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

Galaxies in Flight

This post is an adaptation of a chapter of my book  “The Wraparound Universe” with many more  illustrations.

 

Galaxies in Flight

                     The spawning galaxy in flight is a rainbow trout which goes
back against
the flow of time towards the lowest waters, towards the dark retreats of duration.
Charles Dobzynski (1963)

Since the time of Newton, we have known that white light, passing through a prism, is decomposed into a spectrum of all colors. Violet and blue correspond to the shortest wavelengths or, equivalently, to the largest frequencies; red corresponds to the largest wavelengths and to low frequencies. In 1814, the German optician Joseph von Fraunhofer discovered that the light spectrum from stars is streaked with thin dark lines, while that from candlelight has bright stripes. These phenomena remained puzzling until 1859. It was then that the chemist Robert Bunsen and the physicist Gustav Kirchhoff analyzed the light created from the combustion of different chemical compounds (burned with the now-famous Bunsen burner) and saw that each of them emitted light with its own characteristic spectrum.

Fraunhofer lines in the solar spectrum

At nearly the same time, Christian Doppler discovered in 1842 that moving the source of a sound produced shifts in the frequency of sound waves, a phenomenon experienced by anyone listening to the siren of an ambulance passing by. The French physicist Armand Fizeau noticed the same phenomenon with light waves: depending on whether a source of light was moving closer or farther away, the received frequencies are either raised or lowered with respect to the emitted frequencies. The shift becomes larger as the speed of displacement is increased. If the source is getting closer, the frequency grows, and the light becomes more “blue”; if it moves away, the frequency lowers and the wavelengths stretch out, becoming more “red,” with respect to the spectrum of visible light. Since this shift affects the whole spectrum by the same amount, it is easily quantified by looking at the dark or bright stripes, which are shifted together, either towards the blue or towards the red, and it furnishes an incomparable means of measuring the speed of approach or retreat for light sources.

Shortly after this discovery, astronomers began an ambitious program of spectroscopy, with the aim of measuring the speed of the planets and stars by using their spectral shifts. Continue reading

Expansion and the Infinite

This post is an adaptation of a chapter of my book  “The Wraparound Universe” with many more  illustrations.

Expansion and the Infinite

Space alike to itself
that it grows or denies itself
Stéphane Mallarmé

The Universe is expanding. What does this really mean? Most people imagine an original huge explosion, as the term “big bang” suggests, and the metaphor is constantly used in popular accounts. Some speakers even have the tendency to mime a gesture of expansion with their hands, as if they were holding a piece of space or an immaterial balloon in the process of inflating. The public imagines some matter ejected at prodigious speeds from some center, and tell themselves that it would be better not to be there at the moment of explosion, so as not to be riddled through with particles.

A misleading view of the expanding universe commonly used in popular science

None of all this is accurate. At the big bang, no point in the Universe participated in any explosion. Put simply, if one considers any point whatsoever, we notice that neighboring points are moving away from it. Is this to say that these points are animated by movement, given a speed? No, they are absolutely fixed, and nevertheless they grow apart.

To unravel this paradox, it is necessary to make more precise what one exactly means when speaking of a fixed point. The position of a point is fixed by coordinates: one number for a line (the miles along a highway), two numbers for a surface (latitude and longitude), and three for space in general (length, width, and height). A point is said to be fixed if its coordinates do not change over the course of time. In an arbitrary space, curved or not, the distance between two points is given by the so-called metric formula, which depends on the coordinates and generalizes the Pythagorean theorem. In principle, therefore, the distance between two points does not vary. In an expanding space, on the other hand, this distance grows, while the points do not move, even by a millimeter, meaning that they strictly conserve the same coordinates. These fixed coordinates are known as “comoving” coordinates. In relativistic cosmology, galaxies remain fixed at comoving positions in space. They may dance slight arabesques around these positions, under the influence of local gravitational fields, but the motion which moves them apart from each other resides in the literal expansion of the space which separates them. Continue reading

Non-Euclidean Geometries

This post is an adaptation of a chapter of my book  “The Wraparound Universe” with many more  illustrations.

************************************************************************

Thus we may perhaps, one day, create new Figures
that will allow us to put our trust in the Word,
in order to traverse curved Space, non-Euclidean Space.
Francis Ponge[1]

The oldest known fragment of Euclid’s Elements as part of the Oxyrhynchus papyri, dated from the Ptolemaic period and belonging to the famous Alexandrian Library

 

In book I of the Elements,[2] Euclid poses the five “requests” that, according to him, define planar geometry. These postulates would become the keystone for all of geometry, a system of absolute truths whose validity seemed irrefutable. One of the reasons for this faith is that these postulates seem obvious: the first of them stipulates that a straight line passes between two points, the second that any line segment can be indefinitely prolonged in both directions, the third that, given a point and an interval, it is always possible to trace out a circle having the point for its center and the interval as its radius, the fourth that all right angles are equal to each other. The fifth postulate is however less obvious:

As the sum of the interior angles α and β is less than 180°, according to the fifth postulate the two straight lines extended indefinitely, meet on that side.

“If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.”

 

 

Although the statement does not refer explicitly to parallel lines, the the fifth postulate is currently called “Parallel postulate”. This can be better understood given the more popular version of the fifth postulate due to the Scottish mathematician John Playfair (1748-1819), who demonstrated that it was equivalent to the one given by Euclid : “Given a straight line and a point not belonging to this line, there exists a unique straight line passing through the point which is parallel to the first“.

A picturesque English edition of Euclid’s Elements by Oliver Byrne, 1847.

