Cosmology‎

"That the heaven as a whole neither came into being nor admits of destruction, as some assert, but is one and eternal, with no end or beginning of its total duration, containing and embracing in itself the infinity of time."

"In the beginning the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move."

"There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened."

"There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. It is only myth that attempts to say how the universe came to be, either four thousand or twenty billion years ago."

"Constantly regard the universe as one living being, having one substance and one soul; and observe how all things have reference to one perception, the perception of this one living being; and how all things act with one movement; and how all things are the cooperating causes of all things which exist; observe too the continuous spinning of the thread and the contexture of the web."

"The universe aged: indifferent, harsh, hostile and ultimately lethal."

"Unfortunately, the universe does not come with an instructor’s manual and technical support is as hard to get as it is for some software packages."

"[L]'universe […] est une machine à faire des dieux."

"It is clear that there is no classification of the Universe that is not arbitrary and full of conjectures. The reason for this is very simple: we do not know what kind of thing the universe is."

"We can suspect that there is no universe in the organic, unifying sense, that this ambitious term has. If there is a universe, its aim is not conjectured yet; we have not yet conjectured the words, the definitions, the etymologies, the synonyms, from the secret dictionary of God."

"Man's need of self-esteem entails the need for a sense of control over reality – but no control is possible in a universe which, by one's own concession, contains the supernatural, the miraculous and the causeless, a universe in which one is at the mercy of ghosts and demons, in which one must deal, not with the unknown, but with the unknowable; no control is possible if man proposes, but a ghost disposes; no control is possible if the universe is a haunted house."

"Every notion that any man, dead, living, or unborn, might form as to the universe will necessarily prove wrong."

"The more clearly we can focus our attention on the wonders and realities of the universe about us the less taste we shall have for the destruction of our race. Wonder and humility are wholesome emotions, and they do not exist side by side with a lust for destruction."

"What blessedness it is to dwell amidst this transparent air, which the eye can pierce without limit, amidst these floods of pure, soft, cheering light, under this immeasurable arch of heaven, and in sight of these countless stars! An infinite universe is each moment opened to our view. And this universe is the sign and symbol of Infinite Power, Intelligence, Purity, Bliss, and Love."

"The universe is globe-shaped, either because that is the most perfect shape of all, needing no joint, an integral whole; or because that is the most capacious of shapes, which is most fitting because it is to contain and preserve all...The first and highest of all is the sphere of the fixed stars, which contains itself and all things, and is therefore motionless. It is the location of the universe, to which the motion and position of all the remaining stars is referred. For though some consider that it also changes in some respect, we shall assign another cause for its appearing to do so in our deduction of the Earth's motion. There follows Saturn, the first of the wandering stars, which completes its circuit in thirty years. After it comes Jupiter which moves in a twelve-year long revolution. Next is Mars, which goes round biennially. An annual revolution holds the fourth place, in which as we have said is contained the Earth along with the lunar sphere which is like an epicycle. In fifth place Venus returns every nine months. Lastly, Mercury holds the sixth place, making a circuit in the space of eighty days. In the middle of all is the seat of the Sun. For who in this most beautiful of temples would put this lamp in any other or better place than the one from which it can illuminate everything at the same time? Aptly indeed is he named by some the lantern of the universe, by others the mind, by others the ruler. Trismegistus called him the visible God, Sophocles' Electra, the watcher over all things. Thus indeed the Sun as if seated on a royal throne governs his household of Stars as they circle around him. Earth also is by no means cheated of the Moon's attendance, but as Aristotle says in his book On Animals the Moon has the closest affinity with the Earth. Meanwhile the Earth conceives from the Sun, and is made pregnant with annual offspring. We find, then, in this arrangement the marvellous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultation by the Sun and re-appearance. Indeed Mars in particular at the time when it is visible throughout the night seems to equal Jupiter in size, though marked out by its reddish colour; yet it is scarcely distinguishable among stars of the second magnitude, though recognized by those who track it with careful attention."

"We find then in this arrangement an admirable harmony of the world, and a dependable, harmonious interconnexion of the motion and the size of the paths, such as otherwise cannot be discovered. For here the penetrating observer can note why the forward and the retrograde movement of Jupiter appears greater than that of Saturn, and smaller than that of Mars, and again greater with Venus than with Mercury; and why such retrogression appears oftener with Saturn than with Jupiter, less often with Mars and Venus than with Mercury. Moreover, why Saturn, Jupiter, and Mars, when they rise in the evening, appear greater than when they disappear and reappear [with the sun]...And all this results from the same cause, namely the motion of the earth."

"A man said to the universe: "Sir, I exist!" "However," replied the universe, "The fact has not created in me A sense of obligation.""

"Reason tells me of the extreme difficulty or rather impossibility of conceiving this immense and wonderful Universe, including man with his capability of looking far backwards and far into the future, as the result of blind chance or necessity. When thus reflecting I feel compelled to look to a First Cause having an intelligent mind in some degree analogous to that of man; and I deserve to be called a Theist."

"Even atheistic scientists will wax lyrical about the scale, the majesty, the harmony, the elegance, the sheer ingenuity of the universe of which they form so small and fragile a part. … Science reveals that there is a coherent scheme of things, but scientists do not necessarily interpret that as evidence for meaning or purpose in the universe."

"The overall organization of the universe has suggested to many a modern astronomer an element of design."

"One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe."

"Every movement in the skies or upon the earth proclaims to us that the universe is under government."

"The vastness of the universe—and love, the thing that makes the vastness bearable—is out of reach to the arrogant."

"I do not feel like an alien in the universe. The more I examine the universe and study the details of its architecture, the more evidence I find that the universe in some sense must have known that we were coming."

"Science and religion are two windows that people look through, trying to understand the big universe outside, trying to understand why we are here. The two windows give different views, but they look out at the same universe. Both views are one-sided, neither is complete. Both leave out essential features of the real world. And both are worthy of respect. Trouble arises when either science or religion claims universal jurisdiction, when either religious dogma or scientific dogma claims to be infallible."

"There is an enormous variety of things that we never dreamed of, like... black holes, s, quasars, all these unbelievably active goings-on in the universe... [I]n Aristotle's time the universe... was supposed to be quiescent, it was supposed to be perfect and peaceful, and nothing ever happened in the ; and that remained true... throughout all of the revolutions... It remained the general view of astronomers... through Copernicus, and Galileo, and Newton, and everybody else... until just the last 30 years, and now we know it's not like that at all. In fact the universe is full of violent events, and fantastic strong gravitational fields, and collapsed objects, and huge outpourings of energy. ...The things we understand least are the quasars... the most violent and... energetic objects in the universe, and they're totally... mysterious... and... they're rather frequent; and nobody ever dreamed that they existed... [E]ven after they were found it took a long time before people took them seriously. Nature's imagination is always richer than ours."

"Do I dare Disturb the universe?"

"I went to our Theological College lately, Westcott House, and we had a sort of chat. He told me that without him it was impossible to understand the universe, and I came away having forgotten to reply that it did not occur to me to try to understand the universe. I must not run on like this so. Or rather what I mean is I have just finished the biography of my great aunt. Understanding, or partially understanding, her has been quite a large enough job."

"In the beginning God created the heaven and the earth.And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.And God said, Let there be light: and there was light.And God saw the light, that it was good: and God divided the light from the darkness.And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so.And God called the firmament Heaven. And the evening and the morning were the second day.And God said, Let the waters under the heaven be gathered together unto one place, and let the dry land appear: and it was so.And God called the dry land Earth; and the gathering together of the waters called he Seas: and God saw that it was good.And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so.And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good.And the evening and the morning were the third day.And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years:And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so.And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also.And God set them in the firmament of the heaven to give light upon the earth,And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good.And the evening and the morning were the fourth day.And God said, Let the waters bring forth abundantly the moving creature that hath life, and fowl that may fly above the earth in the open firmament of heaven.And God created great whales, and every living creature that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good.And God blessed them, saying, Be fruitful, and multiply, and fill the waters in the seas, and let fowl multiply in the earth.And the evening and the morning were the fifth day.And God said, Let the earth bring forth the living creature after his kind, cattle, and creeping thing, and beast of the earth after his kind: and it was so.And God made the beast of the earth after his kind, and cattle after their kind, and every thing that creepeth upon the earth after his kind: and God saw that it was good.And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.So God created man in his own image, in the image of God created he him; male and female created he them."

"Science could predict that the universe must have had a beginning."

"Prophets hold a key to the lock in a language. The mechanical image remains only an image to them. This is not a mechanical universe."

"In a world hungry for meaning, [the new religious movement Lifechanyuan, also known as Life Zen Temple ()] dares to ask: What if the universe were not a machine but a mind?"

"Who is this that darkeneth counsel by words without knowledge?Gird up now thy loins like a man; for I will demand of thee, and answer thou me.Where wast thou when I laid the foundations of the earth? declare, if thou hast understanding.Who hath laid the measures thereof, if thou knowest? or who hath stretched the line upon it?Whereupon are the foundations thereof fastened? or who laid the corner stone thereof;When the morning stars sang together, and all the sons of God shouted for joy?"

"Why does the universe appear to have one time and three space dimensions?"

"An interersting thing to keep in mind is that the known universe is made of up quarks, down quarks, electrons, neutrinos, and gauge bosons. All the other quarks and leptons have been made at accelerators (and occasionally by collisions of energetic cosmic rays in the earth's atmosphere), and existed at an early stage of the universe and play no known role in the universe today or since soon after the big bang."

"Cabell and Hitler did not inhabit the same universe."

"Although the universe is under no obligation to make sense, students in pursuit of the PhD are."

"The most terrifying fact about the universe is not that it is hostile but that it is indifferent; but if we can come to terms with this indifference and accept the challenges of life within the boundaries of death — however mutable man may be able to make them — our existence as a species can have genuine meaning and fulfillment. However vast the darkness, we must supply our own light."

"All things are connected with all things throughout the universe, from the insect to the archangel; from the sand-grain to the mountain and the globe; from the dew-drop to the ocean; from the rain-drop to the rainbow; from the pebble on the shore to the sun that blazes in the firmament; from the zephyr that sings among the flowers of the field to the ocean that pours its wild bass in the great anthem of nature. Not only are all things connected with all things, but there is a concatenation of events, so that the character and effects of no one event can terminate in itself. As each event owes some portion of its nature to that which preceded it, so it imparts some of its nature to that which succeeds it, and thus perpetuates the blended good or evil of itself and its predecessors. The single event may thus live on in its influence along the line of all the ages, assuming new shapes, or if clothing itself in the drapery of new events, ever marching onward and upward in the continually growing affairs of time."

"The more we get to know about our universe ... the more the hypothesis that there is a Creator, who designed the universe for a purpose, gains in credibility as the best explanation of why we are here."

"If the whole universe has no meaning, we should never have found out that it has no meaning: just as, if there were no light in the universe and therefore no creatures with eyes, we should never know it was dark. Dark would be without meaning."

"Jove laughed to see The abyss empeopled, his bliss imparted, the throng that was his and no longer he."

"I will shred this Universe down to its last atom, and then with the stones you have collected for me, create a new one; teaming with life, that knows not what it has lost but only what it has been given... A Grateful Universe."

"I addressed no one. I addressed the universe. I addressed a void."

"With the cosmological term, Einstein had given other researchers an intriguing new variable to play with and manipulate in an attempt to fit their s with the new ideas they were considering and with the observations that were starting to be made. It also opened the door for theorists to experiment with the equations — with or without the newly introduced term — to see what other interpretations might be plausible, other than a universe that neither expands nor contracts. One could, of course, conjure up all kinds of conceivable universes with wildly different properties. However, among the conceivable universes, only those that satisfied general relativity’s could be deemed plausible. And among the possible universes sifted out through mathematics, perhaps one of those might bear a close resemblance to the universe we actually inhabit."

"The evidence that has accumulated since the 1930s is that the mass of the Universe is dominated by an exotic nonbaryonic form of matter largely draped around the galaxies. This dark matter approximates an initially low-pressure gas of particles that interact only with gravity, but we know little more than that. Searches for detection thus must follow many difficult paths to a great discovery: what the Universe is made of."

"The universe is full of magical things patiently waiting for our wits to grow sharper."

"It was a glaring omission, a sign of cosmic sloppiness. Not even that, Vasko corrected himself. It was a sign of cosmic obliviousness. The universe didn’t know what was happening here. It didn’t know and it didn’t care. It didn’t even know that it didn’t know."

"All the universe rests within your nature, in the ocean, in the heart, in all life."

"The space of our universe is the hypersurface of a vast expanding hypersphere."

"The Universe is made of stories, not of atoms."

"The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle — another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn't matter what you look like, or what you're made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you'll find it. It's already here. It's inside everything. You don't have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an intelligence that antedates the universe."

"The wide vessel of the universe."

"For nothing this wide Universe I call, Save thou, my Rose; in it thou art my all."

"The universe is God’s son."

"There is no design. The universe isn’t kind or cruel. The universe is vast and indifferent to our desires."

"The universe is, so far as I know, Doctor Mayer, indifferent to what you believe or disbelieve."

"Others hold that the earth has nine corners by which the heavens are supported. Another disagreeing from these would have the earth supported by seven elephants, and the elephants do not sink down because their feet are fixed on a tortoise. When asked who would fix the body of the tortoise, so that it would not collapse, he said that he did not know."

"The heaven, the earth, and all the liquid mayne, The Moones bright Globe, and Starres Titanian, A Spirit within maintaines: and their whole Masse, A Minde, which through each part infus’d doth passe, Fashions, and workes, and wholly doth transpierce All this great body of the Universe."

"I cannot imagine how the clockwork of the universe can exist without a clockmaker."

"The matter which we suppose to be the main constituent of the universe is built out of small self-contained building-blocks, the chemical atoms. It cannot be repeated too often that the word "atom" is nowadays detached from any of the old philosophical speculations: we know precisely that the atoms with which we are dealing are in no sense the simplest conceivable components of the universe. On the contrary, a number of phenomena, especially in the area of spectroscopy, lead to the conclusion that atoms are very complicated structures. So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us."

"The following anecdote is told of William James. [...] After a lecture on cosmology and the structure of the solar system, James was accosted by a little old lady."Your theory that the sun is the centre of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr. James, but it's wrong. I've got a better theory," said the little old lady."And what is that, madam?" inquired James politely."That we live on a crust of earth which is on the back of a giant turtle."Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of her position."If your theory is correct, madam," he asked, "what does this turtle stand on?""You're a very clever man, Mr. James, and that's a very good question," replied the little old lady, "but I have an answer to it. And it's this: The first turtle stands on the back of a second, far larger, turtle, who stands directly under him.""But what does this second turtle stand on?" persisted James patiently.To this, the little old lady crowed triumphantly,"It's no use, Mr. James—it's turtles all the way down.""

"These theories were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past."

"The main efforts of investigators have been in papering over contradictions in the big bang theory, to build up an idea which has become ever more complex and cumbersome."

"I have little hesitation in saying that as a result a sickly pall now hangs over the big bang theory. As I have mentioned earlier, when a pattern of facts becomes set against a theory, experience shows that it rarely recovers."

"In vain would one expect an answer from natural science, which indeed loyally declares that it is faced with an insoluble enigma. It is very true that one would demand too much from natural science as such; but it I salso certain that more deeply penetrates the problem the human spirit poured into philosophical meditation." The problem of the radical origin of the universe, then, is a philosophical problem, not a scientific one. The discourse now proceeds with a passage that is of close interest to us. The Pope argues that a personal subject, a mind enriched today by scientific knowledge, would judge compatible with the present view of the cosmos the idea of a creation of the universe from nothing, by a Creator God. The subject of this recognition - it is worth emphasizing - is not science or the scientific method, but man enriched by scientific knowledge, together with his philosophical and existential reflection. Here are the words of Pius XII: "A mind enlightened and enriched by modern scientific knowledge, which serenely evaluates this problem, is led to break the circle of an entirely independent and autochthonous matter, either because it is uncreated, or because it is self-created, and to trace it back to a Creator Spirit. With the same clear and critical gaze with which it examines and judges facts, it glimpses and recognizes therein the work of creative omnipotence, whose virtue, stirred by the powerful “fiat” uttered billions of years ago by the Creator Spirit, unfolded in the universe, calling into existence with a generous gesture of love matter exuberant with energy. It really seems that today's science, suddenly going back millions of centuries, has succeeded in witnessing that primordial “Fiat lux,” when out of nothingness burst with matter a sea of light and radiation, as the particles of the chemical elements split off and came together in millions of galaxies."

"In the beginning there was an explosion. Not an explosion like those familiar on earth, starting from a definite center and spreading out to engulf more and more of the circumambient air, but an explosion which occurred simultaneously everywhere, filling all space from the beginning, with every particle of matter rushing apart from every other particle. ‘All space’ in this context may mean either all of an infinite universe, or all of a finite universe which curves back on itself like the surface of a sphere. Neither possibility is easy to comprehend, but this will not get in our way; it matters hardly at all in the early universe whether space is finite or infinite. At about one-hundredth of a second, the earliest time about which we can speak with any confidence, the temperature of the universe was about a hundred thousand million (1011) degrees Centigrade. This is much hotter than in the center of even the hottest star, so hot, in fact, that none of the components of ordinary matter, molecules, or atoms, or even the nuclei of atoms, could have held together. Instead, the matter rushing apart in this explosion consisted of various types of the so-called elementary particles, which are the subject of modern high­energy nuclear physics."

"This circumstance of an expanding universe is irritating."

"To admit such possibilities seems senseless to me."

"Bothers science because it clashes with scientific religion—the religion of cause and effect, the belief that every effect has a cause. Now we find that the biggest effect of all, the birth of the universe, violates this article of faith. . . . what came before the Big Bang is the most interesting question of all."

"Ten or twenty billion years ago, something happened—the Big Bang, the event that began our universe. Why it happened is the greatest mystery... That it happened is reasonably clear. All the matter in the universe was concentrated at extremely high density—a kind of cosmic egg, reminiscent of the creation myths of many cultures—perhaps into a mathematical point with no dimensions at all."

"The discovery of the Big Bang and the recession of the galaxies came from a commonplace of nature called the Doppler effect. ...An object approaching us at very high velocities is perceive to have the color of its spectral lines blue-shifted. An object receding from us at very high velocities has its spectral lines red-shifted. ...Following a lead by the astronomer V. M. Slipher... Humason and Hubble found, to their amazement, that the spectra of all distant galaxies are red-shifted."

"The ideas that prove to be of lasting interest are likely to build on the framework of the now standard world picture, the hot big bang model of the expanding universe. The full extent and richness of this picture is not as well understood as I think it ought to be, even among those making some of the most stimulating contributions to the flow of ideas."

