Theories of Everything Quotes

“The success of discovering a thermodynamic principle associated with the gravitational field of a black hole has led to a speculation that there might exist some thermodynamic aspect to the gravitational field of the whole Universe. The simplest assumption to make, following the black hole case, would be that it is the surface area of the boundary of the visible universe. As the Universe expands, this boundary increases and the information available to us about the Universe increases. But this does not seem promising. It would appear to tell us only that the Universe must continue expanding forever, for if it were ever to begin to recollapse the entropy would fall and violate the second law of thermodynamics. The universe can expand in all sorts of different ways and still have the increasing area. What we really want is some principle that tells us why the organization of the Universe changes in the way that it does: why it now expands so uniformally and isotropically.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Then, in 1974, Stephen Hawking made a dramatic discovery. He decided to examine for the forst time what occurs when one applies the notions of quantum mechanics to black holes. What he discovered was that black holes are not completely black. When quantum mechanics is included in the discussion of their properties, it is possible for energy to escape from the surface of the black hole and be recorded by an outside observer. The variation in the strength of the gravitational field near the horizon surface is strong enough to create pairs of particles and antiparticles spontaneously. The energy necessary to do this is extracted from the source of the gravitational field, and as the process continues, so the mass of the black hole ebbs away. If one waits long enough, it should disappear completely unless some unknown physics intervenes in the final stages. Such a discovery was exciting enough, but its most satisfying aspect was the fact that the particles radiated away from the surface of the black hole were found to have all the characteristics of heat radiation, with a temperature precisely equal to the gravitational field at the horizon and an entropy given by its surface area, just as the analogy had suggested. Black holes did possess a non-zero temperature and obeyed the laws of thermodynamics, but only when quantum mechanics was included in their description.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Three laws governing black hole changes were thus found, but it was soon noticed that something unusual was going on. If one merely replaced the words 'surface area' by 'entropy' and 'gravitational field' by 'temperature', then the laws of black hole changes became merely statements of the laws of thermodynamics. The rule that the horizon surface areas can never decrease in physical processes becomes the second law of thermodynamics that the entropy can never decrease; the constancy of the gravitational field around the horizon is the so-called zeroth law of thermodynamics that the temperature must be the same everywhere in a state of thermal equilibrium. The rule linking allowed changes in the defining quantities of the black hole just becomes the first law of thermodynamics, which is more commonly known as the conservation of energy.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“In a Newtonian world, all physical quantities, like energy and spin, can take on any values whatsoever. They range over the entire continuum of numbers. Hence, if one were to form a 'Newtonian hydrogen atom' by setting an electron in circular orbit around a single proton then the electron could move in a closed orbit of any radius because it could possess any orbital speed. As a result, every pair of electrons and protons that came together would be different. The electrons would find themselves in some randomly different orbit. The chemical properties of each of the atoms would be different and their sizes would be different. Even if one were to create an initial population in which the electrons' speeds were the same and the radii of their orbits identical, they would each drift away from their starting state in differing ways as they suffered the buffetings of radiation and other particles. There could not exist a well-defined element called hydrogen with universal properties, even if there existed universal populations of identical electrons and protons. Quantum mechanics shows us why there are identical collective structures. The quantization of energy allows it to come only in discrete packets, and so when an electron and a proton come together there is a single state for them to reside in. The same configuration arises for every pair of electrons and protons that you care to choose. This universal state is what we call the hydrogen atom. Moreover, once it exists, its properties do not drift because of the plethora of tiny perturbations from other particles. In order to change the orbit of the electron around the proton, it has to be hit by a sizeable perturbation that is sufficient to change its energy by a whole quantum packet. Thus the quantization of energy lies at the root of the repeatability of structure in the physical world and the high fidelity of all identical phenomena in the atomic world. With the quantum ambiguity of the microscopic world the macroscopic world would not be intelligible, nor indeed would there be intelligences to take cognisance of any such a totally heterodox non-quantum reality.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“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.