That was my buddy the HISTSCI_HULK expostulating whilst he was indulging in his annoying habit of peering over my shoulder whilst I’m reading.
She never was! That’s simply wrong!
Hulky was getting his nickers in a twist about the following claim:
Hypatia was by all accounts, a fine astronomer and a first rank mathematician…[1]
He bleedin’ weren’t either! Exploded Hulky as he read further on:
…her father, an equally formidable mathematician…
Hulky is, of course, totally correct. Hypatia’s father was Theon of Alexandria and although such judgements are to a large extent subjective, in the normal run of things nobody would classify Theon as a formidable mathematician or Hypatia a fine astronomer and a first rank mathematician.
We start with Theon from whom Hypatia appears to have learnt and inherited everything. Theon was the head of a (note, not ‘the’) Neoplatonic school in Alexandria where he taught philosophy, mathematics and astronomy. The latter two being part of a basic Neoplatonic curriculum. Here Theon is a teacher of astronomy and mathematics not in any way a formidable mathematician.
Theon is most well known in the history of mathematics as the editor and commentator of an edition of the Euclid’s Elements. In fact, the only known Greek edition until a different one was found in the nineteenth century. He also produced commentaries on Euclid’s Data, his Optics and Ptolemaios’ Mathēmatikē Syntaxis. All of these are works of elucidation for students and it is more correct to call Theon a textbook editor.
Theon of Alexandria is best known for having edited the existing text of Euclid’s Elements, shown here in a ninth-century manuscript Vatican Library via Wikimedia Commons
Turing to Hypatia, she appears to have studied under her father and then went on to take over his position as head of his school, also teaching Neoplatonic philosophy with astronomy and mathematics as subsidiaries. Once again, a teacher not a fine astronomer and a first rank mathematician. Unlike Theon there are no known surviving publications by Hypatia.
The Suda, a tenth-century Byzantine encyclopaedia of the ancient Mediterranean world list three mathematical works for her, which it states have all been lost. The Suda credits her with commentaries on the Conic Sections of the third-century BCE Apollonius of Perga, the “Astronomical Table” and the Arithemica of the second- and third-century CE Diophantus of Alexandria. Alan Cameron, however, argues convincingly that she in fact edited the surviving text of Ptolemaeus’ Handy Tables, (the second item on the Suda list) normally attributed to her father Theon as well as a large part of the text of the Almagest her father used for his commentary. Only six of the thirteen books of Apollonius’ Conic Sections exist in Greek; historians argue that the additional four books that exist in Arabic are from Hypatia, a plausible assumption[2]. So once again, what we have is that Hypatia was like her father a textbook editor.
The MacTutor article on Theon contains the following judgement:
Theon was a competent but unoriginal mathematician.
Although we have no direct evidence in her case, the same can almost certainly be said about his daughter, Hypatia. Both of them are Neoplatonic philosophy teachers, a philosophical direction that includes a basic amount of astronomy and mathematics. They both produced textbooks for students by editing existing standard texts and adding commentaries to aid understanding. There is absolutely no evidence that their mathematical competence went beyond this pedagogical level.
Because they both feature fairly prominently in the history of mathematics, people, and unfortunately, not just the quoted author make the lazy, unfounded assumptions that they are “a fine astronomer and a first rank mathematician” and “an equally formidable mathematician.” Assumptions that have absolutely no foundation in the known historical facts. Theon is famous because of his edition of Euclid’s Elements and Hypatia because she was brutally murdered, and not for their mathematical abilities.
I will, however, add, as a sort of footnote, that textbook authors and editors play a very important role in the history of a scientific discipline, a role that unfortunately, all too often, simply gets ignored in the standard accounts of the history of science.
[1] I’m not going to mention the source on this occasion because the assumption made here turns up time and again and has somehow become gospel. I will however be reviewing the book in question in due course.
[2] This paragraph is borrowed from an early blog post about Hypatia that I wrote.
In 1995, Dava Sobel, a relatively obscure science writer, published her latest book, Longitude:The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time[1]. Sobel is a talented writer and she relates with great pathos the tale of the humble, working class carpenter turned clock maker, John Harrison, who struggled for decades against the upper echelons of the establishment and the prejudices of the evil Astronomer Royal, Nevil Maskelyne, to get recognition and just rewards for his brilliantly conceived and skilfully constructed maritime chronometers, which were the long sort after solution to the problem of determining longitude at sea.
The book caught the popular imagination and became a runaway best seller, spawning a television series and a luxury picture book second edition. There is little doubt that it remains the biggest selling popular history of science book ever published.
There is, however, a major problem with Ms Sobel’s magnum opus, never one to let such a thing as the facts get in the way of a good story her book is for large parts closer to a historical novel than a history of science book. In order to maintain her central narrative of good, John Harrison, versus evil, the Board of Longitude and Nevil Maskelyne, Sobel twists and mutates the actually historical facts beyond legitimate interpretation into a warped parody of the actual historical occurrences.
From 2010 to 2015 the Maritime Museum in Greenwich and the Department for the History and Philosophy of Science at the University of Cambridge cooperated on a major research project into the history of the Board of Longitude under the leadership of Simon Schaffer for Cambridge and with Rebekah Higgitt and Richard Dunn as Co-investigators for Greenwich. The other participants were Alexi Baker, Katy Barrett, Eóin Phillips, Nicky Reeves, and Sophie Waring. This project produced a wonderful blog (archived here)[2], workshops, conferences, and public events. As well as creating a digital achieve of the Board of Longitude papers, the project produced a more public finale with the major travelling exhibition in the Maritime Museum, Ships, Clocks & Stars: The Quest for Longitude, in 2014 to celebrate the 300th anniversary of the Longitude Act. After Greenwich the exhibition was also presented in the Mystic Seaport Museum in Mystic, Connecticut, USA from 19 September 2015 to 28 March 2016, and the Australian Maritime Museum from 5 May 2016 to 30 October 2016.
To accompany the exhibition a large format, richly illustrated book was published, not a catalogue, Finding Longitude: How ships, clocks and stars helped solve the longitude problem by Richard Dunn and Rebekah Higgitt.[3] This volume, which I reviewed here, is wider reaching and much better researched than Sobel’s book and does much to correct the one-sided, warped account of the story that she presented. Unfortunately, it won’t be read by anything like the number who read Sobel.
In 2015 the project also delivered up the books Maskelyne: Astronomer Royal, edited by Rebekah Higgitt (The Crowood Press) and Navigational Enterprises in Europe and its Empires, 1730–1850 (Cambridge Imperial and Post-Colonial Studies) edited by Richard Dunn and Rebekah Higgitt (Palgrave Macmillan)
Now, the Board of Longitude research project has birthed a new publication, Katy Barrett’s Looking for Longitude: A Cultural History.[4] This text, originally written as a doctoral thesis during her tenure as a researcher in the Board of Longitude research project has been reworked and published as the volume under review here. However, potential readers need have no fear that this assiduously researched, and exhaustively documented volume is a dry academic tome, only to be taken down from the library shelf for reference purposes. Barrett takes her readers on a vibrant and scintillating journey through the engravings, satires, novels, plays, poems, erotica, religion, politics, and much more of eighteenth-century London.
Satire, plays, poems, erotica…? Isn’t this supposed to be a book about the history of the problem of determining longitude at sea and the solution that were eventually found to this problem? Regular readers of this blog will be aware of the fact that I’m a great supporter of the contextual history of science and technology. Historical developments in science and technology don’t take place in a vacuum but are imbedded in the social, cultural, and political context in which they took place. If you wish to truly understand those historical developments, then you have to understand that context. Katy Barrett has produced a master class in contextual history.
From the very beginning, following the passing of the Longitude Act, the problem of determining longitude and the search for a solution to this problem because a major social theme and eighteenth-century London and the term longitude became, what we would now term, a buzzword and remained so for many decades. It is this historical phenomenon that Barrett’s truly excellent book investigates and illuminates in great detail.
Barrett’s research covers a very wide range of topics with longitude turning up in all sorts of places and contexts. Following an introduction, What Was the Problem with Longitude, which sets out the territory to be explored and the reasons for doing so, the book is divided into three general sections, each divided into two chapters.
The first section deals with visual aspects of the longitude story. Chapter one being centred on cartographical problems and presentations. Chapter two takes us into the world of visual presentations of instruments on paper. A practice with relation to proposed solutions for the longitude problem led eventually to accurate, technical visual presentations becoming standard in patent applications, as Barrett tells us.
The second section views longitude as a mental problem with Chapter three showing how proposed solutions became viewed in the same way as other schemes proposed by the so-called projectors. Schemes designed to produce solutions to a wide range of intractable problems from the realms of finance, politics, religion etc. Here longitude acquired the dubious distinction of becoming compared to such perennial no-hopers as perpetual motion and the philosophers’ stone. Chapter four bears the provocative title Madness or Genius? And looks at the contemporary theories of madness and how they were applied to the proposers of solutions to the longitude problem in particular by the satirists.
The third section introduces the social problem. Chapter five has the intriguing title Polite or Impolite Science? Polite science introduces us, amongst other things, to the fascinating eighteenth century genre in which men explain the new sciences to ladies, a topic that, of course, includes the longitude problem. We also have much on the elegant and informative presentation of instruments and their usage through engravings. Impolite science takes the reader into the fascinating world of scientific erotica, in which both latitude and longitude are frequently used as euphemisms. The sixth and final offering, A Cultural Instrument, continues the metaphorical use of navigation instruments both in erotica and beyond.
It is impossible within the framework of this review to even begin to present or assess the myriad of visual and verbal sources that Barrett examines, analyses, and presents to the reader, woven together in an ever-exhilarating romp through, it seems, all aspects of educated London society in the eighteenth century, illuminating ever more fascinating aspects of the widespread longitude discussion.
Recurring themes that turn up again and again in the different sections of the book are the writings of the satirists, who made the eighteenth century a highpoint in the history of English literary satire, Swift, Arbuthnot, Pope, et al, the equally famous engravings of William Hogarth, and of course the struggles of carpenter turned clockmaker John Harrison, although here he is not presented as a lone hero but as just one of many struggling to present his ideas clearly to the Board of Longitude both visually in engravings and verbally in his writings.
The book has eighty-four captivating illustrations in its scant two-hundred and fifty pages. Here I have to say I have my only complaint. The illustrations are grayscale reproductions of engravings and unfortunately quite a few of them are so dark that it is extremely difficult to make out the fine details about which Barrett writes in her astute analysis.
The illustrations are listed and clearly described in an index at the front of the book. The seeming endless list of primary and secondary sources are included in a complete bibliography at the back, and the pages are full of footnote references to those sources. An index completes the academic apparatus.
I could fill another couple of thousand words with wonderful quotes that Barrett delivers up by the barrow load for her readers, but I will restrict myself to just one riddle:
“Why is a Woman like a Mathematician?”
Surely a riddle to rival Lewis Carroll’s immortal “Why is a raven like a writing desk?”
I shall not reveal the answer, for that you will have to read Katy Barrett’s wonderful book.
As regular readers will know I do a history of astronomy tour of the Renaissance city of Nürnberg. One of the stations on that tour is Fembo House, now the home of the museum of the city of Nürnberg.
Fembo House
From 1730 to 1852, it was the seat of the cartographical publishing house Homännische Erben, that is “Homann’s Heirs” in English. In its time the biggest cartographical publishing house in Germany and probably the biggest in Europe. For six years from 1745, it was the workplace of Tobias Mayer (1723–1762), who was the astronomer-cartographer, who solved the problem of determining longitude by the Lunar Distance method.
Tobias Mayer
He did the work on this during his time in Nürnberg. I talk on my tour about Sobel’s Longitude, which most of my visitors have heard of and even often read and explain why it’s bad and I recommend that they read Dunn& Higgitt’s Finding Longitude instead. In future I shall add that when they have finished that, they should then read Katy Barrett’s Looking for Longitude: A Cultural History!
[1] Dava Sobel, Longitude:The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Walker & Company, 1995
[2] Click on Show Filters then and then find Quest for longitude under the Explore Themes menu – all there, 2010-2015. Thanks to Becky Higgitt for helping me find where Royal Museums Greenwich had hidden them!
[3] Richard Dunn & Rebekah Higgitt, Finding Longitude: How ships, clocks and stars helped solve the longitude problem, Royal Museums Greenwich, Collins, London 2014
[4] Katy Barrett, Looking for Longitude: A Cultural History, Liverpool University Press, Liverpool, 2022
It was not only the philosophers in antiquity who laid down theories that would reappear in the Early Modern Period, as that which we now term physics began to be created, several Ancient Greek mathematicians made contributions that would go on to play a significant role in that creation; most notable are Eudoxus of Cnidus (c. 408–c. 355 BCE), Euclid (fl. [maybe?] 300 BCE), Archimedes (c. 287–c. 212 BCE), Apollonius of Perga (c. 240–c. 190 BCE), Hipparchus (c. 190–c. 120 BCE), and Ptolemaios (c. 100–c. 170 CE). In what follows I shall be taking a brief look at the work of Euclid and Eudoxus, taking Euclid first, although Eudoxus predates him and will deal with the others in later episodes.
