I made these calculations not to suggest any grandiose plan or to reveal large numbers, although of course I ended up with some large numbers, but I was curious what these numbers were. When I calculated I actually thought that these can't be right because they are too small. I can think of much bigger numbers than 10[120] (10 to the 120). There are lots of bigger numbers than that. It was fun to calculate the computational capacity of the universe, but I wanted to get at some picture of how much computation the universe could do if we think of it as performing a computation. These numbers can be interpreted essentially in three ways, two of which are relatively uncontroversial. The first one I already gave you: it's an upper bound to the size of a computer that we could build if we turned everything in the universe into a computer running Windows 2540. That's uncontroversial. So far nobody's managed to find a way to get around that. There's also a second interpretation, which I think is more interesting. One of the things we do with our quantum computers is to use them as analog computers to simulate other physical systems. They're very good at simulating other quantum systems, at simulating quantum field theories, at simulating all sort of effects, down to the quantum mechanical scale that is hard to understand and hard to simulate classically. These numbers are a lower limit to the size of a computer that could simulate the whole universe, because to simulate something you need at least as much stuff as is there. You need as many bits in your simulator as there are bits registered in the system if you are going to simulate it accurately. And if you're going to follow it step by step throughout its evolution, you need at least as many steps in your simulator as the number of steps that occur in the system itself. So these numbers, 10[120] (10 to the 120) ops, 10[90] (10 to the 90) bits of matter —10[120] if you believe in something like holography ­ also form a lower bound on the size of a computer you would need to simulate the universe as a whole, accurately and exactly. That's also uncontroversial.

The third interpretation, which of course is more controversial, arises if we imagine that the universe is itself a computer and that what it's doing is performing a computation. If this is the case, these numbers say how big that computation is — how many ops have been performed on how many bits within the horizon since the universe began. That, of course, is more controversial, and since publishing this paper I've received what is charitably described as "hate mail" from famous scientists. There have been angry letters to the editor of Physical Review Letters. "How dare you publish a paper like this?" they say. Or "It's just absolutely inconceivable. The standards have really gotten low." Thinking of the universe as a computer is controversial. I don't see why it should be so controversial, because many books of science fiction have already regarded the universe as a computer. Indeed, we even know the answer to the question it's computing — it's 42. The universe is clearly not a computer with a Pentium inside. It's not an electronic computer, though of course it operates partly by quantum electro-dynamics, and it's not running Windows — at least not yet. Some of us hope that never happens — though you never can tell — if only because you don't want the universe as a whole to crash on you all of a sudden. Luckily, whatever operating system it has seems to be slightly more reliable so far. But if people try to download the wrong software, or upgrade it in some way, we could have some trouble.

So why is this controversial? For one, it seems to be making a statement that's obviously false. The universe is not an electronic digital computer, it's not running some operating system, and it's not running Windows. Why does it make sense to talk about the universe as performing a computation at all? There's one sense in which it's actually obvious that the universe is performing a computation. If you take any physical system — say this quarter, for example. The quarter can register a lot of information. It registers each atom in it, has a position which registers a certain amount of information, has some jiggling motion which registers a few bits of information, and can be heads or tails. Whether it's heads or tails in the famous flipping a coin is generating a famous bit of information — unless it's Rosenkranz and Guildenstern Are Dead, in which case it always comes up heads. Because the quarter is a physical system, it's also dynamic and evolves in time. Its physical state is transforming. It's easier to notice if I flip it in the air — it evolves in time, it changes, and as it changes it transforms that information, so the information that describes it goes from one state to another — from heads to tails, heads to tails, heads to tails — really fast. The bit flips, again and again and again. In addition, the positions, momentum, and quantum states of the atoms inside are changing, so the information that they're registering is changing. Merely by existing and evolving in time — by existing — any physical system registers information, and by evolving in time it transforms or processes that information.

It doesn't necessarily transform it or process it in the same way that a digital computer does, but it's certainly performing information­processing. From my perspective, it's also uncontroversial that the universe registers 10[90] bits of information, transforms and processes that information at a rate which is determined by its energy divided by Planck's constant. All physical systems can be thought of as registering and processing information, and how one wishes to define computation will determine your view of what computation consists of. If you think of computation as being merely information-processing, then it's rather uncontroversial that the universe is computing, but of course many people regard computation as being more than information-processing. There are formal definitions of what computation consists of. For instance, there are universal Turing machines, and there is a nice definition that's now 70-odd years old of what it means for something to be able to perform digital computation. Indeed, the kind of computers we have sitting on our desks, as opposed to the kinds we have sitting in our heads or the kind that were in that little inchworm that was going along, are universal digital computers. So information-processing where a physical system is merely evolving in time is a more specific, and potentially more powerful kind of computing, because one way to evolve in time is just to sit there like a lump. That's a perfectly fine way of evolving in time, but you might not consider it a computation. Of course, my computer spends a lot of time doing that, so that seems to be a common thing for computers to do.

One of the things that I've been doing recently in my scientific research is to ask this question: Is the universe actually capable of performing things like digital computations? Again, we have strong empirical evidence that computation is possible, because I own a computer. When it's not sitting there like a lump, waiting to be rebooted, it actually performs computation. Whatever the laws of physics are, and we don't know exactly what they are, they do indeed support computation in the form of existing computers. That's one bit of empirical evidence for it.