Category Archives: History of Astronomy

Astrology, data, and statistics

Is western astrology a big data science, or even the very first big data science? Data scientist Alexander Boxer thinks it is and has written a book to back up his claim, A Scheme of HeavenThe History of Astrology and The Search for Our Destiny in Data.[1] 

His justification for having written this book is interesting:

Over two thousand years ago, astrologers became the first to stumble upon the powerful storytelling possibilities inherent in numerical data, possibilities that become all the more persuasive when presented graphically in a chart or figure. Although it took a while for the rest of the world to catch on, the art of weaving a story out of numbers of figures, often a specific course of action, is used everywhere today, from financial forecasts to dieting advice to weather models.

And yet numbers still mislead, figures still mislead, figures still deceive, and predictions still fail–sometimes spectacularly so–even those that rely on exceptionally sophisticated mathematics. So, are the techniques being used today to parse and package quantitative information any more effective that what was devised by astrologers millennia ago?

            In order to make that assessment, it’s first necessary to have a basic understanding of what astrology is and how it works. But that sort of understanding–one that’s at least adequate to resolve some seemingly straightforward technical questions–is surprisingly hard to come by for such a long-lived and influential craft. Being frustrated in my own search for a simple yet competent overview of astrology, I decided I might just as well write one myself. This, curious reader, is the book you now hold in your hands.

Boxer is actually correct “a simple yet competent overview of astrology” doesn’t, as far as I know, exist, so has he succeeded in providing one? My answer is a qualified “yes, no, maybe, probably not!” Large parts of Boxer’s book are excellent, other parts are OK, some parts I found simply baffling, and one of his central claims is simply wrong. The biggest problem with the book, as far as I’m concerned, is that it tries to be too many different things in far too few pages. It wants to be a history of astrology from its beginnings down to the present days, at the same time being a data scientist’s, statistical analysis of fundamental aspects of astrology, as well as presenting a quasi-philosophy of science meta-analysis of some central themes of astrology, and that all whilst attempting to achieve to authors declared central aim of providing “a simple yet competent overview of [western][2] astrology.” All of this in just 263 pages of an octavo book with a medium typeface. He also largely leaves out any serious attempt to present the interpretation of a horoscope, which is actually the essence of astrology.

The excellent bits of Boxer’s book are almost all confined to the technical and mathematical aspects of casting a horoscope and to the data scientist’s statistical analysis of various aspects of astrology. There is for example a competently presented, entire chapter devoted to the nuts and bolts of mathematical astronomy, without which it is impossible to actually cast a horoscope. However, this illustrates one, in my opinion serious error in the book. In the opening chapter Boxer presents a brief greatest hits tour of what he labels the obscure beginnings of astrology. I’ve read accounts of the material he presents here that are longer than his entire book, to which I’ll return in a minute, but that is not what concerns me at the moment. Here he presents for the second time (the first one in in the introduction) one of the excellent illustrations that occur throughout the book. This is a horoscope presented on the mater and tympan of an astrolabe without the rete but with the ecliptic. Also presented are all of the relevant astronomical data, time, in various formats, celestial coordinates in all three variants, geographical coordinates and so forth. See below:

However, there is absolutely no explanation of what is being presented here. Now, I’ve spent a number of years studying this stuff, so I know roughly what I’m looking at, although I need to look up which celestial coordinate system is which, for example. A naïve reader coming to this book to learn about astrology would have no idea what they are looking at and nowhere in the book do they get this diagram explained carefully step for step. The knowledge required is contained in the book, scattered around in various sections and chapters but with no linking references to the diagrams. The celestial coordinates are, for example, explained in the chapter on mathematical astronomy, whereas the astrolabe only gets explained in dribs and drabs about one hundred pages later in the book. The Julian Day Count, one of the methods listed on the diagram to denote the time of the horoscope only gets explained on pages 225-226! The information needed to understand what is in fact an excellent diagram is scattered throughout the book like a scavenger hunt without rules or clues.

Remaining by the topic, the book is liberally illustrated with diagrams and tables to explain themes under discussion, and these are excellently done both from a pedagogical and a graphical viewpoint and this is one of the great strengths of the book. There is not a conventional bibliography but at the end of the book there is an annotated collection of source material for each section of the book. There is also a competent index. 

Following up on the all too brief sketch of the origins of western astrology and the more comprehensive introduction to the basics of astronomy, Boxer now dives into what is without doubt one of the greatest error in the book, he fell in love with Marcus Menilius’ Astronomica. After briefly dismissing our knowledge of astronomy in the last five centuries BCE, a serious error because we actually know far more that Boxer is prepared to admit. However, if he did acknowledge it, he would have to abandon his love affair with Manilius. Boxer correctly explains that although the Roman took over large parts of Alexander’s Hellenistic Empire, they were initially reluctant to adopt the Hellenistic astrology. He illustrates this with the fact that there are absolutely no astrological discussions of Julius Caesar’s assassination in 44 BCE. Enter Marcus Manilius and his Astronomica stage left. 

