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SELECTED READINGS FOR ESSAY 2 (II)
SELECTED READINGS FOR ESSAY 2 (II)
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*******You can read this blog for free! Please, do not copy its content.**************You can read this blog for free! Please, do not copy its content.*******
The cosmic symphony
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Pythagoras’ world was imbued with sound; a sound produced by each and every element within it. On one side there was the divine cosmos, composed of the central fire, also called the “guardpost of Zeus,” the orbiting bodies (including the earth and the counter-earth, the five planets, and the moon) which were inserted in immaterial spheres, and the outermost sphere of the fixed stars. The planets, thought to be gods, in their perpetual revolutions around the sun, “hearth” of the universe, emitted a celestial sound that pervaded the entire cosmos. This sound was the music of the spheres. “The Pythagoreans conceived of the cosmos as a vast lyre, with crystal spheres in the place of strings.”[source] On the other side there was the human being, with its mortal body and eternal soul. Due to its divine nature, only the latter generated its own music.
For Pythagoras, a universe impregnated with harsh sound was inconceivable. Its music had to be harmonious, like the motion of the heavenly bodies in the starry sky. What is more, this observable order of the universe was not pure chance; it was the wonderful design of its creator. Indeed, the demiurge had created the entire world, which included the microcosm, that is, the individual, and the macrocosm, the universe, in harmony. This is an essential point in Pythagoras’ mystical doctrine, for there was no real cosmic harmony without the concord of the human soul. And even if the heavenly music of the spheres was inaudible to human ears, an idea of it could be apprehended by reaching inner harmony. Inner harmony meant to Pythagoras to be in tune with the cosmos, that is, to produce an internal music in harmony with the rest of the surrounding musical universe. There were several religious and ascetical practices with the aim of attaining this state, and it was the duty of the philosopher to restore this harmony wherever it was disturbed.
These are some of the few things that can be said with certainty about the doctrine of Pythagoras; religious man, mystic and philosopher of the sixth century BC. To what extent he also indulged in mathematics, astronomy, and music is still a matter of scholarly debate. Nowadays it is generally thought that the members of the religious community he founded in southern Italy are responsible (in addition to other thinkers of the ancient world who lived much later, the so called Pythagoreans) for many of the ideas originally attributed to him. However, since the evidence has determined without doubt that he was a travelled and wise man, leader of an influential school and venerated as a saint in the antiquity, the possibility that he did indeed inquire into scientific and musical subjects is maintained by many historians of Greek philosophy. For this reason, some scholars have accredited to Pythagoras himself the discovery of an exact numerical relationship between the different notes produced by a plucked string and the corresponding lengths: the octave (2:1), the fifth (3:2), and the fourth (4:3). There is even an ancient tale supporting this position. As the story goes, Pythagoras was passing a smith workshop when he heard the notes the hammers produced when beating the metal. This fortuitous event suggested to him a deep relationship between measurable physical quantities and musical notes. Pythagoras then went back to his school and experimented arduously with several objects in order to determine the precise proportions (see Figure 1).
1. Illustration from Franchinus Gaffurius’ Theorica musicae (1492). Sculpture of Pythagoras on the Portail Royal of Chartres Cathedral.
On the other hand, that Pythagoras was fond of numerical interpretations of the world has been conclusively established. The profane as well as the sacred world were for him susceptible to numerical readings. And deserving scrupulous attention were the integer numbers. For instance, since the number ten was particularly sacred, it was perfect, the Pythagoreans thought that there must be ten planets; this is what gave rise to the unobservable counter-earth introduced in their heliocentric model. This belief in the power of numbers was strengthened by the finding, as above recalled, that the ratios of the first integer numbers could explain musical consonances. The Pythagoreans then consistently applied the mathematical relationship between number and music to the heavens. The pleasant music of the cosmos had to have a precise numerical expression, more or less as the notes of a lyre were numerically related to the lengths of the string. According to this idea, since the earth was located at two-thirds of the distance between the central fire and the sphere of the fixed stars, the pitch of the earth was a perfect fifth. All the other orbiting planets contributed in a similar manner to the symphony of the universe. In this way , connecting cosmos, music, and number, the Pythagoreans had determined the exact mathematical formulas explaining the beautiful music of the spheres.
