- Source of complete "Nicole Oresme article": Oresme-Biography at the ["Nicole Oresme Homepage: www.nicole-oresme.com"] with friendly authorization of its author Ulrich Taschow. There you can also found the complete bibliography of Oresme's work and many other material on Nicole Oresme.
- Nicole Oresme was a brilliant philosopher, psychologist, economist, mathematician, physicist, astronomer and musicologist, a passionate theologian, a competent translator, counselor of King Charles V of France "Le Sage", Bishop of Lisieux, one of the principal founders of modern sciences,[1] probably the most original thinker of the 14th century and - so to speak - the „French Einstein of the 14th century“. And last, not least, like no other of his time Oresme was able to popularize the sciences.
- Portrait of Nicole Oresme: Miniature of Nicole Oresme's Traité de l’espere, Bibliothèque Nationale, Paris, France, fonds français 565, fol. 1r.
Oresme's live
Nicole Oresme: Therefore, I indeed know nothing except that I know that I know nothing.[2]
Oresme was born 1323 (1320-1325 ?) in the village of Allemagne (today's Fleury-sur-Orne) in vicinity of the city Caen, Normandy, in the Diocese of Bayeux. Practically nothing is known concerning his family. The fact that Oresme attended the royally sponsored and subsidized College of Navarre, an institution for students too poor to pay their expenses while studying at the University of Paris, makes it seem probable that he came from a peasant family.
Oresme studied “artes” in Paris (before 1348), obvious together with Jean Buridan (the so-called founder of the French school of natural philosophy), Albert of Saxony and perhaps Marsilius of Inghen, and got there the Magister Artium. In 1348, he was a student of theology in Paris, in 1356, he received his doctorate and in the same year he became grand master (grand-maître) of the College of Navarre. Many of his most thoughtful Latin treatises antedate 1360 (see the chronology of Oresme's works). This shows that Oresme was an already-established schoolman of highest reputation, which attracted the attention of the royal family to him and brought Nicole Oresme into intimate contact with the future Charles V in 1356. Since 1356, during the custody of his father, John II, in England, Charles was regent and from 1364 until 1380 King of France. On November 2, 1359, Oresme became already “secretaire du roi” and in the period following, he seems to have become chaplain and counselor of the king.
There is a long tradition that Nicole Oresme was also the tutor to the dauphin, afterwards Charles V, but this is not quite sure. Charles seems to have had the highest esteem for Oresme’s character and talents, often followed his counsel, and made him write many works in French for the purpose of popularize the sciences and of developing a taste for learning in the kingdom. At Charles’s instance, too, Oresme pronounced a discourse before the papal court at Avignon, denouncing the ecclesiastical disorders of the time. Much can be said for it that Oresme livelong was an intimate friend and consultant of the King Charles, “Le Sage”, until his death on 1380. His influence of Charles’ progressive political, economical, ethical and philosophical thinking was probably quite strong. An extensive investigation of these facts was not tackled yet. Oresme was the most important person of a choice circle of intellectuals like Raoul de Presle, Philippe de Mézières, etc. at Charles’ court. Royal reliance on Oresme’s capabilities is evidenced at the latest in 1356 (see above) and than 1360 when the grand master of Navarre was sent by Dauphin to seek a loan from the municipal authorities of Rouen. In 1361 Oresme, while grand master of Navarre, was appointed archdeacon of Bayeux, with the support of Charles. The fervent schoolman Oresme unwillingly surrendered the interesting post of grand master.
On November 23, 1362, the year of his master of theology, Oresme was appointed already canon of the Cathedral of Rouen. At the time of this appointment to the canonship, Oresme was still teaching regularly at the University of Paris. On February 10, 1363, he was made a canon at La Saint Chapelle, given a semiprebend and on March 18, 1364, Oresme was elevated to the post of dean of the Cathedral of Rouen. In these frequent changes of position it is likely that the royal hand of John II, the father of Charles, was impelled by the suggestions of the dauphin.[3] During his tenure in successive posts at the cathedral of Rouen (1364-1377), Oresme spent much time in Paris, especially in context of the affairs of University. Many documents verify this stays. Nevertheless, we cannot infer that he was also teaching there.
