Let’s first establish that this entire post is speculation. My only claim is that this is a fascinating concept that is a ton of fun to think about!

For the sake of simplicity, I will use the word computer to describe any mechanism used to run a simulation. This will therefore include everything from a desktop computer that we’d be familiar with, to the mind of a super-intelligent life form. If details of the mechanism are relevant, I’ll clarify at that time.

The Simulation Argument

The concept of the simulation is now in the realm of pop science. It’s the idea that this entire universe could be inside a computer. This idea is made more compelling by how close we seem to be to reaching the ability to create such simulations ourselves.

The most famous arguments presented to support this idea were presented by Nick Bostrom in 2003. Here is an excerpt from the abstract:

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. 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.

Or, in other words, the only realistic way humanity will not create simulations is that they either go extinct before they’re able or they choose not to. I think that is fair. With that in mind, it seems to be very likely that we’ll create simulations than not. The conclusion is that, if we can create them, and probably in vast quantities, and the simulated beings are capable of making their own simulations, and those simulated can make simulations, and so on, it seems very unlikely that we’re at the beginning of this apparently infinite series of simulations.

One Obvious Weak Spot

No matter what the makeup of the computer, it will require matter and energy to run. There is a finite supply of those in this universe. To simulate our universe exactly as it is down to the subatomic level would take more matter and energy than we actually have in our universe. For example, if we use 1 bit of information to represent a single electron in the simulation, that bit requires more than 1 electron to actually store and process. With this fact in place, we have to realize that we will have to cut a lot of corners in the universes we simulate.

One solution is to make the simulated universe smaller than ours, either in space (physically smaller) or in time (runs for a shorter period). The smaller the universe, the more likely we’d be to even be capable of simulating it.

Another, and more commonly accepted solution, is to only process the information necessary dependent on the purpose of the simulation. For instance, if we want to create a simulation to study an animal’s behavior in a specific environment, we wouldn’t need to process anything that wouldn’t be directly relevant. If the animals would never come in contact with a specific variety of tree, there’s no reason to have the tree in the simulation. If the animals can’t comprehend space, stars, planets, etc, then we can fake all those details.

This “fudging the details” trick is actually used in current video games. One method is called “dynamic occlusion culling” and it means the part of the world you see is the only world that exists. Everything behind and off to the side of the camera ceases to exist as soon as you turn away.

That quickly and easily gives us back our ability to create a simulation.

In both of these cases, it makes infinitely nested simulations impossible. Each child simulation will have at least slightly fewer resources than the parent simulation to work with to create their simulations. This means that there would be a child simulation that would not have the resources needed to create their own simulations. This is relevant because now we are working with a finite depth of simulations, and that increases the odds of us being the top-level simulation.

Even then, we have the potential to make millions and millions of these simulations. Even if we’re not literally working with infinity, the number is so staggeringly huge, that it feels almost impossible for us to not be inside one. What other option do we have?

The Unknown Variables

Since we’re talking about what created our universe, we literally don’t know. It’s even possible that it is unknowable. We’re trying to weigh probabilities based one possibility. You can’t calculate odds until you actually have the full set of possibilities to compare. Otherwise, we’re talking hunches or educated guesses at best. It may turn out that these hunches are dead on. We may find out they weren’t even close. It does at least seem inevitable that simulations will exist, because it seems inevitable that we will create them. Other than that, who knows?

Mechanisms for a Digital World

If we go forward with the premise that simulations are possible and are contained within a computer, we are forced to go a little deeper to examine what process in the computer is relevant for a simulation to exist.

Consider a simulation running on a desktop computer. If nobody observes the events inside the simulation from outside (via a computer monitor, for example), did the simulation happen? The monitor is simply a way of observing the process. Therefore one would logically conclude that the simulation is happening either way. That means that there is no requirement for us to observe the output of a simulation for us to create one.

What is happening inside the actual computer itself? Quite simply, electrons are shuffled around. That’s how all electronics work. One electron bumps into the next, sending a signal to the other end to perform a specific task. Even inside a computer, where the available paths for the movement of these electrons are carefully chosen, the shuffling of these electrons is meaningless without a way to interpret their movement.

There’s nothing special about how electrons move through a transistor. When a transistor is switched on, the electrons start to flow. When off, they stop. Almost every part of a computer works on principles very similar to this.

If it’s the behavior of the electron that is relevant to a digital world, then the computer itself doesn’t matter. An electron moving outside a computer in a way identical to an electron inside a computer is just as valid. Therefore the logical conclusion appears to be that the requirement for an electron’s movement to create a simulation is that the path of the electron has the potential to be interpreted as a simulation. If that is the case, then no actual computer of any kind is even necessary. In fact, no human interaction is necessary at all. We break free of the intent requirement of an intelligently designed simulation into natural digital worlds (NDWs).

