The Grand Design - Stephen Hawking, Leonard Mlodinow (2010)
Chapter 2. The Rule of Law
Skoll the wolf who shall scare the Moon
Till he flies to the Wood-of-Woe:
Hati the wolf, Hridvitnir’s kin,
Who shall pursue the sun.
—“GRIMNISMAL,” The Elder Edda
N VIKING MYTHOLOGY, Skoll and Hati chase the sun and the moon. When the wolves catch either one, there is an eclipse. When this happens, the people on earth rush to rescue the sun or moon by making as much noise as they can in hopes of scaring off the wolves. There are similar myths in other cultures. But after a time people must have noticed that the sun and moon soon emerged from the eclipse regardless of whether they ran around screaming and banging on things. After a time they must also have noticed that the eclipses didn’t just happen at random: They occurred in regular patterns that repeated themselves. These patterns were most obvious for eclipses of the moon and enabled the ancient Babylonians to predict lunar eclipses fairly accurately even though they didn’t realize that they were caused by the earth blocking the light of the sun. Eclipses of the sun were more difficult to predict because they are visible only in a corridor on the earth about 30 miles wide. Still, once grasped, the patterns made it clear the eclipses were not dependent on the arbitrary whims of supernatural beings, but rather governed by laws.
Despite some early success predicting the motion of celestial bodies, most events in nature appeared to our ancestors to be impossible to predict. Volcanoes, earthquakes, storms, pestilences, and ingrown toenails all seemed to occur without obvious cause or pattern. In ancient times it was natural to ascribe the violent acts of nature to a pantheon of mischievous or malevolent deities. Calamities were often taken as a sign that we had somehow offended the gods. For example, in about 5600 BC the Mount Mazama volcano in Oregon erupted, raining rock and burning ash for years, and leading to the many years of rainfall that eventually filled the volcanic crater today called Crater Lake. The Klamath Indians of Oregon have a legend that faithfully matches every geologic detail of the event but adds a bit of drama by portraying a human as the cause of the catastrophe. The human capacity for guilt is such that people can always find ways to blame themselves. As the legend goes, Llao, the chief of the Below World, falls in love with the beautiful human daughter of a Klamath chief. She spurns him, and in revenge Llao tries to destroy the Klamath with fire. Luckily, according to the legend, Skell, the chief of the Above World, pities the humans and does battle with his underworld counterpart. Eventually Llao, injured, falls back inside Mount Mazama, leaving a huge hole, the crater that eventually filled with water.
Ignorance of nature’s ways led people in ancient times to invent gods to lord it over every aspect of human life. There were gods of love and war; of the sun, earth, and sky; of the oceans and rivers; of rain and thunderstorms; even of earthquakes and volcanoes. When the gods were pleased, mankind was treated to good weather, peace, and freedom from natural disaster and disease. When they were displeased, there came drought, war, pestilence, and epidemics. Since the connection of cause and effect in nature was invisible to their eyes, these gods appeared inscrutable, and people at their mercy. But with Thales of Miletus (ca. 624 BC- ca. 546 BC) about 2,600 years ago, that began to change. The idea arose that nature follows consistent principles that could be deciphered. And so began the long process of replacing the notion of the reign of gods with the concept of a universe that is governed by laws of nature, and created according to a blueprint we could someday learn to read.
Viewed on the timeline of human history, scientific inquiry is a very new endeavor. Our species, Homo sapiens, originated in sub-Saharan Africa around 200,000 BC. Written language dates back only to about 7000 BC, the product of societies centered around the cultivation of grain. (Some of the oldest written inscriptions concern the daily ration of beer allowed to each citizen.) The earliest written records from the great civilization of ancient Greece date back to the ninth century BC, but the height of that civilization, the “classical period,” came several hundred years later, beginning a little before 500 BC. According to Aristotle (384 BC-322 BC), it was around that time that Thales first developed the idea that the world can be understood, that the complex happenings around us could be reduced to simpler principles and explained without resorting to mythical or theological explanations.
