Encyclopedia
Nicole Oresme or
Nicolas d'Oresme was one of the most famous and influential
philosophers of the later
Middle Ages. He was an economist, mathematician, physicist, astronomer, philosopher, psychologist, and musicologist, a passionate theologian and Bishop of
Lisieux, a competent translator, counselor of King
Charles V of France, one of the principal founders and popularizers of modern sciences, and probably one of the most original thinkers of the 14th century.
Oresme's life
Nicole Oresme:
Therefore, I indeed know nothing except that I know that I know nothing.Oresme was born c. 1320-1325 in the village of Allemagne in the vicinity of
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 probable that he came from a peasant family.
Oresme studied the “artes” in Paris , together with Jean Buridan , Albert of Saxony and perhaps Marsilius of Inghen, and there received the Magister Artium. A recently discovered papal letter of provision granting Oresme an expectation of a benefice establishes that he was already a regent master in arts by 1342. This early dating of Oresme's arts degree places him at Paris during the crisis over
William of Ockham's natural philosophy.
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 of the College of Navarre.
Many of his most thoughtful Latin treatises antedate 1360 and show that Oresme was already an established schoolman of the highest reputation, which attracted the attention of the royal family, and brought him into intimate contact with the future
Charles V in 1356.
Beginning in 1356, during the captivity of his father,
John II, in England, Charles acted as regent and from 1364 until 1380, King of France. On November 2, 1359, Oresme became "secretaire du roi" and in the period following, it appears that he became chaplain and counsellor to the king.
There is a long tradition that says that Nicole Oresme was also the tutor to the
dauphin , but this is not quite certain. Charles appears 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 popularizing the sciences and of developing a taste for learning in the kingdom. At Charles’s insistence Oresme delivered a discourse before the papal court at Avignon, denouncing the ecclesiastical disorder of the time.
Much can be said about the fact that Oresme was a lifelong intimate friend and consultant of King Charles, "Le Sage", until his death in 1380. His influence on Charles’ progressive political, economical, ethical and philosophical thinking was probably quite strong, but an extensive investigation of these facts has not been 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, when the grand master of Navarre was sent by the dauphin to seek a loan from the municipal authorities of
Rouen in 1356 and then in 1360. In 1361, with the support of Charles, while still grand master of Navarre, Oresme was appointed archdeacon of
Bayeux. It is known that the fervent schoolman Oresme unwillingly surrendered the interesting post of grand master.
On November 23, 1362, the year he became master of theology, Oresme was appointed canon of the
Cathedral of Rouen. At the time of this appointment, he 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, and was elevated to the post of dean of the Cathedral of
Rouen.
It is likely that the royal hand of John II, the father of Charles, was influenced by the suggestions of the dauphin, in Oresme’s frequent changes of positions.
During his tenure in these successive posts at the Cathedral of Rouen , Oresme spent a lot of time in Paris, especially, in the context of attending to the affairs of the University. Even though many documents verify Oresme’s stays in Paris, nevertheless, we cannot infer that he was also teaching there at that time.
With the commencement of Oresme’s prolonged translating activities at the request of Charles V, he did reside continuously in Paris, as is shown to be true by letters dating from August 28 to November 11, 1372 sent by Charles to Rouen. Oresme’s residency in Paris appears to have been extended by Charles to 1380, when Oresme began working on his translation of
Aristotle’s
Ethics in 1369, which appears to be completed in 1370. Aristotle’s
Politics and
Economics may have been completed between the years of 1372 and 1374, and the
De caelo et mundo in 1377. Oresme received a pension from the royal treasury as early as 1371 as a reward for his great labours.
Because of Oresme’s untiring work for Charles and the royal family, with the king’s support, on August 3, 1377, Oresme attained the post of Bishop of
Lisieux. It appears that Oresme didn’t take up residency at Lisieux until September of 1380, and little is known of the last five years of his life. Oresme died in Lisieux on July 11, 1382, two years after King Charles’ death, and was buried in the cathedral church.
