The Book of Nothing Quotes

“Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“I love cosmology: there’s something uplifting about viewing the entire universe as a single object with a certain shape. What entity, short of God, could be nobler or worthier of man’s attention than the cosmos itself? Forget about interest rates, forget about war and murder, let’s talk about space.” Rudy Rucker21”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“All our puzzles about whether or not lambda exists and, if so, what is responsible for giving it such a strange value, are like questions about the inflationary scalar field's potential landscape. Why is its final vacuum state so fantastically close to the zero line? How does it 'know' where to end up when the scalar field starts rolling downhill in its landscape? Nobody knows the answer to these questions. They are the greatest unsolved problems in gravitation physics and astronomy. The nature of their answers could take many forms. There could exist some deep new principle that links together all the different forces of Nature in a way that dictates the vacuum levels of all the fields of energy that feel their effects. This principle would be unlike any that we know because it would need to control all the possible contributions to lambda that arise at symmetry breakings during the expansion of the Universe. It would need to control physics over a vast range of energies.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“If water is bombarded with intense sound waves, under the right conditions, then air bubbles can form which quickly contract and then suddenly disappear in a flash of light. The conventional explanation of what is being seen here is that a shock wave, a little sonic boom, is created inside the bubble, which dumps its energy, causing the interior to be quickly heated to flash point. But a more dramatic possibility, first suggested by the Nobel prize-winner Julian Schwinger, has been entertained. Suppose the surface of the bubble is acting like a Casimir plate so that, as the bubble shrinks, it excludes more and more wavelengths of the zero point fluctuations from existing within it. They can't simply disappear into nothing; energy must be conserved, so they deposit their energy into light. At present, experimenters are still unconvinced that this is what is really happening, but it is remarkable that so fundamental a question about a highly visible phenomena is still unresolved.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Gravity acts on all forms of mass and energy, but energy comes in a host of very different forms that behave in peculiar ways that were not known in Newton's day. Wotst of all, gravity gravitates. Those waves of gravity that spread out, rippling the curvature of space, carry energy too and that energy acts as a source for its own gravity field. Gravity interacts with itself in a way that light does not.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“This picture of matter curving space and curvaceous space dictating how matter and light will move has several striking features. It brings the non-Euclidean geometries that we talked about in the last chapter out from the library of pure mathematics into the arena of science. The vast collection of geometries describing spaces that are not simply the flat space of Euclid are the ones that Einstein used to capture the possible structures of space distorted by the presence of mass and energy.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“The universe appears to be a system of very low density wherever we look. This is no accident. The expansion of the Universe weds its size and age to the gravitational pull of the material that it contains. In order that a universe expands for long enough to allow the building blocks of life to form in the interiors of stars, by a sequence of nuclear reactions, it must be billions of years old. This means that it must be billions of light years in extent and possess a very small average density of matter and a very low temperature. The low temperature and energy of its material ensures that the sky is dark at night. Turn off our local Sun and there is just too little light around in the Universe to brighten the sky. The night is dark, interspersed only by pinpricks of starlight. Universes that contain life must be big and old, dark and cold. If our Universe was less of a vacuum it could not be an abode for living complexity.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“There are about one hundred billion galaxies within this visible universe and the average density of material within a galaxy is about one million times greater than that in the visible universe as a whole, and corresponds to about one atom in every cubic centimetre.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Navy: Please divert your course 15 degrees to the North to avoid a collision. Civilian: Recommend you divert your course 15 degrees to South to avoid a collision. Navy: This is the Captain of a US Navy ship. I say again, divert your course. Civilian: No, I say again, divert your course. Navy: This is the aircraft carrier Enterprise. We are a large warship of the US Navy. Divert your course now!! Civilian: This is a lighthouse. Your call.” Canadian naval radio conversation38”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“nothing is higher than heaven; nothing is beyond the walls of the world; nothing is lower than hell, or more glorious than virtue.”48”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russell pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russell replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“It is the cosmological vacuum energy that contributes a repulsive lambda force to the gravitational force of Newton.