Are we living in the matrix?

Could we all be living in a computer simulation?

In 2003, philosopher Nick Bostrom proposed "the simulation argument". The thinking goes something like this: imagine a super advanced civilization with immense computing power. If we assume that they had the same thirst for knowledge and understanding of their world as us, then they would probably put their computing power to the task of simulating a whole universe inside their supercomputers for the purpose of research. In fact, they might simulate lots of different universes to understand what differences small changes make. Then perhaps the simulated civilizations might also attain the ability to run their own simulations, such that there are simulations within simulations and quickly the number of simulations vastly outnumbers the one actual reality. If that were true then there could potentially be billions of simulated universes and only one real universe. So in that case, statistically, we are very unlikely to be living in the one real universe!

Bostrom proposed that one of three options is almost certainly true:

1. It is very unlikely that any civilization could ever attain the technology necessary to run high-fidelity simulations of reality
2. It is very unlikely that any civilization with the necessary technology would ever be interested in running high-fidelity simulations of reality
3. It is very likely that we are living in a simulation

Let’s take a look at each of these options in turn. Firstly, technology: could it actually be possible to run a simulation that is as complicated as our reality appears to us? Currently, we are aware of one civilization that has attained the ability to run limited computer simulations: human civilization.

Computing Power

The invention of the first computer is problematic to date due to the various different classifications of computers: the first mechanical computer was invented by Charles Babbage in 1822 and the first really functional modern computer is considered to be the Z1 by German Konrad Zuse in 1938. However, it is safe to say that for the vast majority of human civilization it was unimaginable that aspects of our reality could be simulated by a machine, yet just over the past few decades computing power has increased considerably.

“Between 1970 and the early 2000s ... computers got a thousand times faster,” says Alex Chadwick, computer scientist from Cambridge University, “if planes had done the same thing we'd now be able to fly from London to New York in 28 seconds”.

Moore’s law states that the number of transistors that can fit on an integrated circuit doubles approximately every two years. This has held fast over the past few decades, resulting in ever increasing computer power and speed. It is tied to the fact that we have been able to produce smaller and smaller transistors every year. Therefore, Moore’s law must have an expiration date, because there exists a physical limit as to how small the transistors can be - and that day is coming soon.

So are we reaching the physical limits of computing power? Somehow, I doubt it. Someone living in the middle ages could never have imagined the sort of technology we have today, just as we cannot imagine the sort of technology a super advanced race will have. Some of the ideas scientists are already exploring for the future of computers beyond Moore’s law are: compound semiconductors, nanomagnetic logic and quantum computing.

How to simulate a universe

Having the necessary computing power is one thing, but how do you actually go about simulating a whole universe? Cosmologists today can already simulate aspects of our universe. Nick Henden from Cambridge University uses computer simulations to model the formation of galaxies. To set up the simulation, they tell the computer to simulate a very large box and fill it with particles. "Those particles represent mainly gas and dark matter" says Henden, "and then you apply the physical laws such as gravity... and various other physical processes that are important for the formation of realistic galaxies."  Henden says that these kind of simulations have become much more realistic over the past few decades, as the number of particles they are able to simulate increases, due to increased computing power.

Scientists are also able to simulate parts of the human body. Oxford University’s Elisa Passini builds computer models of human hearts to check whether new drugs would have negative effects on the heart, before they are even tested on animals.  "Our models are a sum of mathematical equations that represent the behaviour of a human's cardiac cell" says Passini.

"There are lots of people working on computer models of human body and physiology" says Passini, "and the idea is in the near future, maybe, we'll get to a point of having a whole virtual human, all simulated." So we may soon be at a point where we can simulate a whole human body with mathmatical equations. But what about consciousness? Surely a computer could not simulate my thoughts and feelings? Then again, if I am just a biological system, then all my thoughts and feelings are just chemical reactions... which can be simulated.

Why are computer simulations useful?

So let’s take a look at the second consideration of Bostrom’s argument. Assuming a super advanced civilization does attain the ability to simulate a full realistic universe as complex as our own, why would they want to?

A good place to start in considering this question is to ask: if we had the ability, would we want to? To which I would answer unquestionably: yes!

Computer simulations are a really powerful investigative tool in research. To understand why they are so useful, let’s look at an example: we want to improve the design of a car to be more aerodynamic.

To measure the drag force on a car we can put the car in a wind tunnel and measure the air pressure upstream and downstream of the car and calculate the difference to obtain the drag. We can then use computer simulations to test out lots of different designs, but first we need to validate the model.

To run the simulation we need to tell the computer the air pressure upstream of the car, the geometry of the car and the walls of the tunnel and the physical equations to apply. To validate the model we look at what the simulation predicts the air pressure downstream of the car to be, and if it agrees with the experiment, then we know that the model is reliable. We can then run the same simulation with a range of car geometries to find the best design. You can even run computer algorithms which adjust the geometries automatically, based on the results of the simulations, to search for the optimum design without any human intervention.

Another advantage of simulations is that we have access to far more data points than in an experiment. With the example of the car in the wind tunnel we only measured the air pressure upstream and downstream of the car. But in the simulations we can zoom in on the air flow around the wing mirror, for example, in order to inform the design of more aerodynamic wing mirrors.

But why would an advanced race want to simulate all of reality in a single simulation? Well, maybe that wouldn't be very useful for engineers, but what about historians? What if future historians want to ask the question: how did the Allies win the second world war? Maybe they would run lots of different simulations with different initial conditions to see how they affect the outcome of the war. Maybe we are living in the only simulation where the Allies did win the war…

To summarise, if we could fully simulate our universe we would jump at the chance. But why should we assume that any other advanced civilisation would have the same thirst for knowledge and understanding of their world as us? Well, this hypothetical civilisation would have to have first reached and then far surpassed our technological level.  Could we have achieved our current technological standing without the desire for knowledge? Newton and Einstein did not discover the laws of gravity and general relativity so that future generations could use satellite navigation to get to their destination. J.J.Thomson did not discover the electron with the scanning electron microscope in mind. And William Gilbert did not study magnetism in the 16th century, so that we could use magnetic hard drives in the 20th century. We cannot presume to know what motivates some hypothetical race, but undoubtedly for humans, curiosity drives innovation.

So are we living in a simulation? And does it even matter?

Bostrom's last option states that if it is possible for a civilisation to have both the ability and the desire to run realistic whole universe simulations, then we are very likely to be living in one. This is purely as statistics argument. It would only take one civilisation to have the ability and desire, for the number of simulated realities to vastly outnumber the one reality, because they will almost certainly run more than one. Think of the number of different simulations we currently run across all branches of science and engineering, almost every research student will run some sort of simulation. Additionally, the simulated civilisations may also attain the ability to run their own simulated realities, so if we are living in a simulation, we may well be several tiers down in the simulation tree.

But this is all nonsense, right? At the end of the day, you know that you are not living in a simulation... but do you? How could you tell? John Barrow, from the department of applied mathmatics and theoretical physics (DAMTP) at Camrbidge University argues that “if we live in a simulated reality we should expect occasional sudden glitches, small drifts in the supposed constants and laws of Nature over time”, such that scientists may observe perplexing inconsistencies, and therefore “the flaws of Nature are as important as the laws of Nature for our understanding of true reality”.

But does it matter? I would argue, from a day-to-day perspective: no. Whether or not we are living in a simulation, this is the reality that we have, so it may as well be the real universe, as far as we are concerned.