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Matter and Magic 

C. V. Vishveswara

To quote Punch in the matter of matter,

What is matter? —— Never mind.

What is mind? —— No matter.

That is a light-hearted way of dismissing two of the most fundamental problems faced by scientists and philosophers. Since antiquity, the nature of matter has been studied and speculated with a view to discovering its fundamental constituents. Both theory and experiment carry an aura of magic in their ancient as well as modern versions.

Among the ancient Greeks perhaps the first one to formulate a basic constituent that could take all possible forms of matter was Thales of Miletus in the sixth century before Christ. An important criterion for such a material is its easy changeability which could be extrapolated to embrace different types of matter. Thales identified water, that would take on all the three states of matter readily, as this fundamental building material. Anaximenes, around the same time, conjectured that it was air that constituted all matter in the universe. Heraclitus, in the fifth century, found fire, with its ever changing form, to be the true candidate for this unique position. Earth was added to these three by Empedocles making up the four ‘elements’.

Fire provided the energy that could change matter from one state to another consisting of the other three elements. Elements could combine or dissociate because of forces of ‘love’ and ‘hate’.

The theory of Empedocles was strongly favoured by Aristotle who developed it further. Each of the four elements possessed two of the four properties, namely hot, cold, wet and dry. Dry and cold combined to form earth; wet and hot, air; cold and wet, water; hot and dry, fire. The qualities shared in common allowed one form to change into another.

Aristotle’s choice had the unfortunate effect of arresting the development of the theory proposed by Leucippus and Democritus. Their atomic theory, surprisingly modern in its conception, had to wait more than two millennia for rebirth and recognition.

The experimental and pragmatic consequence of the theory of elements and their mutability was alchemy. Alchemy reflected the best and the worst in human nature ranging from total dedication and academic pursuit on the one hand to low charlatanism and avarice on the other. Since all matter was mutable, one should be able to change base material into gold. It was believed that this process would be mediated by the legendary Philosopher’s Stone. In their quest for transmutation the alchemists supplemented the theoretical basis propounded by Aristotle with the principle of the two contraries. The two contraries were identified as Sulphur, representing fire and lightness, and Mercury, representing water and heaviness. Depending on the proportions of admixture, these two could in principle produce lead or gold which were therefore inter-convertible. Considerable part of alchemical experimentation involved Sulphur and Mercury. Another secondary objective of alchemy was to produce the "elixir of life", panacea to all human ills and the pathway to immortality. Practice of alchemy was widespread extending from Europe to China. On the one hand, alchemy involved a bizarre mixture of pictorial symbolism, allegory, astrology and sorcery. On the other hand, the serious, dedicated alchemists contributed significantly to the progress of science. This included improvements in metallurgical techniques and advancement of medicinal knowledge. Furthermore, they brought great refinement to laboratory techniques like crystallization and distillation. Alchemists’ notable achievement was the discovery of new elements, namely antimony, arsenic, bismuth, phosphorus, zinc in addition to alcohol, several acids and alkalis.

Often alchemy is scoffed at for its hopeless fantasy and quackery. Just as astronomy in its early days was aided by astrology, sciences was helped by alchemy. Furthermore, the theoretical basis for alchemy was the unity of all matter, a concept towards which modern physics steadily advanced. Alchemy occupies the shadowy region between antique speculation and logical thought. Within a similar framework in the history of science one finds a towering figure that symbolises the transition from mysticism to modern science, namely Kepler.

Kepler is well-known as one of the giants who heralded mathematical method of science. But it is also known that he was deeply immersed in astrology, theological speculation and matters related to alchemy. Kepler opposed the traditional views of alchemy as championed by the English physician Rober Fludd whose model of the cosmos made links between macrocosm and microcosm through the four elements. The cosmos was in fact divided into four spheres corresponding to the four elements. Beyond was the Empyrean and way below the Earth, the abode of the devil. Fludd believed that world-harmony could be understood only through the mysteries of alchemy. Fludd was against all quantitative measurements. Kepler sharply opposed Fludd maintaining that quantitative mathematical proof alone was the characteristic of objective science, declaring that "without mathematical demonstration I am like a blind man . . .". His laws of planetary motion were indeed perfect examples of "mathematical demonstration". But one must realize that even in Kepler this mathematicisation was a process of evolution starting from Pythagorean mysticism.