 

Since the “parallel postulate” was more complicated than the others, the mathematicians following Euclid would try, for many centuries, to prove it from the four preceding ones, all in vain. In the nineteenth century, there occurred one of the great sudden revolutions in the history of mathematics (and also in human thought, as will be seen by what follows): two new geometries which do not satisfy the fifth postulate, but which are perfectly coherent, were discovered. In one of these geometries, called spherical geometry, no parallel line satisfying the conditions can be traced. This is the case for the surface of a sphere; the straight lines become great circles, whose planes pass through the center of the sphere, and since all great circles intersect each other at two diametrically opposed points (in the manner of the terrestrial meridians, which meet at the poles), no “straight line” can be parallel to another.[3] In the other geometry, called hyperbolic geometry, through any given point there passes an infinite number of lines parallel to another straight line. Continue reading

TOTAL SOLAR ECLIPSE 2017 : THE ROLE OF SOLAR ECLIPSES IN ASTROPHYSICS

In view of the total solar eclipse of 2017 Aug 21 through the United States, this is a reminder of the role of solar eclipses in the developments of astronomy and astrophysics.
It is taken from a chapter of my book Glorious Eclipses, presented elsewhere in this blog.

Summary

Eclipses of the Sun and Moon have never ceased to provide us with a host of lessons about the nature of the universe around us. The first of these lessons concerned the celestial bodies directly involved in eclipses: namely the Earth, Moon, and Sun. Indeed, back in antiquity, the proof that the Earth was round, and the first measurements of the respective sizes and distances of the Moon and Sun were deduced from the observation of eclipses. In the 19th century, it was the normally invisible atmosphere of the Sun that was revealed thanks to eclipses. Far from being the perfectly round, and sharply defined ball of hot gas that it appears to the eye – appropriately protected by suitable filters, of course – the Sun is found to be a sprawling giant, overflowing with energy, plasma, and particles, that extends its influence throughout the whole Solar System. Eclipses also provoked the discovery of helium, the second most abundant element in the Sun, and in the universe as a whole. In a more surprising manner, in the 20th century, Einstein’s General Relativity, a fundamental theory about space, was tested experimentally for the first time, thanks to an eclipse. It is on this new vision of the universe, which explains gravitation in terms of the ‘curvature of space-time’, that all our current knowledge of the origin, the structure, and the evolution of the universe, depends, by way of the fascinating concepts of an expanding universe, the Big Bang, and black holes.

During a total eclipse, the Sun’s invisible empire appears : eruptions and prominences rise above the level of the photosphere, and colour the Sun’s inner atmosphere, known as the chromosphere.
The Earth is round
According to Aristotle, lunar eclipses prove that the Earth is round. Indeed, if the Earth were square, or triangular, its shadow projected onto the disk of the Moon at the time of an eclipse would not appear circular. Aristotle’s geometrical argument is shown in several ancient astronomy texts, including Cosmographia, by Petrus Apianus and Gemma Frisius, 1581.

The first demonstration of an astrophysical nature resulting from eclipses is the one given by Aristotle concerning the fact that the Earth is round. The astronomical views of this Greek philosopher are well-known to us, thanks to his two works, known to us as Meteorology and On the Heavens, dating from the 4th century BC. Like other thinkers of his day, Aristotle believed that all heavenly bodies were spherical, because to him heavenly bodies were a reflection of divine perfection, and the sphere is the most outstandingly perfect geometrical figure. But this argument was not a physical demonstration, because, naturally, Aristotle did not have any experimental means of confirming the spherical nature of the planets and stars.
As far as the Moon was concerned, the philosopher adopted an explanation attributed to the Pythagoreans, namely that the observed appearance of the Moon throughout its various phases corresponded to a spherical body, half of which is illuminated by the Sun. As for the spherical nature of the Earth, the proof given by Aristotle is quite original: he notes that an eclipse of the Moon is caused by the shadow of the Earth, and that the circular shape to the edge of the shadow seen on the Moon’s surface implies that our world is spherical

Sizes and distances of the Moon and Sun

The golden age of Greek astronomy flourished at Alexandria. Since its foundation under the reign of Ptolemy Soter (3rd century BC), the Alexandrian school brought together brilliant mathematicians and geometers, such as Euclid, Archimedes, and Apollonius. Similarly, the greatest ancient astronomers Aristachus of Samos, Eratosthenes, and Hipparchus, as well as Ptolemy (2nd century BC), all worked there.

Aristarchus (310-230 BC) is nowadays known for having been the first to voice the heliocentric theory, i.e., that it is the Sun that reigns at the centre of the world system, not the Earth as was believed at the time. His statement does not appear in any known work, but it was reported by Archimedes and by Plutarch. The only work of Aristarchus that has come down to us relates to the sizes and distances of the Sun and the Moon.
The Alexandrian astronomer completely reopened this question, which had been discussed since the 4th century BC. The Pythagoreans had positioned the heights of the celestial bodies according to musical intervals. Eudoxus, the brilliant disciple of Plato, had estimated the diameter of the Sun as nine times that of the Moon. As for Aristarchus, he devised an ingenious geometrical method of calculating the distance ratios of the Sun and Moon.

On the Sizes and Distances of the Sun and the Moon is the only surviving work usually attributed to Aristarchus.

 

Aristarchus of Samos tried to calculate the relative diameter of the moon and sun, as deduced from the line subtending the arc that divides the light and dark portions of the moon during an eclipse.

