Showing posts with label medieval science. Show all posts
Showing posts with label medieval science. Show all posts

Friday, December 27, 2024

The Light Ages: The Surprising Story of Medieval Science

It is difficult to know when to accept history on its own terms. We tend to not condemn the ancient Greeks, Romans, or Jews for having slaves, though we hold the ante-bellum South culpable. I was not surprised by Seb Falk’s story about Brother John Westwyk’s productive labors in mathematical astronomy and the consequential instrumentation of measurement for those works. But I was enlightened by the search for and discovery of the man who wrote an astronomy text commonly credited to Geoffrey Chaucer. 

Chaucer did author A Treatise on the Astrolabe. It was Dompnus Johannes de Westwyke (Brother John of Westwick) who created Equatorie of the Planetis, a book that had been credited to Chaucer. So, Seb Falk interleaves two stories here: the life of Brother John as best it can be built from scant records; and the development of astronomy (and, generally, science) in the Middle Ages. 

Reading this book the first time through, I knew that I would annotate post-its to bookmark passages. The second time through the book, it soon became clear that I should just copy the whole thing here—which, of course, is not allowed.

“Far from the stereotype of a stagnant scientific environment which did no more than preserve the ideas of the ancients, computists in the twelfth and thirteenth centuries continued to refine their astronomical models, with ever more accurate estimates of the solar and lunar cycles. Scholars became more outspoken in their criticism of the increasingly unrealistic ecclesiastical calendar. In the 1260s Franciscan friar and proponent of empirical science Roger Bacon wrote, at the Pope’s request, a series of tracts on educational reform.” (page 74) 

To compute, you must have a computer. God gave you ten fingers, each with two knuckles. Supported and enhanced with recipes for rapid mental arithmetic, you could calculate the rising and setting of the Sun for your locale—and you could measure musical harmonies, also. If you were enrolled at a university in 1325, to complete a bachelor’s degree required completing the Trivium of Logic, Rhetoric, and Grammar; the master’s degree required the Quadrivium of Geometry, Arithmetic, Music, and Astronomy. But attending one of the newly founded universities was expensive. So, monasteries most often paid for a limited education after which the motivated monk studied (and wrote) on his own—and sometimes her own (page 73). 

 

One result of that was that no two books are exactly the same. Copyists used the intentionally available spaces to add their own amendments and emendations, expanding, explaining, and correcting. Books lived. (ref. esp. pages 77 and 124). Knowing this, and expecting that copies will be carried to other places, Brother John Westwick cautioned the next one building an equatorie from his plans: “Nota I conseile the ne write no names of signes til that thow hast proved this commune centre defferent is trewli and justli set.” (Illustration 7.9).


The Light Ages: The Surprising Story of Medieval Science by Seb Falk; W. W. Norton & Company, New York, 2020. (Published in the UK as The Light Ages: A Medieval Journey of Discovery; W. W. Norton & Company, London, 2019.) W. W. Norton's webpage mentions the Best Book awards from The Times, The Telegraph, and BBC History Magazine. I learned of it because it garnered the AAS Historical Astronomy Division Osterbrock Book Award for 2024.


One thread not followed here, which I considered important, is that the manuscript under discussion was first rediscovered by Derek Price deSolla. Price deSolla is also credited with the first rigorous examination of the Antikythera Mechanism (NecessaryFacts here.) No mention of that appears in this book.

 

Previously on Necessary Facts

Science in the Middle Ages 

Astronomical Symbols on Ancient and Medieval Coins 

Galileo’s Two Sciences 

Rescuing Aristotle and the Church 

Copernicus On the Revolution of Heavenly Bodies 

 

 

Monday, November 27, 2017

Joy Hakim's "Aristotle Leads the Way"

Intended for children, The Story of Science: Aristotle Leads the Way by Joy Hakim has many small problems throughout but remains valuable for its sense of life. The author encourages understanding, exploration, discovery, and the integration of knowledge. You can find it remaindered online at prices low enough to gift an entire class of 5th graders, if you choose. Though intended for youngsters, nothing is dumbed down. So the book is enjoyable at an adult level.

