A Theologian's Nightmare by Bertrand Russell

The eminent theologian Dr. Thaddeus dreamt that he died and pursued his course toward heaven. His studies had prepared him and he had no difficulty in finding the way. He knocked at the door of heaven, and was met with a closer scrutiny than he expected. "I ask admission," he said, "because I was a good man and devoted my life to the glory of God." "Man?" said the janitor, "What is that? And how could such a funny creature as you do anything to promote the glory of God?" Dr. Thaddeus was astonished. "You surely cannot be ignorant of man. You must be aware that man is the supreme work of the Creator." "As to that," said the janitor, "I am sorry to hurt your feelings, but what you're saying is news to me. I doubt if anybody up here has ever heard of this thing you call 'man.' However, since you seem distressed, you shall have a chance of consulting our librarian."

The librarian, a globular being with a thousand eyes and one mouth, bent some of his eyes upon Dr. Thaddeus. "What is this?" he asked the janitor. "This," replied the janitor, "says that it is a member of a species called 'man,' which lives in a place called 'Earth.' It has some odd notion that the Creator takes a special interest in this place and this species. I thought perhaps you could enlighten it." "Well," said the librarian kindly to the theologian, "perhaps you can tall me where this place is that you call 'Earth.'" "Oh," said the theologian, "it's part of the Solar System." "And what is the Solar System?" asked the librarian. "Oh," said the theologian, somewhat disconcerted, "my province was Sacred Knowledge, but the question that you are asking belongs to profane knowledge. However, I have learnt enough from my astronomical friends to be able to tell you that the Solar System is part of the Milky Way." "And what is the Milky Way?" asked the librarian. "Oh, the Milky Way is one of the Galaxies, of which, I am told, there are some hundred million." "Well, well," said the librarian, "you could hardly expect me to remember one out of so many. But I do remember to have heard the word galaxy' before. In fact, I believe that one of our sub-librarians specializes in galaxies. Let us send for him and see whether he can help."

After no very long time, the galactic sub-librarian made his appearance. In shape, he was a dodecahedron. It was clear that at one time his surface had been bright, but the dust of the shelves had rendered him dim and opaque. The librarian explained to him that Dr. Thaddeus, in endeavoring to account for his origin, had mentioned galaxies, and it was hoped that information could be obtained from the galactic section of the library. "Well," said the sub-librarian, "I suppose it might become possible in time, but as there are a hundred million galaxies, and each has a volume to itself, it takes some time to find any particular volume. Which is it that this odd molecule desires?" "It is the one called 'The Milky Way,'" Dr. Thaddeus falteringly replied. "All right," said the sub- librarian, "I will find it if I can."

Some three weeks later, he returned, explaining that the extraordinarily efficient card index in the galactic section of the library had enabled him to locate the galaxy as number QX 321,762. "We have employed," he said, "all the five thousand clerks in the galactic section on this search. Perhaps you would like to see the clerk who is specially concerned with the galaxy in question?" The clerk was sent for and turned out to be an octahedron with an eye in each face and a mouth in one of them. He was surprised and dazed to find himself in such a glittering region, away from the shadowy limbo of his shelves. Pulling himself together, he asked, rather shyly, "What is it you wish to know about my galaxy?" Dr. Thaddeus spoke up: "What I want is to know about the Solar System, a collection of heavenly bodies revolving about one of the stars in your galaxy. The star about which they revolve is called 'the Sun.'" "Humph," said the librarian of the Milky Way, "it was hard enough to hit upon the right galaxy, but to hit upon the right star in the galaxy is far more difficult. I know that there are about three hundred billion stars in the galaxy, but I have no knowledge, myself, that would distinguish one of them from another. I believe, however, that at one time a list of the whole three hundred billion was demanded by the Administration and that it is still stored in the basement. If you think it worth while, I will engage special labor from the Other Place to search for this particular star."

It was agreed that, since the question had arisen and since Dr. Thaddeus was evidently suffering some distress, this might be the wisest course.

Several years later, a very weary and dispirited tetrahedron presented himself before the galactic sub-librarian. "I have," he said, "at last discovered the particular star concerning which inquiries have been made, but I am quite at a loss to imagine why it has aroused any special interest. It closely resembles a great many other stars in the same galaxy. It is of average size and temperature, and is surrounded by very much smaller bodies called 'planets.' After minute investigation, I discovered that some, at least, of these planets have parasites, and I think that this thing which has been making inquiries must be one of them."

At this point, Dr. Thaddeus burst out in a passionate and indignant lament: "Why, oh why, did the Creator conceal from us poor inhabitants of Earth that it was not we who prompted Him to create the Heavens? Throughout my long life, I have served Him diligently, believing that He would notice my service and reward me with Eternal Bliss. And now, it seems that He was not even aware that I existed. You tell me that I am an infinitesimal animalcule on a tiny body revolving round an insignificant member of a collection of three hundred billion stars, which is only one of many millions of such collections. I cannot bear it, and can no longer adore my Creator." "Very well," said the janitor, "then you can go to the Other Place."

Here the theologian awoke. "The power of Satan over our sleeping imagination is terrifying," he muttered.