"Once we overcome our fear of being tiny, we find ourselves on the threshold of a vast and awesome Universe that utterly dwarfs—in time, in space, and in potential—the tidy anthropocentric proscenium of our ancestors. We gaze across billions of light-years of space to view the Universe shortly after the Big Bang, and plumb the fine structure of matter. We peer down into the core of our planet, and the blazing interior of our star. We read the genetic language in which is written the diverse skills and propensities of every being on Earth. We uncover hidden chapters in the record of our origins, and with some anguish better understand our nature and prospects. We invent and refine agriculture, without which almost all of us would starve to death. We create medicines and vaccines that save the lives of billions. We communicate at the speed of light, and whip around the Earth in an hour and a half. We have sent dozens of ships to more than seventy worlds, and four spacecraft to the stars. We are right to rejoice in our accomplishments, to be proud that our species has been able to see so far, and to judge our merit in part by the very science that has so deflated our pretensions."

"The first, and main, problem is the very existence of the big bang."

"One may wonder, What came before? If space-time did not exist then, how could everything appear from nothing? . . . Explaining this initial singularity—where and when it all began—still remains the most intractable problem of modern cosmology."

"[Big Bang theory] suggested that matter and motion originated rather as Genesis [in the Bible] suggests, ex nihilo, out of nothing, in a stupendous explosion of light and energy."

"The forces loosed were—are—remarkably (miraculously?) balanced: If the Big Bang had been slightly less violent, the expansion of the universe would have been less rapid, and would soon (in a few million years, or a few minutes—in any case, soon) have collapsed back on itself. If the explosion had been slightly more violent, the universe might have dispersed into a soup too thin to aggregate into stars. The odds against us were—this is just the right word—astronomical. The ratio of matter and energy to the volume of space at the Big Bang must have been within about one quadrillionth of 1 percent of ideal."

"Take but degree away (see above, the one quadrillionth of 1 percent margin for error), . . . and what follows is not just discord but eternal entropy and ice. So, what—who?—was the great Tuner?"

"The big bang theory does not describe the birth of the universe … Another theory describing even earlier times will be needed to explain the original creation of the universe."

"I'll say only this: if we're going to throw the idea of the Big Bang overboard, we won't have much left of current astrophysics and cosmology"

"There are some questions that scientists can never answer, “It may be that the Big Bang happened 12 billion years ago. But why did it happen? . . . How did the particles get there in the first place? What was there before?” Utley concludes: “It seems . . . clearer than ever that science will never satisfy the human hunger for answers.”"

"The big bang and the steady state debate in some ways echoed that between the ideas of Anaximander and Anaxagoras from two and a half millennia earlier. Anaxagoras had envisaged that at one time "all things were together" and that the motive force for the universe originated at a single point... Anaximander on the other hand wanted a universe determined by "the infinite" and needed an "eternal motion" to explain the balancing process of things coming into being and passing away in an eternal universe... ancient philosophy was debating the alternatives of a creation event starting the universe from a single point versus a continuous creation in an eternal universe."

"We are privileged to be part of the first generation who can claim to have a respectable, rational, and coherent description for the creation and evolution of the universe. The Big Bang model offers an elegant explanation of the origin of everything we see in the night sky, making it one of the greatest achievements of the human intellect and spirit. It is the consequence of an insatiable curiosity, a fabulous imagination, acute observation and ruthless logic. Even more wonderful is that the Big Bang model can be understood by everyone."

"The big bang was not an explosion in space; it was more like an explosion of space."

"The big bang happened everywhere. It was not a bomb going off at a particular spot that we can identify as the center of the explosion."

"I am convinced that the race backwards in space and time, to the origins of the Big Bang and the elementary structure of matter, is infinite; logically and spatially inaccessible. I therefore believe that the quarks that make up electrons and protons are not the most elementary particles at all; similarly, there is no single chain of events that led from the Big Bang to us, but an infinity of equally plausible possibilities. Mine is still a faith, because I have no proof of anything."

"The hot big bang standard theory is undoubtedly very impressive and probably true as far as it goes. The big bang is no longer a matter of debate, but one needs to keep in mind that the big bang is not the same as the creation or absolute beginning of the universe. While the standard model is reliable I am much less convinced by its extensions to the time regimes even closer to the magical moment t = 0. Inflation is not yet proved and pre-inflation scenarios seem very speculative. The same is the case with various theories of a universe before the big bang, although such theories cannot be ruled out. It is too early to say with certainty that the age of the universe is finite."

"The Big Bang understood as the event that created the hot, dense gas of cosmic matter was not an explosion starting from a point in space. If it had been, we could detect traces of that initial point today. Instead, astronomical observations teach us that the primordial matter gas was incredibly uniform and homogeneous. This indicates that the universe in its infancy was like a giant pot of well-mixed soup. The Big Bang is the event in which this soup was created, not at any special point, but homogeneously everywhere in the pot. It is a uniform transition that involved a very large, perhaps even infinite, region of space that was suddenly filled with matter. Understanding the Big Bang means understanding what caused this transition."{{NDR|And before the Big Bang, what was there?} Today it is thought that before the Big Bang there was only empty space. A very special empty space, however. There was no matter, but the fabric of space was imbued with a form of energy called precisely vacuum energy capable of exerting repulsive gravity. The effect is quite amazing because it is the exact opposite of the force of gravity we are used to, which can only attract material bodies."

"The Big Bang theory, which is proposed today as the origin of the world, does not contradict the intervention of a divine creator but depends on it. Evolution in nature does not conflict with the notion of Creation, because evolution presupposes the creation of beings who evolve."

"... et al. (2003) ... say “The remarkable agreement between the density inferred from / values and our measurements is an important triumph for the basic big bang model.” This was certainly true given the size of the s on both and the at the time."

"When it comes to the Big Bang, many believe that simply evoking that primordial explosion is enough to explain the origin of the world. But the issue is much deeper than that. Before the Big Bang, the fundamental laws of Nature had to be created: space, time, mass, energy, charges."

"Every time we get slapped down, we can say, Thank you Mother Nature, because it means we're about to learn something important."

"In the beginning, the establishment of first ties between general relativity and astronomy was a tedious exercise involving only a small number of bridge builders, most notably Freundlich, , Willem de Sitter, Arthur Eddington, , and Edwin Hubble."

"[T]wo rather separate research agendas emerged... [1] investigations of what were to become the three classical tests, envisaged by Einstein as early as 1907. ...[2] investigations of cosmological issues, whose only observational basis was the observations. Of the classical tests, both the bending of light and the remained controversial matters until the renaissance... This research agenda involved a small number of astronomers... not necessarily focused on general relativity. The cosmological research involved a separate group, consisting mostly of mathematicians like Howard Robertson and and astronomers with strong mathematical training such as Eddington, Lemaître, George McVittie, and William McCrea. They were mainly interested in how to apply general relativity to cosmological problems, which involved not only understanding cosmic dynamics but also solving the intricate problem of interpreting cosmological solutions to the Einstein equations, in particular separating time (which determined the evolution of the universe) from space (to which simplified assumptions concerning the structure of the universe, such as homogeneity and , were to be applied)."

"The fine-tuning of the universe, about which cosmologists make such a to-do, is both complex and specified and readily yields design. So too, Michael Behe's irreducibly complex biochemical systems readily yield design. The complexity-specification criterion demonstrates that design pervades cosmology and biology. Moreover, it is a transcendent design, not reducible to the physical world. Indeed, no intelligent agent who is strictly physical could have presided over the origin of the universe or the origin of life."

"While in the first quarter of this century physicists and cosmologists were forced to revise the basic notions that govern the natural sciences, in the last quarter of this century biologists will force a revision of the basic notions that govern science itself. After that “first revolution” it was clear that the classical concept of an “ultimate science”, that is an objective description of the world in which there are no subjects (a “subjectless universe”), contains contradictions."

"Why are the heavens not filled with light? Why is the universe plunged into darkness?"

"One may wonder, What came before? If space-time did not exist then, how could everything appear from nothing?... Explaining this initial singularity—where and when it all began—still remains the most intractable problem of modern cosmology."

"Take a look at George Gamow, who is now recognized as one of the great cosmologists of the last hundred years. I speculate that he probably didn't win the Nobel Prize because people could not take him seriously. He wrote children's books. His colleagues have publicly stated his writing children's books on science had an adverse effect on his scientific reputation, and people could not take him seriously when he and his colleagues proposed that there should be a cosmic background radiation, which we now know to be one of the greatest discoveries of 20th-century physics."

"Your accepted conceptions of cosmogony — whether from the theological or scientific standpoints —do not enable you to solve a single anthropological or even ethnical problem and they stand in your way whenever you attempt to solve the problem of the races on this planet. When a man begins to talk about creation and the origin of man, he is butting against the facts incessantly. Go on saying, Our planet and man were created — and you will be fighting against hard facts for ever, analyzing and losing time over trifling details—unable to even grasp the whole. But once admit that our planet and ourselves are no more creations than the ice-berg now before me (in our K.H.'s home) but that both planets and man are—states for a given time; that their present appearance —g eological and anthropological — is transitory and but a condition concomitant of that stage of evolution at which they have arrived in the descending cycle — and all will become plain. You will easily understand what is meant by the one and only element or principle in the universe and that androgynous; the seven-headed serpent Ananda of Vishnu, the Nag around Buddha, the great dragon eternity biting with its active head, its passive tail, from the emanations of which spring worlds, beings and things. You will comprehend the reason why the first philosopher proclaimed all — maya..."

"Dirac spent the autumn term of 1931 at Princeton University, where was a professor. During his stay they got to know each other well. Most likely they discussed cosmology, a science which at the time was experiencing dramatic changes."

"Cosmological observations have entered the era of precision, unlocking its tremendous power as a particle physics laboratory, aiding our search for physics beyond the Standard Model. The great power of cosmology comes from its great range of possibility. Processes far beyond the reach of terrestrial apparatus are possible as the universe scans through orders of magnitude of energy throughout its evolution. On the flip side, the great range of possibility also implies a tremendous difficulty to extract information: without knowing precisely what we are looking for, the cosmological data itself provides little hint of what the underlying might be."

"If all the properties of the universe, such as charge and momentum, balanced out, as Guth, who was a fan as well as a scholar of theories of nothing, pointed out to me, no laws of physics forbade the spontaneous appearance of the universe—or a quantum piece of one. ...Nothing, some physicist implied, might be the ultimate symmetry, everywhere, everywhen the same... Mostly we knew what nothing was not. It was not anything. But it was the possibility of everything. And perhaps such beauty, nothing, was unstable. And the result was every once in an eternity it twitched. ...The first soul brave enough to suggest the universe was indeed nothing was Ed Tryon... [who] blurted it out during a seminar with Sciama, "Suppose the universe is just a quantum fluctuation." Everybody laughed. ... Tryon eventually published these notions in Nature in 1975 and was mostly ignored. Peebles and Dicke had mentioned his work in their famous 1979 paper about enigmas and conundrums."

"Guth... wanted to hear... Alex Vilenkin... describe a new theory of the origin of the universe, of how it could have emerged from nothing. Vilenkin's version of the infant universe... was a kind of metaphysical mole. ...a bubble of universe, space-time, had "tunneled" into a Wheeleresque superspace of possible space-times and then tunneled again into "real" space and time. ...But from where had the universe tunneled into this realm..? In Vilenkin's words, "from nothing." ...Vilenkin's tiny bubble... inflated and went through the standard expansion and evolution of the big bang. ...he, Guth, and Sidney Coleman sat and had a conversation that Lewis Carroll might have enjoyed, about nothing. ..."Nothing," answered Vilenkin... "is no time, no space." ..."There is an epoch without time," [Coleman] said finally as the shadows lengthened. "It is an eternity. So we make a quantum leap from eternity into time." Then, as good physicists did, they repaired to a Chinese restaurant."

"Simple rules can have complex consequences. This simple rule has such a wealth of implications that it is worth examining in detail. It is the far from self-evident guiding principle of reductionism and of most modern investigations into cosmic complexity. Reductionism will not be truly successful until physicists and cosmologists demonstrate that the large-scale phenomena of the world arise from fundamental physics alone. This lofty goal is still out of reach. There is uncertainty not only in how physics generates the structures of our world but also in what the truly fundamental rules of physics are."

"Physics has entered a remarkable era. Ideas that were once the realm of science fiction are now entering our theoretical — and maybe even experimental — grasp. Brand-new theoretical discoveries about extra dimensions have irreversibly changed how particle physicists, astrophysicists, and cosmologists now think about the world. The sheer number and pace of discoveries tells us that we've most likely only scratched the surface of the wondrous possibilities that lie in store. Ideas have taken on a life of their own."

"Today’s cosmology faces problems both early and late, models of the early Universe that cannot be tested, and data indicating that the late Universe accelerates. These problems have been previously been explained by a repulsive “inflation” and another repulsive “dark” energy. Recent studies cast doubt upon these speculations. A cosmology described by simple equations may bring light to this darkness."

"We should, of course, expect that any universe which expands without limit will approach the empty de Sitter case, and that its ultimate fate is a state in which each physical unit—perhaps each nebula or intimate group of nebulae—is the only thing which exists within its own observable universe."

"If the general picture, however, of a Big Bang followed by an expanding Universe is correct, what happened before that? Was the Universe devoid of all matter and then the matter suddenly somehow created? How did that happen? In many cultures, the customary answer is that a God or Gods created the Universe out of nothing. But if we wish to pursue this question courageously, we must of course ask the next question: where did God come from? If we decide that this is an unanswerable question, why not save a step and conclude that the origin of the Universe is an unanswerable question? Or, if we say that God always existed, why not save a step, and conclude that the Universe always existed? That there's no need for a creation, it was always here. These are not easy questions. Cosmology brings us face to face with the deepest mysteries, questions that were once treated only in religion and myth."

"Hindu cosmology... gives a time-scale for the earth and the universe which is consonant with that of modern scientific cosmology."

"The primary challenge of this cosmological transformation of consciousness is the awareness that each being in the universe is an origin of the universe. "The center of the cosmos" refers to that place where the great birth of the universe happened at the beginning of time, but it also refers to the upwelling of the universe as river, as star, as raven, as you, the universe surging into existence anew. The consciousness that learns it is at the origin point of the universe is itself an origin of the universe. The awareness that bubbles up each moment that we identify as ourselves is rooted in the originating activity of the universe. We are all of us arising together at the center of the cosmos."

"Cosmologists have plenty of ego — how can a person not be ego-driven when it's your job to deduce what brought the universe into existence? But without data, their explanations were just tall tales. In this modern era of cosmology, each new observation, each morsel of data wields a two-edged sword: it enables cosmology to thrive on the kind of foundation that so much of the rest of science enjoys, but it also constrains theories that people thought up when there wasn't enough data to say whether they were wrong or not. No science achieves maturity without it.Let there be cosmology."

"Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. ...The most important thing accomplished by the three-degree radiation background in 1965 was to force us to take seriously the idea that there was an early universe."

"The effort to understand the universe is one of the very few things which lifts human life a little above the level of farce and gives it some of the grace of tragedy."

"Cosmology is peculiar among the sciences for it is both the oldest and the youngest. From the dawn of civilization man has speculated about the nature of the starry heavens and the origin of the world, but only in the present century has physical cosmology split away from general philosophy to become an independent discipline."

"I experience the same sense of absurdity when I listen to a cosmologist like Stephen Hawking telling us that the universe began with a big bang fifteen billion years ago, and that physics will shortly create a 'theory of everything' that will answer every possible question about our universe; this entails the corollary that God is an unnecessary hypothesis. Then I think of the day when I suddenly realized that I did not know where space ended, and it becomes obvious that Hawking is also burying his head in the sand. God may be an unnecessary hypothesis for all I know, and I do not have the least objection to Hawking dispensing with him, but until we can understand why there is existence rather than nonexistence, then we simply have no right to make such statements. It is unscientific. The same applies to the biologist Richard Dawkins, with his belief that strict Darwinism can explain everything, and that life is an accidental product of matter. I feel that he is trying to answer the ultimate question by pretending it does not exist."

"Cosmology is a science which has only a few observable facts to work with."

"The Sea Will be the Sea Whatever the drop's philosophy."

"Constantly regard the universe as one living being, having one substance and one soul; and observe how all things have reference to one perception, the perception of this one living being; and how all things act with one movement; and how all things are the cooperating causes of all things which exist; observe too the continuous spinning of the thread and the contexture of the web."

"Similar to a person who is not attached to external pleasures but enjoys happiness in the Atman (soul), the person who perceives Brahman in everything feels everlasting joy."

"Cause, Principle, and One eternal From whom being, life, and movement are suspended, And which extends itself in length, breadth, and depth, To whatever is in Heaven, on Earth, and Hell; With sense, with reason, with mind, I discern, That there is no act, measure, nor calculation, which can comprehend That force, that vastness and that number, Which exceeds whatever is inferior, middle, and highest; Blind error, avaricious time, adverse fortune, Deaf envy, vile madness, jealous iniquity, Crude heart, perverse spirit, insane audacity, Will not be sufficient to obscure the air for me, Will not place the veil before my eyes, Will never bring it about that I shall not Contemplate my beautiful Sun."

"It is manifest... that every soul and spirit hath a certain continuity with the spirit of the universe, so that it must be understood to exist and to be included not only there where it liveth and feeleth, but it is also by its essence and substance diffused throughout immensity... The power of each soul is itself somehow present afar in the universe... Naught is mixed, yet is there some presence. Anything we take in the universe, because it has in itself that which is All in All, includes in its own way the entire soul of the world, which is entirely in any part of it."

"The universal Intellect is the intimate, most real, peculiar and powerful part of the soul of the world. This is the single whole which filleth the whole, illumineth the universe and directeth nature to the production of natural things, as our intellect with the congruous production of natural kinds."

"Our philosophy… reduceth to a single origin and relateth to a single end, and maketh contraries to coincide so that there is one primal foundation both of origin and of end. From this coincidence of contraries, we deduce that ultimately it is divinely true that contraries are within contraries; wherefore it is not difficult to compass the knowledge that each thing is within every other."

"The one infinite is perfect, in simplicity, of itself, absolutely, nor can aught be greater or better, This is the one Whole, God, universal Nature, occupying all space, of whom naught but infinity can give the perfect image or semblance."

"The single spirit doth simultaneously temper the whole together; this is the single soul of all things; all are filled with God."

"All things are in all."

"Before anything else the One must exist eternally; from his power derives everything that always is or will ever be. He is the Eternal and embraces all times. He knows profoundly all events and He himself is everything. He creates everything beyond any beginning of time and beyond any limit of place and space. He is not subject to any numerical law, or to any law of measure or order. He himself is law, number, measure, limit without limit, end without end, act without form."

"The ancient Hindu philosophers stated as a fundamental truth that the world of our sense-experience is all illusion (maya), that change, plurality, and causation are not real, that there is but one reality, God. This is metaphysical Monism of the idealistic-spiritual type, tending towards mysticism."