A brief explanation, the Astronomica is a Latin didactic poem dating to the early first century CE, which happens to be the earliest surviving, relatively complete account of western astrology.  About its probable author Marcus Manilius, we know next to nothing. 

Boxer goes complexly overboard about the Astronomica. He writes:

The Astronomica is a fascinating work in its own right, but it takes on a special significance when we recognise that this poem is, essentially, astrology’s grand unveiling on the historical stage. And like Minerva issuing from Jupiter’s skull fully grown and clad in armour, the Astronomica presents an astrology emerging from obscurity remarkably complete and fully formed. Even today, two thousand years later, there is hardly any astrological idea, no matter how sophisticated or complex, which can’t trace its debut to Manilius’s poem.

If the Astronomica is “astrology’s grand unveiling on the historical stage” then it must have got lousy reviews from the critics. Not one single author in antiquity is known to have quoted the Astronomica. There are a grand total of about thirty existing medieval manuscripts of the work none of them older than the ninth century CE. It does not feature in any other medieval literature and appears to have been largely ignored in the Middle Ages. It was (re)discovered in c. 1416 by the zealous Renaissance Humanist manuscript hunter, Poggio Bracciolini (1380–1459) and only really emerged on the European literary and scientific stage when the editio princeps was published by Regiomontanus (1436–1476) in Nürnberg in 1473. 

In his love affair with the Astronomica, Boxer seems to think that modern horoscope astrology is somehow a Roman invention. Later in the book when taking about Arabic astrology he describes Masha’allah’s theory of astrological historical cycles as the “most significant addition to astrology since Roman times.” Manilius is in fact merely describing an existing system that was created by the Hellenistic Greeks between the fifth and first centuries BCE, something that Boxer acknowledges elsewhere in his book, when he goes overboard about the wonders of ancient Alexandria.

As for the guff about “astrology emerging from obscurity remarkably complete and fully formed” and “there is hardly any astrological idea, no matter how sophisticated or complex, which can’t trace its debut to Manilius’s poem,” as already stated Manilius is reporting on an existing system not creating it. More importantly as the modern commentators point out you wouldn’t be able to cast a horoscope having read it and it contains nothing on planetary influence in astrology, the very heart of the discipline.  In fact, although they adopted astrology and used it widely until the decline of the Empire, in the sixth century, the Romans actually contributed next to nothing to the history of astrology.

However, the chapter ends with an example of Boxer’s biggest strength the data based statistical analysis of various aspect of astrology. He starts here with the personality traits that Manlius attributes to those born under a particular sun sign, setting them out in a handy table first. Using the data of different professional groups, he introduces the reader to the concept of statistical significance and shows that the astrological divisions into personality types doesn’t hold water.

Next up we have Ptolemy the most significant author in the whole of the history of western astrology. He gives an adequate sketch of Ptolemy’s contributions to astronomy, geography and astrology and shows that they are actually three aspects of one intellectual project. In his brief discussion of map projection, he makes not an error, but a misleading statement. Introducing Ptolemy’s Planisphere and the stereographic projection the key to the astrolabe he writes:

For the basic idea of a stereographic projection, imagine looking down on a globe from above its North Pole [my emphasis], and then squashing in into the equator. The visual effect ends up looking like a scoop of ice cream that’s melted onto a warm plate from the bottom out. Because there’s no limit to how far outward these maps spread, it’s customary to extend them only as far as the Tropic of Capricorn.

The following pages contain stereographic projections of the celestial sphere, the terrestrial sphere and four tympans from astrolabes taken for different latitudes. Boxer’s error is that these are taken from the South Pole as projection point. Almost all astrolabes are for the Northern Hemisphere and are projections from the South Pole, there are only a handful of Southern Hemisphere astrolabes with the North Pole as projection point. 

Boxer also makes an error in his etymology of the Name Almagest for Ptolemy’s Mathēmatikē Syntaxis. Almagest comes from the Arabic al-majistī, which in turn comes from the Greek megiste all of which mean the greatest. Boxer justifies this as follows:

The Almagest was the greatest of all ancient treatises on astronomy, just as Ptolemy was the greatest of ancient astronomers.

In fact, all of this derives from the alternative Greek name of the Mathēmatikē SyntaxisHē Megalē Syntaxis meaning The Great Treatise as opposed to a smaller work by Ptolemy on astronomy known as The Small Treatise. In other words, the Almagest is the big book on astronomy as opposed to the small book on astronomy.