(1961)

Aristarchus and Greek Astronomy

Aristarchus of Samos, who lived approximately from 310 to 230 B.C., and was thus about twenty-five years older than Archimedes, is the most interesting of all ancient astronomers, because he advanced the complete Copernican hypothesis, that all the planets, including the earth, revolve in circles round the sun, and that the earth rotates on its axis once in twenty-four hours. It is a little disappointing to find that the only extant work of Aristarchus, On the Sizes and Distances of the Sun and the Moon, adheres to the geocentric view. It is true that, for the problems with which this book deals, it makes no difference which theory is adopted, and he may therefore have thought it unwise to burden his calculations with an unnecessary opposition to the general opinion of astronomers; or he may have only arrived at the Copernican hypothesis after writing this book. Sir Thomas Heath, in his work on Aristarchus, which contains the text of this book with a translation, inclines to the latter view. The evidence that Aristarchus suggested the Copernican view is, in any case, quite conclusive.

The first and best evidence is that of Archimedes, who, as we have seen, was a younger contemporary of Aristarchus. Writing to Gelon, King of Syracuse, he says that Aristarchus brought out "a book consisting of certain hypotheses," and continues: "His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit." There is a passage in Plutarch saying that Cleanthes "thought it was the duty of the Greeks to indict Aristarchus of Samos on the charge of impiety for putting in motion the Hearth of the Universe (i.e. the earth), this being the effect of his attempt to save the phenomena by supposing the heaven to remain at rest and the earth to revolve in an oblique circle, while it rotates, at the same time, about its own axis." Cleanthes was a contemporary of Aristarchus, and died about 232 B.C. In another passage, Plutarch says that Aristarchus advanced this view only as a hypothesis, but that his successor Seleucus maintained it as a definite opinion. (Seleucus flourished about 150 B.C.). Atius and Sextus Empiricus also assert that Aristarchus advanced the heliocentric hypothesis, but do not say that it was set forth by him only as a hypothesis. Even if he did so, it seems not unlikely that he, like Galileo two thousand years later, was influenced by the fear of offending religious prejudices, a fear which the attitude of Cleanthes (mentioned above) shows to have been well grounded.

The Copernican hypothesis, after being advanced, whether positively or tentatively, by Aristarchus, was definitely adopted by Seleucus, but by no other ancient astronomer. This general rejection was mainly due to Hipparchus, who flourished from 161 to 126 B.C. He is described by Heath as "the greatest astronomer of antiquity." He was the first to write systematically on trigonometry; he discovered the precession of the equinoxes; he estimated the length of the lunar month with an error of less than one second; he improved Aristarchus's estimates of the sizes and distances of the sun and moon; he made a catalogue of eight hundred and fifty fixed stars, giving their latitude and longitude. As against the heliocentric hypothesis of Aristarchus, he adopted and improved the theory of epicycles which had been invented by Apollonius, who flourished about 220 B.C.; it was a development of this theory that came to be known, later, as the Ptolemaic system, after the astronomer Ptolemy, who flourished in the middle of the second century A.D. Copernicus came to know something, though not much, of the almost forgotten hypothesis of Aristarchus, and was encouraged by finding ancient authority for his innovation. Otherwise, the effect of this hypothesis on subsequent astronomy was practically nil.

Ancient astronomers, in estimating the sizes of the earth, moon, and sun, and the distances of the moon and sun, used methods which were theoretically valid, but they were hampered by the lack of instruments of precision. Many of their results, in view of this lack, were surprisingly good. Eratosthenes estimated the earth's diameter at 7850 miles, which is only about fifty miles short of the truth. Ptolemy estimated the mean distance of the moon at 29 ½ times the earth's diameter; the correct figure is about 30.7. None of them got anywhere near the size and distance of the sun, which all underestimated. Their estimates, in terms of the earth's diameter, were:

Aristarchus, 180;

Hipparchus, 1245;

Posidonius, 6545.

The correct figure is 11,726. It will be seen that these estimates continually improved (that of Ptolemy, however, showed a retrogression); that of Posidonius is about half the correct figure. On the whole, their picture of the solar system was not so very far from the truth.

Greek astronomy was geometrical, not dynamic. The ancients thought of the motions of the heavenly bodies as uniform and circular, or compounded of circular motions. They had not the conception of force. There were spheres which moved as a whole, and on which the various heavenly bodies were fixed. With Newton and gravitation a new point of view, less geometrical, was introduced. It is curious to observe that there is a reversion to the geometrical point of view in Einstein's General Theory of Relativity, from which the conception of force, in the Newtonian sense, has been banished.

The problem for the astronomer is this: given the apparent motions of the heavenly bodies on the celestial sphere, to introduce, by hypothesis, a third co-ordinate, depth, in such a way as to make the description of the phenomena as simple as possible. The merit of the Copernican hypothesis is not truth, but simplicity; in view of the relativity of motion, no question of truth is involved. The Greeks, in their search for hypotheses which would "save the phenomena," were in effect, though not altogether in intention, tackling the problem in the scientifically correct way. A comparison with their predecessors, and with their successors until Copernicus, must convince every student of their truly astonishing genius.