 He found that the Sun lay at a distance between 18 and 20 times that of the Moon. (In fact, it is 400 times as far.) By an argument based on the observation of eclipses, he determined the diameter of the Moon as one third of that of the Earth, which is very close to the actual value. He also announced that the diameter of the Sun is seven times that of the Earth. Even though Aristarchus considerably underestimated the size of the Sun, because it is actually 109 times as large as the Earth, he had grasped the essential fact that the daytime star was much larger than the Earth. It was precisely this result that led him to the heliocentric hypothesis. He did, in fact, argue that under these circumstances, it was logical to believe that the Earth and the other celestial bodies revolved around the Sun, rather than the reverse. Aristachus was before his time. The world had to wait until 1543 and the work by Copernicus, before the heliocentric theory was again put forward, this time with success.

A century after Aristachus, and again at Alexandria, Hipparchus developed a complete theory of the Moon.   He defined the   lengths of the synodic month (or lunation, the period in which the Moon returns to the same position relative to   the   Sun);   the   draconitic month   (the period for the Moon to return to the same position   relative to the nodes of its   orbit);   and   the anomalistic month (the period for the Moon to return to perigee or apogee). The immense improvements that   Hipparchus brought to theories of the apparent motion of the Moon and Sun enabled him to have far more success than his predecessors in dealing with the problem of predicting eclipses, which had always   been   of   immense   interest.

Hipparchus   considerably   extended Aristarchus’ method: by observing the angular diameter of the shadow of the Earth at the Moon’s distance during a lunar eclipse, and comparing it with the known apparent diameters of the Sun and Moon (about half a degree), he obtained the ratio of the Earth-Moon and   Earth-Sun distances, giving one when   the   other   is   known.   Pappus, another famous   astronomer of the Alexandrian   school,   recounts   that Hipparchus     made     the     following observation of: “An eclipse of the Sun, which in the area of the Hellespont was precisely an exact eclipse of the whole Sun; such that none of it was visible,   but at Alexandria,   in   Egypt, about 4/5 of its diameter were hidden. By means of the foregoing arguments, [Hipparchus] showed that,   measured in   units   where   the   radius   of   the Earth has the value of 1, the smallest distance to the Moon is 71, and the larger 83. Whence the average of 77.

The total solar eclipse mentioned is that of 20 November 129 BC. The actual value of the Earth-Moon distance is 60,4 terrestrial radii.

During a total eclipse of the Sun, the electrified plasma hugs the lines of the sun’s magnetic field, just as iron filings follow those of a magnet. The corona displays narrow filaments over the poles, and extends in a more homogeneous manner in the equatorial regions.
The empire of the Sun

Continue reading

The Edge Paradox

The world has no outside, no beyond, since it contains and embraces everything
Guillaume d’Auvergne (De Universo, 1231)

If the Universe is finite, it seems necessary for it to have a center and a frontier. The center poses hardly any conceptual difficulty: it suffices to place the Earth there, like the geocentric systems of Antiquity (appearances lead one in this direction), or the Sun, as Copernicus did in his heliocentric system. The notion of an “edge” of the Universe is on the other hand more problematic.

Archytas, born in 428 BC in Tarentum (Italy) and died in 347, was a philosopher, mathematician, astronomer, statesman, and strategist. He belonged to the Pythagorean school and was famous for his scientific abilities.

In the fifth century BCE, the Pythagorean Archytas of Tarentum described a paradox that aimed to demonstrate the absurdity of having a material edge to the Universe. His argument would have a considerable career in all future debates on space: if I were at the extremity of the sky, could I extend my hand or stick out a staff? It is absurd to think that I could not; and if I could, that which is found beyond is either a material body, or space. I could therefore move beyond this once again, and so on. If there is always a new space towards which I can extend my hand, this clearly implies an expanse without limits. There is therefore a paradox: if the Universe is finite, it has an edge, but this edge can be passed through indefinitely.

This line of reasoning was taken up by the atomists, such as Lucretius, who gave the image of a spear thrown to the edge of the Universe, and afterwards by all the partisans of an infinite Universe, such as Nicholas of Cusa and Giordano Bruno. Continue reading

Willem Blaeu, a prolific cartographer and globemaker

Detail of a geographic map by W. Blaeu
SUMMARY
A portrait of W. Blaeu by Jeremias Falck, engraving from the Digitale bibliootheek voor de Nederlandse letteren.

Willem Janszoon Blaeu (1571-1638) founded one of history’s greatest cartographic publishing firms in 1599. Mostly renowned as a cartographer, he also made terrestrial and celestial globes, various instruments such as quadrants, a planetarium and a tellurium. He invented mechanical devices for improving the technics of printing. As an astronomer, a former student of Tycho Brahe, Willem Blaeu made careful observations of a moon eclipse, he discovered a variable star now known as P Cygni, and carried out a measurement of a degree on the surface of the earth (as his countryman Snell did in 1617).

THE LIFE AND WORK OF WILLEM BLAEU

The Blaeu family has its origin in the island of Wieringen, where about 1490, Willem Jacobszoon Blauwe – the grandfather of Willem – was born. From his marriage with Anna Jansdochter sprang six children. The second son, Jan Willemsz. (1527- before 1589) was the father of Willem Blaeu, and continued the family tradition by practicing the prosperous trade of herring packer. From his second marriage with Stijntge, Willem Jansz. Blaeu was born at Alkmaar or Uitgeest.

At an early age, Willem Blaeu went to Amsterdam in order to learn the herring trade, in which he was destined to succeed his father. But Willem did not like this work very much, being more inclined to Mathematics and Astronomy. He did not attend a university and worked first as a carpenter and a clerk in the Amsterdam mercantile office of his cousin Hooft.

