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This article is reprinted from the Summer 20001 issue of FIDELIO Magazine.
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by Bruce Director When a Roman soldier killed Archimedes, in 212 B.C.E. the Earth stood still. At least, that was the intention of those Mithra-cult adherents who bear ultimate responsibility for the murder. Of course, the Earth never physically stopped. But, for approximately 1,500 years, from the death of Archimedes, until Cusas completion of On Learned Ignorance in A.C.E. 1440, knowledge of the Earths motion around the sun, with only a few notable exceptions, vanished from the Earth. How is it that knowledge of a physical principle, whose discovery requires no more information than regular observations of the motions of the heavenly bodies, could be obscured for so many years? As the collapse of the so-called New Economy pointedly demonstrates, knowledge does not derive from information. Rather, knowledge is derived only from the cognitive power of the human mind, the power of the mind to rise above the limitations of the senses, and discern the underlying intentions (true causes), of which these sense impressions are but a reflection. The discovery of the concept of the heliocentric solar system by Archimedes predecessor, Aristarchus of Samos, is typical of those types of cognitive discoveries achieved through the method of Socrates and Plato. Its suppression is associated with minds stupefied by the method of Aristotle. With the publication of On Learned Ignorance, Cusa broke the grip of Aristotle over human thought, establishing a new method for scientific investigation which revived the method of Plato, as enriched by the principles of Christianity. These principles, Cusa insisted, were comprehended through human Reason, and were therefore ecumenical, capable of being known to be true by Muslim, Jew, or other non-Christian alike. Although a complete review of the impact of Cusas work for modern science would be an enormous undertaking, far beyond the scope of this present article, a significant insight into the importance of Cusas scientific method can be obtained by tracing the direct impact of Cusa on the astrophysics of Johannes Kepler. The Motion of the Heavenly BodiesAstronomy is the oldest inquiry of science. It is beyond doubt that very ancient, prehistorical cultures had developed a heliocentric conception of the solar system, as this was a necessary prerequisite for the trans-oceanic navigation practiced by Egyptian and other, earlier civilizations. In Prometheus Bound, Aeschylus presents a metaphorical account of those early astronomical discoveries. Prometheus, who had been chained to a rock for all eternity by Zeus, in retaliation for helping humankind, speaks of his first efforts to lift man up to the level of being truly human: Still, listen to the miseries that beset mankindhow they were witless before and I made them have sense and endowed them with reason. I will not speak to upbraid mankind but to set forth the friendly purpose that inspired my blessing.Reason tells us that Prometheuss metaphorical account is truthful. As Lyndon H. LaRouche, Jr. has developed through his principles of physical economy, Man, the only creature endowed with cognition, must rise above his senses, and discover the principles by which the universe is composed, in order to survive and grow. Through the discovery of such universal principles, Man increases his dominion over the entire universe, from the microphysical to the astrophysical, among living processes and non-living ones; that is, the heavens and the Earth. Nowhere is this more evident, than in determining the motion of the heavenly bodies. Without such knowledge, maritime navigation, agriculture, and other advancements of human economy would be impossible. Do not make the mistake of thinking of these accomplishments in pragmatic terms, however. All practical benefits that accrue from astronomy, are a consequence of the fact, that in its pursuit, Man finds his true human nature. Anyone today can re-create, in his own mind, the same paradoxes as those known by the ancients who received Prometheuss beneficence. Go out and look at the sky over the course of a day and night, and over the course of a year. Observe the rising and setting of the sun, the motion of the stars around the sky, the changes in position at which the sun and the stars rise, and the more complicated motions of the five planets, which the ancients called wanderers. Imprisoned as man is by his limited senses, all these motions are presented to him as a complicated tangle of changes in position seen as if projected onto the inside of a sphere. From the standpoint of sense perception, the Earth stands still, and all the heavenly bodies move about it in apparent circles. But, when all these motions are thought of as One, anomalies emerge, which are paradoxical with respect to pre-existing notions about the universe. It is through such paradoxes, that man discovers those concepts that reflect the true causes of the appearances. As Kepler wrote in The New Astronomy: The testimony of the ages confirms that the motions of the planets are orbicular. It is an immediate presumption of reason, reflected in experience, that their gyrations are perfect circles. For among figures, it is circles, and among bodies, the heavens, that are considered the most perfect. However, when experience is seen to teach