One century after the dissolution of the school that Pythagoras had founded in Croton, the Pythagorean tradition was to be revived by one of the greatest minds in ancient Greece: Plato. It is known that Plato was familiar with the work of Archytas, the knowledgeable mathematician leading the Pythagorean community in Tarentum at the time. This expertise, in addition to the philosophical influence that the mathematician could have had on his friend, is considered to be one of the main reasons why many of the mathematical ideas of Pythagoras have reached us. In particular, Plato gave new life to the relationship between mathematics, music, and the cosmos.
Like Pythagoras, Plato imagined that the creator, the demiurge, had created the cosmos with mathematical significance and had filled it with harmonious music. In Plato’s Myth of Er, in the last part of The Republic, he recounts how the songs of the Sirens sitting on each of the planetary spheres produced a harmonious composition. Plato, moreover, also used numerical arguments to support his thesis. There is, however, an important difference between the two philosophers. While Pythagoras considered that numbers and music had concrete manifestations in the physical world, Plato thought of them as abstract entities. It is common belief that Pythagoras experimented with several objects in order to support his theory of harmonics. Plato, in contrast, would have considered this a futile action. Numbers were, for Plato, transcendent realities with an existence beyond the material world; they were eternal and changeless. In addition to this, the only way to apprehend them was by pure thought. This discrepancy between mathematical objects ― numbers and geometrical figures ― and the natural world, was explicitly stated by Plato himself when he observed that Archytas was a great mathematician, but, alas, also a bad philosopher. Thus, according to Plato’s thought, perceptible things are subject to change; we can say that something “was” or “will be,” but, on the other hand, a mathematical object always “is.” As stated in an introduction to Plato’s work: “He holds that these objects alone are changeless, and contrasts their invulnerability to alteration with the constant fluctuation that characterizes objects in the world of sensation; because of these radical differences, the Forms are capable of being known, whereas objects of sensation are not.”[source] It is particularly in Plato’s later work Timaeus, “the single most important text for the future of the Pythagorean tradition,” [source] that he extends on this.
Cicero, one of the most illustrious Romans of antiquity, in the first century BC ideated in his political dialogue De Re Publica a musical cosmos that resembles that of Plato. As in Plato’s Myth of Er, in Cicero’s Scipio’s Dream the universe is imbued with the music of the spheres. In this allegory, the Roman consul and hero Scipio Aemilianus hears in a dream vision the grand and pleasant sound of the seven planetary spheres. Cicero’s dialogue, as well as Plato’s Myth of Er and Timaeus, had an influence that spanned through the Middle Ages and the Renaissance. Two centuries after Cicero, the Roman scientist Claudius Ptolemy wrote comprehensively on mathematics, music, and astronomy. And his approach to music, as to the other physical sciences he studied, was highly mathematical. This was made clear in his Harmonics, where he tried to give explicit mathematical expressions to musical notes. He also wrote about the music of the spheres; but this time, of course, with the centre of the universe occupied by the earth. The Neo-Platonist movement of those centuries, with Plotinus as its most notable figure, is deserving of a special analysis. However, even a short survey of Neo-Platonism would be too large to fit into this brief introduction. Suffice to say that in addition to Plotinus, the Neo-Platonists Porphyry and Iamblichus have been the subject of increasing interest as a way of revealing the continuity of the Pythagorean tradition in Western culture. Concerning the music of the spheres, Iamblichus once wrote: “It is better … to assert that the soul, before she gave herself to body, was an auditor of the divine harmony, and that hence, when she proceeded into body, and heard melodies of such a kind as especially preserve the divine vestige of harmony, she embrace these, from them recollected divine harmony, and tends and is allied to it, and as much as possible participates of it.”[source]
By the first decades of the fourth century Chalcidius translated the first part of Plato’s Timaeus into Latin. A translation which remained until the twelfth century one of the most important books on natural philosophy. In the fifth century, the commentaries of the Neo-platonist Macrobius on Scipio’s Dream were another central contribution to the cosmological discussions of the day and constituted a fundamental link between Greek and Medieval culture. Almost at the same time, the philosopher and theologian Saint Augustine was drawing on Plato and the Neo-Platonists, in particular Plotinus, to deepen and expand on his Christian philosophical thoughts. In fact, the religious questions he delved into after his baptism, in 387, were copiously supported, and motivated, by Platonic reasonings. Another early influence on him was Cicero, from which he quoted profusely during his entire lifetime; quotations including most notably Cicero’s De Re Publica and Scipio’s dream. In Augustine’s conception of a fundamental changeless reality, Plato’s influence is clearly recognizable. However, in contrast to his intellectual predecessor, for Augustine, the most influential Father of the early Church, God was the only truth. All other truths were, whatever their nature, abstract or material, fictitious. And the road to this eternal changeless reality was spiritual rather than rational or sensorial. Reason and experience were useless without belief. For the theologian, truth was an unreachable without faith. Augustine believed reason to be a method enabling on to reach mathematical reality. However, mathematical reality was not equivalent to truthfulness in the Christian sense. Augustine also diverged from Plato in his assessment of the sensorial experience, and in particular music, which Augustine considered to be number made perceptible. His opinions on music were formulated in his De Musica, where he sustained that music was as beautiful and true as mathematics. Another contribution of major was his classification of mathematics into four different branches: arithmetic, geometry, music and astronomy. He wrote abundantly on these topics, including his outstanding De Musica. His classification of the seven liberal arts, the four above mentioned plus grammar, logic and rhetoric, constituted the standard advanced faculty curriculum during the Middle Ages.