Boxer has a rather negative opinion of Ptolemy’s Apotelesmatika commonly called the Tetrabiblos in Greek, or Quadripartitum in Latin, meaning four books, his big book on astrology. He finds it dry, technical, and uninspiring, unlike the Astronomica. After introducing Ptolemy’s astrological geography Boxer once again applies his statistical analysis to Ptolemy’s claims on the geographical acceptance of homosexuality comparing it with the modern data on the topic.

Boxer’s next target is the only substantial collection of actual horoscopes from antiquity, by the second century Hellenistic astrologer, Vettius Valens’ Anthologies. We move from the theoretical, Ptolemy, to the practical, Valens. Here Boxer once again reverts to his role as data scientist and gives an interesting seminar on the theme of “how unique is a horoscope? Along the way he sings a brief eulogy for ancient Alexandria as a centre for the mathematical sciences including of course astrology. He also makes a brief excursion into the philosophy of science evoking the falsifiability criterion of Karl Popper and the separation of science and pseudoscience, a couple of pages that are far too brief for what is a very complex discussion and could have been happily edited out. His work, however, on codifying the basics of a horoscope according to Valens and examining the uniqueness of the result is stimulating and a high point of the book.

Next, Boxer moves onto medieval Arabic astrology but doesn’t really. He starts, as do many authors on this topic, with the horoscopes cast to determine the right time to found the city of Baghdad and having given a brief but largely correct account of why the Abbasid caliphs adopted astrology, and the parallel transmission of astrology into Europe in the High Middle Ages, he then passes rapidly to Masha’allah’s theory of historical cycles based on the conjunctions of Jupiter and Saturn and that’s it! Arabic astrology is a massive topic and given its powerful influence on astrology as its practiced today deserves much more attention in any book claiming to provide a “simple yet competent overview of astrology.” Once again, the chapters strength lies in Boxer’s statistics-based analysis of Masha’allah’s theory, which drifts off into the theories of encryption. One thing that did piss me off was in a discussion of the use of symbols he writes:

By necessity, then, efficacy of this magic will hinge upon the fitness of these symbols to their task: Nowhere is this more evident than in mathematics. (If you don’t believe me, try adding the Roman numerals CXXXIX and DCXXIII together; or, even worse, the Greek numerals 𝛒𝛌𝛉 and 𝛘𝛋𝛄.)

This is pure bullshit! Assuming that you are cognisant with the numeral systems and the values of the symbols than these additions are no more difficult than carrying out the same sums using Hindu-Arabic numerals. Division and multiplication are, at least at first glance, more difficult but there are algorithms for both numerical systems that also make those operations as easy as the algorithms for Hindu-Arabic numerals. The major point, however, is that nobody bothered; arithmetical calculations were carried out using an abacus and the numerals were only used to write down the results. 

Having very inadequately dealt with Arabic astrology, Boxer now turns to Guido Bonatti (died around 1300). Before he gets to him, we get a brief section on the transmission from Arabic into Latin where Boxer manages to conflate and confuse two periods of translation in Toledo, one of the major centres for that work. In the twelfth century translators such as Gerard of Cremona translated the major Greek scientific works from Arabic into Latin often with the help of Jewish intermediaries. Later in the thirteenth century Alfonso X of Castille set up a school of translators in Toledo translating Hebrew and Arabic texts into Latin and Castilian, establishing Castilian as a language of learning.  Boxer goes off into an unfounded speculation about texts being translated from Greek into Syriac into Arabic into Hebrew into Castilian (here Boxer incorrectly uses the term Spanish, a language that didn’t exist at the time) into Latin, with all the resulting errors. This paragraph should have been thrown out by a good editor. We then get a couple of paragraphs of waffle about the medieval universities that appears to exist purely to point out that Abelard and Héloïse named their son astrolabe. These should have been replaced with a sensible account of the medieval universities or thrown out by the same good editor. 

We then get an account of the twelfth and thirteenth centuries war between the Guelphs and Ghibellines in Northern Italy largely to introduce Guido Bonatti, who was a Guelph astrologer and author of the Liber Astronomiae, which Boxer tells us, hyperbolically, is the most influential astrology book of the Middle Ages. Here Boxer makes two major errors. Firstly, he presents judicial astrology, which he defines as follows:

The basic premise of judicial astrology is that you ask the stars a question–a question about pretty much anything–and the stars then reveal a judgement or, in Latin, iudicium. The astrologer’s job is to interpret these judgements on your behalf. So far, so good. The odd thing about judicial astrology, however, was that for many questions, and especially the broad category of yes-or-no questions, the astrologer would determine the stars’ judgement based on their positions in the sky at the moment your question was asked.

What Boxer is actually describing is horary astrology, just one of the four branches of judicial astrology, the other three are natal astrology, mundane astrology, and elective astrology; Boxer goes on later to discuss elective astrology. Judicial astrology was opposed to natural astrology, which meant astrometeorology and astromedicine, or to give it its proper name iatromathematics, neither of which Boxer deals with, in any depth, just giving a two-line nod to astromedicine. 

