John Barrow Quotes

History is full of people who thought they were right -- absolutely right, completely right, without a shadow of a doubt. And because history never seems like history when you are living through it, it is tempting for us to think the same.

Any universe simple enough to be understood is too simple to produce a mind able to understand it -Barrow's Uncertainty Principle

There are only certain intervals of time when life of any sort is possible in an expanding universe and we can practise astronomy only during that habitable time interval in cosmic history.

to paraphrase science writer John D. Barrow … we know they are impossible and yet we can imagine them anyway. Our brains, it turns out, are not prisoners of the world we live in; we can fly free! We can, any time we like, create the impossible.

No non-poetic account of reality can be complete.

Prior to then it was believed that black holes were just cosmic cookie monsters, swallowing everything that came within their gravitational clutches.

To the generations of Americans raised since World War 2, the identities of criminals such as Charles "Pretty Boy" Floyd, Baby Face Nelson, "Ma" Barker, John Dillenger, and Clyde Barrow are no more real than are Luke Skywalker and Indiana Jones. After decades spent in the washing machine of popular culture, their stories have been bled of all reality, to an extent that few Americans today know who these people actually were, much less that they all rose to national prominence at the same time. They were real.

If the deep logic of what determines the value of the fine-structure constant also played a significant role in our understanding of all the physical processes in which the fine-structure constant enters, then we would be stymied. Fortunately, we do not need to know everything before we can know something.

The sciences paint an impersonal and objective account of the world, deliberately devoid of "meaning", telling us about origins and mechanics of life, by revealing nothing of the joys and sorrows of living.

Winning the Origins Lottery Nontheistic models adhere to a central premise that humans arose by strictly natural unguided steps from a bacterial life-form that sprang into being 3.8 billion years ago. Famed evolutionary biologist Francisco Ayala, an advocate for the hypothesis that natural selection and mutations can efficiently generate distinctly different species, nevertheless calculated the probability that humans (or a similarly intelligent species) arose from single-celled organisms as a possibility so small (10-1,000,000) that it might as well be zero (roughly equivalent to the likelihood of winning the California lottery 150,000 consecutive times with the purchase of just one ticket each time).2 He and other evolutionary biologists agree that natural selection and mutations could have yielded any of a virtually infinite number of other outcomes. Astrophysicists Brandon Carter, John Barrow, and Frank Tipler produced an even smaller probability.

I am blood. I am death, I am vengeance,” she said, her voice flat, empty. Then she wiped the seax clean and slipped it into her belt, finally placing timber and stone on to the barrow, sealing Thorkel inside. She stooped, lifted her sack and picked up her spear, then strode out through the gateway. With a hiss of wings Vesli flew around her, hovered over her. “Vesli come with you, help mistress get Breca back,” the tennúr said. “No,” Orka said. “Death is my only companion. Stay and help Spert.” Vesli looked at the two seaxes that had slain Thorkel, thrust inside Orka’s belt. “What are you going to do with them, mistress?” the tennúr asked. Orka looked out, over the sloping hills and down to Fellur village, a smear far below. “I’m going to find the owner of these blades, and give them back to him,” Orka snarled.

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

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.

We can measure the fine structure constant with very great precision, but so far none of our theories has provided an explanation of its measured value. One of the aims of superstring theory is to predict this quantity precisely. Any theory that could do that would be taken very seriously indeed as a potential 'Theory of Everything'.

universal laws prescribe how things will behave not, like human laws, how they ought to behave.

nothing is higher than heaven; nothing is beyond the walls of the world; nothing is lower than hell, or more glorious than virtue.”48

When one looks back across a chasm of seventy years, through a prism of pulp fiction and bad gangster movies, there is a tendency to view the events of 1933-34 as mythic, as folkloric. To the generations of Americans raised since World War II, the identities of criminals such as Charles “Pretty Boy” Floyd, Baby Face Nelson, “Ma” Barker, John Dillinger, and Clyde Barrow are no more real than are Luke Skywalker or Indiana Jones. After decades spent in the washing machine of popular culture, their stories have been bled of all reality, to an extent that few Americans today know who these people actually were, much less that they all rose to national prominence at the same time.

