it has to be a simulation of something. So immediately we know that our understanding of “simulation” has to involve at least two things: A and B. If we say “A is a simulation” it’s implied that there is actually a hidden, unspoken other thing in the conversation: the thing being simulated. It can be a simulation of something concrete (a simulation of a traffic jam) or abstract (a simulation of intelligence), but it’s always a simulation of.

We can write “A is a simulation of B” in a more formal way as a relationship:


What has to be true about A and B for the above statement to be a true statement?

Well, for one thing, A and B can’t be the same thing. You would never say “This puzzle is a simulation of itself.” That’s just silly.

A ≠ B

Also, A and B have to be systems. That means, they have to be something complex enough that you can think of them in terms of their parts or their features, and relationships between their parts or features.

This is critical when we talk about simulation, because for one system to simulate another, there has to be some kind of analogical mapping or “shared structure” between the two.

In other words, even though the parts that make up A are different from the parts that make up B, the relationships that define how the parts of A work together must have something in common with the relationships that define how the parts of B work together.

This may sound complicated, but it’s an idea you are already familiar with in the concept of analogies. One famous analogy is “an atom is like the solar system.”  Of course, physically the nucleus of an atom is nothing like the sun, and electrons are nothing like planets. But there is a set of relationships that are preserved in both:

Electrons are smaller than the nucleus → Planets are smaller than the sun

Electrons orbit the nucleus → Planets orbit the sun

Because the two systems have shared structure (i.e. similar sets of relationships), they are considered analogous.

For A to be a simulation of B, they must in some way (or to some extent, at least) be analogous.

Analogous( A, B )

But not all analogies are simulations. Forrest Gump correctly observes that life is like a box of chocolates, and this is an analogy:

Life is made up of many discrete events → A box contains many separate pieces of chocolate

You cannot always predict ahead of time how an event will turn out → You can’t always tell what the flavor of the chocolate will be before you eat it

… but that doesn’t mean that a box of chocolates is a simulation of life.

When we think of simulation, at least in the sense used by scientist where computer simulations are used as tools to explore and understand other phenomena, there is always a dynamic element: systems A and B both change over time, and that the relationships of their shared structure are preserved with those changes.

Analogous( dA/dt, dB/dt )

This picture of Gray Scott is not a simulation of Gray Scott, because it does not change over time.

This picture of Gray Scott is not a simulation of Gray Scott, because it does not change over time.

This finally starts to narrow down what we commonly think of as “simulations” in modern science. A computer program can simulate a traffic jam, or the weather; or perhaps a robot can simulate an emotional reaction by manipulating its facial features.  In all of these cases, there is a critical element of time: the behavior of the simulation over time parallels the behavior of the thing that it simulates over time. It is this parallel in their behavior that is critical to why we call it a “simulation”.

But there is one more very critical factor as well, at least in the way that the word “simulation” is used by modern scientists: A has to be simpler than B.

This is a feature that isn’t discussed very much when talking about “The Simulation Theory“, but it is absolutely essential to the way scientists use simulations. We create simulations to try to understand extremely complex phenomena, ranging from the spread of disease to the possible origins of life. If the simulation captured every single aspect of the thing it was simulating perfectly and in every detail, it would be useless. It would be just as incomprehensible as the thing we were looking at in the first place.

Complexity(A) < Complexity(B)

This asymmetry is also important for understanding why the common usage of the word “simulation” is not symmetric or reflexive in the mathematical sense: when you say “This computer program is a simulation of a violent storm” it does not logically follow that “A violent storm is a simulation of this computer program.”

Why not? All of the other rules that we have discussed about simulation are symmetric:  A (the computer program) and B (the storm) have parts that interact with one another according to similar rules. In the storm, the flow and eddies of wind follow particular lines and curves over time according to physics; and in the program, the variables representing windflow are programmed with equations that cause them to follow those same lines and curves.

So why isn’t the storm a simulation of my computer program? Because the storm itself is massively more complex, consisting of billion of atoms whizzing around in three dimensions, governed by all of the rules of particle physics at a microscopic–even quantum–level. The computer program does not simulate the storm down the the quantum level: it uses variables that approximate the behavior of the air.


Is that it? Does that cover what it means for something to be a simulation. These rules may be sufficient to identify those things that we commonly think of when we imagine the word “simulation” in common usage: ranging from a simple simulation of spring movement, to simulations of the evolutionary process in robotics. In every case:

  • There are two systems, A and B
  • A ≠ B
  • Analogous( A, B )
  • Analogous( dA/dt, dB/dt )
  • Complexity(A) < Complexity(B)

What do you think?

Philosophical implications of “simulation”

If we take that as our definition of “simulation”, we can return to one of the “big picture” profound questions that Gray asked in his podcast: does the existence of a simulation require there to be a “creator”?

By this definition, the answer is “no”. The above definition allows for simulations to exist in the universe even if nobody in the universe has intentionally created a simulation. In fact, using the above definition, simulations can exist in the universe even if there are no conscious beings in the universe at all.

Some people might think that this definition is too broad. After all, let’s go back to the atom vs solar system analogy from before. Atoms and solar systems both are dynamic and change over time, and at least part of their “shared structure” involves that change over  time: the smaller components “orbit” around the larger component.

Moreover, while planets and stars are amazingly complex, the orbits of the planets are less complex than the movements of electrons. The “solar system model” is a simplified interpretation of what electron movement really is.

So, by the definition presented here, our solar system is a simulation of an atom.

Is that so crazy? Perhaps not.

After all, philosopher John Searle famously once argued that everything is a computer. The only reason we think the bits and blips of a computer “mean” anything is because we are deciding to think of the parallel between the electronic bits and blips and how they relate to other things. I could just as easily interpret the wall of my house as a computer: every time I throw a beanbag at it, it computes the distance to the floor (by making the bean bag travel that distance).

Similarly, almost anything can be a simulation of some sort: one merely has to identify a complex system in the universe that it shares some kind of structure with, but in a simplified way.

Football is a simulation of war. My vacuum cleaner is a simulation of a black hole. My bookshelf is a simulation of the Roman Empire (…at least during the collapsing years). And the life cycle of a single cell is a simulation of the entire history and evolution of the universe, gradually wearing down through the slow work of entropy until eventually all structure dissolves into a murky featureless goo.

When you look at it that way, I completely agree with any futurist who speculates that we are surrounded by simulations in this universe… only, I don’t mean it in quite the same way that they might.