Annotations to

A Brief History of Time by Stephen Hawking ❶

Page 2. ...the distance around the Earth was 400,000 stadia. Aristotle (ca. 384-322 BCE) cited the observations of the position of Polaris (the North Star) at two different latitudes as evidence that the Earth is a sphere. About a century later, Eratosthenes (ca. 275-195 BCE) made a more exact determination of the Earth's shape and size. Eratosthenes was born in Cyrene, an ancient city now in NE Libya. He soon heard of a city with a similar name in southern Egypt. That other town, Cyene, lies on the Tropic of Cancer. It is the home of a famous well in which one could see the sun reflected from the water, deep at the bottom, at midsummer noon in the Northern Hemisphere. The sun is directly in the zenith over the Tropic of Cancer at the Summer Solstice, and it casts no shadows except straight down. Eratosthenes grew up to be an astronomer. When he became head of the great Library in Alexandria, in Egypt (the greatest library of antiquity in the West) he noticed that shadows were cast by standing objects in Alexandria at mid-summer noon. This meant that, at the same moment. the sun's rays must be shining at a different angle in Alexandria than it was in Cyene, about 500 miles to the south. Eratosthenes measured the angle of the rays in Alexandria at midsummer noon and compared it with the angle in Cyene (which, of course, is 0˚ at the same time). The difference he found was 7˚12'. The sun is so far from Earth (about 93 million miles) that its rays are essentially parallel when they reach us,

so any difference in the angle of the rays must be caused by some variation at the surface of the Earth. The geometry of Eratosthanes' measurement is shown in the diagram below. If one knows the distance between the two cities, and also knows what part of a circle (what angle) it represents, it is an easy matter to compute the circumference of the whole circle and also the diameter. The angle found by Eratosthenes is about 1/50th part of a circle. Using the distance of 5,000 stadia as the distance between the two cities gave the circumference of the Earth as about 250,000 stadia, rather smaller than Aristotle's estimate. Once he knew the diameter of the Earth, Erathothenes was able to measure the angle its shadow subtended on the moon during a lunar eclipse. From this he was able to compute the size of the moon and also its distance from the Earth. We do not know the length of the stadia in Eratosthenes' estimate, so we cannot say how accurate his sizing of the Earth was. That depends on how accurately the bematists (the surveyors of Alexander and the Ptolomies) had measured the ground between the two cities. If we use our present units of measurement, together with the measurement of the angle made by Eratosthenes, we can tell how well he came out in principle. The Tropic of Cancer is about 530 miles south of Alexandria and 7˚12' is about 1/50th the circumference. The product of 50 x 530 = 26,500 miles. Modern measurements of the Earth's size make it about 24,900

2

miles at the Equator and a little less through the poles. These measurements

were made about 2000 years after those of Eratosthenes.

Sun!s rays

Equal angles

Alexandria

Cyene(no shadow)

Page 6. ...the whole sky would be as bright as the sun... Even without an infinite static universe, some beings living in other parts of the cosmos might face such a condition. For example, galaxies as large as the Milky Way usually have satellite systems of stars which are arranged in densely-packed spheres. They are called globular clusters. If any beings exist on planets orbiting stars in the center of a globular cluster, the sky would be filled with so many close stars that starlight would be about as bright as daylight. Could there be an astronomy on such a planet, without a starry sky at night to inspire it? Not with the same history as our astronomy, surely. Perhaps the sky as detected by other radiation—the "radio sky" or the "infra-red sky"—would be discovered later, when techniques were sufficiently advanced. This illustrates how important our perspective on Nature is when making discoveries. The science of Astronomy is about 4,000 years old on Earth. We have records of observations made that

long ago which are still valid data today. But until about seventy years ago (1924), most astronomers believed that the Milky Way galaxy was the entire universe. Today, that is so absurd that it is scarcely credible that anyone could have believed it. Today, galaxies are seen as the basic units of astronomy, and there are hundreds of millions of them known to exist. How could we have gone so long without knowing such a basic fact about the universe? It is an accident of our perspective on the cosmos. We just happen to be in a portion of space where large galaxies are very far apart. Our closest large neighbor is the Great Galaxy in Andromeda—about 2.5 million light-years (ly) away. It was a long time before we realized that the smudge of light in the sky was really a great collection of stars, or even how far away it really was. But, if there are astronomers in the region of the sky called by us Coma Berenices, they could never have an astronomy without the idea of galaxies. There, in an ellipsoid cluster only 8 million ly in diameter, are contained

3

11,000 galaxies, with an average separation of 300,000 ly. The sky of a planet in Como Berenices would be littered with galaxies. They would be, by far, the most impressive objects in the night sky. People on such a planet would not have to wait 4,000 years to discover them. As with our geography in space, so with our other perspectives on Nature. Most of all, we are bound into our species. We have a human view of Nature. This is both an advantage and a handicap to our knowledge—in our Psychology as in our Astronomy. Page 9. In an unchanging universe, a beginning in time... The human idea of time appears to have a primary and a secondary meaning. The primary meaning—the one we know first and most immediately—is a function of memory. Without memory, there could be no idea of time at all. Like all other conditions of knowing, a knowledge of time depends on a difference; in this case, a difference between our memory and our present experience. If we can tell the two apart we know time has passed. It also appears to us that time is a vector. It is an arrow that only goes one way. We do not remember the future, although we might say that we know it. Our knowledge of the future is verified in countless ways during an ordinary day, as we set out to do things and do them. It is our predictions of what will happen—usually verified—that supports all our directed action. How else could we set out for home and expect to get there? The place where past, present, and future appear to differ is in our experience of them. We know the present by our senses, the past by memory, and the future by surmise. The three differ in vividness and certainty. Our only certainties lie in the

past. Hindsight is so infallible, we think, that we don't consider it impressive. We give more esteem to knowing the present (being able and graceful in extemporaneous action) and even more to knowing the future. The last has long been considered magical and ultimately powerful. When people believed that witches sold their souls for power, the chief power they got in the bargain was the gift of foretelling. Shakespeare knew this, and used witches telling the future to move the plot along in Macbeth. In antiquity, Sibyls and Oracles had the same powers. We have a human tradition of being certain of the past, sensible of the present and uncertain of the future. But we have found, in psychology, that the past is not so certain after all. Memory is far from infallible and seems less and less like a record waiting to be read and more like a fresh reconstruction, subject to drift and transformations and the influences of the present. We also appreciate more the certainties of the future which support our lives and action. Actually, there is no refuge of certainty in human experience. We have learned in the 20th century that Nature is a matter of probabilities and not simple determinates, and it is so as well with time and memory. The secondary meaning of time is the time made by clocks. This is the time of calibrated interval and it is a purely human invention. With our willing compliance, clocks are now time machines that make a tick-tock time for us to live in. This kind of time is entirely different than the primary, experiential time of the days and seasons. It is really a contrivance for being very precise about intervals. Clocks run on star time. We usually associate astronomy with telescopes, but

4

telescopes only entered astronomy in 1610. We know the date, because the first person to use the instrument for that purpose published a book with his observations. The astronomer was Galileo Galilei and his book was Siderius Nuncias (The Starry Messenger). So, what did astronomers do for the two thousand years of their science before telescopes? They studied time. They tracked the transits of stars and the occurrence of other phenomena (like eclipses and solstices) and put them in relation to each other by measuring time to finer and finer intervals. The first clocks were made by astronomers and were rare and expensive scientific instruments, rather like high-energy accelerators today. Some of them—like ancient Chinese water clocks—were as big as buildings. For a long time only very big clocks were precise enough to be good instruments. The first clocks were instruments for doing science. People did not live by them. That did not happen until the industrial revolution imposed a new idea of work in the daily life of people. Clocks became necessary so workers could meet what historians call "the factory discipline." Almost everything we consider "ordinary living" was transformed by a series of revolutions in human life. The first and greatest revolution was agriculture. The second was the invention of the factory. A factory is really a way to make more wealth out of land than by farming it. But factories—highly organized workplaces for large groups of people—change the basic conditions of human life. The whole idea of leaving home to go to work, for example, originates with the factory, which must assemble its workforce in one place to operate. So also does the idea of punctuality. Farmers and artisans work at home and a few

minutes in timing does not matter when planting a seed or firing a kiln. A factory produces wealth at such a rate that "time is money." Factories cannot operate with part of the workforce absent, and every minute counts, so everyone must be on time. At the beginning, the clock was in the factory and it blew a whistle to wake the workers, tell them to eat breakfast, and start to work. The workforce lived within whistle range of the plant. Later, the factory made it possible to make a cheap clock for every home. Then for every wrist and pocket. Today we are ruled by clock time, we are trained by the tardy bell in school, and we can experience the anxiety of being a quarter minute late for an appointment: a pain no person could have known before the time of the clock. Page 9. ...a good theory if it satisfies two requirements. These are modern views of a valid theory in science, much influenced by the work of Karl Popper (mentioned on page 10). Popper claims that a theory is not a proper scientific concept unless it is, in principle, falsifiable. He means that we can do an experimentum crucis—one which will disprove the theory if it comes out a certain way. Many theories of the past could not meet these criteria—not easily, anyway. One example is the theory of evolution. There is no doubt that Darwin's theory is one of the most durable and influential in all of science. It has not only survived into this century, it has even become a metatheory in science, used to account for the change and "evolution" of thought in science itself. Hawking resorts to the principle of natural selection at the end of this chapter. The theory of evolution has changed a lot in detail and variety of ideas of how exactly it operates, but the