Tycho Brahe and assistants making an astronomical observation at Uraniborg

However, in 1595 he became a student of Tycho Brahe (1546-1601). The celebrated Danish astronomer demanded a high standard of his pupils. Some were invited by him, others were undoubtedly taken on special recommendation. We may therefore presume that young Blaeu had reached a good standard of education and technical skill, since he was considered worthy to become a student of the great astronomer. Blaeu lived on the Island of Hven over the winter of 1595/1596, at Brahe’s famous observatory in Uraniborg. Thanks to this exact knowledge acquired from Brahe, Blaeu was able to make tables for sun declination ; especially he also learned from Brahe to make globes and instruments like the quadrants.

As it is well-known, Tycho Brahe had his own cosmic system, a sort of compromise between the Ptolemaic and Copernican. Willem Blaeu, although a supporter of the Copernican system, remained cautious during the rest of his career. In his books he mentioned the Copernican model as one of the existing theories, besides the Ptolemaic and Tychonic. It will not only save him for confrontations with religious people, but this attitude was also beneficial for his sales.

The Tychonic system of the world depicted in Andreas Cellarius atlas “Harmonia macrocosmica” (1660).

 After his return from Hven in 1596, Blaeu settled in Alkmaar. Very little is known of his stay here. He married, probably in 1597, Marretie or Maertgen, daughter of Cornelis from Uitgeest. Here too, his eldest son Joan was born. Continue reading

A brief history of space (4/4)

Sequel of the preceding post A Brief History of Space (3/4) : From Descartes to Schwarzschild

Cosmology developed rapidly after the completion of general relativity by Albert Einstein, in 1915. In this theory, the Universe does not reduce to a space and a time which are absolute and separate; it is made up of the union of space and time into a four dimensional geometry, which is curved by the presence of matter.

Albert Einstein (here in 1910) developed the theory of relativity and was awarded the 1921 Nobel prize for physics. Image by © Hulton-Deutsch, Collection/CORBIS

It is in fact the curvature of space-time as a whole which allows one to correctly model gravity, and not only the curvature of space, such as Clifford had hoped. The non-Euclidean character of the Universe appeared from then on not as a strangeness, but on the contrary as a physical necessity for taking account of gravitational effects. The curvature is connected to the density of matter. In 1917, Einstein presented the first relativistic model for the universe. Like Riemann, he wanted a closed universe (one whose volume and circumference were perfectly finite and measurable) without a boundary; he also chose the hypersphere to model the spatial part of the Universe.

Einstein static universe in a space-time diagram.

At any rate, Einstein’s model made the hypothesis of a static Universe, with the radius of the hypersphere remaining invariable over the course of time. In truth, the cosmological solutions of relativity allow complete freedom for one to imagine a space which expands or contracts over the course of time: this was demonstrated by the Russian theorist Alexander Friedmann, between 1922 and 1924.

At the same time, the installment of the large telescope at Mount Wilson, in the United States, allowed for a radical change in the cosmic landscape. In 1924, the observations of Edwin Hubble proved that the nebula NGC 6822 was situated far beyond our galaxy. Very rapidly, Hubble and his collaborators showed that this was the case for all of the spiral nebulae, including our famous neighbor, the Andromeda nebula: these are galaxies in their own right, and the Universe is made up of the ensemble of these galaxies. The “island-universes” already envisaged by Thomas Wright, Kant and Johann Heinrich Lambert were legitimized by experiment, and the physical Universe seemed suddenly to be immensely enlarged, passing from a few thousand to several dozen million light-years at the minimum. Beyond this spatial enlargement, the second major discovery concerned the time evolution of the Universe. In 1925, indications accumulated which tended to lead one to believe that other galaxies were systematically moving away from ours, with speeds which were proportional to their distance. Continue reading

A brief history of space (3/4) : from Descartes to Schwarzschild

Sequel of the preceding post A Brief History of Space (2/4) : From Ptolemy to Galileo

At the beginning of XVIIth century, the way was open for new cosmologies, constructed on the basis of infinite space. Until then, the notion of space was conceived in the cosmological and physical order of nature, and not as the “background” of the figures and geometric constructions of Euclid. In other terms, physical space was not mathematicized. It became so thanks to René Descartes (1596 – 1650), who had the idea of specifying each point by three real numbers: its coordinates. The introduction of a universal system of coordinates which entirely criss-crossed space and allowed for the measurement of distances was a reflection of the fact that, for Descartes, the unification and uniformization of the universe in its physical content and its geometric laws was a given. Space is a substance in the same class as material bodies, an infinite ether agitated by vortices without number, at the centers of which were held the stars and their planetary systems.

A portrait of René Descartes

This new conception of the cosmos upset philosophical thought and led it far from the initial enthusiasm of the atomists and Giordano Bruno: “The absolute space which inspired the hexameters of Lucretius, the absolute space which that had been a liberation for Bruno, was a labyrinth and an abyss for Pascal.”[5] As for the scholars, they did not allow themselves to be discouraged by these moods and irresistibly moved towards the infinite universe.

The Descartes system of the world using vortices

The tendency toward the radical geometrization of an infinite space, initiated by Descartes, was consummated by the Englishman Isaac Newton (1642-1727). Newton postulated an absolute space, encompassing not only the background space of mathematics and the physical space of astronomy, but also that of metaphysics, since space was the “sensorium of God.” Physical space, finally identified with geometrical space, was necessarily Euclidean (the only one known at the epoch), without curvature, amorphous and infinite in every direction. At the heart of this immobile framework, Newton explained celestial mechanics in terms of the law of universal attraction, from now on considered responsible for gravitation and the large scale structure of the Universe. With Newton, cosmology took root for more than two centuries in the framework of an infinite Euclidean space and an eternal time.

