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All this might just be an elaborate simulation, running inside a little device sitting on someone’s table.
          –Jean-Luc Picard (Stardate 46424)

If you play video games, you’ll be familiar with the idea that computers can be used to simulate artificial worlds. As computing power has increased over the last 20 years, these “virtual realities” have become more and more detailed and realistic. This idea was taken to its logical conclusion in the movie The Matrix, in which the whole world was revealed to be a vast computer simulation, created by machines 200 years in the future. The entire human race was trapped in this collective illusion, and people went about their daily business in blissful ignorance that they were, in reality, the slaves of the machines.

Could we all be “Sims,” living inside a computer simulation? And if we were, would we realize it–-or would we have been programmed not to? What would it be like to live inside a simulated reality?

Well, computers simulate reality by taking a grid of points in space and computing what would be there at a given time, and then projecting this forward from one moment of time to the next. (Typically this is done by tracking the grid position of each object in the simulation at each moment of simulated time.) But being finite machines, computers can only deal with a finite number of grid points and a finite interval between successive moments of time. In a very powerful computer, the grid may be very finely grained and the time intervals very small, but they can never be infinitesimal. So if we were living inside a simulation, we would notice that space and time are not infinitely divisible. The limitations of the computer’s information-processing power would limit our ability to observe very small quantities of space and time.

As an analogy, consider a digitally recorded movie. The recording consists of a large (but finite) amount of information representing events over a finite span of space and time. The events in the three-dimensional space are represented on a two-dimensional screen, the image is divided into small pixels (the screen contains millions of these); each pixel (representing a spot of light of a certain color and brightness) is divided into three primary colors; each color’s brightness is represented by a level on a scale from 0 to some large number; and the time is divided into short intervals. In this way the whole sequence of events can be transformed into a series of binary digits which in turn are recorded on a suitable medium such as a DVD. With the proper equipment we can play back the DVD and watch the movie. Although the actual information on the DVD is merely a series of ones and zeros, we have the illusion of watching a slice of real life.

Note, however, that the information in the movie is quantized by the process outlined above. If there are 30 frames of information per second, we can know what happens, and where everything is, in each frame, but we cannot see what happens in between the frames. An event lasting less than 1/30 of a second (such as a flash of light) may be captured by the camera or it could in principle “fall between the cracks” and not be recorded at all in the movie. And moving objects will tend to be blurred, so that we will not be able to know their precise position in the frame. Likewise, each frame of the movie is pixelated, so we can never know the exact position of an object: we can only measure it to the nearest pixel. Nor can we reliably detect objects that would be smaller than one pixel in size on the screen. Very small objects (and larger objects a long way off) may not show up at all, not even as a single pixel on the screen. (And, because of the way they are sampled, the colors in the image are not precisely accurate.)

Following this analogy, we would expect that if we were living in a computer simulation, we would find uncertainty in our measurements, especially when looking at small objects over short periods of time. And indeed, the real world turns out to be very much like this. Quantum theory dictates that we cannot accurately know both a particle’s position and its velocity. The more accurately we measure one, the less accurately we can determine the other. This is not due to the inadequacy of our measuring equipment, but is a fundamental constraint imposed by the fact that the particle contains or comprises only a finite quantity of information.

So at first blush, it would appear that we could indeed be living inside a computer simulation.

What sort of simulation might this be? Well, one kind of model that has been extensively studied is the cellular automaton, the best known example of which is Conway’s Game of Life. This consists of a grid of cells, each of which can be either “on” or “off” at any given time. (Time is not continuous in this game, but is measured in discrete clock-ticks.) The game has a rule which specifies, based on the status of a cell and its neighbors at any given time, whether the cell will be “on” or “off” at the next clock-tick.

The surprising thing about the Game of Life is that its single simple rule, applied over and over again to the grid, can produce patterns that behave in amazingly complex ways. (This is the central theme of A New Kind of Science, Steven Wolfram’s exhaustive study of cellular automata, a massive tome that tells you far more than you ever wanted to know about the subject.)

So if simple rules can produce complex behavior, could the Universe be a cellular automaton? I would answer no, for the following reasons:

First, cellular automata rely on a grid, which has “preferred directions” in which phenomena such as light rays would propagate. No such preferred directions have been observed in reality. Space appears to be isotropic, meaning that it looks the same in whichever direction we turn. If there were a grid, objects would appear different when looked at from different directions (e.g. along the grid lines, or at an angle to them).

Second, such a grid would behave like the “luminiferous aether”: the speed of light would be different when measured along or across the direction of Earth’s movement through the grid. However, the famous Michelson-Morley experiment showed this not to be the case, thus disproving the existence of the aether. So it would appear that the Universe cannot be a cellular automaton, nor (for the same reasons) could it be any other kind of computer simulation that uses a grid.

But could it be some other type of computer simulation that avoids reliance on a grid? Once again, I would answer no, but this time for a more powerful reason: a simulation of the Universe would require a giant computer in order to operate. Where would such a computer exist, and what would it be made of? It could not exist in our Universe or it would have to simulate its own operation in real time– a logical impossibility. Such a computer could only exist in another universe, even bigger than ours. And what would that universe be made of? This approach does not solve our philosophical problems, it simply makes them bigger. So, in the spirit of Occam’s Razor, I say it must be discarded, and thankfully reach the conclusion that we are not Sims. Even if we are, in the last analysis, creatures comprised of information, that information is real and natural, not artificial and simulated.

Nick Mitchell, July 2009

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