The History of Western Philosophy, Bertrand Russell, Chapter 24

The Science and Cosmology of Empedocles

The mixture of philosopher, prophet, man of science, and charlatan... was exemplified very completely in Empedocles, who flourished about 440 B.C., and was thus a younger contemporary of Parmenides... He was a citizen of Acragas, on the south coast of Sicily; he was a democratic politician, who at the same time claimed to be a god. In most Greek cities, and especially in those of Sicily, there was a constant conflict between democracy and tyranny; the leaders of whichever party was at the moment defeated were executed or exiled. Those who were exiled seldom scrupled to enter into negotiations with the enemies of Greece—Persia in the East, Carthage in the West. Empedocles, in due course, was banished, but he appears, after his banishment, to have preferred the career of a sage to that of an intriguing refugee. It seems probable that in youth he was more or less Orphic; that before his exile he combined politics and science; and that it was only in later life, as an exile, that he became a prophet.

Legend had much to say about Empedocles. He was supposed to have worked miracles, or what seemed such, sometimes by magic, sometimes by means of his scientific knowledge. He could control the winds, we are told; he restored to life a woman who had seemed dead for thirty days; finally, it is said, he died by leaping into the crater of Etna to prove that he was a god. In the words of the poet:

Great Empedocles, that ardent soul Leapt into Etna, and was roasted whole.

...His most important contribution to science was his discovery of air as a separate substance. This he proved by the observation that when a bucket or any similar vessel is put upside down into water, the water does not enter into the bucket. He says:

"When a girl, playing with a water-clock of shining brass, puts the orifice of the pipe upon her comely hand, and dips the waterclock into the yielding mass of silvery water, the stream does not then flow into the vessel, but the bulk of the air inside, pressing upon the close-packed perforations, keeps it out till she uncovers the compressed stream; but then air escapes and an equal volume of water runs in."

This passage occurs in an explanation of respiration.

He also discovered at least one example of centrifugal force: that if a cup of water is whirled round at the end of a string, the water does not come out.

He knew that there is sex in plants, and he had a theory (somewhat fantastic, it must be admitted) of evolution and the survival of the fittest. Originally, "countless tribes of mortal creatures were scattered abroad endowed with all manner of forms, a wonder to behold." There were heads without necks, arms without shoulders, eyes without foreheads, solitary limbs seeking for union. These things joined together as each might chance; there were shambling creatures with countless hands, creatures with faces and breasts looking in different directions, creatures with the bodies of oxen and the faces of men, and others with the faces of oxen and the bodies of men. There were hermaphrodites combining the natures of men and women, but sterile. In the end, only certain forms survived.

As regards astronomy: he knew that the moon shines by reflected light, and thought that this is also true of the sun; he said that light takes time to travel, but so little time that we cannot observe it; he knew that solar eclipses are caused by the interposition of the moon, a fact which he seems to have learnt from Anaxagoras.

He was the founder of the Italian school of medicine, and the medical school which sprang from him influenced both Plato and Aristotle. According to Burnet, it affected the whole tendency of scientific and philosophical thinking.

All this shows the scientific vigour of his time, which was not equalled in the later ages of Greece.

I come now to his cosmology. It was he... who established earth, air, fire, and water as the four elements (though the word "element" was not used by him). Each of these was everlasting, but they could be mixed in different proportions, and thus produce the changing complex substances that we find in the world. They were combined by Love and separated by Strife. Love and Strife were, for Empedocles, primitive substances on a level with earth, air, fire, and water. There were periods when Love was in the ascendant, and others when Strife was the stronger. There had been a golden age when Love was completely victorious. In that age, men worshipped only the Cyprian Aphrodite. The changes in the world are not governed by any purpose, but only by Chance and Necessity. There is a cycle: when the elements have been thoroughly mixed by Love, Strife gradually sorts them out again; when Strife has separated them, Love gradually reunites them. Thus every compound substance is temporary; only the elements, together with Love and Strife, are everlasting.

...Empedocles held that the material world is a sphere; that in the Golden Age Strife was outside and Love inside; then, gradually, Strife entered and Love was expelled, until, at the worst, Strife will be wholly within and Love wholly without the sphere. Then—though for what reason is not clear—an opposite movement begins, until the Golden Age returns, but not for ever. The whole cycle is then repeated. One might have supposed that either extreme could be stable, but that is not the view of Empedocles. He wished to explain motion while taking account of the arguments of Parmenides, and he had no wish to arrive, at any stage, at an unchanging universe.

The History of Western Philosophy, Bertrand Russell, Chapter 6

Moon-struck, A Jules Vernian Account

The Queen of Night, from her relative proximity and the spectacle rapidly renewed of her different phases, at first divided the attention of the inhabitants of the earth with the sun; but the sun tires the eyesight, and the splendour of its light forces its admirers to lower their eyes.

The blonde Phoebe, more humane, graciously allows herself to be seen in her modest grace; she is gentle to the eye, not ambitious, and yet she sometimes eclipses her brother the radiant Apollo, without ever being eclipsed by him. The Mahommedans understood what gratitude they owed to this faithful friend of the earth, and they ruled their months at 29-1/2 days on her revolution.

The first people of the world dedicated particular worship to this chaste goddess. The Egyptians called her Isis, the Phoenicians Astarte, the Greeks Phoebe, daughter of Jupiter and Latona, and they explained her eclipses by the mysterious visits of Diana and the handsome Endymion. The mythological legend relates that the Nemean lion traversed the country of the moon before its apparition upon earth, and the poet Agesianax, quoted by Plutarch, celebrated in his sweet lines its soft eyes, charming nose, and admirable mouth, formed by the luminous parts of the adorable Selene.

But though the ancients understood the character, temperament, and, in a word, moral qualities of the moon from a mythological point of view, the most learned amongst them remained very ignorant of selenography.

