Category Archives: Essays

My books (4) : The Wraparound Universe

Until now I published as an author 30 books in my native language (French), including 14 science essays, 7 historical novels  and 9 poetry collections (for the interested reader, visit my French blog  here.
Although my various books have been translated in 14 languages (including Chinese, Korean, Bengali…), only 4 of my essays have been translated in English.

The fourth one was :

The Wraparound Universe

316 pages – AK Peters Ltd, 2008 – ISBN 978 1 56881 309 7 – ISBN 0 521 40906 3 (paperback)

WraparoundWhat shape is the universe? Is it curved and closed in on itself? Is it expanding? Where is it headed? Could space be wrapped around itself in a formation that produces ghost images of faraway galaxies? Such are the questions posed by Jean-Pierre Luminet, which he then addresses in clear and accessible language. An expert in black holes and the big bang, he leads us on a voyage through the surprising byways of space-time, where possible topologies of the universe, explorations of the infinite, and cosmic mirages combine their mysterious traits and unlock the imagination.

Praise for The Wraparound Universe

– “Luminet’s deep understanding of the history of cosmology combines with his scientific knowledge and expository skills to produce a delightful introduction to the much-debated question of the shape of the universe. Directed at an intelligent layperson, The Wraparound Universe combines geometrical insights with astronomical observations leading to the idea of a universe that is finite yet has no boundary.” (Jeff Weeks, author of The Shape of Space)
– “This book is well written and nicely illustrated, giving a clear exposition of the mathematical and astronomical ideas involved as well as the various ways of observationally testing this possibility.” (George Ellis, Cape Town University, Templeton Prize)

Available on amazon : click here

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New Scientist, CERN Courier, etc : Click here

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Geometry and the Cosmos (3) : from Ptolemy’s circles to Inflationary Cosmology

Sequel of the previous post Geometry and the Cosmos (2): From the Pre-Socratic Universe to Aristotle’s Two Worlds

Ptolemy’s Circles

Any model of the universe must incorporate the mechanisms determining the motion of the planets and other celestial bodies. From Plato and Aristotle to Kepler, astronomers could not imagine the universe governed by shapes other than circles and spheres, the only geometric forms that could possibly represent divine perfection. This constraint forced them to devise extremely complex systems which would “fit the facts”, in other words account for the apparent movements of the planets and stars as observed from the earth while conforming to the ideological demands of the concept of universal harmony.

Despite the ingenuity of astronomers like Euxodus (see previous post), their circular systems did not accurately describe the complex movements they had observed: the planets accelerated and decelerated and even occasionally went back the way they had come. Moreover, they did not account for the changes in brightness of the planets, which suggested variations in their distance from the earth that were incompatible with the idea that they travelled in circles centred on or near the earth.

How could Aristotelian cosmology be reconciled with astronomical observation? The most elaborate attempt to do so was made by Ptolemy (Claudius Ptolemaeus) in the second century AD. In his Syntaxis Mathematicae, better known by its Latin title Almagest, the Alexandrian thinker succeeded in explaining the motion of each celestial body by a system of extremely elaborate mathematical constructs.

Left : a depiction of Ptolemy at work in a medieval manuscript. Right : A Greek manuscript of the Almagest, IXth century.

Ptolemy adopted the concept of a stationary earth and celestial bodies which could move only in circles. But he multiplied the number of circles and offset them one against the other, proposing complex and ingenious interactions between them. The circle in which a planet moves, called its epicycle, no longer had the earth at its centre as in Eudoxus’ theory, but itself revolved around another circle, called the deferent (or eccentric circle if its own centre is offset from the earth’s position). This theory enabled Ptolemy to “fit the facts” without departing too far from Aristotelian philosophical principles and it survived for 1,500 years — longer than any other idea in the history of science – until the discovery of elliptical orbits by Kepler.

The Motion of the Outer Planets According to Ptolemy. Ptolemy’s theory of planetary morion was first mentioned in his Planetary Hypotheses, which survives only in an Arabic translation, and fully developed in his Almagest. The original Greek title, Syntaxis, means “compendium”, but the work seems to have been known as megiste, “the greatest”, whence the Arabic al-Majesti and subsequently the Latin title Almagestum. The most influential Latin translation was made in 1175 by Gerard of Cremona. The page above, from a later edition of Book X, shows a kinematic model of the motion of the outer planets – Mars, Jupiter and Saturn. The earth remains still while the planets move in a regular pattern relative to an equant point offset from the centre of the planetary sphere. Claude Ptolemy, Almagestum, translated into Latin by Gerard of Cremona, 13th century. Vatican, Biblioteca Apostolica Vaticana, Lat. 2057
Ptolemy’s Epicycles.
The Ptolemaic system was based on three geometric patterns: the epicycle, the eccentric circle and the equant. The epicycle had been invented in the third century BC by Apollonius of Perga, a brilliant mathematician whose most famous work is a treatise on conical sections (ellipses, parabolas and hyperbolas), and developed by Hipparchus a century later.
(a) Epicycle : a planet P rotates in a small circle (epicycle) whose centre (C) is simultaneously moving along the circumference of a large circle, known as the deferent, with the earth (T) at its centre.
(b) Eccentric Circle : the earth is offset from the centre (O) of the deferent. This model breaks the Aristotelian rule which states that the earth must be at the centre of the cosmos.
(c) Equant : despite its complexity, the eccentric circle model does not provide a sufficiently accurate explanation of the apparent motion of the planets. Ptolemy therefore postulated an equant point (E) about which the centre of the epicycle (C) rotates. Both the geometric centre of the deferent (O) and the centre of motion are now offset from the earth’s position (T).
(d) Final Model : the Ptolemaic model plots the motion of the planets according to this sytem, but it was so complicated that it was not fully understood by Western civilisation until the 15th century.
Ptolemy proudly defended its complexity: “We must as far as possible apply the simplest hypotheses to the movements of celestial bodies but, if these are inadequate, we must find others which explain them better.” (Almagest, XII, 2) – a statement which placed him firmly in the vanguard of modern scientific thinking.

 Nevertheless, the system of epicycles and eccentric circles suggested that the earth was not exactly at the centre of the cosmos and Islamic astronomers raised several objections to this infringement of Aristotelian harmony. It was the existence of an equant point offset from the earth that particularly preoccupied later scientists. Copernicus, for example, in his De Revolutionibus announced his intention to rid the celestial model of this “monstrosity”. Continue reading

Geometry and the Cosmos (2) : From the Pre-Socratic Universe to Aristotle’s Two Worlds

 Sequel of the previous post Geometry and the Cosmos (1): Kepler, from polyedra to ellipses 

The Pre-Socratic Universe

Since He [Zeus] himself hath fixed in heaven these signs,
The Stars dividing; and throughout the year
Stars he provides to indicate to men
The seasons’ course, that all things may duly grow.
Aratus, Phaenomena, I, 18.

Although Kepler was the first to determine the motion of the planets by mathematical laws, his search for a rational explanation to the universe was anticipated by numerous earlier thinkers. Even before the time of Socrates a number of philosophers had broken away from accepted mythology and postulated the idea of universal harmony. From the sixth century BC increasingly rational and mathematical ideologies based on the laws of physics began to compete with the traditional belief that the world was controlled by gods with supernatural powers. Most of these thinkers attempted to describe natural phenomena in mechanical terms, with reference to the elements of water, earth and fire. The Ionian philosophers in particular developed new ideas about the heavens, whose signs were used by many of their compatriots to navigate between the islands. Their fundamental notion was that the universe was governed by mechanical laws, by natural principles which could be studied, understood and predicted.

It was Thales of Miletus who propounded one of the first rational explanations of the world, according to which the earth was separate from the sky. Anaximander and Anaximenes, both also natives of Miletus on the coast of Asia Minor, put forward different ideas, which nevertheless derived from the same rationale: they proposed the existence of cosmological systems, explained natural phenomena in terms of a small number of “elements”, and invented new concepts – Anaximander’s “equilibrium” and Anaximenes’ “compression” – which can be regarded as the first recognition of the force of gravity.

The Expanding Universe. According to Empedocles of Acragas (now Agrigento, in Sicily), the universe was held in balance by forces of harmony and conflict, the attractive force of love and the repulsive force of hate alternatively prevailing. This idea of balance can be seen as a mythical precursor of modern astronomical theories whereby the tendency for structures to become compressed by their own gravitational forces is offset by the expansion of the universe, which constantly dilutes all matter.
In Lemaître’s so-called “hesitating universe”, a cosmological model he devised in 1931 from Einstein’s field equations, the evolution of the cosmos is divided into three disctinct phases : two periods of rapid expansion are separated by a period of “stagnation”, representing a sort of equilibrium between the forces of gravitational contraction and expansion.

According to Heraclitus of Ephesus, the day was caused by exhalations from the sun, while the night was the result of dark emissions from the earth. The stars and the planets were bowls of fire which, when turned over, gave rise to eclipses and the phases of the moon. The moon itself, pale and cold, moved in the rarefied air above the earth, whereas the sun, our nearest star, was bright and hot.