"Hen to pan"

"Quantum theory is now discussing instantaneous connections between two entangled quantum objects such as electrons. This phenomenon has been observed in laboratory experiments and scientists believe they have proven it takes place. They’re not talking about faster than the speed of light. Speed has nothing to do with it. The entangled objects somehow communicate instantaneously at a distance. If that is true, distance has no meaning. Light-years have no meaning. Space has no meaning. In a sense, the entangled objects are not even communicating. They are the same thing. At the “quantum level” (and I don’t know what that means), everything may be actually or theoretically linked. All is one. Sun, moon, stars, rain, you, me, everything. All one."

"The man who abides in the will of God wills nothing else than what God is, and what He wills. If he were ill he would not wish to be well. If he really abides in God's will, all pain is to him a joy, all complication, simple: yea, even the pains of hell would be a joy to him. He is free and gone out from himself, and from all that he receives, he must be free. If my eye is to discern colour, it must itself be free from all colour. The eye with which I see God is the same with which God sees me. My eye and God's eye is one eye, and one sight, and one knowledge, and one love."

"Two monads may approach one another, but [without the heart] they will never truly connect."

"The Bhagavadgita combines many different elements from Samkhya and Vedanta philosophy. In matters of religion, its important contribution was the new emphasis placed on devotion, which has since remained a central path in Hinduism. In addition, the popular theism expressed elsewhere in the Mahabharata and the transcendentalism of the Upanishads converge, and a God of personal characteristics is identified with the brahman of the Vedic tradition. The Bhagavadgita thus gives a typology of the three dominant trends of Indian religion: dharma-based householder life, enlightenment-based renunciation, and devotion-based theism."

"Pluralism and monism, philosophical theories that answer “many” and “one,” respectively, to the distinct questions: how many kinds of things are there? and how many things are there? Different answers to each question are compatible, and the possible combination of views provide a popular way of viewing the history of philosophy. Some thinkers have been so attracted to unity that they have denied the multiplicity of things and asserted some form of substantival monism. Thus, Parmenides in the ancient world held that all is being, since whatever is is; Spinoza at the beginning of modern philosophy asserted that there is but one infinite divine substance in which everything else has its finite being as a mode or affect; whereas for Hegel all that is is the Absolute Idea developing through time. Democritus and Leibniz expressed an attributive monism which views the many different substances of the world as being of the same kind. Opposed to such monistic theories are those philosophers for whom the multiplicity and diversity of things rather than their unity is the more striking and important fact."

"Parmenides believed that all Being is what he called the One, and denied absolutely the possibility of change. He believed that the cosmos is full (i.e., no void), uncreated, eternal, indestructible, unchangeable, immobile sphere of being, and all sensory evidence to the contrary is illusory. One Parmenidean fragment stated, "Either a thing is or it is not," meaning that creation and destruction is impossible."

"The Godhead, according to Eckhart, is the universal and eternal Unity comprehending and transcending all diversity. "The Divine nature is Rest," he says in one of the German discourses; and in the Latin fragments we find: "God rests in Himself, and makes all things rest in Him." The three Persons of the Trinity, however, are not mere modes or accidents, but represent a real distinction within the Godhead. God is unchangeable, and at the same time an "everlasting process." The creatures are "absolutely nothing"; but at the same time "God without them would not be God," for God is love, and must objectify Himself; He is goodness, and must impart Himself. As the picture in the mind of the painter, as the poem in the mind of the poet, so was all creation in the mind of God from all eternity, in uncreated simplicity. The ideal world was not created in time; "the Father spake Himself and all the creatures in His Son"; "they exist in the eternal Now" —"a becoming without a becoming, change without change." "The Word of God the Father it the substance of all that exists, the life of all that lives, the principle and cause of life." Of creation he says : "We must not falsely imagine that God stood waiting for something to happen, that He might create the world. For so soon as He was God, so soon as He begat His coeternal and coequal Son, He created the world.""

"Reduced to their most pregnant difference, empiricism means the habit of explaining wholes by parts, and rationalism means the habit of explaining parts by wholes. Rationalism thus preserves affinities with monism, since wholeness goes with union, while empiricism inclines to pluralistic views. No philosophy can ever be anything but a summary sketch, a picture of the world in abridgment, a foreshortened bird's-eye view of the perspective of events. And the first thing to notice is this, that the only material we have at our disposal for making a picture of the whole world is supplied by the various portions of that world of which we have already had experience. We can invent no new forms of conception, applicable to the whole exclusively, and not suggested originally by the parts. All philosophers, accordingly, have conceived of the whole world after the analogy of some particular feature of it which has particularly captivated their attention."

"Pluralism lets things really exist in the each-form or distributively. Monism thinks that the all-form or collective-unit form is the only form that is rational. The all-form allows of no taking up and dropping of connexions, for in the all the parts are essentially and eternally co-implicated. In the each-form, on the contrary, a thing may be connected by intermediary things, with a thing with which it has no immediate or essential connexion. It is thus at all times in many possible connexions which are not necessarily actualized at the moment. They depend on which actual path of intermediation it may functionally strike into: the word 'or' names a genuine reality."

"The instant field of the present is at all times what I call the "pure" experience. It is only virtually or potentially either object or subject as yet. For the time being, it is plain, unqualified actuality or existence, a simple that."

"I believe that the Universe is one being, all its parts are different expressions of the same energy, and they are all in communication with each other, therefore parts of one organic whole. (This is physics, I believe, as well as religion.) The parts change and pass, or die, people and races and rocks and stars, none of them seems to me important in itself, but only the whole. This whole is in all its parts so beautiful, and is felt by me to be so intensely in earnest, that I am compelled to love it and to think of it as divine. It seems to me that this whole alone is worthy of the deeper sort of love and there is peace, freedom, I might say a kind of salvation, in turning one's affections outward toward this one God, rather than inwards on one's self, or on humanity, or on human imaginations and abstractions — the world of spirits. I think it is our privilege and felicity to love God for his beauty, without claiming or expecting love from him. We are not important to him, but he to us."

"If those who lead you say, "See, the Kingdom is in the sky," then the birds of the sky will precede you. If they say to you, "It is in the sea," then the fish will precede you. Rather, the Kingdom is inside of you, and it is outside of you. When you come to know yourselves, then you will become known, and you will realize that it is you who are the sons of the living Father. But if you will not know yourselves, you dwell in poverty and it is you who are that poverty."

"We are all one in God’s seeing."

"The Tao that can be expressed is not the eternal Tao; The name that can be defined is not the unchanging name. Non-existence is called the antecedent of heaven and earth; Existence is the mother of all things. From eternal non-existence, therefore, we serenely observe the mysterious beginning of the Universe; From eternal existence we clearly see the apparent distinctions. These two are the same in source and become different when manifested. This sameness is called profundity. Infinite profundity is the gate whence comes the beginning of all parts of the Universe."

"Since before time and space were, the Tao is. It is beyond is and is not. How do I know this is true? I look inside myself and see."

"There is a thing inherent and natural, Which existed before heaven and earth. Motionless and fathomless, It stands alone and never changes; It pervades everywhere and never becomes exhausted. It may be regarded as the Mother of the Universe. I do not know its name. If I am forced to give it a name, I call it Tao, and I name it as supreme."

"The "concept" of the One is not, properly speaking, a concept at all, since it is never explicitly defined by Plotinus, yet it is nevertheless the foundation and grandest expression of his philosophy. Plotinus does make it clear that no words can do justice to the power of the One; even the name, "the One," is inadequate, for naming already implies discursive knowledge, and since discursive knowledge divides or separates its objects in order to make them intelligible, the One cannot be known through the process of discursive reasoning (Ennead VI.9.4). Knowledge of the One is achieved through the experience of its "power" (dunamis) and its nature, which is to provide a "foundation" (arkhe) and location (topos) for all existents (VI.9.6). The "power" of the One is not a power in the sense of physical or even mental action; the power of the One, as Plotinus speaks of it, is to be understood as the only adequate description of the "manifestation" of a supreme principle that, by its very nature, transcends all predication and discursive understanding."

"The unity and continuity of Vedanta are reflected in the unity and continuity of wave mechanics. In 1925, the world view of physics was a model of a great machine composed of separable interacting material particles. During the next few years, Schrodinger and Heisenberg and their followers created a universe based on super imposed inseparable waves of probability amplitudes. This new view would be entirely consistent with the Vedantic concept of All in One."

"Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things."

"Heart of my heart, we are one with the wind, One with the clouds that are whirled o'er the lea, One in many, O broken and blind, One as the waves are at one with the sea! Ay! when life seems scattered apart, Darkens, ends as a tale that is told, One, we are one, O heart of my heart, One, still one, while the world grows old."

"There is one story left, one road: that it is. And on this road there are very many signs that, being, is uncreated and imperishable, whole, unique, unwavering, and complete."

"The Immortal Principle was first called water by Thales. Anaximenes called it air. The Pythagoreans called it number and were thus the first to see the Immortal Principle as something nonmaterial. Heraclitus called the Immortal Principle fire and introduced change as part of the Principle. He said the world exists as a conflict and tension of opposites. He said there is a One and there is a Many and the One is the universal law which is immanent in all things. Anaxagoras was the first to identify the One as nous, meaning "mind." Parmenides made it clear for the first time that the Immortal Principle, the One, Truth, God, is separate from appearance and from opinion, and the importance of this separation and its effect upon subsequent history cannot be overstated. It's here that the classic mind, for the first time, took leave of its romantic origins and said, "The Good and the True are not necessarily the same," and goes its separate way. Anaxagoras and Parmenides had a listener named Socrates who carried their ideas into full fruition."

"The Bhagavadgita may be treated as a great synthesis of the ideas of the impersonal spiritual monism with personalistic monotheism, of the yoga of action with the yoga of transcendence of action, and these again with yogas of devotion and knowledge."

"Jesus knew — knew — that we're carrying the Kingdom of Heaven around with us, inside, where we're all too goddam stupid and sentimental and unimaginative to look? You have to be a son of God to know that kind of stuff."

"I can't see why anybody — unless he was a child, or an angel, or a lucky simpleton like the pilgrim — would even want to say a prayer to a Jesus who was the least bit different from the way he looks and sounds in the New Testament. My God! He's only the most intelligent man in the Bible, that's all! Who isn't he head and shoulders over? Who? Both Testaments are full of pundits, prophets, disciples, favorite sons, Solomons, Isaiahs, Davids, Pauls — but, my God, who besides Jesus really knew which end was up? Nobody. Not Moses. Don't tell me Moses. He was a nice man, and he kept in beautiful touch with his God, and all that — but that's exactly the point. He had to keep in touch. Jesus realized there is no separation from God."

"I'll tell you a terrible secret — Are you listening to me? There isn't anyone out there who isn't Seymour's Fat Lady. That includes your Professor Tupper, buddy. And all his goddam cousins by the dozens. There isn't anyone anywhere that isn't Seymour's Fat Lady. Don't you know that? Don't you know that goddam secret yet? And don't you know — listen to me, now — don't you know who that Fat Lady really is? . . . Ah, buddy. Ah, buddy. It's Christ Himself. Christ Himself, buddy."

"Inside most people there's a feeling of being separate — separated from everything. … And they're not. They're part of absolutely everyone, and everything."

"There are many monisms. What they share is that they attribute oneness. Where they differ is in what they target and how they count. … Existence monism targets concrete objects and counts by tokens. This is the doctrine that exactly one concrete object token exists. Priority monism also targets concrete objects but counts by basic tokens. This is the doctrine that exactly one concrete object token is basic, and equivalent to the classical doctrine that the whole is prior to its (proper) parts. Neither existence nor priority monism is accorded much respect in contemporary metaphysics, nor are they always properly distinguished. Indeed, the tradition associated with these doctrines has long been dismissed as being somewhere between obscure and ridiculous. But there are serious arguments for monism. Priority monism may especially deserve serious reconsideration, of a kind that it is only now beginning to receive. … there are of course other historically important monisms, including substance monism. Substance monism targets concrete objects and counts by highest types. This is the doctrine that all concrete objects fall under one highest type (perhaps material, or mental, or some neutral underlying type: here the way divides)."

"No self is of itself alone. It has a long chain of intellectual ancestors. The "I" is chained to ancestry by many factors … This is not mere allegory, but an eternal memory."

"The multiplicity is only apparent. This is the doctrine of the Upanishads. And not of the Upanishads only. The mystical experience of the union with God regularly leads to this view, unless strong prejudices stand in the way."

"The Soul appears to be finite because of ignorance. When ignorance is destroyed the Self which does not admit of any multiplicity truly reveals itself by itself: like the Sun when the clouds pass away."

"Like bubbles in the water, the worlds rise, exist and dissolve in the Supreme Self, which is the material cause and the prop of everything."

"He who renouncing all activities, who is free of all the limitations of time, space and direction, worships his own Atman which is present everywhere, which is the destroyer of heat and cold, which is Bliss-Eternal and stainless, becomes All-knowing and All-pervading and attains thereafter Immortality."

"In Sikhism epistemological idealism also leads to metaphysical idealism. Sikhism starts with plurality of objects and ends in monism. It evolves a comprehensive metaphysical system of absolute dynamic non-dualist view of the Reality."

"In the context of Sikhism it [Metaphysical monism] considers atman (spiritual element) and body (material element) as inseparable aspects of a single spiritual cosmic spiritual continuum."

"Sikhism lays more emphasis on dynamism, non-dualism and social involvement. All these characteristics of the spiritual Reality imply that Sikhism puts forth a dynamic metaphysical system. In this dynamic concrete system the differences or modifications are not negated. There is another way to explain the nature of non-dual Reality in terms of them personal and personal unities."

"When you say that if I deny, that the operations of seeing, hearing, attending, wishing, &c., can be ascribed to God, or that they exist in Him in any eminent fashion, you do not know what sort of God mine is; I suspect that you believe there is no greater perfection than such as can be explained by the aforesaid attributes. I am not astonished; for I believe that, if a triangle could speak, it would say, in like manner, that God is eminently triangular, while a circle would say that the divine nature is eminently circular. Thus each would ascribe to God its own attributes, would assume itself to be like God, and look on everything else as ill-shaped. The briefness of a letter and want of time do not allow me to enter into my opinion on the divine nature, or the questions you have propounded. Besides, suggesting difficulties is not the same as producing reasons. That we do many things in the world from conjecture is true, but that our redactions are based on conjecture is false."

"My opinion concerning God differs widely from that which is ordinarily defended by modern Christians. For I hold that God is of all things the cause immanent, as the phrase is, not transient. I say that all things are in God and move in God, thus agreeing with Paul, and, perhaps, with all the ancient philosophers, though the phraseology may be different; I will even venture to affirm that I agree with all the ancient Hebrews, in so far as one may judge from their traditions, though these are in many ways corrupted. The supposition of some, that I endeavour to prove in the Tractatus Theologico-Politicus the unity of God and Nature (meaning by the latter a certain mass or corporeal matter), is wholly erroneous. As regards miracles, I am of opinion that the revelation of God can only be established by the wisdom of the doctrine, not by miracles, or in other words by ignorance."

"All is the Self or Brahman. The saint, the sinner, the lamb, the tiger, even the murderer, as far as they have any reality, can be nothing else, because there is nothing else."

"All knowledge that the world has ever received comes from the mind; the infinite library of the universe is in our own mind."

"All that is real in me is God; all that is real in God is I. The gulf between God and me is thus bridged. Thus by knowing God, we find that the kingdom of heaven is within us."

"This mysterious something has been called God, the Absolute, Nature, Substance, Energy, Space, Ether, Mind, Being, the Void, the Infinite — names and ideas which shift in popularity and respectability with the winds of intellectual fashion, of considering the universe intelligent or stupid, superhuman or subhuman, specific or vague. All of them might be dismissed as nonsense-noises if the notion of an underlying Ground of Being were no more than a product of intellectual speculation. But these names are often used to designate the content of a vivid and almost sensorily concrete experience — the "unitive" experience of the mystic, which, with secondary variations, is found in almost all cultures at all times. This experience is the transformed sense of self which I was discussing in the previous chapter, though in "naturalistic" terms, purified of all hocus-pocus about mind, soul, spirit, and other intellectually gaseous words."

"The really amazing thing is not that life on Earth is balanced on a knife-edge, but that the entire universe is balanced on a knife-edge. You see, even if you dismiss mankind as just a mere hiccup in the great scheme of things, the fact remains that the entire universe seems unreasonably suited to the existence of life — almost contrived — you might say a "put-up job"."

"Amazing fine tuning occurs in the laws that make this [complexity] possible. Realization of the complexity of what is accomplished makes it very difficult not to use the word 'miraculous' without taking a stand as to the ontological status of the word."

"As we survey all the evidence, the thought insistently arises that some supernatural agency - or, rather, Agency - must be involved. Is it possible that suddenly, without intending to, we have stumbled upon scientific proof of the existence of a Supreme Being? Was it God who stepped in and so providentially crafted the cosmos for our benefit?"

"The remarkable fact is that the values of these numbers seem to have been very finely adjusted to make possible the development of life."

"Would you not say to yourself, in whatever language supercalculating intellects use, "Some supercalculating intellect must have designed the properties of the carbon atom, otherwise the chance of my finding such an atom through the blind forces of nature would be less than 1 part in 1040000." Of course you would. … I have always been intrigued by the remarkable relation of the 7.65 Mev energy level in the nucleus of 12C to the 7.12 Mev level in 16O. If you wanted to produce carbon and oxygen in roughly equal quantities by stellar nucleosynthesis, these are the two levels you would have to fix … A common sense interpretation of the facts suggests that a super-intellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature."

"We are, by astronomical standards, a pampered, cosseted, cherished group of creatures. … If the Universe had not been made with the most exacting precision we could never have come into existence. It is my view that these circumstances indicate the universe was created for man to live in."

"Astronomy leads us to a unique event, a universe which was created out of nothing, one with the very delicate balance needed to provide exactly the conditions required to permit life, and one which has an underlying (one might say 'supernatural') plan."

"Wherever physicists look, they see examples of fine tuning."

"With so many errors and misjudgments, and with such a gross lack of understanding of the basic science we have seen exhibited by the supporters of supernatural fine-tuning, we can safely say that their motivation is more wishful thinking than truthful scientific inference. A proper analysis finds there is no evidence that the universe is fine-tuned for us."

"Most constants are adjusted with a deviation of one percent, which means that if the value differs by one percent everything collapses. Physicists can certainly claim that this is a fluke, but it must be acknowledged that this cosmological constant is adjusted to an accuracy of 1/10120. No one thinks that this is solely a fluke. It is the most extreme example of hyperfine regulation..."

"When I began my career as a cosmologist some twenty years ago, I was a convinced atheist. I never in my wildest dreams imagined that one day I would be writing a book purporting to show that the central claims of Judeo-Christian theology are in fact true, that these claims are straightforward deductions of the laws of physics as we now understand them. I have been forced into these conclusions by the inexorable logic of my own special branch of physics."

"The physicists are getting down to the nitty-gritty, they've really just about pared things down to the ultimate details, and the last thing they ever expected to happen is happening. God is showing through."