Thales is credited with the first prediction of a solar eclipse in 585 BC, though the great precision of his prediction was probably a lucky guess. He was a shadowy figure who left behind no writings of his own. His home was one of the intellectual centers in a region called Ionia, which was colonized by the Greeks and exerted an influence that eventually reached from Turkey as far west as Italy. Ionian science was an endeavor marked by a strong interest in uncovering fundamental laws to explain natural phenomena, a tremendous milestone in the history of human ideas. Their approach was rational and in many cases led to conclusions surprisingly similar to what our more sophisticated methods have led us to believe today. It represented a grand beginning. But over the centuries much of Ionian science would be forgotten—only to be rediscovered or reinvented, sometimes more than once.
According to legend, the first mathematical formulation of what we might today call a law of nature dates back to an Ionian named Pythagoras (ca. 580 BC-ca. 490 BC), famous for the theorem named after him: that the square of the hypotenuse (longest side) of a right triangle equals the sum of the squares of the other two sides. Pythagoras is said to have discovered the numerical relationship between the length of the strings used in musical instruments and the harmonic combinations of the sounds. In today’s language we would describe that relationship by saying that the frequency—the number of vibrations per second—of a string vibrating under fixed tension is inversely proportional to the length of the string. From the practical point of view, this explains why bass guitars must have longer strings than ordinary guitars. Pythagoras probably did not really discover this—he also did not discover the theorem that bears his name—but there is evidence that some relation between string length and pitch was known in his day. If so, one could call that simple mathematical formula the first instance of what we now know as theoretical physics.
Apart from the Pythagorean law of strings, the only physical laws known correctly to the ancients were three laws detailed by Archimedes (ca. 287 BC-ca. 212 BC), by far the most eminent physicist of antiquity. In today’s terminology, the law of the lever explains that small forces can lift large weights because the lever amplifies a force according to the ratio of the distances from the lever’s fulcrum. The law of buoyancy states that any object immersed in a fluid will experience an upward force equal to the weight of the displaced fluid. And the law of reflection asserts that the angle between a beam of light and a mirror is equal to the angle between the mirror and the reflected beam. But Archimedes did not call them laws, nor did he explain them with reference to observation and measurement. Instead he treated them as if they were purely mathematical theorems, in an axiomatic system much like the one Euclid created for geometry.
As the Ionian influence spread, there appeared others who saw that the universe possesses an internal order, one that could be understood through observation and reason. Anaximander (ca. 610 BC-ca. 546 BC), a friend and possibly a student of Thales, argued that since human infants are helpless at birth, if the first human had somehow appeared on earth as an infant, it would not have survived. In what may have been humanity’s first inkling of evolution, people, Anaximander reasoned, must therefore have evolved from other animals whose young are hardier. In Sicily, Empedocles (ca. 490 BC-ca. 430 BC) observed the use of an instrument called a clepsydra. Sometimes used as a ladle, it consisted of a sphere with an open neck and small holes in its bottom. When immersed in water it would fill, and if the open neck was then covered, the clepsydra could be lifted out without the water in it falling through the holes. Empedocles noticed that if you cover the neck before you immerse it, a clepsydra does not fill. He reasoned that something invisible must be preventing the water from entering the sphere through the holes—he had discovered the material substance we call air.
Around the same time Democritus (ca 460 BC-ca. 370 BC), from an Ionian colony in northern Greece, pondered what happened when you break or cut an object into pieces. He argued that you ought not to be able to continue the process indefinitely. Instead he postulated that everything, including all living beings, is made of fundamental particles that cannot be cut or broken into parts. He named these ultimate particles atoms, from the Greek adjective meaning “uncuttable.” Democritus believed that every material phenomenon is a product of the collision of atoms. In his view, dubbed atomism, all atoms move around in space, and, unless disturbed, move forward indefinitely. Today that idea is called the law of inertia.
The revolutionary idea that we are but ordinary inhabitants of the universe, not special beings distinguished by existing at its center, was first championed by Aristarchus (ca. 310 BC-ca. 230 BC), one of the last of the Ionian scientists. Only one of his calculations survives, a complex geometric analysis of careful observations he made of the size of the earth’s shadow on the moon during a lunar eclipse. He concluded from his data that the sun must be much larger than the earth. Perhaps inspired by the idea that tiny objects ought to orbit mammoth ones and not the other way around, he became the first person to argue that the earth is not the center of our planetary system, but rather that it and the other planets orbit the much larger sun. It is a small step from the realization that the earth is just another planet to the idea that our sun is nothing special either. Aristarchus suspected that this was the case and believed that the stars we see in the night sky are actually nothing more than distant suns.