5

main principles are as robust as ever after a century and a quarter. But can Darwin's theory meet the criterion of being falsifiable proposed by Popper? What experiment or observation would serve to disprove evolution? It is not clear. The main value of the theory of evolution is that it meets Hawking's first criterion so well; that it accounts in a simple and elegant way for so much of the data of biology, and also makes so much of diverse biological material coherent and unified. Sometimes an idea may not meet all the criteria of theory but it may still be illuminating and informative. Such an idea may be called a schema. A schema is a pattern imposed on a complex reality to help explain it, mediate perception, or guide response. The theory of evolution may be more schema than theory, by present standards, but it is an extraordinarily powerful one. Page 10. ...we still use Newton's theory for all practical purposes... The relation between Relativity and Classical Mechanics is a good example of how human thought is transcendent in its operation. I do not refer to a mystical principle, but to the way in which ideas "overtake" and transcend others in human history. Jean Paul Sartre, the French writer and philosopher, called this operation "depassing." He used the same word the French use when they speak of one car passing another on the road. An idea is "depassed" or transcended when it is overtaken by another one. That is what happened to Classical Mechanics (Newton's great theory) when Einstein invented Relativity. When an idea is transcended it does not become nonsense. The new idea does not simply contradict the old one, it goes beyond it. So Relativity made Classical Mechanics, not into nonsense,

but into a special case. In certain conditions, Classical Mechanics remains true (for all practical purposes), but Relativity is truer because it is true in more conditions than Newton's theory can manage. Because those conditions are unusual in human life (the interior of stars, the core of atoms, traveling in space or near the velocity of light), Newton does well for the average earthly analysis. But we have already extended our human operations into domains where Relativity is better. And Relativity seems to break down in places (sub-atomic particles) where Quantum Mechanics gives better results. Page 11. Each of these partial theories describes and predicts a certain limited class of observations. An ongoing debate in the sciences is whether one should aim for grand theories (like Newton, Darwin, Einstein) or make limited theories of limited range. In the present era, the trend in psychology is strongly toward the latter course. The last time psychology had much interest in grand theorizing was in the mid 1950's. For about two decades (the 1930's to 1950's) there was an attempt to make learning theory the grand theoretical agenda in psychology. This came at the end of the behaviorist period in psychology. There was a hope that all psychological phenomena could be encompassed by a fully developed model of learning. The attempts trailed off in the early 1960's and it has not been revived. There may be a new movement afoot to make neuropsychology or sociobiology the new grand scheme, but most of the tendency right now is to build limited theories for a limited range of phenomena. Grand theories are not in high repute in psychology at present.

6

They are still appearing in many other sciences. William James (1842-1910), one of the most important founders of scientific psychology, would approve the present fashion. He was always suspicious of grand theory and preferred the idea of a "pluralistic universe," one in which no one idea or principle was sufficient for explanation or understanding. He would not be surprised that Relativity and Quantum theory seem to complement each other. What William Blake called "single vision" was the one thing James did not like about Freud when he met him in Massachusetts, at Clark University, in 1909. He complimented Freud on his work and told him that the future of much of psychology must lie with it. But James also told a companion later that Freud had impressed him as a man obsessed with fixed ideas. Page 15. ...before them, people believed Aristotle... To explain an event in the mode of Aristotle, one argues from essences. Events happen as they do because of the intrinsic (the essential) properties of the actors. A thing's essence determines the part it will play in an event. A ball rolls because its roundness makes it move in that way. Both roundness and rolling are expressions of the ball's essence. To explain an event in the mode of Galileo, one argues for a play of forces. It is the forces acting on the ball that produce its motion. So gravitation, impulses or blows, and the geometry of ball and surface deflecting vectors of force are what make a ball roll. Galileo was an important example of this kind of thinking. It was Newton (born on Christmas Day in the year of Galileo's death) who made the most of this idea. He published his three laws of motion in mathematical form in 1687.

In the 1930s Kurt Lewin published a famous analysis of the difference between Aristotelian and Galilean thought. He said that Galileo had carried the day in science and that psychology should adopt the same principles for its explanations. Behaviorism was still near the peak of its influence in psychology, and the play of forces seemed the right model of Nature. Lewin offered a topological and vector psychology as an example. Very Galilean. Lewin seemed to be right. But Aristotle is back. Certain new theories, like Sociobiology, argue that the innate qualities of organisms are what determine our experience and actions—and even our culture. It is all in our genetic code and it will out in the end. This is as close to arguing from essences as one can get today. The essential nature of the actor in an event has made a surprise comeback as an explanatory principle. Page 18f. ...that light travels at a finite, but very high, speed was first discovered in 1676... German scholars in the 19th century were the first to talk about the Zeitgeist. The word is a German noun, so it is capitalized, as the Germans do with all nouns. It means Zeit=time, geist=spirit (or ghost). The spirit of the times. It is the Zeitgeist that makes the context for an idea. It is context to the idea’s text. Since any text only has meaning in a certain context, an idea only has meaning if the time is right for it. If people are not prepared for an idea it cannot prosper, no matter how good it is. It has no social meaning and so no influence on human thought. So, in 1676, O. C. Roemer, a Dane, demonstrated two astonishing facts about one of the most elusive phenomena in Nature, light. He showed that it traveled at a finite speed—that it took time for light to get

7

from one place to another—and that its speed was astonishingly fast compared to the speed of anything else (even though his estimate was about 20% too slow). This is surely one of the most amazing discoveries in the history of the world. But it went nowhere. It took the world two centuries to realize how important these facts were to our understanding of the universe and everything in it. Michelson and Morely refined the measurement of light-speed in 1887. In 1905 Einstein made the speed of light the only constant in Relativity and showed that the finite speed of light meant that there could be no independent, absolute measure of time. The absolute measure of space had been lost in Newton's system because all motion was relative; now absolute time was also gone. Only Relativity was left. Page 20. A similar point was made a few weeks later by a French mathematician... The near-simultaneous discovery of an idea by two or more persons is common in science. There are some famous examples. Newton and Leibnitz on the calculus. Darwin and Wallace on evolution. James and Lange on emotions. And Hawking's example: Einstein and Poincaré on relativity. It is possible that we see, in this phenomenon, another aspect of the context, or Zeitgeist. The context of the time may not only validate an idea, it may also induce it in a prepared population. People living together in a time and culture tend also to think together. So an idea can crop up in more that one place when its time has come. It is another instance of what systems theorists call the recursive effect. In a recursive circuit, cause and effect can switch places at certain points in time or even play both rôles at once.

Nature seems mainly (perhaps only) to work in recursive circuits. Page 23. ...an object called space-time. I don't know why Hawking calls space-time an object. Even speaking casually, I should have thought he would say "something called space-time." Or some such. I think the best choice of words would be "a manifold called space-time," but he may have thought that would be too obscure for a wide audience. I think it would be more precise, though. There is a strong tendency in modern theoretical physics to think in terms of objects, or particles. Even forces are now understood as an exchange of particles, and there is a search for the graviton, the particle that carries the gravitational force. But I don't know of any scheme that thinks of space-time as a particle. The unity of space-time is one of the two most startling consequences of Relativity. The other is the unity of matter-energy. These two unities made radical changes in our world-view and in our most fundamental ideas of the nature of existence. The unities say that space and time are not independent variables, but are convertible from one to the other. They are actually the same thing showing itself in different ways according to the condition of the observer. The same is true of matter and energy. There are several important consequences of this insight for theory in psychology. It bears on our understanding of consciousness and knowledge, the two subjects which first inspired the science of psychology. This will become more clear as we discuss the topics of energy, entropy and information in class.