Oresme's scientific work
Oresme is best known as an economist, mathematician, and a physicist, according to Taschow's book also as a musicologist, psychologist and philosopher. Oresme's economic views are contained in "Commentary on the
Ethics of
Aristotle, of which the French version is dated 1370; "Commentary on the
Politics and the
Economics of Aristotle", French edition, 1371; and
Treatise on Coins . These three works were written in both Latin and French; and all of them, especially the last, stamp their author as the precursor of the science of political economy, and reveal his mastery of the French language. In 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 the usage of Latin words in the scientific language of 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, is included in the
Sacra bibliotheca sanctorum Patrum of Margaronus de la Bigne IX, , p. 159, and in the
Acta publica monetaria of David Thomas de Hagelstein . 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 .
If we are to make some of the following excursions into the fields of Oresme’s universal work such as in mathematics, musicology, psychology, natural philosophy, and physics, we need only illuminate a small part of each of them:
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 , for a long time has been the only source for the study of Oresme's mathematical ideas. In a quality, or accidental form, such as heat, the Scholastics distinguished the
intensio and the
extensio . These two terms were often replaced by
latitudo and
longitudo, and from the time of
Thomas Aquinas until far into the fourteenth century, there was lively debate on the
latitudo formae. For the sake of clarity, 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. Oresme shows that a geometrical property of such a figure could be regarded as corresponding to a property of the form itself. The parameters
longitudo and
latitudo can vary or remain constant. Oresme 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. Oresme proved that this definition is equivalent to an algebraic 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 long precedes
Descartes in the invention of analytical geometry. In this doctrine, Oresme extends to figures of three dimensions.
Besides the longitude and latitude of a form, he considered the
mensura, or
quantitas, of the form, proportional to the area of the figure representing it. He proved this theorem: A form
uniformiter difformis has the same quantity as a
form uniformis of the same longitude and having as latitude the mean between the two extreme limits of the first. He then showed 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 made
Galileo a celebrated person in the seventeenth century. Moreover, this law was never forgotten during the interval between Oresme and Galileo because it was taught at Oxford by William Heytesbury and his followers, then at Paris and in Italy, by all the subsequent followers of this school. In the middle of the sixteenth century, long before Galileo, the Dominican Domingo de 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 . The 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 . In 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:
For instance, Oresme used this method in his musical section of the
Tractatus de configurationibus qualitatum et motuum in context of his “overtone or partial tone theory” to produce irrational proportions of sound in the direction of a “partial tone continuum” .
Finally Oresme was very interested in limits, threshold values and infinite series by means of geometric additions that prepared the way for the infinitesimal calculus of Descartes and Galileo. He proved the divergence of the harmonic series, using the standard method still taught in calculus classes today.
For Oresme’s anticipation of modern stochastic, see below under the heading of "Natural Philosophy".
As Taschow undoubtedly has shown, Oresme transformed the above-discussed graphic method of his
Tractatus de configurationibus qualitatum et motuum from the music-theory of his time. Hence, we come to Oresme’s very important contributions in the field of musicology:
Musicology
In Oresme's "
configuratio qualitatum and the functional pluridimensionality" associated with it, one can see that they 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 and intensio . The complex notational representations of music became, in Oresme's work,
configurationes qualitatum or
difformitates compositae, music functioning once more as the legitimating paradigm.
But the sphere of music did not only provide Oresme's theory with an empirical legitimating, 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 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, acoustical 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, Oresme 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 is 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 by
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 , 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 and a physical phenomenon represents an exceptionally rare case, both for the fourteenth century, at large, and 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. Oresme dealt nearly with every musicological area in the modern sense such as :
- acoustics ,
- musical aesthetics ,
- physiology of voice and hearing ,
- psychology of hearing ,
- musical theory of measurement ,
- music theory ,
- musical performing ,
- music philosophy .
With his very special „theory of species“ Oresme formulated the first and correct theory of wave-mechanics of sound and light, 300 years before
Christian Huygens where 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 and the relation between overtones and tone colour, 450 years before Joseph Sauveur. In his very detailed "physico-mathematical theory of partial tones and tone colour", Oresme anticipated the nineteenth century theory of
Hermann von Helmholtz.
