Information: The New Language of Science

  • Hans Christian von Baeyer
Weidenfeld & Nicolson: 2003. 258 pp. £16.99

What is the Universe made of? A growing number of scientists suspect that information plays a fundamental role in answering this question. Some even go as far as to suggest that information-based concepts may eventually fuse with or replace traditional notions such as particles, fields and forces. The Universe may literally be made of information, they say, an idea neatly encapsulated in physicist John Wheeler's slogan: “It from bit”. Others rather less boldly suggest that taking a point of view based on information theory may yield insights into existing theories such as statistical mechanics and quantum mechanics.

These are speculative ideas, still in the early days of development. Their most encouraging success is perhaps the resolution of the 'Maxwell's demon' paradox, a century-old riddle in the foundations of statistical mechanics. In James Clerk Maxwell's paradoxical thought experiment, a demon of extraordinary dexterity and visual acuity partitions an initially homogeneous gas into two parts, one part containing slow-moving molecules and the other part faster-moving ones. In the thought experiment, the gas is initially spread evenly through a two-chamber container with a connecting trapdoor that can be opened and closed by the demon. By carefully observing the velocity of molecules approaching the trapdoor, and opening or closing it as appropriate, the demon sorts the molecules so that fast molecules enter one chamber and slow ones end up in the other.

The resulting system is more ordered than the original homogeneous gas, and so has lower entropy. Furthermore, by making the trapdoor sufficiently lightweight, the demon can operate it by expending an arbitrarily small amount of energy. Thus, a naive analysis suggests that Maxwell's demon reduces the total entropy of the system, violating the second law of thermodynamics.

This paradox was resolved in 1982, when physicist Charles Bennett, building on earlier work by others, notably Rolf Landauer, showed that this analysis fails to take into account an entropy cost associated with the information acquired by the demon when it observes the velocities of molecules approaching the trapdoor. The cost is an entropic price paid when the demon erases its record of these observations. Remarkably, when this cost is taken into account, the violation of the second law is found to be illusory and the paradox is resolved.

A more recent example of information taking a surprising central role in fundamental science is a bold idea known as the holographic principle. Roughly speaking, this states that the correct way to describe a region of space-time is not through a description of fields and forces in the bulk of the volume, as is conventionally done, but through a theory whose elements are defined on the surface of the region. The motivation for the principle comes in part from results about the thermodynamics of black holes suggesting that the information content of a black hole is proportional to its surface area, not its volume. Some researchers hope that the holographic principle will help lead to a quantum theory of gravity, much as Einstein's principle of equivalence helped to motivate the general theory of relativity.

These and other examples illustrate the intellectual ferment associated with the role of information in fundamental science. It is against this backdrop that Hans Christian von Baeyer's elegant popular book is set.

The book's most appealing feature is its focus on big questions. What is information? What role does information play in fundamental physics? Where else in science does information play a critical role? And what common themes link these areas? Von Baeyer approaches these questions from many angles, giving us a flavour of some of the most interesting answers currently being offered.

There is a nice balance between accepted science and speculative ideas. For example, the standard theory of information, proposed by Claude Shannon in the 1940s, is introduced early in the book. However, von Baeyer admits that Shannon's theory has some shortcomings, and provides a flavour of several other approaches to developing information theories, notably quantum information theory.

Von Baeyer discusses many fascinating topics in a tour that is broad but not deep, taking in genetics, bioinformatics, quantum computation, the foundations of quantum mechanics, and black-hole entropy. He faces, and on the whole overcomes reasonably well, the difficulty faced by popular science writers of needing to simplify without misleading. However, I did notice several unfortunate minor errors of fact.

In summary, von Baeyer has provided an accessible and engaging overview of the emerging role of information as a fundamental building block in science.