To begin I will deal with the maybe above in the life dates of Euclid, which doesn’t refer to the dates but to the man himself. For a man, who supposedly wrote the most successful textbook of any sort in the history of the world, he is remarkably elusive. There are four books attributed to him–the Elements, Optics, Data, Phaenomena–and that is quite literally all that we know about the man:
In 1966, French mathematician Jean Itard, introducing a reissue of François Peyrard’s translation of the Elements, asserted that the book was the work not of an individual but of a group, a school, for which ‘Euclid’ was a collective name. (As it happens, a group of French mathematicians had been publishing under the name ‘Bourbaki’ since the 1930s, providing Itard with the relevant model for his claim about Euclid.) In the twenty-first century it is still sometimes said that the Elements is an accretive text for which there is no need to name an author.[1]
The Elements is a sort of geometrical encyclopaedia that incorporates and systemises the work of several others and as such, one can understand Itard’s thought process, but I shall simply assume that there really was a man, who lived around 300 BCE in ancient Greece, was named Euclid and was the author of the book we know of as the Elements.
In what follows I shall only be dealing with the Elements. I shall cover the Optics in a separate episode over Greek optics. To quote Wikipedia: “Data (Greek: Δεδομένα, Dedomena) is a work by Euclid. It deals with the nature and implications of “given” information in geometrical problems.” The subject matter is closely related to the first four books of Euclid’s Elements. As such it need not concern us here, which is also true of Phaenomena, which is a non-technical introduction to astronomy.
It is almost impossible to overemphasise the significance and importance of the Elements as a textbook in European science over a period of more than two thousand years, only giving way to other texts in the nineteenth century, much to the annoyance of Lewis Carrol, a mathematics lecturer at Oxford University, who wrote a superb play, Euclid and His ModernRivals[2], criticising this development.
Source: My private copy Details see footnote 2
Euclid’s wasn’t the first Elements (Στοιχεῖα, Stoicheia) to be written by an ancient Greek mathematician. The earliest known was written by Hippocrates of Chios (c. 470–410 BCE) of which only one fragment is known to exist embedded in the work of Simplicius of Cilicia (c. 480–c. 560 CE). Other Elements were supposedly written by Leon (fl. 370 BCE), Theudius (4th C BCE) and Hermotimus of Colophon (4th C BCE) all three mentioned by Proclus (412–485 CE). It can be assumed that just as Ptolemaios’ Mathēmatikē Syntaxisbecause it was so superior to all previous astronomy textbooks made them obsolete and they simply disappeared. Now known only through later hearsay or because Ptolemaios mentions them, so Euclid’s Elements made all previous geometry textbooks obsolete, and they too disappeared.
Because it was the only major mathematics textbook to survive antiquity. The opening books formed the geometry part of the quadrivium, the basic mathematical education on the medieval Latin schools and later the undergraduate curriculum on the medieval universities. This meant that, at least within science, if, over the centuries, scholars were doing mathematics they were mostly doing Euclidean geometry. This applies to John Philoponus in the sixth century, to the Oxford Calculatores and the Paris physicists in the fourteenth century, to Tartaglia, Benedetti, Copernicus, and Tyco Brahe in the sixteenth century, and even to Kepler and Galileo in the seventeenth century. The Euclidean element of Newton’s Principia is even greater, but I’ll deal with that in more detail later.
I would need a whole blog series to explain Euclid’s Elements in detail. It has thirteen books and Thomas Heath’s three volume, annotated, English translation runs to more than fourteen hundred pages. However, I will briefly cover some of the salient points that help to explain its longevity.
The first aspect of the Elements is its logical structure. In general, the mathematical propositions within it have proofs. This is new. If you look at the earlier mathematics of Mesopotamia, Egypt, or India there are no proofs. The propositions in these various early forms of mathematics are demonstrated and explained by worked examples. When you have a problem of this type, then you solve it in this way. To use a modern term the mathematics was algorithmic. This changes with Euclid, here mathematical propositions have proofs utilising deductive logic. Perhaps the most well-known example being his proof of the so-called Pythagorean Theorem, which Euclid does not attribute to Pythagoras.
One of the oldest surviving fragments of Euclid’s Elements, found at Oxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagram accompanies Book II, Proposition 5 Source: Wikimedia CommonsBook II Proposition 5 in the first printed edition of The Elementsprinted and published by Erhard Ratdolt in 1482Book II Proposition 5 in Thomas Heath’s translation of The Elements
More significant is the logical structure of the entire book. Book 1 opens with a set of basic self-evidently true concepts that require no proof on which the whole structure of the book is erected using step by step logical deduction, adding new definitions where necessary. The entire book has a coherent logical structure. If you accept the basics, then everything else follows logically and must therefore also be accepted. Caveat, critical examination in the nineteenth century, in particular by Moritz Pash (1843–1930) and David Hilbert (1862–1943), showed that many of Euclid’s definitions were inadequate and some of his logic suffered from lacuna but as the historian of mathematics W. W. Rouse Ball pointed out “the fact that for two thousand years [the Elements] was the usual text-book on the subject raises a strong presumption that it is not unsuitable for that purpose.”[3]
Of interest, is the fact that the Elements is the most obvious work from antiquity that fulfils Aristotle’s fundament epistemological concept: Starting from self-evident premises that require no proof one uses a chain of deductive logic until one arrives at empirically observed facts. This is ironical as Aristotle was fundamentally anti-mathematics because did not consider mathematical object as related in anyway to the real world. Some Aristotle fans argue that he was not anti-mathematics exactly because his epistemology was borrowed from mathematics.
Returning to Newton, not only is his Principia written in Euclidean geometry and not as often falsely assumed in the then new analysis that he helped substantially to create but the whole structure of the work mirrors the same epistemology as used by Euclid in the Elements. This form of epistemology, generally known today as the axiomatic method, is now well-known and widely used in many branches of science and mathematics. Two well known examples in the basics of mathematics are the Peano Axioms for the natural numbers, and the Zermelo-Fraenkel Axioms for set theory.
A short overview of the contents of the thirteen books:
Book I starts with five postulates, including the infamous parallel postulate, and five common notions continuing to cover basics of plane geometry ending with his proof of proposition 47, the Pythagorean theorem and proposition 48, its corollary.
Book II introduces the so-called geometric algebra i.e., presenting and solving algebraic propositions geometrically. It covers a lot of propositions about squares and rectangles, including the general solution of the quadratic equation. Euclid in the reason we use geometrical names quadratic, cubic etc. to refer to algebraic terms.
Book III moves onto circles.
Book IV construction of incircles and circumcircles of triangles and the construction of regular polygons with 4, 5, 6, and 15 sides.
Book V changes gear and we learn about the theory of proportion of magnitudes.
Book VI extends the theory of proportions to plane geometry and the construction of similar figures.
Book VII Elementary number theory, including the Euclidean algorithm for finding the greatest common divider and the lowest common multiple.
Book VIII deals with geometric series
Book IX is the application of Books VII and VIII and includes Proposition 20, Euclid’s elegant proof of the infinity of primes.
Book X deal with incommensurable magnitudes i.e., lines that cannot be used to measure each other, a geometrical presentation of irrational numbers. For example, the diagonal of a unit square, which has length √2, cannot be measured by the side.
Book XI applies Book VI to solid figures.
Book XII determines the volumes of cones, pyramids and cylinders using the method of exhaustion, showing, for example, that the volume of a cone is a third of the volume of the corresponding cylinder, and the volume of a sphere is proportional to the cube of its radius.
Book XIII Constructs and discusses the properties of the five regular Platonic Solids.
Having sketched the Elements, we can now turn our attention to Eudoxus of Cnidus (c. 408–c. 355 BCE) and the reason why we deal with him after Euclid, although he lived earlier. As we saw earlier in the episodes about Plato and Aristotle Eudoxus was the creator of the homocentric spheres model for modelling the orbits of the planets as viewed from the Earth, including a mechanism to recreate retrograde motion. However, Eudoxus was not just an astronomer, he was also an excellent mathematician, who can be counted alongside Archimedes as one of the best Ancient Greek mathematicians. Starting with Book V, much of the latter part of the Elements rests on mathematics created by him.
The theory of proportions, a powerful tool in the geometrical presentation of the Elements, and its subsequent application in other books is due to Eudoxus. Eudoxus’ theory of proportions provides a rigorous definition for the real numbers; a definition that inspired Richard Dedekind in developing his theory of Dedkind cuts. Eudoxus introduced the concept of incommensurable lengths as a replacement for working with irrational numbers.
The mathematics most closely associated with Eudoxus is the method of exhaustion, an early form of integration. It is claimed that the method was first propagated by Antiphon who used inscribed polygons with increasing numbers of sides to approximate the area of a circle. As is so often the case we don’t actually known who exactly this Antiphon was. He is mostly identified with Antiphon of Rhamnus (480–411 BCE) an orator but the identification is highly questionable. Eudoxus took over the theory and made it rigorous. In his hands and later those of Archimedes it proved a powerful tool, in particular for determining areas and volumes. The method of exhaustion was used to prove the following proposition in Book XII of the Elements:
Proposition 2: The area of circles is proportional to the square of their diameters.
Proposition 5: The volumes of two tetrahedra of the same height are proportional to the areas of their triangular bases.
Proposition 10: The volume of a cone is a third of the volume of the corresponding cylinder which has the same base and height.
Proposition 11: The volume of a cone (or cylinder) of the same height is proportional to the area of the base.
Proposition 12: The volume of a cone (or cylinder) that is similar to another is proportional to the cube of the ratio of the diameters of the bases.
Proposition 18: The volume of a sphere is proportional to the cube of its diameter.
Today, the names Euclid and The Elements are for most people just something to do with Ancient Greek mathematics, but, as already emphasised above, no other book in the history of humanity has had such a powerful influence on the discipline of mathematics and also those disciplines that used mathematics such as physics.
[1] Benjamin Wardhaugh, The Book of Wonders: The Many Lives of Euclid’s Elements, William Collins, 2020 ppb. p. 304 Wardhaugh’s book is an excellent guide to the more than 2000-year history of the Elements, you can read my review here.
[2] Lewis Carroll, Euclid and His Modern Rivals, Dover Books, NY, 1973
[3] W. W. Rouse Ball, A short Account of the History of Mathematics, MacMillan, 6th ed., 1915, p. 55
The magnetic compass was an important navigation instrument in the Early Modern Period, but it was not without its problems. In the last third of the sixteenth century a group of English navigators and scholars cooperated loosely in efforts to understand how the magnetic compass actually worked and to see if the known problems could be solved. The most famous of them was the physician William Gilbert[1] (1544?–1603), who published his ground-breaking De Magnete in 1600, an oft overlooked major contribution to the emergence of modern science in the seventeenth century.
William Gilbert artist unkown Source: Wikimedia Commons Title page De magnete 1st edition 1600 Source: Wikimedia commons
But Gilbert was by no means alone and as he himself acknowledges, in Book I Chapter I of his masterpiece, his work rests on the shoulders of a significant number of his countrymen:
There are other learned men who on long sea voyages have observed the difference of magnetic variation[2]; as that most accomplished scholar Thomas Harriot, Robert Hues, Edward Wright, Abraham Kendall, all Englishmen; others have invented and published magnetic instruments and already methods of observing, necessary for mariners and those who make long voyages: as William Borough in his little work the Variations of the Compass, William Barlo (Barlow) in his Supplement, Robert Norman in his New Attractive–the same Robert Norman, skilled navigator and ingenious artificer, who first discovered the dip[3] of the magnetic needle.[4]
Before I tackle Gilbert’s list of Englishmen, who contributed to the history of our understanding of magnetism and the magnetic compass, this episode will briefly deal with the history of the topic before the late sixteenth century.
We only know about magnetism because there are naturally occurring magnets. These are magnetised pieces of the mineral magnetite an iron ore with the chemical formula Fe2+(Fe3+)2O4, which when magnetised is known as lodestone. Magnetite is not naturally magnetic, and it is not actually known how pieces of magnetite become magnetised. The earth’s magnetic field is too weak to magnetise them, and the generally accepted theory is that they become magnetised by lightning strikes, a theory that is strengthened by the fact that lodestone is only found on or near the surface of the earth.
Lodestone attracting small bits of iron Source: Wikimedia Commons
The discovery of the magnetic property of lodestone by the Greeks is traditionally attributed to Thales (c. 624–c. 547 BCE) but as usually we have nothing on the topic from Thales himself. Aristotle (384–322 BCE), who in his On the Soul wrote:
Thales, too, to judge from what is recorded about him, seems to have held soul to be a motive force, since he said that the magnet has a soul in it because it moves the iron.
Not exactly very informative. The earliest Chinese reference to magnetism is in the fourth-century BCE book Guiguzi, a collection of texts on rhetoric, named after its supposed author. The second-century annals Lüshi Chunqiu notes, the lodestone makes iron approach; some (force) is attracting it. The earliest mention of the attraction of a needle is in the first-century work Lunheng, A lodestone attracts a needle.