8

Page 23. An event is something that happens... In the new views of reality of 20th century science, it makes more sense to speak of events than of things or bodies or objects. Events are more "real" in the modern world view of Relativity. To illustrate this point, I quote the clearest statement about space-time I ever read. It is in the article by Bertrand Russell on the philosophical consequences of Relativity, in the 14th edition of the Encyclopedia Britannica, volume 19, pages 99f: In Newtonian dynamics, two events were separated by two kinds of interval, one being distance in space, the other lapse of time. As soon as it was realised that all motion is relative (which happened long before Einstein), distance in space became ambiguous except in the case of simultaneous events, but it was still thought that there was no ambiguity about simultaneity in different places. The special theory of relativity showed, by experimental arguments which were new, and by logical arguments which could have been discovered any time after it became known that light travels with a finite velocity, that simultaneity is only definite when it applies to events in the same place, and becomes more and more ambiguous as the events are more widely removed from each other in space. This statement is not quite correct, since it still uses the notion of "space." The correct statement is this: Events have a four-dimensional order, by means of which we can say that an event A is nearer to event B than to an event C; this is a purely ordinal matter, not involving anything quantitative. But, in addition, there is between neighboring events a quantitative relation called "interval," which fulfills the functions both of distance in space and lapse of time in the traditional dynamics, but fulfills them with a difference. If a body can move so as to be present at both events, the interval is time-like. If a ray of light can move so as to be present at both events, the interval is zero. If neither can happen, the

interval is space-like. When we speak of a body being present "at" an event, we mean that the event occurs at the same place in space-time as one of the events which make up the history of the body; and when we say that two events occur at the same place in space-time, we mean that there is no event between them in the four-dimensional space-time order. All the events which happen to a man at a given moment (in his own time) are, in this sense, in one place; for example, if we hear a noise and see a colour simultaneously, our two perceptions are both in one place in space-time. When one body can be present at two events which are not at one place in space-time, the time-order of the two events is not ambiguous, though the magnitude of the time-interval will be different in different systems of measurement. But whenever the interval between two events is space-like, their time-order will be different in different equally legitimate systems of measurement; in this case, therefore, the time-order does not represent a physical fact. It follows that, when two bodies are in relative motion, like the sun and a planet, there is no such physical fact as "the distance between the bodies at a given time"; this alone shows that Newton's law of gravitation is logically faulty. Fortunately, Einstein has not only pointed out the defect, but remedied it. His arguments against Newton, however, would have remained valid even if his own law of gravitation had not proved right. The fact that time is private to each body, not a single cosmic order, involves changes in the notions of substance and cause, and suggests the substitution of a series of events for a substance with changing states. Page 37. Hubble noted that certain types of stars always have the same luminosity. The stars that Hubble noted are called Cepheid variables. It is not quite right to say that they have the same luminosity, because they are variable stars; their luminosity varies in regular cycles, going from a maximum to a minimum and then back again. The

9

time it takes to make a complete cycle from bright-to dim-to bright is called the star's period; it can be shorter than a day or as long as nearly two months. We now think that Cepheids (pronounced SEF-ee-id) vary because they expand and contract in regular cycles, as if they were breathing. Cepheid variables are called so because they were first observed in the constellation Cepheus. Delta Cephei, the first one to be measured, has a period of four days. But what good was all that to Hubble? By itself, not much. But by the time he made use of Cepheids he had the benefit of another discovery about them. Henrietta Leavitt (1868-1921) was an astronomer at the Harvard College Observatory. In 1912 she began to study the Cepheids in the Magellanic Clouds, named after the first European to report them when he was circumnavigating the globe. The Clouds, patches of light in the sky, are only visible from the southern hemisphere. The Magellanic Clouds are really small galaxies which are the closest neighbors of our own Milky Way galaxy. They are not very far away, on the Cosmic scale: the Large Cloud is about 150,000 ly away and the Small Cloud about 170,000 ly distant. At the time of Leavitt's study, it was not clear that they were outside the Milky Way. Leavitt studied the Cepheids in the Small Cloud and noticed something new about them. Their brightness and their periods seemed to be related. Leavitt noticed this because she was the first one to study a group of Cepheids which were all at about the same distance. Because the Small Cloud is a dwarf galaxy, and is also some distance from us, all of its stars are effectively the same distance away. It is as if we measured the distances from Portland, Oregon to a set of addresses in New York City. The buildings in New York

might be miles apart, but compared to the 3,000 miles between the two cities, they are all about equally far from Portland. The Cepheids studied before had all been within our galaxy and were at varying distances from the Earth. Even the closest Cepheid (which happens to be the North Star, Polaris) is much too far away to be able to measure its distance by parallax (the amount a star appears to move in the sky when the Earth is on one side or the other of its orbit of the Sun). Since a star's apparent brightness is a function of its distance from us, there was no way to know the absolute (true) brightness of a Cepheid like Polaris to compare it with any other. But, with all her Cepheids at a standard distance, Leavitt was able to see that the brightest stars had the longest periods.

Parallax. From the two extremes of the Earth's orbit (bottom), a near star (middle) appears to change its position against the ground of "fixed" stars (top). "Fixed" stars are those so far away that they never seem to move, except with their own, proper motion. Leavitt made a period-luminosity curve, showing that there was a smooth relation between the absolute magnitude and the period of Cepheids. If Cepheids everywhere behaved the same, astronomers would have a new

10

and powerful way to measure distances in the universe. If you know the absolute brightness of a star (by its period), and you measure how bright it appears from Earth, you can tell how far away it is by using the inverse-square law (intensity of radiation is inverse to the square of the distance). It only remained to find the distance to one Cepheid with precision. That step was taken by using statistical methods to estimate distance from the proper motion of stars. The proper motion of a star are the motions in the sky due to the star's own movement, and not because of the motion of our Earth while we observe it. Astronomers had long noticed that groups of stars showed proper motions and they began to study them, using statistical methods to estimate how far away the groups might be. Of course, stars which appeared to move the most were the closest and vice-versa. In 1913, the Danish astronomer, Ejnar Hertzsprung (1873-?) found that a Cepheid of absolute magnitude -2.3 had a period of 6.6 days (minus magnitudes are the brightest). The work was repeated a few years later by an American, Harlow Shapely (1885-?), who found that a Cepheid of the same magnitude had a period of 5.96 days. Close enough. In 1924, Hubble applied the Leavitt yardstick to Cepheids in the Great Galaxy in Andromeda and showed it was one million ly away, far outside the Milky Way. In 1942, Walter Baade (1893-1960) found that there were two different populations of stars in the universe. Cepheids of Population II had been studied by Leavitt, but Cepheids of Population I had absolute magnitudes three or four times brighter for the same periods. The Cepheids Hubble had found in Andromeda were of Population I. When the distance was recalculated with the period-luminosity

curves for Population I stars, the Great Galaxy was found to be 2.5 million ly away. Page 37. ...spiral galaxy that is similar to what we think ours must look like... In 1993, new observations of the Milky Way Galaxy showed that it does not have the shape we have long supposed. It turns out that we do not live in a classic spiral galaxy, like the one pictured in Fig. 3.1 on page 36 of Hawking. Instead, we live in a type of galaxy called a "barred spiral" galaxy, like the one in Eridanus. This type of galaxy is so named because it has a "bar" or band of stars across the center, from which strings of stars trail in a spiral form. It may look something like the following:

A barred galaxy.

This new image of the Milky Way is very hard to get used to. For most of my life I have had the image of the classic spiral galaxy as home. I now feel a little like an alien. Page 40. "Einstein introduced a new "antigravity" force... Here is a telling example of how a well-established world view can influence human ideas about Nature. If there was ever a self-confident theorist in science it was Albert Einstein (1879-

11

1955). He was a modest man by nature but, from the first, he had great confidence that Relativity was correct. He often said so in the period when the theory was in doubt by everyone else. In 1919, the Royal Astronomical Society sent out two expeditions: one to northern Brazil and one to the island of Principe, in the Gulf of Guinea off the coast of west Africa. They went to measure the bright stars near the limb of the sun during the solar eclipse of 29 March of that year. The purpose was to test one of the predictions of Relativity: that light rays were bent by gravitational fields. If it were true, then stars observed near the sun's limb should be displaced from their apparent position when the sun was not present and they could be seen in the night sky. One of Einstein's students was sitting with him when he got the news that his prediction had been confirmed within the allowable error of the observations. When she remarked that he must be very pleased to have his idea supported, Einstein shook his head. "No," he said, "If the test had not come out, I would have been sorry for God. The theory is correct." This is not the remark of an uncertain man. Yet even he was so influenced by the idea that the Universe is eternal and unchanging that he invented an arbitrary constant to make his theory be in accord with a static state. So it was left to someone else—Alexander Friedmann—to take Relativity on its own merits and compute what it must mean for the state of the Universe. Friedmann's view of the matter is the one accepted by most people today. Page 49. ...a region of space-time known as a black hole. The postulation of black holes is an example of the extraordinary series of revolutions which have taken place in

science in the 20th century. Our view of Nature today is radically different from the one held by the scientific community in 1899. One important thing to note about these revolutions in thought is that they have come as much from the tradition of field naturalism as from the laboratory method. This has special meaning to Psychologists because we have mostly promoted the laboratory method as the best choice to move our science forward. We have devalued the tradition of field naturalism for at least seventy years. The laboratory method has its great accomplishments in the 20th century. One of them is molecular biology and the discovery of the genetic code; another, the accomplishments of high-energy physics and chemistry. But we also have major revolutions in Astronomy, Geology, and field Biology. We have the discovery of galaxies, plate-tectonics, and Ethology. Of course, Psychology is properly a part of the last, and we have played our part in the radical change of the study of animal life-histories and behavior in natural settings. Ironically for us, the brilliant start in Comparative Psychology by the Functionalists was almost undone by a fixation on the laboratory. Most of the modern advances in the field have come from Anthropologists, from the work done in Animal Behavior and Ornithology, and by the new science, Ethology. One might say that Ethology had to be founded only because Comparative Psychology had abandoned the field. So the Nobel Prize went to Konrad Lorenz and Niko Tinbergen for founding Ethology to study behavior in the place abandoned by Comparative Psychology. One of my favorite old teachers was Robert Tryon of the University of California. He is famous for his work with strains of "maze-dull" and "maze-bright" rats, but when I worked with