The Ionians were but one of many schools of ancient Greek philosophy, each with different and often contradictory traditions. Unfortunately, the Ionians’ view of nature—that it can be explained through general laws and reduced to a simple set of principles—exerted a powerful influence for only a few centuries. One reason is that Ionian theories often seemed to have no place for the notion of free will or purpose, or the concept that gods intervene in the workings of the world. These were startling omissions as profoundly unsettling to many Greek thinkers as they are to many people today. The philosopher Epicurus (341 BC-270 BC), for example, opposed atomism on the grounds that it is “better to follow the myths about the gods than to become a ‘slave’ to the destiny of natural philosophers.” Aristotle too rejected the concept of atoms because he could not accept that human beings were composed of soulless, inanimate objects. The Ionian idea that the universe is not human-centered was a milestone in our understanding of the cosmos, but it was an idea that would be dropped and not picked up again, or commonly accepted, until Galileo, almost twenty centuries later.
As insightful as some of their speculations about nature were, most of the ideas of the ancient Greeks would not pass muster as valid science in modern times. For one, because the Greeks had not invented the scientific method, their theories were not developed with the goal of experimental verification. So if one scholar claimed an atom moved in a straight line until it collided with a second atom and another scholar claimed it moved in a straight line until it bumped into a cyclops, there was no objective way to settle the argument. Also, there was no clear distinction between human and physical laws. In the fifth century BC, for instance, Anaximander wrote that all things arise from a primary substance, and return to it, lest they “pay fine and penalty for their iniquity.” And according to the Ionian philosopher Heraclitus (ca. 535 BC-ca. 475 BC), the sun behaves as it does because otherwise the goddess of justice will hunt it down. Several hundred years later the Stoics, a school of Greek philosophers that arose around the third century BC, did make a distinction between human statutes and natural laws, but they included rules of human conduct they considered universal—such as veneration of God and obedience to parents—in the category of natural laws. Conversely, they often described physical processes in legal terms and believed them to be in need of enforcement, even though the objects required to “obey” the laws were inanimate. If you think it is hard to get humans to follow traffic laws, imagine convincing an asteroid to move along an ellipse.
This tradition continued to influence the thinkers who succeeded the Greeks for many centuries thereafter. In the thirteenth century the early Christian philosopher Thomas Aquinas (ca. 1225-1274) adopted this view and used it to argue for the existence of God, writing, “It is clear that [inanimate bodies] reach their end not by chance but by intention…. There is therefore, an intelligent personal being by whom everything in nature is ordered to its end.” Even as late as the sixteenth century, the great German astronomer Johannes Kepler (1571-1630) believed that planets had sense perception and consciously followed laws of movement that were grasped by their “mind.”
The notion that the laws of nature had to be intentionally obeyed reflects the ancients’ focus on why nature behaves as it does, rather than on how it behaves. Aristotle was one of the leading proponents of that approach, rejecting the idea of science based principally on observation. Precise measurement and mathematical calculation were in any case difficult in ancient times. The base ten number notation we find so convenient for arithmetic dates back only to around AD 700, when the Hindus took the first great strides toward making that subject a powerful tool. The abbreviations for plus and minus didn’t come until the fifteenth century. And neither the equal sign nor clocks that could measure times to the second existed before the sixteenth century.
Aristotle, however, did not see problems in measurement and calculation as impediments to developing a physics that could produce quantitative predictions. Rather, he saw no need to make them. Instead, Aristotle built his physics upon principles that appealed to him intellectually. He suppressed facts he found unappealing and focused his efforts on the reasons things happen, with relatively little energy invested in detailing exactly what was happening. Aristotle did adjust his conclusions when their blatant disagreement with observation could not be ignored. But those adjustments were often ad hoc explanations that did little more than paste over the contradiction. In that manner, no matter how severely his theory deviated from actuality, he could always alter it just enough to seem to remove the conflict. For example, his theory of motion specified that heavy bodies fall with a constant speed that is proportional to their weight. To explain the fact that objects clearly pick up speed as they fall, he invented a new principle—that bodies proceed more jubilantly, and hence accelerate, when they come closer to their natural place of rest, a principle that today seems a more apt description of certain people than of inanimate objects. Though Aristotle’s theories often had little predictive value, his approach to science dominated Western thought for nearly two thousand years.