Having described horary astrology, albeit under the wrong label, Boxer goes off on a rant how ridiculous it is/was. Then come two more misleading statements, he writes:

Yet however ho-hum this fatalistic outlook may have been during astrology’s early days in Stoic Rome, to deny the existence of free will was a decidedly and damnably heretical opinion in medieval Christian Europe.

[…]

As was obvious to Dante. Petrarch, and many others, astrology–and especially judicial astrology–was fundamentally incompatible with Christian doctrine. 

First off, Stoic Rome was not astrology’s early days, by that time Hellenistic astrology had been around for about four to five hundred years. Yes, Hellenistic astrology was totally deterministic and did in fact clash with the Church doctrine of free will in the beginnings of the High Middle Ages. However, Albertus Magnus and Thomas Aquinas, who laid the foundations of Church doctrine down to the present day, redefined astrology in their writings in the thirteenth century, as acceptable but non-deterministic thus removing the doctrinal clash. In terms of the impact of their work for the acceptance of astrology not just in the Middle Ages, surely it is far more influential than Bonatti’s Liber Astronomiae.

In the passage that I left out of the quote above Boxer writes, amongst other things:

Well, that’s the sort of thinking that could get you burnt at the stake in you insisted on making a fuss about it. The astrologer Cecco d’Ascoli was condemned by the Inquisition on precisely these grounds and burnt at the stake in Florence on September 16, 1327. [i.e., for practicing deterministic astrology]

This is simply not true! In 1324, Cecco d’Ascoli was admonished by the Church and punished for his commentary on the Sphere of John de Sacrobosco, nothing whatsoever to do with astrology. To avoid his punishment he fled from Bologna, where he was professor for astrology, to Florence. Here, he was condemned for trying to determine the nativity of Christ by reading his horoscope, and as a repeat offender was burnt by the Inquisition. Even under the non-deterministic interpretation of judicial astrology from Albertus Magnus and Thomas Aquinas, casting the horoscope of Christ was considered unacceptable. 

Next, Boxer introduces the Houses of Heaven and claims that, “these are astrology’s system of local coordinates the astrological analog to the modern-day quantities azimuth an elevation.” Sorry but this statement is garbage the houses are not a coordinate system, they are divisions of the ecliptic plane. Boxer introduces them here because they play a central role in Bonatti’s horary astrology. Once again Boxer the data scientist comes to the fore with the question whether it would be possible to construct an algorithm to automatically answer questions posed in horary astrology. As usually one of the best parts of the book.

Traditionally, one of the major disputes amongst astrologers in the question how exactly to determine the boundaries of the houses and Boxer now turns his attention to the various solutions presenting nine different solutions that have been used at some time in the history of astrology. 

One system that was very popular in the Renaissance and Early Modern Period was devised by Regiomontanus (1436–1476), which Boxer looks at in somewhat more detail. He starts with a very brief rather hagiographical biographical sketch, which includes the following claim:

By the time he was twenty-six, Regiomontanus had finished a complete reworking Ptolemy’s Almagest using all the newest trigonometrical methods. 

The Epitome of the Almagest was commissioned from Georg von Peuerbach, Regiomontanus’ teacher, and later colleague, by Cardinal Basilios Bessarion in 1460. Peuerbach had only completed six of the thirteen books by 1461 when he died. On his death bed he commissioned Regiomontanus to complete the work. Regiomontanus went off to Italy with Bessarion, basically as his librarian, and spent the next four years travelling through Italy collecting and copying manuscripts for Bessarion’s library. During this time, he probably completed the Epitome. Meaning he was twenty-nine. Although he might have finished it during the next two years, when we don’t know where he was or what he was doing. He intended to publish the finished book when he set up his publishing house in Nürnberg in 1471 but still hadn’t by the time he died in 1476. It was first published by Johannes Hamman in Venice in 1496

Further on Boxer writes:

Thus, when a certain archbishop in Hungary demanded an improved system for determining the Houses of Heaven–in particular one that would be more faithful to the vague instructions given by Ptolemy in his Tetrabiblos–there was only one person to ask.

            Regiomontanus accepted the challenge. In a brash and masterly treatise, he surveyed the existing methods of House division, dismissed them all as inadequate, introduced an entire new method, and provided tables for computing their boundaries at any latitude to the nearest minute of arc.

A nice story but unfortunately not exactly true. The title of the book that Regiomontanus wrote at the request, not demand, of János Vitéz Archbishop of Esztergom, for whom he had been working as a librarian since 1467 was his Tabulae directionum profectionumque. The purpose and content of the book is revealed in the title, this is not a book about the determination of the Houses, which are only secondary product of the book but about calculating directions, also called prorogratio or progression from the original Greek aphesis. A method to determine major events in the life of a horoscope subject including their death, described by Ptolemy in the Tetrabiblos, which was very popular in Renaissance astrology. 