With the commencement of his prolonged translating activities at the request of Charles V, Oresme did reside continuously at Paris, as it shown by letters, dated August 28 and November 11, 1372, from Charles to Rouen. This residency at Paris seems extended by Charles to 1380. Oresme began work on his translation of Aristotle’s Ethics in 1369, completing it in 1370. The Politics and the Economics seem to have been completed between 1372 and 1374, and the De caelo et mundo in 1377. As early as 1371, Oresme received a pension from the royal treasury as reward for his great labours.
On August 3, 1377, Nicole Oresme became for his great merits for Charles and the royal family, with support of the king, the post Bishop of Lisieux. Though, he seems not to have taken up residence at Lisieux until September 1380. Little is known of the latest five years of his live. Oresme died in Lisieux on July 11, 1382, two years after King Charles’ death, and was buried in the cathedral church.
Oresme's scientifical work
Oresme is best known as an economist, mathematician, and a physicist (since Taschow's book "Nicole Oresme und der Frühling der Moderne" also as musicologist, psychologist and philosopher). His economic views are contained in a Commentary on the Ethics of Aristotle, of which the French version is dated 1370; a commentary on the Politics and the Economics of Aristotle, French edition, 1371; and a Treatise on Coins (De origine, natura, jure et mutationibus monetarum). These three works were written in both Latin and French; all three, especially the last, stamp their author as the precursor of the science of political economy, and reveal his mastery of the French language. This way, Oresme became a sooner founder of the French scientific language and terminology. He created a big number of French scientific terms and anticipated by it the scientific discharge of Latin in the 18th century. The French Commentary on the Ethics of Aristotle was printed in Paris in 1488; that on the Politics and the Economics, in 1489. The Treatise on coins, De origine, natura, jure et mutationibus monetarum, was printed in Paris early in the sixteenth century, also at Lyons in 1675, as an appendix to the De re monetaria of Marquardus Freherus, and is included in the Sacra bibliotheca sanctorum Patrum of Margaronus de la Bigne IX, (Paris, 1859), p. 159, and in the Acta publica monetaria of David Thomas de Hagelstein (Augsburg, 1642). The Traictié de la première invention des monnoies in French was printed at Bruges in 1477. For the complete list of Oresme's works see the Oresme-Bibliography.
If we will make in the following some excursions in the fields of Oresme’s universal work, first it is necessary to say that we can illuminate only a very little part of it:
Mathematics:
His most important contributions to mathematics are contained in Tractatus de configuratione qualitatum et motuum, still in manuscript. An abridgment of this work printed as Tractatus de latitudinibus formarum of Johannes de Sancto Martino (1482, 1486, 1505, 1515), has heretofore been the only source for the study of his mathematical ideas. In a quality, or accidental form, such as heat, the Scholastics distinguished the intensio (the degree of heat at each point) and the extensio (e.g., the length of the heated rod): these two terms were often replaced by latitudo and longitudo, and from the time of Thomas Aquinas until far on in the fourteenth century, there was lively debate on the latitudo formae. For the sake of lucidity, Oresme conceived the idea of employing what we should now call rectangular co-ordinates: in modern terminology, a length proportionate to the longitudo was the abscissa at a given point, and a perpendicular at that point, proportional to the latitudo, was the ordinate. He shows that a geometrical property of such a figure could be regarded as corresponding to a property of the form itself only when this property remains constant while the units measuring the longitudo and latitudo vary. Hence, he defines latitudo uniformis as that which is represented by a line parallel to the longitude, and any other latitudo is difformis; the latitudo uniformiter difformis is represented by a right line inclined to the axis of the longitude. He proves that this definition is equivalent to an algebraical relation in which the longitudes and latitudes of any three points would figure: i.e., he gives the equation of the right line, and thus forestalls Descartes in the invention of analytical geometry. This doctrine he extends to figures of three dimensions. Besides the longitude and latitude of a form, he considers the mensura, or quantitas, of the form, proportional to the area of the figure representing it. He proves this theorem: A form uniformiter difformis has the same quantitiy as a form uniformis of the same longitude and having as latitude the mean between the two extreme limits of the first. He then shows that his method of figuring the latitude of forms is applicable to the movement of a point, on condition that the time is taken as longitude and the speed as latitude; quantity is, then, the space covered in a given time. In virtue of this transposition, the theorem of the latitude uniformiter difformis became the law of the space traversed in case of uniformly varied motion: Oresme's demonstration is exactly the same as that which Galileo was to render celebrated in the seventeenth century. Moreover, this law was never forgotten during the interval between Oresme and Galileo: it was taught at Oxford by William Heytesbury and his followers, then, at Paris and in Italy, by all the followers of this school. In the middle of the sixteenth century, long before Galileo, the Dominican Dominic Soto applied the law to the uniformly accelerated falling of heavy bodies and to the uniformly decreasing ascension of projectiles.