Lüshi Chunqiu Source: Wikimedia Commons
The earliest know compass was invented by the Chinese sometime between the second-century BCE and the first-century CE. This was not used for navigation by for geomancy and divination. They were almost certainly used in feng shui an ancient Chines practice which claims to use energy forces to harmonise individuals with their surrounding environment. In the Lunheng is the first reference to a spoon, thought to be made of lodestone pointing in a cardinal direction, but when the south-pointing spoon is thrown upon the ground, it comes to rest pointing south.
Model of a Han dynasty (206 BC–220 AD) south-indicating ladle or sinan made of magnetized lodestones. Source: Wikimedia Commons
The earliest Chinese reference to a magnetised needle is from the Dream Pool Essay (1088) written by the polymath Shen Kuo (1031–195). The earliest Chinese reference to the use of a magnetic compass on land for navigation dates to sometime before 1044 CE, and the first clear evidence of the use of the compass in maritime navigation is from Pingchow Table Talks (dated 1111 to 1117) by the maritime historian, Zhu Yu (960–1279).
The English theologian and writer, Alexander Neckam (1157–1217) published the earliest European reference to the use of the magnetic compass for navigation in his De naturis rerum written between 1187 and 1202:
The sailors, moreover, as they sail over the sea, when in cloudy whether they can no longer profit by the light of the sun, or when the world is wrapped up in the darkness of the shades of night, and they are ignorant to what point of the compass their ship’s course is directed, they touch the magnet with a needle, which (the needle) is whirled round in a circle until, when its motion ceases, its point looks direct to the north.
The earliest known reference to the use of the magnetic compass in navigation in the Muslim world was in the Jawāmi ul-Hikāyāt, a collection of stories from 1232. The reference is to a fish-shaped iron leaf, a typical early Chinese design, indicating a technology transfer. The earliest reference to a compass in the form of a magnetic needle floating in a bowl of water is in a book by Baylak al-Qibjāqī (fl. 1240–1282) written in 1282, relating a voyage he took from Syria to Alexandria in 1242. The Yemini astronomer Al‐Ashraf Umar (c. 1242–1296) wrote the first description of the use of a magnetic compass to determine the qibla (the direction of Mecca for prayer) in a text on astrolabes and sundials late in the thirteenth century.
Of interest is the fact that the Muslim use of the compass is fairly obviously a technology transfer from China, but the first known occurrence postdates the first reference for its use in Europe. Normally, in the Middle Ages, Europe acquired Chinese technology via the Muslim world. In this instance it appears not to be the case. It has suggested that, as with the invention of printing with movable type, that the European use of the compass was an independent reinvention.
Probably the most extraordinary document in the whole history of magnetism and the magnetic compass is the Epistola Petri Peregrini de Maricourt ad Sygerum de Foucaucourt, militem, de magnete (Letter of Peter the Pilgrim of Maricourt to Sygerus of Foucaucourt, Soldier, on the Magnet), one copy of the manuscript of which closes with Actum in castris in obsidione Luceriæ anno domini 1269º 8º die augusti (Done in camp during the siege of Lucera, August 8, 1269). Other than the information contained in the title and in the closing statement, we know absolutely nothing about Petrus Peregrinus or how he came to write is Epistola de magnete, as he and his text are commonly known. Despite the date and although it contains some unsubstantiated speculation this is a scientific study of the magnet and its application as a compass.
The Epistola is in two books the first having ten chapters and the second three. The first book describes the properties and effects of the lodestone. Peregrinus ignores all considerations of its occult powers. He was the first person to emphasise the bipolarity of the magnet and was probably the first to use the word polus (pole) for the magnet in analogy to the celestial poles with which, in his opinion, the free rotating lodestone aligns. Just as the celestial sphere has a north and south pole, so also does every magnet. Having suggested to Sygerus, the addressee of the Epistola, that he shape his lodestone like a sphere, Gilbert would later use the name terrella for such a magnet, he gives a method of finding the poles using an iron needle, basically using it to trace the lines of longitude on his sphere, the poles being where the lines cross.
Having found the poles, he then describes how by floating the magnet in a bowl of water one can distinguish the north and south poles. He describes the effect of one magnet on another, like poles repelling, unlike attracting. Having demonstrated that a magnet divided in the middle becomes two magnets he then correctly concludes that each part of a magnet is itself a magnet. There is more of the same, descriptions of the basic properties of the magnet, how to magnetise an iron needle etc in the first book.
In the second book he describes how to construct both the wet and dry compasses. The wet compass being a bowl of water in which a lodestone encased in a wooden sheath is floated. The dry compass if a magnetised needle pivoted on a pin in a bowl. For both bowls he suggests a transparent cover with graduations marking the cardinal points, to make reading off directions easier. The third chapter of the second book describes his attempt at constructing a magnetic perpetual motion machine.
Mioara Mandela, The Magnetic Declination: A History of the Compass, Springer, 2022 p. 28
There would not be another comparable study of the magnet, magnetism, and the magnetic compass until Gilbert wrote and published his own De Magnete in 1600, which borrowed much from Peregrinus, some of it acknowledged and some not.
Having established the history of the invention of the magnetic compass and the beginnings of its use for navigation, a brief note on its function. Nobody actually knew how or why the compass needle came to rest pointing along a north-south axis. Various unsubstantiated explanations were offered. Most common was that the compass needle pointed either to the North Celestial Pole or to the Pole star. For example, Peregrinus looked to the heavens in the belief that the poles of a magnet receive their virtue from the celestial poles. Other suggestions were an unknown island or an unknown magnetic mountain. Mercator’s largely fantasy map of the Arctic featured a RupesNigra (Black Rock) a phantom island believed to be a black rock located at theMagnetic North Pole or at the North Pole itself. Described by Mercator as 33 “French” miles in size, it purportedly explained why all compasses point to this location (Wikipedia).
Mioara Mandea, The Magnetic Declination: A History of the Compass, Springer, 2022 p. 37
Not long after Alexander Neckam’s description of the wet compass, in about 1240, the Belgian theologian Thomas of Cantimpré (1201–1271), a student of Albertus Magnus (c.1200–1280) and friend of Thomas Aquinas (1225–1274), wrote an account of mariners magnetising a needle and constructing a wet compass:
When clouds prevent sailors from seeing Sun or stars, they take a needle and press its point on the magnetic stone. Then they transfix it through a piece of straw and place it in a basin of water. The stone is then moved round and round the basin faster and faster until the needle, which follows it, is whirling swiftly. At that point the stone is suddenly snatched away, and the needle points towards the Stella Maris. From that position it does not move.
Stella Maris is an alternative name for Polaris or the Pole Star, which is associated with the Virgin Mary, so Thomas thought the compass needle pointed to the Pole Star.
Although they didn’t really know how or why it worked, European navigators at the beginning of the Early Modern Period, as they first began to venture out onto the high seas from the Iberian Peninsula, had a new tool that helped them orientate whilst out on the oceans. This instrument could help them find north and thus determine their sailing direction when the Sun and the stars were not visible. However, as they soon discovered there was a catch, isn’t there always. That catch is what we now call magnetic declination or as they knew it, magnetic variation.
What is magnetic variation? Magnetic variation is the fact that a compass needle does not actually point in the direction of the terrestrial North Pole but to a point some degrees distant from it. This would not be so slim if the amount of magnetic variation was constant, but it varies quite substantially depending on where you are on the earth’s surface, and as we will learn later in this series with time. That means if you determine the magnetic variation for say London in the year 2000 you will get a different value for it when you redetermine it in 2020. This makes the normal magnetic compass not the most reliable of navigation instruments.
As with almost all basic things magnetic, the Chinese are credited with being the first the discover magnetic variation sometime between 800 and 1100 CE. It is not known exactly when the Europeans first became aware of it but the earliest evidence that they had acquired that knowledge is on the compass of a portable sundial made by Georg von Peuerbach (1433–1461) in Vienna in 1451.
Georg von Peuerbach portable compass Vienna 1451
Portable sundials have a built-in compass to enable the user to orientate them correctly for use. Peuerbach’s 1451 portable sundial is the earliest known with a built-in compass. Other portable sundials from the period from Southern German, most notably Nürnberg, also were adjusted for magnetic variation with an average value of 10°E of true north.
Mioara Mandea, The Magnetic Declination: A History of the compass, Springer, 2022 p. 30
The compass makers of Antwerp obviously didn’t really understand variation and simply adopted the Nürnberg value for their compasses gluing the compass needle to the compass card offset by about 10°E. Awareness of variation obviously began to spread and the compass makers of Genoa began to follow the Antwerp model but with the needle offset only by 5°E.
Around 1500 the awareness of magnetic variation began to appear on maps. The famous 1500 Rome Pilgrimage Route Map of Erhard Etzlaub, the Nürnberger sundial maker, has a compass rose at the bottom with the variation marked on it.
Romweg” map, 1500. “South-up” display, as in all of Etzlaub’s maps. Source: Wikimedia Commons
Both the 1544 world map of Sebastian Cabot (c. 1474–c. 1557) and that of Gerard Mercator (1512–1594) from 1569 had information about magnetic variation in their cartouches.
The early Portuguese explorers only sailed down the coast of Africa, so the changes in magnetic variation initially did not play a significant role. However, as the Iberian explorers, beginning with Columbus in 1492, began to cross the Atlantic confusion set in together with a completely false hypothesis. The standard method of crossing the Atlantic was to sail down a latitude. To do this, a navigator sailed up or down the coast of Europe or Africa until the reached the latitude of their intended destination in the Americas. They then turned through ninety degrees and sailed across the ocean on that latitude. It was not the shortest route but in terms of not getting lost on the ocean the safest. Doing this they could measure how the magnetic variation varied as they sailed across. Then came a major shock. Up till now all magnetic variations determined in Europe had been east of true north. Suddenly east of the Azores they measured variations west of true north. E of true north variation became known as positive and W of true north negative variations. Also, around the longitude of the Azores they had made measurements of zero variation.
These discoveries led to João de Lisboa (c. 1470–1525) and Pedro Anes (c. 1475–?) putting forward the hypothesis in 1508, which João de Lisboa then published in his Tratado da agulha de marear (Treatise on the Nautical Compass) in 1514, that the true Azores meridian (25°W of Greenwich) was a zero meridian of magnetic variation and if one sailed 90°E or W of the Azores the variation would gradually rise to 45°. Here was a solution to the longitude problem! The measurements of variation that didn’t at least approximately fit this hypothesis were dismissed as operator or instrument error. This was widely accepted as there was a widespread belief anyway that variation didn’t really exist but was the product of operator or instrument error. Magnetic needles incorrectly mounted, lodestone by magnetisation wrongly applied, and so on and so forth. Perhaps surprisingly João de Lisboa’s theory became widely accepted in the Iberian Peninsula and was still going strong at the end of the sixteenth century, although already discredited. One major stumbling block for his theory is that when the Portuguese finally rounded the southern tip of Africa the compass needles swung wildly and also began to display W of true north variations. These were dismissed as the influence of a magnetic mountain. In Portuguese the Cape of Good Hope was called the Cap de Agulhas, the Cape of the Compass Needles!
In 1529, Pedro Nunes (1509–1578) was appointed Royal Cosmographer of Portugal and in 1537 professor for mathematics on the newly established University of Coimbra.
Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons
In 1537, he published both Tratado em defensam da carta de marear (Treatise Defending the Sea Chart) and Tratado sobre certas dúvidas da navegação (Treatise about some Navigational Doubts), containing his proof that a course of constant compass bearing on the globe is not a great circle but a spiral known as a loxodrome. He also argued that on a sea chart the meridians and parallels should be straight lines perpendicular to each other. This is, of course the information out of which Mercator constructed his 1569 chart. In 1546, Nunes also published a book on navigation in Latin, his De arte atque ratione navigandi, making his ideas available to a wider audience including William Gilbert. Nunes also invented a ‘shadow instrument,’ which made possible combined observation of magnetic direction and solar altitude. He trained navigators in its use.
Title page De arte atque ratione navigandi, 1573 Source: Wikimedia Commons
In 1538, the Portuguese government sent Nunes’ student, João de Castro (1500–1548), Chief Pilot of the Portuguese navy on a three-year voyage to the East Indies during which he made a survey of magnetic variation. In total he made forty-three accurate determinations, which varied wildly, and which totally blew João de Lisboa’s theory out of the water.
Retrato de João de Castro no Livro de Lisuarte de Abreu, c. 1560 Source: Wikimedia Commons
In 1545, the Spanish Royal Cosmographer, Pedro de Medina (1493–1567) published his Arte de Navegar (Art of Navigation) a widely used navigation manual, which maintained that compass needles pointed to the celestial poles and that variation was the product of operator or instrument error, at this point, a no longer viable argument. The Arte de Navegar (Art of Navigation), of his successor, Martin Cortés (1510–1582), published in 1551, and as we have already seen in earlier episodes the first navigation manual translated into English by Richard Eden (C. 1520–1576) in 1561, corrected Pedro de Medina’s view on variation.
