Information

Shannon's central move, Baeyer explains, was to define information as the resolution of uncertainty. Before a message arrives, there are many things it might say. After it arrives, only one remains. The amount of information is a measure of how much doubt got cleared away. A message that tells you something you already knew carries none; a message that could have gone a thousand ways and picks one carries a great deal. Meaning, importance, truth — Shannon set them all aside as someone else's problem.

This is where the coin flip earns its place. A single fair coin has two equally likely outcomes, and learning the result clears exactly one unit of doubt. Shannon called that unit a bit, short for binary digit. Two coins give four possibilities and two bits; ten coins give a thousand-odd possibilities and ten bits. Baeyer is patient with this arithmetic because everything downstream depends on it. Information doubles with each added yes-or-no question, which means it grows not by counting outcomes but by counting the questions needed to name one.

The chapter where the book turns is the one where Baeyer connects Shannon's formula to a piece of nineteenth-century physics: entropy. Physicists had long used entropy to measure disorder — why heat flows from hot to cold, why a smashed cup never reassembles. When Shannon looked for a name for his measure of uncertainty, the mathematician John von Neumann reportedly told him to call it entropy, partly because the formula matched and partly because, in an argument nobody could win, the word would give him an edge.

Baeyer treats that coincidence as anything but coincidental. The entropy of a warm gas measures how many microscopic arrangements of its molecules would look the same from outside — which is exactly a measure of how much we don't know about the specific arrangement. That is missing information, expressed in the language of heat. Suddenly a concept from steam engines and a concept from telephone lines turn out to be the same concept wearing two costumes. This, for Baeyer, is the hinge of the whole book.

Having tied information to physics, Baeyer steps back to the boldest question the subject raises — one associated with the physicist John Archibald Wheeler and his phrase "it from bit." Wheeler's suggestion, which Baeyer treats with equal parts caution and enthusiasm, is that physical reality does not merely carry information but derives from it. Every particle, every field, every measurement might ultimately reduce to answers to yes-or-no questions posed to nature. The stuff of the world would be, at bottom, resolved uncertainty.

Baeyer is careful not to sell this as settled science, and that restraint is what makes his handling of it persuasive. He points to quantum mechanics, where the act of measurement is fundamental and where what we can ever know about a system is sharply limited. In that setting, framing physics in terms of information stops looking like a metaphor. The theory already speaks in probabilities and observations, in what can and cannot be known — the native vocabulary of Shannon's bit rather than of solid billiard-ball matter.

The book began with an embarrassment — that we could not measure the very thing our age is named after — and ends by proposing that this same unmeasured thing might be the bedrock of everything else. Shannon supplied the arithmetic, entropy supplied the bridge to physics, and Wheeler supplied the vertigo. Baeyer's achievement is to move across that whole distance without ever losing the thread, so that the reader who started with a coin flip arrives at the edge of cosmology feeling that each step was earned rather than smuggled in.