Several astronomers, however, of ancient times discovered certain particulars now confirmed by science. Though the Arcadians pretended they had inhabited the earth at an epoch before the moon existed, though Simplicius believed her immovable and fastened to the crystal vault, though Tacitus looked upon her as a fragment broken off from the solar orbit, and Clearch, the disciple of Aristotle, made of her a polished mirror upon which were reflected the images of the ocean — though, in short, others only saw in her a mass of vapours exhaled by the earth, or a globe half fire and half ice that turned on itself, other savants, by means of wise observations and without optical instruments, suspected most of the laws that govern the Queen of Night.

Thus Thales of Miletus, B.C. 460, gave out the opinion that the moon was lighted up by the sun. Aristarchus of Samos gave the right explanation of her phases. Cleomenus taught that she shone by reflected light. Berose the Chaldean discovered that the duration of her movement of rotation was equal to that of her movement of revolution, and he thus explained why the moon always presented the same side. Lastly, Hipparchus, 200 years before the Christian era, discovered some inequalities in the apparent movements of the earth's satellite.

These different observations were afterwards confirmed, and other astronomers profited by them. Ptolemy in the second century, and the Arabian Aboul Wefa in the tenth, completed the remarks of Hipparchus on the inequalities that the moon undergoes whilst following the undulating line of its orbit under the action of the sun. Then Copernicus, in the fifteenth century, and Tycho Brahe, in the sixteenth, completely exposed the system of the world and the part that the moon plays amongst the celestial bodies.

At that epoch her movements were pretty well known, but very little of her physical constitution was known. It was then that Galileo explained the phenomena of light produced in certain phases by the existence of mountains, to which he gave an average height of 27,000 feet.

After him, Hevelius, an astronomer of Dantzig, lowered the highest altitudes to 15,000 feet; but his contemporary, Riccioli, brought them up again to 21,000 feet.

Herschel, at the end of the eighteenth century, armed with a powerful telescope, considerably reduced the preceding measurements. He gave a height of 11,400 feet to the highest mountains, and brought down the average of different heights to little more than 2,400 feet. But Herschel was mistaken too, and the observations of Schroeter, Louville, Halley, Nasmyth, Bianchini, Pastorff, Lohrman, Gruithuysen, and especially the patient studies of MM. Boeer and Moedler, were necessary to definitely resolve the question. Thanks to these savants, the elevation of the mountains of the moon is now perfectly known. Boeer and Moedler measured 1,905 different elevations, of which six exceed 15,000 feet and twenty-two exceed 14,400 feet. Their highest summit towers to a height of 22,606 feet above the surface of the lunar disc.

At the same time the survey of the moon was being completed; she appeared riddled with craters, and her essentially volcanic nature was affirmed by each observation. From the absence of refraction in the rays of the planets occulted by her it is concluded that she can have no atmosphere. This absence of air entails absence of water; it therefore became manifest that the Selenites, in order to live under such conditions, must have a special organisation, and differ singularly from the inhabitants of the earth.

Lastly, thanks to new methods, more perfected instruments searched the moon without intermission, leaving not a point of her surface unexplored, and yet her diameter measures 2,150 miles; her surface is one-thirteenth of the surface of the globe, and her volume one-forty-ninth of the volume of the terrestrial spheroid; but none of her secrets could escape the astronomers' eyes, and these clever savants carried their wonderful observations still further.

Thus they remarked that when the moon was at her full the disc appeared in certain places striped with white lines, and during her phases striped with black lines. By prosecuting the study of these with greater precision they succeeded in making out the exact nature of these lines. They are long and narrow furrows sunk between parallel ridges, bordering generally upon the edges of the craters; their length varied from ten to one hundred miles, and their width was about 1,600 yards. Astronomers called them furrows, and that was all they could do; they could not ascertain whether they were the dried-up beds of ancient rivers or not. The Americans hope, some day or other, to determine this geological question. They also undertake to reconnoitre the series of parallel ramparts discovered on the surface of the moon by Gruithuysen, a learned professor of Munich, who considered them to be a system of elevated fortifications raised by Selenite engineers. These two still obscure points, and doubtless many others, can only be definitely settled by direct communication with the moon.

--From the Earth to the Moon, Jules Verne, Chapter

An Account of Formation of the Solar System in Jules Verne

An observer endued with an infinite range of vision, and placed in that unknown center around which the entire world revolves, might have beheld myriads of atoms filling all space during the chaotic epoch of the universe. Little by little, as ages went on, a change took place; a general law of attraction manifested itself, to which the hitherto errant atoms became obedient: these atoms combined together chemically according to their affinities, formed themselves into molecules, and composed those nebulous masses with which the depths of the heavens are strewed. These masses became immediately endued with a rotary motion around their own central point. This center, formed of indefinite molecules, began to revolve around its own axis during its gradual condensation; then, following the immutable laws of mechanics, in proportion as its bulk diminished by condensation, its rotary motion became accelerated, and these two effects continuing, the result was the formation of one principal star, the center of the nebulous mass.

By attentively watching, the observer would then have perceived the other molecules of the mass, following the example of this central star, become likewise condensed by gradually accelerated rotation, and gravitating round it in the shape of innumerable stars. Thus was formed the Nebulae, of which astronomers have reckoned up nearly 5,000.

