Making order

Information entropy

Entropy didn’t stay in physics. In 1948 the American engineer Claude Shannon, at Bell Labs in New Jersey, founded information theory. At its center he put a quantity with the same mathematical form as Boltzmann’s entropy. Shannon is often called the father of the information age.

Thermal entropy measures disorder: four molecules gathered neatly on one side are easy to find, and spread through the box they are harder to find. Information entropy measures uncertainty, how unpredictable the next message from a source is. Consider two weather forecasters. The first says there’s an 80 percent chance of rain tomorrow. The second says 90 percent. Shannon’s formula gives the first forecast an entropy of 0.72 bits and the second 0.47 bits. The second forecaster leaves you less uncertain, so their forecast carries more information. Information gained is uncertainty removed.

Entropy has no built-in moral value. Low information entropy means certainty, which is what you want from a forecast. High entropy means many possibilities, and sometimes that’s what you want. This course coins a playful term, “confidence entropy,” and admits it is not rigorous. A young person faces many possible futures, and that openness brings hope and confidence. By middle age, the possibilities have narrowed. Perhaps that is why people come to a course like this one: to open up more possibilities for themselves. Whether entropy is good or bad depends on what you need.

Stay open

Back to physical entropy. If disorder always grows, how can anything stay organized, whether a living body, a society, or a planet? The answer can be read out of the definition itself. The entropy of an isolated system never decreases. So don’t be isolated. Open the system to the outside, and it can take in order and push disorder out.

The earth is the grand example. Its usefulness comes from differences: water held high behind a dam and low below it, high pressure here and low pressure there, hot rock deep underground and cool rock near the surface. Those differences give us hydropower, wind, and geothermal heat. If everything evened out, with one water level, one pressure, and one temperature, no energy could be drawn from anything, and the earth would be dead. Living bodies are even more highly ordered, full of structure.

The earth stays ordered because it is open to the sun. Sunlight arrives as concentrated, high-quality energy. It heats some regions more than others, driving winds, rain, and every food chain. The earth then radiates the same amount of energy back into space as low-grade heat, many more photons each carrying less energy. That outflow carries away entropy. As long as the order flowing in outweighs the disorder produced, the earth stays ordered. The same is true of each of us:

What an organism feeds upon is negative entropy.

Erwin Schrödinger, What Is Life?, 1944

Schrödinger, one of the founders of quantum mechanics, whom you’ll meet in Course 6, meant that life survives by drawing order from its surroundings, from food that ultimately comes from sunlight, and discarding disorder back into them as heat and waste.

Ways to fight disorder

This course draws four more strategies from the second law, offered as lessons for anyone running a household, a team, or a company.

Reduce dissipation. Entropy rises through waste, as energy that could do work is frittered away as useless heat. Keep your capacity to do work, and don’t let it drain away.

Find order in disorder. Look at a string of DNA letters. To most people it’s noise, all uncertainty and no information. To a geneticist, a single-letter change at one spot in the hemoglobin gene is the cause of sickle-cell disease, knowledge that can save lives. The more you know, the more order you can see where others see chaos. An example from Chinese sports: when the former NBA star Yao Ming took over the Chinese Basketball Association in 2017, fans grew hopeful. An insider can see order that an outsider, meddling, might only scramble.

Create order out of disorder. In 1900 the French physicist Henri Bénard heated a thin layer of liquid evenly from below. At first nothing happens: the liquid is uniform, in equilibrium, with no pattern at all. But as the heating grows stronger, the bottom gets much hotter than the top and the equilibrium breaks. Some small random disturbance tips the balance, and the liquid organizes itself into a honeycomb of hexagonal cells. Warm liquid rises in the middle of each cell and cool liquid sinks at the edges. The Belgian chemist Ilya Prigogine called such patterns dissipative structures: order that forms far from equilibrium and lasts as long as energy keeps flowing through. He won the 1977 Nobel Prize in Chemistry for this work, and the idea has since spread to biology, economics, and the study of complex systems. In short: take a stagnant pond, throw in a stone, and new order can be born.

Rise into a new dimension. The last strategy is the most metaphorical. In the original Super Mario Bros., Mario lives in two dimensions; in the 3D games, a bush that looked like part of the same flat scene turns out to be in front, and the pipe behind. A two-dimensional being can’t see what a three-dimensional one sees. In the third volume of Liu Cixin’s Three-Body trilogy, an alien civilization destroys the solar system by flattening it into two dimensions. In the film Interstellar, humanity is saved not by fleeing to another planet but by learning to reach across time. In business, the example is Steve Jobs. In this telling, Apple couldn’t win on Microsoft’s terms in personal computers or on Nokia’s terms in phones, so it created a new category, the smartphone with its own ecosystem, and set the terms for everyone else. To see an order that others can’t see, raise your dimension.

The end of classical physics

With heat and entropy, this account of classical physics comes to a close: the classical cosmos, Newton’s mechanism, and now the laws of heat and statistics. What ran through all of it, in this reading, was humanity’s unrelenting demand to know why. A description isn’t enough; there must be a deeper reason. A deeper reason isn’t enough if it isn’t simple and beautiful. Laws of laws, like least action, symmetry, and entropy, may be starting to touch the foundations of nature. Or we may still be far away. Either way, the search won’t stop. Course 6 takes it into the strangest territory of all: quantum mechanics.