The Story of Science: Aristotle Leads the Way 
by Joy Hakim, Smithsonian Books, 2004.
 The consistent problem is the lack of nuance and insight. Joy Hakim just repeats common claims about the ancient Greeks and science in the Middle Ages. She mentions Hypatia of Alexandria, but says nothing about her being the likely last and best editor of Ptolemy’s work. She never acknowledges Aspasia of Miletus. And like almost everyone else, she accepts and asserts that the ancient philosophers did not think it necessary to test theories but attempted all knowledge through pure logic.

Despite those problems and their consequences in presentations from cover to cover, the rich array of integrated facts should deliver years of engagement and encouragement to a young learner. Hakim does more than note the milestones; she reminds the reader of the road just traveled; and she looks to the next horizon.

Detail of Raphael's School at Athens.
Plato points to the sky,
Aristotle reaches for the world.
http://www.museivaticani.va/
Through lavish illustrations, and insightful narratives, she presents the mathematics needed at a level that can be grasped with arithmetic and geometry. Among the very many are the Pythagorean theorem (of course), how Aristarchus estimated the distance to the Moon, Democritus’s formula for the volume of a cone, the true nature of the cone as explained by Apollonius of Perga, and the work done by the lever of Archimedes. Occasional timelines remind us that knowledge is passed across generations to those who cared to learn or rediscover.

Writing about Thomas Aquinas, “An ‘Ox’ Who Bellowed” (Chapter 20), Hakim says:
“In the thirteenth century, Paris is the place to be, if you like tumult and activity. While most of Europe is still feudal, Paris is the center of an emerging market economy. Old ideas are being blown away. … Change is both energizing and upsetting. The feudal world was known. What a free, capitalist world might be like is unknown. It seems to offer little security or control. But there is no stopping the new forces. … In the monasteries, clerics are focused on saving their souls through prayer study and isolation. When it comes to science, they quote Pythagoras, Plato, and Augustine. That trio all concentrated, in one way or another, on ideal forms in nature, which often kept them from considering the real world. But at the budding universities, new scholars, inspired by the rediscovery of Greek science, are interested in understanding the forces of nature. Those new scholars are fascinated by Aristotle. Aristotle looked at the world about him and observed, made notes, and classified its inhabitants—plant and animal.” (page 229-230)
—NSTA Recommends
Teacher’s Guide

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Monday, November 20, 2017

COPERNICUS ON THE REVOLUTION OF HEAVENLY BODIES

It was not just that Copernicus put the sun at the center of the heavenly system. His book asserted modern ideas about the relativity of motion, the acceleration of falling bodies, and the nature of the planets. It is also true that many of his arguments are archaic, typical of the medieval scholasticism that rested on the ancient Greeks. Nonetheless, his heliocentric model changed not just how people viewed the universe, but how they thought about it.
That motion is relative was known to the Greeks. Copernicus cites the Aeneid on the point-of-view that the land slips away as the ship moves past it. (page 519, EB “Great Books” edition). Fire burns brighter at lower altitudes; and when carried to higher altitudes, the fire dies down. (Book I Section; 8. 520, EB). Copernicus says as a matter of fact, not argument, that the planets are “dark bodies” that shine by reflected light. (Book I Section 10; Page 521 EB).

In our era, in school, we learn that Galileo discovered that bodies accelerate when they fall, contrary to Aristotle’s claim that they fall at a constant velocity, determined by their weight.  In fact, Copernicus acknowledged the acceleration of free fall.  In the original edition, Copernicus wrote: “Et quaecunquae decidunt a principio lentum facientia motu velocitatem augent cadendo.” That is rendered today as: "And those which fall downward possess a slow movement at the beginning but increase their velocity as they fall."(Book I Section 8. Page 520 EB)  See also Book III Section 3 where he mentions the motion of a pendulum being faster at the bottom of the arc and slower at the tops.

The acceleration of a body in free fall apparently was known to the “Oxford calculators” of the Merton School who worked about 1325-1350.  They developed a geometric solution for the “mean rate.” The “mean rate” is the average of the initial velocity and the final velocity. Galileo cited their results in The Two New Sciences, Third Day, Theorem I, Proposition I.

