Fundamentals

by Frank Wilczek

  To understand how those fundamental facts can lead, under favorable conditions, to dynamic complexity on a grand scale, we need to bring in two big ideas: combinatorial explosion and provisional stability.

  Combinatorial explosion, in its simplest form, is the rapid growth in the number of overall possibilities as you make several independent choices. Thus, if I can choose any one of ten digits to fill nine different places, then I can make 109, or one billion, different combinations—namely, the numbers 000000000, 000000001, 000000002 . . . 999999999. Ten and nine are reasonably small numbers, but 109 is quite a large one. This demonstrates the essence of combinatorial explosion.

  In DNA, we get to make four choices among nucleotides (guanine, adenine, thymine, cytosine—G, A, T, C) to attach at each spot along a long sugar–phosphate backbone, and there can be many thousands of spots. Proteins, similarly, involve choosing among twenty amino acids attached to stereotyped backbones of variable length. Those architectures support combinatorial explosions of precisely the same type as the decimal expansion of numbers, but in base 4 or base 20. Thus, DNA sequences, which are used to store information, can record enormous quantities of information. And proteins, which provide the structural and functional building blocks for life, form a huge inventory. Different proteins fold into an enormous variety of sizes and shapes, with diverse mechanical and electrical properties.

  Molecules of other kinds, in both the organic and the inorganic worlds, can branch, form loops, agglomerate into membranes, stack regularly into crystals, and do many other tricks. This wealth of possibilities leads to a combinatorial explosion of combinatorial explosions. When you fold in the fact that a single gram of matter contains billions of billions of atoms, it becomes clear that there’s no shortage of material to support complexity on a grand scale. William Blake’s poetic description of an “infinity in the palm of your hand” has a sound scientific basis.

  CONCEIVING COMPLEXITY

  To deliver on that material’s potential, we must be able to sculpt it. We want our atomic building blocks, like Lego bricks, Tinkertoys, or the ball-and-stick models of atoms and molecules used in chemistry classes, to click together easily, to come apart easily, and to stay put in between. This key property, provisional stability, requires a nice balance between stability and changeability.

  Chemists work to determine what’s realistically possible in the world of molecular complexity, and biologists work to determine what actually happened. The work of chemists and biologists is open-ended and endlessly fascinating. I will rely on their goodwill and sense of humor to indulge my drastic simplifications. What can be understood reasonably simply, and what I will describe here, is only how the world, and specifically the Sun-Earth system, “conspires” to make intricate sculpting of matter conceivable.

  Three crucial ingredients make provisional stability possible. They are a high temperature, a low temperature, and an intermediate energy scale. The high temperature is the temperature at the surface of the Sun, around 6,000°C. The low temperature is the temperature at the surface of Earth, around 20°C. The intermediate energy scale is the quantity of energy it takes to make or break a typical chemical bond, which is roughly an electron volt.

  Temperatures around 20°C leave molecules mechanically flexible, but they don’t often break chemical bonds, because the energies they supply rarely reach an electron volt. On the other hand, photons arriving from the surface of the Sun pack more concentrated energy, often exceeding an electron volt. They are capable of breaking chemical bonds. The interplay between that cool, but not frigid, background and that accessible, but not oppressive, supply of concentrated energy makes it possible, but not too easy, to rearrange molecular patterns. This sort of provisional stability available on Earth is just what we need, physically, for dynamic complexity.

  To complete our story of abundant potential for dynamic complexity and how it gets realized on Earth, we need to understand, based on fundamentals, how our Sun manages to fulfill its role. But before turning to that, let us pause to calibrate our own dynamic complexity.

  The basic units of human brains are neurons. The number of neurons in a human brain is roughly one hundred billion, or 100,000,000,000, or 1011. While well below an octillion, this is still an unimaginably large number. It is roughly equal to the number of stars in our galaxy.

  Each neuron is an impressive little information-processing device. Individual neurons are wired together through many connections. Typical neurons can make hundreds or even a few thousand connections to other neurons. Much of what we learn is encoded in the varying strength of these connections, as useful patterns of influence get reinforced and useless ones whittled away. Peak connectivity occurs between the ages of two and three, but peak complexity occurs later, after a lot of selective whittling.

  If we consider the possible ways for that many neurons with that many connections to get wired up, we get into dizzying numbers, well beyond octillions. Our skulls host mind-blowing combinatorial explosions. We should not be shocked to find that this unimaginably large number of neurons, wired in such unimaginably intricate patterns, working together, can do astonishing things. Walt Whitman really did contain multitudes. So do I. So do you.

  FUEL TO BURN, SLOWLY

  The Sun runs on nuclear fuel. It is a giant fusion reactor. The nuclear burning process that drives the Sun is the conversion of hydrogen into helium. A hydrogen atom contains one proton and one electron. A helium atom contains two protons, two neutrons, and two electrons. In the Sun, a chain of reactions results in the conversion of four hydrogen atoms into one helium atom plus two neutrinos, releasing energy.