Meanwhile, the Greeks were amassing measurements which would enable them to plot the stars more accurately. This required specialised instruments – gnomons to measure the sun’s shadow, compasses to fix the positions of the stars in the sky, etc. – as well as a system of notation which anyone could understand (previously the study of astronomy had been restricted to priests): how many fingers’ width above the horizon was such and such a star; where was due north, and so on. As well as mining the extensive archive of observations made by the Egyptians and Babylonians, the Greeks developed their own system of records. The pre-Socratic thinkers refined and analysed the basic ideas of their predecessors from Miletus with the result that the mechanistic view of the world gradually lost currency and a belief in underlying harmony became de rigueur. As early as 450 BC Anaxagoras of Clazomenae was accused of impiety for referring to the sun as a mass of hot metal, to the moon as a second earth and to the stars as burning stones – views no longer considered seemly. Continue reading

My books (3) : Celestial Treasury

Until now I published as an author 30 books in my native language (French), including 14 science essays, 7 historical novels  and 9 poetry collections (for the interested reader, visit my French blog  here.
Although my various books have been translated in 14 languages (including Chinese, Korean, Bengali…), only 4 of my essays have been translated in English.

The third one was :

Celestial Treasury: From the music of the spheres to the conquest of space.

Translated from French by Joe Laredo
Cambridge University Press, 2001 — ISBN 0 521 80040 4

FigCiel-engThroughout history, the mysterious dark skies above us have inspired our imaginations in countless ways, influencing our endeavours in science and philosophy, religion, literature and art. Celestial Treasury is a truly beautiful book showing the richness of astronomical theories and illustrations in Western civilization through the ages, exploring their evolution, and comparing ancient and modern throughout. From Greek verse, mediaeval manuscripts and Victorian poetry to spacecraft photographs and computer-generated star charts, the unprecedented wealth of these portrayals is quite breathtaking.

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• Review in Astronomy & Geophysics, 2001 December (Vol.42), 6.32
Big and beautiful

This is such a book as would have the most hardened reviewer reaching for the overworked superlatives. Impressive in size and sumptuous in production, for what is actually quite a reasonable price in present-day terms, it contrives to set forth much of the aesthetic attraction of astronomy both ancient and modern.

Originating as an exhibition catalogue and drawing material from many libraries in Europe, the authors have marshalled a stunning array of historical and modem imagery under the general headings of “The harmony of the world”, “Uranometry”, “Cosmogenesis”, and “Creatures of the sky”. Originally published in French as Figures Du Ciel, a title which implies a much more restricted scope than it actually bas — the English title is far more appropriate — it is here elegantly translated by Joe Laredo. Not the least of its virtues is that as the original edition was jointly published by the Bibliothèque Nationale, the authors have been able to obtain readier access to the treasures of that institution than many other researchers find possible, especially since the move.

Many of the illustrations from conventional astronomical rare books are familiar, though the hand-colouring of different copies makes a fascinating comparison, but others are less so — apart from the unique manuscript sources, the authors have made appropriate use of decorative embossed book covers, illustrations from l9th and 20th century books, especially early science fiction, early space art and even comic books. It can be a trifle disconcerting to find, for example, a modern map of the cosmic microwave background radiation juxtaposed with a l4th century manuscript, but such comparisons can be quite reasonable as long as they are not taken too literally; I feel, though, the series of illustrations comparing the illustrations of the days of creation from the Nuremberg Chronicle with stages in cosmic evolution and the development of life is a little forced. There are one or two isolated nods towards world views outside the main stream leading down from Classical via Arabic to modem western science, but the Hindu Triad and the brief nods towards Chinese, Aztec and Babylonian astronomy seem lonely and isolated and might have been better omitted if there was not room to treat them more fully.

Although the innumerable illustrations are the most prominent feature of the book, the authors’ impeccable credentials as high officials of the CNRS and as successful popularizers of astronomy lend the text authority and style. Occasionally, as used to be said of Sir James Jeans, they get lost in descriptions of immensity and hugeness; but then, in the words of the late Douglas Adams, “Space is big, really big!”. The authors have carefully described the significance of the thought behind the historic images, and the whole book will make a marvellous crib for captions and exhibitions, as well as being ideal fodder for picture researchers. One might pick up small factual disagreements and pedantic quibbles, or take issue with certain aspects of the book production; the truncated and varying sized pages seem to add little but confusion, and I am not clear why the key map from Doppelmaier’s New Celestial Atlas (p108) has been truncated. Lt is also a great shame that a proper index of subjects could not have been added rather than just one of names.

But despite any venial criticism of minutiae, the whole book is a striking demonstration of my own conviction that the most valuable use of historical imagery is to provide an accessible entry point to the subject; such beautiful images, intelligently explained, can engage the interest and commitment of the mathematically challenged in a way that the Schwarzschild Radius or the Chandrasekhar Limit will never do. A book that anybody with the slightest interest in the subject would be delighted to find waiting after the annual visit of the red-coated gentleman with the sub-orbital reindeer!

P D Hingley.

• Review in The Los Angeles Times, March 17, 2002

by Margaret Wertheim

The Sky’s the Limit

Artists and scientists, Robert Oppenheimer wrote, “live always at the ‘edge of mystery’–the boundary of the unknown” and for no group of scientific practitioners is this characterization more apposite than cosmologists, they who dare to envision the universal whole.

Few areas of inquiry bring human minds so constantly into contact with the event horizons of current understanding, so posing the greatest challenges. As a creative response to the ineluctable desire to know how and from whence we arise, cosmological theorizing, for all its claims to truth, is an exercise of the grandest sort in myth-making. That at least is the thesis underlying Marc Lachièze-Rey and Jean-Pierre Luminet’s sumptuous “Celestial Treasury.”

Ostensibly a history of (primarily Western) cosmological thinking, “Celestial Treasury” advances a far more radical agenda. Rather than presenting their subject as a progressive history, onward and upward from pagan darkness to the light of contemporary scientific genius, Luminet and Lachièze-Rey subversively interweave ancient and modern ideas, continually, if gently, alerting the reader to profound resonances between past and present.

For all our superior observational technology, our sophisticated theoretical frameworks and our fiendishly complex mathematics, we are not so far from our forebears as we often like to think.

Consider the ancient Greeks’ idea that everything in the physical world is composed of four basic elements: earth, water, air and fire. Antiquated baloney, you might think, but Luminet and Lachièze-Rey point out that contemporary physics rests on a not-dissimilar premise.

Today the four “elemental” constituents said to be responsible for all phenomena are the four fundamental forces: gravity, the electromagnetic force and the strong and weak nuclear forces (which hold together the nuclei of atoms). These forces, they write, “have an identical function to the elements of the classical world.”

In our drive to know the universe, it is the imagination that engages first, long before the analytical or empiricist spirit kicks in. Johannes Kepler, the great precursor to Isaac Newton and the founding father of modern astrophysics, envisioned the universe as God’s play: As he saw it, the aim of the astronomer was to learn to play God’s game. To do that, the mind must be open to the “facts,” but critically it must also be creatively susceptible. As Albert Einstein once declared: “The gift of fantasy has meant more to me than any talent for abstract, positive thought.”

Throughout history, the creative impulse has been a central engine of cosmological theorizing. Take, for example, the Greek and medieval view that the dance of the planets and stars must be explained by a combination of strictly circular motions. Just as a windup ballerina can be made to perform a complex dance, even though her mechanism consists only of circular gears, so cosmologists for 2,000 years believed the motions of the heavenly bodies could be described by an intricate celestial clockwork.

The apotheosis of this imaginative mechanizing was the dizzyingly elaborate system of the Alexandrian astronomer Claudius Ptolemy. So complex was Ptolemy’s system that in the 13th century Alfonso the Great, seeing the labors of his astronomers, is said to have remarked that had he been present at the Creation he would have given the Lord some hints about simplification. The Ptolemaic conception of the cosmos dominated both Arab and European views of the heavens until the 17th century, when Kepler, Newton and others radically re-envisioned the universe, replacing the cosmic gears with a quasi-infinite network of stellar masses held in place by the force of gravity.

But be not so quick to judge Ptolemy’s vision. Luminet and Lachièze-Rey (an astronomer and astrophysicist, respectively) note that in principle a Ptolemaic-style system could account for the heavenly dance with a high degree of accuracy. In the 19th century, the French mathematician Jean Baptiste Joseph Fourier demonstrated that, in fact, any periodic motion can be described by a combination of circular motions.

Moreover, physics today retains a love affair with the circle. Current favorite contender for a unified theory of the four forces is string theory, which holds that all particles can be understood as the various vibrational states of microscopic circular loops, or “strings.”

Throughout history, cosmological ideas have refracted again and again through our mental prisms, metamorphosing into new variations on old themes. One of the great joys of this book is seeing the ways in which certain tropes keep returning, as if they hold some peculiar power of enchantment over the human mind.