The Greeks’ Christian successors rejected the idea that the universe is governed by indifferent natural law. They also rejected the idea that humans do not hold a privileged place within that universe. And though the medieval period had no single coherent philosophical system, a common theme was that the universe is God’s dollhouse, and religion a far worthier study than the phenomena of nature. Indeed, in 1277 Bishop Tempier of Paris, acting on the instructions of Pope John XXI, published a list of 219 errors or heresies that were to be condemned. Among the heresies was the idea that nature follows laws, because this conflicts with God’s omnipotence. Interestingly, Pope John was killed by the effects of the law of gravity a few months later when the roof of his palace fell in on him.
The modern concept of laws of nature emerged in the seventeenth century. Kepler seems to have been the first scientist to understand the term in the sense of modern science, though as we’ve said, he retained an animistic view of physical objects. Galileo (1564-1642) did not use the term “law” in his most scientific works (though it appears in some translations of those works). Whether or not he used the word, however, Galileo did uncover a great many laws, and advocated the important principles that observation is the basis of science and that the purpose of science is to research the quantitative relationships that exist between physical phenomena. But the person who first explicitly and rigorously formulated the concept of laws of nature as we understand them was René Descartes (1596-1650).
Descartes believed that all physical phenomena must be explained in terms of the collisions of moving masses, which were governed by three laws—precursors of Newton’s famous laws of motion. He asserted that those laws of nature were valid in all places and at all times, and stated explicitly that obedience to these laws does not imply that these moving bodies have minds. Descartes also understood the importance of what we today call “initial conditions.” Those describe the state of a system at the beginning of whatever interval of time over which one seeks to make predictions. With a given set of initial conditions, the laws of nature determine how a system will evolve over time, but without a specific set of initial conditions, the evolution cannot be specified. If, for example, at time zero a pigeon directly overhead lets something go, the path of that falling object is determined by Newton’s laws. But the outcome will be very different depending on whether, at time zero, the pigeon is sitting still on a telephone wire or flying by at 20 miles per hour. In order to apply the laws of physics one must know how a system started off, or at least its state at some definite time. (One can also use the laws to follow a system backward in time.)
With this renewed belief in the existence of laws of nature came new attempts to reconcile those laws with the concept of God. According to Descartes, God could at will alter the truth or falsity of ethical propositions or mathematical theorems, but not nature. He believed that God ordained the laws of nature but had no choice in the laws; rather, he picked them because the laws we experience are the only possible laws. This would seem to impinge on God’s authority, but Descartes got around that by arguing that the laws are unalterable because they are a reflection of God’s own intrinsic nature. If that were true, one might think that God still had the choice of creating a variety of different worlds, each corresponding to a different set of initial conditions, but Descartes also denied this. No matter what the arrangement of matter at the beginning of the universe, he argued, over time a world identical to ours would evolve. Moreover, Descartes felt, once God set the world going, he left it entirely alone.
A similar position (with some exceptions) was adopted by Isaac Newton (1643-1727). Newton was the person who won widespread acceptance of the modern concept of a scientific law with his three laws of motion and his law of gravity, which accounted for the orbits of the earth, moon, and planets, and explained phenomena such as the tides. The handful of equations he created, and the elaborate mathematical framework we have since derived from them, are still taught today, and employed whenever an architect designs a building, an engineer designs a car, or a physicist calculates how to aim a rocket meant to land on Mars. As the poet Alexander Pope said:
Nature and Nature’s laws lay hid in night:
God said, Let Newton be! and all was light.
Today most scientists would say a law of nature is a rule that is based upon an observed regularity and provides predictions that go beyond the immediate situations upon which it is based. For example, we might notice that the sun has risen in the east every morning of our lives, and postulate the law “The sun always rises in the east.” This is a generalization that goes beyond our limited observations of the rising sun and makes testable predictions about the future. On the other hand, a statement such as “The computers in this office are black” is not a law of nature because it relates only to the computers within the office and makes no predictions such as “If my office purchases a new computer, it will be black.”