Most of On the Revolution of Heavenly Spheres is tedious for anyone not passionate about the geometric arguments. Copernicus had to prove his claims to the thinkers of his time in the language of their culture. The same was true of Newton’s Principia. Richard Feynman attempted to recreate a proof for his own lecture and found that he could not because he did not know enough geometry: we do it all with calculus now. Copernicus provides extensive ephemeris tables of his own measurements. But he also worked out trigonometric tables of “half-sines.” (We call it the “sine” in school, but it is actually the half.)  And he showed how his sun-centered circles explain all of the apparent motions in longitude, oppositions, retrograde, etc. And he often cited Ptolemy, who also made good measurements of the same events.

Copernicus’s On the Revolution of Heavenly Spheres is easily available in modern translations. Several archives have full scans of the original 1543 publication.
Made available electronically by the NASAAstrophysics Data System (ADS) 
The ADS wishes to acknowledge the Lehigh University, Digital Library ("The Problem of the Planets") for providing the scans of the book. (http://digital.lib.lehigh.edu/planets/ )

The Smithsonian also has one of the 1543 editions in its Dibner collection. (See https://airandspace.si.edu/exhibitions/explore-the-universe/online/kiosks/dibner/) The image title says: Nicholas Copernicus, De Revolutionibus Orbium Coelestium Libri VI (Basel, 1543), but the title page says “Norimbergae” i.e., “Nuremberg.”

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Monday, February 23, 2015

An Abundance of Talent: the 2015 Austin Energy Regional Science Festival

For the fourth time, I served as a judge for behavioral and social sciences in our local science fair.  Again, I met an array of talented and motivated teenagers.  They were intelligent (of course), actively curious about the world around them, willing to step out from the crowd and put themselves in the scales to be judged.  They asked interesting questions and pursued the answers wherever the data took them.  But they were, after all, children.  Some of them assumed far too easily that an experiment that does not validate the hypothesis is therefore a failure.  They never heard of Karl Popper.  That failing is not theirs, but of their mentors – or the lack of them. 
Middle school (junior high) presentation
on noise levels in the school building
 I am pleased and proud to have argued for the first place winner in senior high school  behavioral and social sciences. (See all of the Awards here.) One of the judges said that when he challenged her on a point of mathematics, she did not have the answer.  I responded with some history: last year, she asked every one of the mathematics and science teachers in her high school for help with statistics and she got no replies to her emails. So, she went to the university; and some UT doctoral candidates tutored her in statistics.  So, too, this year, did she seek and find outside help in order to extend and expand her work in statistical methods.  Personally, I was the one who was challenged.  I got an A-minus in my undergraduate class in statistics.  After reading her abstract this year, I downloaded several tutorials: she knew more than I did.
 
Middle School enquiry into which advertising
message draws the most responses
We expect a lot from kids. The German word for “teenager” is Halbstark: half-strong.  That speaks to the core of the problem in a way that the Latin “adolescent” (becoming adult) does not.  My daughter had a mole on her wrist; and she would show me how it moved around as she grew.  For them, life is an intense process.  We judge them as if they were adults.  As a geometer would say, it is obvious by inspection that they are not. Yet, objectively, nothing less is fair to them in the intellectual pursuit of science.
 
Classical, country, dub step, meditation, or pop:
does any help you concentrate on a task?
“If you all were graded on a 100-point scale, 91 would be failing.”  As often as I said it, I could see that it did not sink in, not this year, not in the previous years. This year, I asked one panicked entrant if any other display was clearly head and shoulders better than hers.  The person with the neighboring display chimed in: “The right answer is ‘No.’” 
 
Middle School entry: What is Your "Pawsonality"?
Can a psychological profile predict your preference for a pet?
It is not just kids at science fairs.  I enter and I judge museum quality exhibits at numismatic conventions.  (“Four out of five? How dare they!”)  In the West Wing episodes that bridge the first and second seasons, President Jed Bartlett says that decisions are made by those who show up.  In this context, the future of science, engineering, and technology belongs to – and will be claimed by – those who enter the competitive field of scientific research.
 
Another middle school entry on the Stroop Effect.
This took second place.
The value in this for the learner is figuring out how to
create a novel experiment and enter it in a competition.

The best of them do it alone; but they all deserve mentoring.  That 9-point gap between first and last could easily be closed by a working technician, engineer, or scientist who made the time to volunteer with a school starting in August or September. It is not a matter of showing them how, but of asking science-talented pupils those tough questions early on. 