"How surprising it is that the laws of nature and the initial conditions of the universe should allow for the existence of beings who could observe it. Life as we know it would be impossible if any one of several physical quantities had slightly different values."

"A life-giving factor lies at the centre of the whole machinery and design of the world."

"Virgo Supercluster, the region where the Milky Way resides,"

"Hydra-Centaurus Supercluster, which contains the Great Attractor, the Laniakea central gravitational point,"

"Pavo-Indus Supercluster."

"The name Laniakea was suggested by Nawa‘a Napoleon, an associate professor of Hawaiian Language and chair of the Department of Languages, Linguistics, and Literature at Kapiolani Community College, a part of the University of Hawaii system. … The name honors Polynesian navigators who used knowledge of the heavens to voyage across the immensity of the Pacific Ocean."

"Astronomers have mapped the cosmic watershed in which our Milky Way Galaxy is a droplet. The massive structure, which the research team dubs the Laniakea Supercluster, extends more than 500 million light-years and contains 100,000 large galaxies. The work, published in the September 4th Nature, is the first to trace our local supercluster on such a large scale. It also provides a physical way to define what a supercluster actually is."

"Scientists previously placed the Milky Way in the Virgo Supercluster, but under Tully and colleagues' definition, this region becomes just an appendage of the much larger Laniakea, which is 160 million parsecs (520 million light years) across and contains the mass of 100 million billion Suns."

"This week, scientists add a new line to our planetary coordinates: the Laniakea galaxy supercluster. Do not bother googling the name. It really is brand new, coined by an international group of astronomers … Our place in the Universe, for so long one of the core mysteries of human existence that scientists and this journal are dedicated to unravelling, just got a little clearer. Laniakea, the scientists write, is our home supercluster, the one in which the Milky Way resides. What kind of home is it? It is big — some 160 million parsecs across. Although not as big as some superclusters, it is the largest in our local neighbourhood, which is surprisingly crowded given the vast emptiness of most of the cosmological void. It is a home that has been hiding in plain sight, colossal and all around us, yet unnoticed by previous astronomical surveys. …The name Laniakea has Hawaiian roots, and roughly translated means spacious heaven. It is a beautiful address to have. And one that comes just in time for the new school year and a new curious generation."

"For the first time, astronomers have outlined and named the network of galaxies that includes the Milky Way, adding a line to our cosmic address and further defining our place in the universe. They call it Laniakea, which is Hawaiian for “immense heaven.”"

"It’s like water dividing at a watershed, where it flows either to the left or right of a height of land."

"We have finally established the contours that define the supercluster of galaxies we can call home … This is not unlike finding out for the first time that your hometown is actually part of much larger country that borders other nations."

"This Voyager spacecraft was constructed by the United States of America. We are a community of 240 million human beings among the more than 4 billion who inhabit the planet Earth. We human beings are still divided into nation states, but these states are rapidly becoming a single global civilization. We cast this message into the cosmos. It is likely to survive a billion years into our future, when our civilization is profoundly altered and the surface of the Earth may be vastly changed. Of the 200 billion stars in the Milky Way galaxy, some - perhaps many - may have inhabited planets and spacefaring civilizations. If one such civilization intercepts Voyager and can understand these recorded contents, here is our message: This is a present from a small distant world, a token of our sounds, our science, our images, our music, our thoughts, and our feelings. We are attempting to survive our time so we may live into yours. We hope someday, having solved the problems we face, to join a community of galactic civilizations. This record represents our hope and our determination, and our good will in a vast and awesome universe."

"I say looking at the next 100 years that there are two trends in the world today. The first trend is toward what we call a type one civilization, a planetary civilization... The danger is the transition between type zero and type one and that’s where we are today. We are a type zero civilization. We get our energy from dead plants, oil and coal. But if you get a calculator you can calculate when we will attain type one status. The answer is: in about 100 years we will become planetary. We’ll be able to harness all the energy output of the planet earth. We’ll play with the weather, earthquakes, volcanoes. Anything planetary we will play with. The danger period is now, because we still have the savagery. We still have all the passions. We have all the sectarian, fundamentalist ideas circulating around, but we also have nuclear weapons. ...capable of wiping out life on earth. So I see two trends in the world today. The first trend is toward a multicultural, scientific, tolerant society and everywhere I go I see aspects of that birth. For example, what is the Internet? Many people have written about the Internet. Billions and billions of words written about the Internet, but to me as a physicist the Internet is the beginning of a type one telephone system, a planetary telephone system. So we’re privileged to be alive to witness the birth of type one technology... And what is the European Union? The European Union is the beginning of a type one economy. And how come these European countries, which have slaughtered each other ever since the ice melted 10,000 years ago, how come they have banded together, put aside their differences to create the European Union? ...so we’re beginning to see the beginning of a type one economy as well..."

"Since, in the long run, every planetary society will be endangered by impacts from space, every surviving civilization is obliged to become spacefaring — not because of exploratory or romantic zeal, but for the most practical reason imaginable: staying alive."

"This is the moment of the homogenization of the world, when the diversities of societies are eroding, when a global civilization is emerging. There are no exotic places left on Earth to dream about. And for this reason there remains an even greater and more poignant need today for a vehicle, a device, to get us somewhere else. Not all of us; only a few – to the deserts of the Moon, the ancient seacoasts of Mars, the forests of the sky. There is something comforting in the idea that one day a few representatives of our little terrestrial village might venture to the great galactic cities."

"... almost any inflationary model has the property that it produces not just one big bang but ultimately an infinite number of them, at an exponentially increasing rate — and that's what we we call eternal inflation. It's eternal only into the future — we don't think it's eternal into the past — so the word "eternal" is not quite being used in its dictionary definition ..."

"Our point is that we should be talking about the contemporary version of inflation, warts and all, not some defunct relic. Logically, if the outcome of inflation is highly sensitive to initial conditions that are not yet understood, as the respondents concede, the outcome cannot be determined. And if inflation produces a multiverse in which, to quote a previous statement from one of the responding authors (Guth), “anything that can happen will happen”—it makes no sense whatsoever to talk about predictions. Unlike the Standard Model, even after fixing all the parameters, any inflationary model gives an infinite diversity of outcomes with none preferred over any other. This makes inflation immune from any observational test."

"The definition of inflation is extraordinarily simple: it is any period of the Universe's evolution during which the scale factor, describing the size of the Universe, is accelerating. This leads to a very rapid expansion of the Universe, though perhaps a better way of thinking of this is that the characteristic scale of the Universe, given by the Hubble length, is shrinking relative to any fixed scale caught up in the rapid expansion. In that sense, inflation is actually akin to zooming in on a small part of the initial Universe."

"I think inflation is too flexible of an idea for that to make sense."

"The theory of cosmic inflation offers an attractive resolution of some of the great paradoxes in cosmology: why the universe is so large, flat and uniform on large scales, and how density variations arose. Inflation has rightly dominated cosmological thinking for the past two decades, helping stimulate the development of high-precision observational programmes. The survival of simple inflationary models in the face of an impressive observational onslaught has been interpreted as convincing evidence of the correctness of the basic idea. In this paper, I review inflation, but highlight its weaknesses, explaining my reasons for believing that a more complete theory may supersede inflation without necessarily incorporating it."

"As for inflation, scientists believe it occurred in the early universe at a temperature far above the energy of particle accelerators and relatively close to the energy at which quantum gravity becomes important. We do not yet have a convincing, detailed model of how and why inflation transpired because the models of particle physics that we have are not adequate at the huge energies of inflation. Understanding inflation requires a much better knowledge of particle physics than we have now, and possibly a full knowledge of string theory and quantum gravity."

"Is string theory a futile exercise as physics, as I believe it to be? It is an interesting mathematical specialty and has produced and will produce mathematics useful in other contexts, but it seems no more vital as mathematics than other areas of very abstract or specialized math, and doesn't on that basis justify the incredible amount of effort expended on it."

"... within , string theory is a complex subject. There are few large particle theory groups within major universities that do not have at least one person doing string theory. In total, there are probably a couple of thousand people at universities around the world whose mortgage is paid either by doing string theory, using string theory, working with tools made within string theory, solving problems using methods developed in string theory, or simply having their mental map of the world at the set by string theory."

"The real world as we know it happens at energies well below the Planck scale, so it is very well described by effective field theory. There is a continuous infinity of consistent effective field theories. Remarkably, only a measure zero fraction of those seem to be obtainable from string theory. These effective field theories arise as low energy descriptions of certain "vacua" of string theory, which in some approximation schemes can be thought of as solutions to the equations of motion for the compactification space."

"... one of the main beefs with the string theory is that it is so flexible you can get almost anything out of it. ... String theorists themselves are not too happy about it."

"String theorists, of course, continue to do whatever it is that string theorists do."

"String theory... resolves the central dilemma confronting contemporary physics—the incompatibility between quantum mechanics and general relativity—and that unifies our understanding of all of nature's fundamental material constituents and forces. But to accomplish these feats, ...string theory requires that the universe have extra space dimensions. ... Physicists have found that a key signal that a quantum mechanical theory has gone haywire is that particular calculations yield "probabilities" that are not within... acceptable range. For instance... infinite probabilities. ...string theory cures these infinities. ...a residual ...problem remains. In the early days ...calculations yielded negative probabilities ...so string theory appeared to be awash in its own quantum-mechanical hot water. ... Physicists found that the troublesome calculations were highly sensitive to the number of independent directions to which a string can vibrate. ...if strings could vibrate in nine independent spatial directions, all of the negative probabilities would cancel out. ... Kaluza and Klein provide a loophole... in addition to our familiar three... there are six other curled-up... rather than just postulating the existence of extra dimensions, as had been done by Kaluza, Klein, and their followers, string theory requires them."

"Currently, string theorists are in a position analogous to an Einstein bereft of the equivalence principle. ...[A] central organizing principle that embraces ...all ...features of the theory within one overarching and systematic framework ...is still missing."

"Now, this change from point-particles to strings that are so small they look like points might not sound like it would accomplish much. But it does. Superstring theory successfully merges general relativity and quantum mechanics."

"To build matter itself from geometry — that in a sense is what string theory does. It can be thought of that way, especially in a theory like the heterotic string which is inherently a theory of gravity in which the particles of matter as well as the other forces of nature emerge in the same way that gravity emerges from geometry. Einstein would have been pleased with this, at least with the goal, if not the realization. … He would have liked the fact that there is an underlying geometrical principle — which, unfortunately, we don’t really yet understand."

"Question 5. String Phenomenology Here there are many questions that can all be summarized by asking whether one can construct a totally realistic four-dimensional model which is consistent with string theory and agrees with observation?"

"The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory. ...each of the 24 modes in the Ramanujan function corresponds to a physical vibration of a string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. ...The string vibrates in ten dimensions because it requires... generalized Ramanujan functions in order to remain self-consistent."

"We actually have a candidate for the mind of God. The mind of God we believe is cosmic music, the music of strings resonating through 11 dimensional hyperspace. That is the mind of God."

"I have no idea whether the properties of the universe as we know it are fundamental or emergent, but I believe that the mere possibility of the latter should give the string theorists pause, for it would imply that more than one set of microscopic equations is consistent with experiment — so that we are blind to these equations until better experiments are designed — and also that the true nature of the microscopic equations is irrelevant to our world."

"String theory is, in fact, a textbook case of a Deceitful Turkey, a beautiful set of ideas that will always remain just barely out of reach. Far from a wonderful technological hope for a greater tomorrow, it is instead the tragic consequence of an obsolete belief system—in which emergence plays no role and dark law does not exist."

"One can ask whether the situation today in string theory is really as favorable as it was for field theory in the early 60's. It is difficult to know. Then, of course we had many more experiments to tell us how quantum field theories actually behave. To offset that, we have today more experience and greater mathematical sophistication."

"Consistent, relativistic string theories had already been written down in two, ten or twenty-six dimensions (the last being relevant only to bosonic strings) in the 1970s. A closed string is a loop which replaces a spacetime point. Its quantum oscillations correspond to particles of higher spins and higher masses, which may be arranged in a linear trajectory in a spin-versus-mass ... (Regge) plot. If the slope parameter of this trajectory — the only parameter in the theory — is adjusted to equal the Newtonian constant, one can show, quite miraculously, that in the zeroth order of the closed bosonic string there emerges from the string theory Einstein's gravity in its fullness! (The higher orders give modifications to Einstein's theory, with corrections which have a range of length = 10–33 cm.)"

"The most recent chapter in our new understanding of nonperturbative effects in string theory has been the incorporation of unstable branes and open string tachyons into the overall framework of the theory. It has turned out that an understanding of unstable D-branes is necessary to properly describe all D-branes. This is natural from the point of view of K-theory, where brane configurations which are equivalent under the annihilation of unstable branes are identified ... The long-mysterious tachyon instability of open string theory has finally been given a physical interpretation: it is the instability of the D-brane that supports the existence of open strings. The instability disappears in the tachyon vacuum, in which the D-brane decays. Moreover, the belief that D-branes are solitonic solutions of string theory has been confirmed: starting with the appropriate tachyonic field theory of unstable space-filling branes, one can describe lower dimensional D-branes as solitonic solutions. Lower dimensional D-branes are thereby essentially obtained as solitons of the tachyon field theory, so, in some sense, lower-dimensional D-branes can be thought of as being made of tachyons! It has also been shown that the physics of unstable D-branes is captured by string field theory, thus making it a candidate for a non-perturbative formulation of string theory capable of describing changes of the string background."

"... all of these caveats really work only against the idea that the final theory of nature is a quantum field theory. They leave open the view, which is in fact the point of view of my book, that although you can not argue that relativity plus quantum mechanics plus cluster decomposition necessarily leads only to quantum field theory, it is very likely that any quantum theory that at sufficiently low energy and large distances looks Lorentz invariant and satisfies the cluster decomposition principle will also at sufficiently low energy look like a quantum field theory. Picking up a phrase from Arthur Wightman, I’ll call this a folk theorem. At any rate, this folk theorem is satisfied by string theory, and we don’t know of any counterexamples."

"From the beginning it was clear that, despite its successes, the Standard Model of elementary particles would have to be embedded in a broader theory that would incorporate gravitation as well as the strong and electroweak interactions. There is at present only one plausible candidate for such a theory: it is the theory of strings, which started in the 1960s as a not-very-successful model of hadrons, and only later emerged as a possible theory of all forces."

"It's possible that the true structures in the underlying theory are something quite different — and the obvious candidate is strings. That direction, I think, is certainly worth working on. We don't whether that's the correct direction."

"String theory at its finest is, or should be, a new branch of geometry. ...I, myself, believe rather strongly that the proper setting for string theory will prove to be a suitable elaboration of the geometrical ideas upon which Einstein based general relativity."

"I would expect that a proper elucidation of what string theory really is all about would involve a revolution in our concepts of the basic laws of physics - similar in scope to any that occurred in the past."

"It's been said that string theory is part of the physics of the twenty-first century that fell by chance into the twentieth century. That's a remark that was made by a leading physicist about fifteen years ago. ...String theory was invented essentially by accident in a long series of events, starting with the Veneziano model... No one invented it on purpose, it was invented in a lucky accident. ...By rights, string theory shouldn't have been invented until our knowledge of some of the areas that are prerequisite... had developed to the point that it was possible for us to have the right concept of what it is all about."

"Generally speaking, all the really great ideas of physics are really spin-offs of string theory... Some of them were discovered first, but I consider that a mere accident of the development on planet earth. On planet earth, they were discovered in this order [general relativity, quantum field theory, superstrings, and supersymmetry]... But I don't believe, if there are many civilizations in the universe, that those four ideas were discovered in that order in each civilization."

"I feel that we are so close with string theory that—in my moments of greatest optimism—I imagine that any day, the final form of the theory may drop out of the sky and land in someone's lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory than anything we have had before and that well into the twenty-first century, when I am too old to have any useful thoughts on the subject, younger physicists will have to decide whether we have in fact found the final theory."

"String theory is not like anything else ever discovered. It is an incredible panoply of ideas about math and physics, so vast, so rich you could say almost anything about it."

"Unlike a Feynman graph, which is divided into different lines, which can represent particles of different types with different masses and spins, any part of a string world sheet is equivalent to any other so "there is only one string." Whatever particles there are going to be represent different states of vibration of one basic string. Also there are not any vertices in the string world sheet so we do not have the freedom to tell the string how to interact."

"... The way in which string theory addresses the cosmological constant problem can be summarized as follows: • Fundamentally, space is nine-dimensional. There are many distinct ways (perhaps 10500) of turning nine-dimensional space into three-dimensional space by compactifying six dimensions. ... • Distinct compactifications correspond to different three-dimensional metastable vacua with different amounts of vacuum energy. In a small fraction of vacua, the cosmological constant will be accidentally small. • All vacua are dynamically produced as large, widely separated regions in space-time. • Regions with Λ 1 contain at most a few bits of information and thus no complex structures of any kind. Therefore, observers find themselves in regions with Λ ≪ 1."

"The theoretical view of the actual universe, if it is in correspondence to our reasoning, is the following. The curvature of space is variable in time and place, according to the distribution of matter, but we may roughly approximate it by means of a spherical space. ...this view is logically consistent, and from the standpoint of the general theory of relativity lies nearest at hand [i.e. is most obvious]; whether, from the standpoint of present astronomical knowledge, it is tenable, will not be discussed here. In order to arrive at this consistent view, we admittedly had to introduce an extension of the field equations of gravitation, which is not justified by our actual knowledge of gravitation. It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [] is not introduced. The term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocity of the stars."

"Most constants are adjusted with a deviation of one percent, which means that if the value differs by one percent everything collapses. Physicists can certainly claim that this is a fluke, but it must be acknowledged that this cosmological constant is adjusted to an accuracy of 1/10120. No one thinks that this is solely a fluke. It is the most extreme example of hyperfine regulation... (Leonard Susskind)"

"Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life."

"After putting the finishing touches on general relativity in 1915, Einstein applied his new equations for gravity to a variety of problems. ... Despite the mounting successes of general relativity, for years after he first applied his theory to the most immense of all challenges—understanding the entire universe—Einstein absolutely refused to accept the answer that emerged from the mathematics. Before the work of Friedmann and Lemaître... Einstein, too, had realized that the equations of general relativity showed that the universe could not be static; the fabric of space could stretch or it could shrink, but it could not maintain a fixed size. This suggested that the universe might have had a definite beginning, when the fabric was maximally compressed, and might even have a definite end. Einstein stubbornly balked at this... because he and everyone else "knew" that the universe was eternal and, on the largest scales, fixed and unchanging. Thus, notwithstanding the beauty and successes of general relativity, Einstein reopened his notebook and sought a modification of the equations... It didn't take him long. In 1917 he achieved the goal by introducing a new term... the cosmological constant."