Perhaps my favorite example is the continually recurring fascination with the Platonic solids: a unique set of five forms whose crystalline symmetry has held artists and astronomers, mystics and mathematicians in thrall for thousands of years. As with the cube, whose faces are all squares, the Platonic solids are perfectly regular polyhedra, having all their faces the same. There are just five such forms possible: along with the cube (which has six sides), are the tetrahedron (four sides), the octahedron (eight sides), the icosahedron (20 sides) and the dodecahedron (12 sides). Since their discovery, these five forms have been imbued with almost mystical power.

Plato paired the first four with the four basic elements: Earth was paired with the cube, water with the icosahedron and so on. The fifth, the dodecahedron, he equated with the supposed fifth element, or quintessence, the mysterious substance of which the celestial bodies were said to be composed.

In the 17th century, Kepler thought he had found in these five forms the secret of the planets’ arrangement in the solar system. He turned out to be wrong, but, bizarrely, the idea of a polyhedral arrangement to the cosmos has resurfaced within the framework of general relativity, which allows for some truly extraordinary topologies, including ones in which space takes on a pseudo-crystalline structure.

One such arrangement is an infinite lattice of dodecahedrons. “Celestial Treasury” includes an exquisite computer image of this enigmatic spatial structure from the Geometry Center at the University of Minnesota.

In making their case for cosmological resonances through the ages, Luminet and Lachièze-Rey critically rely not just on words but also on pictures. The uniqueness of this book lies in its juxtaposition of historical images with those generated by contemporary astrophysics, such as the contrasting of Kepler’s polyhedral model with the Minnesota computer model.

Likewise, illustrations from medieval manuscripts of the six days of biblical creation sit side by side with computer simulations of black holes and the origins of space time; Renaissance visions of stellar vortexes are paired with photographs of spiral galaxies taken by the Hubble Space Telescope.

Replete with extended foldouts and delicately detailed inserts, “Celestial Treasury” is a stunningly beautiful survey of the science, mythology and iconography of the cosmos through the ages. This is the most gorgeous coffee-table cosmology book in years.

Such lavish production bespeaks its origins: The book is an offshoot of a 1998 exhibition entitled “Figures du Ciel” at the Bibliothèque Nationale de France, and it is from that library’s extensive collection that most of the older images are taken.

As with two recently ended and superb exhibitions in our own city–“Treasures of the Great Libraries of Los Angeles” at the UCLA Hammer Museum and “Devices of Wonder” at the Getty–“Celestial Treasury” demonstrates that science can be an engine not only of knowledge but also of aesthetic inspiration. Beneath the radar of pedagogical impulse, science, like art, stirs our imaginations.

Margaret Wertheim is the author of “The Pearly Gates of Cyberspace: A History of Space From Dante to the Internet.”

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EXCERPT FROM CHAP. 1 “THE HARMONY OF THE WORLD”

 

The Fabric of the World

Any macroscopic conception of the universe is also a conception of its microscopic structure. The question whether matter can be broken down indefinitely is an ancient one. The Greeks in particular put forward ideas as to its composition: in keeping with their belief in a rational, unified and harmonious universe, not only did there have to be a limited number of fundamental elements, but there must also be laws governing their combination and transformation.

The Milesian philosophers showed their preoccupation with coherence and their aspiration towards universality by asserting the predominance of one element over all others in the universe: for Thales it was water, for Anaximenes air, for Heraclitus fire and for Anaximander apeiron — a forerunner of Aristotle’s ether.

The search for a single primordial element is a recurring feature of natural philosophy. In the fifth century bc Parmenides of Elea and his pupil Zeno hypothesised that the universe consisted of a single substance, “Oneness”, which was motionless and of infinite mass, enveloping all things without any space between them. In the 12th century ad the English prelate Robert Grosseteste, who is widely considered to be one of the founding fathers of empirical science, regarded light as the most elementary substance and the primary constituent of the world. This idea, which was in keeping with Christian doctrine (God created light, from which everything else followed), is also close to modern thinking, especially that of physicists who are seeking a unified theory of matter and the interaction between bodies.

In the mid-fifth century bc the philosopher and soothsayer Empedocles (who claimed divine ancestry) offered a synthesis of his predecessors’ ideas: he proposed that the primordial material was a combination of the four eternal and incorruptible elements, earth, water, air and fire. In his Origin of the Elements he describes how these elements temporarily combine to form the various sublunary bodies: “Birth is not the beginning of life, and death is not the end; the components of our bodies are merely assembled and disassembled. Birth and death are but the names given to this process by man.”

Elements and Polyhedra

The four element system was adopted by Plato, whose Timaeus describes the sublunary world as subject to a series of transformations – birth-corruption-death – of the four elements brought into being by the Creator. Plato then develops his ideas on representing the cosmos in geometric terms. This sublunary world is far less harmonious than the superlunary world; consequently each of the four elements comprising it must be represented by a shape somewhat less symmetrical, less pleasing and perfect than a sphere, i.e. one of five “Platonic solids”, nowadays known as regular polyhedra. Earth is shown by a cube, water by an icosahedron, air by an octahedron and fire by a tetrahedron (or pyramid). Plato thought carefully about the relationship between each element and its representative shape: for example, a cube is the most difficult shape to move, so it is associated with earth, the heaviest element; an icosahedron has more sides than any other Platonic solid (five triangles meet at each point), giving it a virtually round, fluid structure which is most clearly associated with water; and so on.

Being corruptible, these four elements cannot exist in the sky. There is, however, a fifth regular polyhedron, the dodecahedron, vhich consists of 12 pentagons and is therefore the three-limensional equivalent of the pentagon, considered to be a “magic” nape. To Plato each perfect solid represented the essence of its :orresponding element so, when his contemporary Theaetetus pointed out to him that the dodecahedron was the fifth regular polyhedron (there are only five), Plato postulated a fifth essence in prder to unify his geometric model of the world. In the Middle Ages pis fifth essence was to be known as “quintessence”, but in ppinomis, a work published after Timaeus and generally attributed to Plato, it is called aither, meaning “eternal flux”. Of the five jerfect solids the dodecahedron is the nearest to a sphere, the symbol of celestial perfection.

In general Aristotle appropriated the Platonic model of the :osmos, but he did not adopt the idea of a correspondence between he elements and the regular solids. His main concern was to iistinguish between two worlds, between two kinds of activity. The mperfect sublunary world was governed by “lower activity”: everything is composed of corruptible matter and tends to revert to he natural state of its predominant element. For example, if a stone s dropped, it naturally falls towards the centre of the earth, since :arth is its predominant element. Fire, on the other hand, rises into he air. All natural movement is directed either upwards or iownwards, either towards or away from the centre of the earth [then considered to be at the centre of the cosmos). As for the four dements, they are distinguished by their basic characteristics: earth s cold and dry, air is warm and humid, etc. If these characteristics ire changed, one element can be transformed into another. In the iublunary world such transformations are continually taking place, .vhich accounts for its constantly changing nature.

The Aristotelian picture is completed by the “upper activity” of he superlunary world of planets and stars, whose “physicality”, mquestionably real and tangible as it is, consists of the fifth element, quintessence.

Plato’s polyhedra, which Kepler himself used to account for the orbital motion of the planets, were central to the way the world was represented in succeeding centuries. In the Renaissance, artists such as Piero della Francesca and Paolo Ucello were fascinated by them. phis Divine Proportion of 1509, which was illustrated by Leonardo la Vinci, the mathematician and theologian Luca Pacioli used them 😮 define his laws of just proportion, applicable to music, architecture, calligraphy and other arts.

The Nature of the Ether

After Aristotle the nature of the fifth element changed repeatedly and was the subject of constant debate. In the fourth century BC one of his successors, Theophrastus, rejected the idea of a fifth element altogether, likening the sky to a sort of “ethereal fire” (Manilius, Astronomicon Poeticon). Three hundred years later Xenarchus also dismissed Aristotle’s ether and argued that there could not be only two basic geometric shapes (a straight line and a circle). It was not until the 16th century that the ether was redeemed. Descartes mentions a “subtle substance” filling all space and accounting for his “vortices” and consequently all cosmic interaction. The 17th century Dutch physicist Christiaan Huygens applied the idea to light, which he regarded as a disturbance of an omnipresent “luminiferous ether”. For Newton light was composed of particles and independent of Huygens’ undulatory theory. On the other hand he postulated a kind of “gravitational ether”, a substance occupying all space and capable of transmitting the force of gravity. The idea of light being composed of waves was revived in the 19th century, when it was thought to be transmitted by vibrations in the ether. According to James Clerk Maxwell, electromagnetic waves were also propagated by the ether.

The exact nature of the ether has been the subject of repeated controversy. Does it have physical properties? How does it relate to space, to quantum fields, to a vacuum? Does it move relative to the earth? This last question was the subject of a series of experiments (the most famous being the Michelson-Morley experiment in 1887) and hypotheses leading to the theories of relativity which revolutionised man’s concept of the ether. According to the general theory of relativity, it is the distortion (or curvature) of space-time that conveys gravitational interaction and ripples of space-time that convey energy. The curvature of space-time has exactly the same characteristics as Newton’s “gravitational ether”: it is simultaneously physical and geometric. The other great theory of modern physics, quantum physics (more precisely quantum field theory), presents an alternative view of the ether as the “quantum vacuum”, which has energy and fluctuations but whose nature is still unclear. The concepts of “gravitational ether”and quantum vacuum are central to their respective disciplines, yet the two are irreconcilable. This is the impasse facing modern physics. Its resolution may yet come from further investigation into the nature of the ether, the vacuum, space..