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.

Einstein argued that the laws of Nature should appear to be the same for all observers in the Universe, no matter where they were or how they were moving. If they were not then there would exist privileged observers for whom the laws of Nature looked simpler than they did for other observers.

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.

THE MEETING" "Scant rain had fallen and the summer sun Had scorched with waves of heat the ripening corn, That August nightfall, as I crossed the down Work-weary, half in dream. Beside a fence Skirting a penning’s edge, an old man waited Motionless in the mist, with downcast head And clothing weather-worn. I asked his name And why he lingered at so lonely a place. “I was a shepherd here. Two hundred seasons I roamed these windswept downlands with my flock. No fences barred our progress and we’d travel Wherever the bite grew deep. In summer drought I’d climb from flower-banked combe to barrow’d hill-top To find a missing straggler or set snares By wood or turmon-patch. In gales of March I’d crouch nightlong tending my suckling lambs. “I was a ploughman, too. Year upon year I trudged half-doubled, hands clenched to my shafts, Guiding my turning furrow. Overhead, Cloud-patterns built and faded, many a song Of lark and pewit melodied my toil. I durst not pause to heed them, rising at dawn To groom and dress my team: by daylight’s end My boots hung heavy, clodded with chalk and flint. “And then I was a carter. With my skill I built the reeded dew-pond, sliced out hay From the dense-matted rick. At harvest time, My wain piled high with sheaves, I urged the horses Back to the master’s barn with shouts and curses Before the scurrying storm. Through sunlit days On this same slope where you now stand, my friend, I stood till dusk scything the poppied fields. “My cob-built home has crumbled. Hereabouts Few folk remember me: and though you stare Till time’s conclusion you’ll not glimpse me striding The broad, bare down with flock or toiling team. Yet in this landscape still my spirit lingers: Down the long bottom where the tractors rumble, On the steep hanging where wild grasses murmur, In the sparse covert where the dog-fox patters.” My comrade turned aside. From the damp sward Drifted a scent of melilot and thyme; From far across the down a barn owl shouted, Circling the silence of that summer evening: But in an instant, as I stepped towards him Striving to view his face, his contour altered. Before me, in the vaporous gloaming, stood Nothing of flesh, only a post of wood.

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

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.

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.

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.

theory. “The development of the general theory of relativity introduced Einstein to the power of abstract mathematical formalisms, notably that of tensor calculus,” writes the astrophysicist John Barrow. “A deep physical insight orchestrated the mathematics of general relativity, but in the years that followed the balance tipped the other way. Einstein’s search for a unified theory was characterized by a fascination with the abstract formalisms themselves.”44 In his Oxford lecture, Einstein began with a nod to empiricism: “All knowledge of reality starts from experience and ends in it.” But he immediately proceeded to emphasize the role that “pure reason” and logical deductions play. He conceded, without apology, that his success using tensor calculus to come up with the equations of general relativity had converted him to a faith in a mathematical approach, one that emphasized the simplicity and elegance of equations more than the role of experience. The fact that this method paid off in general relativity, he said, “justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas.”45 That is an elegant—and also astonishingly interesting—creed. It captured the essence of Einstein’s thought during the decades when mathematical “simplicity” guided him in his search for a unified field theory. And it echoed the great Isaac Newton’s declaration in book 3 of the Principia: “Nature is pleased with simplicity.” But Einstein offered no proof of this creed, one that seems belied by modern particle physics.46 Nor did he ever fully explain what, exactly, he meant by mathematical simplicity. Instead, he merely asserted his deep intuition that this is the way God would make the universe. “I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other,” he claimed.

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.

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.

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.