Newton around 1700

All the problems are not resolved in Newtonian cosmology, far from it. On the question of the distribution of stars in space, for example, Newton believed that they must occupy a finite volume since, he argued, if they occupied an infinite space, they would be infinite in number, the force of gravitation would be infinite, and the universe would be unstable. Newton moreover supposed that the stars were uniformly spread within a finite mass|like a galaxy, for example. But a problem of instability remained: since each celestial body is attracted by every other one, at the least movement, at the least mechanical perturbation, all the bodies in the universe would fall towards a unique center, and the universe would collapse. Newton’s universe is therefore only viable if it does not admit motion on the large scale: its space is rigid and its time immobile. Continue reading

A Brief History of Space (2/4) : from Ptolemy to Galileo

Sequel of the preceding post A Brief History of Space (1/4).

The cosmology of Aristotle, as perfected by Ptolemy and reintroduced thanks to arabic translations and commentaries, was adapted to satisfy the demands of the theologians. Notably, that which is situated beyond the last material sphere of the world acquired the status of, if not physical, at least ethereal or spiritual space. Baptized “Empyrean”, it was considered to be the residence of God, the angels and the saints. The medieval cosmos was not only finite, but quite small: the distance from the Earth to the sphere of the fixed stars was estimated to be 20,000 terrestrial radii, because of which Paradise, at its edge, was reasonably accessible to the souls of the deceased. The Christian naturally found his place at the center of this construction.

In this medieval system of the world designed by Apianus in 1520, the whole universe is finite, bounded by a spherical layer containing the fixed stars, beyond which lies the Empyreum, the house of God and Saints.
In this medieval system of the world designed by Apianus in 1520, the whole universe is finite, bounded by a spherical layer containing the fixed stars, beyond which lies the Empyreum, the house of God and Saints.

A Hierachical universe according to Dante's Divine Comedy
A Hierarchical universe according to Dante’s Divine Comedy

 

Nicholas of Cusa
Nicholas of Cusa

This model of the universe imposed itself until the seventeenth century, without nevertheless impeding the resurgence of atomist ideas. After the rediscovery of the manuscript of Lucretius De rerum natura, the German cardinal Nicholas of Cusa (1401-1464) argued in favor of an infinite Universe, of a plurality of inhabited worlds, and of an Earth in motion. However, his arguments remained primarily metaphysical: the universe is infinite because it is the work of God, who could not possibly be limited in His works.

When the Polish canon Nicolaus Copernicus (1473-1543) proposed his heliocentric system, in which the Sun is at the geometric center of the world while the Earth turns around it and around itself, he kept the idea of a closed cosmos, surrounded by the sphere of fixed stars. Even if this is two thousand times further away than in the Ptolemeian model, the universe nevertheless remained bounded.

A romantic depiction of Copernicus
A romantic depiction of Copernicus and his new model of the universe

We must wait several decades more for the first cracks to appear in the Aristotelian edifice. In 1572, a new star was observed by the Dane Tycho Brahe (1546-1601), who showed that it was situated in the sphere of fixed stars, that is to say in the celestial region until then presumed to be immovable. In 1576, the Englishman Thomas Digges (1545-1595), a staunch Copernican, maintained that the stars were not distributed on a thin layer, at the surface of the eighth and last sphere of the world, but extended endlessly upwards. Digges nevertheless was not proposing a physical conception of infinite space: for him, the sky and the stars remained Empyrean, God’s realm, and in this regard did not truly belong to our world.

copernicus-diag Syst-Digges

An epistemological rupture[1] was triggered by two Italian philosophers. In 1587, Francesco Patrizi (1529-1597) produced Of Physical and Mathematical Space[2], where he put forth the revolutionary idea that the true object of geometry was space in itself, and not figures, as had been believed since Euclid. Patrizi inaugurated a new understanding of infinite physical space, in which it obeyed mathematical laws and was therefore accessible to understanding. But it is above all his contemporary Giordano Bruno (1548-1600) who is attributed with the true paternity of infinite cosmology. brunoThe first book of his De immenso is entirely dedicated to a logical definition of infinite space. Bruno argued from physical, and no longer exclusively theological, basics. His cosmological thought was inspired by the atomism of Lucretius, the reasoning of Nicholas of Cusa, and the Copernican hypothesis. From the latter, Bruno retained heliocentrism and the ordering of the solar system, but rejected the cosmological finitism. A precursor to Kepler and Newton, he also refuted the cult of sphericity and of uniform circular motion for describing celestial motion. His bold and original writings were not understood by his contemporaries, most notably Galileo. Above all they were firmly opposed by the Church. In fact, the true philosophical subversion of the end of the sixteenth century did not reside so much in the heliocentric affirmation of Copernicus as in that of the infinite multiplicity of worlds. Camped at the front ranks of the anti-Aristotelian battle, Bruno, carried away by his passion for infinity, refused to abjure and was burned at the stake in Rome.