  If you recall our discussion of neutron decay in the preceding chapter, you might think there’s been a typo just now. There we saw that isolated neutrons want to turn into protons. That decay process liberates energy, because neutrons are slightly heavier than protons. In our description of solar burning, we’ve got the opposite happening—protons turning into neutrons. But it’s not a typo. In a helium nucleus there are powerful attractions among the protons and neutrons, due to the strong force. By bringing together the separate pieces, one gains a lot of energy. Thus, protons can turn into bound neutrons, with energy to spare.

  Transformations between protons and neutrons, in either direction, require the weak force. That makes neutron decay a slow process, by particle physics standards, as we discussed earlier. In the Sun’s nuclear burning, the slowness of the weak force gets greatly amplified. In that burning process, one must bring the particles together before transforming them. But those close encounters are fleeting, so “quality time” accumulates very slowly. It takes billions of years, on average, for protons in the Sun to convert into (bound) neutrons. Thus, thankfully, the Sun’s fuel supply will last for several billion more years. On the other hand, the amount of hydrogen in the Sun is so enormous that even this slow burning is enough to keep it shining.

  SUMMING UP: THAT ART THOU

  This completes our account of how dynamic complexity arises on Earth, from the perspective of physical fundamentals. It grounds biology, and ultimately psychology and economics, within our deep understanding of material reality.

  Each of the four fundamental forces plays a different, crucial role in this story. Gravity keeps Earth in orbit around the Sun, at a nice distance, where the equilibrium temperature supports dynamic complexity. The electromagnetic force, QED, weaves atoms into molecules. The strong force, QCD, supplies the attractions that make nuclear burning possible. The weak force enables the transformations that allow nuclear burning to proceed, but only slowly.

  THE FUTURE OF MATERIAL ABUNDANCE

  New Places, New Pieces, New Minds

  The principle that the essence of human purposes is expressed through flows of information in dynamic complexity, rather than through details of chemistry and physiology, is both mind-expanding and liberating. It challenges us to imagine how minds could emerge elsewhe
re in the universe, and it prepares us to embrace those minds within our circle of empathy.

  To thrive, human bodies require specific conditions, including temperatures within a narrow range, air that contains a special mix of molecules and is free of toxins, a reliable supply of water and nutrients, and protection from ultraviolet radiation and cosmic rays. These conditions exist within a thin layer near the surface of Earth, but they are very rare within the universe as a whole. Colonization of space by humans, in our Earth-adapted bodies, is a crazily difficult project.

  Expanding the sphere of influence of human information is a much easier, more realistic goal, and it is no less meaningful. The actuators and sensors we send can create and explore on our behalf—and stay in touch.

  Our profound understanding of matter gives us several ways to manufacture large-scale dynamic complexity that are quite different from making and breaking chemical bonds. We can supplement, or even replace, chemistry with electronics and photonics.

  Digital photography is a convincing, mature example of how that occurs. Here the primary sensors—charge-coupled devices, or CCDs—count electrons liberated by photons and record the resulting numbers in arrays of 0s and 1s, encoded using any of the formats described earlier. This information, which encodes the image, can be processed in many ways; for example, to remove noise, highlight interesting features, or otherwise beautify the picture. Then, after processing, you can translate the information back into images, by using it to instruct displays. All that processing is done electronically, in computers or specialized chips. Photographic plates, emulsions, and darkrooms, which once gave photography an aura of romance and mystery—while making it much more time-consuming and difficult—are on the wane.

  The evolving patterns of connection and chemistry-driven electrical activity in human brains are the apex of dynamic complexity, and of mind, today. But the importance of other embodiments of dynamic complexity is increasing, and there’s plenty of room for it to grow.

  Inside modern computers, information is stored and processed in arrangements and rearrangements of electrons, as opposed to entire atoms or molecules. The energies involved can be much smaller, and the processing can be much faster. To represent information, we have either a high concentration of electrons (leading to a low voltage, interpreted as “0”), or a low concentration (leading to a high voltage, interpreted as “1”) in each of billions or trillions of tiny buckets. In this way, we manufacture a combinatorial explosion of provisionally stable units. It is a versatile platform for dynamic complexity.

  It is also possible to use the direction of electron spins—up or down—instead of the electrons’ concentration, to embody 0 and 1. Manipulating spin directions is more delicate work than pushing charge around, but in principle it can be faster and more energy efficient. We can also work with photons instead of electrons, and monitor their concentrations (amplitude), colors (wavelength), or spin (polarization).

  These post-chemical platforms for dynamic complexity have big advantages in speed, size, and energy efficiency. They are also more open to controlled exploitation of the richness of the quantum world.* They can support continued growth of mind in the cosmos for a long time, and on a vast scale.

  How Things Could Go Wrong

  With great power comes great responsibility.

  —Peter Parker (Spider-Man)

  An overarching message from our fundamentals is that there’s plenty of space, plenty of time, and plenty of matter and energy. The physical world offers us humans a future much bigger, longer, and richer than what we’ve achieved so far—if we don’t blow it.

