Tag Archives: Plato

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

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

The Pre-Socratic Universe

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

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

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

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

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

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

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

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