The Pythagoreans believed that the Creator or the Ordering One had structured the Cosmos — the word originally meant Order — as a harmonious whole in concordance with the symmetries and correlations intrinsic to the numbers and their geometrical representations. Stemming from this conception of the universe grew the complex mysticism of numbers and geometrical figures. Specific characteristics were attributed to them and hidden meaning read in their interrelations. For instance, five was considered to be the most important number, the symbol of health and harmony; it was the emblem of love, being the offspring of the union between the first female number two and the first male number three. Its geometric counterpart, the pentagram, exhibited so many intriguing, magical properties that it was chosen as the sign of brotherhood among the Pythagoreans. The secret knowledge originating from the Pythagoreans cascaded down the centuries along diverse channels, such as the cults of Kabbala, Freemasonry and Rosicrucianism. But never did the original geometric mysticism exercise such a profound and far-reaching influence on an individual as in the case of Kepler during his early years that witnessed his quasi-scientific fantasies slowly transmuted into the pure gold of his three laws of planetary motion.

The inspiration that fashioned Kepler’s ideas and fueled his relentless explorations had its roots deep within the Pythagorean and Platonic geometric mysticism. He expounded the divine status of geometry in his Harmonices Mundi, the Harmony of the World. "Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (What exists in God that is not God himself?); geometry provided God with a model for the Creation and was implanted into man, together with God’s own likeness — and not merely conveyed to his mind through the eyes."

God picked as his building blocks of the universe the Platonic solids because of their perfect symmetry. It is an incredible fact, but true, that, although there can be an infinite number of symmetric two-dimensional figures, there exist five — and only five — such solids in three dimensions. In each instance, the solid is bound by faces which are themselves symmetric two-dimensional geometric figures of a particular kind. These are the tetrahedron (made of four equilateral triangles), the cube, the octahedron (eight equilateral triangles), the dodecahedron (twelve pentagons) and the icosahedron (twenty equilateral triangles). Each of these corresponded to a basic element of nature, for example, the tetrahedron with fire, the cube with earth and so on. The dodecahedron, being composed of the magical pentagons, occupied the highest place among the constituents of the universe. This represented the additional fifth element ether (quinta essentia) or all of space as we may call it in our modern terminology. While geometry admitted this unique set of precisely five perfect solids, was it a mere accident that nature had decreed the existence of six planets with exactly five intervals in between? Surely, this was a crucial clue to the mystery of the cosmic structure. This explained why there were six planets, no more no less. Would not the five solids decide the sizes of the planetary orbits and the order in which they had been arranged as well? The orbits could be drawn as circles or spheres either circumscribing the Platonic solids or inscribed within them. When chosen properly, the five solids seemed to fit roughly the known orbits of the six planets. Kepler was to remark on this revelation in ‘the preface to the reader’ of his Mysterium Cosmographicum. "I saw one symmetric solid after the other fit in so precisely between the appropriate orbits that if a peasant were to ask you on what kind of hook the heavens are fastened so that they don’t fall down, it will be easy for thee to answer him. Farewell!"

This was only the beginning and not the end. Had Kepler ceased his probing at this stage, satisfied by the fruition of his fantasies, his name might not have found a place even in the footnotes to astronomy and cosmology. But, his scientific objectivity drove him to test and justify his model against the available astronomical data. In this venture, he was obliged to replace his two-dimensional spheres by spherical shells in order to accommodate deviations of the orbits from perfect circles — the first step towards the realization of elliptical orbits. Obsessed with the desire to prove the validity of his model, not only did he criticize Copernicus for his inexactitude, but he even dared to accuse him of deliberate cheating. Nevertheless, years of excruciatingly painstaking research finally converged on to the three famous laws of planetary motion. With these laws firmly established, the artificial scaffolding of the universe Kepler had erected could be dismantled and the true order of the cosmos revealed. The planetary orbits were asymmetric ellipses and not the ideal circles of the Greeks. On the other hand, with Kepler’s work, Apollonius’ Conic Sections, a purely intellectual creation, found its niche within the realm of cosmic reality. Plato in his Timaeus had described how God had created the planets as the regular keepers of time, and Kepler had now found the exact law that regulated their divine duty. In addition to all this, it was Kepler who introduced, however vaguely and hesitantly, the idea of a force — or ‘soul’ as he termed it — emanating from the sun and impelling the planets in their heavenly courses. Starting from the nebulous mysticism of an antique era, Kepler had unveiled the true face of the cosmos for contemplation by other giants like Newton.