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Friday, August 3, 2012

Science in the Middle Ages

Objectivists value the scientific method as the cornerstone of the engineering achievements of our civilization from structural trusses and direct current to alternating current and cybernetics.  We too easily see the Middle Ages as a time of ignorance and barbarism in which learning was chained to (and by) theology.  The reality is more complicated.

“The Middle Ages was a period ruled by the Witch Doctor, in a firm, if mutually jealous alliance with Attila. The Witch Doctor controlled every aspect of human life and thought, while the feudal Attilas looted one another’s domains, collected material tributes from serfs – who worked, lived, and served in subhuman conditions – and maintained the power to burn heretics at the stake.
“Philosophy, in that era, existed as a “handmaiden of theology,” and the dominant influence was, appropriately, Plato, in the form of Plotinus and Augustine. Aristotle’s works were lost to the scholars of Europe for centuries. The prelude to the Renaissance was the return of Aristotle via Thomas Aquinas.” – Ayn Rand, “For the New Intellectual.”

Astronomy, in particular was not dormant, nor could it be.  The problem of Easter required bringing lunar and solar calendars into alignment.  Whether biology, botany, and medicine had any hint of modernism is a difficult question, but can only be answered with direct citations to contemporary works.  Like the revolution of the Earth on its axis and the orbit of the Earth about the Sun, proof contrary to spontaneous generation did not come until the 1840s. As with astrology versus astronomy, it is too easy to dismiss alchemy as not being "real" chemistry. While its paradigms are not ours, the practices were utilitarian: dying wool and leather were important crafts. Paints, pigments, and finishes also were consequential.

“Historians have long recognized that the rebirth of science in twelfth-century Europe flowed from a search for ancient scientific texts. But this search presupposes knowledge and interest; we only seek what we know to be valuable. The emergence of scholarly interest after centuries of apparent stagnation seems paradoxical. This book resolves that seeming contradiction by describing four active traditions of early medieval astronomy: one divided the year by observing the Sun; another computed the date of Easter Full Moon; the third determined the time for monastic prayers by watching the course of the stars; and the classical tradition of geometrical astronomy provided a framework for the cosmos. Most of these astronomies were practical; they sustained the communities in which they flourished and reflected and reinforced the values of those communities. These astronomical traditions motivated the search for ancient learning that led to the Scientific Renaissance of the twelfth century.” (Astronomies and Cultures in Early Medieval Europe by Stephen C. McCluskey. Cambridge University Press,  1997.) 

“Measurements by clepsydras prove … that although the earth is at the center of the universe, it is eccentric to the sun's orbit. At times the sun is borne at a greater distance from the earth than at other times. When the sun is climbing upwards in Cancer and Gemini, in the steeper tracts of its course, it takes longer, lingering 32 days in Gemini; but it requires less time in the lower tracts, 28 days in Sagittarius, the elapsed time for the other signs varying between those extremes (848-849) . “Dominant Traditions in Early Medieval Latin Science” by William H. Stahl, Isis, Vol. 50, No. 2 (Jun., 1959), pp. 95-124. 

Mean Speed from the Oxford
Calculators used by Galileo
"The sorry state of scientific studies at the close of the Roman Empire in the fifth century reflected Roman, not medieval, failures and short-comings." "How Science Survived: Medieval Manuscripts as Fossils” by Sharon Larimer Gilman and Florence Eliza Glaze. Science, New Series, Vol. 307, No. 5713 (Feb. 25, 2005), pp. 1208-1209.

“The dominant explanation of human behavior at this time was astrology.  Charles, like most of his contemporaries, ruled with the advice of the recognized social scientists of the day, the court astrologers. In this vein Oresme was ordered by Charles to translate Ptolemy's Quadripartitum from Latin into French. This order discharged, Oresme then attempted to debunk the popular conceptions in an attack on judicial astrology, Contra judiciaros astronomos (1360), which he later translated into French. There is no hint in the historical record that Oresme's efforts altered the predominance of astrology in the determinance of social policy; indeed, he returned to the attack ten years later with a treatise entitled Contra divinatores horoscopios, and in a series of Quaestiones (a stylized form of question and answer popular with academicians of the period).”
“Nicole Oresme and Medieval Social Science: The 14th Century Debunker of Astrology Wrote anEarly Monetary Treatise” by Kevin B. Bales, American Journal of Economics and Sociology, Vol. 42, No. 1 (Jan., 1983), pp. 101-111.