Atoms

The extraordinary popularity of Aristotle’s system of elements meant that the alternative view of matter being composed of atoms, although at least as logical and persuasive, did not develop until the 17th century.

An atomistic structure was proposed as early as the fifth century bc, a generation before Socrates, by Leucippus of Miletus (or Elea) and his disciple Democritus of Abdera, whose work is best known through Aristotle’s Metaphysics. While Leucippus is usually credited with few books, including The Great World System, Democritus was a prolific author known to have written at least 52 books, although some of them are quite short. His Concise World System is a continuation of Leucippus’ work.

Leucippus and Democritus were reacting against the theories of Parmenides and Zeno of Elea, rejecting their idea of an infinite, static, all-embracing substance. They argued that our senses detect movement and that consequently there must be empty space. Their conclusion was a bipartite structure: “The first principles of the universe are atoms and empty space; everything is merely thought to exist.” The four elements of Empedocles have no place in their theory; nor does any such thing as quintessence. Everything is composed   of   atoms   (from the Greek atomos, meaning “indivisible”), which cannot be further broken down because they contain no empty space (for things to be broken apart there must be space between them) and are incredibly compact and heavy. Atoms are also eternal; in other words they have always existed and they cannot change or die. In his treatise De Generatione et Corruptione Aristotle records Democritus’ and Leucippus’ view that these “indivisible bodies” are “are infinite both in number and in the forms which they take, while the compounds differ from one another in their constituents and the position and arrangement of these.”31 The less space there is in a material, the denser it is. Fire, for example, is simply matter whose atoms are widely separated: being of low density it escapes the material that produces it. Celestial bodies are made from the least dense material.

Atomistic theory, which was pursued by Epicurus and Lucretius, was completely overshadowed by Aristotelianism but revived in the 17th century, particularly by the French philosopher Pierre Gassendi, and has become the basis of modern physics, even though our ideas about atoms are quite different from those of the ancient Greek philosophers.

The atom of contemporary science, far from being a compact mass, consists mostly of empty space in which tiny particles revolve around an extremely dense nucleus. The ancient atom in fact corresponds more closely to our idea of an elementary particle. These particles, which constitute the fundamental “building blocks” of every known chemical element, are indivisible masses surrounded by space. The fact that they exist throughout the universe has been proved by spectral analysis of the most distant stars and galaxies.

Harmony and Particles

The regular solids used by Plato and Kepler to represent the elements and the planetary orbits are absolutely symmetrical. To create a concrete model of the planets’ orbits, which were puzzling astronomers, Kepler used geometric shapes that he knew were symmetrical, thereby expressing his vision of cosmic harmony. Today physicists are faced with similar problems: how should they classify the numerous particles which experiments suggest are elementary or fundamental? How should they interpret the similarities and differences between them? How should they analyse their actions and reactions? Like Kepler they have looked to their stock of tools for expressing harmonious or symmetrical relationships for an answer. This they have found in the mathematical theory of groups, which permits the classification of geometric symmetries.

According to modern group theory to each regular polyhedron corresponds a “polyhedral group” (all possible displacements it can be subjected to without changing shape). To a sphere corresponds a higher dimensional group, but even this is just a particular case of a general class of transformations, the “symmetry groups”. In particle physics certain particles are associated with other particles or families of particles, forming “gauge theories”. Gauge theories allow the behaviour of particles – especially the way they interact -to be precisely described. The result is a “harmonious” classification of particles and their interactions, e.g. U(l), SU(2), SU(3).

These theories are undoubtedly more successful than Kepler’s geometric explanation of planetary orbits; yet no physicist would pretend to understand any better than Kepler did where such harmony comes from. He at least was able to interpret it as the will of God!

A Polyhedral Universe

Regular polyhedra appear again in relation to the structure of matter. Although Kepler was forced to abandon them in favour of ellipses as a method of describing the structure of the solar system, he retained his fascination for these almost perfect shapes. In looking at the group of semi-regular polyhedra (rhomboids, prisms, etc.) which incorporates the group of regular solids but also includes non-convex shapes, Kepler discovered “stellation”. In his De Niva Sexangula (The Six-Cornered Snowflake) of 1610 he used five- and six-pointed star shapes to represent the structure of snow crystals, thereby laying the foundation of modern crystallography. In crystallography, polyhedral symmetry reigns supreme. In the 18th century alchemy gave way to the less far-reaching but more rational science of chemistry, which is concerned with the geometric structure of molecules and crystals, underlying that of matter itself. Many molecules have extraordinary structures. The numerous possible arrangements of carbon atoms and other similar atoms, which are rich in symmetry, are often types of polyhedron. An entire branch of organic chemistry, which plays such an important part in modern chemistry, is based on the benzene molecule (C6H ), a beautiful hexagonal shape. Not long ago chemists discovered an even more remarkable molecule: fullerene (C60), which consists of a football-shaped polyhedron surrounded by sixty carbon atoms. First simulated in 1985 this molecule has already generated a new branch of applied chemistry and the number of possible applications for fullerene is still rising. It has recently been detected – as the ion C6+0 – in outer space, where it absorbs light from distant stars, and is the largest molecule (more precisely the largest chemical complex) known to exist in space. It is estimated that such molecules account for some two per cent of all the carbon in the universe.

Polyhedra even have an unexpected relevance to modern cosmology, which is investigating the possibility that space itself is in some way polyhedral and that the cosmos as a whole has a crystallographic structure. According to the general theory of relativity, space has a geometric structure characterised by curvature and topology. This idea fascinated several of the founders of 20th century cosmology such as De Sitter, Friedmann and Lemaitre; it then rather lost favour before regaining popularity in recent years. In “topologically multi-connected” models, which can initially seem confusing, space is represented by a “fundamental polyhedron”. The simplest of these models use cubes or parallelepipeds (shapes consisting of six parallelograms) to create a “toroidal” space, but there is an almost infinite number of variations. The common feature of these fundamental polyhedra is that they are symmetrical, so that one face can be related to another: the corresponding points on each face are therefore “linked” in such a way that physical space is the result of a complex “folding” process. The fundamental geometric symmetry of the universe is matched by the symmetry of the polyhedron.

From the point of view of the celestial observer, these “folded” models introduce a radically new perspective. The usual interpretation of the sky is that it consists of a straightforward projection of the space, which is vast if not infinite: each point of light that we can see corresponds to a specific star, galaxy or other celestial body – the further away the fainter. This is not at all the case with a multi-connected model, according to which each actual celestial body is represented by a whole series of “ghosts” so that what we see in the sky is not the universe as it really is, but several different images of the universe, from different angles and distances, superimposed upon one another!

Symmetry in Modern Physics

Symmetry is one of the most fundamental concepts in geometry, whose principal concern is to find “pure” shapes – the equivalent of the physicist’s search for fundamental elements. One of the simplest symmetrical shapes is the sphere, which is symmetrical with respect to any straight line passing through its centre. Others are the regular polyhedra (the Platonic solids), which are symmetrical with respect to a finite number of lines passing through their centre.

Symmetry is so prevalent in nature – from the human body to atoms and crystals – that it is difficult to imagine it not being central to our understanding of the world and its creation. Although symmetry was studied by the French mathematician Evariste Galois in the early 1830s and by the German Emmy Noether around 1916, its importance was not fully understood until the development of group theory later in the 20th century. Symmetry is also omnipresent in the arts. The (subjective) notion of beauty is, however, often associated with a slight asymmetry. The most beautiful faces are not exactly symmetrical; the best architects mix the symmetrical with the unexpected. Similarly physicists study symmetry breakdowns and show how these are as fundamental to nature as symmetry itself.

In recent times physics has become increasingly concerned with geometry, emphasising the “Platonic” nature of modern science. A striking example is quantum theory and in particular the theory of elementary particles; in attempting to describe the structure of atoms, in other words the invisible universe, particle physicists have resorted to abstractions based on geometric concepts. Just as Pythagoras himself would have approved of the quantum numbers representing the various levels of placement of electrons around an atomic nucleus, so Plato would have been delighted by the shape of the mathematical wave functions describing the hydrogen atom.

Cosmogenesis (8) : The Nebular Hypothesis

Sequel of the preceding post Cosmogenesis (7) : The Date of the Creation

The Nebular Hypothesis

The ancient Babylonians had a different idea of how the world began. They believed that it had evolved rather than being created instantaneously. Assyrian inscriptions have been found which suggest that the cosmos evolved after the Great Flood and that the animal kingdom originated from earth and water. This idea was at least partially incorporated into a monotheist doctrine and found its way into the sacred texts of the Jews, neighbors and disciples of the Babylonians. It was also taken up by the early Ionian philosophers, including Anaximander and Anaximenes, and by the Stoics and atomists.