Barrels of oysters wrapped in seaweed came by boat from Stollport. Fat beam and trout were carried in dripping wooden boxes lined with wet straw. A great conger eel arrived in a crate large enough to hold a cannon and appeared so fearsome Mister Bunce quelled the kitchen boys' mock-screams only by bringing out Mister Stone to take his pick among the screechers. Sacks of raisins, currants, dried prunes and figs piled up in the dry larder. In the wet room, soused brawn, salted ling and gallipots of anchovies crowded the shelves and floor. In the butchery, Colin and Luke marshalled four undercooks, six men from the Estate armed with saws, a grumbling Barney Curle and his barrow to skin, draw and joint the hogs. Simeon, Tam Yallop and the other bakers lugged in sacks of meal from the Callock Marwood mill while a dray from the ale-house made journeys over the hill, past the gatehouse and into the yard until the buttery and cellar were filled with kegs and barrels. Rhenish wine arrived in a covered wagon, the dark oak tuns resting on a thick bed of bracken. Scents of cinnamon and saffron drifted out of the spice room.

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.

The quantum wavelength of a particle gets smaller the more massive the particle. Situations are dominated by quantum waviness when the quantum wavelength of their participants exceeds their physical size. Everyday objects, like cars and speeding cricket balls, have such high masses that their quantum wavelengths are vastly smaller than their sizes and we can forget about quantum influences when driving cars or watching cricket matches.

We have never explained the numerical value of any of the constants of Nature.

belief in the ultimate simplicity and unity behind the rules that constrain the Universe leads us to expect that there exists a single unchanging pattern behind the appearances. Under different conditions this single pattern will crystallise into superficially distinct patterns that show up as the four separate forces governing the world around us. It has gradually become clear how this patterning probably works.

In our solar system life first evolved surprisingly soon after the formation of a hospitable terrestrial environment. There is something unusual about this. Suppose the typical time that it takes for life to evolve is called t(bio), then from the evidence of our solar system, which is about 4.6 billion years old, it seems that the time it takes for stars to settle down and create a stable source of heat and light, t(star), is not very different to t(bio) because we have found simple forms of terrestrial bacterial life that are several billion years old.

We can easily imagine worlds in which the constants of Nature take on slightly different numerical values where living beings like ourselves would not be possible. Make the fine structure constant bigger and there can be no atoms, make the strength of gravity greater and stars exhaust their fuel very quickly, reduce the strength of nuclear forces and there can be no biochemistry, and so on.

A condition, like the existence of stars or certain chemical elements, is identified as a necessary condition for the existence of any form of chemical complexity, of which life is the most impressive known example. This does not mean that if this condition is met that life must exist, will never die out if it does exist, or that the fact that this condition holds in our Universe means that it was ‘designed’ with life in mind.

The specific nuclear reaction that is needed to make carbon is a rather improbable one. It requires three nuclei of helium to come together to fuse into a single nucleus of carbon.

If the fine structure constant, that governs the strength of electromagnetic forces, were changed by more than 4 per cent or the strong force by more than 0.4 of one per cent then the production of carbon or oxygen would be reduced by factors of between 30 and 1000.

A change of more than 0.4 per cent in the constants governing the strength of the strong nuclear force or more than 4 per cent in the fine structure constant would destroy almost all carbon or almost all oxygen in every star.

by means of evolution by natural selection, which showed how living things can become well adapted to their environments over the course of time under a very wide range of circumstances, so long as the environment is not changing too quickly. Complexity could develop from simplicity without direct Divine intervention.

I do not feel like an alien in this 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.’ Freeman Dyson24

The more simultaneous variations of other constants one includes in these considerations, the more restrictive is the region where life, as we know it, can exist. It is very likely that if variations can be made then they are not all independent. Rather, making a small change in one constant might alter one or more of the others as well. This would tend to make the restrictions on most variations become even more tightly constrained.

the values of the constants of Nature are rather bio-friendly. If they are changed by even a small amount the world becomes lifeless and barren instead of a home for interesting complexity

Already we see a trend in our own technological societies towards the fabrication of smaller and smaller machines that consume less and less energy and produce almost no waste. Taken to its logical conclusion, we expect advanced life-forms to be as small as the laws of physics allow.

we might mention that this could explain why there is no evidence of extraterrestrial life in the Universe. If it is truly advanced, even by our standards, it will most likely be very small, down on the molecular scale. All sorts of advantages then accrue. There is lots of room there – huge populations can be sustained. Powerful, intrinsically quantum computation can be harnessed. Little raw material is required and space travel is easier. You can also avoid being detected by civilisations of clumsy bipeds living on bright planets that beam continuous radio noise into interplanetary space.