Johannes Kepler (1571-1630), another great artisan of the astronomical revolution, tried at first to construct a universal model founded on the use of particular geometric figures: the regular polyhedra. He failed at this attempt; the ordering of planetary orbits as calculated did not correspond to the new experimental data collected by Tycho Brahe. After discovering the elliptical nature of the planetary trajectories, Kepler overturned the Aristotelian dogma of circular and uniform motion as the ultimate explanation of celestial movement. He nevertheless refused to follow Bruno in his arguments for the infinitude of the universe. He considered this notion to be purely metaphysical and, since it was not founded on Kepler_Epitomeexperiment, denuded of scientific meaning: “In truth, an infinite body cannot be understood by thought. In fact the concepts of the mind on the subject of the infinite refer themselves either to the meaning of the word `infinite,’ or indeed to something which exceeds any conceivable numeric, visual or tactile measurement; that is to say to something which is not infinite in action, seeing that an infinite measurement is not conceivable.”[3] Kepler supported his argument by expressing for the first time an astronomical paradox that seemed to be an obstacle to the concept of infinite space, and which would be extensively discussed: the “paradox of the dark night.” Just like the edge paradox, this problem would not be satisfactorily resolved until the middle of the nineteenth century, although by completely different arguments.

Starting in 1609, the telescope observations of Galileo (1564-1642) furnished the first direct indications of the universality of the laws of nature. On the question of spatial infinity, however, Galileo, like Kepler, adopted the prudent attitude of the physicist: “Don’t you know that it is as yet undecided (and I believe that it will ever be so for human knowledge) whether the Universe is finite or, on the contrary, infinite?” [4]

systemegalilee001

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[1] See Alexander Koyre, From the Closed World to the Infinite Universe, New York: Harper Torchbook, 1958.

[2] De spacio physico et mathematico ; See R. Brickman, “On Physical Space, Francesco Patrizi”, Journal of the History of Ideas, vol.4, 224 (1943).

[3] De stella nova, 1606. Unfortunately there is no English translation for this masterpiece.

[4] Letter to Ingoli, quoted in A. Koyré, From the Close World to the Infinite Universe, The John Hopkins Press 1957, p. 97.

A Brief History of Space (1/4)

This post is based on a chapter of my book  “The Wraparound Universe” but is much more illustrated.  The chapter is divided into 4 parts, here is the first one.

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That which keeps quiet beyond everything, is this in fact simply what I name Space? . . . Space! An idea! A word! A breath!
Jean Tardieu

There is no space or time given a priori; to each moment in human history, to each degree of perfection of our physical theories of the Universe, there corresponds a conception of those fundamental categories of thought known as space, time, and matter. To each new conception, our mental image of the Universe must adapt itself, and we must accept that “common sense” was found lacking. For example, if space is limited by a boundary, what is there beyond it? Nothing? It is difficult to imagine that, by voyaging sufficiently far in a given direction, one could reach a point beyond which nothing more exists, not even space. It is just as troubling to think of an infinitely large Universe. What would be the meaning of any measurable, that is to say finite, thing with respect to the infinite?

A possible representation of Anaximander learning Pythagoras on his left, detail of Raphael's famous painting The School of Athens.
A possible representation of Anaximander learning Pythagoras on his left, detail of Raphael’s famous painting The School of Athens.

These types of questions were formulated in the sixth century BCE, in ancient Greece, where they rapidly became the object of controversy. The first schools of scholars and philosophers, called “presocratic” (although they were spread over two centuries and were quite different from each other), each attempted in their way to rationally explain the “world,” meaning the ensemble formed by the Earth and the stars, conceived as an organized system. For Anaximander, from the school of Miletus, the world where observable phenomena take place was necessarily finite. Nevertheless, it was plunged within a surrounding medium, the apeiron, corresponding to what we today consider as space. This term signifies both infinite (unlimited, eternal) and indefinite (undetermined). For his contemporary, Thales, the universal medium was made of water, and the world was a hemispheric bubble floating in the middle of this infinite liquid mass.

We meet up again with this intuitive conception of a finite material world bathing in an infinite receptacle space with other thinkers: Heraclitus, Empedocles, and especially the Stoics, who added the idea of a world in pulsation, passing through periodic phases of explosions and deflagrations.

Atomism, founded in the fifth century by Leucippus and Democritus, advocated a completely different version of cosmic infinity. It maintained that the Universe was constructed from two primordial elements: atoms and the void. Indivisible and elementary, (atomos means “that which cannot be divided”), atoms exist for all eternity, only differing in their size and shape. They are infinite in number. All bodies result from the coalescence of atoms in motion; the number of combinations being infinite, it follows that the celestial bodies are themselves infinite in number: this is the thesis of the plurality of worlds. The formation of these worlds is produced within a receptacle without bounds: the void (kenon). This “space” has no other property than being infinite and accordingly matter has no influence on it: it is absolute, given a priori.

Part of a fresco in the portico of the National University of Athens representing Anaxagoras.
Part of a fresco in the portico of the National University of Athens representing Anaxagoras.

The atomist philosophy was strongly criticized by Socrates, Plato, and Aristotle. Moreover, by affirming that the universe is not governed by gods, but by elementary matter and the void, it inevitably entered into conflict with the religious authorities. In the fourth century BCE, Anaxagoras of Clazomenae was the first scholar in history to be accused of impiety; however, defended by powerful friends, he was acquitted and was able to flee far from the hostility of Athens. Thanks to its two most illustrious spokesmen, Epicurus (341-270 BCE), who founded the first school that allowed female students and Lucretius (first century BCE), author of a magnificent cosmological poem, On the Nature of Things, atomism continued to flourish until the advent of Christianity. It was however marginalized over the course of the first centuries of the christian era, and would not again be part of mainstream science until the seventeenth century. 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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PRESS REVIEWS

• 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 (10) : A Modern Account

Sequel of the preceding post Cosmogenesis (9) : The Big Bang Discovery and End of the Cosmogenesis Series.