12

him he had become a specialist in multivariate analysis. He was fond of saying that Psychologists would do better if we were more like Astronomers. It was a long time before I really understood his remark. Now I realize that he meant we should be more ready to meet Nature on Her own terms, in natural settings, and not be so quick about carting Her off to the laboratory. Of course, it would mean a patient, sustained effort in our observations. Astronomy must often wait for decades for observations to mean anything. Barnard's star is the second-closest star to our Sun (the first is the well-known Alpha Centauri cluster, 4.3 ly away). In the late 1940's, small movements of Barnard's star hinted that it might have an invisible companion of small mass—a planet? This was something worth studying, so a pilot program began to find out if the study was feasible. The pilot observations—pretty routine stuff for Astronomers—took fourteen years. Rat Psychologists usually put the animals on a reversed-light schedule. The rats are put in a room without windows where the light is on at night and off in the daytime. This is for the convenience of the experimenters, because rats are nocturnal and are only ready to run mazes when the "sun" goes down. If you put a rat in a maze in the "daytime" it will curl up and go to sleep. So we arrange Nature for our convenience. But for over 4,000 years, Astronomers have been getting up to go to work when everyone else is going to bed. Astronomy is a field naturalist science. We don't know how to put the Universe on a reverse-light schedule and it will not fit into a laboratory. Astronomers have always met Nature on Her own terms. Page 54. ...this obviously ridiculous result...

It was not only theoretical consequences, but also actual observations which made the doctrine of a continuous energy function seem incorrect to Max Planck (1858-1947). He was studying the radiation produced by heating a black body. [See black body and black body radiation in the Glossary for Baggot] When the radiation from a black body is measured, the "continuous energy" idea predicts a result which is not observed. There seems to be too little energy appearing at the low wave lengths. Electromagnetic energy is highest when wavelength is short and frequency high (ultraviolet) and lowest when wavelength is long and frequency low (infrared). But instead of peaking at the ultraviolet end of the curve, the peak of radiated energy was more toward the middle frequencies with a drop off at both ends. The graph of energy by frequency tends to a Gaussian form like the normal frequency curve. Even more puzzling, the theory predicted correctly at the infrared end but was completely off at the ultraviolet end. Why the loss of energy at high frequencies?

e

high

high lowlow

frequencies

predicted

observed

Planck had his inspiration in 1900, when he was out walking with his young son. It came to him that electromagnetic energy was not continuous but came in packets of fixed sizes. The amount of energy in a "packet" was a function of its electromagnetic frequency and was expressed by the equation

13

e = hν where e stands for the energy, ν (the Greek letter, nu) is the frequency, and h is Planck's constant. Planck called his packet a quantum. Very high-energy radiation events are rare and limited by the amount of energy put into the system, so the total energy showing at the high-frequency end of the graph is low. Very low-energy events are common, but don't contribute much when they occur, so the curve is also low at the low-frequency end. Events of middle energies are fairly common and contribute enough to raise the middle of the curve. When Planck's proposal was applied to the theory, the equations predicted the observed radiation perfectly at both ends of the spectrum. Planck's theory of quanta is the basis of quantum theory, one of the two great physical theories of this century. The other one is Relativity. Page 55. ...the principle of economy known as Occam's razor... William of Occam (1280-1349) lived and worked in Occam (or Ockham), Oxford and Paris. He stated his famous principle that "what is done with fewer principles is done in vain with more." Occam's razor (which shaves away extra principles in an argument, leaving only those necessary for the purpose) is a chief criterion for judging an argument in philosophy, including Natural Philosophy, or science. One often hears that a theory must be beautiful to be true. The criteria of beauty include simplicity and elegance and parsimony, all of which live quite easily with Occam's razor. Occam's principle is one of the main reasons that supernaturalism is not popular in science. William himself concluded that reasoned proofs for the existence of God were unconvincing. He said the same for the necessity for

moral principles. Both must be matters of faith, he thought. Pages 55ff. ...Heisenberg, Erwin Schrödinger and Paul Dirac... This is an uneasy company. Of course, what Hawking says about them is true (he would not be mistaken about that), but he does not mention that they were on opposite sides of a long and heated argument which is not resolved to this day. The argument has to do with what is the correct view of Nature. The chief adversaries were Einstein and Neils Bohr (1885-1962), the great Danish physicist. Bohr insisted that quantum mechanics had led to a new insight into causality; that it had made ambiguity an unavoidable feature of our knowledge of Nature. Einstein emphatically disagreed. The two led an epic battle during the 1920's and 1930's over how the physical world would be conceived. Bohr's view was called the Copenhagen Interpretation of quantum mechanics, or CI for short. The Einstein camp had no particular name, but came to be called the Einstein-Podolsky position (or E-P) after a paper written by the two opposing CI. Podolsky's first name is Boris. There were two things about CI that sorely distressed the E-P faction. One was the basic uncertainty inherent in the behavior of quantum particles. The properties of quantum particles answer to statistical laws which do not permit determinate predictions under any conditions of knowledge. Particles which can take on different states are said to be in superposition to those states until they are actually measured. For example, if a particle can show right or left spin, it is said to be in superposition to right and left spin until it is measured. It is then said to collapse into, say, right spin if that value is observed. It cannot be said to have been in right

14

spin the whole time; that only came about when it was observed. The second unacceptable idea is non-locality. The E-P camp called non-locality "spooky action at a distance." It is the principle that any measurement of one part of a divided quantum particle at one location instantly determines the states of the other part of that particle wherever in the Universe it may be. This implies communication at greater than the speed of light, which Relativity does not allow. The CI camp claims that no communication takes place but that the determinations of the other parts are true none-the-less because, until the measurement takes place, the particles are in superposition to their possible states. Werner Heisenberg (1901-?) was in the CI camp. His famous Uncertainty Principle is one of the features of quantum mechanics which so distresses the E-P faction. It is one of the things Einstein meant when he wrote in a letter to CI-advocate Max Born (1882-?):

Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice.

Erwin Schrödinger (1887-1961) was a staunch member of the E-P camp, although he was the inventor of the wave-packet concept of the electron which became a main feature of quantum mechanics. He, like Einstein, would not give up the idea of a determinate reality which could be known to an arbitrary level of precision. He also did not like the idea of superposition, the assertion that until the state of a quantum particle is measured it has no value—CI does not say the value is unknown before measurement, it says it does not exist until then. It says that it does not exist

until it is observed by some observer. This Berkeleyan thesis so exasperated Schrödinger that he made up the famous puzzle of "Schrödinger's cat" to stump the CI faction. If we put a cat in a box, said Schrödinger, and we also put in a particle detector arranged to act as a switch which releases a poison into the box, we can send a quantum particle through the detector from outside. We set the detector to release the poison if the spin is left and not to do so if the spin is right. Now, suppose we do not look at the detector after we send the particle through. Is the cat alive or dead? According to CI the cat is in a superposition of being alive or dead, but that does not comport with the world as we usually experience it. The cats we see are alive or dead and not suspended inbetween. Paul Dirac was mainly in the CI camp, but he did one of the first reconciliations between Relativity and quantum mechanics, so he might be said to occupy a kind of middle ground. The modern extension of his work is quantum field theory. He provided the relativistic quantum theory of the electron by writing a wave equation for a free electron which placed it in space-time instead of just in space. This means that the electron's position has four coordinates: x, y, z, and ct. The last coordinate is the velocity of light (c) times time (t). Note that this comes out as a distance, like the other three dimensions (the light-year is an example). Dirac showed that Schrödinger's wave equations were "unbalanced" on the time dimension and that his new form of the equations put time on an equal footing. One result was that the solution took the form of a quadratic equation with half the solutions representing negative energy. Dirac took those solutions seriously and

15

predicted the existence of antimatter, later verified by experiment. It was also Dirac who defined "spin" as the first purely quantum property of a particle: electron "spin" refers to two possible orientations of the electron's magnetic moment, it does not mean the electron is spinning in the usual sense familiar to us. The puzzle of quantum mechanics is still troubling to many, but it has endured as the only theoretical basis of modern high-energy physics. Its predicted effects also underlie most of the electronic devices we have today, like transistors. Some people prefer the version of quantum mechanics invented in 1952 by the American physicist, David Bohm (1917-1992). He was a pupil of Robert Oppenheimer (1904-?) and he was hounded out of the country, and out of his American citizenship, by the House UnAmerican Activities Committee in the 1950's. Princeton University colluded in this outrage against one of its own faculty. Bohm wrote a classic defence of CI in the late 1940's. Later, he devised a version of quantum theory which assumes an entirely determinate view of particle states at all times (no superposition) and also accounts for all the experimental data. It is interesting, however, that his theory also shows that our knowledge of particle states, in principle, is limited to come out the same as it does in CI. So Bohm leaves us with the same uncertainties, but for different reasons. Bishop Berkeley would love it. Bohm's theory also leaves the principle of non-locality intact. Today, we have no version of quantum theory that spares us the "spooky action at a distance" that troubled Albert Einstein seventy years ago.