A portrait of Democritus (460-370 BC), the founder of atomistic theory.
A portrait of Democritus (460-370 BC), the founder of atomistic theory.

Democritus developed a theory that the world had originated from the void, a vast region in which atoms were swirling in a whirlpool or vortex. The heaviest matter was sucked into the center of the vortex and condensed to form the earth. The lightest matter was thrown to the outside where it revolved so rapidly that it eventually ignited to form the stars and planets. These celestial bodies, as well as the earth itself, were kept in position by centrifugal force. This concept admitted the possibility that the universe contained an infinite number of objects. It also anticipated the 19th century theory of the origin of the solar system, known as the nebular hypothesis, according to which a “primitive nebula” condensed to form the sun and planets.

The idea of universal evolution had a strong influence on classical thought and developed in various directions during Greek and Roman times. In the first century BC Lucretius extended the theories of atomism and evolution to cover every natural phenomenon[i] and argued that all living things originated from earth. Two centuries later, in his medical treatise On the Use of the Parts of the Body[ii], the Greek physician Galen (Claudius Galenus) expressed the essentially Stoic view that matter is eternal and that even God is subject to the laws of nature: contrary to the literal interpretation of the Genesis story, he could not have “formed man from the dust of the ground”; he could only have shaped the dust according to the laws governing the behaviour of matter. The Church Fathers, who insisted that the Creation was instantaneous, rejected any sort of evolutionary theory; to them the ideas of the Stoics and atomists were heretical.

In the second half of the 16th century the idea of universal evolution began to be incorporated into the new system of scientific thought resulting from the work of Copernicus, Kepler, Galileo, Descartes and Newton. According to Descartes, for example, space consisted of “whirlpools” of matter whose motion was governed by the laws of physics. Newton, with his theory of universal attraction, was accused of having substituted gravitation for providence, for having replaced God’s spiritual influence on the cosmos by a material mechanism[iii]. A new view of the world had nevertheless been established, whereby the workings of the universe were subject not to the whim of the Almighty but to the laws of physics – it was an irreversible step. Continue reading

Cosmogenesis (7) : The Date of the Creation

Sequel of the preceding post Cosmogenesis (6) : The Creation in the Renaissance

The Date of the Creation

None of the traditional myths gives a precise date for the Creation. The very idea of putting dates to the history of the world seems to have been foreign to the mentality of the ancients. For them the origin of the universe was simply a notion which helped them to understand the separation of reality into two regions: formless chaos and cosmic order. It was the Jewish/Christian preoccupation with time as a linear process which prompted the question: when was the Creation? From then on the greatest theologians (from Eusebius of Caesarea in the fourth century to James Ussher, Irish prelate and archbishop of Armagh, in the 17th century) and scientists (from Kepler to Newton) would attempt to provide the answer.

For centuries the only clues were to be found in the Bible, which was thought to be able at least to provide an upper limit to the age of the world. From studying the Bible, the vast majority of scholars put the date of the Creation at around 4000 BC, the most common method of calculation being to count the number of generations between Adam and Jesus. St Luke[i] and other commentators list 75 generations, which at approximately 50 years per generation make 4000 BC a plausible date. This reasoning was accepted until the 18th century, even though Ronsard ended his Hymn to the Sky of 1555 with the words: “Your beauty is such that I simply cannot believe / It is but four or five thousand years since your beginning.

More precise estimates gradually appeared. According to the theologian and historian the Venerable Bede in the eighth century and Vincent de Beauvais in the 13th, the Creation took place in the spring.

Depiction of the Venerable Bede from the Nuremberg Chronicle, 1493
Depiction of the Venerable Bede from the Nuremberg Chronicle, 1493

In his historical treatise Annales Veteris Testamenti, a Prima Mundi Origine Deducti (Annals of the Old Testament, Traced Back to the Origin of the World) of 1650, James Ussher attempted to determine precisely the dates of the great biblical events by checking them against historical facts and astronomical phenomena. According to his calculations the first day of the Creation was 23rd October 4004 BC (beginning at midday) and Adam and Eve were expelled from the Garden of Eden on Monday 19th November, Noah’s Ark went aground on the summit of Mount Ararat on 5th May 1491 BC, and so on.

Similarly, in 1642, the Vice-Chancellor of Cambridge University, John Lightfoot, an eminent Hebrew scholar, stated that “heaven and earth, centre and circumference, were created all together, in the same instant” and that “man was created by the Trinity on October 23, 4004 BC at nine o’clock in the morning.”[ii] Continue reading

Cosmogenesis (6) : The Creation in the Renaissance

Sequel of the preceding post Cosmogenesis (5) : The Order of the Creation

The Creation in the Renaissance

Hartmann Schedel’s Nuremberg Chronicle, published in 1493, effectively marks the watershed between medieval scholarship and Renaissance speculation. It is the manifestation of a desire for completeness, amalgamating the principal accounts of the Creation (Genesis, Plato’s Timaeus, Hesiod’s Theogony, Ovid’s Metamorphoses) into a single, all-embracing narrative.

The Creation in a Renaissance Edition of Ovid's Metamorphoses. Ovide moralisé (Ovid Moralised) is a French text written in the late Middle Ages which regards Ovid's Metamorphoses as having anticipated the scriptures. The early humanists inherited this view and, throughout the 16th century, the Metamorphoses were treated as a manual of morality and wisdom and subjected to numerous glosses and commentaries. This edition, published in Lyons in 1519, includes commentaries by Raphael Regius, an Italian teacher of grammar and rhetoric, and Petrus Lavinius, a Dominican monk who was part of the humanist circle in Lyon. The engraving illustrating the Creation was inspired by the Italian woodcuts in the first edition of Regius' commentary, which was published in Venice in 1493. The fact that the artist drew the Creator as Christ rather than Jupiter shows how Ovid's poem had been adapted to match Christian legend. Ovid, P. Ovidii Nasonis Metamorphoseos Libri Moralizati, Cum Pulcherrimis Fabularum Principalium Figuris, Lyons, Jacques Mareschal, 1519.
The Creation in a Renaissance Edition of Ovid’s Metamorphoses.
Ovide moralisé (Ovid Moralised) is a French text written in the late Middle Ages which regards Ovid’s Metamorphoses as having anticipated the scriptures. The early humanists inherited this view and, throughout the 16th century, the Metamorphoses were treated as a manual of morality and wisdom and subjected to numerous glosses and commentaries. This edition, published in Lyons in 1519, includes commentaries by Raphael Regius, an Italian teacher of grammar and rhetoric, and Petrus Lavinius, a Dominican monk who was part of the humanist circle in Lyon. The engraving illustrating the Creation was inspired by the Italian woodcuts in the first edition of Regius’ commentary, which was published in Venice in 1493. The fact that the artist drew the Creator as Christ rather than Jupiter shows how Ovid’s poem had been adapted to match Christian legend. Ovid, P. Ovidii Nasonis Metamorphoseos Libri Moralizati, Cum Pulcherrimis Fabularum Principalium Figuris, Lyons, Jacques Mareschal, 1519.

Heptaplus (1490), by the Italian philosopher Pico Della Mirandola, is a scholarly exercise in seven volumes, each of seven chapters, which attempts to synthesise the various traditions deriving from the Creation myth: that of the Platonists and the Peripatetic School, that of the Evangelists, Church Fathers and Cabbalists, and that of the Islamic philosophers such as Avicenna (Ibn Sina) and Averroes (Ibn Rushd). In particular Mirandola tries to find a hidden meaning to the first two words of Genesis, “In principio”, using the Cabbalist method of making anagrams.

In 1578 Guillaume de Saluste, known as Du Bartas, published an epic poem based on Genesis and inspired by Ovid’s Metamorphoses entitled La Sepmaine (The Week). In “The First Day” Du Bartas attempts to describe chaos by using words in a confused way, using puns and antonyms:

This primordial world was form without form,
A confused heap, a shapeless melange,
A void of voids, an uncontrolled mass,
A Chaos of Chaos, a random mound
Where all the elements were heaped together,
Where liquid quarrelled with solid,
Blunt with sharp, cold with hot,
Hard with soft, low with high,
Bitter with sweet: in short a war
In which the earth was one with the sky. [i]
Continue reading

Cosmogenesis (5) : The Order of the Creation

Sequel of the preceding post Cosmogenesis (4) : The Creator

The order of the Creation

“Order and Truth are born when Passion is aroused. From them is born Night and from Night the Ocean and its waves. From the Ocean’s waves is born the Year, which apportions Night and Day and governs all that the eye sees. The Creator gave shape first to the Sun and Moon, then to the Sky and the Earth, then to the Air and finally to Light.”
Rig-veda, X, 190.

According to Vedic tradition the Creation took place in a completely different order from that specified by the familiar Jewish/Christian story: on the first day God created matter and light out of chaos; on the second day He,  created the air by separating the sky from the waters; on the third day He divided the earth and the waters; on the fourth day He created the celestial bodies, on the fifth the fish and the birds and on the sixth the animals and man; finally, on the seventh day, God rested and contemplated his work.

