Cosmologists

"Einstein's pioneer application in 1917 of his newly developed general relativity to the problem of world-structure ushered in a new phase in the theoretical approach to the subject. Then, some seven years later, Hubble's discovery of Cepheid variables in the Andromeda nebula finally settled the long-debated question concerning this and similar nebulae in the Milky Way."

"Let us suppose that an explosion occurs on Mars, which is observed by an astronomer on earth, who records the instant when he sees the flash. If light travelled instantaneously with an infinite velocity, this instant would coincide with the time... recorded by the... observer on Mars. In this way a meaning could be attached automatically to absolute time and the simultaneity of events at different places; indeed, the classical theory is now regarded as the limiting form of Einstein's theory when the velocity of light becomes infinite. But as there is a mass of experimental evidence supporting the view that light takes a finite time to travel... the terrestrial observer must correct the time recorded on his watch. This correction... will depend on assumptions concerning the velocity of light and the measurement of distance. Thus the concept of a world-wide simultaneity ceases to be a primitive idea."

"Einstein had spent the previous thirty years showing how we could understand the behaviour of whole universes with simple maths. Gamow saw that those universes must have had a past that was unimaginably different to the present. What had stopped them both in their tracks was Gamow's suggestion that the laws of physics could describe something being created out of nothing."

"Aristotle believed that the world did not come into being at some time in the past; it had always existed and it would always exist, unchanged in essence for ever. He placed a high premium on symmetry and believed that the sphere was the most perfect of all shapes. Hence the universe must be spherical. ...An important feature of the spherical shape... was the fact that when a sphere rotates it does not cut into empty space where there is no matter and it leaves no empty space behind. ...A vacuum was impossible. It could no more exist than an infinite physical quantity. ...Circular motion was the most perfect and natural movement of all."

"The Indian system of counting is probably the most successful intellectual innovation ever devised by human beings. It has been universally adopted. ...It is the nearest thing we have to a universal language."

"Einstein showed us how to find all the possible universes that were consistent with the laws of physics and the character of gravity, how to reconstruct their pasts and predict their futures. But actually finding them was no easy task."

"Just focusing on what exists now seems a bit exclusive. And if we include everything that has ever existed as part of the universe, why not include the future as well? This seems to leave us with the definition that the universe is everything that has ever existed, does exist, or will ever exist."

"The quantum revolution showed us why the old picture of a vacuum as an empty box was untenable. ...Gradually, this exotic new picture of quantum nothingness succumbed to experimental exploration... in the form of vacuum tubes, light bulbs and X-rays. Now the 'empty' space itself started to be probed. ...There was always something left: a vacuum energy that permeated every fibre of the Universe."

"Einstein showed us that the Universe might contain a mysterious form of vacuum energy. ...Last year, two teams of astronomers used Earth's most powerful telescopes... to gather persuasive evidence for the reality of the cosmic vacuum energy. Its effects are dramatic. It is accelerating the expansion of the Universe."

"The physicist's concept of nothing—the vacuum... began as empty space—the void... turned into a stagnant ether through which all the motions of the Universe swam, vanished in Einstein's hands, then re-emerged in the twentieth-century quantum picture of how Nature works."

"There is a good deal more to nothing than meets the eye."

"The Indian religious traditions... accepted the concept of non-being on an equal footing with that of being. Like many other Eastern religions, the Indian culture regarded Nothing as a state from which one might have come and to which one might return.. Where Western religious traditions sought to flee from nothingness... a state of non-being was something to be actively sought by Buddhist and Hindus in order to achieve Nirvana: oneness with the Cosmos."

"Everyone knows there are billions and billions of stars, and national debts conjure up similar astronomical numbers. Yet we have found a way to hide the zeros: 109 doesn't look as bad as 1,000,000,000."

"The Greek tradition was a complete contrast to that of the Far East. ...the Greeks placed logic at the pinnacle of human thinking. Their sceptical attitude towards the wielding of 'non-being' as some sort of 'something' that could be subject to logical development was exemplified by Parmenides' influential arguments against the concept of empty space. ...He maintained that you can only speak about what is: what is not cannot be thought of, and what cannot be thought of cannot be. ...more unexpected was the further conclusion that time, motion nor change could exist either."

"In the spring of 1845, William Parsons, the third Earl of Rosse, began observing with his great six-foot telescope... The Earl was excited by what he was the first human to see: spiral patterns of stars, seemingly swirling in great 'spiral convolutions' about the centre of the galaxy. ...No one could ever have seen the spiral pattern of stars in a galaxy unless they had looked through Rosse's telescope or seen his drawings. ...I believe that Van Gogh would have seen those drawings in the press following the publicity attracted by them, or in Flammarion's book... and gained his astronomical inspiration from them."

"Scientific pictures are often not just about science. They may... have an undeniable aesthetic quality. They may even have been primarily works of art that possess a scientific message."

"If one looks at the special problems that were the mainsprings of progress along the oldest and most persistent lines of human inquiry, then one finds Nothing, suitably disguised as something, never far from the centre of things."