This error by Boxer is rather bizarre because he describes the method of aphesis, albeit wrongly, whilst dealing with Manilius earlier in his book. Here he writes:

…a procedure … entailed identifying two key points on a birth horoscope: the “starter” and “destroyer.” As time elapsed from the moment of birth, the destroyer revolved along with the heavens towards the starters original position, all the while shooting evil rays at it. When the destroyer finally reached the starter, it was game over: death. The number of hours and minutes it took for the destroyer to reach the starter was then converted to the number of years and months the individual was expected to live.

A very colourful description but actually fundamentally wrong. First the astrologer has to determine the starter on the ecliptic, which is often the moment of birth but not necessarily. Then various destroyers are identified signalling major events in the life of the subjects not just their death, also on the ecliptic. Both points, started and destroyer are projected using spherical trigonometry onto the celestial equator and the number of degrees between the projected points is the time in years. Regiomontanus’ Tabulae directionum provide the mathematical apparatus to carry out this not particularly simple mathematical process. 

Which system of Houses division is still disputed amongst astrologers and Boxer possesses the impertinence to suggest they should use a particular system because he finds it mathematically the most elegant. 

The chapter closes with a short discourse on time, unequal hours, and equinoctial hours, which serves two functions to introduce the index or rule on the astrolabe which makes possible the conversion between unequal and equal hours. Boxer then states:

That the development of the mechanical clock occurred precisely when the most intricate astrological algorithms were in vogue is a historical synchronicity too striking to ignore.

[…]

In fact, the technological crossover between astrology and clock design was significant.

Here he is referring back to an earlier statement on the previous page:

This is why the earliest mechanical clocks of which the one in Prague’s old town square is the most magnificent example had astrolabe-style faces.

Source: Wikimedia Commons

Unfortunately for Boxer’s enthusiasm David S Landes, a leading historian of the clock, argues convincingly that the simple mechanical clock with a “normal” clock face preceded the astrolabe-style clock faces.

The next chapter opens with Tycho Brahe and the nova of 1572. Here once again Boxer choses to distort history for dramatic effect. He writes:

Yet, by all accounts, Tycho wanted nothing to do with Denmark’s administration, its wars, its politics, or its pageantry.

            For a nobleman like Tycho, the purpose of a university education was not to obtain a degree–that would have been unthinkably déclassé–but merely to pick up a little worldly polish of the sort that might prove serviceable in war and diplomacy. In this respect, Tycho’s education backfired spectacularly. He returned from Germany utterly captivated by the latest advances in alchemy, astronomy, and astrology.

Boxer carries on in this manner presenting Tycho as a rebel kicking against the pricks. What he neglects to mention is that although Tycho’s decision to become a professional astronomer was somewhat unorthodox, in all his endeavours Tycho received strong support from his maternal uncle Peder Oxe. Oxe was a university graduate, and a strong supporter of Paracelsian alchemical medicine, who just happened to be the Danish finance minister and Steward of the Realm, de facto prime minister, and politically by far the most powerful man in the whole of Denmark. 

Boxer closes his short section on Tycho with another piece of purple prose:

Tycho’s supernova is of tremendous historical importance because it was the first detailed observation which the old cosmological framework simply could not explain away. Something was rotten in the state of astronomy indeed. Tycho’s new star was a small crack in what had been considered a pristine crystalline firmament. There would be others–so many, in fact, that the entire system would soon collapse and shatter. It wasn’t just the heavens which had proven themselves mutable. A revolution was underway, and science, philosophy astronomy–and astrology–would never be the same.

The immutability of the heavens had been discussed and disputed by astronomers throughout Europe with respect to comets (sub– or supralunar?) since Paolo dal Pozzo Toscanelli (1397–1482) viewed them as supralunar based on his observations of the comet of 1456. The observations and reports of the 1572 supernova by many European astronomers only increased an ongoing debate. A debate that was only one part of a general trend to reform astronomy, which started around 1400 and in which everything was up for discussion. The period also saw a revival of Stoic philosophy and cosmology contra Aristotelian philosophy and cosmology. The supernova of 1572 was not the dramatic turning point that Boxer paints it as.

Boxer now delivers, what I regard as the absolute low point of the book, in that he presents the hairbrained theory of Peter Usher that Shakespeare’s Hamlet is “an elaborate astronomical analogy.” He does however backpedal and state, “I enjoy reading this quite a bit, even if I don’t find it very persuasive.” So, why include it at all?