According to Genesis the separation of light and darkness took place on the first day, the sun and moon not appearing until the fourth. The light which existed on the first day therefore did not come from the sun. Here the bible is perpetuating an ancient belief that light and darkness are independent of the sun, moon and stars, which exist not to provide light but merely to increase it, to distinguish between day and night, to mark the changing of the seasons, and so on. “We must remember that daylight is one thing and sunlight, moonlight and starlight another – the sun’s purpose is to give daylight additional brilliance,” wrote St Ambrose in his Hexameron.

This idea is clearly illustrated by the mosaics in St Mark’s cathedral in Venice and by the frescos in the baptistery in Florence and the basilica of St Francis at Assisi, all of which show the Creator placing in the sky two discs of equal size distinguished only by their colour or by an inscription.

The Creation of Light. The ceiling of St Mark's cathedral in Venice is adorned with a series of beautiful mosaics illustrating the story of Genesis. The pictures relating to the Creation, in the first cupola, were probably completed around 1220 and are modelled on the Cotton bible, a 5th or 6th century illuminated copy of an -ancient Greek manuscript.
The Creation of Light. The ceiling of St Mark’s cathedral in Venice is adorned with a series of beautiful mosaics illustrating the story of Genesis. The pictures relating to the Creation, in the first cupola, were probably completed around 1220 and are modelled on the Cotton bible, a 5th or 6th century illuminated copy of an -ancient Greek manuscript.

Whereas mythical and religious stories describe the creation of the world (by one or more gods), scientific “accounts” are concerned with the formation and evolution of the universe and its content. There are, however, many parallels between these two approaches.

The Creation of Heaven and Earth. The caption to this bible illustration reads: "The Creation of Heaven and Earth, of Trees, Plants, Stars and all the Animals". The engraving therefore represents the first five days of the Creation. God the Father is seen setting the sun and moon among the clouds and the stars; below are the creatures of the land (left) and the sea (right). Engraving by Jean Cousin, in Figures de la Bible, Paris, 1614.
The Creation of Heaven and Earth. The caption to this bible illustration reads: “The Creation of Heaven and Earth, of Trees, Plants, Stars and all the Animals”. The engraving therefore represents the first five days of the Creation. God the Father is seen setting the sun and moon among the clouds and the stars; below are the creatures of the land (left) and the sea (right). Engraving by Jean Cousin, in Figures de la Bible, Paris, 1614.

 

The Creation of the World According to the Nuremberg Chronicle Continue reading

Cosmogenesis (4) : The Creator

Sequel of the preceding post Cosmogenesis (3) : Time and Creation

The Creator

The fundamental theological question about the Creation is: who created the universe? The Christian doctrine of the Holy Trinity asserts that God comprises three Persons: the Father, the Son and the Holy Spirit. Some theologians have regarded God as the first Person of the Trinity, “the omnipotent Father”, Creator of heaven and earth. Others have focused on the image of the “Spirit of God moving upon the face of the waters” and envisaged the Holy Spirit as the Creator. Others again, in an attempt to reconcile these viewpoints, have maintained that the Holy Trinity itself created the world – a reminder of the Vedic belief in a supreme being incarnated as a single body (Trimurti) with three heads: those of Brahma, Vishnu and Siva.

The Hindu Triad. One of the central images of Indian mythology is the Hindu Triad (Trimurti) of Brahma, the creator, Vishnu, the maintainer, and Siva, the destroyer. In this picture they are shown combined into a single body with four arms. Album of paintings of Indian gods and rulers, 1831. Paintings with captions in Tamil and French. BNF, Manuscripts, Indian 744.
The Hindu Triad. One of the central images of Indian mythology is the Hindu Triad (Trimurti) of Brahma, the creator, Vishnu, the maintainer, and Siva, the destroyer. In this picture they are shown combined into a single body with four arms.
Album of paintings of Indian gods and rulers, 1831. Paintings with captions in Tamil and French. BNF, Manuscripts, Indian 744.

These different theological perspectives are reflected throughout the Middle Ages (in fact right up to the 18th century) in religious art, where one or other interpretation of the Genesis story is illustrated in mosaics, paintings, sculptures, stained glass windows, illuminations and engravings.

The most familiar image of the Creator is the patriarchal figure of the Father (the archetypal example being Michelangelo’s fresco on the ceiling of the Sistine Chapel).

God the Father Dividing the Light from the Darkness. In this 16th century engraving, which was clearly influenced by the work of Michelangelo, the Creator, in the form of the first Person of the Holy Trinity, God the Father, is dividing the light (represented by the sun) from the darkness (represented by the moon). Engraving by Raphael Sadeler, in Thesaurus Historia..., 1585
God the Father Dividing the Light from the Darkness. In this 16th century engraving, which was clearly influenced by the work of Michelangelo, the Creator, in the form of the first Person of the Holy Trinity, God the Father, is dividing the light (represented by the sun) from the darkness (represented by the moon).
Engraving by Raphael Sadeler, in Thesaurus Historia…, 1585
Young Christ as Creator. The wonderful fresco adorning the cupola of the baptistery of San Giovanni in Padua is the work of the Florentine artist Giusto Dei Menabuoi, who was active in the second half of the 14th century. It shows God the Son as Creator. Giusto Dei Menabuoi, [The Creation of the World], 14th century.
Young Christ as Creator. The wonderful fresco adorning the cupola of the baptistery of San Giovanni in Padua is the work of the Florentine artist Giusto Dei Menabuoi, who was active in the second half of the 14th century. It shows God the Son as Creator.
Giusto Dei Menabuoi, [The Creation of the World], 14th century.

As the Holy Spirit the Creator is represented by a dove (the ancient Christian symbol of the Divine Spirit) – in the work of Robert Fludd, for example – or by the Hebrew word “Jehova” surrounded by a symbol of fire (recalling the burning bush from which Moses received the word of God). In a few cases the Creator is shown as a young Christ figure – in the 13th century mosaics of the Basilica of San Marco in Venice and the 14th century frescos of Giusto Dei Menabuoi in Padua, for example. Continue reading

Cosmogenesis (2) : Chaos and Metamorphosis

Sequel of the preceding post Cosmogenesis (1) : From Myth to Myth

Chaos and Metamorphosis

 

The ancient Greeks had a great variety of myths relating to the history of the world. Although they all shared a language and a culture, each village, each tribe had its own beliefs, its own version of the Creation story and its own gods who were responsible for cosmic order.

213 The Birth of the Gods According to Hesiod's Theogony (8th-7th century BC) is a history of the gods. It begins with Gaea, goddess of the Earth, the primordial element from which all the deities emerged. By herself she gave birth to the sea and the sky as well as to the gods Uranus and Pontus; by Uranus she then mothered numerous other deities: the Titans (including Cronos) and Titanesses, the Cyclops and the Giants. The work continues with an account of how Zeus became lord of the universe after decisive battles against the Titans and against the monster Typhoeus. This story of the creation of the world out of the struggle between the forces of order (cosmos) and the forces of disorder (chaos) had a strong influence on Greek cosmological thinking. In this illustration by Georges Braque, Hesiod is seen receiving the torch of Hebrew tradition from Moses. Hesiod, Theogony, Paris, Maeght, 1955.
The Birth of the Gods According to Hesiod’s Theogony (8th-7th century BC) is a history of the gods. It begins with Gaea, goddess of the Earth, the primordial element from which all the deities emerged. By herself she gave birth to the sea and the sky as well as to the gods Uranus and Pontus; by Uranus she then mothered numerous other deities: the Titans (including Cronos) and Titanesses, the Cyclops and the Giants. The work continues with an account of how Zeus became lord of the universe after decisive battles against the Titans and against the monster Typhoeus. This story of the creation of the world out of the struggle between the forces of order (cosmos) and the forces of disorder (chaos) had a strong influence on Greek cosmological thinking.
In this illustration by Georges Braque, Hesiod is seen receiving the torch of Hebrew tradition from Moses.
Hesiod, Theogony, Paris, Maeght, 1955.

Hesiod’s Theogony (8th-7th century BC) was the first attempt to synthesize these traditions, which probably dated back to the Assyrian and Babylonian civilizations. In recounting the stages in the emergence of the gods from primordial chaos Theogony offers an answer to the eternal questions of cosmogony: who created the world; what were the basic materials from which it was made; which came first, the gods, the stars or the elements?

Not only did Theogony have a strong influence on Greek thought, it also anticipated in many ways today’s theories of the origin of the world – particularly the idea of primordial chaos. Since the universe appears to have an ordered structure (albeit an imperfect one), it seems logical to regard the state which preceded the Creation as one of disorder and confusion. This notion has provoked greater controversy than almost any other in the history of cosmogony.

Ovid’s Metamorphoses also trawled Greek mythology, as well as Roman legend, in attempting to reconstruct the series of metamorphoses the world had undergone between the original state of Chaos and Julius Caesar’s supposed transformation into a star:

“Before the sea and the lands and the sky that covers all,
there was one face of nature in her whole orb
(they call it Chaos), a rough unordered mass,
nothing except inactive weight and heaped together
the discordant seeds of unassembled things.” [i] Continue reading

Cosmogenesis (1) : From Myth to Myth

Introduction

Every society has a story, rooted in its most ancient traditions, of how the earth and sky originated. Most of these stories attribute the origin of all things to a Creator -whether god, element or idea.