Now step outside spacetime and look in at what happens there. Histories of individuals are paths through the block. If they curve back upon themselves to form closed loops then we would judge time travel to occur. But the paths are what they are. There is no history that is ‘changed’ by doing that. Time travel allows us to be part of the past but not to change the past. The only time-travelling histories that are possible are self-consistent paths. On any closed path there is no well-defined division between the future and the past.

there could be more than three dimensions of space but they had to be small and unchanging if they were to avoid altering the character of the world that we experience.

In recent years astronomers have made newspaper headlines all over the world by mapping this radiation in exquisite detail with receivers carried on balloons and satellites. We know that the radiation has the spectrum of pure heat radiation to very high precision and its temperature is the same in different directions on the sky to an accuracy of about one part in 100,000.

If the constants of Nature are slowly changing then we could be on a one-way slide to extinction. We have learnt that our existence exploits many peculiar coincidences between the values of different constants of Nature, and that the observed values of the constants fall within some very narrow windows of opportunity for the existence of life.

If constants like G and α do not vary in time, then the standard history of our Universe has a simple broad-brush appearance. During the first 300,000 years the dominant energy in the Universe is radiation and the temperature is greater than 3000 degrees and too hot for any atoms or molecules to exist. The Universe is a huge soup of electrons, photons of light and nuclei.

There are three trajectories for an expanding universe to follow (see p. 184). The ‘closed’ universe expands too slowly to overcome the decelerating effects of gravity and eventually it collapses back to high density. The ‘open’ universe has lots more expansion energy than gravitational deceleration and the expansion runs away forever. The in-between world, that is often called the ‘flat’ or ‘critical’ universe, has a perfect balance between expansion energy and gravity and keeps on expanding for ever. Our Universe is tantalisingly close to this critical or ‘flat’ state today.

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.

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.

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.

The ubiquity of chaotic phenomena raises a further problem for our dreams of omniscience through the medium of a Theory of Everything. Even if we can overcome the problem of initial conditions to determine the most natural or uniquely consistent starting state, we may have to face the reality that there is inevitable uncertainty surrounding the prescription of the initial state which makes the prediction of the exact future state of the Universe impossible. Only statistical statements will be possible.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

One of the most striking properties of the visible universe is the preponderance of matter over antimatter. Although particle accelerators produce matter and antimatter in equal abundances quite routinely and there is a democratic relationship between the two, we see no antiplanets, no antistars, no antigalaxies, and there is no evidence of any antimatter in the cosmic rays that come from outside our solar system. Nor do we see any evidence of the wholesale annihilation of matter and antimatter which would erupt anywhere in the Universe where the two came into contact. Thus, for some mysterious reason, there exists a form of cosmic favouritism. The observable universe is made of matter rather than antimatter. The other thing that it most obviously consists of is radiation. Indeed, on a straight count the photons have it; for there are on the average about two billion photons of light to be found for every proton in the Universe. Since every time a proton meets an antiproton and annihilates, two photons of light are produced, we can see that a universe such as ours, possessing about two billion photons for every proton, needs to have arisen from a hot dense state in which there were on average a billion and one protons for every billion antiprotons. A billion antiprotons knock out a billion protons producing two billion photons for every left-over proton. But why should the early Universe possess such a weird skewness of matter over antimatter to start off with?

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.

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.

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.

The old believe everything: the middle-aged suspect everything: the young know everything.’ Oscar Wilde53

Natural units tell us that in a well-defined sense the Universe is very old already, about 1060 Planck times old. Life on Earth didn't appear until after the Universe was 1059 Planck times old. We were a late arrival.