Page 63. ...four basic elements, earth, air, fire, and water. ...the British chemist and physicist, John Dalton... Aristotle may have cited these four elements, but they were not his invention. They dated from the pre-Socratics. They were proposed by Empedocles of Agrigentum (490-430 BCE). His proposal (which is really a version of elementism, a belief which is still firmly held in the community of science today) was part of a long effort to understand Being. The Milesian philosophers (from the city of Miletus in Asia Minor in the 6th century BCE) proposed a single entity which was the ground of all being. Anaximander proposed a single cosmic stuff or principle he called "the Infinite." Thales had first identified the basic stuff as water. Heraclitus of Ephesus (536-470 BCE), called "The Obscure" by his friends, disputed a single ground of being and proposed that all was flux or change. Only the "destiny" or the "way" of the world endured. It reminds me of the Tao of Lao Tse. Heraclitus first proposed the idea that there is a uniform, natural law. This is the view in science today. The Eleatic school was founded in Elea, a Greek colony in southern Italy, near the Gulf of Salerno. The city—and the philosophy—were reputedly founded by Xenophanes of Colophon. He was a contemporary of Pythagoras (both about 570-480 BCE). Parmenedes and Zeno (about 490-430 BCE) were Eleatics. Their doctrine was that permanent matter makes up Being, with change and difference mere illusions. This is where Empedocles comes in. He proposed a mediating theory: four immutable substances (elements) in the Eleatic mode, and provision for movement, or change (Heraclitus) by two forces, love and hate. He also proposed a form of evolution by

16

survival of the fittest. Aristotle kept the elements, but his version of the forces were those given by Hawking: gravity and levity. Aristotle was one of the first practitioners of natural science the way we think of it today. In 1799, the French chemist, Joseph Proust (1754-1826) showed, by careful work, that copper carbonate always contained the same proportions of copper, carbon, and oxygen, no matter how prepared. He called it the law of definite proportions. John Dalton (1766-1844) realized the significance of this discovery and stated the law of multiple proportions, in which certain elements (irreducible units) always combined in the same or even multiples of the same proportions, no matter their quantity. It was as if the elements came in indivisible particles which could only combine in whole pieces. The particles would have to be very small. Dalton saw the resemblance of his idea to that of Democritus of Abdera (470-380 BCE), a contemporary of Socrates, who had proposed just such indivisible particles 21 centuries before. Democritus had called them "atoms," meaning "indivisibles." Dalton decided to call them by the same name. Page 65. ...an enigmatic quotation from James Joyce. It is the first line of the last "chapter" of Book II of Finnigan's Wake. Joyce's "chapters" are not named or numbered, so the reference for the line, in a notation used by Joyce scholars, is 383:1 (page 383, line 1). The whole passage is a kind of opening verse and goes as follows:

—Three quarks for Muster Mark! Sure he hasn't got much of a bark And sure any he has it's all beside the mark. But O, Wreneagle Almighty, wouldn't un be a sky of a lark

To see that old buzzard whooping about for uns shirt in the dark And he hunting round for uns speckled trousers around by Palmerstown Park? Hohohoho, moulty Mark! You're the rummest old rooster ever flopped out of a Noah's ark And you think you're cock of the wark. Fowls, up! Tristy's the spry young spark That'll tread her and wed her and bed her and red her Without ever winking the tail of a feather And that's how that chap's going to make his money and mark!

This may be enigmatic at first, but it is less so as one begins to know Joyce's mind. In Finnigan's Wake there is a lot of play on the story of Tristan and Isolde. This passage is plainly some of it. There is also a "bird motif" in the whole way Joyce carries it out. We can follow a trail of clues. Let's begin with quark. It is not a word invented by Joyce (though he does make some neologisms in Wake). In The Third Census of Finnigan's Wake, Adeline Glasheen notes that quark is in both the OED (Oxford English Dictionary) and the 1934 edition of Webster's Unabridged. I look in the OED and find it means to croak. There are three citations. One is from 1860 and refers to "the gurgling and quarking of spring frogs in a pond." In 1893, it's "Rooks... cawing and quarking" and, later in the same work, "The herons quarked harshly." The OED gives the pronounciation of quark as having the sound of au (as in authority) in the middle. The word derives either from an imitative form of the sound of frogs and birds or from an adoption into English of the German quarken. So, Three croaks for Muster Mark! Instead of three cheers. A dirisive start for whatever is to come. What then comes is plainly Tristan and Isolde as a feathered tale. Muster Mark must be King Mark, husband to Isolde and

17

cuckold in the story. He's an old buzzard, but O, Wreneagle Almighty, in mocking acknowledgement of kingship.

The wren, the wren, The king of all birds

sing Irish children on 26 December, when they parade with a dead bird on a pole as a scapegoat for their sins. There is a complicated play, in Finnigan's Wake, on the theme of two Marks; King Mark and St. Mark. Mark is sometimes a Mark Lyons, who lives in Munster. The lion is the symbol for St. Mark, writer of one of the four Gospels. So, Muster Mark is the "Munster-Mister" Mark, it seems. But this is surely the King Mark version of the character. The rest of the passage leaves no doubt. "Muster Mark" is a pitiful bird, ineffectual and bumbling. And "moulty Mark" (a ragged image) fancies himself the "cock of the wark" (a dirisive echo of quark? and wark means "a pain") but "Tristy's (Tristan) the spry young spark" who will tread, wed, bed and red Isolde. Meaning number 9 for tread in the OED is "The action of a male bird in intercourse." The OED also gives various meanings of red as to set aflame, blush, glow, and the like, not to mention the red blood of Isolde's broken hymen. In Finnigan's Wake, there is a running play through the book on the colors red and white. In the classic tale, Isolde is "Isolde of the White Hands"—she who is made red by Tristan in this passage. The couple do all this behind Muster Mark's back without him feeling the tweak of his tail. Three quarks for the old guy! All this barely enters into the astonishing, deep thicket of symbol-play in Finnigan's Wake. The connections are so dense and everwidening, that reading it is like walking deeper and deeper into a forest of language. Like a forest, it displays, at once, the most bewildering detail and grand, encompassing shape.

So, I suppose Joyce's line is an enigma in the same way that Nature is. Works of Philosophy (like a scientific theory) are wonderful as astute decodings of Nature's enigmatic display. Works of art are wonderful as bits of Nature Herself. Like Nature, a work of art awaits decoding, and reveals layers of wonder to any questing eye. Page 67. ...Pauli's exclusion principle. The principle proposed by Wolfgang Pauli (1900-1958) is really about reconciling an ancient principle with a peculiarity of quantum wave-particles (so called because they act as either waves or as particles). The ancient principle is that two things that are different are distinguishable in some way. Even twins are distinguishable because they occupy different positions in space. The peculiarity of quantum wave-particles is that they were designed by Planck, from the beginning, to be indistinguishable. As one writer puts it:

...Planck had to assume that the total energy could be split up into a collection of indistinguishable but independent elements (or 'packets'), each with an energy ε, which were then statistically distributed over a large number of distinguishable oscillators. Planck may have had more than half an eye on the result he was aiming for, because in making the energy elements indistinguishable he was following a very different path from Boltzmann.

When Pauli addressed the question of why electrons occupied the orbitals they did in an atom, he had to make the particles distinguishable. He proposed the rule that no two electrons in an atom could have the same set of quantum numbers. [see quantum number in the Baggot Glossary] One electron excludes others from the same identity. Later, the

18

principle was extended to all quantum particles. In Relativity, there is no absolute frame of reference for anything. This means that two particles are distinguished by the their differences in mass-energy or by the intervals between them in space-time. The closer they are on one of these measures, the more different they are on the other. This relation between energy state and position is governed by Heisenberg's Uncertainty Principle. In Relativity, a particle's position is only known by its interval (in space-time) from other particles. To say that two particles are very close together, means that we know their position with great precision. There is no other criterion of position except the interval, so a smaller interval means knowing position more precisely. But, unless the two particles are the same particle, the more alike (closer) they are in position, they more different they must be in momentum (because the more precisely we know one, the less precisely we know the other). So, to say that two particles are very close, means that their momenta are very different. That means that they have a "high velocity" (relative to each other, the only criterion of velocity in Relativity). It would be more precise to say that the difference in mass-energy between the two is very great, but we may say that they have a "high velocity" as a way of speaking, as Hawking says on page 68. Page 69. The force-carrying particles...are said to be virtual... Note the boldness of theoretical physicists in their use of completely hypothetical entities in their models of Nature. The custom is much more widespread in the physical sciences than in Psychology. Psychologists are much more reluctant to make theories with

elements of this sort. Why should this be the case? One reason is that physical theories have a highly precise mathematical representation. Because of the tight logical framework provided by mathematics, one can move from observables to unobservables with much greater confidence. Everything is caged-in by the precision of the equations. Recall the readiness of Dirac to predict antimatter because his equations produced solutions with negative roots. If a mathematical theory in Psychology ended in a quadratic equation, we would most likely discard either the negative or the positive roots as meaningless. Another reason is probably the high confidence of physical scientists in the reality of their subject matter and their in their identity as scientists. It is possible for a physicist or chemist to have a career as a pure theoretician and rise to great eminence (like Einstein or Bohr) and leave testing the theory to the experimenters. It is harder for a Psychologist to achieve a like career. It is surely ironic that it was a physicist—Einstein—who made the thought experiment famous in science. It was not a Psychologist. We don't approve of experiments in thought. Someone would insist that the principles be operationized. William James would be exasperated. Page 81. We now know that really both theories are correct. The dual nature of light as wave of particle is founded on the way it behaves when we observe it. In a certain apparatus, a photon acts like a wave: it combines with other photons to show diffraction and interference effects which are like other wave phenomena, like those in water, for example. But in another apparatus, photons will act like

