We can find out how many bits per second we get into and out of our ultimate laptop. And we find we can get around 10 to the 40, or 10 to the 41, or perhaps, in honor of Douglas Adams and his mystical number 42, even 10 to the 42 bits per second in and out of our ultimate laptop. So you can calculate all these different parameters that you might think are interesting, and that tells you how good a modem you could possibly have for this ultimate laptop — how many bits per second can you get in and out over the Ultimate Internet, whatever the ultimate Internet would be. I guess the Ultimate Internet is just space/time itself in this picture.

I noted that you can't possibly do better than this, right? These are the laws of physics. But you might be able to do better in other ways. For example, let's think about the architecture of this computer. I've got this computer that's doing 10 to the 51 ops per second, or 10 to the 31 bits. Each bit can flip 10 to the 20 times per second. That's pretty fast. The next question is how long does it take a bit on this side of the computer to send a signal to a bit on that side of the computer in the course of time it takes it to do an operation.

As we've established, it has a liter volume, which is about ten centimeters on each side, so it takes about ten to the minus ten seconds for light to go from one side to another — one ten billionth of a second for light to go from this side to the other. These bits are flipping 10 to the 20 times per second — a hundred billion billion times per second. This bit is flipping ten billion times in the course of time it takes a signal to go from one side of the computer to the other. This is not a very serial computation. A lot of action is taking place over here in the time it takes to communicate when all the action is taking place over on this side of the computer. This is what's called a parallel computation.

You could say that in the kinds of densities of matter that we're familiar with, like a kilogram per liter volume, which is the density of water, we find that we can only perform a very parallel computation, if we operate at the ultimate limits of computation; lots of computational action takes place over here during the time it takes a signal to go from here to there and back again.

How can we do better? How could we make the computation more serial?

Let's suppose that we want our machine to do more serial computation, so in the time it takes to send a signal from one side of the computer to the other, there are fewer ops that are being done. The obvious solution is to make the computer smaller, because if I make the computer smaller by a factor of two, it only takes half the time for light, for a signal, for information, to go from one side of the computer to the other.

If I make it smaller by a factor of ten billion, it only takes one ten billionth of the time for its signal to go from one side of the computer to the other. You also find that when you make it smaller, these pieces of the computer tend to speed up, because you tend to have more energy per bit available in each case. If you go through the calculation you find out that as the computer gets smaller and smaller, as all the mass is compressed into a smaller and smaller volume, you can do a more serial computation.

When does this process stop? When can every bit in the computer talk with every other bit, in the course of time it takes for a bit to flip? When can everybody get to talk with everybody else in the same amount of time that it takes them to talk with their neighbors?

As you make the computer smaller and smaller, it gets denser and denser, until you have a kilogram of matter in an ever smaller volume. Eventually the matter assumes more and more interesting configurations, until it's actually going to take a very high pressure to keep this system down at this very small volume. The matter assumes stranger and stranger configurations, and tends to get hotter and hotter and hotter, until at a certain point a bad thing happens. The bad thing that happens is that it's no longer possible for light to escape from it — it becomes a black hole.

What happens to our computation at this point. This is probably very bad for a computation, right? Or rather, it's going to be bad for input-output. Input is good, because stuff goes in, but output is bad because it doesn't come out since it's a black hole. Luckily, however, we're safe in this, because the very laws of quantum mechanics that we were using to calculate how much information a physical system can compute, how fast it can perform computations, and how much information it can register, actually hold.

Stephen Hawking showed, in the 1970s, that black holes, if you treat them quantum-mechanically, actually can radiate out information. There's an interesting controversy as to whether that information has anything to do with the information that went in. Stephen Hawking and John Preskill have a famous bet, where Preskill says yes — the information that comes out of a black hole reflects the information that went in. Hawking says no — the information that comes out of a black hole when it radiates doesn't have anything to do with the information that went in; the information that went in goes away. I don't know the answer to this.

But let's suppose for a moment that Hawking is wrong and Preskill is right. Let's suppose for a moment that in fact the information that comes out of a black hole when it evaporates, radiates information the wave length of the radiation coming out which is the radius of the black hole. This black hole, this kilogram black hole, is really radiating at a whopping rate; it's radiating out these photons with wave lengths of 10 to the minus 27 meters, this is not something you would actually wish to be close to — it would be very dangerous. In fact it would look a lot like a huge explosion. But let's suppose that in fact that information that's being radiated out by the black hole is in fact the information that went in to construct it, but simply transformed in a particular way. What you then see is that the black hole can be thought of in some sense as performing a computation.

You take the information about the matter that's used to form the black hole, you program it in the sense that you give it a particular configuration, you put this electron here, you put that electron there, you make that thing vibrate like this, and then you collapse this into a black hole, 10 to the minus 27 seconds later, in one hundred billion billionth of a second, the thing goes cablooey, and you get all this information out again, but now the information has been transformed, by some dynamics, and we don't know what this dynamics is, into a new form.

In fact we would need to know something like string theory or quantum gravity to figure out how it's been transformed. But you can imagine that this could in fact function as a computer. We don't know how to make it compute, but indeed, it's taking in information, it's transforming it in a systematic form according to the laws of physics, all right, and then poop! It spits it out again.

It's a dangerous thing — the Ultimate Laptop was already pretty dangerous, because it looked like a thermonuclear explosion inside of a liter bottle of coca cola. This is even worse, because in fact it looks like a thermonuclear explosion except that it started out at a radius of 10 to the minus 27 meters, one billion billion billionth of a meter, so it's really radiating at a very massive rate. But suppose you could somehow read information coming out of the black hole. You would indeed have performed the ultimate computation that you could have performed using a kilogram of matter, in this case confining it to a volume of 10 to the minus 81 cubic meters. Pretty minuscule but we're allowed to imagine this happening.

Is there anything more to the story?

After writing my paper on the ultimate laptop in Nature, I realized this was insufficiently ambitious; that of course the obvious question to ask at this point is not what is the ultimate computational capacity of a kilogram of matter, but instead to ask what is the ultimate computational capacity of the universe as a whole? After all, the universe is processing information, right? Just by existing, all physical systems register information, just by evolving their own natural physical dynamics, they transform that information, they process it. So the question then is how much information has the universe processed since the Big Bang?