Others might point to the warning that the most dangerous thing in science is the idea that arrives before its time.

At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of the world are the values of the dimensionless constants of Nature. If all masses are doubled in value you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged.

Everything that is made of atoms has a density quite close to the density of a single atom given by the mass of an atom divided by its volume.

Suppose we take the whole mass inside the visible Universe19 and determine its quantum wavelength. We can ask when this quantum wavelength of the visible Universe exceeds its size. The answer is when the Universe is smaller than the Planck length in size (10–33 cm), less than the Planck time in age (10–43 secs), and hotter than the Planck temperature (1032 degrees). Planck's units mark the boundary of applicability of our current theories. To understand what the world is like on a scale smaller than the Planck length we have to understand fully how quantum uncertainty becomes entangled with gravity.

One of the curious problems of physics is that it has two beautifully effective theories – quantum mechanics and general relativity – but they govern different realms of Nature.

Quantum mechanics holds sway in the microworld of atoms and elementary particles. It teaches us that every mass in Nature, however solid or pointlike it may appear, has a wavelike aspect. This wave is not like a water wave. It is more analogous to a crime wave or a wave of hysteria: it is a wave of information.

We have seen that the process of stellar alchemy takes time – billions of years of it. And because our Universe is expanding it needs to be billions of light years in size if it is to have enough time to produce the building blocks for living complexity. A universe that was only as big as our Milky Way galaxy, with its 100 billion stars, would be little more than a month old.

The impact over the following centuries of Copernicus' leap away from the prejudices of anthropocentrism was felt across the whole spectrum of human investigation. We began to appreciate our place in the Universe was by no means central. Indeed, in many respects, it appeared to be almost peripheral.

Another consequence of an old expanding universe, besides its large size, is that it is cold, dark and lonely. When any ball of gas or radiation is expanded in volume, the temperature of its constituents falls off in proportion to the increase in its size. A universe that is big and old enough to contain the building blocks of complexity will be very cold and the levels of average radiant energy so low that space will everywhere appear dark.

Einstein enunciated what he called the Principle of Covariance: that laws of Nature should be expressed in a form that will look the same for all observers, no matter where they are located and no matter how they are moving.

If we were to smooth out all the material in the Universe into a uniform sea of atoms we would see just how little of anything there is. There would be little more than about 1 atom in every cubic metre of space. No laboratory on Earth could produce an artificial vacuum that was anywhere near as empty as that. The best vacuum achievable today contains approximately 1000 billion atoms in a cubic metre.

Typical stars, like our Sun, emit a wind of electrically-charged particles from their surface which will strip off the atmospheres of orbiting planets unless the wind can be deflected by a planetary magnetic field. In our solar system the Earth's magnetic field has protected its atmosphere from the solar wind but Mars, unprotected by any magnetic field, lost its atmosphere long ago.

For many years it had been claimed that the average achievement by pupils in some South-East Asian countries was significantly higher than in the United Kingdom. Then it came to light that the weakest pupils in that country were removed from the total who were evaluated at an earlier stage in the educational process. Clearly, the effect of their removal is to skew the average attainments to be higher than they would otherwise be.

Here, uniquely, came the day of the death of the gods. When they fled to the barrows, and when one, without shelter, captured the forever by a ruse, naming it but one night and a single daytime

The first physicist to stress the all-encompassing role of [the fine-structure constant] and [the proton/electron mass ratio] in determining the inevitable structure of atomic systems seems to have been Max Born.

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.

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.

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.

Yet, despite the symmetry of the laws of Nature, we observe the outcomes of those symmetrical laws to be assymetrical states and structures.

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.

Each of us is a complicated assymetrical outcome of the laws of electromagnetism and gravity.

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.

It is the cosmological vacuum energy that contributes a repulsive lambda force to the gravitational force of Newton.

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.

We know what we are, but know not what we may be.