something different to those who pay careful attention, namely, that the planets deviate from simple circular paths, it gives rise to a powerful sense of wonder, which at length drives men to look into causes.2How Man rises above the senses to knowledge through Reason, is the implicit subject of all Platos dialogues. In the Timaeus, Plato presents God, the Creator of the Universe, as the Composer, who constructed the universe according to those principles of harmony which his greatest creature, Man, would recognize as beautiful. As Philo of Alexandria, the First-century A.C.E. Jewish philosopher, demonstrates, Platos view of God, Man, and Nature, is absolutely congruent with the Mosaic principle expressed in the beginning of the Book of Genesis, that Man is created in the image of God.3 The question for science, posed by Plato, is, What is the relationship of that which comes to us through the senses, and the underlying truth those sense impressions reflect? Furthermore, How does the Mind find that truth? This requires the method Plato develops in The Republic, by which the Mind ascends successively from sense perception, to opinion, to understanding (dianoia), to reason (nous): This then is the class that I described as intelligible, it is true, but with the reservation first that the soul is compelled to employ assumptions in the investigation of it, not proceeding to a first principle because of its inability to extricate itself from and rise above its assumptions, and second, that it uses as images or likenesses the very objects that are themselves copied and adumbrated by the class below them, and that in comparison with these latter are esteemed as clear and held in honor ... and by the other section of the intelligible I mean that which the Mind itself lays hold of by the power of dialectics, treating its assumptions not as absolute beginnings but literally as hypotheses, underpinnings, footings, and springboards so to speak, to enable it to rise to that which requires no assumption and is the starting-point of all, and after attaining to that again taking hold of the first dependencies from it, so to proceed downward to the conclusion, making no use whatever of any object of sense, but only of pure ideas moving on through ideas to ideas and ending with ideas. ...In the Timaeus, Plato shows how this method of discovery manifests itself in the physical universe. He explains that the spherical bounding of human vision conforms to, and accurately reflects, the harmonic principles embedded in the created world by God the Composer.* This is demonstrated specifically by the role of the five regular solids, both from the standpoint of geometry, and of physics [See Figure 1].
Figure 1
Plato summarizes the discoveries from Pythagoras to Theatetus, that the sphere (and, implicitly, the space it reflects) is not infinitely divisible, but rather, is restricted to five, and only five, perfectly regular divisions.† This characteristic of the manifold of human vision, manifests itself in the physical universe, by the relationship of the five regular solids to the organization of matter. Astronomy, Plato says in The Republic, is the science of solids in motion. Astronomy, therefore, must seek to find the harmonic principles in the complicated visible motions of the planets, as well as seek out their underlying causes. But, by underlying causes, Plato did not mean mechanical interactions of the action-reaction (push-me/pull-me) type. Rather, Plato sought the universal principles that guided the motions. Those universal principles were an expression of the intention of the Creator, who composed the world according to Reason. It is that reason which science seeks as the cause of the physical motions. Plato recognized an inherent paradox in the study of astronomy, however. The visible motions of the planets are not the true ones: The resolution of the this paradox depends, not upon what is in the sky, but upon what is in the mind. It depends upon the conception of Mans nature from which it is approached. It is in this paradox, that Plato encouraged his students to seek knowledge of the physical world. Such bold ventures produced the accomplishments of Aristarchus of Samos, who, Archimedes reports, developed a heliocentric concept of the solar system; Erathosthenes of Alexandria, who determined the sphericity of the Earth; and Archimedes, whose discoveries of principles allowed him to proclaim, Give me a place to stand, and I will move the Earth! But, it is also in this paradox, that Aristotle lured the cowardly and the weak-minded away from seeking the truth, arguing that Mans cognitive powers were ultimately impotent to raise him above his senses. For Aristotles physics, the laws governing the Earth were completely different than those governing the heavens. Physical action is not governed by Reason, but rather, is the result of mechanical interactions. Man, bound to the Earth, is doomed to ultimate ignorance on matters concerning the nature of God and the physical universe; he can speculate about God and physics, but, the action of his mind, according to Aristotle, is fundamentally separated from them. The only knowable truths, are those conclusions that follow deductively from a given set of axioms, according to the rules of formal logic. Such conclusions, of course, are never susceptible to determination as universal truths, as they depend upon the unprovable validity of the axioms from which they follow.