In Algorismus proportionum and De proportionibus proportionum Oresme developed the first calculation-method of powers with fractional irrational exponents, i.e. the calculation with irrational proportions (proportio proportionum). Basis of this method was Oresme’s equalization of continuous magnitudes and discrete numbers, an idea that Oresme took out of the musical monochord-theory (sectio canonis). This way Oresme overcame the Pythagorean prohibition of regular division of Pythagorean intervals like 8/9, 1/2, 3/4, 2/3 and provided the tool to generate the equal temperament 250 years before Simon Stevin. Here an example for the equal division of octave in 12 parts: File:Formula oresme.jpg
Oresme used this method for instance also in his musical section of the Tractatus de configurationibus qualitatum et motuum in context of his “overtone or partial tone theory” (see below) to produce irrational proportions of sound (ugly timbre or tone colour) in the direction of a “partial tone continuum” (white noise).[4]
Finally Oresme was very interested in limits, threshold values and infinite series by means of geometric additions (Tractatus de configurationibus qualitatum et motuum, Questiones super geometriam Euclidis) that prepared the infinitesimal calculus of Descartes and Galilei.
For Oresme’s anticipation of modern stochastic see below "Natural Philosophy".
As Taschow has shown doubtless, Oresme transformed the above-discussed graphic method of his Tractatus de configuratione qualitatum et motuum from the music-theory of his time. Therefore, we come to Oresme’s very important merits in the field of musicology:[5]
Musicology:
Oresme's very configuratio qualitatum and the functional pluridimensionality associated with it are closely related to contemporary musicological diagrams and most importantly to musical notation, which equally quantifies and visually represents the variations of a sonus according to given measures of extensio (time intervals) and intensio (pitch). The complex notational representations of music became, in Oresme's work, configurationes qualitatum or difformitates compositae, with music functioning once more as the legitimating paradigm. But the sphere of music did not only provide Oresme's theory with an empirical legitimation, it also helped to exemplify the various types of uniform and difform configurations Oresme had developed, notably the idea that the configurationes endowed qualities with specific effects, aesthetical or otherwise, which could be analytically captured by their geometric representation. This last point helps explain Oresme's overarching aesthetical approach to natural phenomena, which was based on the conviction that the aesthetic evaluation of (graphically representable) sense experience provided an adequate principle of analysis. In this context, music played once more an important role as the model for the „aesthetics of complexity and of the infinite“, favored by the mentalité of the fourteenth century. Oresme sought the parameters of the sonus experimentally both on the microstructural, acoustic level of the single tone and on the macrostructural level of unison or polyphonic music. In attempting to capture analytically the various physical, psychological and aesthetic parameters of the sonus according to extensio and intensio, he wished to represent them as the conditions for the infinitely variable grades of pulchritudo and turpitudo. The degree to which he developed this method is unique for the Middle Ages, representing the most complete mathematical description of musical phenomena before Galileo's Discorsi. Noteworthy in this enterprise are not only the discovery of “partial tones”or overtones three centuries before Marin Mersenne, but also the recognition of the relation between overtones and tone colour, which Oresme explained in a detailed physico-mathematical theory, whose level of complexity was only to be reached again in the nineteenth century with Hermann von Helmholtz. Finally, we must also mention Oresme’s mechanistic understanding of the sonus in his Tractatus de configuratione et qualitatum motuum as a specific discontinuous type of movement (vibration), of resonance as an overtone phenomenon, and of the relation of consonance and dissonance, which went even beyond the successful but wrong coincidence theory of consonance formulated in the seventeenth century. Oresme's demonstration of a correspondence between a mathematical method (configuration qualitatum et motuum) and a physical phenomenon (sound) represents an exceptionally rare case, both for the fourteenth century at large as for Oresme’s work in particular. The sections of the Tractatus de configurationibus dealing with music are milestones in the development of the quantifying spirit that characterizes the modern epoch.