We then move on to a very rapid sketch of the so-called astronomical revolution with the usual Copernicus=>Tycho/Kepler=>Galileo=>Newton cliché. Boxer now allows himself a real humdinger:

            Clearly Tycho’s commitment to a geocentric cosmos ran much deeper than astronomical arguments alone. IN fact, so central was the Earth’s fixity to Tycho’s philosophy that he proposed a compromise cosmology, one in which Mercury, Venus, Mars, Jupiter, and Saturn orbited the Sun, as in the Copernican system, but the Sun and Moon orbited the Earth as in the Ptolemaic system. It sounds ungainly, and Tycho may have been the only person who ever thought otherwise… [my emphasis].

Tycho may have been the only person? A handful of astronomers all independently came up with the so-called Tychonic geo-heliocentric system around the same time, as an alternative to the Copernican system, leading Tycho to accuse others of plagiarism. From about 1620 till about 1660 the majority of European astronomers thought a Tychonic model with diurnal rotation was the most probable system for the known universe.

Boxer finally gets back on course with the next section where he investigates the use of the words, astronomy, astrology, and mathematics to describe either astronomy or astrology as we know them. A very well-done section. This is followed by a section on the Gregorian calendar reform and why it was necessary, relatively good except for a false claim about Copernicus. He writes:

Copernicus cited the prospect of a more accurate calendar as one reason why he hoped (quite wrongly) that his new, Sun-centered theory of the universe might be well received by the Church.

I have no idea where Boxer found this but it’s simply not true. Copernicus’s only connection with the calendar reform was when he was approached around 1520, like many other European astronomers, to contribute to the calendar reform, he declined, stating that one first needed to accurately determine the length of the year. The chapter closes with a brief account of Kepler’s attitude and contributions to astrology, which falsely claims that he rejected astrology at the end of his life. He didn’t, he rejected traditional horoscope astrology most of his life, although he earned money with it, but believed till the end in his own system of celestial influence.

The final section of the book deals with modern forms of astrology. We have the Madame Blavatsky’s Theosophical Society and her creation of spiritual astrology. The creation of the popular twelve-paragraph newspaper horoscope and finally the creation of psychological astrology, first by the theosophist Alan Leo and developed further by psychoanalyst Carl Jung. Here Boxer delivers, what I regard as the biggest error in his entire book. He writes:

Yet the converse opinion–that every good astrologer must also be a good psychoanalyst–is pretty much the default amongst modern astrologers and their clients alike. For the professional astrologer, this represents a tremendous job promotion. A classical astrologer was, first and foremost, a human calculator, one whose most important qualification was his ability to solve long and tedious mathematical equations. [My emphasis]

Here Boxer, the mathematician, shows that he has literally not understood the difference between casting a horoscope and interpreting a horoscope. In fact, in his book he never really addresses the interpretation of horoscopes, which is the real work of a classical astrology. From the few hints that Boxer gives when discussing horary astrology (which he falsely labels judicial astrology) and elective astrology, he appears to think that you just plug in the planetary positions and the horoscopic spits out the interpretation algorithmically. Nothing could be further from the truth. 

Ptolemy writes at the beginning of the Tetrabiblos, I paraphrase, the science of the stars has two aspects, the first deals with the positions of the stars [our astronomy, his Almagest] and is precise, the second deals with their influence [our astrology, his Tetrabiblos], which is not precise. The first involves casting horoscopes and is mathematical, the second with their interpretations and is not mathematical.

If an astrologer, let us say in the sixteenth century the golden age of astrology, casts a full birth horoscope with planetary positions, houses, aspects, lunar nodes (which Boxer doesn’t deal with as being unnecessarily confusing, directions (explained wrongly by Boxer), lots of fortune (which he doesn’t even mention), etc. You have a very complex collection of material that has to be weighed up very carefully against each other. It is highly unlikely that any two professional astrologers would give the same interpretation, each arguing for their interpretation and explaining why the other interpretation is wrong. Very much of this art of interpretation is based on simplel psychology. A court astrologer, who is basically a political advisor, is going to include many psychological, political, and social factors into the interpretation that he delivers up for employer. 

I recently copyedited the translation of a chapter from a thirteenth century Arabic treatise on astrology that dealt with the interaction of the lunar nodes with the houses when practicing elective astrology. The complexity of the interpretive factors that have to be taking into consideration is mindboggling, so please don’t claim that “a classical astrologer was, first and foremost, a human calculator,” it simply isn’t true. 

If you have read this far you might come to the conclusion that my opinion of Boxer’s book is entirely negative, it isn’t. I think there is an excellent, interesting, and important book struggling to get out of a pool of confusion. Boxer’s strength is that of the data scientist and statistician and his sympathetic to astrology statistical analyses of various aspect of astrology are excellent and very much worth reading for anybody interested in the topic. His book cannot be considered a history of western astrology as he simply leaves much too much out. In fact, it is clear that those things he chooses to include are those that give him the possibility to apply his statistical analysis. Is it a “competent overview of astrology”? No, he leaves too much out, for example any competent overview of astrology must include the lunar nodes and their function in astrology and makes too many errors in his presentations of both the history of astrology and astronomy. Most importantly astrology is about the interpretation of horoscopes, a topic that he does his best to avoid.