Aristotles separation of the Earth from the heavens the human mind, from God and the created world, has been used historically to justify all the unspeakable evils carried out by oligarchical regimes. According to this underlying dogma, law in Earthly society does not reflect universal principles, but, rather, as Hitler legal theorist Carl Schmitt and U.S. Supreme Court Justice Antonin Scalia assert, is the arbitrary will of whoever has the power to make the rules. This conforms perfectly to the worldview of the pro-oligarchical cults of Babylon, the Delphic Oracle of Pythian Apollo, or the Roman Mithra-cult which became transmogrified into various pseudo-Christian cults broadly characterized as Gnostic.‡ Aristotle was the standpoint adopted by Claudius Ptolemy, who rejected the accomplishments of Platos Academy, limiting knowledge to that which could be derived by formal logical deduction from an unchanging, fixed set of axioms, based on the sense impression that the Earth was fixed and unmoved, while the heavenly bodies moved about it in perfect circles. Ptolemy also adopted Aristotles mechanical explanations of the planetary motions, asserting that the heavens were filled by solid, crystalline spheres, along whose great circles the planets moved. Such motions were produced by the grinding of these solid orbs against one another, and the erratic motions of the planets were governed by a demi-god, a sort of supernatural bus driver, who steered each planet along its course. The murder of Archimedes marked the ascendency of this craven mind-set, which gained currency under the Roman Empire as vox populi, what is today called popular opinion. A mind-set, as can be seen in the case of Archimedes, that will kill what it cant understand, but instinctively fears. Learned IgnoranceIn On Learned Ignorance, Cusa presents a thorough-composed conception of God, Man, and Nature, and of how the human mind can, through the method of Learned Ignorance, rise above the senses, and come to know this conception. It would be impossible, as well as unjust and misleading, to present Cusas dialogue in a reduced form, and claim to have achieved an accurate representation of the ideas. Nevertheless, we attempt, imperfectly, to summarize certain facets of this concept here, for the purpose of tracing its influence on Keplers astrophysics. Cusa begins: God placed a desire in all things to exist in the best manner, and he gave them the instruments by which to achieve this end. For Man, the best manner of existence is to know the truth, for which he has been endowed with the powers of cognition. The intellect insatiably desires to attain unto the true through scrutinizing all things by means of its innate faculty of inference. The mind judges that which it does not know, by making a comparative relationship with what it does. However, this presents an inherent paradox for science: Both the precise combinations in corporeal things and the congruent relating of known to unknown surpass human reason to such an extent that Socrates seemed to himself to know nothing except that he did not know. ... Therefore, if the foregoing points are true, then since the desire in us is not in vain, assuredly we desire to know that we do not know. If we can fully attain unto this knowledge or our ignorance, we will attain unto learned ignorance. ... The more he knows that he is unknowing, the more learned he will be.6So, it is in the nature of knowing the way we do not know, that we are able to gain increasingly less-imperfect knowledge of the truth. Cusa begins by investigating through Learned Ignorance, the nature of the Absolute Maximum, which the faith of all nations indubitably believes to be God. This Absolute Maximum, while pure Oneness, is by its very nature triune, comprising oneness, equality, and union.