According to modern physics the universe has undergone a gradual process of expansion and cooling ever since the big bang; at the same time increasingly complex physical structures have evolved. The history of the universe can conveniently be divided into two main periods: the first million years (infancy) and the remaining 15 billion years (maturity).

The Infant Universe

The Bubble Theory of Cosmogenesis. According to some models constructed according to the laws of quantum physics, the observable universe is merely one of a multitude of ephemeral "bubbles" created by spontaneous fluctuations in the quantum vacuum. The universe as a whole is like a rapidly expanding foam, each "baby universe" giving birth to more "baby universes" and so on in an eternally self-reproducing system. Artistic view by S. Numazawa.
The Bubble Theory of Cosmogenesis. According to some models constructed according to the laws of quantum physics, the observable universe is merely one of a multitude of ephemeral “bubbles” created by spontaneous fluctuations in the quantum vacuum. The universe as a whole is like a rapidly expanding foam, each “baby universe” giving birth to more “baby universes” and so on in an eternally self-reproducing system.
Artistic view by S. Numazawa.

During the Planck era, time and the dimensions of space as we know them were so intimately linked as to be practically indistinguishable. Various speculative theories of “quantum cosmogenesis”, as yet in their infancy, attempt to explain how our universe emerged at the end of the Planck era. Some physicists refer to its “spontaneous emergence”, others to an infinite number of separate “cosmic bubbles” arising from the quantum vacuum like foam from the surface of the sea.

Between 10-43 and 10-32 seconds after the big bang the infant universe consisted of elementary particles bound by a primeval superforce. A few billiseconds later gravity separated itself from the surviving electrostrong force, which in turn, as the temperature fell to 1027 degrees, divided into the strong force and the electroweak force. Recent experiments in high energy physics suggest that these “symmetry breakdowns” had spectacular consequences: the appearance of strange objects; “topological defects” such as “cosmic strings”; even the onset of “inflation” – a very short period during which the universe grew immeasurably. The fundamental constituents of matter – quarks, electrons and neutrinos – also appeared at this time.

10-11 seconds after the big bang the temperature of the universe had dropped to 1015 degrees and the electroweak force split into an electromagnetic and a weak force, thus establishing the four fundamental forces  and fixing the physical conditions for the formation of complex structures.

10-6 seconds after the big bang all quarks were “linked” in threes by the strong force to form the first nucleons, i.e. protons and neutrons. By this time the temperature had fallen to a billion degrees as the universe continued to expand. As particles became more widely spaced, they collided less frequently but one hundred seconds or so later the crucial process of nucleosynthesis began. Neutrons and protons combined to form the simplest atomic nuclei: hydrogen, helium and lithium (in various isotopes). Most of the universe, however, remained as isolated protons, i.e. as hydrogen nuclei.

Nucleosynthesis took place only for a very short time: the universe was cooling so rapidly that there was only time for the lightest elements to form. These therefore constitute 99 per cent of the visible matter in the universe today (75% hydrogen and 24% helium). The remaining one per cent, consisting of heavier elements like carbon, nitrogen and oxygen, would not be created until billions of years later, when the stars were formed.

Nucleosynthesis. Scientists at the particle accelerator near Caen in France (known as GANIL — Grand Accélérateur National d'lons Lourds) have managed to fuse heavy ions by making them collide at high speed. These computer-generated images show the fusion of a lanthanum nucleus with a copper nucleus. Such experiments help scientists to understand the process of nucleosynthesis which, during the first few seconds after the big bang, caused the fusion of hydrogen ions and helium ions, creating the first lightweight elements. Nucleosynthesis is one way of testing big bang theory, whose predictions as to the quantity of each element in the universe can be compared with experimental results. Indeed they are remarkably similar: the universe does in fact comprise 75% hydrogen (in mass) and between 24 and 25% helium (in mass). There is an equally close correlation between the predicted and observed prevalence of deuterium and tritium. Other experimental results are valuable in limiting the possibilities open to those refining big bang theory. Montage by Philippe Chomaz (GANIL)
Nucleosynthesis. Scientists at the particle accelerator near Caen in France (known as GANIL — Grand Accélérateur National d’lons Lourds) have managed to fuse heavy ions by making them collide at high speed. These computer-generated images show the fusion of a lanthanum nucleus with a copper nucleus. Such experiments help scientists to understand the process of nucleosynthesis which, during the first few seconds after the big bang, caused the fusion of hydrogen ions and helium ions, creating the first lightweight elements. Nucleosynthesis is one way of testing big bang theory, whose predictions as to the quantity of each element in the universe can be compared with experimental results. Indeed they are remarkably similar: the universe does in fact comprise 75% hydrogen (in mass) and between 24 and 25% helium (in mass). There is an equally close correlation between the predicted and observed prevalence of deuterium and tritium. Other experimental results are valuable in limiting the possibilities open to those refining big bang theory.
Montage by Philippe Chomaz (GANIL)

Until it was 300,000 years old the universe remained opaque; in other words it emitted no radiation: the density of electrons prevented photons from moving freely. But the universe, consisting of a “soup” of particles and radiation, continued to cool and expand until, at 3,000 degrees, it became transparent and emitted its first electromagnetic signal in the form of what we now detect as cosmic background radiation.