Among these 5,000 nebulae there is one which has received the name of the Milky Way, and which contains eighteen millions of stars, each of which has become the center of a solar world.

If the observer had then specially directed his attention to one of the more humble and less brilliant of these stellar bodies, a star of the fourth class, that which is arrogantly called the Sun, all the phenomena to which the formation of the Universe is to be ascribed would have been successively fulfilled before his eyes. In fact, he would have perceived this sun, as yet in the gaseous state, and composed of moving molecules, revolving round its axis in order to accomplish its work of concentration. This motion, faithful to the laws of mechanics, would have been accelerated with the diminution of its volume; and a moment would have arrived when the centrifugal force would have overpowered the centripetal, which causes the molecules all to tend toward the center.

Another phenomenon would now have passed before the observer's eye, and the molecules situated on the plane of the equator, escaping like a stone from a sling of which the cord had suddenly snapped, would have formed around the sun sundry concentric rings resembling that of Saturn. In their turn, again, these rings of cosmical matter, excited by a rotary motion about the central mass, would have been broken up and decomposed into secondary nebulosities, that is to say, into planets. Similarly he would have observed these planets throw off one or more rings each, which became the origin of the secondary bodies which we call satellites.

Thus, then, advancing from atom to molecule, from molecule to nebulous mass, from that to principal star, from star to sun, from sun to planet, and hence to satellite, we have the whole series of transformations undergone by the heavenly bodies during the first days of the world.

The sun seems lost amidst the immensities of the stellar universe, and yet it is related, by actual theories of science, to the nebula of the Milky Way. Centre of a world, and small as it appears amidst the ethereal regions, it is still enormous, for its size is 1,400,000 times that of the earth. Around it gravitate eight planets, struck off from its own mass in the first days of creation. These are, in proceeding from the nearest to the most distant, Mercury, Venus, the Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Between Mars and Jupiter circulate regularly other smaller bodies, the wandering debris, perhaps, of a star broken up into thousands of pieces, of which the telescope has discovered eighty-two at present. Some of these asteroids are so small that they could be walked round in a single day by going at a gymnastic pace.

Now, of those attendant bodies which the sun maintains in their elliptical orbits by the great law of gravitation, some few in turn possess satellites. Uranus has eight, Saturn eight, Jupiter four, Neptune possibly three, and the Earth one. This last, one of the least important of the entire solar system, we call the Moon; and it is she whom the daring genius of the Americans professed its intention of conquering.

-- From the Earth to the Moon, Jules Verne, Chapter 5

Big Bang and the Fractal Universe

The Big Bang theory did not allow much room for optimism concerning our future. However, 15 years ago, physicists realized that the theory should be modified because it was plagued by many complicated problems related not only to our future, but to our past and present as well. For example, the standard Big Bang theory combined with the modem theory of elementary particles predicts the existence of many superheavy stable particles carrying magnetic charge: magnetic monopoles. These objects have a typical mass times that of the proton. According to the standard Big Bang theory, monopoles should appear at the very early stages of the evolution of the Universe, and they should now be as abundant as protons. In that case, the mean density of matter in the Universe would be about 15 orders of magnitude higher than its present value of about 10^-29 g/cm³

Originally, we hoped that this problem would disappear when more complicated theories of elementary particles were considered. Unfortunately, despite the rapid development of elementary particle physics, the monopole problem remained unsolved, and many new ones have been added: the gravitino problem, Polonyi field problem, domain wall problem, axion window problem, and so on. Physicists were forced to look more attentively at the basic assumptions of the standard cosmological theory. We have found that many of the assumptions are very suspicious.

The main problem of the Big Bang cosmology is the very existence of the Big Bang. What was before the Big Bang? Where did the Universe come from? If space-time did not exist for times less than 0, how could everything appear from nothing? What appeared first: the Universe or the laws determining its evolution? When we were born, the laws determining our development were written in the genetic code of our parents. But where were the laws of physics written when there was no Universe?

The problem of cosmological singularity still remains the most difficult problem of modem cosmology. However, we can now look at it from a totally different point of view. At school we are taught that two parallel lines never cross. However, general relativity tells us that our Universe is curved. The Universe may be open, in which case parallel lines diverge from one another, or it may be closed, and parallel lines cross each other like meridian lines on a globe. The only natural length parameter in general relativity is the Planck length l_p approximately 10^-33 cm. At smaller distances, the standard concept of space becomes inapplicable because of large quantum fluctuations. Therefore, we would expect our space to be very curved, with a typical radius of curvature about 10^-33 cm. We see, however, that our Universe is just about flat on a scale of 10²⁸ cm, the radius of the observable part of the Universe. The results of our observations differ from our theoretical expectations by more than 60 orders of magnitude!

Why are there so many different people on Earth? Well, Earth is large, so it can accommodate a lot of people. But why is Earth so large? (In fact, it is extremely small compared with the whole Universe.) Why is the Universe so large? A typical answer is that the Universe is large because it is a Universe, so it should be large, should it not? However, let us consider the Universe of a typical size l_p just emerging from the Big Bang. Let us assume that this Universe had the greatest possible density at which we can still describe it in terms of usual space and time. This is the so-called Planck density, 10⁹⁴ g/cm³, which corresponds to matter consisting of particles displaced at the Planck distance l_p from each other. We do not know how to describe matter with a greater density. But if we take the Planck size universe with the Planck density, we can easily understand, by definition of the Planck density, that such a universe can contain only a few particles. The standard assumption of the Big Bang cosmology is that the total number of elementary particles in the Universe almost does not change during the expansion of the Universe. Thus, a typical universe should contain one particle, maybe ten particles, but not 10⁸⁸ particles, which is the number contained in the part of the Universe we see now. This is a contradiction by 88 orders of magnitude.