Ironically, one of Cusas most important discoveries concerning the principle of Learned Ignorance, was his correction of a conceptual error of Archimedes, specifically the impossibility of squaring the circle.* This discovery provided a means to grasp more clearly the relationship of God to Man, and the created world, and also laid the basis for understanding the existence and significance of transcendental magnitudes. Both concepts were crucial to Keplers later discoveries. Cusa writes, Whatever is not truth, cannot measure truth precisely. (By comparison, a noncircle cannot measure a circle, whose being is something indivisible.) Hence, the intellect, which is not truth, never comprehends truth so precisely that truth cannot be comprehended infinitely more precisely. For the intellect is to truth as an inscribed polygon is to the inscribing circle. The more angles the inscribed polygon has, the more similar it is to the circle. However, even if the number of its angles is increased ad infinitum, the polygon never becomes equal to the circle unless it is resolved into an identity with the circle.This incommensurability of the curved to the straight, provides the means by which to grasp the relationship between God, the Creator, and the created world; The Absolute Maximum bounds the universe in the same way that the circle bounds the polygon. Just as the polygon is derived from the circle, not the circle from the polygon, so the Absolute Maximum unfolds and enfolds the Universe, which is an imperfect likeness of it. The triune nature of the Absolute Maximum is thus expressed in the Universe, as the relationship between the Creator, the Created, and the act of creation. But, since the universe is a contracted maximum, those principles are reflected imperfectly. From this standpoint, Cusa draws specific conclusions concerning the nature of the physical universe: Wherefore it follows, that, except for God, all positable things differ. Therefore, one motion cannot be equal to another; nor can one motion be the measure of another, since, necessarily, the measure, and the thing measured differ. Although these points will be of use to you regarding an infinite number of things, nevertheless, if you transfer them to astronomy, you will recognize that the art of calculating lacks precision, since it presupposes that the motion of all the other planets can be measured by reference to the motion of the sun. Even the ordering of the heavens, with respect to whatever kind of place, or with respect to the risings and settings of the constellations, or to the elevation of a pole, and to things having to do with these, is not precisely knowable. And since no two places agree precisely in time and setting, it is evident that judgments about the stars are, in their specificity, far from precise.From these principles, Cusa rejects the fraud of Claudius Ptolemys geocentric solar system: Hence, if we consider the various movements of the spheres, we will see that it is not possible for the world-machine to have as a fixed and immovable center, either our perceptible earth or air or fire or any other thing. For, with regard to motion, we do not come to an unqualifiedly minimum, i.e., a fixed center. Hence the world does not have a fixed circumference. ... Therefore, since it is not possible for the world to be enclosed between a physical center and a physical circumference, the world of which God is the center and the circumference is not understood. ...The concluding statement in the extract above, was a declaration that the EmperorAristotlehad no clothes. Cusa was stating what anyone could see in the heavens for himself, that the physical universe did not obey the a priori assumptions of Aristotles world of a fixed center. The stars themselves compelled the discovery of a new concept concerning Man and Nature. More importantly, Cusa was demonstrating the method by which the human mind could attain truthful knowledge of the motions of the heavenly bodies. Keplers Transformation of AstrophysicsCusas revolution began to force a retreat of the Aristotelian control over astronomy. Confronted with the discrepancy between the true motions of the planets, and the motions predicted by the geocentric system of Claudius Ptolemy, Nicholas Copernicus re-introduced the heliocentric conception of the solar system of Aristarchus of Samos. However, the poison of Aristotle was still embedded in the Copernican system. While he copied the form of Cusas conclusions, placing the Earth in motion around the sun, Copernicus failed to apply Cusas method of Learned Ignorance. Under the Copernican system, the planets all revolve around the sun in perfect circlesthat is, the non-uniform motion of the planets had ultimately to be resolved mathematically into uniform circular actiondespite the fact that Cusa had already shown that no such perfect motion was possible in the created world. Even more fundamentally, Copernicus would not totally break with the Aristotelian stricture that knowledge of the physical universe, and the principles by which God composed it, were essentially beyond human comprehension. Thus, Copernicus never claimed the heliocentric system was actually true, but only that it provided a better means of mathematical computation. In 1595, Johannes Kepler brought forth his first work on planetary motion, Mysterium Cosmographicum (The Secret of the Universe), in which Cusas method of Learned Ignorance was applied to achieve a revolutionary conception of the nature of the physical universe. As the subtitle of this work indicates, Kepler completely rejected Aristotle and, instead of simply providing just another mathematical model, sought the true and particular causes of the number, size, and periodic motions of the heavens. By true causes, Kepler understood, as did Plato and Cusa, the Reason, or intention, according to which God composed the universe as he did. As Kepler announced at the beginning of the Mysterium: I pass over in silence the fact that this very matter, of Creation, which the philosophers [Aristotelians-BD] denied, is a strong argument, when we perceive how God, like one of our own architects, approached the task of construction the universe with order and pattern, and laid out the individuals parts accordingly as if it were not art which imitated Nature, but God himself had looked to the mode of building of Man who was to be.7These words of Kepler echo those of Cusa from the On Learned Ignorance of nearly 150 years earlier: Who would not admire this Artisan, who with regard to the spheres, the stars, and the