A million years after the big bang the first atoms were formed, when electrons were captured by hydrogen and helium nuclei, and these atoms combined into molecules to create vast clouds of hydrogen, out of which stars would later emerge. Continue reading

Cosmogenesis (9) : The Big Bang Discovery

Sequel of the preceding post Cosmogenesis (8) : The Nebular Hypothesis

Star Clusters and Nebulae. This page from "Telescopic views of Nebulae and Clusters by the Earl of Rosse and Sir J. Herschel" (1875) includes a variety of drawings of nebulosities by different observers. There are star clusters and gaseous nebulae (now known to belong to our own galaxy) as well as other galaxies. Observational techniques of the time were unable to distinguish between these very different types of objects.
Star Clusters and Nebulae. This page from “Telescopic views of Nebulae and Clusters by the Earl of Rosse and Sir J. Herschel” (1875) includes a variety of drawings of nebulosities by different observers. There are star clusters and gaseous nebulae (now known to belong to our own galaxy) as well as other galaxies. Observational techniques of the time were unable to distinguish between these very different types of objects.

In the first quarter of the 20th century cosmology became a distinct scientific discipline, thanks in part to the theoretical advance made in 1915 by Einstein with his theory of general relativity and in part to the revolution in observational techniques which revealed the true extent of the universe. Having at last been able to measure the distance of certain spiral nebulae, Edwin Hubble could confirm in 1925 that there existed other galaxies like our own.

His colleague Vesto Slipher had previously discovered that the radiation from these galaxies was constantly shifting towards the red end of the optical spectrum, which suggested that they were moving away from us at great speed. This movement was not understood until scientists came to accept an idea based on the theory of general relativity and first proposed by Alexandre Friedmann in 1922 and independently Georges Lemaître in 1927: that space was constantly expanding and consequently increasing the distance between galaxies. This idea proved to be one of the most significant discoveries of the century[i].

Alexander Friedmann in 1922
Alexander Friedmann in 1922

In an article which appeared in 1922, entitled “On the Curvature of Space“, Friedmann took the step which Einstein had balked at: he abandoned the theory of a static universe, proposing a “dynamic” alternative in which space varied with time. For the first time the problem of the beginning and the end of the universe was couched in purely scientific terms. Friedmann suggested that the universe was several tens of billions of years old, much older than the earth (then estimated to be about one billion years old) or the oldest known celestial objects. It was a remarkable prediction, the most recent estimate for the age of the universe being between 10 and 20 billion years.

In 1927, in a seminal article entitled “A Homogeneous Universe of Constant Mass and Increasing Radius Accounting for the Radial Velocity of Extra-Galactic Nebulae“, Lemaître explained the observations of Hubble and Slipher by interpreting them, within the context of general relativity, as manifestations of the expansion of the universe. This expansion was taking place uniformly across the entire universe (which might be finite or infinite), not outwards from a particular point (in this sense the often quoted analogy of a balloon being inflated is misleading). It was not a case of matter moving within a fixed geometric framework, but of the framework itself dilating, of the very “fabric” of space-time stretching. Continue reading

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 (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 (3) : Time and Creation

Sequel of the preceding post Cosmogenesis (2) : Chaos and Metamorphosis

Time and Creation

In any discussion of the creation of the world the paradoxical and complex question of temporality inevitably arises. If the Creation is regarded as an event, it must have taken place at some point in time, on a specific date. If time is regarded as a linear phenomenon, as it is in the Western world, this necessarily raises the problem whether anything existed before the Creation and, if so, what. But if time itself existed before the Creation, it cannot be part of the world as we know it – something which is difficult to imagine…

A Treatise on the Hexameron. St Ambrose (c. 339-394), who was bishop of Milan, was a believer in "Platonic Christianity" and one of the first Church Fathers, along with Origen and St Basil, to deliver sermons on the six days of the Creation, which he collected into a treatise. His Hexameron (shown here in an 11th century manuscript copy) is more than an exegesis; it is a veritable encyclopaedia anticipating those of the Middle Ages: the third book is concerned with plants, the fifth with birds and fish, and the second part of the sixth book with the anatomy of the human body. Paris, BNF, Manuscripts, Lat. 1720.
A Treatise on the Hexameron. St Ambrose (c. 339-394), who was bishop of Milan, was a believer in “Platonic Christianity” and one of the first Church Fathers, along with Origen and St Basil, to deliver sermons on the six days of the Creation, which he collected into a treatise. His Hexameron (shown here in an 11th century manuscript copy) is more than an exegesis; it is a veritable encyclopaedia anticipating those of the Middle Ages: the third book is concerned with plants, the fifth with birds and fish, and the second part of the sixth book with the anatomy of the human body.
Paris, BNF, Manuscripts, Lat. 1720.

This paradox was pondered by Medieval scholars, who were forced to conclude that the world and time were created simultaneously. In the fourth century the Bishop of Milan, St Ambrose, wrote in his Hexameron: “In the beginning of time, therefore, God created heaven and earth. Time proceeds from this world, not before the world.”[1]. In the early 13th century the French philosopher and theologian William of Auvergne (also known as William of Paris) pursued a similar line of reasoning in his thinking about time: “Just as there is nothing beyond or outside the World, since it contains and includes all things, so there is nothing before or preceding time, which began with the creation of the World, since it contains all the periods of which it is comprised. This poses the question: What was before the beginning of time? or, since the word ‘before’ implies the existence of time, In the time preceding the beginning of time, did anything exist?”[2]

The same questions continue to be asked today, and scientists who are asked to give public lectures on big bang theory and the expansion of the universe commonly face two kinds of questions: “What was there before the big bang?” and “What is there for the universe to expand into?” – in other words “Did time exist before time began?” and “Is there space beyond the limit of space?” The solution of modern physics to these paradoxes is that the universe consists of space-time and therefore the creation of the world cannot be regarded as a temporal phenomenon. 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