Our modern understanding of the term “law of nature” is an issue philosophers argue at length, and it is a more subtle question than one may at first think. For example, the philosopher John W. Carroll compared the statement “All gold spheres are less than a mile in diameter” to a statement like “All uranium-235 spheres are less than a mile in diameter.” Our observations of the world tell us that there are no gold spheres larger than a mile wide, and we can be pretty confident there never will be. Still, we have no reason to believe that there couldn’t be one, and so the statement is not considered a law. On the other hand, the statement “All uranium-235 spheres are less than a mile in diameter” could be thought of as a law of nature because, according to what we know about nuclear physics, once a sphere of uranium-235 grew to a diameter greater than about six inches, it would demolish itself in a nuclear explosion. Hence we can be sure that such spheres do not exist. (Nor would it be a good idea to try to make one!) This distinction matters because it illustrates that not all generalizations we observe can be thought of as laws of nature, and that most laws of nature exist as part of a larger, interconnected system of laws.
In modern science laws of nature are usually phrased in mathematics. They can be either exact or approximate, but they must have been observed to hold without exception—if not universally, then at least under a stipulated set of conditions. For example, we now know that Newton’s laws must be modified if objects are moving at velocities near the speed of light. Yet we still consider Newton’s laws to be laws because they hold, at least to a very good approximation, for the conditions of the everyday world, in which the speeds we encounter are far below the speed of light.
If nature is governed by laws, three questions arise:
1. What is the origin of the laws?
2. Are there any exceptions to the laws, i.e., miracles?
3. Is there only one set of possible laws?
These important questions have been addressed in varying ways by scientists, philosophers, and theologians. The answer traditionally given to the first question—the answer of Kepler, Galileo, Descartes, and Newton—was that the laws were the work of God. However, this is no more than a definition of God as the embodiment of the laws of nature. Unless one endows God with some other attributes, such as being the God of the Old Testament, employing God as a response to the first question merely substitutes one mystery for another. So if we involve God in the answer to the first question, the real crunch comes with the second question: Are there miracles, exceptions to the laws?
Opinions about the answer to the second question have been sharply divided. Plato and Aristotle, the most influential ancient Greek writers, held that there can be no exceptions to the laws. But if one takes the biblical view, then God not only created the laws but can be appealed to by prayer to make exceptions—to heal the terminally ill, to bring premature ends to droughts, or to reinstate croquet as an Olympic sport. In opposition to Descartes’s view, almost all Christian thinkers maintained that God must be able to suspend the laws to accomplish miracles. Even Newton believed in miracles of a sort. He thought that the orbit of the planets would be unstable because the gravitational attraction of one planet for another would cause disturbances to the orbits that would grow with time and would result in the planets either falling into the sun or being flung out of the solar system. God must keep on resetting the orbits, he believed, or “wind the celestial watch, lest it run down.” However, Pierre-Simon, marquis de Laplace (1749-1827), commonly known as Laplace, argued that the perturbations would be periodic, that is, marked by repeated cycles, rather than being cumulative. The solar system would thus reset itself, and there would be no need for divine intervention to explain why it had survived to the present day.
It is Laplace who is usually credited with first clearly postulating scientific determinism: Given the state of the universe at one time, a complete set of laws fully determines both the future and the past. This would exclude the possibility of miracles or an active role for God. The scientific determinism that Laplace formulated is the modern scientist’s answer to question two. It is, in fact, the basis of all modern science, and a principle that is important throughout this book. A scientific law is not a scientific law if it holds only when some supernatural being decides not to intervene. Recognizing this, Napoleon is said to have asked Laplace how God fit into this picture. Laplace replied: “Sire, I have not needed that hypothesis.”
Since people live in the universe and interact with the other objects in it, scientific determinism must hold for people as well. Many, however, while accepting that scientific determinism governs physical processes, would make an exception for human behavior because they believe we have free will. Descartes, for instance, in order to preserve the idea of free will, asserted that the human mind was something different from the physical world and did not follow its laws. In his view a person consists of two ingredients, a body and a soul. Bodies are nothing but ordinary machines, but the soul is not subject to scientific law. Descartes was very interested in anatomy and physiology and regarded a tiny organ in the center of the brain, called the pineal gland, as the principal seat of the soul. That gland, he believed, was the place where all our thoughts are formed, the wellspring of our free will.