Oresme, the younger friend of Philippe de Vitry, the famous music-theorist, composer and Bishop of Meaux, is the founder of modern musicology. He nearly dealed with every musicological area in modern sense (see U. Taschow, "Nicole Oresme und der Frühling der Moderne") like:
- acoustics (Expositio super de anima, Quaestiones de anima, De causis mirabilium, De configurationibus, De commensurabilitate vel incommensurabilitate),
- musical aesthetics (De configurationibus, De commensurabilitate vel incommensurabilitate),
- physiology of voice and hearing (Quaestiones de sensu, Expositio super de anima),
- psycholoy of hearing (Quaestiones de anima, De causis mirabilium, Quaestiones de sensu),
- musical theory of measurement (Tractatus specialis de monocordi,[6] De configurationibus, Algorismus proportionum),
- music theory (De configurationibus),
- musical performing (De configurationibus),
- music philosophy (De commensurabilitate vel incommensurabilitate).
With his very special „theory of species“(multiplicatio specierum) Oresme formulated the first and correct theory of wave-mechanics of sound and light, 300 years before Christian Huygens: Oresme describes a pure energy-transport without material spreading. The terminus „species“ in Oresme’s sense means the same as our modern term „wave form“.
Oresme discovered also the phenomenon of partial tones or overtones, 300 years before Mersenne (see above) and the relation between overtones and tone colour, 450 years before Joseph Sauveur. His very detailed physico-mathematical theory of partial tones and tone colour anticipated the nineteenth century theory of Hermann von Helmholtz.
In his musical aesthetics Oresme formulated a modern subjective theory of perception: Not the objective beauty of God’s creation but the construtive process of perception causes the beauty or ugliness in the senses. Therefore, every individual perceives another „world“.
Many of Oresme’s insights in other disciplines like mathematics, physics, philosophy, psychology which anticipate the self-image of modern time, are closely bound up with the „Model Music” (unusual for present-day thinking): The Musica functioned as a kind of „Computer of the Middle Ages”and in this sense it represented the all embracing hymn of new quantitative-analytic consciousness in 14th century.