"The miracle of physics that I'm talking about here is something that was actually known since the time of Einstein's general relativity; that gravity is not always attractive. Gravity can act repulsively. Einstein introduced this in 1916... in the form of the cosmological constant, and the original motivation of modifying the equations of general relativity to allow this was because Einstein thought that the universe was static, and he realized that ordinary gravity would cause the universe to collapse if it was static. ...The fact that general relativity can support this gravitational repulsion, still being consistent with all the principles that general relativity incorporates, is the important thing which Einstein himself did discover.."

"In 1917 de Sitter showed that Einstein's field equations could be solved by a model that was completely empty apart from the cosmological constant—i.e. a model with no matter whatsoever, just dark energy. This was the first model of an expanding universe. although this was unclear at the time. The whole principle of general relativity was to write equations for physics that were valid for all observers, independently of the coordinates used. But this means that the same solution can be written in various different ways... Thus de Sitter viewed his solution as static, but with a tendency for the rate of ticking clocks to depend on position. This phenomenon was already familiar in the form of gravitational time dilation... so it is understandable that the de Sitter effect was viewed in the same way. It took a while before it was proved (by Weyl, in 1923) that the prediction was of a redshifting of spectral lines that increased linearly with distance (i.e. Hubble's law). ..."

"Even today, our picture of a world woven together by a gravitational force, and electromagnetic force, a strong force, and a weak force may be incomplete. Astronomers are gathering evidence that an additional fundamental interaction, a repulsive effect opposite to gravity, may be at work over vast distances and possibly changing with time."

"In Einstein's scheme there was no end, no outside. Shoot an arrow or a light beam infinitely far in any direction and it would come back and hit you in the butt. ...But there was a problem with the curved-back universe. Such a configuration was unstable, it would fly apart or collapse. Einstein didn't know about galaxies. He thought, and was reassured as much by the best astronomers of the time, that the universe was a static cloud of stars. To explain why his curved universe didn't collapse like a struck tent, therefore, he fudged his equations with a term he called the cosmological constant, which produced a long-range repulsive force to counteract cosmic gravity. It made the equations ugly and he never really liked it. That was in 1917, twelve years before Hubble showed that the universe was full of galaxies rushing away from each other."

"When the Higgs field froze and symmetry broke, Tye and Guth knew, energy had to be released... Under normal circumstance this energy went into beefing up the masses of particles like the weak force bosons that had been massless before. If the universe supercooled, however, all this energy would remain unreleased... according to Einstein, it was the density of matter and energy in the universe that determined the dynamics of space-time. ...The issue of vacuum energy had been a tricky problem for physics ever since Einstein. According to quantum theory, even the ordinary "true" vacuum should be boiling with energy—infinite energy... due to the the so-called s that produced the transient dense dance of s. This energy... could exert a repulsive force on the cosmos just like the infamous cosmological constant... quantum theories had reinvented it in the form of vacuum fluctuations. The orderly measured pace of the expansion of the universe suggested strongly that the cosmological constant was zero, yet quantum theory suggested it was infinite. Not even Hawking claimed to understand the cosmological constant problem... a trapdoor deep at the heart of physics."

"It's a term that Einstein recognized as allowed by his theory — he threw it in and then, in disgust, threw it out again ... It's back!"

"[Einstein's cosmological constant] is a name without any meaning. ...We have, in fact, not the slightest inkling of what it's real significance is. It is put in the equations in order to give the greatest possible degree of mathematical generality."

"There is no direct observational evidence for the curvature [of space], the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor that value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing the curvature at all. Historically the term containing the 'cosmological constant λ' was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of λ."

"It was early 1932, when Einstein and I both were at the California Institute of Technology in Pasedena, and we just decided to look for a simple relativistic model that agreed reasonably well with the known observational data, namely, the Hubble recession rate and the mean density of matter in the universe. So we took the space curvature to be zero and also the cosmological constant and the pressure term to be zero, and then it follows straightforwardly that the density is proportional to the square of the Hubble constant. It gives a value for the density that is high, but not impossibly high. That's about all there was to it. It was not an important paper, although Einstein apparently thought that it was. He was pleased to have a simple model with no cosmological constant. That's it."

"String theory seems to be incompatible with a world in which a cosmological constant has a positive sign, which is what the observations indicate."

"The most far-reaching implication of general relativity... is that the universe is not static, as in the orthodox view, but is dynamic, either contracting or expanding. Einstein, as visionary as he was, balked at the idea... One reason... was that, if the universe is currently expanding, then... it must have started from a single point. All space and time would have to be bound up in that "point," an infinitely dense, infinitely small "singularity." ...this struck Einstein as absurd. He therefore tried to sidestep the logic of his equations, and modified them by adding... a "cosmological constant." The term represented a force, of unknown nature, that would counteract the gravitational attraction of the mass of the universe. That is, the two forces would cancel... it is the kind of rabbit-out-of-the-hat idea that most scientists would label ad-hoc. ...Ironically, Einstein's approach contained a foolishly simple mistake: His universe would not be stable... like a pencil balanced on its point."

"Our particular laws are not at all unique. ...they could change from place to place and from time to time. The Laws of Physics are much like the weather... controlled by invisible influences in space almost the same way as that temperature, humidity, air pressure, and wind velocity control how rain and snow and hail form. ...The Landscape... is the space of possibilities... all the possible environments permitted by the theory. ...[T]heoretical physicists ...have always believed that the laws of nature are the unique, inevitable consequence of some elegant mathematical principle. ...the empirical evidence points much more convincingly to the opposite conclusion. The universe has more in common with a Rube Goldberg machine than with a unique consequence of mathematical symmetry. ...Two key discoveries are driving the paradigm shift—the success of inflationary cosmology and the existence of a small cosmological constant."

"At about the time of Malcadena's discovery, physicists started to become convinced (by cosmologists) that we live in a world with a nonvanishing cosmological constant [footnote: 10-23 in Planck units...[t]he incredible smallness... had fooled almost all physicists into believing that it didn't exist.], smaller by far than any other physical constant... the main determinant of the future history of the universe... also known as ... a thorn in the side of physicists for almost a century. ...If \Lambda is positive, the cosomological term creates a repulsive force that increases with distance; if it is negative, the new force is attractive; if \Lambda is zero, there is no new force and we can ignore it."

"The cosmological constant['s]... most important consequence: the repulsive force, acting at cosmological distances, causes space to expand exponentially. There is nothing new about the universe expanding, but without a cosmological constant, the rate of expansion would gradually slow down. Indeed, it could even reverse itself and begin to contract, eventually imploding in a giant cosmic crunch. Instead, as a consequence of the cosmological constant, the universe appears to be doubling in size about every fifteen billion years, and all indications are that it will do so indefinitely."

"The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity. It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties."

"It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. ...The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake."

"De Sitter proposed three types of nonstatic universes: the oscillating universes and the expanding universes of the first or second kiind. The main characteristic of the expanding "family" of the first kiind is that the radius is continually increasing from a definite initial time when it had the value zero. The universe becomes infinitely large after an infinite time. In the second kind... the radius possesses at the initial time a definite minimum value... in the Einstein model... the cosmological constant is supposed to be equal to the reciprocal of R2, whereas de Sitter computed for his interpretation the constant to be equal to 3/R2. Whitrow correctly points out the significant fact that in special relativity the cosmological constant is omitted..."

"A star does not evolve over its lifetime through each spectral type, as Russell once thought; rather, each star experiences its own distinct history, based on its mass at birth. Smaller stars, such as tiny s, will never reach the red-giant stage but just dully burn away like red-hot ovens. Stars that are born with appreciably more mass than our Sun, such as the white-hot O and B stars, will burn swiftly and eventually blow up, leaving behind a city-sized or even a black hole, a gravitational pit from which no light or matter can escape. ...the term black hole wasn't even coined until 1968. Yet the first tentative steps toward understanding this great metamorphosis, the distinct and striking stages in a star's life, were taken at the turn of the century. The elements in the stars themselves were telling the tale in the spectral messages they were telegraphing throughout the cosmos."

"After the nuclear fuel is used up, the star goes into a state of gravitational collapse. All parts of the star fall more or less freely inward... [Y]ou would imagine that the freefall could not continue... because the falling material would... arrive at the center... But Einstein's equations have the peculiar consequence... permanent freefall without ever reaching the bottom... what we call a black hole. ...[T]he space ...is so strongly curved that space and time become interchanged... time becomes space and... space becomes time. More precisely, if you observe... from the outside, you see... motion slow down and stop because the direction of time inside... is perpendicular to the direction of time as seen from the outside. The collapsing star can continue to fall freely forever..."

""Schwarzschild's solution"—revealed a stunning implication of general relativity. He showed that if the mass of a star is concentrated in a small enough spherical region, so that it's mass divided by its radius exceeds a particular critical value, the resulting space-time warp is so radical that anything, including light, that gets too close to the star will be unable to escape its gravitational grip. ...John Wheeler ...called them black holes—black because they cannot emit light, holes because anything getting too close falls into them, never to return. The name stuck."

"Black holes have the universe's most inscrutable poker faces. ...When you've seen one black hole with a given mass, charge, and spin (though you've learned these thing indirectly, through their effect on surrounding gas and stars...) you've definitely seen them all. ...black holes contain the highest possible ...a measure of the number of rearrangements of an object's internal constituents that have no effect on its appearance. ...Black holes have a monopoly on maximal disorder. ...As matter takes the plunge across a black hole's ravenous , not only does the black hole's entropy increase, but its size increases as well. ...the amount of entropy ...tells us something about space itself: the maximum entropy that can be crammed into a region of space—any region of space, anywhere, anytime—is equal to the entropy contained within a black hole whose size equals the region in question."

"A natural guess is that... a black hole's entropy is... proportional to its volume. But in the 1970s and Stephen Hawking discovered that this isn't right. Their... analyses showed that the entropy... is proportional to the area of its event horizon... less than what we'd naïvely guess. ...Berkenstein and Hawking found that... each square being one by one Planck length... the black hole's entropy equals the number of such squares that can fit on its surface... each Planck square is a minimal unit of space, and each carries a minimal, single unit of entropy. This suggests that there is nothing, even in principle, that can take place within a Planck square, because any such activity could support disorder and hence the Planck square could contain more than a single unit of entropy... Once again... we are led to the notion of an elemental spatial entity."

"[F]or a physicist, the upper limit to entropy... is a critical, almost sacred quantity. ...the Bekenstein and Hawking result tells us that a theory that includes gravity is, in some sense, simpler than a theory that doesn't. ...If the maximum entropy in any given region of space is proportional to the region's surface area and not its volume, then perhaps the true, fundamental degrees of freedom—the attributes that have the potential to give rise to that disorder—actually reside on the region's surface and not within its volume. Maybe... the universe's physical processes take place on a thin, distant surface that surrounds us, and all we see and experience is merely a projection of those processes. Maybe... the universe is rather like a hologram."

"The subject of this book is the structure of space-time on length-scales from 10-13 cm, the radius of an elementary particle, up to 1028 cm, the radius of the universe. ...we base our treatment on Einstein's General Theory of Relativity. This theory leads to two remarkable predictions about the universe: first, that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly, that there is a singularity in our past which constitutes, in some sense, a beginning to the universe."

"So Einstein was wrong when he said, "God does not play dice." Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can't be seen."

"I'm sorry to disappoint science fiction fans, but if information is preserved, there is no possibility of using black holes to travel to other universes. If you jump into a black hole, your mass energy will be returned to our universe but in a mangled form which contains the information about what you were like but in a state where it can not be easily recognized. It is like burning an encyclopedia. Information is not lost, if one keeps the smoke and the ashes. But it is difficult to read. In practice, it would be too difficult to re-build a macroscopic object like an encyclopedia that fell inside a black hole from information in the radiation, but the information preserving result is important for microscopic processes involving virtual black holes."

"Black holes ain't as black as they are painted. They are not the eternal prisons they were once thought. Things can get out of a black hole, both to the outside, and possibly to another universe. So if you feel you are in a black hole, don't give up. There's a way out."

"It is hard to understand how this infinitely dense singularity can evaporate into nothing. For matter inside the black hole to leak out into the universe requires that it travel faster than the speed of light."

"Is the reader feeling confused about the status of the black hole information paradox and black holes in general? So am I!"

"Experimentalists dream of some spectacular discovery such as the proof of the existence of black holes to justify the more than eight billion dollars it has cost to build the LHC."

"A large part of the relativity community is in denial - refusing even to contemplate the idea that black holes may not exist in nature, or seriously consider the idea that any kind of new matter such as the new putative dark energy can play a fundamental role in gravity theory."

"Hawking's intitial foray into quantum gravity was more modest than Wheeler's and other[s]... a sneak approach. He first wanted to know what the effect was of an ordinary, classic, curved-space gravitational field on a quantum system. He called this the semiclassical approach. Until that day, most quantum calculations had been done as if gravity didn't exist—they were hard enough without it in normal flat space-time... [Hawking accomplished this by] envisioning an "atom" whose nucleus was a catastrophically powerful black hole... Starobinsky ventured the opinion that rotating black holes would spray elementary particles. ...It was known from Penrose's work, among others, that you could extract energy from the spin of a black hole just like any other dynamo... in particles and radiation just like it did from a particle generator. ...But Hawking ...resolved to redo the calculation for himself ...he decided to warm up first, by calculating the rate of emission from a nonrotating quantum hole. He knew the answer should be no emission. ...his results were embarrassing. His imaginary black hole was spewing matter and radiation... he was reluctant to tell anybody but his closest friends; he was afraid Bekenstein would hear about it. ...It meant that holes had temperatures, just as Bekenstein's work implied."

"Even though a black hole is practically invisible, astronomers can infer its presence from the effects it has on spacetime itself. ...Andrea Ghez... uses s to study the motions of stars near the center of our galaxy. By watching how these stars move, she is really measuring the curvature of spacetime—the strength of gravity—in the heart of the Milky Way. ...Ghez realized that the stars are wheeling about an invisible, supermassive object that weighs more than two and a half million times as much as our sun. The black hole... dubbed ... cannot be seen directly, but Ghez was able to find it because of the effect it has on spacetime, on the stars orbiting it. Ghez's technique is quite similar to what Vera Rubin did when she made the first compelling case for ."

"I was very fortunate to know the great astrophysicist Subrahmanyan Chandrasekhar during his last years. Chandra, as we called him, was the first to discover that general relativity implied that stars above a certain mass would collapse into what we now call a black hole. Much later, he wrote a beautiful book describing the different solutions of the equations of general relativity that describe black holes. As I got to know him, Chandra shocked me by speaking of a deep anger toward Einstein. Chandra was upset that Einstein, after inventing general relativity, had abandoned this masterpiece, leaving it to others to struggle through it."

"There is no shortage of candidates for... baryonic . It may come in many forms—clouds of gas or dust, large planetlike objects, various forms of degraded stars, and black holes. ...MACHOS could include black holes and burned-out stars, such as s or s... Black holes are perhaps the most intriguing, and the most difficult to detect and quantify. As far back as the eighteenth century, scientists speculated about worlds so massive that nothing escaped their gravitational grip, not even light. In the early twentieth century, J. Robert Oppenheimer used Einstein's general theory of relativity to explain how a black hole might form: The black hole would warp adjacent space so deeply that the would exceed the speed of light... hence nothing... could leave... The center of the Milky Way emits intense gamma radiation—the death cry, perhaps, of stars falling into a black hole. Black holes may also be distributed in galactic halos, where they might constitute a substantial fraction of baryonic dark matter."

"According to Newton's law of gravity, every object in the universe attracts every other object... with a gravitational force... F = \frac{m M G}{R^2}... almost as famous as E = mc^2... On the left side is the force, F, between two masses... On the right side, the bigger mass is M and the smaller mass is m. ...The last symbol... G, is a numerical constant called Newton's constant. ...Ironically, Newton never knew the value of his own constant. ...G was too small to measure until the end of the eighteenth century. ...Cavindish found that the force between a pair of one-kilogram masses separated by one meter is approximately 6.6 x 10-11 newtons. (The Newton is... about one-fifth of a pound.) ...Newton had one lucky break... the special mathematical properties of the inverse square law. ...[B]y the miracle of mathematics, you can pretend that the entire mass is located at a single point. This... allowed Newton to calculate the ... Escape \; velocity = \sqrt{2MG/R} ... the bigger the mass [M] and the smaller the radius R, the larger the escape velocity. ...to compute the R_s... plug in the speed of light for the escape velocity... R_s = \frac{2MG}{c^2}... is proportional to the mass. That's all there is to dark stars... at the level that Laplace and Michell were able to understand them."

"[A]round 1967, Wheeler became very interested in the gravitationally collapsed objects that had described in 1917. At the time they were called black stars or dark stars. ...Wheeler began calling them black holes. At first the name was blackballed by the... '. ...the term ...was deemed obscene! But John fought it... Amusingly, John's next coinage was the saying "Black holes have no hair." ...he was making a very serious point about black hole horizons. ...[Each a] smooth ...perfectly regular, featureless sphere. Apart from their mass and rotational speed, every black hole was exactly like every other. Or so it was thought."

"Theory of relativity"

"It is now clear that astronomers came across indirect manifestations of the CMB long before the 1960s. In 1941, Andrew McKellar discovered cyanide molecules (HCN) in interstellar space. ... As the object of research, McKellar chose absorption lines caused by cyanide molecules in the star 'ε' of Ophiuchis. He concluded that these lines could only be caused by absorption of light by rotating molecules. Relatively simple calculations allowed McKellar to conclude that the excitation of rotational degrees of freedom of cyanide molecules required the presence of external radiation with an effective temperature of 2.3 K. Neither McKellar himself, nor anyone else, suspected that he had stumbled on a manifestation of the cosmic microwave background."

"The standard Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology is based on the cosmological principle, which posits that the universe is homogeneous and isotropic on large scales. This assumption is supported by the smoothness of the CMB, which has temperature fluctuations of only ∼ 1 part in 100,000 on small angular scales. These higher multipoles of the CMB angular power spectrum are attributed to Gaussian density fluctuations created in the early universe with a nearly scale-invariant spectrum, which have grown through gravitational instability to create the large-scale structure in the present universe. The dipole anisotropy of the CMB is however much larger, being ∼ 1 part in 1000 as observed in the heliocentric rest frame. This is interpreted as due to our motion with respect to the rest frame in which the CMB is isotropic, and is thus called the kinematic dipole."

"... we know in particular that for the first 380,000 years of the universe it was filled with a fireball. And we know this for sure because we've seen the fireball. In fact we've seen it , and we've take a photograph of it. This is called the cosmic microwave background radiation, but a much better name for it is the Fireball That Filled the Universe When It Was Much Younger."

"We seem to live in a remarkably economical X-ray universe, in that the observed cosmic X-ray background (CXRB) is produced with almost the least cosmic effort possible. It is not dominated by luminous obscured quasars thundering out huge amounts of power at z ≈ 2–4 but rather by moderate-luminosity, obscured AGNs at z ≈ 0.5–2."

