Sean watches a panel discussion on whether the universe is a computer, looks up the definition of a computer, and decides that instead the universe is a calculation. If thinking about the universe as a computer is designed to make computer scientists feel important, thinking about the universe as a calculation seems designed to make theoretical physicists feel important ? But what I find interesting is that Sean points to a question asked by Tony Leggett: “What kind of process does not count as a computation?”
Now first of all, let me preface this by saying that the word “computation” has a much more specific meaning for me that it probably does for most physicists. That is I consider “computer” to be equivalent to a device which computes in a fashion easily mapped to that of a Turing machine. Thus for me “computer” has a much specific meaning that what I think Sean or most of the commenters on his post think of as a computer.
So, given this definition of a computer, I think a computer scientist would probably immediately respond to Leggett’s question with a discussion of computable functions. There are certainly universes I can imagine which perform evolutions which are not computable functions. For example there might be a universe where data describing a Turing machine and an input to this Turing machine evolves in time to data describing whether this Turing machine halts (this is not a computable function.) Of course this evolution law is for a physics that will probably look very different from our universe, where all we seem to be able to build are Turing machine-like devices. Nonetheless, such laws of physics can certainly be written down.
But I also think there is another answer to Leggett which is often overlooked. This is the opposite end of the stick. In the previous paragraph I described a universe where the evolution of the universe is more powerful than a Turing machine. So…certainly another answer to this question is that we can imagine universes where the power of the physical evolution is not enough to perform universal computation. Indeed we can also easily write down physics for just such universes, as for example, in cellular automata which are not universal.
Further, and I think more interestingly, is the possibility that our universe is not a computer because its evolution is not predictable or controllable enough. In other words, it might be possible that our universe does not allow for computation (classical or quantum) because the evolution is subject to too much noise or inability of systems to control each other. Indeed I would argue that most of our universe is exactly in that situation. The Diet Coke on my desk is not a computing device, as far as I can tell, because I do not have enough control over it. Could I turn it into a computing device? Perhaps. Okay, who am I kidding. I just drank all of the Diet Coke, so now I’d have to make a computing device from the plastic. Possible? Possibly. But right now I don’t think I have much of a right to call it a computer.
Now you might say: but I have a computer on my desk, so certainly I have experimental evidence that our universe allows for computation. But I would argue that your computer only proves that computers can exist for a timespan of a few decades. And indeed, your hard drive isn’t really that good of a storage device, and a few centuries from now, the software on such a drive, if you just let it sit there, will probably no longer function. Very few are the physical processes which allow digital computation. On the other hand, we do have some theoretical reasons combined with experimental evidence to believe that our universe does allow for computation. This comes from our understanding of the laws of physics combined with results in fault-tolerant computation. But if pushed I would probably say that we haven’t put this full theory together, i.e. deriving fault-tolerant quantum computation from the first principles of our physical laws (of which we don’t really have a fundamental theory at all, so right now this exercise is fundamentally flawed.)
So, at this point you might be thinking: but aren’t you confounding what the universe can do (i.e. whether we can build a computer) with what the universe is? If I say, for example, that our universe does not allow for universal robust computation, why can’t you just say “but the laws of physics can be thought of as doing a computation.” But this is exactly the point: if I tell you that the universe is a computer, then if computation is not possible in our universe, then this computation that the universe is doing is not experimentally accessible. And if its not experimentally accessible, it ain’t science, and so can be used at best as metaphysics (which is not to say that such a metaphysics might not allow you to think differently and solve problems from this perspective. But that is another story.)
So I think the question “Is the universe a computer?” really does have some content beyond just thinking about uncomputable laws of evolution. The question asks whether the evolution of our universe is, at a fundamental level, one which is predictable and controllable enough to warrant the moniker of computer. And this is a wonderful question, because, I think we have some ideas about the answer to this question, but as we learn more about physics, we will learn more about the ultimate answer to this question.