Psychology:
Since the work of Taschow „Nicole und der Frühling der Moderne“ (book 2, 3 and 4) it is also known that Oresme was an outstanding psychologist. With a strong empirical method, he investigated the whole complex of phenomenons of the human psyche. Oresme was confident in the activity of „inner senses“ (sensus interior) and in the constructivity, complexity and subjectivity of perception of world. With this quite progressive features he was a typical exponent of the „Parisian Psychological School“ (Jean Buridan, Barthelemy de Bruges, Jean de Jandun, Henry of Hesse etc.) and nearly related with the scientists of optics (Alhazen, Roger Bacon, Witelo, John Pecham etc.). But in addition the innovative and bold mind of Oresme anticipated very important facts of the psychology of the 19th and 20th century especially in the fields of cognitive psychology, perception psychology, psychology of consciousness and psycho-physics:
So, Oresme discovered the psychological "unconscious" and its great importance for perception and behaviour. On this base he formulated his inspired "theory of unconscious conclusions of perception" (500 years before Hermann von Helmholtz) and his “hypothesis of two attentions“ – a conscious and a unconscious attention (20th century knowledge). In his modern theory of cognition Oresme showed that there exist no thought-content like categories, terms, qualities and quantities out of the human consciousness. For instance Oresme unmasked the so-called “primary qualities” like size, position, shape, motion, rest etc. of the 17th century scientists (Galilei, John Locke etc.), that should be objective in outer nature, as very complex cognitive constructions of psyche under the individual conditions of human body and soul. Because reality is only at the expansionless moment (instantia) Oresme reasoned that therefore no motion could exist except in consciousness. It means that motion is a result of human perception and memory in the sense of active composition of “before” and “later”. This clever theory becomes plausible for example in the field of sound: Oresme wrote, “if a creature would exist without memory it never could hears a sound…”[7] Sound is a human construction and nothing other.
In his modern "psycho-cybernetics" and "information theory" Oresme solved the "dualism-problem" of physical and psychical world by using the three-part schema “species - materia - qualitas sensibilis” of his brilliant "''species'' theory" (in modern terms: information - medium - meaning). The transportable species (information) like a waveform of sound changes its medium (wood, air, water, nervous system etc.) and the inner sense (''sensus interior'') constructs in unconscious conclusions a subjective meaning from it.
Oresme also developed already a first "psycho-physics", that shows many similarities with the approach of Gustav Theodor Fechner, the founder of modern psycho-physics. Oresme’s ideas of psyche are strong mechanistically. Physical and psychical processes are equivalent in its structure of motion (configuratio qualitatum et motuum). Every structure has a qualitative (psychical) and a quantitative (physical) moment, and this is the reason why psychological processes (intensities) can be measured like physical. This way Oresme supplied the first scientific legitimation of measurement of psyche and (contra Aristotle and Scholastics) even of immaterial soul.
However, the strongest focus Oresme drew to the psychology of perception. Among a lot of parts in writings he composed, unique for the whole Middle Ages, a special treatise on perception and its disorder and delusion (De causis mirabilium), where he examined every sense (sight, hearing, touch, smell, taste) and cognitive functions. With the same method like psychologists of the 20th century by means of analysis of delusions and disorders he recognized already many essential laws of perception like for instance the "Gestaltgesetze" (shape-law) 500 years before Christian von Ehrenfels, investigated limits of perception (maxima et minima) etc (see ibid. U. Taschow, "Nicole Oresme und der Frühling der Moderne").
Natural Philosophy:
Taschow’s work (Nicole Oresme und der Frühling der Moderne) reveals also the very complex cosmos of Oresme’s philosophical thinking. Oresme anticipated many essential views of the self-image of modern time like his insight into the incommensurability of natural proportions, into the complexity, indetermination and infinite changeability of the world etc. In Oresme’s linear-progressive world every time everything is unique new and by this way also the human knowledge.
The excellent model for this new infinite world of the 14th century (in contrast to the in endless repetitions captivated musica mundana of antiquity) was the Oresmian machina musica. For Oresme the music analogously shows that with a limited number of proportions and parameters somebody could produce very complex, infinite varying and never repeating structures (De configurationibus qualitatum et motuum, De commensurabilitate vel incommensurabilitate, Quaestio contra divinatores). That is the same message as of the “chaos theory” of 20th century where the iteration of simplest formulas produces a high complex world with none predictably behaviour.