"LOFAR is a new European radio interferometer operating at frequencies 15–240 MHz (van Haarlem et al., 2013) and represents a milestone in terms of radio survey speed compared to existing telescopes. The LOFAR Surveys Key Science Project aims to carry out a tiered survey. ... These surveys will open the low-frequency electromagnetic spectrum for exploration, allowing unprecedented studies of the radio population across cosmic time and opening up new parameter space for searches for rare, unusual objects such as high-z radio quasars in a systematic way. Perhaps, one of the most tantalizing prospects are the 21 cm absorption line measurements using LOFAR along sight lines toward z > 6 radio quasars."

"The continuum spectrum of a quasar can often be described, over a broad frequency range, by a power law of the form S\nu \propto \nu–\alpha ... where \alpha is the spectral index. \alpha = 0 corresponds to a flat spectrum, whereas \alpha = 1 describes a spectrum in which the same energy is emitted in every logarithmic frequency interval."

"Quasars were several hundred times more numerous when the universe was much younger. They were most numerous when the universe was about twenty percent of its current age, a time in the history of the universe sometimes called "cosmic noon"."

"General relativity"

"Where did you get this Christmas tree?" "Nowhere." "Did you cut down the Yggdrasil?" "Maybe..."

"An ash I know there stands, Yggdrasill is its name, a tall tree, showered with shining loam. From there come the dews that drop in the valleys. It stands forever green over Urðr's well."

"Does Yggdrasil drink from it because it is the Well of Wisdom, or is it the Well of Wisdom because Yggdrasil drinks from it?"

"I know that I hung on the windy tree Nine full nights, Pierced by a spear offered to Odin Myself to myself of which none knows Upon that tree Where its roots run..."

"Since 1974, the guiding principle for building extensions of the standard model has been the so-called desert hypothesis. ... Its premise is that there is no new physics between the energy scales of electroweak unification (109 GeV or 1 TeV) and the vicinity of the Planck mass MPl (1019 GeV). That implies an enormous "desert," 16 orders of magnitude wide, where one would expect to encounter nothing new. MPl is the mass at which a particle's Compton wavelength becomes equal to its Schwarzschild radius—a realm where one can't do without a quantum theory of gravity. ... The leading contender for the elaboration of the desert picture has been the supersymmetric extension of the standard model ..."

"Let me come finally to the question that is of more direct interest to the audience here: ‘what are the scales of string unification?’ or put more provocatively, ‘will we see strings and extra dimensions at the LHC?’ (this is also discussed in Peskin’s talk ...) The conventional (and conservative) hypothesis is that the string, compactification and Planck scales lie all to within two or three orders of magnitude from each other, and are hence far beyond direct experimental reach. The non-gravitational physics at lower energies is thus described by a 4d supersymmetric quantum field theory (SQFT), which must at least include in it the MSSM. This conventional hypothesis is supported by the following three solid facts : (i) Softly broken SQFTs can indeed be extrapolated consistently to near-Planckian energies without destabilizing the electroweak scale ; (ii) the hypothesis is (almost) automatic in the weakly-coupled heterotic string theory, and (iii) the minimal (or ‘desert’) string-unification assumption is in remarkable agreement with some of the measured low-energy parameters of our world."

"The most natural expectation away from asymptotic limits in moduli space of supergravity theories is the desert scenario, where there are few states between massless fields and the quantum gravity cutoff. In this paper we initiate a systematic study of these regions deep in the moduli space, and use it to place a bound on the number of massless modes by relating it to the black hole species problem. There exists a consistent sub-Planckian UV cutoff (the species scale) which resolves the black hole species problem without bounding the number of light modes. We reevaluate this in the context of supersymmetric string vacua in the desert region and show that even though heuristically the species scale is compatible with expectations, the BPS states of the actual string vacua lead to a stronger dependence of the cutoff scale on the number of massless modes. We propose that this discrepancy, which can be captured by the “BPS desert conjecture”, resurrects the idea of a uniform bound on the number of light modes as a way to avoid the black hole species problem. This conjecture also implies a stronger form of the Tadpole Conjecture, which leads to an obstruction in stabilizing all moduli semi-classically for large number of moduli in flux compactifications."

"Pythagorean mathematics, the theory of the four elements of Thales of Miletus, Epicurean materialism, Platonic idealism, Judaism, Islam, and modern science are rooted in Egyptian cosmogony and science."

"Miró... showed a series of canvases in which form submitted to strong colouring expressed a new two-dimensional cosmogony, in no way related to abstraction."

"Perhaps, with the introduction of more rational views of cosmogony and anthropology, and broader and more generous principles of psychology into our elementary text-books, through the union of a sounder physics with a larger metaphysics, our children's children may finally learn that there are inalienable animal as well as human rights, and that, in respect to the ties of moral obligation and the claims to kind and just treatment which they imply, not only "all nations of men," as Paul affirmed on Mar's Hill, but, as the Indian sage declared, "all living creatures are of one blood." "Metempsychosis", p. 164"

"The cosmogony of the Manava Dharmashastra is the broadest and most comprehensive we have thus far encountered."

"Urusvati knows that cosmogony and religion should be carefully studied. One should appreciate the words of the Great Pilgrim when He said that He had come to fulfill the previous Law. 170."

"Your accepted conceptions of cosmogony — whether from the theological or scientific standpoints —do not enable you to solve a single anthropological or even ethical problem and they stand in your way whenever you attempt to solve the problem of the races on this planet... Go on saying, Our planet and man were created — and you will be fighting against hard facts for ever, analyzing and losing time over trifling details—unable to even grasp the whole. But once admit that... both planets and man are — states for a given time; that their present appearance — geological and anthropological — is transitory and but a condition concomitant of that stage of evolution at which they have arrived in the descending cycle — and all will become plain. You will easily understand what is meant by the one and only element or principle in the universe and that androgynous; the seven-headed serpent Ananda of Vishnu, the Nag around Buddha, the great dragon eternity biting with its active head, its passive tail, from the emanations of which spring worlds, beings and things. You will comprehend the reason why the first philosopher proclaimed all — maya..."

"If Gods are made in the image of men, cosmogonies reflect the forms of terrestrial states. In an empire ruled absolutely by one man the notion of an universe under the control of a single God seemed obvious and reasonable.... The Christian God was a magnified and somewhat flattering portrait of Tiberius and Caligula."

"Radha’s elevated status, her role as a cosmic queen equal to or superior Krishna giving her a central role in the cosmogony in the Brahma Vivarta Purana... As creator of the universe we find Radha playing a role that is extremely atypical of her earlier history, the role of a mother. In the Brahma Vaivarta Purana, however, she is often called by names that suggest that her motherly role, vis-à-vis the created world. She is called mother of Vishnu, mother of the world, and mother of all."

"Two principles, according to the Settembrinian cosmogony, were in perpetual conflict for possession of the world: force and justice, tyranny and freedom, superstition and knowledge; the law of permanence and the law of change, of ceaseless fermentation issuing in progress."

"Uru and Svati are found in cosmogony. The signs of approaching Aquarius and its combination with Saturn are again being repeated. One can see once more how the cosmogony of the Atlanteans was on the right path. Not only was the chemism of the rays known at that time, but also the actual cooperation of the luminaries. After long wanderings, humanity again approaches just that. 516."

"Amid all the beliefs of Europe, and of Asia, that of the Indian Brahmins seems to me infinitely the most alluring. And the reason why I love the Brahmin more than the other schools of Asiatic thought is because it seems to me to contain them all. Greater than all European philosophies, it is even capable of adjusting itself to the vast hypotheses of modern science. Our Christian religions have tried in vain, when there were no other choice open to them, to adapt themselves to the progress of science. But after having allowed myself to be swept away by the powerful rhythm of Brahmin thought, along the curve or life, with its movement of alternating ascent and return, I come back to my own century, and while finding therein the immense projections of a new cosmogony, offspring of the genius of Einstein, or deriving freely from the discoveries, I yet do not feel that I enter a strange land. I yet can hear resounding still the cosmic symphony of all those planets which forever succeed each other, are extinguished and once more illumined, with their living souls, their humanities, their gods – according to the laws of the eternal To Become, the Brahmin Samsara – I hear Siva dancing, dancing in the heart of the world, in my own heart."

"Man hath ever made a cosmogony in keeping with his views in physics; a scheme of government in keeping with his cosmogony; a theory of ethics in keeping with his government, and a code of law and theology in keeping with his ethics. Every perception of the human mind modifies human practice. Science is but the theory of art."

"Extra spatial dimensions could be a good thing. ... In a nongravitational theory, the spacetime geometry is a rigid background on which the dynamics takes place. In that setup, the fact that we observe four-dimensional Minkowski spacetime is a compelling argument to formulate the theory in that background geometry. As you know very well, this is part of the story of the Standard Model. However, in a gravitational theory that abides by the general principles laid out by Einstein, the spacetime geometry is determined by the dynamical equations. In such a setup extra dimensions can make sense provided that the equations of the theory have a solution for which the geometry is the product of four-dimensional Minkowski spacetime and a compact manifold that is sufficiently small to have eluded detection. It turns out that there are many such solutions. Moreover, the details of the compact manifold play a crucial role in determining the symmetries and particle content of the effective low-energy theory in four dimensions, even when the compact dimensions are much too small to observe directly."

"Why try to unite the four forces in a single theory? Why not simply use Einstein’s theory of general relativity to govern big things and quantum mechanics for little ones? Some concepts, such as the Big Bang or how black holes form, live in both domains. When we combine equations of the four forces to describe these ideas, our answers usually end up being either zero or infinity. … Here’s where string theory comes to the rescue. By adding seven hidden dimensions to the familiar three and another for time, plus antiparticles and a mirror set of particles called superparticles, the math starts to make sense. The force of gravity is diluted because it permeates into one or more of the hidden dimensions. Dark matter and dark energy also may invisibly shape our universe from these phantom dimensions."

"Both ancient and medieval observers had noted that in many respects nature appeared to be governed by the principle of simplicity, and they had recorded the substance of their observations to this effect in the form of proverbial s which had become currently accepted bits of man's conception of the world. That falling bodies moved perpendicularly towards the earth, that light travelled in straight lines, that projectiles did not vary from the direction in which they were impelled, and countless other familiar facts of experience, had given rise to such common proverbs as: 'Natura semper agit per vias brevissimas'; 'natura nihil facit frustra'; 'natura neque redundat in superfluis neque deficit in necessariis' [Nature always acts by the shortest path; nature does nothing in vain; nature never overflows into the unnecessary, nor is she deficient in what is necessary]. This notion, that nature performs her duties in the most commodious fashion, without extra labour, would have tended to decrease somewhat the repulsion which most minds must have felt at Copernicus; the cumbrous epicycles had been decreased in number, various irregularities in the Ptolemaic scheme were eliminated... That such a tremendous shift in the point of reference could be legitimate was a suggestion quite beyond the grasp of people trained for centuries to think in terms of a homocentric philosophy and a geocentric physics. ...Copernicus could take the step because... he had definitely placed himself in... [the] dissenting Platonic movement. ...It was no accident that he became familiar with the remains of the early Pythagoreans, who almost alone among the ancients had ventured to suggest a non-geocentric astronomy."

"Ptolemy... against the champions of this or that cosmology of the heavens... had dared to claim that it is legitimate to interpret the facts of astronomy by the simplest geometrical scheme which will 'save the phenomena,' no matter whose metaphysics might be upset. His conception of the physical structure of the earth, however, prevented him from carrying through in earnest this principle of relativity, as his objections to the hypothesis that the earth moves amply show."

"Galileo had the experience of beholding the heavens as they actually are for perhaps the first time, and wherever he looked he found evidence to support the Copernican system against the Ptolemaic, or at least weaken the authority of the ancients. This shattering experience—of observing the depths of the universe, of being the first mortal to know what the heavens are actually like—made so deep an impression... that it is only by considering the events of 1609... that one can understand the subsequent direction of his life."

"The Greek philosopher, Plato, in the fourth century B.C. asked his students if they could devise a theory or explanation to explain this erratic planetary motion using some form of circular motion. Being keen observers, the Greeks came up with the most logical and obvious conclusions; namely, that the earth was the center about which the sun, the moon, planets, and the stars rotated. This model of the universe is called a geocentric or earth-centered model. It satisfactorily explained the daily motion of the stars and sun by assuming that they were attached to invisible crystalline spheres that rotated about the earth. The axis of the sphere of the sun was tilted with respect to that of the stars to account for the variation of the sun's height at with the various seasons. Since the sun appears to move through the stars and was brighter, it was assumed to be nearer to the earth than the stars. The spheres of the Moon, Mercury, and Venus were placed within the sphere of the sun while those of Mars, Jupiter, and Saturn were placed outside the sphere of the sun but within the sphere of the stars."

"The fundamental core of contemporary Darwinism, the theory of DNA-based reproduction and evolution, is now beyond dispute among scientists. It demonstrates its power every day, contributing crucially to the explanation of planet-sized facts of geology and meteorology, through middle-sized facts of ecology and agronomy, down to the latest microscopic facts of genetic engineering. It unifies all of biology and the history of our planet into a single grand story. Like Gulliver tied down in Lilliput, it is unbudgable, not because of some one or two huge chains of argument that might — hope against hope — have weak links in them, but because it is securely tied by thousands of threads of evidence anchoring it to virtually every other area of human knowledge. New discoveries may conceivably lead to dramatic, even "revolutionary" shifts in the Darwinian theory, but the hope that it will be "refuted" by some shattering breakthrough is about as reasonable as the hope that we will return to a geocentric vision and discard Copernicus."

"The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein's special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein's amazing revelations have likewise sunk into the commonplaces of educated thought."

"Fundamental changes in science have always been accompanied by deeper digging toward the philosophical foundations. Changes like the transition from the Ptolemaic to the Copernican system, from Euclidean to non-Euclidean geometry, from Newtonian to relativistic mechanics... have brought about a radical change in our common-sense explanation of the world. From all these considerations everyone who is to get a satisfactory understanding of twentieth century science will have to absorb a good deal of philosophical thought. But he will soon feel the same thing holds for a thorough understanding of the science which originated in any period of history."

"Persisting in their original resolve to destroy me and everything mine by any means they can think of, these men are aware of my views in astronomy and philosophy. They know that as to the arrangement of the parts of the universe, I hold the sun to be situated motionless in the center of the revolution of the celestial orbs while the earth revolves about the sun. They know also that I support this position not only by refuting the arguments of Ptolemy and Aristotle, but by producing many counter-arguments; in particular, some which relate to physical effects whose causes can perhaps be assigned in no other way. In addition there are astronomical arguments derived from many things in my new celestial discoveries that plainly confute the Ptolemaic system while admirably agreeing with and confirming the contrary hypothesis."

"It may be true that and (not science and evolution) are among the causes of atheism and materialism. It is at least equally true that biblical literalism, from its earlier flat-earth and geocentric forms to its recent young-earth and flood-geology forms, is one of the major causes of atheism and materialism. Many scientists and intellectuals have simply taken the literalists at their word and rejected biblical materials as being superseded or contradicted by modern science. Without having in hand a clear and persuasive alternative, they have concluded that it is nobler to be damned by the literalists than to dismiss the best testimony of research and reason. Intellectual honesty and integrity demand it."

"The odd thing about this story is that the heliocentric view was known in Europe long before Copernicus but, for various reasons, was totally ignored by the "established" dogma... All this time all kinds of absurdities were written about the heavens, the celestial spheres, the Empyrean and so on, which constituted the “established” view. And all the time the real knowledge was there and all those schoolmen, could, with some practical observation and sensible application of Mathematics, have found out that the Ptolemaic system was not true. But they did not: they preferred to argue about such weighty matters as how many angles could sit on the point of a pin. And when the proofs were presented to them in black and white, hard and irrefutable mathematical demonstrations, they still rejected them preferring the comforts of the ‘‘established” dogma. Theology (and Church interests) decided what was acceptable, not Mathematics."

"I shall try to sum up the main obstacles which arrested the progress of science for such an immeasurable time. The first was the splitting of the world into two spheres, and the mental split which resulted from it. The second was the geocentric dogma, the blind eye turned on the promising line of thought which had started with the Pythagoreans and stopped abruptly with Aristarchus of Samos. The third was the dogma of uniform motion in perfect circles. The fourth was the divorcement of science from mathematics. The fifth was the inability to realize that a body at rest tended to stay at rest, a body in motion tended to stay in motion. The main achievement of the first part of the scientific revolution was the removal of these five cardinal obstacles. This was done chiefly by three men: Copernicus, Kepler and Galileo. After that, the road was open to the Newtonian synthesis; from there on the journey led with rapidly gaining speed to the atomic age."

"Joseph Ratzinger has stood still because as a Bavarian Catholic in the Hellenistic tradition, interpreted in Roman terms, he wanted to stand still. To this degree he represented and represents a different basic model of theology and church, as different from mine as in astronomy Ptolemy's geocentric picture of the world is different from Copernicus' heliocentric picture."

"Let us... examine the point on which Newton, apparently with sound reasons, rests his distinction of absolute and relative motion. If the earth is affected with an absolute rotation about its axis, centrifugal forces are set up in the earth: it assumes an oblate form, the acceleration of gravity is diminished at the equator, the plane of Foucault's pendulum rotates, and so on. All these phenomena disappear if the earth is at rest and the other heavenly bodies are affected with absolute motion round it, such that the same relative rotation is produced. This is, indeed, the case, if we start ab initio from the idea of absolute space. But if we take our stand on the basis of facts, we shall find we have knowledge only of relative spaces and motions. Relatively, not considering the unknown and neglected medium of space, the motions of the universe are the same whether we adopt the Ptolemaic or the Copernican mode of view. Both views are, indeed, equally correct; only the latter is more simple and more practical. The universe is not twice given, with an earth at rest and an earth in motion; but only once, with its relative motions, alone determinable. It is, accordingly, not permitted us to say how things would be if the earth did not rotate. We may interpret the one case that is given us, in different ways. If, however, we so interpret it that we come into conflict with experience, our interpretation is simply wrong. The principles of mechanics can, indeed, be so conceived, that even for relative rotations centrifugal forces arise."

"Talk of the sublime, the exalted, the eternal, the passionate, of glory, challenge, or majesty fills some of us with bewilderment, discomfort, and embarrassment; others with sour resentment or scornful disbelief. To reinstate such values seems to us like trying to reinstate Ptolemaic astronomy—equally misguided, incomprehensible, and inimical to our perceived interests."

"It became clear that our Galaxy is only one system among many, and that the universe is far vaster than the particular stellar system to which the Sun and planets belong. Since then developments have been more rapid than at any time since the days of Copernicus, Digges and Bruno when the geocentric hypothesis of the cosmos received its death-blow."

"These seven bodies were the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn, all of which were documented by the Babylonians over three thousand years ago. Until the sixteenth century, the most commonly held view was that the Earth was at the centre of the Universe and that the seven bodies revolved around the Earth."