The standard assumption of the Big Bang theory is that all parts of the Universe began their expansion simultaneously, at the moment t = 0. But how could different parts of the Universe synchronize the beginning of their expansion if they did not have any time for it? Who gave the command?

Our Universe, on a very large scale, is extremely homogeneous. On a scale of 10¹⁰ light years, the distribution of matter departs from perfect homogeneity by less than 1 part in 100,000. For a long time nobody had any idea why the Universe was so homogeneous. But those who do not have good ideas sometimes have good principles. One of the cornerstones of the standard cosmology was the cosmological principle, which asserts that the Universe must be homogeneous. However, the Universe contains stars, galaxies, and other important deviations from homogeneity. We have two opposite problems to solve. First, we must explain why our Universe is so homogeneous, and then we should suggest some mechanism that produced galaxies.

All these problems (and others) are extremely difficult. That is why it is very encouraging that most of these problems can be resolved in the context of one simple theory of the evolution of the Universe — the inflationary scenario. Meanwhile, some of its consequences are even more surprising. Instead of the Universe looking like a single expanding ball created in the Big Bang, we envisage it now as a huge, growing fractal consisting of many inflating balls that are producing new balls that are producing new balls, ad infinitum.

--The Origin and Evolution of the Universe, Ben Zuckerman, Matthew Arnold Malkan, Chapter 7: Future of the Universe

Big Bang: Limitations of the Theory

The Big Bang theory is the accepted theory about the evolution of the Universe over billions of years. However, the theory is often misunderstood as dealing with an initial explosion. Judging by the title of Steven Weinberg's popular exposition, The First Three Minutes, it seems as if the Universe has a beginning and as if we can describe processes right from the very first instant.

The Big Bang theory is a combination of two theoretical systems describing the processes happening to the contents of the Universe: general relativity for spacetime and quantum theory for matter. This implies three limits to the Big Bang theory:

On the left the Big Bang model is depicted as a cone, with each horizontal slice representing the three-dimensional universe at a given moment of time. On the right the major uncertainties are stressed.

1. Current theories about matter are valid only up to a finite temperature, and hence valid only after the first fraction of a second following the Singularity, the initial moment entailed by general relativity. This implies a, perhaps temporary, epistemological boundary to the domain where the Big Bang theory can be trusted. Further speculations have to deal with temperatures and densities for which particle physics is not yet well established.

2. Closer to the Singularity there comes a moment, presumably the ‘Planck Time’—a number constructed from the fundamental constants of quantum theory and gravity, about 10^-43 seconds after the initial Singularity—when general relativity must be replaced by a quantum theory of gravity. Theories of space and time applicable before the Planck Time are not known; even the meaningfulness of 'space' and 'time' is uncertain. (Which is troublesome; once time is no longer meaningful, it becomes unclear what can be meant by 'before'.)

3. The initial Singularity itself is a third limit, at least if there is such an initial Singularity. The Big Bang theory results in unrealistic numbers, like infinite density and so on. For some time it was assumed that the unrealistic breakdown of the solutions was a feature of idealizations made in the calculations, for instance the assumption of perfect homogeneity. However, it has since been shown that such peculiarities are unavoidable in general relativity, once certain very general assumptions are made, like causality and a positive energy density. On the other hand, general relativity itself is probably invalid in the moments before the Planck Time. Whether there is such a singular moment in a theory of quantum gravity which is to supersede general relativity cannot be decided a priori, before such a theory of quantum gravity has been proposed.

The first and second limits are clearly limits to our present knowledge, the third, the Singularity, seems to be an edge of reality, but is hidden behind the other two.

- 'Beyond the Big Bang: Quantum Cosmologies and God', Willem B. Drees, Chapter 2: Quantum Cosmologies and the Beginning.

Brahe and Kepler

Tycho Brahe had a love-hate relationship with his brash young assistant Johannes Kepler. Over the year and a half they worked together, Kepler and Brahe fought, Kepler left in angry fits or Brahe would order him to leave, then one or the other would beg to work together again. For some reason they needed each other. Brahe's observations of the universe were unsurpassed throughout the world. Kepler wanted access to them to devise better descriptions of how the heavens worked. Brahe, in turn, needed Kepler's brilliant math skills to help prove his own theories.

But they rubbed each other the wrong way, and Brahe wanted to keep him occupied and out of his hair. "Describe for me the orbit of Mars," he told Kepler in 1600, knowing full well that all the greats of history had wrestled with the prickly warrior planet and come up short.

"Give me a week," replied Kepler.

Kepler was overconfident. It would take him eight years to hammer out the orbit, but when he did, he turned Ptolemy's model on its head. He described the way the planets move with three laws that are still taught in introductory physics classes around the world.