19

particles, showing particular strikes on a target as clusters of points. There was a very different response to these observations in the two camps fighting over the meaning of Quantum reality [see note, pp55ff]. The CI faction (led by Bohr) accepted the duality and made it the basis of a new principle in scientific theory which Bohr called Complementarity. the E-P faction (led by Einstein) rejected the uncertain nature of light as one or the other and insisted that the one, true nature of light was yet to be discovered. This disagreement has never been resolved. Bohr's new principle of Complimentarity was never generally adopted by the scientific community, in spite of his persistent efforts to convince his colleagues that it was an important insight into Nature. The idea, however, will prove to be useful to us when we attempt some applications of the information sciences to psychological theory. Page 83. ...they must have very different velocities. See the note at page 67. Note that velocity and speed are different. Speed is a scalar quantity and has only a magnitude. Velocity is a vector; it has a magnitude and a direction. If two velocities are different, they differ in either magnitude or direction or both. Page 84. ...the ultimate fate of massive stars. Chandrasekhar's discovery is the beginning of the trail that ultimately led to the theoretical consequences of runaway gravitation and black holes. It was a decisive turning point in physics and astronomy. But it was a very traumatic event for the discoverer. Chandrasekhar (born in 1911) is the nephew of C. V. Raman, who won the Nobel Prize in 1930. With this family

background, he had been inspired to study astrophysics by his admiration for the work of Sir Arthur Eddington. He came to England expressly to study with the great astrophysicist. Chandrasekhar was only twenty-four when he presented his theory of gravitational collapse to a meeting of the Royal Astronomical Society in 1935. He was chagrined when Eddington rose after his talk and ridiculed the whole thesis as a reductio ad absurdum. His teacher had given him no warning that he opposed it. The young man left England two years later for America and has been in the University of Chicago ever since. He wrote a book on his theory of collapsing stars in 1937 and then abandoned the whole subject for other matters. He did not return to the topic of gravitational collapse until 1974, when he did some work on black holes. If he had not been traumatized by his teacher's treacherous attack, might he have gone on to postulate black holes in 1937 or 1938? We cannot say. Page 84. One of the first to be discovered... Sirius is the brightest star in the night sky because it is so close and so hot. It is only 8.8 ly away with a spectrum that peaks in the hot, blue wavelengths. Friedrich Bessel (1784-1846) was one of the first modern astronomers to devote most of his time to the outer universe of stars outside the solar system. In 1838 he announced the first measurement of the parallax of a star [see note at p. 37]. It was 61 Cygni, about 6 ly away. He had observed a lot of stars during his measurements, and, in 1834, he had noticed that Sirius and Procyon shifted position in a wavy pattern from year to year. Bessel guessed that the two stars must be moving in orbits around something.

20

The somethings were invisible and—judging by their effects—massive; perhaps burned-out stars. Astronomers called them "dark companions." In 1862, Alvan Clark, an American instrument maker testing a new telescope, saw the dark companion of Sirius. It was a very faint star which was named Sirius B. It is just as massive as our Sun, but 400 times dimmer. It seemed to be a burned-out star as first supposed. But, in 1914, Walter Adams measured the spectrum of Sirius B and showed that it burned as hot as Sirius A (the bright, blue star in our sky). How could such a hot star with the mass of our Sun appear so dim? It had to be very small in diameter; no more than twice that of the Earth, but with the mass of our Sun. Its density had to be almost 3,000 times greater than platinum—a new state of matter! The dark companion of Procyon (Procyon B) was also discovered to be a superdense star. They were white dwarfs. Page 84. They were not actually detected until much later. Unfortunately, Lev Landau (born 1908) probably did not live to see the verification of his prediction. He was awarded the Nobel Prize in 1962, but in that same year, on 7 January, he was nearly killed in an automobile accident near Moscow. He broke eleven bones and fractured his skull. He was only kept alive by drastic methods and never fully recovered. It is doubtful that he ever heard the news of the discovery of the first neutron star. I am not sure when the discovery was made, but I know of a failed attempt to find one for the first time in the Crab Nebula in 1964, two years after Landau's accident. Page 88. At this singularity the laws of science and our ability to predict the future would break down.

Here is stated the limit of Natural Philosophy. The limit is self-imposed by the decision of scientists to do no metaphysics. Natural Philosophy is the philosophy of Nature, and it makes no appeal to anything outside it. At the event horizon of a black hole, science lays down its instruments and theories. We go no further. The place beyond belongs to metaphysics. Page 88. "God abhors a naked singularity." This is another way to say that scientific theory abhors infinities. One of the signs of a flaw in the physical theory of Nature is the occurrence of "troublesome infinities," as one theorist put it. Such states are not defined and are taken as the limits of physical reality—the place where a theoretical concept breaks down or ceases to exist in Nature. Infinities (either very large or very small, infinity or its reciprocal) define the limits of existence or being in Nature. There are many examples. The temperature of absolute zero cannot be reached in this Universe because at that temperature the volume of a gas would be zero. Matter would occupy no space. This is a limit of being. Another example is the one of two particles discussed in the note at page 67. If we ever find that the space-time interval between two particles has become zero, then we must admit that the difference in the momenta of the two must be infinite. So we conclude that there are not two particles, but only one. There is a collapse of Being as the two particles become a single one. This must be so because an infinite difference in mass-energy is not defined in this Cosmos. Page 89. ...no one's life would ever be safe...

21

Yes, no one's. Not even the life of the person who might do the preemptive assassination, because there would be no telling what the cumulative effect of the murder of a person's parent might be. Chaos theory implies that even minor changes in events may have a spreading and cumulative effect which would utterly change the fates of the actors. It is quite conceivable that if I set out to prevent your birth that I would inadvertently prevent my own as well. This is the meaning of the familiar scenario in which the flapping of a butterfly's wings in Brazil produces a hurricane in the Gulf of Mexico. Chaos theory gives a new slant on a very old bit of human wisdom which says that when people set out to control their destinies they are liable to collide with one disaster while avoiding another. This is the hazard of knowing the future or altering the past to suit our purposes. The oracle's prophecy is a feature of many cautionary tales on this theme. The prophecies have a way of coming out in the most unexpected way when the person struggles to escape the predicted fate. So we dodge an arrow with an adroit leap into the path of a speeding chariot. The moral of these tales is about hubris and vain striving. The arrow dodger who comes to a bad end is usually the one responsible for the fight in the first place. He would rather win than change his bad habits. Oracles seem to like irony, and they lie in wait for villains. The warnings are not out of date. Science is often the modern oracle. Our present struggles to save the biosphere while keeping our bad habits is a like instance of arrogant and ruthless striving. We think we can continue our self-indulgence and then tinker with the planet to set it right. It is more arrow-dodging: much too crude and too much

an afterthought. It would be better to repair our relations with the Earth. Page 96. Such jets are indeed observed... The search for black holes has now brought us very near to finding one. The latest discovery was made after the publication of Hawking's book (1988), in the Summer of 1994. There have been several good candidates for black holes, as Hawking says in 1988, but this last one is much the best so far. The discovery was made with the repaired Hubble Space Telescope, which has remarkable powers of resolution on distant objects. The latest observations were made by a team headed by two American astronomers: Holland Ford, of the Space Telescope Science Institute in Baltimore; and Richard Harms, of the Applied Research Corporation in Landover, Maryland. They used Hubble to study the inner regions of M87, a large elliptical galaxy in the Virgo Cluster, about 50 million ly from Earth. There they found a previously unknown disk of gas that, 60 ly from its center, is whirling at a speed of 750 kilometers per second. This is about 25 times faster than the Earth travels around the Sun. To give matter that kind of orbital speed at a distance of 60 ly, the central mass must be very large indeed. The Earth, for example, traveling much slower, is only eight light-minutes from the Sun. Harms and his team estimate that the central mass must fall between 2 billion and 3 billion solar masses. To complete the picture, we have the expected gas jets, shooting out of the center of M87 at approximately right angles to the plane of the disk. This long, radio-emitting jet was what attracted the team's attention to M87. These observations are the best evidence yet for a black hole, but Hubble cannot resolve the singularity itself. If