  Many things could go wrong. Plagues have ravaged human civilizations in the past and caused significant setbacks, as have earthquakes and volcanic eruptions. An unfortunate collision of Earth with cosmic debris doomed the dinosaurs. We can and should work to mitigate those dangers. But here, to close this chapter, I will briefly highlight two possible human-made failure modes that loom large today, and that are closely connected to its themes.

  Our Sun supplies Earth, at a steady rate, with far more energy than humans presently use. Technology to capture a larger fraction of that energy is developing rapidly, and there is little doubt that in the foreseeable future—barring catastrophe—we will be able to use it to support a richer world economy, sustainably.

  At the moment, however, it is easier and more convenient to tap into solar energy that was captured long ago by plant life, and now is stored in fossil fuels—coal and oil. Unfortunately, burning those fuels on a large scale releases enough carbon dioxide and other pollutants into our atmosphere to alter its properties. The polluted atmosphere traps more of the Sun’s energy, causing Earth’s average temperature to rise. This is the first human-generated crisis looming over us.

  Our sister planet, Venus, is a jewel of the night sky. It is a warning beacon, too. Its atmosphere, rich in carbon dioxide, traps the Sun’s energy extremely efficiently. Surface temperatures on Venus approach 460°C (860°F), which is hot enough to melt lead, and precludes complex chemistry. Venus is closer to the Sun than is Earth, but if we put it at Earth’s orbit, its temperature would still be alarmingly high—about 340°C (645°F). Earth won’t get that hot anytime soon, but even a few degrees of added temperature will have drastic, possibly catastrophic effects. Rising temperatures are causing polar ice to melt, leading to rising sea levels; violent weather patterns are emerging, driven by increased atmospheric moisture; and we are disrupting the lives of temperature-sensitive plants and animals, thus endangering our food supplies (and our friends).

  The second human-generated threat is nuclear weaponry. As scientists explored the strong and weak forces, they discovered potent new fuels based on nuclear rather than chemical burning. Famously, this enabled the construction of new sorts of bombs, with much greater destructive power. Were a significant fraction of those bombs to be used in warfare, many millions of people would perish in horrible ways, and important centers of civilization would become uninhabitable wastelands. Human progress would be set back catastrophically, and perhaps irreversibly.

  The blessings of economic growth and scientific knowledge come together with severe dangers. Those dangers can be avoided. Whether they will be is an open question.

  II

  Beginnings and Ends

  6

  COSMIC HISTORY IS AN OPEN BOOK

  Our first five fundamentals have described the basic ingredients of physical reality: space, time, fields, laws, and dynamic complexity. They addressed “what there is.” Our next two will address “how it got this way.”

  People have speculated about the origin of the physical world ever since there have been people. Anthropologists have recorded creation stories from many cultures. Literature contains many others, some of which have, at different times and places, been accorded sacred authority. But adequate intellectual and technical tools to address the question of physical origins first became available in the twentieth century.

  Over the past few decades, a remarkably clear picture of the broad outline of cosmic history has emerged. The crucial breakthrough was Hubble’s work on the distance and motion of galaxies. Hubble discovered that distant galaxies are moving away from us, with velocities proportional to their distances. That universal expansion, run backward in time, suggests that the matter in the universe was once much more densely packed together, and that the universe once looked quite different from what we see around us today.

  What was it like? In the text of this chapter I will address that question, in three steps. First, I’ll present a bold guess about the early state of the universe, commonly known as the big bang theory. I will emphasize its strange simplicity. Second, I’ll sketch the cosmic history which follows from that guess. Finally, I’ll discuss some of the main observable consequences that flow from this history, and the evidence that has accumulated for it. The multifaceted success of this hypothetical history justifie
s the bold guess that launched it.

  That said, the observational evidence thins out, and our equations cease to be reliable guides, when we look toward the very beginning. At the close of this chapter, I will discuss promising prospects, both theoretical and observational, for seeing deeper.

  SCOPE AND LIMITS

  The work will teach you how to do it.

  —Anonymous (quoted in a fortune cookie)

  Science often resembles the game of Jeopardy!, where answers suggest what the right questions are. The great mathematical astronomer Johannes Kepler, a hero in some of our earlier discussions, considered many aspects of the solar system in his work. His questions about the shape of planetary orbits and the speeds with which the planets traverse them had good* answers, now famous as Kepler’s laws of planetary motion. But Kepler also wrestled with the problems of why there are six planets (as was thought at the time) and why they are at the distances from the Sun that they are. He had some amusing ideas on those subjects, which brought in music—“the music of the spheres”—and the Platonic solids. But those ideas never gelled into good answers. Today, scientists think that Kepler wasn’t asking the right questions. Our fundamental laws, and our fundamental understanding of cosmic history, suggest that the size and shape of our solar system is a rather accidental feature of the universe. Its ultimate form is caught up in details of how a mess of gas, rocks, and dust collapsed and condensed to make the system we observe today. We see our solar system as one among many in the universe. In other systems we often observe different numbers of planets in different arrangements than what Kepler was hoping to explain. Since Kepler’s day, too, our own solar system has grown to include Uranus, Neptune, asteroids, Pluto, and a lot of other stuff.