In 1562, Jean Taisnier (1508–1562) a Wallonian musician, mathematician and astrologer, who taught in various European cities and universities and was the author of a number of cosmographical and divinatory texts, published an edition of Petrus Peregrinus’ Epistola de magnete together with the 1554 Demonstratio proportionum motuum localium (Treatise on the fall of bodies) by Giambattista Benedetti (1530–1590) under the title Opusculum perpetua memoria dignissimum, De Natura Magnetis et ejus effectibus, Item De Motu Continuo (A little work worthy of preservation, On the Nature of the Magnet and its Effects, and another On Perpetual Motion) without mentioning either author and with his own author portrait.
Woodcut: Author-portrait of Jan Taisnier, 1562, aged 53 (Wellcome Collection) via Wikimedia Commons
However, confusion still ruled on variation and its causes, as the English navigators and mathematici, who I shall be looking at in detail in future episodes of this series, began to tackle the problems of the magnet, magnetism, and the magnetic compass.
The quote I brought at the beginning of this essay from William Gilbert’s De magnete (1600), listing some but not all of the people I shall be dealing with, is followed by an incredible chauvinistic rant about the efforts of the Early Modern Europeans to make sense of magnetism, the compass, and variation some of which I have sketched above:
Many others I pass by of purpose: Frenchmen, Germans, and Spaniards of recent times who in their writings, mostly composed in their vernacular languages, either misuse the teachings of others, and like furbishers send forth ancient things dressed with ne names and tricked in an apparel of new words as in prostitutes’ finery; or who publish things not even worthy of record; who, pilfering some book, grasp for themselves from other authors, and go a-begging for some patron, or go a-fishing among the inexperienced and the young for a reputation; who seem to transmit from hand to hand, as it were, erroneous teachings in every science and out of their own store now and again to add somewhat of error.[5]
[1] I have to make the obligator comment that William Gilbert and I attended the same grammar school, he was a couple of year ahead of me.
In the last episode I outlined those aspects of Aristotle’s philosophy that would go on to play a significant role of the history of physics in later centuries. Because Aristotelian philosophy came to play such a central role in medieval thought in the High Middle Ages, there is a strong tendency to think that it also dominated the philosophical scene throughout antiquity. However, this was not the case. Although his school, the Lyceum, survived his death in 332 BCE and under the leadership of Theophrastus (c. 371–c. 287 BCE) enjoyed a good reputation. Theophrastus produced some good science, but it was natural history–biology, botany–not physics as indeed the majority of Aristotle’s scientific work had been. After Theophrastus died the Lyceum went into decline. However, the school was in no way dominant, the main philosophy of Ancient Greek following Aristotle being Stoicism and Epicureanism. Both of these philosophical directions “shared the aim of attaining tranquillity or freedom from worry (ataraxia), yet their explanations of the world were often radically different, even opposed.”[1]
Epicurus (341–270) had a rather negative attitude towards natural philosophy:
Epicurus was content for his followers to have an ‘in principle’ approach to understanding the world. He explained that it is not necessary to become too caught up in details. In fact, he argues that less is more, because knowing less can prevent confusion and worry. In Epicurus’ view, there is a distinct possibility of being blinded by science, and this is to be avoided. While Epicurus indicates that he had himself worked out the details of his views more fully, he advocates that a summary is sufficient. A physical theory that can withstand objections and leads to peace of mind should be accepted.[2]
Portrait of Epicurus, founder of the Epicurean school. Roman copy after a lost Hellenistic original. Source: Wikimedia Commons
Epicurean natural philosophy was retrograde, it rejected the developments made by Empedocles, Plato, Eudoxus, and Aristotle and returned to the views of the Atomists. There existed only bodies and space and the bodies were composed of atoms. Because space, the void was infinite and had no centre they rejected Aristotle’s arguments for a spherical earth at the centre of a spherical cosmos and supported a flat earth floating in the void. As with so many of these figures, Epicurus supposedly wrote a large number of books of which only a few short works survive. However, the Roman poet and philosopher, Lucretius (c. 99–c. 55 BCE) presented the Epicurean philosophy and physical theory in his poem, De rerum natura (On the Nature ofThings), This would go on to play a role in the introduction of a particle theory of matter in the Early Modern Period.
Opening of Pope Sixtus IV’s 1483 manuscript of De rerum natura, scribed by Girolamo di Matteo de Tauris Source:Wikimedia Commons
Unlike Epicureanism, Stoicism did not have a single direction determining founder, although Zeno of Citium (c. 334–c. 226) BCE, is regarded as the first Stoic.
Zeno of Citium. Bust in the Farnese collection, Naples. Photo by Paolo Monti, 1969. Source: Wikimedia Commons
He developed his ideas out of the philosophy of the Cynics being, for a time, a pupil of Crates of Thebes (c. 365–c. 285 BCE). However, equally important in the early phase of Stoicism were, Zeno’s pupil Cleanthes of Assos (c. 330–c. 230 BCE) and his pupil Chrysippus of Soli (C. 279–c. 206 BCE).
Chrysippos of Soli, third founder of Stoicism. Marble, Roman copy after a lost Hellenistic original of the late 3rd century BC. Source: Wikimedia Commons
As with almost all major Greek philosophers in this period, according to hearsay, they all wrote lots of books but only fragments of their actual writings have survived. Most of the reports on what they actually believed and practiced come from writers active centuries after they lived. As opposed to Epicurus and Epicureanism, Stoic philosophy is thought to be the result of a collective of writers rather than one dominant individual.
The Stoic philosophy has three major pillars logic, physics (natural philosophy), and ethics. As this series is about the history of the evolution of physics I shall ignore the ethics, although it was the ethics that made, and still makes, Stoicism attractive to many people. The Stoics, like Aristotle, placed a strong emphasis on logic but whereas Aristotle laid his emphasis on logical deductive reasoning using the syllogism, which is a logic of classes, the Stoics are credited with developing the earliest European logic of proposition or predicative logic. This development is usually attributed to Chrysippus but we have little or nothing of his original texts and rely on later reports by Diogenes Laëtius (fl. 3rd century CE), Sextus Empiricus (2nd century CE), Galen (129–c. 216 CE), Aulus Gellius (c. 125–after 180 CE), Alexander of Aphrodisias (fl. 200 CE), and Cicero (106–43 BCE).
Stoic physic is interesting both for its similarities with and differences to Aristotle. Unlike Epicurus, the Stoics accepted the basic Platonic-Aristotelian model of the cosmos as a sphere with a spherical Earth at its centre. They were in fact mainly responsible for the acceptance of this model by the Roman. They also largely accepted the existing astronomical model of the planets revolving around the Earth on circular orbits. However, their cosmology had a major difference to that of Aristotle that would become highly significant when Stoicism was revived in the Early Modern Period.
The Stoics were pandeists, that is they believed that god was the cosmos and everything in it and the cosmos and everything in it was god. As a result, their matter theory was radically different to that of both Plato and Aristotle. To quote Wikipedia:
According to the Stoics, the Universe is a material reasoning substance (logos), which was divided into two classes: the active and the passive. The passive substance is matter, which “lies sluggish, a substance ready for any use, but sure to remain unemployed if no one sets it in motion.” The active substance is an intelligent aether or primordial fire (pneuma) which acts on the passive matter:
The universe itself is God and the universal outpouring of its soul; it is this same world’s guiding principle, operating in mind and reason, together with the common nature of things and the totality that embraces all existence; then the foreordained might and necessity of the future; then fire and the principle of aether; then those elements whose natural state is one of flux and transition, such as water, earth, and air; then the sun, the moon, the stars; and the universal existence in which all things are contained.
— Chrysippus, in Cicero, De Natura Deorum, i. 39
For their cosmology, a major consequence of this philosophy was that the Stoics rejected Aristotle’s division of the cosmos into the supralunar and sublunar spheres, they were both the same for the Stoics, and they considered comets, which as I said in the last episode played a major role in the emergence of modern astronomy, to be a supralunar phenomenon as opposed to Aristotle who regarded them as a meteorological or atmospheric phenomenon.
Both Epicureanism and Stoicism were very popular amongst educated Romans, such as Cicero and Seneca (c. 54 BCE–c. 39 CE), and the later Greek philosopher Plutarch (c. 46–119 BCE), who quoted and discussed Epicurean and Stoic philosophers in their writings. They remained so until about 300 CE when they in turn faded into the background and were replaced by the Neoplatonist. However, those writers who paid the most attention to them were those Latin stylists who were most popular amongst the Humanist philosophers of the Renaissance and so their ideas experienced a revival in the Early Modern Period and there had an impact on the evolution of science.
[1] Liba Taub, Ancient Greek and Roman Science: A Very Short Introduction, OUP, 2023 p.
Old Hulky[2] was thinking of taking time off for the summer and retiring to an ice floe[3] in the North Atlantic for a couple of weeks to escape the heat wave, when Neil deGrasse Tyson has to go and publish a piece of history of astronomy inanity that would have to look hard to find its equal and now he’s on the rampage–stomp, stomp, stomp…
If you know anything about the history of astronomy read the following and weep:
‘For thousands of years, humans reasonably assumed the Moon to be a flat disk of light that waxed and waned – until the 17th century, when Galileo dared turn his freshly perfected telescope skyward, revealing a textured sphere with jagged mountains drenched in sunlight and sloping valleys cloaked in shadow. From that moment onward, the heavens and all the celestial objects therein became worlds…’ [4]
Hulky thinks that NdGT must be a male of the species Bos taurus because he can pack so much bovine manure into just one paragraph of sixty-four words!
For thousands of years, humans reasonably assumed the Moon to be a flat disk of light that waxed and waned – until the 17th century…
Hulky: I think he’s just making shit up!
I’m afraid I have to agree with my combative friend. I have spent half a lifetime studying and researching the European history of astronomy and have never come across a theory about the Moon from anybody that even halfway resembles the piece of ahistorical verbal garbage that NdGT spews out in the sentence above. Let us briefly look at the lunar theories held and developed by the Ancient Greeks that were dominant in European thought up to the Early Modern Period.
Starting with the Pre-Socratics, apparently Anaximander really did think that the Moon was a flat disc but both Thales and Parmenides claimed it was a sphere. Anaxagoras thought that both the Sun and the Moon were big stones, and that moonlight was in fact reflected sunlight. However, as I have stated in the past I view claims about the beliefs of the Pre-Socratics, which are based on hearsay often hundreds of years after they lived, very sceptically, so I’ll turn to more reliable sources. For Aristotle, all seven planets (asteres planētai, wandering stars)–Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn–were perfect unblemished spheres, made of aether, the fifth element or quintessence. Generally, in Aristotelian cosmology, which dominated thought in Europe from the twelfth down to the seventeenth century, the Moon is illuminated with Sun light, a model that is used to explain both the phases of the Moon and eclipses. Although there existed a debate as to whether the Moon had its own light.
Maybe, NdGT doesn’t like philosophers and prefers astronomers. In his Mathēmatikē Syntaxis, written around 150 CE, Ptolemaeus, whose astronomy dominated in Europe, again from the twelfth down to the seventeenth century, we can read the following in Book IV:
For the distance between the sphere [my emphasis] of the moon and the centre of the earth…[5]
Or Book V
The ratios of the volumes of the bodies are immediately derivable from the ratios of the diameters of sun, moon and earth.[6]
Both quotes leave no doubt that for Ptolemaeus the Moon was a sphere.
…when Galileo dared turn his freshly perfected telescope skyward…
When I was young there was a widely spread myth that Galileo invented the telescope. It has in the meantime largely disappeared, although it still crops up from time to time. It would appear that it has been replaced with the equally mythical claim that Galileo perfected the telescope. This is the second time that NdGT has recently made this claim.
Hulky: He obviously believes that if you repeat a myth often enough then the suckers will believe it
Galileo succeeded in raising the magnification of the telescope originally launched by Hans Lipperhey in Middelburg in 1608, as did Thomas Harriot, Simon Marius, and Antonio Santini, and later many others but to talk of a perfected telescope is a joke. The early telescope lenses were made of very poor-quality glass and the grinding and polishing of those lenses left much to be desired. Suffering from both spherical and chromatic aberration, the images the early telescopes produced were blurred and had coloured fringes. As a result, there were lots of false sightings reported in the seventeenth century. That anybody was actually able to make accurate observations with those very poor-quality telescopes borders on a miracle.
…revealing a textured sphere with jagged mountains drenched in sunlight and sloping valleys cloaked in shadow.
Hulky: fancies himself as a bleeding poet, don’t he?
Probably due to his training as an artist, Galileo was able to interpret the dark patches he could observe on the Moon as shadows cast by uplands.
From that moment onward, the heavens and all the celestial objects therein became worlds…’
As I have pointed out on more than one occasion, Galileo’s hypothesis that the Moon’s surface was not perfectly smooth as Aristotle’s cosmology required but was Earth like with mountains and valleys was not as new or as spectacular as it is mostly presented.