regions of the stars, used such skill that there is though without complete precision both harmony of all things and a diversity of all things? This Artisan considered in advance the sizes, the placing, and the motion of the stars in the one world; and He ordained the distances of the stars in such way that unless each region were as it is, it could neither exist nor exist in such a place and with such an order nor could the universe exist.Kepler found that the ordering principle determining the number of the planets, their sizes, and the positions of their orbits, was expressed by the proportions of the five perfectly regular solids presented by Plato in the Timeaus. Just as important as this result, was the method by which Kepler arrived at it, since it exemplified Cusas method. As previously stated, it is already a significant advance to seek the true causes of the motions of the heavenly bodies. But, it was a further revolution to actually determine, Why it was that way and not otherwise, as Kepler stated in the beginning of the Mysterium. To discover this, Kepler first attempted to find some series of numbers, which would correspond to the actual number of planets and the size of their orbits. Despite much effort, this proved fruitless. Failing at that, Kepler sought the principle in two dimensions, seeking a series of inscribed and circumscribed polygons, whose proportions would correspond to the number and size of the actual planetary orbits. This too proved fruitless. Finally Kepler made the leap, Why should there be plane figures between solid spheres? It would be more appropriate to try solid bodies. Thus was born Keplers discovery that the number, size, and position of the (then-)visible planets, corresponded to the principle of construction of the five Platonic solids [See Figure 2].
Figure 2
It was matter which God created in the beginning; and if we know the definition of matter, I think it will be fairly clear why God created matter and not any other thing in the beginning. I say that what God intended was quantity. To achieve it he needed everything which pertains to the essence of matter; and quantity is a form of matter, in virtue of its being matter, and the source of its definition. Now God decided that quantity should exist before all other things so that there should be a means of comparing a curved with a straight line. For in this one respect Nicholas of Cusa and others seem to me divine, that they attached so much importance to the relationship between a straight and a curved line and dared to liken a curve to God, a straight line to his creatures; and those who tried to compare the Creator to his creatures, God to Man, and divine judgements to human judgements did not perform much more valuable a service than those who tried to compare a curve with a straight line, a circle with a square.The significance of Cusas demonstration of the transcendental relationship between the curved and the straight, was thus demonstrated by Kepler to manifest itself in the actual construction of the physical universe. Keplers further discoveries demonstrated that this manifestation was not simply limited to the role of the Platonic solids in the construction of the heavens, but, as Cusa himself understood, was embedded in the very nature of the physical action. Keplers 1609 The New Astronomy is based on this deeper manifestation of the transcendental relationship between the curved and the straight. Keplers polyhedral hypothesis, that the number and size of the planetary orbits were determined by inscribing and circumscribing spheres around the five Platonic solids, was not sufficient to account fully for the true motions of the planets. Orbits derived from this hypothesis, were circles. The true motions of the planets indicated the existence of another principlenamely, that the planets do not move uniformly in their orbits. They can be observed to be always speeding up to a maximum speed and slowing down to a minimum [See Figure 3].
Figure 3
Ptolemy, Copernicus, and Keplers sometime collaborator, Tycho Brahe, all calculated this observed non-uniform motion as a result of colligating circles [See Figure 4].
Figure 4
Here, Kepler pointed out that the three radically different systems shared a common error, the embedded error of the Aristotle. All three imposed, a priori, the mathematics of perfect circlesand hence, assumed the reality of uniform motionon the physical universe: The three opinions are for all practical purposes equivalent to a hairs breadth, and produce the same results, he wrote, in the introduction to The New Astronomy. Consequently, it is impossible to tell which of the three opinions is true, says Kepler. The common error in all three opinions is, that they assume a pre-existing mathematical structure (perfect circles), and then force the physical observations to conform to that mathematical idea. As Copernicus puts it in his Revolutions of the Heavenly Spheres: The movement of the celestial bodies is regular, circular, and everlastingor else compounded of circular movements. But, the observed motions of the planets are not regular, so why assume a priori that these motions must derive from circles? Kepler took a completely different, revolutionary approach, one based on Plato and Cusa. Rather than force the observations to conform to pre-existing mathematical assumptions, he sought the physical reason for the observed non-uniform motion, and then conformed his mathematics to that physical hypothesis: Indeed, all things are so interconnected, involved, and intertwined with one another that after trying many different approaches to the reform of astronomical calculations, some well trodden by the ancients and others constructed in emulation of them and by their example, none other could succeed than the one founded upon the motions physical causes themselves, which I establish in this work.What was so frightening about the planets having non-uniform motion, that it kept Aristotles grip over three very different types of thinkers, such as Ptolemy, Brahe, and Copernicus? Again, Cusa gives the answer. If the planets were moving uniformly about the sun in perfect circles, then each planets motion would be governed by an unchanging principle; that is, its speed would be constant, it would always be the same distance from the sun (or Earth), and its direction would always be at a right angle to a line connecting the planet to the sun [See Figure 5(a)]. However, if the planets were moving non-uniformly, the speed and direction would be constantly changing [See Figure 5(b)].