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“When one looks at the numbers, the situation becomes even more perplexing. The effect of lambda grows steadily with respect to the familiar Newtonian force of gravity as the Universe gets bigger. If it is only recently becoming the dominant force, after billions of years of expansion of the Universe, it must have started out enormously smaller than the Newtonian force. The distance of that final minimum energy level in Figure 8.14 from the zero line in order to explain the value of lambda inferred from the supernova observations is bizarre: roughly 10^-120 - that is, 1 divided by 10 followed by 119 zeros! This is the smallest number ever encountered in science. Why is it not zero? How can the minimum level be tuned so precisely? If it were 10 followed by just 117 zeros, then the galaxies could not form. Extraordinary fine tuning is needed to explain such extreme numbers. Extraordinary fine tuning is needed to explain such extreme numbers. And, if this were not bad enough, the vacuum seems to have its own defence mechanism to prevent us finding easy answers to this problem. Even if inflation does have some magical property which we have so far missed that would set the vacuum energy exactly to zero when inflation ends, it would not stay like that. As the Universe keeps on expanding and cooling it passes through several temperatures at which the breaking of a symmetry occurs in a potential landscape, rather like that which occurs in the example of the magnet that we saw at the beginning of the chapter. Every time this happens, a new contribution to the vaccum energy is liberated and contributes to a new lambda term that is always vastly bigger than our observation allows. And, by 'vastly bigger' here, we don't just mean that it is a few times bigger than the value inferred from observations, so that in the future some small correction to the calculations, or change in the trend of the observations, might make theory and observation fit hand in glove. We are talking about an overestimate by a factor of about 10 followed by 120 zeros! You can't get much more wrong than that.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“We know what we are, but know not what we may be.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Universes that expand too slowly will collapse back to a big crunch before galaxies can form; universes that expand too quickly do not allow islands of matter to condense out into galaxies and form stars.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“One of Nature's deep secrets is the fact that the outcomes of the laws of Nature do not have to possess the same symmetries as the laws themselves. The outcomes are far more complicated, and far less symmetrical, than the laws. Consequently, they are far more difficult to understand. In this way it is possible to have a Universe governed by a very small number of simple symmetrical laws (perhaps just a single law) yet manifesting a stupendous array of complex, asymmetrical states and structures that might even be able to think about themselves.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Each of us is a complicated assymetrical outcome of the laws of electromagnetism and gravity.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Yet, despite the symmetry of the laws of Nature, we observe the outcomes of those symmetrical laws to be assymetrical states and structures.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“The phenomenon of symmetry breaking reveals something deeply significant about the workings of the universe. The laws of Nature are unerringly symmetrical. They do not have preferences for particular times, places and directions. Indeed, we have found that one of the most powerful guides to their forms is precisely such a requirement. Einstein was the first to recognise how this principle had been used only partially by Galileo and Newton. He elevated it to a central requirement for the laws of Nature to satisfy: that they appear the same to all observers in the Universe, no matter how they are moving or where they are located. There cannot be privileged observers for whom everything looks simpler than it does for others. To countenance such observers would be the ultimate anti-Copernican perspective on the Universe. This democratic principle is a powerful guide to arriving at the most general expression of Nature's laws.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Thus we see that the quantisation of atomic energies into a ladder of seperate values, rather than allowing them to take on the entire continuum of possible values, lies at the heart of the life-supporting stability and uniformity of the world around us.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Curiously, Schrodinger's equation describes the change in the probability that we will obtain a particular result if we conduct an experiment. It is telling us something about what we can know about the world. Thus, when we say that a particle is behaving like a wave, we should not think of this wave as if it were a water wave or a sound wave. It is more appropriate to regard it as a wave of information or probability, like a crime wave or a wave of hysteria. For, if a wave of hysteria passes through a population, it means that we are more likely to find hysterical behaviour there. Likewise, if an electron wave passes through your laboratory it means that you are more likely to detect an electron there. There is complete determinism in quantum theory, but not at the level of appearances or the things that are measured. Schrodinger's amazing equation gives a completely deterministic description of the change of the quantity (called the wave function') which captures the wavelike aspect of a given situation. But the wave function is not observable. It allows you only to calculate the result of a measurement in terms of the probabilities of different outcomes. It might tell you that fifty percent of the time you will find the atom to have one state, and fifty percent of the time, another. And, remarkably, in the microscopic realm, this is exactly what the results of successive measurements tell you: not the same result every time but a pattern of outcomes in which some are more likely than others.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“First, energy is quantised: in atoms it does not take on all possible values but only a ladder of specific values whose separation is fixed by the value of a new constant of Nature, dubbed Planck's constant and represented by the letter h. An intuitive picture of how the wavelike character of the orbital behaviour leads to quantisation can be seen in Figure 7.1, where we can see how only a whole number of wave cycles can fit into an orbit. Second, all particles possess a wavelike aspect. They behave as waves with a wavelength that is inversely proportional to their mass and velocity. When that quantum wavelength is much smaller than the physical size of the particle it will behave like a simple particle, but when its quantum wavelength becomes at least as large as the particle's size then wavelike quantum aspects will start to be significant and dominate the particle's behaviour, producing novel behaviour. Typically, as objects increase in mass, their quantum wavelengths shrink to become far smaller than their physical size, and they behave in a non-quantum or 'classical' way, like simple particles.