That the moon was Earth like and for some that the well-known markings on the Moon, the man in the moon etc., are in fact a mountainous landscape was a view held by various in antiquity, such as Thales, Orpheus, Anaxagoras, Democritus, Pythagoras, Philolaus, Plutarch and Lucian. In particular Plutarch (c. 46–c. 120 CE) in his Onthe Face of the Moon in his Moralia, having dismissed other theories including Aristotle’s wrote:
Just as our earth contains gulfs that are deep and extensive, one here pouring in towards us through the Pillars of Herakles and outside the Caspian and the Red Sea with its gulfs, so those features are depths and hollows of the Moon. The largest of them is called “Hecate’s Recess,” where the souls suffer and extract penalties for whatever they have endured or committed after having already become spirits; and the two long ones are called “the Gates,” for through them pass the souls now to the side of the Moon that faces heaven and now back to the side that faces Earth. The side of the Moon towards heaven is named “Elysian plain,” the hither side, “House of counter-terrestrial Persephone.”[7]
Plutarch’s Moralia was a well-known, widely read, and much-loved text amongst Renaissance Humanists, so Galileo’s discovery was really not that sensational.
As, unfortunately, all too often NdGT is once again feeding his poor, benighted acolytes a diet of highly inaccurate, fanciful, ahistorical garbage. If I were National Geographic or their parent company Penguin Random House, I would be ashamed to have this detritus associated with my brand name.
[1] With apologies to Richard Rogers and Lorenz Hart
[2] Hulky is the Renaissance Mathematicus pet name for the HISTSCI_HULK
[3] Recommended to him by his friend Frankenstein’s much maligned monster as a good place to escape from the stress of civilisation.
[4] Neil deGrasse Tyson & Lindsey Nyx Walker, To Infinity and Beyond: A Journey of Cosmic Discovery, A StarTalk Book, National Geographic, NY, 2023, p. 17
[5] Ptolemy’s Almagest, Translated and Annotated by G. J. Toomer, Princeton University Press, ppb. 1998, p. 173
I have gained a reputation for pointing out and demolishing myths in the history of science. One area where these are particularly prevalent is in the history of the European Middle Ages. With numerous people claiming that there was little or no science during this period and what there was, was all wrong, usually blaming this situation on the Catholic Church. The people making these claims completely ignore the quite extensive literature on the history of medieval science written by such excellent historians as David C Lindberg, Edward Grant, Stephen C McCluskey, Bruce S Eastwood, Alastair C Crombie, and John E Murdoch amongst others. For those who don’t wish to plough through the academic literature, there is also a selection of excellent popular books on the subject, which I can warmly recommend. For example, David C Lindberg, The Beginnings of Western Science: The European Tradition inPhilosophical, Religious, and Institutional Context, Prehistory to A.D. 1450, (Chicago UP, 2nd ed. 2007), or perhaps Seb Falk, The Light Ages: The Surprising Story of Medieval Science(Norton, 2020), which I reviewed here. Finally, James Hannam, God’s Philosophers: How the Medieval World Laid the Foundations of Modern Science, (Icon Books, 2009).
One of the most persistent myths against which my friend the HISTSCI_HULK has rampaged on several occasions is that, during the European Middle Ages, people believed that the world was flat. Following up on his excellent God’s Philosophers, James Hannam has now delivered the book that should squash that myth for ever, but I fear won’t, The Globe: How the Earth Became Round.[1]
The blog post title is not just a piss poor play on words of the book’s subtitle, in his just over three-hundred pages, Hannam takes his readers on a journey both chronological and geographically around the world starting around 3000 BCE in the fertile crescent to England in the twentieth century on a wild zig zag course. The opening three chapters give brief but informative accounts of the image of the heavens and the earth of the ancient Babylonians, the ancient Egyptians, and the ancient Persians, all of whom believed in a flat earth with themselves at the centre under a ceiling like heaven, with varying explanations as to where the sun went at night and the moon during the day.
Imago Mundi Babylonian map, the oldest known world map, 6th century BCE Babylonia. Now in the British Museum. Source: Wikimedia Commons
Having only devoted one brief chapter to each of these great ancient civilisations, Hannam now devotes six chapters to Ancient Greece! Seems unfair but it is here that the main action takes place, over a period of about four centuries the Earth transitioned from flat to spherical in Greek thought and Hannam, here, details each phase of that transition. He proceeds from Archaic Greece, the poems of Homer and Hesiod describing a circular flat earth, moving on to the Origins of Greek Thought, where he is refreshingly sceptical about claims made about Thales’ views. Next up are the Pre-Socratics and Socrates ending with Socrates death. Socrates is, of course followed by Plato and the earliest confirmed mention of a spherical Earth, Plato, in his Phaedo dialogue, supposedly quoting Socrates:
“I assumed that [Anaxagoras] would begin by informing us whether the Earth is flat or round, and then he’d explain why it had to be that way because that was what was better.”[2]
The following chapter on Plato goes deep into the discussion, as to where and from whom the idea that the Earth is a sphere first comes from, as it is obvious from the way that Plato writes about it that the discussion flat or round was already under way. After Plato comes Aristotle and we have the first clear statement that the Earth is a sphere, why it must be a sphere and empirical evidence that supports the statement that the Earth is a sphere:
Bust of Aristotle. Marble, Roman copy after a Greek bronze original by Lysippos from 330 BC Source: Wikimedia Commons
Aristotle concluded his discission by showing how the theory of the Globe explained observations that might seem otherwise inexplicable. In the first place, he said that when there is a lunar eclipse the shadow of the Earth on the Moon is always curved. This corroborates what he had already shown from his first principles. The umbra during a lunar eclipse follows from the shape of the Earth. If it is a ball, its shadow must always be an arc.
His second piece of empirical evidence is the way the visible stars change as we travel north or south. He noted that some stars, which are visible in Egypt and Cyprus, can’t be seen in the north. He is almost certainly referring to Eudoxus’ observations of Canopus. It is bright enough to be hard to miss in Egypt, albeit usually low in the sky. Its absence from view in Athens would have been obvious to anyone who had seen it further south. This is only explicable if the Earth is rounded, if it were a flat plane, everyone would see the same stars. Since it is spherical, it’s inevitable that our view of the heavens will change with latitude.[3]
So, we have reached our objective, Aristotle demonstrated that the Earth is a sphere and not flat. End of story! No! Everything up till now was merely a prelude, the real story is just beginning. Hannam closes his section on Aristotle with the following:
By any conventional standards he [Aristotle] knew the Earth was a sphere, and he was probably the first person who did. On that basis, he discovered the theory of the Globe. As we will see in the remainder of this book, everyone today who knows the Earth is round indirectly learnt it from Aristotle. This makes the Globe the greatest scientific achievement of antiquity. It’s only because we take it as obvious that we don’t give Aristotle the credit he deserves.[4]
Hannam now take his readers of a journey through history and around the globe explaining how different cultures reacted when confronted, either directly or indirectly, with Aristotle’s truth. What their own vision of the Earth’s form was before that confrontation. Who came to accept the new vision, who reacted against it, rejecting. It’s a complex story that Hannam handles with verve, explicating clearly and accurately every twist and turn.
First off, Hannam stays with the Greeks and explains how the Stoics, who succeeded Aristotle as philosophical flavour of the century by supporting his conviction that the Earth was a sphere spread and established the view not only amongst the Greek but also the Romans, many leading figures having adopted the Stoic philosophy. The Stoics main rivals, the Epicureans, however, having adopted the cosmological theories of the Atomists reject the sphere maintaining that the Earth was flat. Their rejection of the sphere followed from their belief that the Earth was not the centre of the cosmos, the starting point of Aristotle’s argument for the sphere. Hannam also takes a close look at Greek cartography, if the Earth is a sphere how do you represent in in a flat diagram? Hannam moves on to a discussion of Roman culture and the representation of the Orbis within that culture.
In these sections Hannam points out that the Greek and Roman terms, such as the Latin Orbis, can mean both circle and sphere. Orbis is etymologically the origin of both orbit, a circle, and orb, a sphere. So, a modicum of caution is required when interpreting the historical texts.
Our journey now takes us through India, the Sassanian Persian Empire, Early Judaism and with it for the first time the Biblical view of the shape of the Earth and on into Christianity. Christianity had of course a problem with the inherent contradiction between the Bible, the infallible word of God, and the words of Aristotle. This led to a spirited discussion in the early Church that Hannam explicates, with his usual clarity. There was not just one but multiple discussion in the various early Christian communities. He we get one of the most notorious flat earther from antiquity, Cosmas Indicopleutes, who often gets quoted by those claiming that the people in the Middle Ages believed the world to be flat. The last of the so-called Abrahamic religions, Islam, comes next. With once again multiple discussion in particular about the discrepancy between the Koran and Aristotle. We had early Judaism now we have later Judaism in particular Moses Maimonides.
Europe in the Early Middle Ages is our next port of call. Mostly Aristotelian, most notably Augustine, but with exceptions most notably Lactantius, who would later feature in Copernicus’ De revolutionibus. Of interest here is Isidore of Seville (c.560-636) one of the most important encyclopaedists from late antiquity, who is in his writing more that ambiguous abut the shape of the Earth. Hannam argues fairly convincingly that, although he accepted Ptolemy’s astronomy and cosmology, he was a flat earther. However, Jürgen Hamel in his Die Vorstellung von der Kugelgestalt der Erde in europäischen Mittelalter bis zum Ende des 13. Jahrhunderts – dargestellt nach den Quellen,[5](an excellent book if you can read German) agues equally convincingly that he wasn’t. I guess with Isidore, you pays your money and makes your choice.
Moving on to the next chapter, High Medieval Views of the World: ‘The Earth has the shape of a globe’, we are well into the territory of those promoting the myth that people in the Middle Ages believed that the Earth was flat; a myth that Hannam proceeds to demolish with style. The money quote is:
Take the coronation orb, which has been part of the regalia presented to kings and emperors from late antiquity. The orb represents the Earth, while the cross on top symbolises that the secular power was subject to the will of God. Presumably, if people in the Middle Ages had thought the Earth was flat, they would have presented their rulers with a diner plate instead.[6]
Frauenkirche Nürnberg Clock with the Holy Roman Emperor in the middle holding the Orb and Sceptre 1309! Source: Wikimedia Commons
We move into the Early Modern Period with Columbus and Copernicus: ‘New worlds will be found,’ where Hannam also demolishes the myth that people thought Columbus would fall of the edge of the world and the equally stupid myth that Columbus proved that the world was round. We get a brief guest appearance of the world’s oldest surveying terrestrial globe, Martin Behaim’s Erdapfel (1492-94).
Martin Behaim’s Erdapfel GNM Nürnberg
Columbus is followed naturally by Magellan and the first circumnavigation. The chapter closes with a brief look at what Copernicus has to say about the shape of the Earth and also why he said it.
China’s tradition view of the Earth and its reaction to the idea that it is actually a globe is a difficult and complex story, stretching over two chapters, which Hannam manages to relate with his usually sureness and style.
Moving into the modern period brief nods at the attempts to measure the size of the globe and the problems of determining longitude lead into the eighteenth-century dispute over the actual shape of the Earth, Newton & Huygens vs the Cassinis, oblate spheroid or prolate spheroid and the only part of Hannam’s entire narrative that I think is slapdash and shoddy. This is one of the most important episodes in the history of geodesy that also had ramifications for the theory of gravity and led to an indirect proof of diurnal rotation. It deserves more that Hannam’s sloppy two paragraph account.
This penultimate chapter contains two further sections, the first are brief accounts of explorers and missionaries bringing the news of the spherical shape of the Earth to communities that still hadn’t received it and how they reacted. The second is a brief account of the origins of modern Flat-Earth supporters in the nineteenth century. The final chapter continues with the flat earthers of the twentieth century. For theses two sections Hannam’s primary source is Christine Garwood’s excellent Flat Earth: The History of an Infamous Idea,[7] which I highly recommend if you are interested in the topic. The chapter proceeds with brief accounts of Draper-White conflict thesis and then moves on to the modern fantasy authors C. S. Lewis, J. R. R. Tolkien, and Terry Pratchett, who all knew better but still placed their fantasy novels in flat earth medieval settings.
Hannam’s book has extensive endnotes that mostly refer to the equally extensive bibliography. The book also has an extensive index. The book is richly illustrated but in the proof copy I was supplied with to write this review they are unfortunately very poor quality grey scale reproductions. I can only assume that they are better in the published version of the book.
James Hannam’s book is truly first class and should become a standard work on the topic. He covers a very wide range of material in a comparatively small number of pages. Each section of the book is relatively brief but concise, historically accurate, and highly informative. He writes extremely well, and his prose is clear and light to read. Anybody who takes the trouble to read this book will at the end know when, where and how the various populations of the Earth became aware that their home was on a large sphere floating through space. A fact first truly recognised by Aristotle in the fourth century BCE and slowly disseminated around the globe over a period of more than two thousand years. Hannam has produce a first-class documentation of that dissemination.