Figure 5
Kepler demonstrates that the relationship of the speed and direction of the planet at each moment, to the characteristic of the whole orbit, depends on those transcendental magnitudes discovered by Cusa. This implies that a quality of cognition, or Mind, is governing the planets motion. But, how does the planet know how to adjust its speed and direction at each moment? And, more significantly, and more terrifying to an Aristotelian, How can the human mind know what the planet knows? Especially, since the planets action depends upon just those transcendental magnitudes, which Cusa had demonstrated were not susceptible to precise mathematical calculation? This problem is not so terrifying for a thinker who follows Cusas principle of Learned Ignorance. As cited above, Cusa had already stated that physical action could not occur according to perfect circles, and that precise calculation of a planets motion is as impossible as squaring the circle. Rather than cringe at the expression of transcendental magnitudes, Cusas Learned Ignorance teaches us to rejoice at this paradox, as it urges us on to new discoveries. But, the question remains, What is the underlying principle that expresses itself as the quality of Mind, governing the planets orbit? That quality of Mind, is not, as Aristotelians such as Ptolemy maintain, an irrational demi-god residing in each planet, possessed with innate intelligence, and capable of arbitrary action. Rather, each planet acts as if it had a Mind, because its action expresses an intention of the underlying principles governing the universe as a whole. That is, the planets motion expresses the intention of the Divine Mind, whose intentions also govern the human mind, created in the image of God. This Keplerian concept of Mind is congruent with the thinking of Plato and Cusa. For example, in On Learned Ignorance, Cusa revives Platos concept of Mind, resituating it from the standpoint of Christianity, and cleaning up the influence of Aristotle on the medieval Neo-Platonists, who, in Cusas time, were the dominant exponents of Platonism: All wise agree that possible being cannot come to be actual except through actual being, for nothing can bring itself into actual being, lest it be the cause of itself, for it would be before it was. ... Some called this excellent actualizing nature mind; others called it intelligence, others world-soul, others, fate-substantiated, others (e.g., Platonists) connecting necessity. ... The Harmonies: A Still More Basic PrincipleFrom these considerations, Kepler came to the discovery that the non-uniform motion of the planets was not simply an appearance, but was the true physical motion. This led him to the ultimate discovery, that the principle governing this non-uniform motion was expressed in the principle, equal areas, equal times, and that the orbits of the planets were, in first approximation, elliptical [See Figure 6].
Figure 6
But this left open the question, What were the principles governing the determination of the eccentricities?, since Keplers polyhedral hypothesis accounts only for circular orbits. Pursuing Cusas method further, Kepler sought a still more basic principle, which would answer the question, Why these eccentricities and not others? To answer this question, Kepler looked to the relationship between the maximum and minimum speeds of the planets, and found this relationship to correspond to musical harmonies [See Figure 7].