"There seems to be a vast landscape of possible universes. ... We live in one in which life is possible, but if the universe were only slightly different, beings like us could not exist. What are we to make of this fine-tuning? Is it evident that the universe, after all, was designed by a benevolent creator? Or does science offer a different explanation?"

"The old cosmological constant problem is to understand why the is so small; the new problem is to understand why it is comparable to the present mass density. ... does not help with either; anthropic considerations offer a possibility of solving both. In theories with a that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else."

"Once one starts to admit anthropic interpretations of fine-tuning problems like the cosmological constant, it is clear that such a proposal might be made for other fine-tuning problems, such as the problem of the Higgs boson mass. Certainly, we would not be here if the Higgs boson mass, and hence also the and and and masses, were greatly bigger. If they were near the , for example, any collection of more than a few elementary particles would collapse into a Black Hole. More generally, if the elementary particle masses were scaled up by a factor N, the number of elementary particles in a star or planet would scale down like N–3, and for very modest N the stars would stop shining."

"Whitrow... proposed an anthropic resolution of the venerable philosophical question Why physical space has three dimensions? (arguing that with a space of different dimensionality there would be no living being to pose the question) and, similarly to [Grigory Moiseevich] Idlis, alluded around 1955 to an anthropic explanation of the size of the observable universe. Anyway, he never published these last ideas, which were developed years later by Wheeler. The only reference to Whitrow’s argument that appeared in print during the 1950s seems to be that due to the philosopher of religion Eric Lionel Mascall, who attributed to the English’s mathematician thatit may be necessary for the universe to have the enormous size and complexity which modern astronomy has revealed, in order for the earth to be a possible habitation for living beings."

"The gap between a dumb and a clever person may appear large from an anthropocentric perspective, yet in a less parochial view the two have nearly indistinguishable minds."

"To say that Nature displays intelligence doesn't make you a Christian fundamentalist. Einstein said as much, and a fascinating theory called the anthropic principle has been seriously considered by Stephen Hawking, among others."

"The really amazing thing is not that life on Earth is balanced on a knife-edge, but that the entire universe is balanced on a knife-edge. You see, even if you dismiss mankind as just a mere hiccup in the great scheme of things, the fact remains that the entire universe seems unreasonably suited to the existence of life — almost contrived — you might say a "put-up job"."

"Matter in quantum mechanics is not an inert substance but an active agent, constantly making choices between alternative possibilities according to probabilistic laws. ...It appears that mind, as manifested by the capacity to make choices, is to some extent inherent in every electron. ...Our brains appear to be devices for the amplification of the mental component of the quantum choices made by molecules inside our heads. ...There is evidence from peculiar features of the laws of nature that the universe as a whole is hospitable to the growth of mind. ...an extension of the Anthropic Principle up to a universal scale."

"Science does not accept Aristotelian styles of explanation, that a stone falls because of its nature... it likes to be on Earth... Within science, all causes must be local and instrumental. Purpose is not acceptable as an explanation... Action at a distance, either in space or time, is forbidden. Especially, teleological influences of final goals upon phenomena are forbidden. ...The choice of laws of nature, and the choice of initial conditions for the universe, are questions belonging to meta-science and not to science. Science is restricted to the explanation of phenomena within the universe. Teleology is not forbidden when explanations go beyond ...into meta-science. The most familiar example of a meta-scientific explanation is the so-called Anthropic Principle. ...It accords with the spirit of modern science that we have two complementary styles of explanation, the teleological style allowing a role for purpose in the universe at large, and the non-teleological style excluding purpose..."

"What we hear about eternal inflation or the string landscape, seems somehow unavoidably to lead to some kind of multiverse. However, it seems to me there is a fundamental problem there. Once of course you have the multiverse, then you can start playing around and try to find probability or getting to the anthropic principle, or whatever. But the point is that the picture is essentially a classical one, and it is difficult to see that if you have many universes, coming essentially with an inflationary state, that there would not be plenty of horizons in this. Now the quantum mechanics of horizons is, I think, perfectly not understood. The simplest example is the black hole, where after all nobody knows really if the problem lies in the singularity or if it lies really already in the horizon."

"Why was there a Big Bang? What, if anything, came before? What mechanisms generated the exponential inflation of the early Universe? What are dark matter and dark energy, which dominate today's Universe? How did the first stars and galaxies form? Why are the fundamental constants of nature what they are? Must we depend on the Cosmic Anthropic Principle to 'answer' such questions? Is our Universe unique, or must we appeal to a Multiverse? What will be the ultimate fate of our Universe?"

"I think the Anthropic Cosmological Principle brings to us an idea perhaps as old as humanity itself: that we are not at all just an accidental anomaly, the microscopic caprice of a tiny particle whirling in the endless depth of the universe. Instead, we are mysteriously connected to the entire universe, we are mirrored in it, just as the entire evolution of the universe is mirrored in us."

"Until recently, it might have seemed that we were an unhappy bit of mildew on a heavenly body whirling in space among many that have no mildew on them at all. this was something that classical science could explain. Yet, the moment it begins to appear that we are deeply connected to the entire universe, science reaches the outer limits of its powers. Because it is founded on the search for universal laws, it cannot deal with singularity, that is, with uniqueness. The universe is a unique event and a unique story, and so far we are the unique point of that story. But unique events and stories are the domain of poetry, not science. With the formulation of the Anthropic Cosmological Principle, science has found itself on the border between formula and story, between science and myth. In that, however, science has paradoxically returned, in a roundabout way, to man, and offers him — in new clothing — his lost integrity. It does so by anchoring him once more in the cosmos."

"What makes the Anthropic Principle and the Gaia Hypothesis so inspiring? One simple thing: Both remind us, in modern language, of what we have long suspected, of what we have long projected into our forgotten myths and perhaps what has always lain dormant within us as archetypes. That is, the awareness of our being anchored in the earth and the universe, the awareness that we are not here alone nor for ourselves alone, but that we are an integral part of higher, mysterious entities against whom it is not advisable to blaspheme. This forgotten awareness is encoded in all religions. All cultures anticipate it in various forms. It is one of the things that form the basis of man's understanding of himself, of his place in the world, and ultimately of the world as such."

"There ought to be something very special about the boundary conditions of the universe and what can be more special than that there is no boundary?"

"... when non-perturbative phenomena are included, there is no problem from the string theory point of view in effecting continuous transitions between Calabi-Yau spaces of different topology. This shows that stringy ideas about geometry are really more general than those found in classical Riemannian geometry. The moduli space of Calabi-Yau manifolds should thus be regarded as a continuously connected whole, rather than a series of different ones individually associated with different topological objects ... Thus, questions about the topology of Calabi-Yau spaces must be treated on the same footing as questions about the metric on the spaces. That is, the issue of topology is another aspect of the the moduli fields. These considerations are relevant to understanding the ground state of the universe."

"Many scientists are still ashamed of using the . Just as the friends of were afraid of using the name , the opponents of the anthropic principle often say that they do not want to use the 'A' in their research."

"The theory of the inflationary multiverse changes the way we think about our place in the world. According to its most popular version, our world may consist of infinitely many exponentially large parts, exhibiting different sets of low-energy laws of physics. Since these parts are extremely large, the interior of each of them behaves as if it were a separate universe, practically unaffected by the rest of the world. This picture, combined with the theory of eternal inflation and anthropic considerations, may help to solve many difficult problems of modern physics, including the cosmological constant problem."

"What the anthropic principle depends upon is the idea that whatever is the nature of the universe, or universe portion that we see about us, being subject to whatever dynamical laws govern its actions, this must be strongly favourable to our very existence."

"Whereas originally the hopes for string theory, and its descendants, were that some kind of uniqueness would be arrived at, whereby the theory would supply mathematical explanations for the measured numbers of experimental physics, the string theorists were driven to find refugee in the strong anthropic argument in an attempt to narrow down an absolutely vast number of alternatives. In my own view, this a very sad and unhelpful place for a theory to find itself."

"In fact Sax was suspicious of all the current cosmology, placing humanity as it did right at the center of things, time after time. It suggested to Sax that all these formulations were artifacts of human perception only, the strong anthropic principle seeping into everything they saw, like color."

"By inclination, Weinberg is an extreme reductionist. But he is also a realist and acknowledges when something is not working the way he might want it to. In 1987 the arch-reductionist concluded that certain facts seemed to be inconsistent with any explanation based on the usual kind of mathematical reasoning. Instead, it seemed they might be true only because if they were not, we observers could not be here to observe them. Weinberg undoubtedly disliked such anthropic-principle explanations. But when, to his disappointment, he found that the anthropic principle might explain the apparent vanishing of the cosmological constant, he said so loudly and clearly, despite the great hostility of the physics community toward the principle."

"The old cosmological constant problem is to understand why the is so small; the new problem is to understand why it is comparable to the present mass density. ... does not help with either; anthropic considerations offer a possibility of solving both. In theories with a that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else."

"We are participators in bringing into being not only the near and here but the far away and long ago. We are in this sense, participators in bringing about something of the universe in the distant past and if we have one explanation for what's happening in the distant past why should we need more?"

"Once one starts to admit anthropic interpretations of fine-tuning problems like the cosmological constant, it is clear that such a proposal might be made for other fine-tuning problems, such as the problem of the Higgs boson mass. Certainly, we would not be here if the Higgs boson mass, and hence also the and and and masses, were greatly bigger. If they were near the , for example, any collection of more than a few elementary particles would collapse into a Black Hole. More generally, if the elementary particle masses were scaled up by a factor N, the number of elementary particles in a star or planet would scale down like N–3, and for very modest N the stars would stop shining."

"Blow, winds, and crack your cheeks! rage! blow! You cataracts and hurricanoes, spout Till you have drench’d our steeples, drown’d the cocks! You sulphurous and thought-executing fires, Vaunt-couriers to oak-cleaving thunderbolts, Singe my white head! And thou, all-shaking thunder, Smite flat the thick rotundity o’ the world! Crack nature’s moulds, all germins spill at once That make ingrateful man!"

"The soul, secur’d in her existence, smiles At the drawn dagger, and defies its point. The stars shall fade away, the sun himself Grow dim with age, and nature sink in years, But thou shalt flourish in immortal youth, Unhurt amidst the war of elements, The wreck of matter, and the crush of worlds."

"Some say the world will end in fire, Some say in ice. From what I’ve tasted of desire I hold with those who favor fire. But if it had to perish twice, I think I know enough of hate To know that for destruction ice Is also great And would suffice."

"This is the way the world ends This is the way the world ends This is the way the world ends Not with a bang but a whimper."

"This circumstance of an expanding universe is irritating. ...To admit such possibilities seems senseless to me."

"If a distant galaxy is moving relative to us, its entire is Doppler-shifted in frequency. Its s are displaced relative to those of stationary light sources. Thanks to this effect, we know that distant galaxies recede from the solar system at speeds proportional to their distances from us. That's the effect that told us of the expanding universe, and of its birth, long ago, in the Big Bang."

"All kinds of questions remain. Many have to do with cosmology. How did the universe originate? How did the galaxies become distributed in space like the suds in the kitchen sink..? Why is the cosmological constant apparently very tiny but non-zero and has a peculiar value that leads the universe to expand more rapidly?"

"All of this picture of the expansion is exciting, pleasant, coherent, well in order. But what if the s are not to be interpreted by the Doppler-Fizeau law in the classical mechanical view, or general relativistically, by the fact that the ratio of the of a photon (as measured by a co-moving observer) to the space radius of curvature is independent of ? Not speaking of quasars, the first indications for non-Doppler redshifts for a galaxy have been provided... What if not all galaxies were formed at the dawn of the Big Bang; what if some are being formed now? Then, at least, the can be anything larger than the age of our own Galaxy..."

"Red-shifts are produced either in the nebulae, where the light originates, or in the intervening space through which the light travels. If the source is in the nebulae, then red-shifts are probably velocity-shifts and the nebulae are receding. If the source lies in the intervening space, the explanation of red-shifts is unknown, but the nebulae are sensibly stationary."

"A book, too, can be a star, explosive material, capable of stirring up fresh life endlessly, a living fire to lighten the darkness, leading out into the expanding universe."

"The definition of inflation is extraordinarily simple: it is any period of the Universe's evolution during which the scale factor, describing the size of the Universe, is accelerating. This leads to a very rapid expansion of the Universe, though perhaps a better way of thinking of this is that the characteristic scale of the Universe, given by the Hubble length, is shrinking relative to any fixed scale caught up in the rapid expansion. In that sense, inflation is actually akin to zooming in on a small part of the initial Universe."

"One of the few authors to have explicitly connected the physical issue of the expansion of the universe with the philosophical topic of the metaphysical status of space is Gerald James Whitrow."

"In 1917 de Sitter showed that Einstein's field equations could be solved by a model that was completely empty apart from the cosmological constant—i.e. a model with no matter whatsoever, just . This was the first model of an expanding universe. although this was unclear at the time. The whole principle of general relativity was to write equations for physics that were valid for all observers, independently of the coordinates used. But this means that the same solution can be written in various different ways... Thus de Sitter viewed his solution as static, but with a tendency for the rate of ticking clocks to depend on position. This phenomenon was already familiar in the form of gravitational ... so it is understandable that the de Sitter effect was viewed in the same way. It took a while before it was proved (by Weyl, in 1923) that the prediction was of a redshifting of spectral lines that increased linearly with distance (i.e. ). ..."

"This model of the expanding universe I shall call the substratum. It achieves in the private Euclidean space of each fundamental observer the objects for which Einstein developed his closed spherical space. Although it is finite in volume, in the measures of any chosen observer, it has all the properties of an infinite space in that its boundary is forever inaccessible and its contents comprise an infinity of members. It is also homogeneous in the sense that each member stands in the same relation to the rest. This description of the substratum holds good in the scale of time in which the galaxies or fundamental particles are receding from one another with uniform velocities. This choice of the scale of time, together with the theory of equivalent time-keepers... makes possible the application of the Lorentz formulae to the private Euclidean spaces of the various observers. It thus brings the theory of the expanding universe into line with other branches of physics, which use the Lorentz formulæ and adopt Euclidean private spaces. ...[T]here is no more need to require a curvature for space itself in the field of cosmology than in any other department of physics. The observer at the origin is fully entitled to select a private Euclidean space in which to describe phenomena, and when he concedes a similar right to every other equivalent observer and imposes the condition of the same world-view of each observer, he is inevitably led to the model of the substratum which we have discussed."

"The ideas that prove to be of lasting interest are likely to build on the framework of the now standard world picture, the hot big bang model of the expanding universe. The full extent and richness of this picture is not as well understood as I think it ought to be, even among those making some of the most stimulating contributions to the flow of ideas."

"We should, of course, expect that any universe which expands without limit will approach the empty de Sitter case, and that its ultimate fate is a state in which each physical unit—perhaps each nebula or intimate group of nebulae—is the only thing which exists within its own observable universe."

"If the general picture, however, of a Big Bang followed by an expanding Universe is correct, what happened before that? Was the Universe devoid of all matter and then the matter suddenly somehow created? How did that happen? In many cultures, the customary answer is that a God or Gods created the Universe out of nothing. But if we wish to pursue this question courageously, we must of course ask the next question: where did God come from? If we decide that this is an unanswerable question, why not save a step and conclude that the origin of the Universe is an unanswerable question? Or, if we say that God always existed, why not save a step, and conclude that the Universe always existed? That there's no need for a creation, it was always here. These are not easy questions. Cosmology brings us face to face with the deepest mysteries, questions that were once treated only in religion and myth."

"The most far-reaching implication of general relativity... is that the universe is not static, as in the orthodox view, but is dynamic, either contracting or expanding. Einstein, as visionary as he was, balked at the idea... One reason... was that, if the universe is currently expanding, then... it must have started from a single point. All space and time would have to be bound up in that "point," an infinitely dense, infinitely small "singularity." ...this struck Einstein as absurd. He therefore tried to sidestep the logic of his equations, and modified them by adding... a "cosmological constant." The term represented a force, of unknown nature, that would counteract the gravitational attraction of the mass of the universe. That is, the two forces would cancel... it is the kind of rabbit-out-of-the-hat idea that most scientists would label ad-hoc. ...Ironically, Einstein's approach contained a foolishly simple mistake: His universe would not be stable... like a pencil balanced on its point."

"The cosmological constant['s]... most important consequence: the repulsive force, acting at cosmological distances, causes space to expand exponentially. There is nothing new about the universe expanding, but without a cosmological constant, the rate of expansion would gradually slow down. Indeed, it could even reverse itself and begin to contract, eventually imploding in a giant cosmic crunch. Instead, as a consequence of the cosmological constant, the universe appears to be doubling in size about every fifteen billion years, and all indications are that it will do so indefinitely."

"De Sitter proposed three types of nonstatic universes: the oscillating universes and the expanding universes of the first or second kiind. The main characteristic of the expanding "family" of the first kiind is that the radius is continually increasing from a definite initial time when it had the value zero. The universe becomes infinitely large after an infinite time. In the second kind... the radius possesses at the initial time a definite minimum value... in the Einstein model... the cosmological constant is supposed to be equal to the reciprocal of R2, whereas de Sitter computed for his interpretation the constant to be equal to 3/R2. Whitrow correctly points out the significant fact that in special relativity the cosmological constant is omitted..."

"[W]e stress... the wide range of validity exhibited by s in theoretical physics. ...[I]t has ...been demonstrated how they can be employed to derive equations of optics, dynamics of particles and rigid bodies, and electromagnetism. In addition, physicists have succeeded in formulating the laws of elasticity and hydrodynamics as variational principles, and even Einstein's law of gravitation was included in this category by Hilbert, who found a scaler function... for which \partial\int\mathfrak{h}\,dx_0\,dx_1\,dx_2\,dx_3=0 is equivalent to Einstein's law. This function has been called the "curvature," an identification which induced Whittaker to describe Hilbert's principle in the laconic words, "gravitation simply represents a continual effort of the universe to straighten itself out.""

"The general theory of relativity considers physical space-time as a four-dimensional manifold whose line element coefficients g_{\mu \nu} satisfy the differential equationsG_{\mu \nu} = \lambda g_{\mu \nu} \qquad .\;.\;.\;.\;.\;.\; (1)in all regions free from matter and electromagnetic field, where G_{\mu \nu} is the contracted Riemann-Christoffel tensor associated with the fundamental tensor g_{\mu \nu}, and \lambda is the ."

"An "empty world," i.e., a homogeneous manifold at all points at which equations (1) are satisfied, has, according to the theory, a constant Riemann curvature, and any deviation from this fundamental solution is to be directly attributed to the influence of matter or energy."

"In considerations involving the nature of the world as a whole the irregularities caused by the aggregation of matter into stars and stellar systems may be ignored; and if we further assume that the total matter in the world has but little effect on its macroscopic properties, we may consider them as being determined by the solution of an empty world."