“WHEN historians and historians of science flatly state that Ptolemy's Almagest and Geography dominated the fields of astronomy and geography for fourteen centuries, they are apt to mislead unwary readers into supposing that Ptolemy was the supreme authority in Latin science during that period. Quite the contrary, his works might almost as well never have been written for all the influence they had in the Latin West until translations were produced from Greek or Arabic texts in Toledo and Sicily in the twelfth century.' If there was any dominant tradition of Latin science in the first thirteen centuries of the Christian Era, it was a stream of encyclopedic literature, the main course of which may be traced backwards through the Latin encyclopedist Varro and the Platonizing Stoic Posidonius; to trace sources beyond them is difficult indeed. In any case it is well to bear in mind that this stream of encyclopedic works skirts around Ptolemy without being appreciably influenced by him. We can trace its course through the extant writings of Pliny, Theon of Smyrna, Cleomedes, Geminus, and numerous others.

“Of the three, Martianus Capella offers the best account of encyclopedic science and will be discussed first. He seems to have flourished in the first half of the fifth century.  Martianus Capella wanted to produce an encyclopedia in the Varronian tradition and, by excluding two of Varro's disciplines, medicine and architecture, laid the foundation of the medieval trivia and quadrivia.

The first work of Archimedes translated into Latin was the Measurement of the Circle. It was translated from the Arabic twice in the twelfth century.' The first translation, which I have argued (but not surely) was done by Plato of Tivoli, was most inferior; just three manuscripts are known, only one of which is medieval. Apparently not long after this first translation the great translator Gerard of Cremona again used the Arabic text and rendered the Measurement of the Circle into Latin. This time the translation was quite accurate, and so before 1187 a faithful version of this short but important treatise became available. We are fortunate that this version was included in MS Bibliotheque Nationale, Fonds latin 9335, a handsome codex of Gerard translations. Incidentally, this manuscript is one of the best examples of intelligent copying of scientific works. It has marginal variant readings which cite alternate copies. The drawings are carefully made. Even more important the transcription of numbers - even of six places - is almost perfect. “The Impact of Archimedes on Medieval Science,” by Marshall Clagett, Isis, Vol. 50, No. 4 (Dec., 1959), pp. 419-429. 

"Among late thirteenth and fourteenth century philosophers, the Averroists have been particularly noticed by historians as advocates of the autonomy of the sciences. In arguing, for example, that physics might give an answer to the question of the eternity of the world different from the answer given in accordance with Christian belief, Boethius of Dacia based himself largely on a conception of physics as an independent discipline with its own principles, rational methods, and conclusions. This approach to the autonomy of the sciences was not, however, the only influential one in this period. Another basis for the autonomy of physics is found in the work of certain Oxford commentators on Aristotle's Physics, most prominently in William of Ockham's Expositio super octo libros Physicorum. This second approach makes physics autonomous by placing greatest confidence not in deductively and causally prior principles of physics, which some thought could be proved or made known by metaphysics, but rather in propositions accepted on the basis of experience, if not known in themselves. The primary evidence cited in the following paper." “The a Posteriori Foundations of Natural Science: Some Medieval Commentaries on Aristotle's Physics, Book I, Chapters 1 and 2” by Edith Dudley Sylla, Synthese, Vol. 40, No. 1, Jan., 1979, pp. 147-187.
 In The Logical Leap, Objectivist physicist and philosopher David Harriman denigrates medieval science. In Chapter 3 "The Mathematical Universe" under the subhead "The Birth of Celestial Physics" on page 85 (ppb), Harriman says that with the Ptolemaic Model, the relative sizes of the orbits of the planets could not be calculated.  That leads to an interesting contradiction.  If it is true that the Geocentric model prevents such calcuations, then they must have used some other model, because the relative sizes of the orbits were known.  On the other hand, perhaps the geometry and observations of the time did, indeed, allow them to make those calculations, even assuming the Geocentric model.  My reference for that is Astronomies and Cultures in Early Medieval Europe by Stephen McCluskey (Cambridge, 1998).  In fact, because of the religious viewpoint, the very scale of the measurable universe and the comparatively small size of the (spherical; not flat) Earth, were substantiating evidence to the relative unimportance of Earthly affairs. Saturn's orbit was estimated to be 72 million miles from Earth. (McCluskey, page 203).