Brahe and Kepler's names aren't well known outside the world of astronomy, but their contributions to science were as crucial as those of the more famous Copernicus and Galileo. In fact, some historians argue that the vision of a sun-centered cosmos that Copernicus devised in the 1500s wasn't so revolutionary—although Copernicus championed a moving earth, he clung unquestioningly to Aristotelian ideals such as circular motion. He wrote: "It is altogether absurd that a heavenly body should not always move with a uniform velocity in a perfect circle." In fact, Copernicus tried to connect to the ancients by writing his most important treatise, De Revolutionibus Orbium (The Revolutions of the Celestial Orbs), which echoed Ptolemy's Amalgaest, with each chapter of his book correlating to a chapter in Ptolemy. Moreover, Copernicus cited pre-Aristotelian philosophers such as the Pythagoreans to support his ideas for a sun-centered universe. To overturn Aristotle, he reached back even farther in time—not what one would call really taking a leap into the unknown.

Not to belittle Copernicus—he certainly provided a jump from the status quo. He also used a new concept to choose his theory: simplicity. Or even, one could say, beauty. The austerity of the simple Copernican system gave it an aesthetically appealing quality missing from Ptolemy's rings within rings. In modern times, scientists have almost deified this simplicity concept, known as Occam's Razor. If two theories fit the data, choose the simpler of the two. If you can explain the cosmos with just a few orbits instead of all those epicycles, then stick to the former.

But, alas for Copernicus, his simple ring system of planets orbiting a slightly off-center sun didn't correspond to reality substantially better than Ptolemy's model. Sticky Mars was still out of whack. Copernicus's De Revolutionibus Orbium was edited by a man named Rheticus, who, legend has it, became so frustrated with mapping the path of the red planet that he called upon the spirit world to help. A demon appeared, threw him against a couple of walls, and shouted, “Thus are the motions of Mars!"

Until someone decided to map the orbit of Mars first and then determine the math that described it instead of the other way around, no one was going to produce a complete model of the sky. That was not something Copernicus, firmly enmeshed in the philosophies of his day, was capable of doing. It was Brahe and Kepler, with their willingness to really observe what they were studying, to insist that the observations match their theories, who nudged cosmology a little closer to modern-day "science."

That these two characters—for they were definitely both characters—had the chance to come together and collaborate is almost beyond belief. Brahe was of Danish nobility, Kepler of the German lower class, but together they provided the most accurate depictions of the stars until that time.

--'The Big Bang Theory: What It Is, Where It Came From, and Why It Works', Karen C. Fox

Humans Look into the Universe

Humans have always looked into the night sky and wondered about the mysteries hidden in its depths. Developing our modern understanding of the universe and its origins has taken thousands of years, with many wrong turns and detours along the way.

Until the 1500s, most natural philosophers (the early scientists) thought our planet was the center of the universe. If Earth were moving through space, they reasoned, we would be thrown off or blown away by violent winds. In their theory, stars and planets circled Earth, held in a series of invisible crystal spheres. It certainly looked like the natural philosophers were right. After all, as we gaze up at the sky, don't we seem to be standing still? The Moon, the Sun, and the stars travel across the sky in great circles above us.

This geocentric (Earth-centered) theory survived for almost two thousand years. It was supported in the writings of the Greek philosopher Aristotle around 350 BCE. About five hundred years later, in the second century A.D., the Egyptian astronomer Ptolemy wrote a detailed explanation of why Earth must be at the center of the universe.

Not all early astronomers agreed with this theory, however. Aristarchus of Samos, a Greek astronomer who lived from about 310-230 BCE thought Earth revolved around the Sun. But for two thousand years, Aristotle's geocentric theory was accepted by most scientists. The powerful Catholic Church, which relied on his teachings, also supported the geocentric idea because some biblical passages suggested that the Sun moved while Earth remained in one place. Few people were willing to dispute the church's favored theory. Anyone who challenged it was in danger of being imprisoned or even executed.

We have since learned that our planet is just a tiny speck circling an ordinary star, somewhere in a vast ocean of stars. Our understanding of the universe began to change around 1500, with the work of Polish astronomer Nicolaus Copernicus. Copernicus believed Earth and the other planets traveled in circular orbits around the Sun. His theory more accurately described the paths of the planets and stars in the sky than the geocentric theory did. But Copernicus's theory also removed Earth from its special place at the center of the universe.

Copernicus knew his idea was contrary to church teachings. Revealing it could be punished by death. He didn't publish his revolutionary idea until the very last days of his life. Copernicus's idea has been an essential part of cosmology ever since. The Copernican principle says Earth does not occupy a special, central time or place in the universe.

In 1609 Austrian astronomer Johannes Kepler improved upon Copernicus's idea. Kepler used mathematics to analyze the orbits of the known planets and found that they all follow the same rules of motion. The planets, he discovered, travel around the Sun in elliptical (oval) orbits, not circles. Each moves more slowly as its orbit takes it farther from the Sun, then speeds up again as it moves closer. Kepler also found that a planet's speed is proportional to its distance from the Sun. The farther a planet is from the Sun, the more slowly it moves. In short, the motions of the heavenly bodies follow regular mathematical rules.

In 1610 the Italian scientist Galileo Galilei provided additional support for Copernicus's theory. The telescope had recently been invented, and Galileo made his own improvements on the instrument. With his new telescope, Galileo found four moons orbiting Jupiter. These moons were further proof that not every object in the sky circled Earth. Galileo's discovery made it easier to believe that planets could revolve around the Sun, much as the moons revolved around Jupiter.