The next step is the inevitable conclusion that the electron itself doesn’t matter. It’s simply the movement. It’s the potential to interpret that movement as a digital world that matters. An NDW could be run using photons or protons or hydrogen atoms or mosquitoes or fish or planets or stars. Any moving thing or collection of moving things could be used.

Time is another interesting factor of simulations. Again, let’s go back to desktop computers. The first personal computers were incredibly slow compared to what we have now. Let’s imagine that we tried to play a full HD movie on such a machine, and it managed to play the video at a rate of one frame per minute. Watching it from out point of view is so slow, it’s practically meaningless. Now imagine you lived in that movie as it was playing. To you, there wouldn’t be a gap between the “slices of time” (frames). Everything would appear perfectly normal. This same concept can be applied to the speed at which a digital world is generated. A single particle lazily meandering through space for billions of years could easily be responsible for centuries of time in an NDW.

The opposite is therefore also true. A collection of incredibly fast moving particles could be responsible for creating years in a digital world in mere seconds in their own.

Is motion even a prerequisite? If it’s the potential of interpretation that is relevant, than one could use other sources other than movement. Form, for instance. The earliest computers used punch cards as a way of storing and computing. The computer was more of an interpreter of what the cards contained. It was the physical shape of the cards with the potential in that case. Not the movement.

If form and movement work, is there anything that doesn’t? Color, taste, temperature, acidity, placement, orientation, sound, and mass would all work. In fact, anything that possesses variable qualities has the potential we’re after.

This all suggests that a single particle could be involved in countless other overlapping NDWs within the exact same space. It’s like books on a shelf where the books are all sharing some pages with each other.

Let’s imagine that the fewest particles required for a digital world is 1 million. Lets say we are also limiting ourselves to interpreting the movement of those particles into an NDW. The exact same movement of those exact same 1 million particles can still be interpreted in a myriad of ways, with each way being a completely distinct and equally real NDW.

An NDW can be generated by as little as a single string in string theory to as much as the entire observable universe.

If we now circle back to an intelligently designed simulation inside a computer of some kind, we can now see that there would be countless other naturally occurring digital worlds running in the exact same space using the exact same matter and energy.

Nesting Worlds

Inside NDWs that resulted in intelligent life similar to ours, it’s certainly possible that life would evolve intellectually much like our own, to the point of creating simulations. Even if the NDW had no big bang, and it began with intelligent life already in full swing, those beings would be up against the same enormous volume of NDWs of their universe.

Likewise, an intentionally created simulation in our universe is still going to possess a vast number of NDWs inside it. Not only is the matter that is used to create the simulation used to simultaneously create several NDWs, the simulation itself is producing them.

Probability of Life in Natural Digital Worlds vs Simulations

As I pointed out above, working with probabilities without having all the necessary data is quite speculative. We may find that life is an inevitability in all universes. Perhaps we will find that life is nearly impossible and an incredible rarity. If all we are relying on is intuition and hunches, then we aren’t really talking about probability. With that in mind, there are a few interesting things to think about that would play a factor in the probability calculations.

Not all simulations would have life. Even now we run simulations where life isn’t even relevant to what we’re studying. This establishes the fact that neither simulations or NDWs have a 100% chance of containing life.

It is literally impossible for the number of simulations to exceed the number of NDWs. This is demonstrated by the fact that simulations will occupy the same space as an enormous number of NDWs.

With the sheer volume of NDWs, even if only the absolute tiniest fraction of all NDWs resulted in some form of life, that alone would be more than humanity could ever make. Even if humanity could somehow keep pace with the universe, the universe already has a 14 billion year head start at this.

Conclusion

Given that nearly any combination of time, space, energy, and matter, and any combination of any of their measurable properties has the same potential to be interpreted as a digital world as the electrons moving inside a computer, the number of digital worlds must be an incomprehensibly huge number. The minute fraction of those that contain intelligent life would also be just as incomprehensible. No matter how fast humanity creates simulations, it is physically impossible to get ahead. Humanity will never even come even remotely close to the number of NDWs.

With all this in mind, returning to the simulation argument, following the premise that digital worlds are either the only or at least most common sources of existence (debatable in itself) it is far more reasonable to conclude that we are not in an intelligently engineered simulation, but are in fact in a naturally occurring digital world that was spawned from the random properties of elements inside our parent universe.