Kepler’s cosmic structure involving the Platonic solids that represented five elements was very much in consonance with Pythagorean-Platonic theories. It reflected the sentiment Pythagoras had expressed:

There is geometry in the humming of the strings.

There is music in the spacing of the spheres.

Hermann Weyl commented in his Space, Time, Matter: "We are overwhelmed by a feeling of freedom won — the mind has cast off the fetters which have held it captive. Our ears have caught a few of the fundamental chords from that harmony of the spheres of which Pythagoras and Kepler once dreamed."

In a way, matter through the elements had been incorporated into this geometric harmony. But the true picture of the planetary system — the macrocosm — was to be elucidated through Kepler’s three laws. Concepts inherent to this system were to find their echoes in the atomic structure — the microcosm. The atomic physicist Arnold Sommerfeld wondered: "Would Kepler, the Mystic who, like Pythagoras and Plato, tried to find and to enjoy the harmonies of the Cosmos — would he have been surprised that atomic physics had re-discovered the very same harmonies in the building stones of matter, and this is even purer form?" The simple Bohr atom, even with refinements, resembled the Keplerian planetary system. Even the wave mechanical model with probability clouds of electron display harmonies that are reminiscent of both types of Keplerian models. Once again one wonders whether Kepler would be disappointed that the atom does not bear exact resemblance to his cosmic order.

Apparently Sommerfeld did not think so. After all Kepler himself had written about replacing geometrical picture by mathematical formalism in his Astronomia Nova, "At last, I have brought to life and found true far beyond my hope and expectations that the whole nature of harmonies in the celestial movements really exists — not in the way I thought previously, but in a completely different, yet absolutely perfect manner."

Discoveries made in the realm of nuclear structure, along with atomic theory more or less firmly established the unity of matter — the cherished dream of ages. The forces of ‘love’ and ‘hate’ have been replaced by the fundamental interactions of nature. Through them the dream of alchemists has also been achieved — namely the transmutation of elements. The neutron has turned out to be the modern day Philosopher’s Stone. Atom smashers are being built with ever increasing size, strength and expenditure. These not only probe the structure of matter deeper but throw light on the unity of the fundamental forces.

The fifth element space had a long history of its own. It was Isaac Newton who for the first time, invoked the attributes of all-pervading absolute space within the context of physical laws. His ideas came under attack on both theological and physical grounds. Bishop Berkeley condemned the ‘dangerous dilemma of thinking either real space is God or else there is something besides God which is eternal, uncreated, infinite, indivisible, unmutable both of which may justly be thought pernicious and absurd.’ Einstein wrote, "It conflicts with one’s scientific understanding to conceive of a thing which acts but cannot be acted upon." Matter had no influence on Newton’s space. But, Einstein’s general theory of relativity — the new theory of gravitation — completely changed this picture.

The English geometer William Clifford had envisaged ‘little hills’ on the otherwise flat space and visualized the passage of this spatial curvature equivalent to the motion of matter. This vision in which space, matter and geometry are interwoven was given concrete shape by general relativity. Here matter through gravitation, curves space. On the other hand, there have been attempts to describe the contents and qualities of the physical world, including matter, purely in terms of space and its attributes. "There is nothing in the world except empty curved space" wrote John Wheeler, "Matter, charge, electromagnetism and other fields are only manifestations of the curvature of space."

The grandest application of Einstein’s theory lies in the description of the universe as a whole. One arrives at a curved evolving universe that started from a singular state in which density, temperature and space curvature are all infinite. This is the point of cosmic origin near which unanswered questions regarding the nature of matter and the unity of all the four fundamental forces of nature including gravitation remain as a challenge to the theorist. This is the uncharted terrain of modern alchemy.

The magic of new discoveries and the mystery of the unanswered questions hold sway as science probes even deeper into the heart of matter. The quest continues, a saga without beginning, a story without end.


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