22

there is a black hole at the center of M87 it would be about 5 billion kilometers in radius, but at a distance of 50 million ly not even sharp-eyed Hubble can see it for us. Page 104. This radiation is required in order to prevent violation of the second law. Why is it necessary for all bodies—and especially ones at low temperature—to radiate energy to preserve the second law of thermodynamics? At first it may seem contradictory to suppose that a cool body will radiate energy to its warmer surroundings. It may seem that this would be in contradiction to a condition of the Universe that supports the law of entropy: that energy always flows downhill, from a high-energy source to a low-energy sink. But the details of what we actually observe are these: energy is always in flux in Nature and moves about constantly. It is simply a matter of probabilities where it goes and where it accumulates. Energy is liable to move anywhere, but is more likely to move in some ways than in others. This is one of the consequences of statistical mechanics in general and, in particular, of the statistical theory of thermodynamics. Both of these developments of the late 19th century took on their full theoretical force in the 20th. The general condition of energy is that it is in flux. It moves in and out of all sources. All low-energy (cool) bodies absorb radiation and tend to become warmer. However, if they never radiated energy, if they kept all that came in, the energy they absorb would accumulate and they would become hot in time. This would be a violation of the second law because it would be a negentropic process. Once hot, the formerly-cool body would make a

gradient with its surroundings, heat would flow from it, and it would be capable of doing work. This does not happen because the body loses energy at nearly the rate that it gains it. It radiates energy. The net of the flux in and out stabilizes at a certain point when the temperature of the body is in equilibrium with its surroundings. It is when the net flux out and the net flux in just balance which is the state of highest entropy. Not no radiation, but balanced radiation, is the true condition of maximum entropy. This flow follows statistical laws. The condition of uniform temperature is the most probable one, so a system is most likely to be in that state and so it moves spontaneously toward it over time. The law allows that now and then—perhaps once in a million, million years, say—a system will be in a highly improbable state and negentropy will occur. All the molecules of air in a room (and all the calories stored in their motion) will collect in one corner . There would then be a sort of "little bang" as the negentropic state of the molecules sets about doing the work of refilling (and rewarming) the whole room again. Page 104. ...at exactly the correct rate to prevent violations of the second law. This discovery of the rate of radiation from a black hole is an example of the remarkable durability of Carnot's (1796-1832) discovery, later defined as the law of entropy by Clausius (1822-1888). There are not many scientific principles from the 19th Century left standing after the many discoveries and revolutions of the 20th, but the second law of thermodynamics is one of them. The discovery, in the 1940's, that the equations defining information have the same form as those defining entropy in statistical thermodynamics confirmed a link

23

between the concepts of information and energy which had been realized earlier by several theorists, notably Maxwell (1831-1879), Lewis (1875-1946), and others. Page 106. ...the apparent temperature of the black hole. Note the peculiar "as if" property of this radiation which resolves a paradox of observation. The black hole does not allow anything to escape from it and yet must radiate to be consistent with the second law [see note at page 105, above]. But how can a black hole radiate without acting contrary to its defined nature? It does it by acting on the space nearby in such a way that virtual particle/antiparticle pairs form, and, through the interplay described by Hawking, produce detectable radiation. In short, the black hole produces an effect in its neighborhood which is as good as radiation from it, as seen by an outside observer. To those of us still in this universe (that is, not passed beyond the event horizon of a black hole), the black hole appears to radiate in conformity with the second law. It is as if events still in this universe must remain consistent with each other, no matter what might be happening just outside the universe (beyond the event horizon). Page 112. ...both the great theories of this century... I suppose one might talk a long time about what are the greatest discoveries in science in the 20th century. We will soon be able to have that conversation, because the century is almost at an end. In fact, we could even ask, at that time, what is the greatest discovery in science in the last thousand years, because we will soon cross the boundary of time into the third millennium of the Common Era. What shall we decide then?

Hawking nominates relativity and quantum mechanics for the champion Theories in the last hundred years. Perhaps, for the Millennium, he would say Newton's classical mechanics—it would probably be either Newton or Darwin's theory of evolution. In the category of Discovery, there are more candidates. Which shall it be for the century: The discovery of galaxies? or plate tectonics and continental drift? or the structure of DNA? or exploration of the solar system by spacecraft? And for the Millennium: shall it be the circulation of the blood? or radioactivity? or the unity of electricity and magnetism? or the circum-navigation of the Earth? The discoveries of Psychology and the Social Sciences do not seem to rank very high on the lists, by these criteria. But perhaps one might ask another question. Perhaps we might ask: What is the biggest scientific news of the 20th century? What is the most important thing that has happened in science in the last hundred years as it affects human life? One might nominate the progress of medicine and its prolonging of the life span and lowering of the death rate. These will certainly have a profound effect on human population growth, and that will some day face us with the great crisis of limiting our numbers—a crisis that no species has ever solved without a catastrophic event. If we manage it without catastrophe, we will be the first ones to do so on Earth. Or one might propose the information and transportation revolutions, which now connect all human lives on Earth into one community for the first time in our history. Or we might nominate space flight. Everyone will have his or her candidate. My vote for the greatest scientific news of the 20th century is the

24

growth of the knowledge and method for controlling human consciousness. It seems much more profound an effect than any purely material development. Techniques of propaganda and persuasion are not new in human life, but the psychological sciences were applied to control the beliefs and attitudes of populations with such great effect during WW I (1914-1918), that social psychology was founded in America, in large part, to study the effects of rumor and propaganda. Shortly after the war—in the 1920's and 1930's—Edward L. Bernays (a cousin-in-law of Freud) applied the principle of unconscious motivation to advertising. It was then that attempts began to make buying a product (as a car, say) a sexual experience. It is the beginning of the modern era of advertising. By the beginning of WW II (1939-1945), ministers of propaganda were cabinet-level officers in national governments, and this trend continued through the Cold War and beyond. Today, control of opinion and belief is commonplace and determines large areas of national and international life. It dominates elections in all democracies, largely subverting the democratic ideal of an informed citizenry. The group of psychologists led by Hovland at Yale in the 1950's and 1960's, did important research in the methods of persuasion. The persuading arts (in which Psychology is heavily implicated) got a great increment of power when broadcast radio (1921) and television (1945) increased the range and power of a message. We close the 20th century with the electronic and information revolutions well advanced and in place. The next hundred years will be played out according to how humanity copes with the enormous power of the media of communication and the effect of the messages carried by them on human

consciousness. It is now passé for political power to be deployed with physical force—especially domestically in industrialized cultures. Physical force is for amateurs. It is much more effective to control opinion and belief. Even the Drug War is about the control of consciousness. Alterations of consciousness which are not safely within systems of authoritarian control—like approved religion or state ceremony—are intolerable to a social system posited on control. This is especially true if the experience is transcendent, ecstatic, or psychedelic. Such experiences are safe as long as they are rare, so they are allowed to the ascetic or the hermit who achieves them by long and arduous discipline or by torture of the body. But they cannot be tolerated in large numbers of people who might experience a loss of acculturation and perceive Nature and society in a new way. Those effects are much too unpredictable. The Drug War is not about medicine and it is not about health. If it were, it would not be a War and it would not be waged with violence. War is not a matter of Science or Medicine. War is Politics. Page 120. ...a small amount of the heavier elements collected together... Ever since the work of Eddington (1882-1910) and Jeans (1887-1946) on the origins and evolution of gaseous stars, we have known that what seems at first a purely poetic conceit is really the literal truth: we are made of stardust. And not only us. All the living creatures on the Earth, the Earth itself, and even our Sun, are likewise made of that same stardust. The Sun and our whole solar system are a second-generation star-system, made from the debris of an exploding, older star. The earlier generation stars formed from clouds of hydrogen, the simplest element. When they ignited and burned

25

with the power of their gravitational mass, they became great fusion furnaces, making helium first and, later, heavier elements. The debris of these heavier elements, shot away by explosion in the late stages of their lives, recollected to form star systems like our own. So our Sun is a "heavy star," with planets also full of the heavy elements made in those ancient furnaces. Without the work done by those ancient stars, our whole existence would not be possible. Page 121. ...and ultimately the human race. I suppose that Hawking might not mean it that way, but this comes uneasily close to saying that we are the end of evolution. In the 19th Century, there was a lot of talk about humanity being the culmination of evolution and the great end-point of the development of life. There is less of that today, but it is still an idea that comes too easy for us. It is an aspect of our human-centered view of Nature that gets us into constant trouble managing our untidy and pugnacious lives on our home planet. We have no reason to think that Evolution has stopped, just because we are now here. We may be, ourselves, on our way to becoming some future species with abilities that would make us seem puny in our powers of understanding and action. Or we might become extinct. Page 121. ...nearly the critical rate.. This is another kind of "principle of uncertainty" in our knowledge of the universe. It is not the same as Heisenberg's famous principle, but it shows how the nature of Nature can hinge on the most subtle matters, which are then difficult for us to understand or know. If the rate of expansion of the universe were much slower or much

faster, we would not be in doubt about its ultimate fate. But the rate of expansion is so near the critical change point that we cannot tell with certainty what the outcome will be. So we must hunt for more information about, say, the amount of mass-energy in the universe to try to find a basis for a decision. There are many things in science—and especially many in Psychology and the social sciences—which are matters of great subtlety and land us in the same fix as the cosmologists. Page 122. ...developed from small differences... We have a basis, in the modern theory of chaotic processes, for understanding how those very small differences might now have very large effects. If the universe is a chaotic system, then very small differences in initial conditions can have colossal effects after the long time the universe has been in its present state. This is the effect made famous by the example connecting flapping butterfly wings to hurricanes (see note at p. 89). It is another instance of the critical effect of small differences in the value of a variable in a complex system which is open to exchanges from several sources. Living creatures and our life histories are systems of that sort. It is another example of the truth that life is not a problem in engineering. Page 122. ...God chose the initial configuration... Here we see the astrophysicist and cosmologist dabbling in metaphysics. Cosmologists are very likely to stray into metaphysics because they are concerned with such fundamental questions. They work their way right up to the shoreline of natural philosophy. They really do not have license to go further, but some of them