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“All the best physical theories are associated with equations which allow the continuation of data defined at present into the future, and hence allow prediction. But this situation requires space and time to possess a rather particular type of mathematical property which we shall call 'natural structure'. Other theories, like those describing statistical or probabilistic outcomes, which attempt to use mathematics for prediction, often fail to possess a mathematical substratum with a 'natural structure' of this sort, and so there is no guarantee that its future states are smooth continuations of its present ones.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“As we look way back into the first instants of the Big Bang, we find the quantum world that we described in Chapter 3. From that state, where like effects do not follow from like causes, there must somehow emerge a world resembling our own, where the results of most observations are definite. This is by no means inevitable and may require the Universe to have emerged from a rather special primeval state.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Since so much of the physical universe, from brain waves to quantum waves, relies upon travelling waves we appreciate the key role played by the dimensionality of our space in rendering its contents intelligible to us.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Particle physicists are the most deeply Platonic because their entire subject is built upon a belief that the deepest workings of the world are based upon symmetries. They examine symmetry after symmetry, confident in the expectation that the biggest and the best will have found employ in the grand scheme of things.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Most scientists and mathematicians operate as if Platonism is true regardless of whether they believe that it is. That is, they work as though there were an unknown realm of truth to be discovered.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Besides the traditional questions of where or what the Platonic world of perfect mathematical blueprints actually is, this view moves us towards a number of deep and fascinating questions. It elevates mathematics pretty close to the status of God in traditional theology. Just take any work of medieval theology and alter the word 'God' to 'mathematics' wherever it appears and it makes pretty good sense. Mathematics is part of the world, and yet transcends it. It must exist before and after the Universe. In this respect, it is reminiscent of our discussion of the nature of time in earlier chapters. In the Newtonian world-view, both space and time were absolute and independent of the events played out upon them. Then the Einsteinian transformation of our concepts of space and time (whose radicalness is obscured by the fact that the concepts retained the same names) linked space and time to events going on within the Universe. Maybe a similar evolution of this interpretation of mathematics will emerge? Although at present mathematics seems to transcend the Universe because cosmologists think they can actually describe the Universe as a whole in terms of mathematics and use mathematics to study the process of creation and annihilation of universes, perhaps the nature of mathematics will become more closely associated with physically realizable processes like counting or computing?”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Impressed by the success of high-level mathematics in the formulation of the general theory of relativity in 1915, we find that Einstein's life-long quest for a unified field theory was dominated by the search for more general mathematical formalisms that could bring together the existing descriptions of gravity and electromagnetism. We find none of Einstein's compelling thought experiments and beautifully simple physical reasoning that lay at the heart of his early success. As the last quotation tells, he had become convinced that by pursuing mathematical formalisms alone, the compelling simplicity of a unified description of the world would become inescapable.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Moreover, there is no known reason why the geometry of space and time should be described by the particular types of curved geometry defined by Riemann. There exist other more complicated varieties that could in principle have been employed by Nature. Only observation can at present tell us which mathematics is chosen by Nature for employment in particular situations. This may of course merely be a transient manifestation of our relative ignorance of the bigger picture in which everything that is not excluded is demanded.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“But, as powerful mathematicians like Minkowski and Hilbert found striking harmony between their pure mathematical results and the workings of the physical world, many found the claims for such a harmony hard to resist. Thus, in the early years of the twentieth century, we begin to see why Minkowski's application of complex numbers to the description of space and time was hailed by one physicist as 'one of the greatest revolutions in our accepted views'.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Grosseteste influenced Roger Bacon's ideas about mathematics and Nature. Bacon wrote hundreds of pages on the subject and, indeed, no historical figure has ever appeared more preoccupied with the question than he. He believed that mathematical knowledge was innate to the human mind and mathematics was a unique form of thought known both by ourselves and by Nature. Its uniqueness is characterized by the fact that it allows complete certainty to be achieved and hence our knowledge of Nature can be secure only in so far as we found it upon mathematical principles.