[1] Alexander Boxer, A Scheme of HeavenThe History of Astrology and The Search for Our Destiny in Data

[2] Although he constantly refers to astrology rather than western astrology, he does state that his book doesn’t deal with other forms of astrology such as Indian or Chinese. 

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Filed under Book Reviews, History of Astrology, History of Astronomy

Is he  Moonstruck? 

Definition of moonstruck: affected by or as if by the moon: such as: mentally unbalanced

There was a total lunar eclipse on Monday 16 May. This celestial event was, of course, widely announced in advance on social media, with experts giving start and end times as well as duration. They also give detailed explanation of why, how, and when lunar eclipses take place. This meant that worldwide literally millions of people were happily, even excitedly, looking forward, weather permitting, to observing it. So, TV celebrity and aging popinjay Neil deGrasse Tyson decided to dump on all of these people when he tweeted to his 14.6 million followers the following tweet on 16 May:

Lunar eclipses are so un-spectacular that if nobody told you what was happening to the Moon you’d probably not notice at all. Just sayin’.

Ignoring, for a second, the glaring, factual inaccuracy contained in this tweet, it has to be a very serious candidate for the most mean-spirited tweet of the year if not of the decade. One has to seriously ask, why did he do this? Has he become such a desperate, attention-seeking whore that he needs to try and ruin the simple enjoyment of millions world-wide just to provoke a reaction on Twitter?

As a historian of both astronomy and astrology, I expect a man, who once upon a time in his life was an astrophysicist, not to display such ignorance, so publicly in such a spectacular manner. “Lunar eclipses are so un-spectacular…” really? “If nobody told you what was happening to the Moon you’d probably not notice at all,” only if you’ve got your head firmly entrenched in your posterior orifice.

The moon glows red over Columbus, Ohio on Sunday Source

The phenomenon of light pollution, which makes life so difficult for modern astronomers, is actually a very recent development that only became a factor in celestial observation during the course of the twentieth century. Before the eighteenth century, street lighting was confined to large towns and consisted candles or oil lamps and didn’t cause serious light pollution. Even the invention of gas street lighting in the eighteenth century, or of electric street lighting in the nineteenth had no noticeable effect on the night sky. It was first in the twentieth century with the widespread use of strong electric lighting at night that the night skies in towns and cities became so artificially bright as to obscure the night-time celestial sphere. Even then a full moon remains clearly visible for all who are not visually handicapped. 

In the millennia of human existence before the invention of street lighting, the moon was the brightest object in the sky, particularly when full, on a clear night. Lunar eclipses only occur at full moon, and if you happened to be outside in, shall we say, for example, in the eighth century CE, during full moon and the moon started to disappear finally vanishing completely behind a dark shadow, you just might happen to notice. “Just sayin’.” 

Of course, people fucking noticed! Every culture on the Earth, that existed before they discovered the scientific explanation of why lunar eclipses take place has myths, legends, and folktales to explain what happened, when the full moon suddenly started to disappear. For the Maya and the Inca in Middle America, the moon got devoured by a jaguar, which also explained the colour of the so-called blood moon. In ancient Mesopotamia, it was belived that the eclipse was the result of demons attacking the moon and that it presaged an attack upon, or even the death of the king. For the ancient Chinese a lunar eclipse was caused by a dragon biting the moon. For something they didn’t notice, people went to a lot of trouble to invent reasons to explain it.

Tyson, as per usual, doubled down on his mean-spirited tweet with a follow up:

Lunar eclipses occur on average every two or three years and are visible to all the billions of people who can see the Moon when it happens. So, contrary to what you may have been told, lunar eclipses are not rare.

Yes, Mr “I used to be an astrophysicist”, we now know the frequency of lunar eclipses, what sort of eclipse will occur, total, partial penumbral, and can predict the occurrence and duration down to the minute, but have you taken the trouble in your arrogance to ask how we acquired that knowledge? 

Tyson is one of those science communicators, who looks down his nose at the occult sciences, and if he mentions them at all, it is only to sneer at them and the gullible people who believe in them. However, it is to the Babylonian belief in astrology that we owe our original scientific knowledge of the frequency of lunar eclipses. The moon played a central role in Babylonian omen astrology and as noted above, lunar eclipses were considered to presage danger or even death to the king. Because of this, beginning in about 700 BCE the Babylonians began a series of systematic accurate observations and records of eclipses which they continued for about seven hundred years. From this accumulated data they derived the saros series an accurate predictive cycle for eclipses. To quote Wikipedia:

A series of eclipses that are separated by one saros is called a saros series. It corresponds to:

  • 6,585.321347 solar days
  • 18.029 years
  • 223 synodic months
  • 241.999 draconic months
  • 18.999 eclipse years (38 eclipse seasons)
  • 238.992 anomalistic months

The 19 eclipse years means that if there is a solar eclipse (or lunar eclipse), then after one saros a new moon will take place at the same node of the orbit of the Moon, and under these circumstances another eclipse can occur.