[1] James Hannam, The Globe: How the Earth Became Round, Reaction Books, London, 2023
[5] Jürgen Hamel, Die Vorstellung von der Kugelgestalt der Erde in europäischen Mittelalter bis zum Ende des 13. Jahrhunderts – dargestellt nach den Quellen, Abhandlung zur Geschichte der Geowissenschaften und Religion/Umwelt-Forschung, Neue Folge, Band 3 pp. 51-52
There is very little doubt that Aristotle (384–§22 BCE) is the predominant figure in the narrative of the history of European science in the twenty-two centuries from 400 BCE to 1800 CE, and even after that he remains a central figure in the discourse. The general literature on Aristotle as a philosopher would fill a sizable library and the specific literature on his contributions to the history of science would fill a whole wing of that library. In this post, I will be limiting myself to a brief description of those aspects of his philosophy that had an impact on the history of physics.
As already explained in the first episode of this series, although Aristotle gave us the word physics in his book title τὰ φυσικά (ta physika), what he means with this is very different from what is meant by the modern use of the term physics. As this series is actually about the evolution of modern physics in the early modern period, I shall here only deal with various aspects of Aristotle’s philosophy that relate to that evolution and they are by no means confined to his τὰ φυσικά (ta physika).
Before I start, a brief biographical note on Aristotle. Born in Stagira in Northern Greece, the son of the prominent physician Nicomachus (fl. c. 375 BCE), who died whilst he was still young, he was brought up by a guardian. In his late teens he joined Plato’s Academy in Athens, where he remained until the death of Plato in 347/348 BCE. Around 343 BCE he left Athens at the request of Philip II of Macedon to become the tutor to his son Alexander (356–323 BCE), the future Alexander III of Macedon, better known as Alexander the Great. Around 340 BCE he returned to Athens and set up his own school of philosophy, the Lyceum. Having, for so long, been a pupil of Plato much of his philosophy was formed either by acceptance or rejection of Plato’s teaching.
Bust of Aristotle. Marble, Roman copy after a Greek bronze original by Lysippos from 330 BC; the alabaster mantle is a modern addition. Source: Wikimedia Commons
One major area of acceptance, that would have consequences up to the seventeenth century, was his adoption of the cosmological and astronomical theories of Plato and Eudoxus, together with the four element theory, originally expounded by Empedocles. Aristotle took over the basic two sphere model from Plato. The cosmos is a sphere, which would become the sphere of the stars in astronomy, and the Earth is a sphere at its centre. Unlike Plato, Aristotle explains why the Earth is a sphere and also gives empirical evidence to show that it is truly a sphere. He argued that if something with gravitas falls then it falls towards the centre of the cosmos until it stops. The natural consequence of everything falling towards a centre from all direction is a sphere. This fall was not due to a force but to the tendency for objects to return to their natural or proper place. So, objects that have gravitas i.e., those predominantly consisting of earth or water, return to the Earth. Those with levitas, consisting predominantly of air or fire rise up into the atmosphere.
Of course, he has to explain why the celestial objects don’t fall to the Earth. Aristotle divides the cosmos into two zones, everything below the orbit of the Moon i.e., sublunar and everything above the orbit of the Moon i.e., supralunar. The sublunar zone consists of the four elements and is subject to change and corruption, whereas the supralunar zone consists of a fifth element, the aether or quintessence, which is unchanging and incorruptible. Natural motion in the supralunar zone is, once again following Plato and Empedocles, uniform circular motion.
Unlike his predecessors, Aristotle provides empirical arguments to demonstrate that the Earth is actually a sphere, to quote James Hannam:
Aristotle concluded his discission by showing how the theory of the Globe explained observations that might seem otherwise inexplicable. In the first place, he said that when there is a lunar eclipse the shadow of the Earth on the Moon is always curved. This corroborates what he had already shown from his first principles. The umbra during a lunar eclipse follows from the shape of the Earth. If it is a ball, its shadow must always be an arc.
His second piece of empirical evidence is the way the visible stars change as we travel north or south. He noted that some stars, which are visible in Egypt and Cyprus, can’t be seen in the north. He is almost certainly referring to Eudoxus’ observations of Canopus. It is bright enough to be hard to miss in Egypt, albeit usually low in the sky. Its absence from view in Athens would have been obvious to anyone who had seen it further south. This is only explicable if the Earth is rounded, if it were a flat plane, everyone would see the same stars. Since it is spherical, it’s inevitable that our view of the heavens will change with latitude.[1]
Hannam closes his section on Aristotle with the following:
By any conventional standards he [Aristotle] knew the Earth was a sphere, and he was probably the first person who did. On that basis, he discovered the theory of the Globe. As we will see in the remainder of this book, everyone today who knows the Earth is round indirectly learnt it from Aristotle. This makes the Globe the greatest scientific achievement of antiquity. It’s only because we take it as obvious that we don’t give Aristotle the credit he deserves.[2]
For the planets Aristotle takes over the concentric or homocentric spheres of Eudoxus and Callippus but adds more spheres filling out the spaces between the planets making a complete set of spheres within spheres from the Moon to the stars. All motion within the heavens is driven by a sort of friction drive by the outer most sphere. This in turn is driven by an unmoved mover, a concept that appealed to the Church in the medieval period, who simply assumed that the unmoved mover was God. Although more scientific in his explanations than any of his predecessors, Aristotle can, at times, also be totally metaphysical. What motivates the unmoved mover? The spheres have souls, and it is the love of those souls for the unmoved mover that motivates it. The origin of the phrase, “love makes the world go round.”
As is generally well known, having defined fall as natural motion, Aristotle now goes on to elucidate his laws of fall, which, of course, everybody knows were wrong being first brilliantly corrected by Galileo in the seventeenth century. Firstly, Aristotle’s laws of fall are not as wrong as people think, and secondly, they were, as we shall see in later episodes, challenged and corrected much earlier than Galileo.
Aristotle’s laws of fall are actually based on simple everyday empirical observation. If I drop a lead ball from an oak tree it evidently falls to the ground faster than an acorn that I dislodge whilst dropping the ball. In real life not all objects fall at the same speed. It is only in a vacuum that this is the case. People tend to ignore the all-important “vacuum” when praising Galileo’s enthronement of Aristotle’s laws of fall. Naturally if I drop a two lead balls of different weights, they do fall at approximately the same speed but even here the heavier ball will hit the ground a split second earlier than the lighter one.
Aristotle argued that the rate of fall was directly proportional to the weight of the falling object and indirectly proportional to the resistance of the medium through which it falls.
Aristotle’s laws of motion. In On the Heavens he states that objects fall at a speed proportional to their weight and inversely proportional to the density of the fluid they are immersed in. This is a correct approximation for objects in Earth’s gravitational field moving in air or water. Source: Wikimedia Commons
This is a good first approximation for objects on the Earth falling through air or water. Having established this Aristotle then argued that the void (a vacuum) could not exist because in the void a falling object would accelerate to infinity and that was an absurdity. Interestingly he also argues that in a vacuum all objects would fall at the same speed, an absurdity! Galileo anyone? It is quite common to express his laws of fall either symbolically or even mathematically, but Aristotle never did either.
As already said, although Aristotle gave us the word physics, he uses it in a very different way. For Aristotle physics is the study of natural things, which he sees as the study of the general principles of change. Change is for Aristotle universal, plants grow and then die, there is quantitative change with respect to size and number and so forth. Most important from our point of view is that he considers motion to be change of place.
In Aristotle’s theories of motion, having dealt with natural motion he now had to define and deal with unnatural motion. Of course, there was only natural motion in the uncorruptible supralunar area. On Earth beyond natural motion there was voluntary motion and unnatural motion. Voluntary motion is such as animals moving and need not concern us here. Unnatural motion requires a cause, and it is here that Aristotle’s whole theory of motion ran into difficulties.
If I have a horse and cart or I push a wheelbarrow, then the cart only moves if the horse pulls and the wheelbarrow only moves if I push. If the horse stops pulling or if I stop pushing then the motion stops, no real problems here, although it is difficult to fit this type of motion into the laws of motion that applies to the falling object. Aristotle’s real problems start with projectile motion. If I fire an arrow with a bow or throw a ball, why does the arrow after it has left the bow string or the ball after it has left my hand continue to fly through the air? There is now apparently nothing propelling the arrow or ball. Aristotle’s escape from this impasse is, to say the least, dodgy. He argued that the air displaced by the flying object rushed around to the back and pushed it further along its course. This weak point in his theory was exploited comparatively early by his critics, i.e., long before the seventeenth century.
Aristotle rejected atomism arguing there was no limit to how far one could divide something, so no smallest particles, atoms. His own theory of matter was that there is primal material. Objects consist of two things material and form. This is important because it plays a role in his fourfold theory of cause that dominated his whole philosophy of nature.
According to Aristotle everything in nature has four causes:
The Material Cause: The material out of which it is composed.
The Formal Cause: The pattern or form that makes the material into a particular type of thing.
The Efficient Cause: In general that which brings an object about
The Final Cause: The purpose for the existence of the object in question
The four causes also apply to abstract concepts such as motion, each motion has a material, a formal, an efficient, and a final cause.
Aristotle argued by analogy with woodwork that a thing takes its form from four causes: in the case of a table, the wood used (material cause), its design (formal cause), the tools and techniques used (efficient cause), and its decorative or practical purpose (final cause). Source: Wikimedia Commons
Today, we regard the final cause, for which the technical term is teleology, as bizarre. Since at least the nineteenth century it is not thought that most things have an intrinsic purpose for their existence, they just exist. However, in the Middle Ages, the high point of Aristotelian thought in science, it would have chimed with Christian thought, “everything has a place in God’s great plan.
Introducing Aristotle’s four causes takes us along to, perhaps Aristotle’s greatest contribution to the development of science his methodology and his epistemology, i.e., his theory of knowledge. In six works, collectively known as the Organon, he laid out the earliest known introduction to formal logic. How do I argue correctly, so that I transport truth from my premises to my conclusions. Our understanding of logic and the logic that we use have evolved since Aristotle, but logic still lies at the heart of all formal scientific proofs. Stealing from Wikipedia the six Aristotelian works on logic are:
The Categories (Latin: Categoriae) introduces Aristotle’s 10-fold classification of that which exists: substance, quantity, quality, relation, place, time, situation, condition, action, and passion.
On Interpretation (Latin: De Interpretatione) introduces Aristotle’s conception of proposition and judgement, and the various relations between affirmative, negative, universal, and particular propositions.
The Prior Analytics (Latin: Analytica Priora) introduces his syllogistic method argues for its correctness, and discusses inductive inference.
The Posterior Analytics (Latin: Analytica Posteriora) deals with definition, demonstration, inductive reasoning, and scientific knowledge.
The Topics (Latin: Topica) treats issues in constructing valid arguments, and inference that is probable, rather than certain. It is in this treatise that Aristotle mentions the Predicables, later discussed by Porphy and the scholastic logicians.
The On Sophistical Refutations (Latin: De Sophisticis Elenchis) gives a treatment of logical fallacies, and provides a key link to Aristotle’s tractate on rhetoric.
Added 17 August
Although not really clearly spelt out, Aristotle propagated an axiomatic deductive system for securing knowledge. Starting from self-evident premises that require no proof one uses a chain of deductive logic until one arrives at empirically observed facts. Although we would regard his premise that the Earth is a sphere because all falling objects fall to the centre of the universe as self-evident, this is the form of argument, sketched above, he uses to demonstrate that the Earth is really a sphere.
It is important to note, for the evolution of scientific thought in Europe throughout the centuries after Aristotle, that when applied to nature he didn’t regard mathematical proofs as valid. He argued that the objects of mathematics were not natural and so could not be applied to nature. He did however allow mathematics in what were termed the mixed sciences, astronomy, statics, and optics. For Aristotle mathematical astronomy merely delivered empirical information on the position of the celestial bodies. Their true nature was, however, delivered by non-mathematical cosmology. I shall deal with statics and optics separately.
In recent times, various voices have claimed that the adherence to Aristotle’s vision of science hindered the evolution of the discipline. It is a similar claim to that of the gnu atheists that Christianity blocked the evolution of science. In the case of Aristotle, I think we should bear in mind that in antiquity his popularity waned fairly quickly after his death, and he was superceded by the Stoics and then the Epicureans as the flavour of the century in philosophy and although this included the period of the greatest Greek mathematicians Archimedes (c. 287–c.212 BCE) Apollonius of Perga (c. 240–c. 190 BCE), who both made significant advances in both pure and applied mathematics, it cannot be said that the world advanced significantly towards modern science.
[1] James Hannam, The Globe: How the Earth Became Round, Reaktion Books, London, 2023 p. 93
All of these books went through several editions, showing that there was an eager and expanding market for vernacular literature on navigation in the period. A market that was also exploited by the gentlemanly humanist scholar Thomas Blundeville (c. 1522–c. 1606), probably writing for a different, more popular, readership than the others.
Thomas was born in the manor house of Newton Flotman in Norfolk, a small village about 13 km south of Norwich. He was the eldest of four sons of Edward Blundevill (1492–1568) and Elizabeth Godsalve. He had one sister and two half-brothers from his father’s second marriage to Barbara Drake. Unfortunately, as is all too often the case, that is all we know about his background, his upbringing, or his education.