Figure 7
As he stated in the introduction to Book IV of The Epitome of Copernican Astronomy: In the farthest movements of any two planets, the universe was stamped with the adornment of harmonic proportions, and accordingly, in order that this adornment might be brought into concord with the movements, the eccentricities which fell to the lot of each planet had to be brought into concord.8Keplers harmonic orderings, once again, revealed a new manifestation of concepts originally brought forward by Cusa. The harmonic intervals, which Kepler found to be reflected among the planetary orbits, were, like the individual motions of the planets, dependent on transcendental magnitudes, a result anticipated by Cusa in On Learned Ignorance: Press onward: Conformably to the rule, there is no precision in music. Therefore it is not the case that one thing perfectly harmonizes with another in weight or length or thickness. Nor is it possible to find between the different sounds of flutes, bells, human voices, and other instruments comparative relations which are precisely harmonic so precisely that a more precise one could not be exhibited. ... Ascend now to the the recognition that the maximum, most precise harmony is an equality-of-comparative relation which a living and bodily man cannot hear. For since this harmony is every proportion (ratio), it would attract to itself our souls reason [ratio] just as infinite Light attracts all light so that the soul, freed from perceptible objects, would not without rapture hear with the intellects ear this supremely concordant harmony. A certain immensely pleasant contemplation could here be engaged in not only regarding the immortality of our intellectual, rational spirit (which harbors in its nature incorruptible reason, through which the mind attains, of itself , to the concordant and the discordant likeness in musical things), but also regarding the eternal joy into which the blessed are conducted, once they are freed from the things of this world. But I will deal with this topic elsewhere.These musical paradoxes, sparked by Cusa and Kepler, laid the groundwork for their more complete elaboration, in the domain of musical composition, by J.S. Bachs development of the well-tempered system of polyphony. Kepler developed his completed hypothesis of planetary motion in his 1619 Harmonies of the World. At the conclusion of that work, Kepler appended an, Epilogue Concerning the sun by Way of Conjecture, which provides a poetical summary of the development of his ideas from Pythagoras through Cusa: From the celestial music to the hearer; from the Muses to Apollo the leader of the Dance; from the six planets revolving and making consonances, to the sun at the center of all the circuits, immovable in place, but rotating into itself. ...And so, it is fitting that anyone wishing to study astronomy today, should begin by first getting to know Nicolaus of Cusa, whose birth we celebrate this year.
1. Aeschylus, Prometheus Bound, ed. by Herbert Weir Smyth, www.perseus.tufts.edu. 2. Johannes Kepler, The New Astronomy (Astronomia Nova), trans. by William Donahue (Cambridge: Cambridge University Press, 1992). 3. See Philo, On the Account of the Worlds Creation Given by Moses, trans. by F.H. Colson and G.H. Whitaker, in Philo, I, Loeb Classical Library (Cambridge, Harvard University Press, 1929.) 4. Plato, The Republic, trans. by Paul Shorey, in Plato, VI (Books VI-X), Loeb Classical Library (Cambridge, Mass.: Harvard University Press, 1935). 5. Plato, Timaeus, trans. by R.G. Bury, in Plato, IX, Loeb Classical Library (Cambridge, Mass.: Harvard University Press, 1929). (back to box) 6. Nicholas of Cusa on Learned Ignorance: A Translation and Appraisal of De Docta Ignorantia, trans. by Jasper Hopkins (Minneapolis: The Arthur Banning Press, 1985), 2nd edition. 7. Johannes Kepler, Mysterium Cosmographicum (The Secret of the Universe), trans. by A.M. Duncan (New York: Abaris Books, 1981). 8. Johannes Kepler, Epitome of Copernican Astronomy: Books IV and V, trans. by Charles Glenn Wallis, in Great Books of the Western World (Chicago: Encyclopedia Britiannica, 1939). 9. Johannes Kepler, The Harmonies of the World (Harmonice Mundi) trans. by Charles Glenn Wallis, ibid.
schiller@schillerinstitute.org The Schiller Institute Thank you for supporting the Schiller Institute. Your membership and contributions enable us to publish FIDELIO Magazine, and to sponsor concerts, conferences, and other activities which represent critical interventions into the policy making and cultural life of the nation and the world. Contributions and memberships are not tax-deductible. Home | Search | About | Fidelio | Economy | Strategy | The LaRouche Frameup | Conferences © Copyright Schiller Institute, Inc. 2006. All Rights Reserved.
schiller@schillerinstitute.org The Schiller Institute Thank you for supporting the Schiller Institute. Your membership and contributions enable us to publish FIDELIO Magazine, and to sponsor concerts, conferences, and other activities which represent critical interventions into the policy making and cultural life of the nation and the world. Contributions and memberships are not tax-deductible. Home | Search | About | Fidelio | Economy | Strategy | The LaRouche Frameup | Conferences © Copyright Schiller Institute, Inc. 2006. All Rights Reserved. |
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