"The solution of (1), which represents a homogeneous manifold, may be written in the form:ds^2 = \frac{d\rho^2}{1 - \kappa^2\rho^2} - \rho^2 (d\theta^2 + sin^2 \theta \; d\phi^2) + (1 - \kappa^2 \rho^2)\; c^2 d\tau^2, \qquad (2)where \kappa = \sqrt \frac{\lambda}{3}. If we consider \rho as determining distance from the origin... and \tau as measuring the proper-time of a clock at the origin, we are led to the de Sitter spherical world..."

"O. Heckmann has pointed out that the non-static solutions of the field equations of the general theory of relativity with constant density do not necessarily imply a positive curvature of three-dimensional space, but that this curvature may also be negative or zero. There is no direct observational evidence for the curvature, the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor that value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing the curvature at all. Historically the term containing the "cosmological constant" λ was introduced into the field equations in order to enable us to account theoretically for the existence of a finite mean density in a static universe. It now appears that in the dynamical case this end can be reached without the introduction of λ."

"The determination of the coefficient of expansion h depends on the measured red-shifts, which do not introduce any appreciable uncertainty, and the distances of the extra-galactic nebulae, which are still very uncertain. The density depends on the assumed masses of these nebulae and on the scale of distance, and involves, moreover, the assumption that all the material mass in the universe is concentrated in the nebulae. It does not seem probable that this latter assumption will introduce any appreciable factor of uncertainty."

"Although... the density... corresponding to the assumption of zero curvature and to the coefficient of expansion... may perhaps be on the high side, it... is of the correct order of magnitude, and we must conclude that... it is possible to represent the facts without assuming a curvature of three-dimensional space. The curvature is, however, essentially determinable, and an increase in the precision of the data derived from observations will enable us in the future to fix its sign and to determine its value."

"Why should not the space be there already, and the material system expand into it..? ...[I]f the speed of recession continues to increase outwards, it will ere long approach the speed of light, so that something must break down. The result is that the system becomes a ... such a system cannot expand without the space also expanding. ...[E]xpansion of space has often been given too much prominence ...and readers have been led to think that it is more directly concerned in the explanation of the motions of the nebule than is... the case. ...If we adopt open space we encounter certain difficulties (not necessarily insuperable) which closed space entirely avoids; and we do not want... speculation as to the solution of difficulties which need never arise. If we wish to be noncommittal, we shall naturally work in terms of a closed universe of finite radius R, since we can at any time revert to an infinite universe by making R infinite."

"The immediate results of introducing the cosmical term into the law of gravitation was the appearance... of two universes—the Einstein universe and the de Sitter universe. Both were closed spherical universes; so that a traveller going on and on in the same direction would at last find himself back at the starting-point... Both claimed to be static universes... thus they provided a permanent framework within which the small-scale systems—galaxies and stars—could change and evolve. ...[H]owever ...in de Sitter's universe there would be an apparent recession of remote objects ...At that time only three radial velocities were known, and these ...lamely supported de Sitter ...2 to 1. ...But in 1922 ...V. M. Sipher furnished me ...measures of 40 spiral nebulæ for ...my book Mathematical Theory of Relativity. ...[T]he majority had become 36 to 4 ..."

"The situation has been summed up in the statement that Einstein’s universe contains matter but no motion and de Sitter’s contains motion but no matter. ...[T]he actual universe containing both matter and motion does not correspond exactly to either... Which is the better choice for a first approximation? Shall we put a little motion into Einstein’s world of inert matter, or... a little matter into de Sitter’s ?"

"The choice between Einstein’s and de Sitter’s models... [W]e are not now restricted to these... extremes; we have... the whole chain of intermediate solutions between motionless matter and matterless motion... [W]e can pick... the right proportion of matter and motion to correspond with what we observe. ...[E]arlier... it was the preconceived idea that a static solution was a necessity... an unchanging background of space. ...[T]his ...should strictly have barred... de Sitter’s solution, but ...it was the precursor of the other non-static solutions..."

"[I]nvestigation of non-static solutions was carried out by A. Friedmann in 1922. His solutions were rediscovered in 1927 by Abbé G. Lemaître, who brilliantly developed the astronomical theory... and... remained unknown until 1930... In the meantime the solutions had been discovered... by H. P. Robertson, and through him... interest was... realised. The astronomical application, stimulated by Hubble and Humason’s observational work on the spiral nebule, was also being rediscovered, but it had not been carried so far as in Lemaître’s paper."

"The intermediate solutions of Friedmann and Lemaitre are "expanding universes." Both the material system and the closed space, in which it exists, are expanding. At one end we have Einstein’s universe with no motion and therefore in equilibrium. Then... we have model universes showing more and more rapid expansion until we reach de Sitter’s... The rate of expansion increases all the way along the series and the density diminishes; de Sitter’s universe is the limit when the average density of celestial matter approaches zero. The series of expanding universes then stops... but because there is nothing left to expand."

"[T]he most satisfying theory would be one which made the beginning not too unæsthetically abrupt. This... can only be satisfied by an Einstein universe with all... major forces balanced. Accordingly, the primordial state of things... is an even distribution of s and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. ...[T]he density of this distribution can be calculated ...[at] about one proton and electron per litre. ...[S]mall irregular tendencies accumulate, and evolution gets under way. ...[T]he formation of condensations ultimately ...become the galaxies; this ...started off an expansion, which ...automatically increased in speed until ...now manifested ...in the recession of the spiral nebulae. As the matter drew closer... in the condensations... evolutionary processes followed—evolution of stars... of... more complex elements... of planets and life."

"Within the galaxy the average world-curvature is... thousands of times greater than Lamaître's average for the universe... his formulæ are inapplicable. The result... only the intergalactic distances expand. The galaxies... are unaffected... —s, stars, human observers and their apparatus, atoms—are entirely free from expansion. Although the cosmical repulsion or expansive tendency is present in all of these... it is checked by much larger forces... [T]he demarcation between permanent and dispersing systems is... abrupt. It corresponds to the distinction between periodic and aperiodic phenomena."

"If you think... the shattering of the bubble universe is... tragic... [W]hen the worst has happened our galaxy... will be left intact. ...not so bad a prospect."

"All change is relative. The universe is expanding relatively to our common material standards; our material standards are shrinking relatively to the size of the universe. The theory of the "expanding universe" might also be called the theory of the "shrinking atom". ...[T]ake the... universe as our standard of constancy... he sees us shrinking... only the intergalactic spaces remain the same. The earth spirals round the sun in an ever‑decreasing orbit. ...Our years will ...decrease in geometrical progression in the cosmic scale of time. ... Owing to the property of geometrical progressions an infinite number of our years will add up to a finite cosmic time; so that what we should call the end of eternity is an ordinary finite date in the cosmic calendar. But on that date the universe has expanded to infinity in our reckoning, and we have shrunk to nothing in the reckoning of the cosmic being. ...When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing."

"If the astronomers are right, it is a straightforward conclusion from the observational measurements that the system of galaxies is expanding—or, since the system of the galaxies is all we know—that the universe is expanding. There is no subtlety or metaphysics about it ...But are we sure of the observational facts? Scientific men are rather fond of saying pontifically that one ought to be quite sure of one's observational facts before embarking on theory. Fortunately those who give this advice do not practice what they preach. Observation and theory get on best when they are mixed together, both helping one another in the pursuit of truth. It is a good rule not to put overmuch confidence in a theory until it has been confirmed by observation. I hope I shall not shock the experimental physicists too much if I add that it is also a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory. So in starting to theorise about the expanding universe I am not taking it for granted that the observational evidence which we have been considering is entirely certain."

"It is scarcely true... that we observe these velocities of recession. We observe a shift of the spectrum to the red; and although such... is usually due to recession... it is not inconceivable that it should arise from another cause."

"[I]t was theory that first suggested a systematic recession of the spiral nebulae and so led to a search for this effect. The theoretical possibility was first discovered by W. de Sitter in 1917. Only three radial velocities were known at that time, and they... lamely supported his theory by... 2 to 1. Since then... support is far more unanimous... mainly due to V. M. Slipher... and M. L. Humason... The linear law of proportionality between speed and distance was found by E. H. Hubble. Meanwhile the theory has also developed, and... taken the form... associated with... A. Friedman and G. Lemaître."

"The theory of relativity predicts... a... force... we call the cosmical repulsion... directly proportional to the distance... It is so weak... we can leave it out of... motions of the planets... or any motion within... our... galaxy. ...[S]ince it increases... to the distance we... if we go far enough, find it significant."

"I have said the repulsion is proportional to the distance... Distance from what? From anywhere you like. ...Cosmical repulsion is a dispersing force tending to make a system expand uniformly—not diverging from any centre in particular, but such that all internal distances increase at the same rate. That corresponds precisely to the kind of expansion we observe in the system of the galaxies."

"I have said that relativity theory predicts a force of cosmical repulsion. ...[R]elativity theory does not talk of anything so crude as force; it describes... curvature of space-time. But for practical purposes... nearly equivalent to the Newtonian force of gravitation... [T]he actual relativity effect is represented with sufficient accuracy by a force of cosmical repulsion... up to the greatest distances... we... observe."

"The galaxies exert on one another their ordinary gravitational attraction approximately according to Newton's law. This makes them tend to cling together. So we... have a contest of two forces, Newtonian attraction... and cosmical repulsion... If our theory is right cosmical repulsion must have got the upper hand... Having got the advantage, cosmical repulsion will keep it; because, as the nebulae become further apart, their mutual attraction will become weaker..."

"is a congruence geometry, or equivalently the space comprising its elements is homogeneous and isotropic; the intrinsic relations between... elements of a configuration are unaffected by the position or orientation of the configuration. ...[M]otions of are the familiar translations and rotations... made in proving the theorems of Euclid."

"[O]nly in a homogeneous and isotropic space can the traditional concept of a rigid body be maintained."

"That the existence of these motions (the "axiom of free mobility") is a desideratum, if not... a necessity, for a geometry applicable to physical space, has been forcefully argued on a priori grounds by von Helmholtz, Whitehead, Russell and others; for only in a homogeneous and isotropic space can the traditional concept of a rigid body be maintained."

"Euclidean geometry is only one of several congruence geometries... Each of these geometries is characterized by a real number K, which for Euclidean geometry is 0, for the hyperbolic negative, and for the spherical and elliptic geometries, positive. In the case of 2-dimensional congruence spaces... K may be interpreted as the ' of the surface into the third dimension—whence it derives its name..."

"[W]e propose... to deal exclusively with properties intrinsic to the space... measured within the space itself... in terms of... inner properties."

"Measurements which may be made on the surface of the earth... is an example of a 2-dimensional congruence space of positive curvature K = \frac{1}{R^2}... [C]onsider... a "small circle" of radius r (measured on the surface!)... its perimeter L and area A... are clearly less than the corresponding measures 2\pi r and \pi r^2... in the Euclidean plane. ...for sufficiently small r (i.e., small compared with R) these quantities on the sphere are given by 1):L = 2 \pi r (1 - \frac{Kr^2}{6} + ...), A = \pi r^2 (1 - \frac{Kr^2}{12} + ...)"

"In the sum \sigma of the three angles of a triangle (whose sides are arcs of s) is greater than two right angles [180°]; it can... be shown that this "spherical excess" is given by 2)\sigma - \pi = K \deltawhere \delta is the area of the spherical triangle and the angles are measured in s (in which 180° = \pi [radians]). Further, each full line (great circle) is of finite length 2 \pi R, and any two full lines meet in two points—there are no parallels!"

"[T]he space constant K... "" may in principle at least be determined by measurement on the surface, without recourse to its embodiment in a higher dimensional space."

"These formulae [in (1) and (2) above] may be shown to be valid for a circle or a triangle in the hyperbolic plane... for which K < 0. Accordingly here the perimeter and area of a circle are greater, and the sum of the three angles of a triangle are less, than the corresponding quantities in the Euclidean plane. It can also be shown that each full line is of infinite length, that through a given point outside a given line an infinity of full lines may be drawn which do not meet the given line (the two lines bounding the family are said to be "parallel" to the given line), and that two full lines which meet do so in but one point."

"The value of the intrinsic approach is especially apparent in considering 3-dimensional congruence spaces... The intrinsic geometry of such a space of curvature K provides formulae for the surface area S and the volume V of a "small sphere" of radius r, whose leading terms are 3)S = 4 \pi r^2 (1 - \frac{Kr^2}{3} + ...), V = \frac{4}{3} \pi r^3 (1 - \frac{Kr^2}{5} + ...)."

"In all these congruence geometries, except the Euclidean, there is at hand a natural unit of length R = \frac{1}{K^\frac{1}{2}}; this length we shall, without prejudice, call the "radius of curvature" of the space."

"We have merely (!) to measure the volume V of a sphere of radius r or the sum \sigma of the angles of a triangle of measured are \delta, and from the results to compute the value of K."

"What is needed is a homely experiment which could be carried out in the basement with parts from an old sewing machine and an Ingersoll watch, with an old file of Popular Mechanics standing by for reference! This I am, alas, afraid we have not achieved, but I do believe that the following example... is adequate to expose the principles..."

"Let a thin, flat metal plate be heated... so that the temperature T is not uniform... clamp or otherwise constrain the plate to keep it from buckling... [and] remain [reasonably] flat... Make simple geometric measurements... with a short metal rule, which has a certain coefficient of expansion c... What is the geometry of the plate as revealed by the results of those measurements? ...[T]he geometry will not turn out to be Euclidean, for the rule will expand more in the hotter regions... [T]he plate will seem to have a negative curvature K... the kind of structure exhibited... in the neighborhood of a ".""

"What is the true geometry of the plate? ...Anyone examining the situation will prefer Poincaré's common-sense solution... to attribute it Euclidean geometry, and to consider the measured deviations... as due to the actions of a force (thermal stresses in the rule). ...On employing a brass rule in place of one of steel we would find that the local curvature is trebled—and an ideal rule (c = 0) would... lead to Euclidean geometry."

"In what respect... does the general theory of relativity differ...? The answer is: in its universality; the force of gravitation in the geometrical structure acts equally on all matter. There is here a close analogy between the gravitational mass M...(Sun) and the inertial mass m... (Earth) on the one hand, and the heat conduction k of the field (plate)... and the coefficient of expansion c... on the other. ...The success of the general relativity theory... is attributable to the fact that the gravitational and inertial masses of any body are... rigorously proportional for all matter."

"The field equation may... be given a geometrical foundation, at least to a first approximation, by replacing it with the requirement that the mean curvature of the space vanish at any point at which no heat is being applied to the medium—in complete analogy with... the general theory of relativity by which classical field equations are replaced by the requirement that the Ricci contracted curvature tensor vanish."

"Now it is the practice of astronomers to assume that brightness falls off inversely with the square of the "distance" of an object—as it would do in Euclidean space, if there were no absorption... We must therefore examine the relation between this astronomer's "distance" d... and the distance r which appears as an element of the geometry."

"All the light which is radiated... will, after it has traveled a distance r, lie on the surface of a sphere whose area S is given by the first of the formulae (3). And since the practical procedure... in determining d is equivalent to assuming that all this light lies on the surface of a Euclidean sphere of radius d, it follows...4 \pi d^2 = S = 4 \pi r^2 (1 - \frac{K r^2}{3} + ...);whence, to our approximation 4)d = r (1- \frac{K r^2}{6} + ...), or r = d (1 + \frac{K d^2}{6} + ...)."

"[T]he astronomical data give the number N of nebulae counted out to a given inferred "distance" d, and in order to determine the curvature... we must express N, or equivalently V, to which it is assumed proportional, in terms of d. ...from the second of formulae (3) and... (4)... to the approximation here adopted, 5)V = \frac{4}{3} \pi d^2 (1 + \frac{3}{10} K d^2 + ...);...plotting N against... d and comparing... with the formula (5), it should be possible operationally to determine the "curvature" K."

"This... is an outrageously over-simplified account of the assumptions and procedures..."

"The search for the curvature K indicates that, after making all known corrections, the number N seems to increase faster with d than the third power, which would be expected in a Euclidean space, hence K is positive. The space implied thereby is therefore bounded, of finite total volume, and of a present "radius of curvature" R = \frac{1}{K^\frac{1}{2}} which is found to be of the order of 500 million light years. Other observations, on the "red shift" of light from these distant objects, enable us to conclude with perhaps more assurance that this radius is increasing..."

"Hubble was inclined, from about 1936, to reject the Doppler-effect interpretation of the red shifts and to regard the nebulae as stationary; but theoretical cosmologists, notably McVittie... and Heckmann... severely criticized Hubble’s method...and disputed his conclusions. Although these criticisms... came to be generally accepted, it still seemed that the available data were open to rival interpretations, depending on the method of analysis..."

"At last, in 1949, the... ... was ready... Humason... succeeded in photographing the spectra of two remote galaxies in the . These exhibited red-shifts which, on the Doppler interpretation, indicated... one-fifth of the velocity of light. [I]n 1956, with... photoelectric equipment attached... [W. A.] Baum obtained a red-shift... recessional velocity of about two-fifths of the velocity of light."

"[I]n... 1952, Baade... announced that Hubble’s entire distance scale was in error... According to Baade, the distances formerly assigned to all extragalactic objects must be multiplied by a factor of about two. Later it was generally accepted that this... was probably nearer three. ...[I]t followed that the sizes of all such objects had been underestimated. ...Therefore ...this nebula must be... twice as far away... [T]he average absolute magnitude at maximum brightness of novae... in the Milky Way attain on the average... 7.4, whereas those... in the Andromeda... 5.7... [T]he apparent anomaly could be removed by placing... Andromeda... rather more than twice as far as previously. ...[[w:Distance measure|[E]xtragalactic distances]] had ...been underestimated because of an error in converting... relative distances of s into an absolute scale. ...Baade's revision ...applied only to extragalactic objects... [and] had momentous consequences concerning the size and , for the scale of both was correspondingly increased."

"An important new survey of the law relating red-shifts and magnitudes published in 1956 by Humason, Mayall and Sandage suggested... that the expansion of the universe may have been faster in the past... so that its age may be somewhat less than that estimated on the hypothesis of uniform expansion. But... caution, for a recent review (1958) by Sandage of Hubble's criteria for constructing the extragalactic distance-scale has revealed that, not only must his Cepheid criterion be corrected but also... the brightest star criterion..."

"As for Hubble’s brightest star criterion, Sandage... has shown that objects in the of galaxies which Hubble believed to be highly luminous stars are... regions of glowing of intrinsic luminosity... two magnitudes brighter... If Sandage’s result is accepted, then the distances of all galaxies beyond those in which Cepheids can be detected... must be augmented by a factor... between 5 and 10... with the result that the rate of increase of velocity with distance will be reduced to between 5O and 100 kilometres per second per megaparsec. Consequently, taking 80 as a rough average... the , if it has expanded uniformly, will have to be increased to about 13-5 thousand million years. If... it was expanding more rapidly in the past... this... might be reduced to about 9 thousand million years."