In the Western world all discussions of the origin of the world were dominated until the 18th century by the story of Genesis, which describes the Creation as an ordered process that took seven days. The development of mechanistic theories in the 18th century meant that the idea of an organized Creation gave way to the concept of evolution, and in the 19th century astrophysicists discovered that stars had their origin in clouds of gas. Big bang theory, conceived at the beginning of the 20th century, was subsequently developed into a more or less complete account of the history of the cosmos, from the birth of space, time and matter out of the quantum vacuum until the emergence of life.

Today sophisticated telescopes show us how the first galaxies were formed, how clouds of hydrogen gave birth to stars and how the planets emerged from swirling dust. We now know that creation is still going on in our universe but the origin of life remains an enigma. How did life forms appear? The universe’s best kept secret continues to baffle scientists.

From Myth to Myth

What are the origins of the universe, of the sky, of the earth, of life, of man? These questions have given rise to many different myths and legends and continue to be the subject of intensive research by astrophysicists, biologists and anthropologists. What were once fanciful stories are now scientific models but, whatever form they take, ideas about the origins of the universe both reflect and enrich the imagination of the people who generate them. Every society has developed its own stories to explain the creation of the world; most of them are ancient myths rooted in religion.

Whereas in monotheistic religions God is believed to have existed before the Creation, in most other kinds of religion the gods themselves are thought to originate from a creative element such as Desire, the Tree of the Universe, the Mundane Egg, Water, Chaos or the Void.

Babylonian Gods. An inscription on the back of this stone carving tells us that it was a gift from the Kassite king Melishishu II to his son. The picture shows the symbols representing the gods carved on the front. On the right the principal deities -Anu, god of the sky, and Enlil, god of the atmosphere - are each shown as a sort of tiara standing on a plinth. Next a ram's head above a creature half-goat half-fish represents Ea, god of the Waters of the Abyss. The symbol on the left might be for the goddess Ninhursag. Above these are the three celestial divinities: a crescent for Sin, god of the moon, a star for Ishatar and an image of the sun for Shamash. Stone from Kassite era (1202-1188 BC). Paris, Louvre.
Babylonian Gods. An inscription on the back of this stone carving tells us that it was a gift from the Kassite king Melishishu II to his son. The picture shows the symbols representing the gods carved on the front. On the right the principal deities -Anu, god of the sky, and Enlil, god of the atmosphere – are each shown as a sort of tiara standing on a plinth. Next a ram’s head above a creature half-goat half-fish represents Ea, god of the Waters of the Abyss. The symbol on the left might be for the goddess Ninhursag. Above these are the three celestial divinities: a crescent for Sin, god of the moon, a star for Ishatar and an image of the sun for Shamash.
Stone from Kassite era (1202-1188 BC). Paris, Louvre.
The Chinese giant Pangu
The Chinese giant Pangu

Ideas like these appear in the Rig-veda, one of the four sacred books of the Brahmins and the oldest surviving written record of Indian culture which were compiled between 2000 and 1500 BC. The Tree of the Universe, symbol of the outward growth of the world and of its organic unity, is mentioned in ancient Indian legends as well as in those of the Babylonians and Scandinavians (who call it Yggdrasil). The anthropomorphic symbol of Desire was invoked by the Phoenicians and by the Maoris of New Zealand. The Mundane Egg, from which the Hindu Prajapatis (lords of all living things) emerged, also gave birth to the gods Ogo and Nommo, worshipped by the Dogon of Mali, and the Chinese giant Pan Gu as well as constituting the celestial vault in the legend of Orpheus.

Birth of Gods and Cosmic Egg according to the Upanishad
Birth of Gods and Cosmic Egg according to the Upanishad

A belief in some such primordial element, of which there are traces in every culture, underlies man’s thinking about the history of the cosmos like a primitive universal symbol buried in the collective subconscious. This may explain the vague links which can always be discerned between this or that creation myth and modern scientific descriptions of the origin of the universe – for example, big bang theory. There is therefore nothing mysterious or surprising about these correspondences other than that certain ways of thinking about the world should be so ingrained in the human mind. Continue reading

My books (2) : Glorious Eclipses

Until now I published as an author 30 books in my native language (French), including 14 science essays, 7 historical novels  and 9 poetry collections (for the interested reader, visit my French blog  here.
Although my various books have been translated in 14 languages (including Chinese, Korean, Bengali…), 4 of my essays have been translated in English.

The second one was :

Glorious Eclipses : Their Past, Their Present, Their Future

Translated from French by Storm Dunlop
Cambridge University Press, 2001 -ISBN 0 521 79148 0

GEclipsesThis beautiful volume deals with eclipses of all kinds – lunar, solar and even those elsewhere in the Solar System and beyond. Bringing together in one place all aspects of eclipses, it is written by the perfect team : Serge Brunier is a life-long chaser of eclipses, and internationally-known astronomy writer and photographer, whilst Jean-Pierre Luminet is a famous astrophysicist with a special interest in astronomical history. Lavishly illustrated throughout, Glorious Eclipses covers the history of eclipses from ancient times, the celestial mechanics involved, their observation and scientific interest. Personal accounts are given of recent eclipses – up to and including the last total solar eclipse of the 20th century : the one on August 11th 1999 that passed across Europe, Romania, Turkey and India. This unique book contains the best photographs taken all along its path and is the perfect souvenir for all those who tried or wished to see it. In addition, it contains all you need to know about forthcoming eclipses up to 2060, complete with NASA maps and data.

 

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EXCERPT : FOREWORD

Why should a theoretical astrophysicist, who has rarely peered through the eyepiece of a telescope, preferring to speculate on the invisible architecture of space-time by means of dry equations, be interested in eclipses, to the extent of writing a book about them?

It is true that Einstein’s general theory of relativity, which has been a constant intellectual delight for me over so many years, was first proved experimentally thanks to a ‘simple’ solar eclipse. That was on 29 May 1919. But such an argument satisfies only the intellect. When it comes to the soul, it demands a greater spectacle, a more tangible emotion.

I was not yet ten on 15 February 1961, when a total eclipse of the Sun crossed the Provence where I was born. All I can recall is preparing smoked glass under the watchful eye of our schoolmistress. Clouds over Cavaillon probably spoilt the spectacle, because I have no memory of the eclipse itself…

Then… then I waited nearly forty years before finally seeing a total eclipse of the Sun. That was on 26 February 1998, in the Sierra Nevada de Santa Maria, in the north of Colombia. Serge Brunier and a few other colleagues, genuine eclipse chasers, had finally convinced me that any astrophysicist worthy of the name should not ‘die a fool’! It is true that, obviously, such a recurrent and ‘nearby’ astronomical event might seem somewhat prosaic to someone who spends his life in abstract research on models of the Big Bang, black holes, and the realms of space-time.

On that day, however, between 10:59 and 11:03, I experienced what John Couch Adams described so well, some 150 years before. The English mathematician-astronomer, less accustomed to handle telescopes than complex equations of celestial mechanics – he predicted the existence of the planet Neptune through calculation – witnessed a total eclipse of the Sun for the very first time in his career during the summer of 1846. He subsequently described the extraordinary emotions he felt as an astronomer – and, moreover, an experienced one – who realized that he was a novice when he discovered this astounding cosmic drama for the very first time.

The darkness that descends suddenly in the very middle of the brilliance of the day; this new light that arises from the obscurity; the planets aligned like a necklace of pearls in a configuration that is never seen by night; and the Sun’s flamboyant corona…

These few minutes in which time seems suspended, create the almost palpable feeling of being, transiently, part of the invisible harmony that rules the universe. It is as if a sudden opening in the opaque veil of space allows our inner vision to reach into the otherwise hidden depths of the cosmos, giving us humans – mere insignificant specks of dust – an all-too-brief instant to see the other side of the picture.

To me, the invisible is not restricted to dark objects that our telescopes cannot detect. It is also, and in particular, the secret architecture of the universe, the insubstantial framework of our theoretical constructs. I have always been moved by black. Not black as in absence, but rather black as revealing light. According to the painter Francois Jacqmin ‘Shadow is an insatiable star-studded watchfulness. It is the black diamond that the soul perceives when the infinite rises to the surface.’ Astrophysics and cosmology team with examples where black is all-important. It is in the black of the night that one sees stars, or, in other words, that one perceives the immensity of the cosmos. This same night-time darkness reveals the whole evolution of the cosmos, and the finite nature of time. The mass of the universe is largely dominated by dark matter; massive, non-luminous objects, which through their gravitational attraction govern the dynamics of the cosmos. As for black holes, the epitome of invisibility, they are perhaps secret doorways opening onto other regions of space-time.