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“In the Middle Ages, this conflict between the Platonic and Aristotelian views of the relationship between mathematics and the world began to re-emerge after the sleep of centuries. The question became intricately entwined with the labyrinthine syntheses of Aristotelian and Platonic ideas within early Christian theology. Influential thinkers like Augustine and Boethius implicitly supported the Platonic emphasis upon the primary character of mathematics. Both of them pointed to the fact that things were created in the beginning 'according to measure, number, and weight' or 'according to the pattern of numbers'. This they took to exhibit an intrinsic feature of the mind of God and thus mathematics took its place as an essential part of the medieval quadrivum without which the search for all knowledge was impaired. Yet Boethius later veered towards the Aristotelian viewpoint that some act of mental abstraction occurs en route from physics to mathematics which renders these two subjects qualitatively distinct.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Aristotle draws a sharp dividing-line between the activities of the physicist and those of the mathematician. The mathematician limits his enquiry to the quantifiable aspects of the world and so dramatically restricts what is describable in mathematical terms. Physics, for Aristotle, was far wider in scope and encompassed the earthly reality of sensible things. Whereas Plato had maintained that mathematics was the true and deep reality of which the physical world was but a pale reflection, Aristotle claimed mathematics to be but a superficial representation of a piece of physical reality. Such is the contrast between idealism and realism in the ancient world.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Aristotle's later view of the relationship between mathematics and Nature could not have been more different. He wanted to rescue physical science from the mathematical stranglehold that Plato had placed upon it. He believed there to exist three completely autonomous realms of purely theoretical knowledge-metaphysics, mathematics, and physics-each possessing its own methods of explanation and accordant subject matter. But over-arching these divisions there existed a more general principle of 'homogeneity'-that like follows like-which mush always be obeyed:”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Plato argued that the material world of visible things was but a shadow of the true reality of eternal forms. He proceeds to explain the nether world of eternal blueprints most completely in the case of the elements of matter: earth, air, fire, and water. These he represents by geometrical solids: the earth by a cube, water by an icosahedron, air by an octahedron, and fire by a tetrahedron. His position is that ultimately the elements are just these solid geometrical shapes not simply that they possess geometrical shapes as one of their properties. The transmutation of elements one into the other is then explained by the merger and dissolution of triangles. This strictly mathematical description characterizes Plato's discussion of many other physical problems, For him, mathematics is a pointer to the ultimate reality of the world of forms that overshadows the visible world of sense data. The better we can grasp it, the closer we can come to true knowledge. Thus, for Plato, mathematics is more fundamental, truer, closer to the eternal forms of which the visible world is an imperfect reflection, than the objects of physical science. Because the world is mathematical at its deepest level, all visible phenomena will have mathematical aspects and be describable by mathematics to a greater or lesser extent, determined by their closeness to their underlying forms.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“The ease with which collaboration occurs in mathematical research and the essential similarity of the fruits of such collaboration to that of individual work points suggestively towards a powerful objective element behind the scenes that is discovered rather than invented.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“The fact that simultaneous discovery occurs in mathematics, as well as the sciences, points toward some objective element within their subject matter that is independent of the psyche of the investigator.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“If the Universe possesses intrinsically random elements in their make up, inherited from its quantum origins or from random symmetry-breakings during its early evolution, then we must take our own existence into account when evaluating the correspondence between reality and the cosmological predictions of any Theory of Everything. Moreover, if these random cosmological elements lead to a Universe which differs significantly from place to place over the very large distances, then our local observations of a possibly infinite Universe will inevitably leave our knowledge of its global structure seriously incomplete.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“The great unanswered question is whether there exists some undiscovered organizing principle which complements the known laws of Nature and dictates the overall evolution of the Universe. To be a true addition to what we know of Nature's laws, this principle would need to differ from any laws of gravitation and particle physics that might emerge in final form from some Theory of Everything. It would not be specific to Universes but would govern the evolution of any complex system. True, its general notions ought to be tailored in some way to the notions which characterize the specific things that go on in an evolving universe-the clustering of matter into stars and galaxies, the conversion of matter into radiation-but it would also need to govern the invisible ways in which the gravitational field of the Universe can change. Any such discovery would be profoundly interesting because the Universe appears to be far more orderly than we have any right to expect. It has a tiny entropy level compared with the largest value that we could conceive of it possessing if we were to reorganize the observed matter into other configurations. This implies that the entropy level at the beginning of the expansion of the Universe must have been staggeringly small, which implies that the initial conditions were very special indeed.