In the sixth century Augustine’s classification was then taken up by Boethius, who grouped the seven subjects into what he dubbed the quadrivium and the trivium. Due to his philosophical eclecticism, merging together Plato and Aristotle with the Christian faith, Boethius is usually considered a Christian Neo-Platonist. In fact, one of the main contributions Boethius made to Western culture is that he recaptured the Pythagorean-Platonist tradition and incorporated it into the Catholic doctrine. In the inexorably fading Roman Empire, today he symbolizes the transition between classical culture and Scholasticism. His massive interpretive work on Greek philosophers, including several translations into Latin and many original evaluations, made him into one of the dominant figures of the Middle Ages. According to the medievalist Jacques Le Goff, everything that was known during the Middle Ages about Aristotle came from Boethius: “The middle ages owed all that it was to know of Aristotle before the mid-twelfth century to Boethius.”[source] Of special interest to our discussion is the fact that the exceptional role played by music during those centuries is due to him. In particular, he emphasized the pre-eminence of music as science of the number and science of the cosmos. As he wrote: “Thus we can begin to understand the apt doctrine of Plato which holds the soul of the universe is united by a musical concord.”[source] It is also thanks to Boethius’ solid works that the trivium and the quadrivium were at the core of education for every Middle Ages student. At that time there was the conviction that following the basic subjects of the trivium, the abstraction of the new subjects covered by the quadrivium could provide the student with the tools needed to immerse themselves into more metaphysical themes such as theology and philosophy. That is, the quadrivium was not intended to teach the occurrence of mundane phenomena, but rather to prepare the mind for more theoretical transcendent issues. Boethius’ books Musica and Arithmetica had an enduring influence on medieval thinking and beyond. These were standard textbooks during the Renaissance, and were still is use in modern Europe.
In the High and Late Middle Ages Plato and Aristotle were still centre stage. But they were read differently. New translations, critical examinations, controversial interpretations, and hot discussions marked the intellectual scene. In the aftermath of this radical period, a novel world-view arose: modern science, with Johannes Kepler one of its most salient figures. The harmony between music and the universe was admitted by Kepler, who thought that the celestial spheres could produce a beautiful, though inaudible, music. His ideas were deeply influenced by Pythagoras, Plato and Augustine. In particular, in his Mysterium Cosmographicum “he was possessed and enchanted by the idea of harmony; he erected an astrological system for himself on the basis of his psychology; he held the thought that a World Soul embraces and professes Plato’s idealistic theory of knowledge.”[source] Kepler thought that the heavenly motions were nothing but a continual music of several voices.
This is in broad terms the historical relationship connecting music and physics, or theoretical physics as Kuhn would say, in the Western world. This is where we should look if we want to discover the origins of the passionate interest that mathematicians and theoretical physicists have for music. But, what about the last part of Kuhn’s extract quoted above: “Some having had great difficulty choosing between a scientific and a musical career”? The process of deciding on a career is something more concrete than the millenarian relationship we have related. And it is this that will provide us with the clues needed to examine string theorist arguments. But, first, who were those theoretical physicists who had to decide between a career in music or in physics.
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SELECTED READINGS FOR ESSAY 2 (II)
SELECTED READINGS FOR ESSAY 2 (II)
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