“COGITO ergo sum” was Descartes's stab at providing a demonstration of the fact of his own existence. John Archibald Wheeler, an American physicist, tried to go one better. He coined the phrase “it from bit” to provide a proof of the existence of everything in the universe. Dr Wheeler's idea is that if a thing contains a “bit” of information, which is the amount necessary to answer any yes-or-no question, then it must exist.

Although less lucidly phrased than Descartes's, Dr Wheeler's notion has exerted a powerful influence on physicists over the years. It has led some of them to add information to the catalogue of fundamental ingredients from which the universe is concocted, alongside matter and energy. It has also fuelled the development of a new branch of science. Researchers still study the physics of stars and atoms to discover how much matter and energy the universe contains, of course. But they now study the physics of information to work out how much of that the universe holds, as well.

One such physicist, Seth Lloyd of the Massachusetts Institute of Technology, recently took this approach to its logical conclusion by trying to calculate the maximum computing capacity of the entire cosmos. His results, published in the current issue of *Physical Review Letters*, lend support to Dr Wheeler's notion that information theory can provide important insights into physical reality.

## A bit more like it

Dr Lloyd began by imagining the universe as a single, enormous computer. Like a standard laptop, such a computer would become more powerful as the size of its hardware shrank and its software became more efficient—that is, consumed less energy when manipulating a bit of information. But this race to the bottom must end when these factors reach certain fundamental physical limits.

The first of these limits, on energy, imposes a cap on how fast the universe-as-computer could switch a bit of information from one state to the other (a process known in the jargon as a logical operation). A bit may be constructed from any object that can take on two states. The smallest pieces of hardware in the universe that are suitable for this task are particles such as atoms and electrons. Both possess a quantum property known as “spin” that can be flipped from pointing up to pointing down. But flipping even an electron's spin consumes energy. Moreover, the faster a spin is flipped, the more energy the process consumes.

Since the universe contains only a finite amount of energy, there is a limit to the rate at which it can perform such operations. Using current estimates of the amount of energy in the universe, Dr Lloyd was able to arrive at a total for the number of operations per second that the universe could perform, were it a computer. By multiplying that number by the age of the universe—ten billion years—he arrived at the grand total. The universe, it transpires, could have performed 10^{120} (a one followed by 120 zeroes) logical operations during its history.

So much for the universe's software. Totting up the amount of hardware, or physical bits, that the universe-as-computer contains was the second challenge. To work this number out, Dr Lloyd turned to another physical property of the universe—its entropy, or disorder.

Scientists have long known that any physical system, such as the atoms in a particular volume of gas, can be thought of as containing information. The bits of information in such a system correspond to how the system's components exhibit certain features such as energy, spin and charge. The more degrees of freedom, or disorder, in the system, the more bits of information it can be said to possess.

The universe would be at its most disordered, and thus at its richest in bits, if all the matter in it were converted into radiation rather than being its current mixture of matter and energy. (Energy and matter are interchangeable; the rate of exchange was laid out by Einstein in his well-known equation, E=mc^{2}.) That is because matter is locked into position, and thus has fewer degrees of freedom than footloose energy. By working backwards from the upper estimate of entropy in a pure-radiation universe, Dr Lloyd guessed that, if every particle in the universe had every possible degree of freedom available to it, the universe would hold 10^{90} bits. In addition, quantum theory suggests that entropy is added to the universe by gravitational fields such as those curled up inside black holes. Adding this in, Dr Lloyd reckoned that the sum works out at about 10^{120} bits.

## Mixed metaphors

That is a pleasing coincidence. Since the number-of-operations estimate came from information theory, and the number-of-bits estimate came from physics, Dr Lloyd takes the coincidence between the two as evidence of an underlying connection between information theory and physical reality. At the absolute maximum, therefore, the universe-as-computer could have performed one operation on each of its bits. In keeping with Dr Wheeler's view, the universe could therefore be seen as the “it” that has emerged from a one-time setting of each of its constituent bits.

Dr Lloyd is a believer in the large-scale feasibility of quantum computers—devices that promise to deliver enormous computational power by placing individual bits of information in two states at once, so that they can process many different logical combinations simultaneously. The small quantum computers that have been built so far use individual atoms as their physical bits. Sceptics doubt that such devices, which now hold fewer than ten bits, can be expanded much farther. What grander proof could Dr Lloyd offer that a large quantum computer could be made to work, than the suggestion that the entire universe is one itself?

From the Big Bang onwards, says Dr Lloyd, the universe has been “computing its own dynamical evolution”. If it all sounds too fanciful to be true, chalk it up to the tendency of quantum physics to attach the most exact probabilities to even the most remote outcomes. If somebody is determined to count angels on a pinhead, he may as well be precise about noting how many there are.

This article appeared in the Science & technology section of the print edition under the headline "It's all just number-crunching"