"Mathematics became an experimental subject. Individuals could follow previously intractable problems by simply watching what happened when they were programmed into a personal computer. ...The PC revolution has made science more visual and more immediate. ...by creating films of imaginary experiences of mathematical worlds. ...Words are no longer enough."

"While we have no reason to expect that our position in the universe is special in every way, we would be equally misled were we to assume that it could not be special in any way."

"Even today, there persists... a feeling that the creation of the Universe out of nothing must violate some basic conservation law that stops one from getting something for nothing. Nevertheless, there is actually no evidence that the Universe as a whole possesses a non-zero value of any such conserved quantity. The total mass-energy of all the constituents of a finite Universe appears to be always equal in magnitude but opposite in sign to the total gravitational potential energies of those particles. ...Similarly, there is no evidence that the Universe possesses any overall net rotation or electric charge."

"There is no formula that can deliver all truth, all harmony, all simplicity. No Theory of Everything can ever provide total insight. For, to see through everything, would leave us seeing nothing at all."

"The living world is not a marble palace. It is a higgledy-piggledy outcome of natural selection and the competition between many interacting factors. The outcome is often neither elegant nor symmetrical."

"We say that the string is 'random' if there is no other representation of the string which is shorter than itself. But we will say that it is 'non-random' if there does exist such an abbreviated representation. ...In general, the shorter the possible representation... the less random... On this view we recognize science to be the search for algorithmic compressions."

"It is simplest to think of mathematics as the catalogue of all possible patterns. ...When viewed in this way, it is inevitable that the world is described by mathematics. ...In many ways the search for a Theory of Everything is a manifestation of a faith that this compression goes all the way down to the bedrock of reality..."

"We have witnessed a revolution in the history of science. Not the sort of revolution that philosophers of science once believed in—they don't happen any more—but a revolution brought about by new tools, different ways of seeing, and novel ways of understanding. Nothing old needed to be overthrown to make way for the new. The future of science will be increasingly dominated by artificial images and simulations."

"It is not hard to see why the Eastern holistic perspective made scientific progress so difficult. It denies the intuition that one can study the parts of the world in isolation from the rest—that one can analyze the world..."

"Scanning the past millennia of human achievement reveals just how much has been achieved during the last three hundred years since Newton set in motion the effective mathematization of Nature. We found that the world is curiously adapted to a simple mathematical description. It is enigma enough that the world is described by mathematics; but by simple mathematics, of the sort that a few years energetic study now produces familiarity with, this is an enigma within an enigma."

"Each of the most basic physical laws that we know corresponds to some invariance, which in turn is equivalent to a collection of changes which form a symmetry group. ...whilst leaving some underlying theme unchanged. ...for example, the conservation of energy is equivalent to the invariance of the laws of motion with respect to translations backwards or forwards in time... the conservation of linear momentum is equivalent to the invariance of the laws of motion with respect to the position of your laboratory in space, and the conservation of angular momentum to an invariance with respect to directional orientation... discovery of conservation laws indicated that Nature possessed built-in sustaining principles which prevented the world from just ceasing to be. There were fewer roles for the Deity to play..."

"Ultimate explanation no longer means only a story that encompasses everything."

"By interlinking causes, by searching always for unity in the face of superficial diversity, modern scientific explanations prize depth above breadth. A deep and narrow theory can, and often does, graduate to become a deep and broad one. A broad and shallow theory never does."

"Gods reappear in unlimited numbers in the guise of the simulators who have the power of life and death over the simulated realities that they bring into being. The simulators determine the laws, and can change the laws, that govern their worlds. They can engineer anthropic fine-tunings. They can pull the plug on the simulation at any moment, intervene or distance themselves from their simulation; watch as the simulated creatures argue about whether there is a god who controls or intervenes, work miracles or impose their ethical principles upon the simulated reality."

"Images and pictures... have played a key role in shaping our scientific picture of the world. ...Carefully constructed families of pictures can act as a calculus all their own. Like any successful systems of symbols, with an appropriate grammar they enlarge the number of things that we can do without consciously thinking."

"If musical appreciation is a by-product of a more general pattern-processing propensity of the brain, then why are our senses heightened by pink noises? It is significant that the world around us is full of variations with 1/f spectra. Benoit Mandelbrot has pioneered the study of natural and computer-generated patterns that are scale-free. (He calls them fractals...) Mandelbrot draws attention to the fact that there is a pattern to the noise spectrum displayed by the human nervous system. At the extremities of the body... it tends to be of white-noise form; but, as one approaches closer to the central nervous system and the brain, these variations become 1/f-like. Our nervous system may act as a spectral filter to prevent the brain from being swamped with uninteresting white background noise about the world..."

"...logical contradictions will inevitably arise and the laws of the simulations will appear to break down now and again. The inhabitants of the simulation—especially the simulated scientists—will occasionally be puzzled by the experimental results they obtain. The simulated astronomers, might, for instance, make observations that show that their so-called constants of Nature are very slowly changing."

"Copernicus' picture did more than picture the solar system correctly: it painted a new world picture."

"The abstractions of Einstein's curved space and time gave rise to analogies and pictures that played a new explanatory role. Space and time gave way to space-time, visible light was augmented by images across the rest of the electromagnetic spectrum, and we realised that we could see back towards the apparent beginnings of time."