Just as important, Galileo first explained the idea of inertia. Inertia is the property of all matter to remain in motion (or at rest) unless a force acts to change its motion. One such force is friction—the force that slows the motion of two surfaces that touch each other. Galileo realized that in empty space, without friction, an object like a star or a planet could keep moving forever. Through Galileo's work, astronomers came to understand that everything in the universe is in constant motion.

The key to understanding the motion of the stars and planets became available in 1687, when English physicist Isaac Newton published his laws of motion and the law of universal gravitation. Newton's laws predicted the motion of objects on Earth. Even more important, the same laws calculated the motion of the planets. According to Newton's laws, an apple falling to Earth and the Moon falling in its orbit around Earth both follow the same rules. Newton realized that the Moon constantly falls toward Earth, but the Moon also moves forward fast enough to keep falling past Earth. That's how it maintains a constant orbit instead of colliding with Earth. The same laws of physics apply to the Sun, Earth, and the other planets. This may seem obvious to us. But in the 1600s, Newton's laws were revolutionary. They allowed scientists to explain events happening far from our own world.

Astronomers continued to gather more information about the stars. Larger, more powerful telescopes let them see farther and farther into space. One of the objects that had puzzled early astronomers was the Milky Way. What was this faint streak of light painted across the night sky? Galileo was the first astronomer to see individual stars in the Milky Way. In 1750 English astronomer Thomas Wright proposed that the entire Milky Way was actually a broad band of many stars.

Astronomers were also finding small, fuzzy patches of light scattered across the sky. They called these objects nebulae, from the Latin word for "cloud." In 1755 the German philosopher Emmanuel Kant suggested nebulae might be "island universes," or galaxies, made up of many individual stars. The word galaxy comes from the Greek word for "milk." The name we use for these large, spinning clouds of stars comes from the ancient name for our own galaxy.

British astronomer William Herschel studied nebulae through his telescope. He made a careful catalog of more than two thousand nebulae he found across the sky. Herschel confirmed Kant's hypothesis about the composition of these objects in 1785. His powerful telescope showed individual stars in several nebulae. In the late 1700s, Herschel also studied the movement of binary stars—pairs of stars that orbit one another. He discovered that their orbits follow Newton's laws. This proved that Newton's laws were truly universal—they could be applied to objects anywhere in the universe.

By the mid-1800s, astronomers were using photographic film to study the heavens. They kept their camera lenses open for long periods of time. This gathered much more faint light than you could with a simple snapshot. These long exposures displayed many thousands of stars invisible to the naked eye.

--The Big Bang, by Paul Fleischer

The Singularity That Started It All

The universe began 15 billion years ago with an explosion from an infinitely small mathematical singularity. The singularity was not "somewhere." The fabric of space-time came into existence with explosion. There was no "before," at least none that we can presently know. Space swelled from the singularity like a balloon inflating from nothing.

During the first trillion-trillion-trillionth of a second, matter and antimatter flickered in and out of existence. The fate of the universe hung precariously in the balance, it might grow, or it might collapse back into nothingness. Suddenly it ballooned to enormous size (after all, we are here), in what cosmologists call the inflationary epoch, bringing the first true particles of matter — the quarks — into existence. Within a millionth of a second the rapid swelling ceased, and the quarks began to be confined to protons, neutrons and electrons. The universe continued to expand and cool, but now at a more stately pace. Already the universe was vastly larger than what we are able to observe today. Within a few more minutes, protons and neutrons combined into the first atomic nuclei — hydrogen and helium — but still the universe was too hot for the nuclei to shag electrons and make atoms. Not until 300,000 years after the beginning did the first atoms appear.

Irregularities in the gassy universe of hydrogen and helium were accentuated by gravity. Within a billion years after the beginning, the first stars and galaxies were born. There were not yet any Earthlike planets orbiting the stars of the earliest galaxies, because there were not yet significant quantities of the heavy elements (these would be cooked up later in stars). Nor had the Sun yet been born. But within a few billion years, the universe had begun to look familiar on the largest scale.

--An Intimate Look at the Night Sky, Boston Globe Science Columnist Chet Raymo

The Astonishing Origin of the Universe

The age of the universe is estimated to be anywhere from thirteen to fifteen billion years. That kind of time is incomprehensible. More staggering yet is the almost universally accepted scenario among cosmologists that in the blink of an eye, our current cosmos burst forth from a pinpoint of extremely dense and hot "quark-gluon plasma" — a primordial state of matter best described as a remarkably tiny dot of free-wheeling quark particles and the gluons binding them. This pinpoint of plasma expanded so rapidly the "event" has become widely known as the "big bang."

That term was first coined by the late British astronomer Fred Hoyle, who tackled some of the biggest questions in twentieth-century science. Later, in an international competition for a better name, the term survived over thirteen thousand proposed alternatives judged by a panel of my former ABC colleague Hugh Downs, the later astronomer Carl Sagan and the exceptional science writer Timothy Ferris.

Before the "bang," say the experts, there was no space — everything was contained in the pinpoint. Today, the process of space expansion continues as the galaxies in our cosmos are flung farther away from each other. One obvious question is what preceded the big bang, and what existed outside the "boundaries" of space as it was exploding. When I put this to a friend who is a world-renowned cosmologist, he started trying to explain to me the virtual vacuum-concept before stopping with a smile and saying, "You just go back to the beginning — and that's it."

--Finding God in the Questions, Timothy Johnson