Roger Penrose
The Road To Reality: A Complete Guide To The Laws Of The Universe
### ISBN 13 : 9780679454434

Book by Roger Penrose

*Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.*

**Prologue**

Am-tep was the King’s chief craftsman, an artist of consummate skills. It was night, and he lay sleeping on his workshop couch, tired after a handsomely productive evening’s work. But his sleep was restless – perhaps from an intangible tension that had seemed to be in the air. Indeed, he was not certain that he was asleep at all when it happened. Daytime had come – quite suddenly – when his bones told him that surely it must still be night.

He stood up abruptly. Something was odd. The dawn’s light could not be in the north; yet the red light shone alarmingly through his broad window that looked out northwards over the sea. He moved to the window and stared out, incredulous in amazement. The Sun had never before risen in the north! In his dazed state, it took him a few moments to realize that this could not possibly be the Sun. It was a distant shaft of a deep fiery red light that beamed vertically upwards from the water into the heavens.

As he stood there, a dark cloud became apparent at the head of the beam, giving the whole structure the appearance of a distant giant parasol, glowing evilly, with a smoky flaming staff. The parasol’s hood began to spread and darken – a daemon from the underworld. The night had been clear, but now the stars disappeared one by one, swallowed up behind this advancing monstrous creature from Hell.

Though terror must have been his natural reaction, he did not move, transfixed for several minutes by the scene’s perfect symmetry and awesome beauty. But then the terrible cloud began to bend slightly to the east, caught up by the prevailing winds. Perhaps he gained some comfort from this and the spell was momentarily broken. But apprehension at once returned to him as he seemed to sense a strange disturbance in the ground beneath, accompanied by ominous-sounding rumblings of a nature quite unfamiliar to him. He began to wonder what it was that could have caused this fury. Never before had he witnessed a God’s anger of such magnitude.

His first reaction was to blame himself for the design on the sacrificial cup that he had just completed – he had worried about it at the time. Had his depiction of the Bull-God not been sufficiently fearsome? Had that god been offended? But the absurdity of this thought soon struck him. The fury he had just witnessed could not have been the result of such a trivial action, and was surely not aimed at him specifically. But he knew that there would be trouble at the Great Palace. The Priest-King would waste no time in attempting to appease this Daemon-God. There would be sacrifices. The traditional offerings of fruits or even animals would not suffice to pacify an anger of this magnitude. The sacrifices would have to be human.

Quite suddenly, and to his utter surprise, he was blown backwards across the room by an impulsive blast of air followed by a violent wind. The noise was so extreme that he was momentarily deafened. Many of his beautifully adorned pots were whisked from their shelves and smashed to pieces against the wall behind. As he lay on the floor in a far corner of the room where he had been swept away by the blast, he began to recover his senses, and saw that the room was in turmoil. He was horrified to see one of his favourite great urns shattered to small pieces, and the wonderfully detailed designs, which he had so carefully crafted, reduced to nothing.

Am-tep arose unsteadily from the floor and after a while again approached the window, this time with considerable trepidation, to re-examine that terrible scene across the sea. Now he thought he saw a disturbance, illuminated by that far-off furnace, coming towards him. This appeared to be a vast trough in the water, moving rapidly towards the shore, followed by a cliff-like wall of wave. He again became transfixed, watching the approaching wave begin to acquire gigantic proportions. Eventually the disturbance reached the shore and the sea immediately before him drained away, leaving many ships stranded on the newly formed beach. Then the cliff-wave entered the vacated region and struck with a terrible violence. Without exception the ships were shattered, and many nearby houses instantly destroyed. Though the water rose to great heights in the air before him, his own house was spared, for it sat on high ground a good way from the sea.

The Great Palace too was spared. But Am-tep feared that worse might come, and he was right – though he knew not how right he was. He did know, however, that no ordinary human sacrifice of a slave could now be sufficient. Something more would be needed to pacify the tempestuous anger of this terrible God. His thoughts turned to his sons and daughters, and to his newly born grandson. Even they might not be safe.