In his musical aesthetics, Oresme formulated a modern subjective "theory of perception", which was not the perception of objective beauty of God’s creation, but the constructive process of perception, which causes the perception of beauty or ugliness in the senses. Therefore, one can see that 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 times, are closely bound up with the "Model Music" . 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
Because of the work of Taschow it is also known that Oresme was an outstanding psychologist. By using a strong empirical method, he investigated the whole complex of phenomena of the human psyche. Oresme was confident in the activity of "inner senses" and in the constructiveness, complexity and subjectivity of the perception of world. By using this quite progressive features, Oresme was a typical exponent of the "Parisian Psychological School" and his work was closely related with the scientists of optics . 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.
Oresme discovered the psychological "unconscious" and its great importance for perception and behaviour. On this basis, he formulated his inspired "theory of unconscious conclusions of perception" and his “hypothesis of two attentions“, concerning the conscious and an unconscious attention as seen in 20th century knowledge.
In his modern "theory of cognition", Oresme showed that no thought-content-like, categories, terms, qualities and quantities, out of human consciousness, exist. For instance, Oresme unmasked the so-called "primary qualities" such as size, position, shape, motion, rest etc. of the 17th century scientists , .), and argued that they were not 'objective' in outer nature, but should be seen as very complex cognitive constructions of psyche under the individual conditions of the human body and soul.
Because reality is only at the "expansionless moment" 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 the 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 hear a sound…" Sound is a human construction and nothing more.
In his modern "psycho-cybernetics" and "
information theory" Oresme solved the "dualism-problem" of the physical and the psychical world by using the three-part schema “
species -
materia -
qualitas sensibilis” of his brilliant "species-theory" . The transportable
species , like a
waveform of sound, changes its medium and the inner sense constructs by means of "unconscious conclusions" a subjective meaning from it.
Oresme had already developed 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 strongly mechanistic. Physical and psychical processes are equivalent in their structure of motion . Every structure has a qualitative and a quantitative moment; and therefore psychological processes can be measured like physical ones. In this way, Oresme supplied the first scientific legitimating of measurement of psyche and contra
Aristotle and the Scholastics) even of the 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 , where he examined every sense and cognitive functions. With the same method used by psychologists of the 20th century, namely by means of analysis of delusions and disorders, Oresme recognized already many essential laws of perception, for instance the "Gestaltgesetze" 500 years before Christian von Ehrenfels, limits of perception , etc.
Natural philosophy
Taschow’s work reveals also the very complex cosmos of Oresme’s philosophical thinking. Oresme anticipated many essential views of the self-image of modern times, such as, his insight into the incommensurability of natural proportions, into the complexity, the indetermination and the 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 was the Oresmian
machina musica. For Oresme the music analogously showed that, with a limited number of proportions and parameters, someone could produce very complex, infinitely varying and never repeating structures . That is the same message as of the “
chaos theory” of the 20th century where the iteration of the simplest formulas produce a highly complex world with no predictably of behaviour.
Based on the musico-mathematical principles of incommensurability,
irrationality and complexity, Oresme finally created a dynamic structure-model for the constitution of substantial species and individuals of nature, the so-called "theory of
perfectio specierum" .
By means of using an analogy of the musical qualities with the “first and second qualities” of
Empedocles, an Oresmian individual turns into a
self-organizing system which takes the trouble to get to his optimal system state defending against disturbing environmental influences. This “automatic control loop” influences the substantial form , already present in the modern sense, in the principles of biological
evolution, "adaptation" and "mutation" of genetic material.
It is quite evident, that Oresme’s revolutionary theory overcame 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 investigation 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 and mathematical fields:
For instance, Oresme laid down two psychological rules . The first rule says: With an increase in the number of unconscious judgments of perception grows the probability of misjudgements and in this way, the probability of errors of perception. The second rule says: The more the number of unconscious judgments of perception exceed a diffuse limit, the more improbable is a fundamental error of perception because it 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 grey 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 . Oresme states: "If we take a finite multitude of positive integers, then 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 probable that this number is not a cube. It is like in game , where somebody asks whether a hidden number is a cube. One has more surety to answer with ‘No’ because this seems to be more probable .
