Monday, September 17, 2007

The Matrix Revisited

In the Wachowski brothers' movie The Matrix, it is suggested that the world we experience is only a computer simulation. Our real bodies are in coffins on an Earth ruled by robots; our nervous system is connected to the computer to make us experience this simulated world.

The robots keep us that way to use us as batteries for their energy needs. Considering the Law of Conservation of Energy, this is of course utter bullshit. But another theory might be less far-fetched: suppose that the entire universe around us, including ourselves, is just the product of one big computer simulation.

This article gives a fairly rigorous argument that we probably live in a simulation, provided that most civilizations live to be capable of, and interested in, running such a simulation. It also draws some interesting conclusions from this.

The article does not claim that we are simulated beings, and neither do I. Unless some bright hacker rises, follows small mammals around and swallows brightly coloured drugs, we're probably never going to know if we live inside a computer. But there is some empirical evidence. If you look closely at our fundamental laws of physics, it turns out that some of them are very convenient for computer simulation… as if they've been designed that way.

  1. Relativity. In particular, the fact that all movement of matter, energy and information is limited to the speed of light. Consider that our own computers become more and more parallel. It is reasonable to believe that the ultra-advanced computer, let's call it Deep Thought, is also a highly parallel computer. The weak point of parallel computers is the locality of data: transferring data between processors is relatively time-consuming. Limiting communication to the speed of light allows you to run sections of the universe on different processors with minimal communication between them.
  2. Quantization. Energy is quantized: it only occurs in discrete packets. No fractional energy quanta can exist. Any computer we know is discrete in operation, and is unable to store numbers to arbitrary precision. Possibly Deep Thought suffers from the same limitation. I would not be surprised if one day we found that time and distance exist in discrete units as well, and the real numbers turn out to be a concept that exists only in mathematicians' minds.
  3. Schrödinger's cat. One of the main ideas of quantum physics is that the state of an object is undetermined (the living and dead states of the cat are superposed) until someone takes an observation, thereby interfering with the experiment. How convenient: Deep Thought does not even need to compute what's going on with the cat until that information is actually needed! This is called lazy evaluation and is used in many of our own programming languages to save computational effort.
  4. Dark matter. Astronomers found that objects in the universe does not move the way they should, considering the amount of matter attracting them. The difference is attributed to dark matter, which cannot be observed directly, but does produce a gravitational effect. It seems like a hack made up by astronomers, but what if it's actually a hack made up by the programmers of Deep Thought? Suppose you are a superbeing, who finds after having made up all these beautiful laws of physics for your toy universe, that it is not stable? Back to the drawing board – or just add some invisible, intangible matter for some extra gravitation? (It might be possible for us to compute whether our universe could be stable without any dark matter, so this argument could be verified or falsified.)

The problem with this and many similar theories is that they are very hard or impossible to disprove. This particular theory can never be disproved. It might be proved by realizing that a computer system is involved. Any computer system we know contains bugs, so perhaps Deep Thought is not flawless either. If we find a way to trigger a bug in the programming of the universe, we might have evidence of what lies beyond. Or we manage to crash the complete system, and hope that their system administrators have made a decent backup…

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