Am-tep had been right to fear new human sacrifices. A young girl and a youth of good birth had been soon apprehended and taken to a nearby temple, high on the slopes of a mountain. The ensuing ritual was well under way when yet another catastrophe struck. The ground shook with devastating violence, whence the temple roof fell in, instantly killing all the priests and their intended sacrificial victims. As it happened, they would lie there in mid-ritual – entombed for over three-and-a-half millennia!

The devastation was frightful, but not final. Many on the island where Am-tep and his people lived survived the terrible earthquake, though the Great Palace was itself almost totally destroyed. Much would be rebuilt over the years. Even the Palace would recover much of its original splendour, constructed on the ruins of the old. Yet Am-tep had vowed to leave the island. His world had now changed irreparably.

In the world he knew, there had been a thousand years of peace, prosperity, and culture where the Earth-Goddess had reigned. Wonderful art had been allowed to flourish. There was much trade with neighbouring lands. The magnificent Great Palace was a huge luxurious labyrinth, a virtual city in itself, adorned by superb frescoes of animals and flowers. There was running water, excellent drainage, and flushed sewers. War was almost unknown and defences unnecessary. Now, Am-tep perceived the Earth-Goddess overthrown by a Being with entirely different values.

It was some years before Am-tep actually left the island, accompanied by his surviving family, on a ship rebuilt by his youngest son, who was a skilled carpenter and seaman. Am-tep’s grandson had developed into an alert child, with an interest in everything in the world around. The voyage took some days, but the weather had been supremely calm. One clear night, Am-tep was explaining to his grandson about the patterns in the stars, when an odd thought overtook him:

Am-tep knew these patterns well, for he had a keen artist’s eye. Surely, he thought, those tiny candles of light in the sky should have been blown at least a little from their positions by the violence of that night, just as his pots had been smashed and his great urn shattered. The Moon also had kept her face, just as before, and her route across the star-filled heavens had changed not one whit, as far as Am-tep could tell. For many moons after the Catastrophe, the skies had appeared different. There had been darkness and strange clouds, and the Moon and Sun had sometimes worn unusual colours. But this had now passed, and their motions seemed utterly undisturbed. The tiny stars, likewise, had been quite unmoved.

If the heavens had shown such little concern for the Catastrophe, having a stature far greater even than that terrible Daemon, Am-tep reasoned, why should the forces controlling the Daemon itself show concern for what the little people on the island had been doing, with their foolish rituals and human sacrifice? He felt embarrassed by his

Yet Am-tep was still troubled by the question ‘why?’ What deep forces control the behaviour of the world, and why do they sometimes burst forth in violent and seemingly incomprehensible ways? He shared his questions with his grandson, but there were no answers.

. . .

A century passed by, and then a millennium, and still there were no answers.

. . .

Amphos the craftsman had lived all his life in the same small town as his father and his father before him, and his father’s father before that. He made his living constructing beautifully decorated gold bracelets, earrings, ceremonial cups, and other fine products of his artistic skills. Such work had been the family trade for some forty generations – a line unbroken since Am-tep had settled there eleven hundred years before.

But it was not just artistic skills that had been passed down from generation to generation. Am-tep’s questions troubled Amphos just as they had troubled Am-tep earlier. The great story of the Catastrophe that destroyed an ancient peaceful civilization had been handed down from father to son. Am-tep’s perception of the Catastrophe had also survived with his descendants. Amphos, too, understood that the heavens had a magnitude and stature so great as to be quite unconcerned by that terrible event. Nevertheless, the event had had a catastrophic effect on the little people with their cities and their human sacrifices and insignificant religious rituals. Thus, by comparison, the event itself must have been the result of enormous forces quite unconcerned by those trivial actions of human beings. Yet the nature of those forces was as unknown in Amphos’s day as it was to Am-tep.

Amphos had studied the structure of plants, insects and other small animals, and crystalline rocks. His keen eye for observation had served him well in his decorative designs. He took an interest in agriculture and was fascinated by the growth of wheat and other plants fr...

*The Road to Reality* is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book.

Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections.

*The Road to Reality* is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit.

*Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.*

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**Description du livre **Knopf, 2005. État : New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Preface Acknowledgements Notation Prologue 1 The roots of science 1.1 The quest for the forces that shape the world 1.2 Mathematical truth 1.3 Is Plato's mathematical world 'real'? 1.4 Three worlds and three deep mysteries 1.5 The Good, the True, and the Beautiful 2 An ancient theorem and a modern question 2.1 The Pythagorean theorem 2.2 Euclid's postulates 2.3 Similar-areas proof of the Pythagorean theorem 2.4 Hyperbolic geometry: conformal picture 2.5 Other representations of hyperbolic geometry 2.6 Historical aspects of hyperbolic geometry 2.7 Relation to physical space 3 Kinds of number in the physical world 3.1 A Pythagorean catastrophe? 3.2 The real-number system 3.3 Real numbers in the physical world 3.4 Do natural numbers need the physical world? 3.5 Discrete numbers in the physical world 4 Magical complex numbers 4.1 The magic number 'i' 4.2 Solving equations with complex numbers 4.3 Convergence of power series 4.4 Caspar Wessel's complex plane 4.5 How to construct the Mandelbrot set 5 Geometry of logarithms, powers, and roots 5.1 Geometry of complex algebra 5.2 The idea of the complex logarithm 5.3 Multiple valuedness, natural logarithms 5.4 Complex powers 5.5 Some relations to modern particle physics 6 Real-number calculus 6.1 What makes an honest function? 6.2 Slopes of functions 6.3 Higher derivatives; C1-smooth functions 6.4 The 'Eulerian' notion of a function? 6.5 The rules of differentiation 6.6 Integration 7 Complex-number calculus 7.1 Complex smoothness; holomorphic functions 7.2 Contour integration 7.3 Power series from complex smoothness 7.4 Analytic continuation 8 Riemann surfaces and complex mappings 8.1 The idea of a Riemann surface 8.2 Conformal mappings 8.3 The Riemann sphere 8.4 The genus of a compact Riemann surface 8.5 The Riemann mapping theorem 9 Fourier decomposition and hyperfunctions 9.1 Fourier series 9.2 Functions on a circle 9.3 Frequency splitting on the Riemann sphere 9.4 The Fourier transform 9.5 Frequency splitting from the Fourier transform 9.6 What kind of function is appropriate? 9.7 Hyperfunctions 10 Surfaces 10.1 Complex dimensions and real dimensions 10.2 Smoothness, partial derivatives 10.3 Vector Fields and 1-forms 10.4 Components, scalar products 10.5 The CauchyRiemann equations 11 Hypercomplex numbers 11.1 The algebra of quaternions 11.2 The physical role of quaternions? 11.3 Geometry of quaternions 11.4 How to compose rotations 11.5 Clifford algebras 11.6 Grassmann algebras 12 Manifolds of n dimensions 12.1 Why study higher-dimensional manifolds? 12.2 Manifolds and coordinate patches 12.3 Scalars, vectors, and covectors 12.4 Grassmann products 12.5 Integrals of forms 12.6 Exterior derivative 12.7 Volume element; summation convention 12.8 Tensors; abstract-index and diagrammatic notation 12.9 Complex manifolds 13 Symmetry groups 13.1 Groups of transformations 13.2 Subgroups and simple groups 13.3 Linear transformations and matrices 13.4 Determinants and traces 13.5 Eigenvalues and eigenvectors 13.6 Representation theory and Lie algebras 13.7 Tensor representation spaces; reducibility 13.8 Orthogonal groups 13.9 Unitary groups 13.10 Symplectic groups 14 Calculus on manifolds 14.1 Differentiation on a manifold? 14.2 Parallel transport 14.3 Covariant derivative 14.4 Curvature and torsion 14.5 Geodesics, parallelograms, and curvature 14.6 Lie derivative 14.7 What a metric can do for you 14.8 Symplectic manifolds <br. N° de réf. du libraire ABE_book_new_0679454438

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