"The legacy of the great monotheistic religions is the expectation of a single over-arching explanation for the Universe. ...There is no logical reason why the Universe should not contain surds of arbitrary elements that do not relate to the rest."

"A less inflexible picture of mathematics is one that focuses on the fact that it is an open-ended human activity. Inventionism is the belief that mathematics is nothing more than what mathematicians do. ...We invent mathematics; we do not discover it. ...The independent discovery of the same mathematical theorems by different mathematicians from totally different economic, cultural, and political backgrounds—often at widely separated times in history—argues against such a simple view. The inventionist could respond by pointing to the universality of human languages. ...One might expect that those aspects of this universal grammar that share features of logic, and hence counting, would also make counting appear instinctive. In fact, although simple counting... is fairly universal in ancient and primitive cultures, virtually none of them went on to carry out mathematical operations more sophisticated than counting. This suggests that these higher mathematical operations are not genetically programmed into the human brain... They are more likely to be by-products of multi-purpose pattern-recognition capabilities."

"Unfortunately, truth is neither a listable nor a decidable property; nor is the truth of a statement of arithmetic. The American logician John Myhill has used the term 'prospective' to characterize those attributes of the world that are neither listable nor decidable. They are properties that cannot be recognized by the application of some formula, made to conform to a rule, or generated by some computer program. They are characterized by incessant novelty that cannot be encompassed by any finite set of rules. 'Beauty', 'ugliness', 'truth', 'harmony', simplicity', and 'poetry' are names we give to some of the attributes of this sort. There is no way of listing all examples of beauty or ugliness, nor any procedure for saying whether or not something possesses either of those attributes, without redefining them in some more restrictive fashion that kills their prospective character."

"The spooky ether was persistent. It took an Einstein to remove it from the Universe. ...Gradually, over the last twenty years, the vacuum has turned out to be more unusual, more fluid, less empty, and less intangible than even Einstein could have imagined. Its presence is felt on the very smallest and largest dimensions over which the forces of Nature act."

"Our sensitivity to changes of pitch ... is underused in musical sound. Western music, in particular, is based on scales that use pitch changes that are at least twenty times bigger than the smallest changes that we could perceive. If we used our discriminatory power to full, we could generate an undulating sea of sound that displayed continuously changing frequency rather like the undersea sonic songs of dolphins and whales."

"If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one."

"Location is not, as the estate agents say, everything. We must also consider our place in history."

"The logic of the Greeks prevents them having the idea at all and it is to the Indian cultures that we must look to find thinkers who are comfortable with the idea that Nothing might be something."

"The laws of Nature are based upon the existence of a pattern, linking one state of affairs to another; and where there is pattern, there is symmetry. Yet...the symmetries that the laws enshrine are broken in... outcomes. Suppose that we balance a needle on its point and then release it. The law of gravity, which governs its subsequent motion, is perfectly democratic. It has no preference for any particular direction in the Universe: it is symmetrical in this respect. Yet, when the needle falls, it must fall in a particular direction. The directional symmetry of the underlying law is broken, therefore... By the same token, the fallen needle hides the symmetry of the law... Such 'symmetry-breaking' governs much of what we see in the Universe... It allows a Universe governed by a small number of symmetrical laws to manifest an infinite diversity of complex, asymmetrical states. This is how the Universe can be at once, simple and complicated."

"Hundreds of years ago, natural theologians tried to impress their readers with stories of the wondrous symmetries of Nature; now we see that, ironically, it is the departures from those symmetries that makes life possible. It is upon the flaws of Nature, not the laws of Nature, that the possibility of our existence hinges. ...The laws and constants of Nature are features that enforce uniformity and simplicity, while initial conditions and symmetry breakings permit complexity and diversity."

"Where there is life there is a pattern, and where there is a pattern there is mathematics. Once that germ of rationality and order exists to turn a chaos into a cosmos, then so does mathematics. There could not be a non-mathematical Universe containing living observers."

"Ancient belief in a cosmos composed of spheres, producing music as angels guided them through the heavens, was still flourishing in Elizabethan times. ...There is a good deal more to Pythagorean musical theory than celestial harmony. Besides the music of the celestial spheres (musica mundana), two other varieties of music were distinguished: the sound of instruments...(musica instrumentalis), and the continuous unheard music that emanated from the human body (musica humana), which arises from a resonance between the body and the soul. ...In the medieval world, the status of music is revealed by its position within the Quadrivium—the fourfold curriculum—alongside arithmetic, geometry, and astronomy. Medieval students... believed all forms of harmony to derive from a common source. Before Boethius' studies in the ninth century, the idea of musical harmony was not considered independently of wider matters of celestial or ethical harmony."

"You cannot do physics or cosmology without an assumed philosophical basis. You can choose not to think about that basis: it will still be there as an unexamined foundation of what you do."

"Attempts to explain values in terms of neuroscience or evolutionary theory in fact have nothing whatever to say about what is good or bad. That is a philosophical or religious question (scientists trying to explain ethics from these kinds of approaches always surreptitiously introduce some unexamined concept of what is a good life by the back door)."