Another aspect of eclipses enthrals me: their historical and cultural dimension. I have always been attracted by the way in which different forms of human invention interact. Science, despite being an effective and rational approach to truth, nevertheless remains incomplete. Art, philosophy, and the comparative study of traditions, myths and religions, are all complementary approaches that are indispensable for anyone who wants to gain a greater insight into where they fit in the cosmic scheme of things.

In unfolding the story of people, their civilizations, and their relationships with heavenly phenomena, one cannot but be fascinated to see how past eclipses have influenced their course. The impression of a supernatural power engendered by the sudden disappearance of the Sun or the Moon has often struck human beings, frightened by an apparently hostile and incomprehensible nature, to the extent of changing their behaviour.

That’s enough. My colleague, Serge Brunier, and I decided to write a book that alternated between these ‘two voices’. After all, the various types of eclipses are created by the Earth and the Moon taking it in turn to pass in front of each other beneath the blazing Sun…

Eclipses are a benign contagious virus, which once it has infected you, recurs at intervals. Which is why, for the eclipse of 11 August 1999, I went deep into the Iranian desert, to be (almost) certain of finding a sky devoid of clouds.

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PRESS REVIEWS

An extrordinarily beautiful book, Glorious Eclipses guides us elegantly through the history of obscurations of the sun and moon – from the ancient Chinese belief that a dragon was devouring the daytime star through current theories and on to celestial events forthcoming in the next six decades. Some of the most startling images come from the days when photography was in its infancy and astronomers still made drawings of eclipses.

Scientific American, June 2001


Darkness at noon

At first sight, this is the ultimate eclipse book. Oversize, well-produced photographs in a large-format book are accompanied by interesting text covering a wide variety of eclipses phenomena. The partnership of an astronomer writer/editor and a professional astronomer, albeit a cosmologist, successfully brings the beauty of total solar eclipses to the fore.

Although the writers alternate, the difference is not jarring, perhaps thanks to the expert translator, Storm Dunlop. In a chapter entitled “The great cosmic clockwork”, Serge Brunier, long-time editor of the French popular astronomy journal Ciel et Espace, discusses the many kinds of eclipses and occultations (when one astronomical body occults, or hides, another). He even includes the eagerly awaited 2004 transit of Venus – the passage of Venus across the face of the Sun. This will be the first transit of Venus visibe from Earth since 1882.

The reproduction of photographs in 25 cm x 35 cm format on heavy stock is outstanding. For example, we see Saturn’s rings extending across a double page for almost half a metre in a Hubble Space Telescope image. The authors justify using this image, which shows the shadow of Saturn’s satellite Titan on Saturn’s clouds, by pointing out that it corresponds to an eclipse of the Sun by Titan as seen from Saturn. It’s a pity, though, that Brunier calls himself an “eclipse chaser” – that common but misleading phrase seemps to imply that people can outrun, or even outfly, eclipses, which has never been done.

Brunier is responsible for some of the most magnificent photographs, such as one from the 1991 total solar eclipse visible from the Mauna Kea Observatory in Hawaii, with a few telescopes in the foreground. But the image I found most arresting is not one of this; it is a wide-angle shot of the 1991 eclipse viewed through a hole in the clouds and showing the front of Reims Cathedral in the left foreground.

In his chapters on the history and cultural significance of eclipses, Jean-Pierre Luminet reproduces a remarkable set of historical images related to solar and lunar eclipses from around the world. These are no doubt related to his work on an exhibition of astronomical atlases held in Paris at the Bibliothèque Nationale in 1998.

It was good to read about myths that cast eclipses in a favourable light rather than as evil omens. Luminet also describes the history of scientific discovery through observations of solar eclipses. One example is the discovery at the 1868 total solar eclipse of the spectrum of the solar chomosphere – the layer of the Sun just above the surface that becomes briefly visible at the beginning and end of totality. The element helium was also discovered at this eclipse.

There is much that is excellent in the book. The charts of future eclipses at the end of the book are redrawn at the highest quality. Lunar eclipses are included in the text, photos and charts, looking almost as dramatic on the page as the solar ecipses, even though they are much less so in reality. As a book of history, myth, literature, photography and expeditionary experiences, Glorious Eclipses is outstanding, despite its omission of the solar research carried out at recent eclipses.

Jay Pasachoff, Nature, vol. 410, 29 march 2001.


Wonder of day turned into light

A total eclipse of the Sun is about as astonishing a treat as nature provides. For a few minutes, the Moon exactly covers the Sun, making night from day and displaying the otherwise invisible solar atmosphere. This book celebrates eclipses of both Sun and Moon (the rather less spectacular sweeping of Earth’s shadow across the lunar surface) from many directions, including the complex history of eclipse observations and their declining but still real scientific value.

Serge Brunier and Jean-Pierre Luminet are respectively a science journalist and photographer, and a senior astronomer. This book, well translated from French by Storm Dunlop, makes the most of their strengths. It displays a deep understanding of history, some gripping science and a wealth of images, both of eclipses and of the many ways in which they have been represented over the years.

(…)

If you want to take up eclipse chasing, the book’s maps of future eclipses will tell you when and where to be, and its illstrations will tell you what to expect and how to observe in safety. There are explanations of the eclipse cycle, or Saros, and of the fact that in the far future, there will be no more solar elipses as the Moon’s distance from the Earth increases.

The book also provides generous coverage of lunar eclipses and of related events such as occultations and transits. There is even space to reveal how planets in other solar systems are being detected as they eclipse their own star as seen from Earth. Eclipses still make cutting-edge science thousands of years after they first caused dismay to our ancestors.

Martin Ince, Deputy Editor, The Times Higher, March 9 2001.


Not in the shade

This attractive and beautifully illustrated book, by two Paris astronomers and dedicated eclipse-chasers, was originally published in French under the title Eclipses, Les Rendez-vous Celestes (Larousse-Bordas/HER, 1999). The present English translation is by Storm Dunlop. This book is a veritable mine of information on eclipses and is suitable for anyone who has an interest in eclipses, be they amateur or professional astronomer, photographer or historian.

The scene is set in the first chapter, which captures much of the appeal of total solar eclipses and leaves the reader in no doubt as to why eclipse chasers will travel vast distances to witness a few minutes of totality.

In chapters two and three, the historical and literary aspects of both solar and lunar eclipses are discussed. Although there is some sound history in the first of these chapters, there is also much speculation – especially with regard to such torical and literary aspects of both such diverse matters as Stonehenge, Thales, and the date of the Crucifixion of Jesus. Regrettably, there are several serious errors. Thus the “Assyrian tablet dating from the

2nd century BC” (p40) is in fact from Babylonia, several centuries after the demise of Assyria. Thucydides reports three eclipses, not just two (p43). “According to the Evangelists,” Jesus was not “crucified on a Thursday,” (p44). Chapter three contains some intriguing literary allusions to eclipses in prose and poetry – both ancient and modern.

Chapters four to seven provide the main substance of this book and are both fascinating and informative. They deal respectively with: the cause of both lunar and solar eclipses; lunar and planetary occultations and also Mercury and Venus transits; total solar eclipse phenomena; and the famous or infamous (depending on the wearher) 1999 eclipse. In particular, it is gond to see a discussion of occultations and transits – which, in a sense, are eclipses in their own right.

The final chapter contains helpful hints for observing and photographing eclipses and also a series of attractive maps showing the visibility of future solar and lunar eclipses – with special emphasis on those over the next 20 years. Unfortunately many of the individual solar eclipse maps (p156–69) are confusing; in each case the maps show “Total eclipse begins at sunrise”, “Path of totality” and “Total eclipse ends at sunset” whether the eclipse was annular or total.

Overall, this is a splendid hook, profusely illustrated.

F Richard Stephenson. Astronomy & Geophysics, 2001 December (Vol.42), 6.33

Doppelmayer-14-P

My books (1) : Black holes

Until now I published as an author 30 books in my native language (French), including 14 science essays, 7 historical novels  and 9 poetry collections (for the interested reader, visit my French blog  here.
Although my various books have been translated in 14 languages (including Chinese, Korean, Bengali…), only 4 of my essays have been translated in English.

The first one was :

Black Holes

312 pages – Cambridge University Press, 1992 – ISBN 0 521 40029 5 (hardback) – ISBN 0 521 40906 3 (paperback) – Foreword by Joseph Silk.

black-holesBlack holes are the most fascinating discovery of modern astronomy. They have already become legendary, and form the basis of many myths and fantasies. Are they really the monsters of science fiction which devour light and stars? Are they purely hypothetical objects from the theory of relativity or are they an observable reality?
In answering these questions, the author takes us on a fabulous voyage through space and time. He explains how stars are born, light up and die. He takes us into the strange world of supernovae, X-ray stars and quasars. We travel on a journey to the very edge of the universe and to the limits on contemporary physics.
The amount of information conveyed is impressive. The intended audience is readers with some understanding of physics who are seeking a coherent, accurate nonmathematical overview of black-hole physics and all the astronomical situations that the discipline seems to explain. Also, any student embarking on a serious technical study of general relativity or astrophysics will find the book a first-rate overview of an important part of the story. (…) This is an outstanding work of scientific exposition.” — John Barrow, Nature Continue reading