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“For even if we expunged all the matter in the Universe the lambda force could still exist, causing the universe to expand or contract. It was always there, acting on everything but unaffected by anything. It began to look like an omnipresent form of energy that remained when everything that could be removed from a universe had been removed, and that sounds very much like somebody's definition of a vacuum.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“The pulsar is like a lighthouse beam spinning at high speed. Every time it comes around to face us we see a flash. Its rotation can be very accurately monitored by timing observations of its periodic pulses. Twenty years of observations have shown that the pulsing of the binary pulsar is slowing at exactly the rate predicted if the system is losing energy by radiating gravitational waves at the rate predicted by Einstein's theory.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Anselm conceives of God as something than which nothing greater or more perfect can be conceived. Since this idea arises in our minds it certainly has an intellectual existence. But does it have an existence outside of our minds? Anselm argued that it must, for otherwise we fall into a contradiction. For we could imagine something greater than that which nothing greater can be conceived; that is the mental conception we have together, plus the added attribute of real existence.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“There is, as we shall see, a real and precise difference between the number zero and the concept of a set that posesses no members - the null, or empty set. Indeed, the second idea, pointless as it sounds, turns out to be by far the most fruitful of the two. From it, all of the rest of mathematics can be created step by step.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Non-Euclidean' became a byword for non-absolute knowledge. It also served to illustrate most vividly the gap between mathematics and the natural world. Mathematics was much bigger than physical reality. There were mathematical systems that described aspects of Nature, but there were others that did not. Later, mathematicians would use these discoveries about geometry to discover that there were other logics as well. Aristotle's system was, like Euclid's, just one of many possibilities. Even the concept of truth was not absolute. What is false in one logical system can be true in another. In Euclid's geometry of flat surfaces, parallel lines never meet, but on curved surfaces they can. These discoveries revealed the difference between mathematics and science. Mathematics was something bigger than science, requiring only self-consistency to be valid. It contained all possible patterns of logic. Some of those patterns were followed by parts of Nature; others were not. Mathematics was open-ended, uncompleteable, infinite; the physical universe was smaller.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“When an important change takes place in science, in which a new theory takes the stagw, the incoming theory is generally an extension of the old theory which has the property of becoming more and more like the old theory in some limiting situation. In effect, it reveals that the old theory was an approximation (usually a very good one) to the new one that holds under a particular range of conditions. Thus, Einstein's special theory of relativity becomes Newton's theory of motion when speeds are far less than that of light, Einstein's general theory of relativity becomes Newton's theory of gravity when gravitational fields are weak and bodies move at speeds less than that of light. In recent years we have even begun to map out what the successor to Einstein's theory may look like. It appears that Einstein's theory of general relativity is a limiting, low-energy case of a far deeper and wider theory, which has been dubbed M theory.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“Fitzgerald had noticed that if this sqrt(I-v^2/c^2) correction factor was applied to the analysis of Michelson's apparatus fixed on the earth's surface as it moved around the Sun, it could explain why Michelson measured no effect from the ether. The arm of the interferometer contracts by a factor sqrt(I-v^2/c^2) in the direction of its motion through the ether at a speed v. At an orbital speed of 29 kilometers per second this results in a contraction of only one part in 200,000,000 in the direction of the Earth's orbital motion. The length of the arm perpendicular to the ether's motion is unaffected. This small contraction effect exactly counterbalances the time delay expected from the presence of a stationary ether. If the Fitzgerald-Lorentz contraction occurred then it allowed the existence of a stationary ether to be reconciled with the null result of the Michelson-Morley experiment. Space need not be empty after all.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe

“We have seen that our numerical zero derives originally from the Hindu sunya, meaning void or emptiness, deriving from the Sanskrit name for the mark denoting emptiness, or sunya-bindu, meaning an empty dot. These developed between the sixth and eighth centuries. By the ninth century, the assimilation of Indian mathematics by the Arab world led to the literal translation of sunya into Arabic as as-sifr, which also means 'empty' or the 'absence of anything'. We still see a residue of this because it is the origin of the English word 'cipher'. Originally, it meant 'Nothing', or if used insultingly of a person it would mean that they were a nonentity-a nobody-as in King Lear where the fool says to the King "Now thou art an 0 without a figure. I am better than thou art now. I am a fool, thou art nothing.”
― John D. Barrow, The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe