2.2 Early & Medieval Physics

Or Was There Any Scientific Progress At All During the "Dark" Ages?

Working from Aristotle’s premise that celestial motion is circular, his successors developed a geocentric model for celestial motion. The result, attributed to Claudius Ptolemy (~AD 90–~168), yielded a remarkably accurate mathematical description of the relative motion of the planets with respect to the celestial firmament. In the simplest form, each planet rotates on a smaller orbit (an “epicycle”) whose center rotates on a larger orbit (a “deferent”), as shown in Figure 2.6.

Figure 2.6: The Ptolemaic model explained apparent planetary motion in terms of epicycles and deferents [[i]].

The Ptolemaic superposition of circular motions models the periodic retrograde motion of planets against the fixed stars to a respectable degree of accuracy. An arbitrarily good match to observations may be obtained by superimposing additional epicycles: more epicycles deliver better agreement.

Epicycles and deferents have a bad reputation in physics as ad hoc mechanisms that patch up an erroneous theory in overly complicated ways. That’s unfortunate, because the Ptolemaic model was truly an intellectual masterpiece. It illustrates the value of “superposition:” the notion that the whole, in this case the motion of the planets, may be broken down into the sum of its parts: the epicycles and deferents.

Even today, a fundamental concept in contemporary physics and engineering is “Fourier analysis,” in which sine waves of various amplitudes and frequencies are combined to yield an arbitrarily close match to an arbitrary time domain waveform. The frequency harmonics of Fourier analysis have no more actual reality than Ptolemaic epicycles and deferents. They merely provide a convenient model for understanding and analyzing more complex phenomena [[ii]]. The Ptolemaic model is similar in spirit, superimposing circular motions to create an arbitrarily good approximation to what we now know are the actual motions. Although the circular epicycles and deferents of the Ptolemaic model have long been exorcized from celestial mechanics, their intellectual offspring are alive and well and pervasive throughout engineering and science in the spectral harmonics of Fourier analysis.

The actual geometry of motion involves more than just the straight lines and circles of traditional Euclidean geometry, however. Around 200 BC, Apollonius of Perga (late third–early second centuries BC) drew together earlier work from Euclid (mid-fourth to mid-third centuries BC) and Archimedes (287–212 BC) to describe the geometry of motion: the geometry of conic sections [[iii]]. Unfortunately, much of this work was lost, and the science of motion would not incorporate conic sections for more than a thousand years.

The science of motion requires more complicated geometry: a class of curves called “conic sections.” One obtains conic sections from the intersection of cones and planes as in Figure 2.7. Consider a first plane with principal axes P₁-P₁’ and R₁-R₁’ orthogonal to each other and to the central axis A-A’ of the cone. The intersection between this orthogonal plane and the cone is a circle, as in Figure 2.7(a).

Consider a second plane with principal axes P₂-P₂’ and R₂-R₂’ orthogonal to each other. Rotate the second plane about axis R₂-R₂’ so that axis P₂-P₂’ is no longer orthogonal to the central axis A-A’ of the cone. The intersection between this tilted plane and the cone is an ellipse, also depicted in Figure 2.7(a).

Figure 2.7: Conic sections: (a) circle and eclipse, (b) parabola, and (c) hyperbolas.

Cone side axis C-C’ intersects plane axis P₂-P₂’. If we continue the rotation until axis P-P’ lies parallel to cone axis C-C’, the intersection between this plane and the cone is a parabola, as depicted in Figure 2.7(b). Continue the rotation further until axis P-P’ lies parallel to cone axis A-A’. The intersection between this plane and the cone is a hyperbola, as depicted in Figure 2.7(c).

As the French physicist Henri Poincaré (1854–1912) noted, “The savant must work with method; science is made of facts as a house of stones; but an accumulation of facts is no more a science than a pile of stones a house” [[iv]]. Aristotle’s conclusions were taken for granted. His methods were largely forgotten, until his scientific and philosophic works were re-introduced to the Western world in the thirteenth – that “greatest of centuries” [[v]].

There is a school of thought that the medieval period was a time of stagnation and superstition as progress lay dormant awaiting the renaissance and the enlightenment. “It will, therefore, be unnecessary to go into any detail respecting the history of the school philosophy of the thirteenth, fourteenth, and fifteenth centuries,” argued historian of science, William Whewell (1794–1866). “We may suppose it to have been, during the intermediate time, such as it was at first and at last” [[vi]]. Another writes, “The history of science in the Middle Ages makes but sorry reading. It was, so far as science is concerned, a period of ignorance, misunderstanding, and neglect” [[vii]]. Ernst Mach (1838–1916) in his classic The Science of Mechanics cites no authority after Archimedes (287–212 BC) and before Leonardo (1452–1519) [[viii]].

And yet, a variety of investigators emerged in the thirteenth century to build the foundations of modern experimental science from rediscovered Hellenic and Eastern wisdom channeled through Moorish Spain and elsewhere. The Dominicans (or “Black Friars”) took an early lead in scholarly achievement under the example of Saint Albert of Cologne or “Albertus Magnus” (~1200–1280). In addition to commentaries on Aristotle’s work [[x]], Albert’s works include some 20 volumes and 500,000 words on topics ranging from metals and minerals, mechanics, anatomy, and geography, to alchemy and chemistry [[xi]]. So popular were his lectures that there was no building large enough in Paris to contain the crowds who assembled to hear them, and Albert was compelled to lecture in the open air as shown in Figure 2.8 [[xii]]. Albert’s greatest legacy, however, was his students.

Figure 2.8: Albert of Cologne (~1200–1280) expounding his doctrines in the streets of Paris, 1245 [[ix]].

Doctor of the Church, Saint Thomas Aquinas (1224–1274) wrote the Summa Theologica and extensive commentaries on scripture and the works of Aristotle. He held that God reveals himself through nature, so to study nature is to study God. However, his approach relied heavily on formulaic syllogism. A typical question would be answered in four parts:

• Objections to the yet-to-be-stated conclusion;

• A counter-statement (beginning with “On the contrary…”) citing authorities like Aristotle, Church Fathers, or Scripture;

• The actual thesis (beginning with “I answer that…”); and;

• Replies to the thesis, as needed.

Aristotle and other great works of classical antiquity were becoming more widely available, thanks in large part to Albert and Thomas. However, a 1286 decree that the Dominicans must as a matter of policy defend the doctrine of Aquinas did not encourage creative inquiry [[xiii]]. And for centuries no university degree could be earned without knowledge of Aristotle’s works [[xiv]]. These policies and Aquinas’s reliance on formulaic syllogism hindered progress and reinforced the stereotype of the rigid, authority-bound Schoolmen, disconnected from physical reality.

In 1536, Pierre de la Ramée (1515–1572) presented a masters’ thesis arguing that everything Aristotle said was falsehood. “Petrus Ramus,” as he was known in Latinized form, successfully defended his audacious thesis against the united efforts of the faculty of arts to rebut him, thus earning his degree [[xv]]. A few years later in 1543, when Ramus published an attack on Aristotelian thinking, his books were condemned by the University of Paris and he was forbidden to lecture [[xvi]]. Ramus ultimately became a Protestant and perished in the 1572 Saint Bartholomew’s Day Massacre [[xvii]]. Figure 2.9 shows Thomas Aquinas and Petrus Ramus.

Figure 2.9: Thomas Aquinas (1225–1274) left [[xviii]], and Petrus Ramus (1515–1572) right [[xix]].

The treatment Aristotle suffered at the hands of some of his medieval adherents is parodied by Molière in his 1673 play Le Malade imaginaire. A bachelor candidate in medicine being grilled by doctors offers the following pseudo-Aristotelian answer:

The learned doctor asks me
The cause and reason why
Opium produces sleep?
To which I answer
Because it possesses
A dormitive power
Whose nature it is
To bring drowsiness to the senses [[xx]].

The doctors judged this a brilliant response. The shadow of an Aristotelian explanation is maintained by reference to a causal “power” and the “nature” of this power. Having been stripped of Aristotle’s demand for “experience” and his requirement of an “intimate association with nature and its phenomena” however, the explanation is cut off from reality, reduced to Platonic sophistry, an appeal to occult or hidden powers. The overthrow of this scholastic misinterpretation and corruption of Aristotle required a return to Aristotelianism: a renewed emphasis on the lessons to be learned and the conclusions to be drawn from a careful examination of the evidence available in nature. That revolution was already underway in parallel with the Schoolmen’s syllogisms, thanks to another student of Albertus Magnus.

Roger Bacon (~1220–1292) began his studies at Oxford under the Franciscan friar, Robert Grosseteste (~1168–1253). Grosseteste made a careful study of the Greek language with the assistance of a Greek monk fluent in the language [[xxi]]. He championed the application of mathematical methods to science, particularly optics, and the necessity to test the results of deductive reasoning by observation and experiment [[xxii]]. Grosseteste proposed a two-step method: “first, a combination of induction and deduction, which he called ‘resolution and composition,’ for arriving at definitions; and secondly, what he called verification and falsification” by which those definitions could be evaluated [[xxiii]].

Figure 2.9: Robert Grosseteste (~1168–1253) left [[xxiv]], and Roger Bacon (1219 – 1292) right [[xxv]] with an optical experiment.

Bacon completed a course of study at Oxford, followed by studies at the University of Paris under Albertus Magnus and others before returning to Oxford in 1250. After the death in 1253 of his patron and protector, Grosseteste, Bacon fell out of favor. Figure 2.9 shows Grosseteste and Bacon.

Having become a Franciscan and falling under their discipline, Bacon “wrote with more candor than tact” on the subject of educational reform. His superiors prohibited him from lecturing and ultimately dispatched him to Paris in 1257 and confined him for his critical views. In 1265, the election of Pope Clement IV (1190–1268) opened a window of opportunity. Bacon appealed to the Pope and was ordered to explain his philosophy and methods. In eighteen months, he wrote three long treatises, Opus Maius, Opus Minus, and Opus Tertium, on which his fame largely rests. Released, Bacon returned to Oxford in 1268 and began another period of productive research. The death of Clement IV in 1268 lost Bacon another protector, and in 1278 Bacon’s work on such topics as experimental optics, “burning glasses,” and gunpowder led to the condemnation of his writings and another long confinement during which he nevertheless remained an active scholar. Bacon was released in 1292 and spent his few remaining days at peace in Oxford [[xxvi]].

Despite his challenging career, Bacon continued and extended upon Robert Grosseteste’s advocacy of observational and experimental science. Even Whewell, who argued medieval scholastic philosophy was “such as it was at first and at last,” acknowledged:

Roger Bacon's works are not only so far beyond his age in the knowledge which they contain, but so different from the temper of the times, in his assertion of the supremacy of experiment, and in his contemplation of the future progress of knowledge, that it is difficult to conceive how such a character could then exist [[xxvii]].

The school of thought founded by Grosseteste and Bacon “championed independence of judgement and first-hand knowledge, the study of languages and physics, rather than dependence on authority, and its influence was still alive in the [Franciscan] Order in the fourteenth century,” inspiring such figures as John Duns Scotus (1265–1308) and in particular, William of Ockham (1287–1347), who championed common sense, direct observation, and induction [[xxviii]].

In the 14^th century, the kinematics of uniform and varying motion was already commonly known and taught at Oxford [[xxix]]. Extensive studies by French scientist and historian Pierre Duhem (1861–1916) demonstrate the main kinematical properties of uniformly accelerated motions (still attributed to Galileo by most physics texts) were discovered and proved by scholars at Oxford between 1328 and 1350 [[xxx]]. That body of scientific discovery quickly diffused throughout France, Italy, and Europe in general despite the social upheavals accompanying The Black Death (1346–1353), which killed at least a third of the population [[xxxi]].

Seb Falk’s The Light Ages, offers a more pleasant story of the period centered around English monk, John of Westwyck (~1350–~1400). Surviving documentation suggests around 1393 he built a planetary equatorium or astrolabe, a sophisticated mechanical calculator for predicting planetary positions. Our knowledge of his work comes from a single surviving manuscript at first erroneously attributed to Geoffrey Chaucer (~1340s–1400) and only identified as the work of John of Westwyck in 2014 [[xxxii]]. Figure 2.10 shows a 1326 astrolabe similar to one described by Chaucer. The distinguished astronomer was also reputed to be an excellent poet.

Figure 2.10: The “Chaucer Astrolabe” dated 1326.

Next time, we discuss a fascinating transitional character between medieval and modern science: Francis Bacon (1561 – 1626).

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[i] Schantz, Hans G., The Art and Science of Ultrawideband Antennas, 2^nd ed., (Norwood, MA: Artech House, 2015), pp. 272-273. See: http://amzn.to/2vsQkFa.

[ii] Harmuth, Henning, Sequence Theory, New York: Academic Press, 1977, pp. 1-17. Harmuth’s Essay has been reprinted elsewhere as “The Dogma of the Circle.” See: https://amzn.to/3GM53Pj.

[iii] Boyer, Carl B., A History of Mathematics, 2^nd ed., New York: John Wiley & Sons, 1989, pp. 144-157. See: https://amzn.to/3RNhbG8

[iv] Poincare, Henri, Science and Hypothesis, (New York: The Science Press, 1905), p. 101. See: https://amzn.to/44qUDPl.

[v] Walsh, James J., The Thirteenth Greatest of Centuries, New York: Catholic Summer School Press:: 1913. See: https://amzn.to/44ESmja  

[vi] Whewell, William, History of the Inductive Sciences, From the Earliest to the Present Time, 3^rd ed. vol. 1 of 3, London: John W. Parker and Son, West Strand, 1857, p. 9. See: https://amzn.to/3NuZx7u.

[vii] Hart, Ivor B., Makers of Science Mathematics Physics Astronomy, London: Oxford University Press, 1924, pp. 52-4. See: https://amzn.to/41pbOQN.

[viii] Truesdell, Clifford A., Essays in the History of Mechanics, New York: Springer-Verlag, 1968, p. 27.

[ix] Albertus Magnus expounding his doctrines of physical science in the streets of Paris ca. 1245. Oil painting by Ernest Board. Wellcome Collection. Public Domain Mark. Source: Wellcome Collection. See: https://wellcomecollection.org/works/yqpycvye

[x] Whewell, William, History of the Inductive Sciences, From the Earliest to the Present Time, 3^rd ed. vol. 1 of 3, London: John W. Parker and Son, West Strand, 1857, p. 326. See: https://amzn.to/3NuZx7u.

[xi] Walsh, James J., The Thirteenth Greatest of Centuries, New York: Catholic Summer School Press, 1913, p. 46. See: https://amzn.to/44ESmja  or see: https://www.google.com/books/edition/The_Thirteenth_Greatest_of_Centuries/_rofAAAAIAAJ

[xii] Vaughan, Roger William Bede, The life and labours of saint Thomas of Aquin., London: Burns and Oates, 1875, p. 87.

[xiii] Previte-Orton, C.W., The Shorter Cambridge Medieval History, vol. 2, Cambridge: At the University Press, 1966, p. 676. See: https://archive.org/details/shortercambridge0002cwpr.

[xiv] Whewell, William, History of the Inductive Sciences, From the Earliest to the Present Time, 3^rd ed. vol. 1 of 3, London: John W. Parker and Son, West Strand, 1857, p. 327. See: https://amzn.to/3NuZx7u.

[xv] Waddington, Charles, RAMUS: PIERRE DE LA RAMÉE SA VIE SES ÉCRITS ET SES OPINIONS, Paris: Librairie de Ch. Meyrueis et Ce, Editeurs, 1855, p. 28.

[xvi] Whewell, William, History of the Inductive Sciences, From the Earliest to the Present Time, 3^rd ed. vol. 1 of 3, London: John W. Parker and Son, West Strand, 1857, p. 327. See: https://amzn.to/3NuZx7u.

[xvii] Whewell, William, History of the Inductive Sciences, From the Earliest to the Present Time, 3^rd ed. vol. 1 of 3, London: John W. Parker and Son, West Strand, 1857, p. 429. See: https://amzn.to/3NuZx7u.

[xviii] Crivelli, Carlo, “Saint Thomas Aquinas,” 1476. See: https://commons.wikimedia.org/wiki/File:Polittico_del_1476,_s._tommaso_d%27aquino.jpg

[xix] Board, Ernest, “Roger Bacon in his observatory at Merton College, Oxford. Oil painting.” Wellcome Collection. Source: Wellcome Collection. See: https://wellcomecollection.org/works/ej92m7hc/images?id=w74kp37m

[xx] Park, David, The How and the Why, (Princeton, NJ: Princeton University Press, 1988), p. 187. See: http://amzn.to/2GyPCK0

[xxi] Hart, Ivor B., Makers of Science Mathematics Physics Astronomy, London: Oxford University Press, 1924, pp. 52-4. See: https://amzn.to/41pbOQN.

[xxii] Previte-Orton, C.W., The Shorter Cambridge Medieval History, vol. 2, Cambridge: At the University Press, 1966, p. 1096. See: https://archive.org/details/shortercambridge0002cwpr.

[xxiii] Crombie, A.C., Robert Grosseteste and the origins of experimental science, 1100-1700, Oxford: Clarendon Press, 1953, p. 61.

[xxiv] Bishop Robert Grosseteste, window on the South transept Westernmost. St Paul's Parish Church, Morton, Near Gainsborough. See: https://en.wikiquote.org/wiki/Robert_Grosseteste#/media/File:Bishop_Robert_Grosseteste,_1896.jpg

[xxv] Board, Ernest, Roger Bacon in his observatory at Merton College, Oxford. Oil painting. Wellcome Collection. Source: Wellcome Collection. See: https://wellcomecollection.org/works/ej92m7hc/images?id=w74kp37m

[xxvi] Hart, Ivor B., Makers of Science Mathematics Physics Astronomy, London: Oxford University Press, 1924, pp. 60-1. See: https://amzn.to/41pbOQN.

[xxvii] Whewell, William, History of the Inductive Sciences, From the Earliest to the Present Time, 3^rd ed. vol. 1 of 3, London: John W. Parker and Son, West Strand, 1857, p. 326. See: https://amzn.to/3NuZx7u.

[xxviii] Previte-Orton, C.W., The Shorter Cambridge Medieval History, vol. 2, Cambridge: At the University Press, 1966, p. 1096. See: https://archive.org/details/shortercambridge0002cwpr.

[xxix] Dugas, René, A History of Mechanics, New York: Dover, 1988, p. 68. Originally published 1955. See: https://amzn.to/4822YuM.

[xxx] Truesdell, Clifford A., Essays in the History of Mechanics, New York: Springer-Verlag, 1968, p. 30.

[xxxi] Previte-Orton, C.W., The Shorter Cambridge Medieval History, vol. 2, Cambridge: At the University Press, 1966, p. 847. See: https://archive.org/details/shortercambridge0002cwpr.

[xxxii] Falk, Seb, The Light Ages, New York: W.W. Norton & Company, Inc., 2020. See: https://amzn.to/4726qUL.