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We have been searching for the theory of the Universe, the Grand Unified Theory, or GUTs if you must, for a long time. Physicists have persuaded governments to spend billions on particle accelerators to help provide data but could it be that the answer lies in your PC. Could the secret be that the Universe is just a computer…
Stephen Wolfram, the man who among other things gave us the maths program Mathematica, certainly thinks that computing is the key to everything.
In May 2002 he published a huge book, “A New Kind of Science” that outlined his ideas. (You can also read it online.) At the time newspapers contained headlines to the effect that Wolfram was the new Newton or the new Einstein – but what do newspapers know!
Some readers have claimed to have had their eyes opened to a new way of seeing. Others have claimed that it is just regurgitated stuff with some mysticism thrown in. To find out which it is we have to look a little closer at some of its central ideas.
Rules, programs and theories
The first question we have to answer is what do computers have to do with theories?
A scientific theory of something is a lot like a program. It explains the underlying mechanisms that make the usually complex phenomena look simple.
Consider for a moment the theory of gravity. At first we have a lot of very different phenomena to explain, apples falling, the Moon orbiting the Earth etc, but then we have a single theory – i.e. that all matter attracts all other matter – which explains the lot.
Consider what it would mean if a theory was as complex as the phenomena it accounted for. There would be no point in having the theory because the phenomena themselves would be just as compact a description.
So a theory is an explanation which is considerably simpler than the phenomenon it explains. Of course this begs the question of what exactly we mean by “explanation” or by “simpler” but you can see what the general idea is.
You can also probably see that a theory is like a set of rules or instructions for generating the phenomenon. If you wanted to you could take the theory and use it to create a simulation of the real phenomenon – an accurate model of the Moon rotating around the Earth say.
The point is that a theory is a prescription or recipe for producing the phenomenon which is considerably simpler than the phenomenon it produces.
Now you might begin to see the similarity between a theory and a computer program.
A program is a set of rules that makes a computer produce some behavior and that behavior can be a lot more complicated than the program might lead you to believe. Indeed this is the foundation of algorithmic information theory where the measure of the information contained in a thing is just the number of bits needed for the shortest program that creates it.
This is more or less the total content of Stephen Wolfram’s book but he presents it in more than 1000 pages. Of course this is something of an over- simplification in that there is a lot more discussion and, dare I say it, fun stuff in the book than in my one-line version.
This view of what a theory is also answers the question “is the Universe just a big computer?”
Of course it is. If theories are programs the Universe must just be a big computer that runs the program that corresponds to what we see around us.
This conclusion should now seem fairly obvious but it is worth noting that not everyone agrees with it.
There are two main counter-arguments to the idea. The first is that there might not be a theory of everything and hence no program. After all why should the Universe be built in such a way that a description of it is actually simpler than it is?
In other words it is possible that the Universe isn't reducable to a smaller program that generates it. After all there are plenty of mathematical objects which don't have smaller generating programs - most irrational numbers for example.
There are a number of arguments that suggest that the Universe probably does have a theory but the odd thing is that the same arguments can be used to show why it doesn’t!
For example, if the Universe has no program how does it decide what is going to happen when two particles collide?
If you believe in the program it is obvious that the Universe computes what happens next by just letting it happen - it's the ultimate analog computer.
If you don’t believe then you can simply say that what happens, happens and it doesn’t necessarily prove that there is logic, let alone a simpler description to be discovered!
At the moment at least it seems to be a matter of taste how you look at the existence of a theory of everything but since we have been lucky enough to find ever better theories so far why not continue to believe that this might just happen.
Notice that none of this discussion is invalidated by the non-determinism contained in quantum mechanics. It is fine for the program that the universe follows to be based on probabilities. Quantum mechanics is just as much a theory and just as much a program as Newtonian mechanics.
The real problem is that we have difficulty believing in a Universe where precisely what happens next isn’t determined by the precise conditions just before it happened. To rearrange Einstein’s quote it really is OK for God to play dice with the Universe – it is still a program.