26

cannot resist putting a toe in the water, as Hawking does here. Page 123. ...it is likely that the universe started out in a chaotic and disordered state... Of course this is unless the universe just happens to be a low-probability event. There is a general tendency in purely theoretical models of Nature to assume that the things that happen must be the high-probability outcomes. But there is no essential constraint from statistical mechanics and statistical thermo-dynamics which prohibits low-probability events. Low probability events may happen, and this universe may simply be one of them. Nor is this an argument that there is some agent which made the universe happen in this unlikely way. It is simply a kind of working convention in physical theory to find that reality is a likely state. But note that physical theory does not say that the observed state of Nature is impossible—it quite explicitly says that it is a possible state of the universe. It is only the unlikelyness which is troublesome. But that no more troubles me than the outcome of Evolution, which is equally unlikely, but possible. I suspect that this resistance to unlikely states of Nature in physical theory comes from a philosophical set derived from its mathematical basis. It seems inelegant and it seems to violate Occam's razor (see note at page 55). Pages 124. ...the anthropic principle...; page 126. ...this whole vast construction exists simply for our sake. The various versions of the anthropic principle are really versions of metaphysics which are packaged so that they can be smuggled into Natural Philosophy. It poses questions which

are essentially metaphysical in terms which can be addressed in Nature. There are two aspects of the anthropic principle (so named because it hinges on whether the universe is specially arranged so that we might exist) which seem peculiar to me, and even unnecessary. One is the resistance to the idea that the universe is a low-probability event. I said something about that in the last note above. The second is its prescriptive premise. The prescriptive premise means that the state of the universe is conceived in terms of its end points, as if the initial principles setting it up were somehow directed toward some end. I don't mean directed in the sense of an agent (that is not an essential part of the anthropic principle), but rather in the sense that it implies a teleological element, where the end determines the origins. Scientists generally abhor teleology. I can think of two things to say about that problem. One is that there is nothing in the most general physical theory (i.e., relativity and quantum mechanics) which says that time must flow one way, so this makes the idea of effects making causes a little murky, anyway, and not entirely out of order. It is only the second law of thermodynamics which gives time an arrow. (It is peculiar that the human experience seems more in conformity with the second law in this respect. We don't remember the future. See note at p. 9.) The other thing is that I see no need for a prescriptive approach in the first place. I can live quite comfortably with a retrospective one. The retrospective approach is the one taken in the theory of evolution. Evolution does not ask what arrangements had to be made in advance to produce Homo sapiens. It takes H. sapiens as an evident outcome and asks what the most likely trail to that outcome might have been. It goes

27

further, it says also that the circumstances must have suited the arrival of H. sapiens for us to have happened at all. The low probability of our appearance in the biosphere is not a problem for evolution because any outcome is improbable in advance, and only brought to a certainty by some circumstance of history which is, in principle, unpredictable. It can only be know afterward—retrospectively. If cosmologists took this approach to the anthropic principle, the dilemma would at once disappear. We are compatible with this state of the universe because it is only in such an hospitable place that we could exist to ponder it at all. Once we are here, we must find that our birthplace was a place we could be born. This is the retrospective view. Page 129. "...the universe is the ultimate free lunch." Note how the first law of thermo-dynamics is transcended in this theory, as the second law was transcended in the theoretic account of the radiation from a black hole (note at page 104). In both cases, the laws stand, but the allowable conditions in Nature permit states which seem impossible at first, but turn out to be one of the possible states of the wonderful and complex place in which we exist. That place has the property of always exploding our metaphors of its nature while leaving them standing intact. The same feat we have always attributed to oracles. Page 133. Was it all just a lucky chance? Of course, the retrospective view of evolution says that it was. All of evolution is nothing but an account of all the lucky chances that have ever happened. This is the great difference of the Darwinian theory from the great physical theories like relativity and

quantum mechanics. Evolution is based on the biological observation of growth, essentially unpredictable in the particulars, but remaining predictable in general. It produces unique forms which can only be known by their histories—retrospectively. Page 144. An intact cup on the table is a state of high order... Hawking's statement about the cup is true enough, as a way of speaking, but it is not strictly true as it regards the second law. Actually what we mean by "a state of high order" is a state which is both negentropic and which has somehow been specified or selected. Another example of ordered versus disordered states will clarify this point. What do we mean when we say that a bookshelf is in good order? And what do we mean when we say that it is in disarray? We may consider the first state—the ordered shelf—to be one in which the books are ordered according to the last names of the authors, or according to the call numbers written on their backs in a library. We can see that this is a state of negentropy because we are informed by it: we can easily find our way to a desired book. Bookshelves tend to get into disarray for the same reason that any entropy increases: the particular arrangement we call ordered for a bookshelf is only one of the many arrangements the books might be in. If people take and replace books from the shelf without attending to the order, the books are likely to be in one of the other many possible states instead of in the one state that we call ordered. That one state is vastly outnumbered by all the other states the books might be in, so it is not likely that the one state will remain instead of changing to one of the others as books are removed and replaced over time. The only thing that will ensure the continuing negentropy of the ordered

28

bookshelf is the input of information and energy by the librarian who resorts any books out of order on the shelf. An ordered bookshelf obeys the second law. But suppose that our idea of an ordered bookshelf changed. Suppose that we now order our books according to title instead of alphabetically by author. Or by subject matter first and then, within subjects, by author. These are all feasible arrangements. We can easily do it, and, in many cases that is just what we do. In most library classifications, for example, something like that is the scheme used to order books on shelves. Once we decide on the new order of books on the shelf, our old arrangement becomes one of the entropic states we wish to avoid! We must now exert energy and input information to prevent that old state from occurring, just as we once input our energy and information to keep it in place. The old arrangement has become one of the states of disorder, defined as such by our new arrangement of choice. Now we can think again about the broken cup. The intact cup on the table is only the negentropic state because that is the arrangement of the cup's parts which we have selected as ordered. Actually, if we considered the state of the broken cup on the floor—exactly as it is, each piece placed and turned just so and in no other arrangement—as our selected state, then the intact cup on the table would be one of the negentropic states. We would then have to input energy and information to the intact cup to restore the particular instance of broken-cup we have selected as our definition of order. We usually define an intact cup as order because we have a particular utility (holding tea for drinking) in mind when we define order. If the broken cup on the floor were a part of some sculptural art display, its particular arrangement

would become as negentropic as any intact cup in ordinary use for drinking. The broken-cup-as-art would then require as much attention to prevent it from taking up one of its other possible forms as the intact cup on the table, and maintaining its unique state would obey the second law. The second law really hinges on the relative probabilities of the various states that a system may assume. The moment we define one particular condition of Nature as order, all other becomes disorder and represents negentropy. Any one, particular instance of gas molecules in a chamber might be negentropic if we select it out of all the other possible arrangements of position and velocity. This is even true of an arrangement which represents "uniform temperature" when averaged with many other, similar arrangements. To keep that one arrangement of molecules from becoming some other arrangement requires input of energy and information, and that process obeys the second law. Page 166. ...we have come to recognize that events cannot be predicted with complete accuracy...there is always a degree of uncertainty. Hawking states one of the most important changes in science at the turn of the 20th century. It is a world view which differs from the one of the previous three centuries in two main aspects. The first aspect is the view of scientific knowledge based on prob-abilities instead of determinate facts. In classical mechanics, it was possible to know events in Nature to an arbitrary degree of certainty, and the work of science was to find out the last few decimal places of Nature's constants and variables. This view was held by eminent philosophers and scientists as late as 1900.

29

It was Psychology that pioneered the application of statistics to scientific observation in the work of Francis Galton. The methods were soon extended in the work of Karl Pearson, one of Galton's students, and taken up in experimental agriculture by R. A. Fisher, who developed analysis of variance. Classical mechanics became statistical mechanics and classical thermodynamics turned into statistical thermodynamics. This was the stage set for Shannon in the 1940's when he became interested in the definition of information. The second aspect of this revolution in the conception of knowledge is the famous Uncertainty Principle of quantum mechanics. As we see time and again in Hawking, Heisenberg's famous discovery has become a main landmark for physical theory. It shows us the limit to our knowledge, and, when our theories approach the center of Nature's mystery, it is by that landmark that we know when we are as close as we can come to seeing Nature's true face. Hugo du Coudray Department of Psychology Portland State University Portland, Oregon 97207 hrhm@pdx.edu