Do people have free will? If we have free will, where in the evolutionary tree did it develop? Do blue-green algae or bacteria have free will, or is their behavior automatic and within the realm of scientific law? Is it only multicelled organisms that have free will, or only mammals? We might think that a chimpanzee is exercising free will when it chooses to chomp on a banana, or a cat when it rips up your sofa, but what about the roundworm called Caenorhabditis elegans—a simple creature made of only 959 cells? It probably never thinks, “That was damn tasty bacteria I got to dine on back there,” yet it too has a definite preference in food and will either settle for an unattractive meal or go foraging for something better, depending on recent experience. Is that the exercise of free will?
Though we feel that we can choose what we do, our understanding of the molecular basis of biology shows that biological processes are governed by the laws of physics and chemistry and therefore are as determined as the orbits of the planets. Recent experiments in neuroscience support the view that it is our physical brain, following the known laws of science, that determines our actions, and not some agency that exists outside those laws. For example, a study of patients undergoing awake brain surgery found that by electrically stimulating the appropriate regions of the brain, one could create in the patient the desire to move the hand, arm, or foot, or to move the lips and talk. It is hard to imagine how free will can operate if our behavior is determined by physical law, so it seems that we are no more than biological machines and that free will is just an illusion.
While conceding that human behavior is indeed determined by the laws of nature, it also seems reasonable to conclude that the outcome is determined in such a complicated way and with so many variables as to make it impossible in practice to predict. For that one would need a knowledge of the initial state of each of the thousand trillion trillion molecules in the human body and to solve something like that number of equations. That would take a few billion years, which would be a bit late to duck when the person opposite aimed a blow.
Because it is so impractical to use the underlying physical laws to predict human behavior, we adopt what is called an effective theory. In physics, an effective theory is a framework created to model certain observed phenomena without describing in detail all of the underlying processes. For example, we cannot solve exactly the equations governing the gravitational interactions of every atom in a person’s body with every atom in the earth. But for all practical purposes the gravitational force between a person and the earth can be described in terms of just a few numbers, such as the person’s total mass. Similarly, we cannot solve the equations governing the behavior of complex atoms and molecules, but we have developed an effective theory called chemistry that provides an adequate explanation of how atoms and molecules behave in chemical reactions without accounting for every detail of the interactions. In the case of people, since we cannot solve the equations that determine our behavior, we use the effective theory that people have free will. The study of our will, and of the behavior that arises from it, is the science of psychology. Economics is also an effective theory, based on the notion of free will plus the assumption that people evaluate their possible alternative courses of action and choose the best. That effective theory is only moderately successful in predicting behavior because, as we all know, decisions are often not rational or are based on a defective analysis of the consequences of the choice. That is why the world is in such a mess.
The third question addresses the issue of whether the laws that determine both the universe and human behavior are unique. If your answer to the first question is that God created the laws, then this question asks, did God have any latitude in choosing them? Both Aristotle and Plato believed, like Descartes and later Einstein, that the principles of nature exist out of “necessity,” that is, because they are the only rules that make logical sense. Due to his belief in the origin of the laws of nature in logic, Aristotle and his followers felt that one could “derive” those laws without paying a lot of attention to how nature actually behaved. That, and the focus on why objects follow rules rather than on the specifics of what the rules are, led him to mainly qualitative laws that were often wrong and in any case did not prove very useful, even if they did dominate scientific thought for many centuries. It was only much later that people such as Galileo dared to challenge the authority of Aristotle and observe what nature actually did, rather than what pure “reason” said it ought to do.
This book is rooted in the concept of scientific determinism, which implies that the answer to question two is that there are no miracles, or exceptions to the laws of nature. We will, however, return to address in depth questions one and three, the issues of how the laws arose and whether they are the only possible laws. But first, in the next chapter, we will address the issue of what it is that the laws of nature describe. Most scientists would say they are the mathematical reflection of an external reality that exists independent of the observer who sees it. But as we ponder the manner in which we observe and form concepts about our surroundings, we bump into the question, do we really have reason to believe that an objective reality exists?