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“At first, one might think that something like thermodynamics is a rather restrictive concept because it concerns itself with temperature and heat. But its application is not just restricted to all things thermal. It is possible to relate the notion of entropy, which is a measure of disorder, to the more general and fruitful notions of 'information', of which we have already made use in discussing the richness of certain systems of axioms and rules of reasoning. We can think of the entropy of a large object like a black hole as being equal to the number of different ways in which its most elementary constituents can be rearranged in order to give the same large-scale state. This tells us the number of binary digits ('bits') that are needed to specify in every detail the internal configuration of the constituents out of which the black hole is composed. Moreover, we can also appreciate that, when a black hole horizon forms, a certain amount of information is forever lost to the outside observer when a horizon forms around a region of the universe to create a black hole.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“The deep significance of this discovery appears to be that we have found a physical situation where two different natural principles, of quantum mechanics and general relativity, come together, which admits of a simple thermodynamic description. We expected all the rules governing how things behave in such a quantum gravitational situation to be complicated and novel. Many undoubtedly are; yet we find that the tried and tested principles of thermodynamics encompass them within their dominion. Besides giving physicists confidence that they might be able to elucidate still more complicated problems of basic science by appeal to simple thermodynamic principles, this case history bolsters our faith in thermodynamics as a paradigm for a 'law' governing the organization of complex systems.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“A future world of computer circuits, getting smaller and smaller, yet faster and faster, is a plausible future "life- form" more technically competent than our own. The smaller a circuit can be made, the smaller are the regions over which voltages appear, and hence the smaller these voltages can be. Tiny layers of material just a few atoms thick allow the electronic properties of a material to be finely tuned and rendered far more effective. The first transistors were made of germanium but were far from reliable and failed at high temperatures. When high-quality silicon crystals could be grown they were used in a generation of faster and more reliable silicon transistors and integrated circuitry. Newer materials like gallium arsenide allow electrons to travel through them even faster than through silicon and has given rise to the line of cray supercomputers. The evolution of computer power is represented in figure 7.3. Undoubtedly other materials will eventually take over. The story may even come full circle back to carbon again. Pure carbon in the form of diamond is about the best conductor of heat, a property that is a premium in a densely packed array of circuits.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Today, a science fiction writer looking for a futuristic tale of silicon dominance would not pick upon the chemistry of silicon so much as the physics of silicon for his prognostications. But this form of silicon life could not have evolved spontaneously : it requires a carbon-based life-form to act as a catalyst. We are that catalyst.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Humans are distinguished further by the highly effective way in which they have pooled the individual intelligence of single individuals to produce a collective intelligence that greatly outweighs the capability of any single individual.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Complexity is a delicate business. Chemical and molecular bonds require a particular range of temperature in which to operate. Liquid water exists over a mere one hundred degree range on the centigrade scale. Even Earth-based life is concentrated towards particular climatic zones. The temperature at the Earth's surface keeps it tantalizingly balanced between recurrent ice ages and the roasting that results from a runaway greenhouse effect. Very slight differences in the size of our planet or its distance from the Sun would have tipped the scales irretrievably towards one or other of these fates. That such a delicate balance, which is essentially the outcome of those random symmetry-breakings that we discussed in Chapter 6, should be so crucial suggests that natural complexity may be a rather rare thing in the Universe.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation

“Life as we know, and partially understand it, is a classical example of what can occur when a sufficient level of complexity is attained. Consciousness appears to be a manifestation of an even more elaborate level of organization.”
― John D. Barrow, Theories of Everything: The Quest for Ultimate Explanation