Of course, since publication of the Nature article, people keep calling me up to order one of these laptops; unfortunately the fabrication plant to build it has not yet been constructed. You might then actually ask why it is that our conventional laptops, are so slow by comparison when we've been on this Moore's Law track for 50 years now? The answer is that they make the mistake, which could be regarded as a safety feature of the laptop, of locking up most of their energy in the form of matter, so that rather than using that energy to manipulate information and transform it, most of it goes into making the laptop sit around and be a laptop.

As you can tell, if I were to take a week's energy output of all the world's nuclear power plants and liberate it all at once, I would have something that looked a lot like a thermonuclear explosion, because a thermonuclear explosion is essentially taking roughly a kilogram of matter and turning it into energy. So you can see right away that the ultimate laptop would have some relatively severe packaging problems. Since I am a professor of mechanical engineering at MIT, I think packaging problems is where it's at. We're talking about some very severe material and fabrication problems to prevent this thing from taking not only you but the entire city of Boston out with it when you boot it up the first time.

Needless to say, we didn't actually figure out how we were going to put this thing into a package, but that's part of the fun of doing calculations according to the ultimate laws of physics. We decided to figure out how many ops per second we could perform, and to worry about the packaging afterwards. Now that we've got 10 to the 51 ops per second the next question is: what's the memory space of this laptop.

When I go out to buy a new laptop, I first ask how many ops per second can it perform? If it's something like a hundred megahertz, it's pretty slow by current standards; if it's a gigahertz, that's pretty fast though we're still very far away from the 10 to the 51 ops per second. With a gigahertz, we're approaching 10 to the 10th, 10 to the 11th, 10 to the 12th, depending how ops per second are currently counted. Next, how many bits do I have — how big is the hard drive for this computer, or how big is its RAM? We can also use the laws of physics to calculate that figure. And computing memory capability is something that people could have done back in the early decades of this century.

We know how to count bits. We take the number of states, and the number of states is two raised to the power of the number of bits. Ten bits, two to the tenth states, 1024 states. Twenty bits, two to the 20 bits, roughly a million states. You keep on going and you find that with about 300 bits, two to the 300, well, it's about ten to the one hundred, which is essentially a bit greater than the number of particles in the universe. If you had 300 bits, you could assign every particle in the universe a serial number, which is a powerful use of information. You can use a very small number of bits to label a huge number of bits.

How many bits does this ultimate laptop have?

I have a kilogram of matter confined to the volume of a liter; how many states, how many possible states for matter confined to the volume of a liter can there possibly be?

This happened to be a calculation that I knew how to do, because I had studied cosmology, and in cosmology there's this event, called the Big Bang, which happened a long time ago, about 13 billion years ago, and during the Big Bang, matter was at extremely high densities and pressures.

I learned from cosmology how to calculate the number of states for matter of very high densities and pressures. In actuality, the density is not that great. I have a kilogram of matter in a liter. The density is similar to what we might normally expect today. However, if you want to ask what the number of states is for this matter in a liter, I've got to calculate every possible configuration, every possible elementary quantum state for this kilogram of matter in a liter of volume. It turns out, when you count most of these states, that this matter looks like it's in the midst of a thermonuclear explosion. Like a little piece of the Big Bang — a few seconds after the universe was born — when the temperature was around a billion degrees. At a billion degrees, if you ask what most states for matter are if it's completely liberated and able to do whatever it wants, you'll find that it looks like a lot like a plasma at a billion degrees Kelvin. Electrons and positrons are forming out of nothing, going back into photons again, there's a lot of elementary particles whizzing about and it's very hot. Lots of stuff is happening and you can still count the number of possible states using the conventional methods that people use to count states in the early universe; you take the logarithm of the number of states, get a quantity that's normally thought of as being the entropy of the system (the entropy is simply the logarithm of the number of states which also gives you the number of bits, because the logarithm of the number of states, the base 2, is the number of bits — because the number of bits raised to the power of — 2 to the power of the number of bits is the number of states. What more do I need to say?)

When we count them, we find that there are roughly 10 to the 31 bits available. That means that there's 2 to the 10 to the 31 possible states that this matter could be in. That's a lot of states – but we can count them. The interesting thing about that is that you notice we've got 10 to the 31 bits, we're performing 10 to the 51 ops per second, so each bit can perform about 10 to the 20 ops per second. What does this quantity mean?

It turns out that the quantity — if you like, the number of ops per second per bit is essentially the temperature of this plasma. And I take this plasma, I multiply it by Bell's constant, divide by Planck's constant, and what I get is the energy per bit, essentially; that's what temperature is. It tells you the energy per bit. It tells you how much energy is available for a bit to perform a logical operation. Since I know if I have a certain amount of energy I could perform a certain number of operations per second, then the temperature tells me how many ops per bit per second I can perform.

Then I know not only the number of ops per second, and the number of bits, but also the number of ops per bit per second that can be performed by this ultimate laptop, a kilogram of matter in a liter volume; it's the number of ops per bit per second that could be performed by these elementary particles back at the beginning of time by the Big Bang; it's just the total number of ops that each bit can perform per second. The number of times it can flip, the number of times it can interact with its neighboring bits, the number of elementary logical operations. And it's a number, right? 10 to the 20. Just the way that the total number of bits, 10 to the 31, is a number — it's a physical parameter that characterizes a kilogram of matter and a liter of volume. Similarly, 10 to the 51 ops per second is the number of ops per second that characterize a kilogram of matter, whether it's in a liter volume or not.

We've gone a long way down this road, so there's no point in stopping — at least in these theoretical exercises where nobody gets hurt. So far all we've used are the elementary constants of nature, the speed of light, which tells us the rate of converting matter into energy or E = MC2. The speed of light tells us how much energy we get from a particular mass. Then we use the Planck scale, the quantum scale, because the quantum scale tells you both how many operations per second you can get from a certain amount of energy, and it also tells you how to count the number of states available for a certain amount of energy. So by taking the speed of light, and the quantum scale, we are able to calculate the number of ops per second that a certain amount of matter can perform, and we're able to calculate the amount of memory space that we have available for our ultimate computer.

Then we can also calculate all sorts of interesting issues, like what's the possible input-output rate for all these bits in a liter of volume. That can actually be calculated quite easily from what I've just described, because to get all this information into and out of a liter volume — take a laptop computer — you can say okay, here's all these bits, they're sitting in a liter volume, let's move this liter volume over, by its own distance, at the speed of light. You're not going to be able to get the information in or out faster than that.