The authors of Athenae Cantabrigienses claim that he studied at Cambridge but there are no details of his having studied there. He is said to have been in Cambridge at the same time as John Dee (1527–c. 1608) but there is no corroboration of this, although they were friends in later life. However, based on his publications Blundeville does appear to have obtained a good education somewhere, somehow. Blundeville seems to have lived in London for some time before returning to live in Newton Flotman Manor, which he inherited, when his father died in 1568. Much of his writing also seems to indicate that he spent some time in Italy.
Blundeville was well connected, along with his acquaintances with John Dee, Edward Wright, and Edmund Gunter he was also friends with Henry Briggs (1561–1630). Elizabeth I’s favourite Robert Dudley, 1st Earl of Leicester, who took a great interest in the expanding field of exploration and maritime trade, investing in many companies and endeavours, was one of his patrons. He was also, for a time, mathematics tutor to Elizabeth Bacon, daughter of Sir William Bacon (1510–1579, Lord Keeper of the Great Seal, and elder half sister of Francis Bacon (1561–1626), 1st Viscount St Alban. He was also mathematics tutor in the household of the judge Francis Wyndham (d. 1592) of Norwich. We will return to his tutorship later.
Blundeville only turned to writing on mathematics, astronomy, and navigation late in life having previously published books on a wide range of topics.
Blundeville’s first publication, 1561, was a partial verse translation of Plutarch’s Moralia, entitled Three Moral Treatises, which was to mark the accession of Elizabeth I to the throne and one of which was dedicated to her:
‘Three Morall Treatises, no less pleasant than necessary for all men to read, whereof the one is called the Learned Prince, the other the Fruites of Foes, the thyrde the Porte of Rest,’ The first two pieces are in verse, the third in prose; the first is dedicated to the queen. Prefixed to the second piece are three four-line stanzas by Roger Ascham.
About the same time, he published The arte of ryding and breakinge greate horses, an abridged and adapted translation of Gli ordini di cavalcare by Federico Grisone a Neapolitan nobleman and an early master of dressage.
Grisone’s book was the first book on equitation published in early modern Europe and Blundeville’s translation the first in English. Blundeville followed this in 1565/6 with The fower chiefyst offices belonging to Horsemanshippe, which included a revised translation of Grisone together with other treatises.
In 1570, under the title A very briefe and profitable Treatise, declaring howe many Counsels and what manner of Counselers a Prince that will governe well ought to have. he translated into English, Alfonso d’Woa’s Italian translation of a Spanish treatise by Federigo Furio Ceriól. He now followed up with historiography, his True Order and Methode (1574) was a loose translation and summery of historiographical works by the Italians Jacopo Aconcio (c. 1520–c. 1566) and Francesco Patrizzi (1529–1597). The first work emphasised the importance of historiography as a prerequisite for a counsellor. Both volumes were dedicated to the Earl of Leicester.
In 1575 he wrote Arte of Logike, which was first published in 1599. Strongly Ramist it displays the influences Galen (129–216 CE), De Methodo (1558) of Jacopo Aconcio (c. 1520–c. 1566), Philip Melanchthon (1497–1560), and Thomas Wilson (1524–1581).
Arte of Logike Plainely taught in the English tongue, according to the best approved authors. Very necessary for all students in any profession, how to defend any argument against all subtill sophisters, and cauelling schismatikes, and how to confute their false syllogismes, and captious arguments. By M. Blundevile.
It contains a section on fallacies and examples of Aristotelian and Copernican arguments on the motion of the Earth.
This is very typical of Blundeville’s publications. He is rather more a synthesist of the works of others than an original thinker. This is very clear in his mathematical and geographical works. Blunderville published three mathematical works covering a wide range including cartography, studies in magnetism, astronomy, and navigation. The first of these works was his A Briefe Description of Universal Mappes and Cardes
This contains the following interesting passage:
For mine owne part, having to seek out, in these latter Maps, the way by sea or land to any place I would use none other instrument by direction then half a Circle divided with lines like a Mariner’s Flie [compass rose] [my emphasis]. Truly, I do thinke the use of this flie a more easie and speedy way of direction, then the manifold tracing of the Maps or Mariners Cards, with such crosse lines as commonly are drawn therein…
What Blundeville is describing here is the humble geometrical protractor, which we all used at school to draw or measure angles. This is the earliest known reference to a protractor, and he is credited with its invention.
Blundeville’s second mathematical work, is the most important of all his publications, M. Bludeville His exercises… or to give it its full title:
M. BLVNDEVILE
His Exercises, containing sixe Treatises, the titles wherof are set down
in the next printed page: which Treatises are verie necessarie to be read and learned of all yoong Gentlemen that haue not bene exercised in such disciplines, and yet are desirous to haue knowledge as well in Cosmographie, Astronomie, and Geographie, as also in the Arte of Navigation, in which Arte it is impossible to profite without the helpe of these, or such like instructions. To the furtherance of which Arte of Navigation, the said M. Blundevile speciallie wrote the said Treatises and of meere good will doth dedicate the same to all the young Gentlemen of this Realme.
This is a fat quarto volume of 350 pages, which covers a lot of territory. Blundeville is not aiming for originality but has read and synthesised the works of Martín Cortés de Albacar(1510–1582), Pedro de Medina (1493–1567), William Bourne (c. 1535–1582), Robert Norman (before 1560–after 1596), William Borough (1536–1599), Michel Coignet (1549–1623), and Thomas Hood (1556–1620) and is very much up to date on the latest developments.
The first treatise:
First, a verie easie Arithmeticke so plainlie written as any man of a mean capacitie may easilie learn the same without the helpe of any teacher.
What cause first mooved the Author to write this Arithmeticke, and with what order it is here taught, which order the contents of the chapters therof hereafter following doe plainly shew.
I Began this Arithmeticke more than seuen yeares since for a vertuous Gentlewoman, and my verie deare frend M. Elizabeth Bacon, the daughter of Sir Nicholas Bacon Knight, a man of most excellent wit, and of most deepe iudgment, and sometime Lord Keeper of the great Seale of England, and latelie (as shee hath bene manie yeares past) the most loving and faithfull wife of my worshipfull friend M. Iustice Wyndham, not long since deceased, who for his integritie of life, and for his wisedome and iustice daylie shewed in gouernement, and also for his good hospitalitie deserued great commendation. And though at her request I had made this Arithmeticke so plaine and easie as was possible (to my seeming) yet her continuall sicknesse would not suffer her to exercise her selfe therein. And because that diuerse having seene it, and liking my plaine order of teaching therein, were desirous to haue copies thereof, I thought good therefore to print the same, and to augment it with many necessarie rules meet for those that are desirous to studie any part of Cosmographie, Astronomie, or Geographie, and speciallie the Arte of Navigation, in which without Arithmeticke, as I haue said before, they shall hardly profit.
And moreover, I haue thought good to adde vnto mine Arithmeticke, as an appendix depending thereon, the vse of the Tables of the three right lines belonging to a circle, which lines are called Sines, lines tangent, and lines secant, whereby many profitable and necessarie conclusions aswell of Astronomie, as of Geometrie are to be wrought only by the help of Arithmeticke, which Ta∣bles are set downe by Clauius the Iesuite, a most excellent Mathematician, in his booke of demonstrations made vpon the Spherickes of Theodosius, more trulie printed than those of Monte Regio, which booke whilest I read at mine owne house, together with a loving friend of mine, I took such delight therein, as I mind (God willing) if God giue me life, to translate all those propositions, which Clauius himselfe hath set downe of his owne, touching the quantitie of Angles, and of their sides, as well in right line triangles, as in Sphericall triangles: of which matter, a Monte Regio wrote diffusedlie and at large, so Copernicus wrote of the same brieflie, but therewith somewhat obscurelie, as Clauius saith. Moreover, in reading the Geometrie of Albertus Durcrus, that excellent painter, and finding manie of his conclusions verie obscurelie interpreted by his Latine interpreter (for he himselfe wrote in high Dutch) I requested a friend of mine, whome I knewe to haue spent some time in the studie of the Mathematicals, not onelie plainelie to translate the foresaide Durerus into English, but also to adde thereunto manie necessary propositions of his owne, which my request he hath (I thanke him) verie well perfourmed, not onely to my satisfaction, but also to the great commo∣ditie and profite of all those that desire to bee perfect in Architecture, in the Arte of Painting, in free Masons craft, in Ioyners craft, in Carvers craft, or anie such like Arte commodious and serviceable in any common Wealth, and I hope that he will put the same in print ere it be long, his name I conceale at his owne earnest intreatie, although much against my will, but I hope that he will make himselfe known in the publishing of his Arithmeticke, and the great Arte of Algebra, the one being almost finished, and the other to bee vndertaken at his best leasure, as also in the printing of Durerus, vnto whom he hath added many necessary Geometrical conclusions, not heard of heretofore, together with divers other of his workes as wel in Geometrie as as in other of the Mathe∣maticall sciences, if he be not called away from these his studies by other affaires. In the mean time I pray al young Gentlemen and seamen to take these my labours already ended in good part, whereby I seeke neither praise nor glorie, but onely to profite my countrey.
Blundeville obviously prefers the trigonometry of Christoph Clavius over that of Johannes Regiomontanus but is well acquainted with both. More interesting is the fact that he took his geometry from Albertus Durcrus or Durerus, who is obviously Albrecht Dürer and his Underweysung der Messung mit dem Zirkel und Richtscheyt(Instruction in Measurement with Compass and Straightedge, 1525. Blundeville even goes so far as to have an English translation made from the original German (high Dutch!), as he considers the Latin translation defective.
Title page of Albrecht Dürer’s Underweysung der Messung mit dem Zirkel und Richtscheyt
The second treatise:
Item the first principles of Cosmographie, and especi∣ally a plaine treatise of the Spheare, representing the shape of the whole world, together with the chiefest and most necessarie vses of the said Spheare.
The third treatise:
Item a plaine and full description of both the Globes, aswell Terrestriall as Celestiall, and all the chiefest and most necessary vses of the same, in the end whereof are set downe the chiefest vses of the Ephemerides of Iohan∣nes Stadius, and of certaine necessarie Tables therein con∣tained for the better finding out of the true place of the Sunne and Moone, and of all the rest of the Planets vpon the Celestiall Globe.
A plaine description of the two globes of Mercator, that is to say, of the Terrestriall Globe, and of the Celestiall Globe, and of either of them, together with the most necessary vses thereof, and first of the Terrestriall Globe, written by M. Blundeuill.
This ends with A briefe description of the two great Globes lately set forth first by M. Sanderson, and the by M. Molineux.
The first voyage of Sir Francis Drake by sea vnto the West and East Indies both outward and homeward.
The voyage of M. Candish vntothe West and East Indies, described on the Terrestriall Globe by blew line.
Johannes Stadius’ ephemerides were the first ephemerides based on Copernicus’ De revolutionibus.
The fourth treatise:
Item a plaine and full description of Petrus Plancius his vniversall Mappe, lately set forth in the yeare of our Lord 1592. contayning more places newly found, aswell in the East and West Indies, as also towards the North Pole, which no other Map made heretofore hath, whereunto is also added how to find out the true distance betwixt anie two places on the land or sea, their longitudes and la∣titudes being first knowne, and thereby you may correct the skales or Tronkes that be not trulie set downe in anie Map or Carde.
This map was published under the title, Nova et exacta Terrarum Orbis Tabula geographica ac hydrographica.
Petrus Plancius’ world map from 1594
The fifth treatise:
Item, A briefe and plaine description of M. Blagraue his Astrolabe, otherwise called the Mathematicall Iewel, shewing the most necessary vses thereof, and meetest for sea men to know.
Title Page Source Note the title page illustration is an armillary sphere and not the Mathematical Jewel
The sixth treatise:
Item the first & chiefest principles of Navigation more plainlie and more orderly taught than they haue bene heretofore by some that haue written thereof, lately col∣lected out of the best modern writers, and treaters of that Arte.
Towards the end of this section, we find the first published account of Edward Wright’s mathematical solution of the construction of the Mercator chart
in the meane time to reforme the saide faults, Mercator hath in his vniuersal carde or Mappe made the spaces of the Parallels of latitude to bée wider euerie one than other from the E∣quinoctiall towards either of the Poles, by what rule I knowe not, vnlesse it be by such a Table, as my friende M. Wright of Caius colledge in Cambridge at my request sent me (I thanke him) not long since for that purpose, which Table with his consent, I haue here plainlie set downe together with the vse thereof as followeth.
The Table followeth on the other side of the leafe.
The first edition was published in 1594 and was obviously a success with a second edition in 1597, a third in 1606, and a fourth in 1613. The eighth and final edition appeared in 1638. Beginning with the second edition two extra treatises were added. The first was his A Briefe Description of Universal Mappes and Cardes. The second, the true order of making Ptolomie his Tables.
Blundeville’s Exercises contains almost everything that was actual at the end of the sixteenth century in mathematics, cartography, and navigation.
Blundeville’s final book was The Theoriques of the Seuen Planets written with some assistance from Lancelot Browne (c. 1545–1605) a friend of William Gilbert (c. 1544–1603), and like Gilbert a royal physician, published in 1602:
THE Theoriques of the seuen Planets, shewing all their diuerse motions, and all other Accidents, cal∣led Passions, thereunto belonging. Now more plainly set forth in our mother tongue by M. Blundeuile, than euer they haue been heretofore in any other tongue whatsoeuer, and that with such pleasant demonstratiue figures, as eue∣ry man that hath any skill in Arithmeticke, may easily vnderstand the same. A Booke most necessarie for all Gentlemen that are desirous to be skil∣full in Astronomie, and for all Pilots and Sea-men, or any others that loue to serue the Prince on the Sea, or by the Sea to trauell into forraine Countries.
Whereunto is added by the said Master Blundeuile, a breefe Extract by him made, of Maginus his Theoriques, for the better vnderstanding of the Prutenicall Tables, to calculate thereby the diuerse mo∣tions of the seuen Planets.
There is also hereto added, The making, description, and vse, of two most ingenious and necessarie Instruments for Sea-men, to find out thereby the latitude of any Place vpon the Sea or Land, in the darkest night that is, without the helpe of Sunne, Moone, or Starr. First inuented by M. Doctor Gilbert, a most excellent Philosopher, and one of the ordinarie Physicians to her Maiestie: and now here plainely set downe in our mother tongue by Master Blundeuile.
LONDON, Printed by Adam Islip. 1602.
A short Appendix annexed to the former Treatise by Edward Wright, at the motion of the right Worshipfull M. Doctor Gilbert.
To the Reader.
Being aduertised by diuers of my good friends, how fauorably it hath pleased the Gentlemen, both of the Court and Country, and specially the Gentlemen of the Innes of Court, to accept of my poore Pamphlets, entituled Blundeuiles Exercises; yea, and that many haue earnestly studied the same, because they plainly teach the first Principles, as well of Geographie as of Astronomie: I thought I could not shew my selfe any way more thankfull vnto them, than by setting forth the Theoriques of the Planets, vvhich I haue collected, partly out of Ptolomey, and partly out of Purbachius, and of his Commentator Reinholdus, also out of Copernicus, but most out of Mestelyn, whom I haue cheefely followed, because his method and order of writing greatly contenteth my humor. I haue also in many things followed Maginus, a later vvriter, vvho came not vnto my hands, before that I had almost ended the first part of my booke, neither should I haue had him at all, if my good friend M. Doctor Browne, one of the ordinarie Physicians to her Maiestie, had not gotten him for me…
It is interesting to note the sources that Blundeville consulted to write what is basically an astronomy-astrology* textbook. He names Ptolemy, Georg von Peuerbach’s Theoricae novae planetarum and Erasmus Reinhold’s commentary on it, Copernicus, but names Michael Mästlin as his primary source. Although Copernicus is a named source, the book is, as one would expect at the juncture, solidly geocentric. *Blundeville never mentions the word astrology in any of his astronomy texts, but it is clear from the contents of his books that they were also written for and expected to be used by astrologers.
The Theoriques contains an appendix on the use of magnetic declination to determine the height of the pole very much state of the art research.
Because the making and vsing of the foresaid Instrument, for finding the latitude by the declination of the Mag∣neticall Needle, will bee too troublesome for the most part of Sea-men, being notwithstanding a thing most worthie to be put in daily practise, especially by such as vndertake long voyages: it was thought meet by my worshipfull friend M. Doctor Gilbert, that (ac∣cording to M. Blundeuiles earnest request) this Table following should be hereunto adioined; which M. Henry Brigs (professor of Geometrie in Gre∣sham Colledge at London) calculated and made out of the doctrine and ta∣bles of Triangles, according to the Geometricall grounds and reason of this Instrument, appearing in the 7 and 8 Chapter of M. Doctor Gilberts fift booke of the Loadstone. By helpe of which Table, the Magneticall declination being giuen, the height of the Pole may most easily be found, after this manner.
It is very clear that Thomas Blundeville was a very well connected and integral part of the scientific scene in England at the end of the sixteenth century. An obviously erudite scholar he distilled a wide range of the actual literature on astronomy, cartography, and navigation in popular form into his books making it available to a wide readership. In this endeavour he was obviously very successful as the numerous editions of The Exercises show.
In the last episode I was rude about the pre-Socratics and today I intend to be rude about another more noted Ancient Greek philosopher. Quite logically, Socrates (c. 470–399 BCE) follows on from the pre-Socratics, who was followed by his pupil Plato (c. 428–348 BCE), in turn followed by his pupil Aristotle (384–322 BCE). Socrates, Plato, and Aristotle the much-heralded triumvirate of Ancient Greek philosophy. Socrates left no writings and most of what we know about him comes from his pupils Plato and Xenophon. He needn’t bother us here as he wasn’t really interested in natural philosophy. To quote James Hannam:
Late in his [Socrates] life, he was scornful of natural philosophers, not least because the concocted a multiplicity of explanations for phenomena and never agreed on anything. From this, he concluded that none of them knew what they were talking about.[1]
Portrait of Socrates. Marble, Roman artwork (1st century), perhaps a copy of a lost bronze statue made by Lysippos. Source: Wikimedia Commons
On the other hand, Plato and Aristotle, are the dynamic duo of the history of European science from the fourth century BCE down to the seventeenth century CE, continually weaving in and out of the main narrative. In the case of Plato, viewed rationally there is very little reason why he should have featured in any way prominently in the European history of science; put in modern terminology Plato was not a scientist and his extensive writings contain next to nothing that could be termed science. However, in a couple of his dialogues he includes aspects of cosmology, mostly borrowed from the pre-Socratics, that continued to feature prominently down the centuries, attached to the name Plato.
Plato holding his Timaeus, detail from the Vatican fresco The School of Athens by Raphael Source: Wikimedia Commons
Plato’s acceptance of mathematics as a medium to describe natural philosophy (although it’s not something that he did himself) in contrast to Aristotle’s rejection of mathematics (because the objects of mathematics were not part of nature) led earlier historians to claim that the mathematization of science, in the early modern period, a prominent feature of the so-called scientific revolution, came about through a change from qualitative Aristotelian philosophy to a neo-Platonic quantitative philosophy. I personally, as I explained in my Renaissance Science series, think there are other more significant drivers of the mathematization of the scientific disciplines in the early modern period, although a more favourable view of Platonic philosophy might have played a minor role in that transition.
Plato’s first significant contribution to the scientific debate was the fact that he provides the earliest extant reference to a spherical earth. Previously, all advanced cultures had assumed that the earth was flat. In the Phaedo, Socrates talking about reading Anaxagoras “I assumed that [Anaxagoras] would begin by informing us whether the Earth is flat or round, and then he’d explain why it had to be that way because that was what was better.”[2] We don’t know who first hypothesised that the world was a sphere, Diogenes Laertius (fl. first half 3rd century CE), writing more than five hundred years later says it was Parmenides but he also said it was Pythagoras, Hesiod, and Anaximander. Remember why I’m sceptical about the things attributed to the pre-Socratics. It is obvious from the Plato quote that a discussion of the hypothesis was already taking place, when he wrote the Phaedo, and it is possible that he had the idea from the Pythagorean, Philolaus (c. 470–c. 385 BCE), but nothing is known for certain. Later in the Phaedo, Socrates says, “In the first place the Earth is spherical and in the centre of the heavens. It needs neither air nor any other such force to keep it from falling. The uniformity of the heavens and the equilibrium of the Earth itself are sufficient to support it.” Although spoken by Socrates it is fairly obvious that Plato is presenting his own view here; a view that adopted by Aristotle would become standard in European cosmology.
The nearest that Plato comes to a scientific text is in his Timaeus, a dialogue on the nature of the world, but like all his other works really a dialogue on ethics. Far from being the, from philosophers, much heralded logos in place of mythos, the Timaeus is a highly mythological tale about the creation of the world by a demiurge or divine craftsman. I’m not going to give an account of the metaphysical twists and turns of the Timaeus and simply filter out those ideas that found its way into mainstream European natural philosophical. One almost bizarre aspect of the dialogue is that although Timaeus gives a fairly detailed explanation of the creation of the Earth by the demiurge, he adds that one “should not look for anything more than a likely story.”
The universe is a sphere with the Earth at its centre. The Earth is not explicitly described as a sphere although it implies that it is a sphere. The demiurge creates the Earth out of Empedocles’ four element–earth, water, air, fire–in varying combinations. For Plato, with his belief in a mathematical world, the four elements now have the forms of four of the regular geometrical solids– Fire-Tetrahedron, Air-Octahedron, Water–Icosahedron, Earth–Cube–a concept that remains in discussion down to at least Kepler.
For Plato, once again borrowing from Empedocles, the planets orbit the Earth, at the centre of the universe, in circular orbits at a uniform speed. Another concept that continued to be largely adhered to down to the seventeenth century. Famously, Galileo in his Dialogo held firm to Plato’s circular orbits, despite the work of Kepler showing the orbits of the planets to be ellipses, which vary in speed.
Adhering to the conditions prescribed by Plato, Eudoxus of Cnidus (c. 480–c. 355 BCE), who is said to have been a student of the Pythagorean Archytas (c. 425–c. 350 BCE) and I member of Plato’s school, the Academy, constructed the earliest known Greek geometrical model of the cosmos, a homocentric or concentric spheres model. Each celestial body has a set of nested spheres with the Earth as a common centre but differing axels. But careful choice of the diameter of the spheres and the position of the axels, Eudoxus was able to create a reasonable model of the seeming irrational movement of the planets using only uniform circular motion.
In most modern reconstructions of the Eudoxan model, the Moon is assigned three spheres:
The outermost rotates westward once in 24 hours, explaining rising and setting.
The second rotates eastward once in a month, explaining the monthly motion of the Moon through the zodiac.
The third also completes its revolution in a month, but its axis is tilted at a slightly different angle, explaining motion in latitude (deviation from the ecliptic), and the motion of the lunar nodes.
The Sun is also assigned three spheres. The second completes its motion in a year instead of a month. The inclusion of a third sphere implies that Eudoxus mistakenly believed that the Sun had motion in latitude.
The five visible planets (Mercury, Venus, Mars, Jupiter, and Saturn) are assigned four spheres each:
The outermost explains the daily motion.
The second explains the planet’s motion through the zodiac.
The third and fourth together explain retrogradation, when a planet appears to slow down, then briefly reverse its motion through the zodiac. By inclining the axes of the two spheres with respect to each other, and rotating them in opposite directions but with equal periods, Eudoxus could make a point on the inner sphere trace out a figure-eight shape, or hippopede.
Wikipedia
Simplified schematic of Eudoxus’s concentric sphere model. The Earth (blue) sits in the center of the nested spheres that control the motion of the planet (red). The planet is shown embedded in a tilted sphere that carries it around the zodiac. This sphere is nested in a sphere that rotates daily on the polar axis of the fixed stars.When all four spheres start rotating on their axes, the planet will appear to move along a complex path that resembles its observed motion across the sky.Source
Callippus (c. 370–c. 300 BCE), a student of Eudoxus and of the Academy, extended Eudoxus’ model, adding seven spheres to the original 27, one for the sphere of fixed stars. As we will see, this was the model that Aristotle, with modification, adopted, but which was already rejected by other astronomers in antiquity. However, it enjoyed several revivals over the centuries.
Benjamin Jowett (1817–1893), a Plato expert and translator said, “Of all the writings of Plato, the Timaeus is the most obscure and repulsive to the modern reader.” In the normal run of events the Timaeus should not have had much impact on the unfolding of the history of science. Unfortunately, in late antiquity and the early medieval period the only work of Plato that was widely available to a Latin reading audience was the partial translation of the Timaeus by Cicero (106–43 BCE) and the almost complete translation by Calcidius (late 4. Century CE). George Sarton (1884–1956) one of the founders of the modern history of science in the twentieth century said this about the Timaeus, in his A History of Science (Harvard University Press, 1959)
The influence of Timaeus upon later times was enormous and essentially evil. A large portion of Timaeus had been translated into Latin by Chalcidius, and that translation remained for over eight centuries the only Platonic text known in the Latin West. Yet the fame of Plato had reached them, and thus the Latin Timaeus became a kind of Platonic evangel which many scholars were ready to interpret literally. The scientific perversities of Timaeus were mistaken for scientific truths. I cannot mention any other work whose influence was more mischievous, except the Revelations of John the Divine. The apocalypse, however, was accepted as a religious book, the Timaeus as a scientific one; errors and superstition are never more dangerous than when offered to us under the cloak of science.
[1] James Hannam, The Globe: How the Earth Became Round, Reaktion Books, London, 2023 p. 74
If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.
John S. Wilkins 30th August 2009
Culture is part of the unholy trinity—culture, chaos, and cock-up—which roam through our versions of history, substituting for traditional theories of causation. – Filipe Fernández–Armesto “Pathfinders: A Global History of Exploration”
The Renaissance Mathematicus 