Based on the musico-mathematical principles of incommensurability, irrationality and complexity finally Oresme created a dynamic structure-model for the constitution of substantial species and individuals of nature, the so-called theory of perfectio specierum (De configurationibus qualitatum et motuum, Quaestiones super de generatione et corruptione, Tractatus de perfectionibus specierum). By means of analogy of the musical qualities with the “first and second qualities” of Empedocles the Oresmian individual turns into a self-organizing system which takes trouble to get his optimal system state against disturbing environmental influence. This “automatic control loop” influences the substantial form (forma substantialis) already in the modern sense of principles of biological evolution, adaption and mutation of gene-material. It is quite evident, that Oresme’s revolutionary theory overcomes the Aristotelian-scholastic dogma of the unchanging substantial species and anticipated principles of the system theory, self-organisation and biological evolution of Charles Darwin.
A further very progressive approach was Oresme’s extensive investigations of statistical approximate values and measurements by means of margins of error. He formulated his theory of probabilities as well as in the psychological, physical as mathematical field:
For instance Oresme laid down two psychological rules (De causis mirabilium). The first rule says: With an increase of number of unconscious judgments of perception (depth of meaning) grows the probability of misjudgments and this way of errors of perception. The second rule says: The more the number of unconscious judgments of perception exceeds a diffuse limit[8] the more improbable is a fundamental error of perception because never breaks down the vast majority of unconscious judgments. The knowledge-theoretical point of these depending on each other rules is that perception is nothing more than a probability value in the gray area of these two rules. Perception is never an objective “photography” but a complex construction without absolute evidence.
Now we provide an example for Oresme’s mathematical anticipation of elements of modern stochastic (De proportionibus proportionum). Oresme states: If we take a finite multitude of positive integers, than it is the number of perfect integers or the number of cubes much lesser than other numbers. In addition, the more numbers we take, the larger is the relationship of the non-cubes to the cubes or of the imperfect integers to perfect integers. Therefore if we do not know something about a number than it is probably (verisimile) that this number is no cube. It is like in games (sicut est in ludis), where somebody asks, whether a hidden number is a cube. It is more careful to answer with ‘no’ because this seems to be more probably (probabilius et verisimilius). Oresme than looks at a multitude of 100 different mathematical objects that he has formed in a certain way, and he determines that from it (100 • 99) : 2 = 4950 combinations from each two elements can be formed. From those, 4925 show a certain interesting quality E, whereas the remaining does not have this quality E. Finally, Oresme calculates the quotient 4925 : 25 = 197 : 1 and concludes from it: It is probably (verisimile) that if somebody is looking for such an unknown combination, this will show the quality E. Thus Oresme calculates the number of the favorable and the number of the unfavorable cases and their quotient. By it, he yet does not have the quotient from the number of the favorable and the entire number of the equally-possible cases, just not our modern “measure of probability”. But Oresme still has developed a clever tool to judge the “easiness”of arrival of an event quantitatively. Oresme used terms for his calculations of probability like verisimile, probabile / probabilius, improbabile / improbabilius, verisimile / verisimilius / maxime verisimile and possibile equaliter. No one before Oresme and long time after him used these words in context of games and aleatory probabilities. We can find Oresme’s method first again at Galileo Galilei and Blaire Pascal in 17th century.
In conclusion we want to refer shortly to an example of Oresme’s probability theory in physics. In his works De commensurabilitate vel incommensurabilitate, De proportionibus proportionum, Ad pauca respicientes etc. Oresme says if we take two unknown natural magnitudes like motion, time, distance etc. than it is more probable (verisimillius et probabilius) that the ratio of those is irrational than rational. This theorem applies for Oresme generally to entire nature, to the earthly and to the celestial world. It has great effects on Oresme’s view of necessity and contingency, and this way of his view of law of nature (leges naturae) and his criticism of astrology (see U. Taschow, "Nicole Oresme und der Frühling der Moderne").
It is obviously that Oresme was inspired for his probability theory in physics, mathematics and perception psychology by music: The division of monochord (sectio canonis) proved the sense of hearing and the mathematical reason clearly that most of the divisions of chord produce irrational, i.e. dissonant intervals (see U. Taschow, "Nicole Oresme und der Frühling der Moderne").