Oresme than looked at a multitude of 100 different mathematical objects that he had formed in a certain way, and he determined that from it : 2 = 4950 combinations from each two elements can be formed. From those, 4925 show a certain interesting quality E, whereas the remaining do not have this quality E. Finally, Oresme calculated the quotient 4925 : 25 = 197 : 1 and concluded from it that it is probable that, if somebody is looking for such an unknown combination, this will show the quality E.
Thus Oresme calculated the number of the favourable and the number of the unfavourable cases and their quotients. But yet, he did not have the quotient from the number of the favourable and the entire number of the equally-possible cases. He did not quite have our modern "measure of probability". But Oresme still had 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 even a long time after him, used these words in context of games and aleatory probabilities. We can find Oresme’s methods again later in
Galileo's and
Blaise Pascal's works in the 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., then it is more probable that the ratio of these two are irrational rather than rational. According to Oresme this theorem applies generally to the whole nature, to the earthly and to the celestial world. It has great effect on Oresme’s views of necessity and contingency, and in this way, of his view of the law of nature and his criticism of astrology.
It is obvious that Oresme was inspired for his "probability theory in physics, mathematics and perception psychology" from his work in music: The division of monochord proved the sense of hearing and the mathematical reason clearly that most of the divisions of chord produce irrational, i.e.
dissonant intervals.
Physics
Oresme’s physical teachings are set forth in two French works, the
Traité de la sphère, twice printed in Paris , 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 Aristotelian theory of weight, which said that the natural location of heavy bodies is in the centre of the world, and that of light bodies in the concavity of the moon's orb, Oresme countered by proposing the following: "The elements tend to dispose themselves in such a manner that, from the centre to the periphery their specific weight diminishes by degrees." Oresme thought that a similar rule may exist in worlds other than ours. 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 devoted the gloss following chapters xxiv and xxv of the
Traité du ciel et du monde. Oresme 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 showed that the reasons proposed by the physics of
Aristotle against the movement of the earth were not valid. Oresme than pointed out, in particular, the principle of the solution of the difficulty drawn from the movement of projectiles. Next he solved the objections based on the texts of Holy Scripture. In interpreting these passages he laid down rules universally followed by Catholic exegetics of the present day. Finally, he adduces the argument of simplicity for the theory that the earth moves, and not the heavens, and in the whole of his argument in favour of the earth's motion Oresme is both more explicit and much clearer than that given by
Copernicus.
Above, we were occupied with Oresme’s theory of wave-mechanics of sound and light. Therefore, it will not astonish us 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 more 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
overtones and tone colour Oresme analogized these musical facts with the phenomenon of mixture of colours on a rotating top.
We will close with Oresme’s genial discovery of the curvature of light through atmospheric
refraction: In his treatise
De visione stellarum Oresme asked if the stars are really where they seem to be. By using optics, Oresme answered that they are not. Two centuries before the Scientific Revolution, Oresme proposed the qualitatively correct solution to the problem of atmospheric refraction, that light travels along a curve through a medium of uniformly varying density, and he arrived at this solution using infinitesimals. Oresme concluded that nearly nothing in the heavens or on earth is seen where it truly is, calling all visual sense data into doubt. This solution had escaped both
Ptolemy and
Alhazen. It had even escaped
Kepler in the 17th century, and up to now, the credit for its first discovery has been given to
Robert Hooke and its mathematical resolution to
Isaac Newton.
These short excerpts of Oresme's enormous work show that he was one of the most innovative scientists in the "Spring of Modern Age" and a pioneer in the modern world.
See also
Footnotes
References
- Taschow, Ulrich. Nicole Oresme und der Frühling der Moderne: Die Ursprünge unserer modernen quantitativ-metrischen Weltaneignungsstrategien und neuzeitlichen Bewusstseins- und Wissenschaftskultur. Halle: Avox Medien-Verlag, 2003, 4 Books in 2 Volumes. ISBN 3-936979-00-6
External links
- Oresme Biography from which the above article was taken, with friendly authorization of its author Ulrich Taschow. There you can also find the complete bibliography of Oresme's work and many other materials on Nicole Oresme.