Physics:
Oresme’s physical teachings are set forth in two French works, the Traité de la sphère, twice printed in Paris (first edition without date; second, 1508), and the Traité du ciel et du monde, written in 1377 at the request of King Charles V, but never printed. In most of the essential problems of statics and dynamics, Oresme follows the opinions advocated in Paris by his predecessor, Jean Buridan de Béthune, and his contemporary, Albert of Saxony. In opposition to the Aristotelean theory of weight, according to which the natural ___location of heavy bodies is the centre of the world, and that of light bodies the concavity of the moon's orb, he proposes the following: The elements tend to dispose themselves in such manner that, from the centre to the periphery their specific weight diminishes by degrees. He thinks that a similar rule may exist in worlds other than this. This is the doctrine later substituted for the Aristotelian by Copernicus and his followers, such as Giordano Bruno. The latter argued in a manner so similar to Oresme's that it would seem he had read the Traité du ciel et du monde. But Oresme had a much stronger claim to be regarded as the precursor of Copernicus when one considers what he says of the diurnal motion of the earth, to which he devotes the gloss following chapters xxiv and xxv of the Traité du ciel et du monde. He begins by establishing that no experiment can decide whether the heavens move form east to west or the earth from west to east; for sensible experience can never establish more than one relative motion. He then shows that the reasons proposed by the physics of Aristotle against the movement of the earth are not valid. He points out, in particular, the principle of the solution of the difficulty drawn from the movement of projectiles. Next he solves the objections based on the texts of Holy Scripture. In interpreting these passages he lays down rules universally followed by Catholic exegetists of the present day. Finally, he adduces the argument of simplicity for the theory that the earth moves, and not the heavens, and the whole of his argument in favour of the earth's motion is both more explicit and much clearer than that given by Copernicus.
Above we had already occupied with Oresme’s theory of wave-mechanics of sound and light. Therefore, it will not astonish that Oresme for the first time assumed that colour and light are of the same nature. In Oresme’s absolute correct view colour is nothing other than broken and reflected white light: i.e. the colours are parts of white light. Also this clever theory was inspired by Oresme’s musicological investigations: In his theory of partial tones and ton colour Oresme analogized this musical facts with the phenomenon of mixture of colours on a rotating top.[9]
Footnotes:
[1] Some historians immediately will complain about formulations like “founder”, “anticipation” (see below) and try to impute an anachronism. But that’s not true and an great misunderstanding resultant on the ignorance of Taschow’ theory of evolutionary consciousness. See: Ulrich Taschow, "Nicole Oresme und der Frühling der Moderne", Avox Medien-Verlag, Halle 2005, four books, 1001 pages (Nicole Oresme Homepage: www.nicole-oresme.com). In this theory of consciousness is no place for an idea of linear evolution. But the conservative idea of linear evolution would be the decisive condition for a view of anachronism.
[2] Nicole Oresme, Quodlibeta, MS Paris, BN lat. 15126, 98v.
[3] The peace treaty of Brétigny 1360 rescued John II from his custody in England. Because of the escape of his in England as hostage leaved son, the duke of Anjou, John II came back to London in 1364. On April 8, 1364, he died there.
[4] See Ulrich Taschow, "Nicole Oresme und der Frühling der Moderne", Halle 2003, book 1, pages 142-163.
[5] See Ulrich Taschow, "Nicole Oresme und der Frühling der Moderne", Halle 2003, book 1, pages 59-204. For Oresme's complex musicological writing see also book 3 and 4.
[6] This source is missing.
[7] Nicole Oresme, Quaestiones de anima: Si esset aliquod animal quod nullo haberet retentivam et non sentiret nisi in praesentia, tunc non proprie perciperet sonum. Patet statim propter hoc quod est res successiva sicut motus; ideo oportet aliqualiter recolere de praeterito.
[8] See Ulrich Taschow, "Nicole Oresme und der Frühling der Moderne", Halle 2003, book 4, pages 820-822.
[9] See Ulrich Taschow, "Nicole Oresme und der Frühling der Moderne", Halle 2003, book 1, pages 150-153.