The saros series is still used today to predict eclipses. This is a first-class example of how science works: make observations, collect data, look for patterns, derive a law.

I could go on about full moons and lunar eclipses throughout the history of astronomy, but I think I have made my point and will just briefly mention a couple of other examples.

One of the early scientific societies, the Lunar Society of Birmingham, known popularly as The Lunatics, which included Erasmus Darwin, James Watt, Matthew Boulton, Josiah Wedgewood, and even Benjamin Franklin amongst its shifting membership over the years, derived its name from the fact that their meetings were always held at full moon, so that the members could safely find their way home. If a a lunar eclipse fell on a full moon, they would all, being amateur astronomers, have stayed at home to observe it.

As an American, one would have thought that Tyson might have mentioned one of the most famous lunar eclipse stories in history. On his fourth voyage in 1504, Columbus beached his last two remaining ships on the island of Jamaica on 25 June. The indigenous population of the island were reluctant after many months to continue feeding Columbus and his crew. He persuaded them to do so by using the ephemerides of Abraham Zacuto to predict the total lunar eclipse of 1 March 1504. 

Tyson could have used the total lunar eclipse of 16 May as a teaching moment to interest people for astronomy and its history, instead he chose to mock and ridicule those, who were looking forward to observing this celestial phenomenon. He has the cheek to call himself a science communicator, words fail me.

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Filed under History of Astrology, History of Astronomy

A Clock is a Thing that Ticks

As I have mentioned a few times in the past, I came late to the computer and the Internet. No Sinclairs, Ataris, or Commadores in my life, my first computer was a Bondi Blue iMac G3. All of which is kind of ironic, because by the time I acquired that G3, I was something of an expert on the history of computing and computing devices. Having acquired my G3, I then took baby steps into the deep waters of the Internet. My initial interest was in music websites starting with the Grateful Dead. Did I mention that I’m a Dead Head? One day I stumbled across Mark Chu-Carroll’s Good Math, Bad Math blog, which in turn introduced me to the Science Blogs collective of which it was a part. Here I discovered, amongst other, the Evolving Thoughts blog of John Wilkins. Who, more than any other, was responsible for me starting my own blog. Another blog that I started reading regularly was Uncertain Principles by the American physicist Chad Orzel, who wrote amusing dialogues explain modern physics to his dog Emmy. A publisher obviously thought they were good, they were, and they soon appeared as a book, How to Teach Physics to Your Dog (Scribner, 2010), launching his career as a writer of popular science books. This was followed by How to Teach Relativity to Your Dog (Basic Books, 2012) with the original book now retitled as How to Teach [Quantum] Physics to Your Dog. Leaving the canine world, he then published Eureka: Discovering Your Inner Scientist (Basic Books, 2014) followed by Breakfast With EinsteinThe Exotic Physics of Everyday Objects (BenBella Books, 2018). 

All of the above is a longwinded introduction to the fact that this is a review of Chad Orzel’s latest A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks[1].

Astute, regular readers might have noticed that I reviewed Davis Rooney’s excellent volume on the history of timekeeping About TimeA History of Civilisation in Twelve Clocks (Viking, 2021) back in September last year and they might ask themselves if and how the two books differ and whether having read the one it is worth reading the other? I follow both authors, and they follow each other, on Twitter and there were several exchanges during last year as to whether they were covering the same territory with their books. However, I can honestly report that if one is interested in the history of time keeping then one can read both books profitably, as they complement rather than copy each other. Whereas Rooney concentrates on the social, cultural, and political aspects of measuring time, Orzel concentrates on the physics of how time was measured.

The title of this blog post is the title of the introductory chapter of Orzel’s book. This definition I viewed with maximum scepsis until I read his explication of it:

At the most basic level a clock is a thing that ticks.

The “tick” here can be the audible physical tick we associate with a mechanical clock like the one in Union’s Memorial Chapel, caused by collision between gear teeth as a heavy pendulum swings back and forth. It can also be a more subtle physical effect, like the alternating voltage that provides the time signal for the electronic wall clock in our classrooms. It can be exceedingly fast, like the nine-billion-times-a-second oscillations of the microwaves used in the atomic clock that provides the time signals transmitted to smartphones via the internet, or ponderously slow like the changing position of the rising sun on the horizon.

In every one of these clocks, though, there is a tick: a regular repeated action that can be counted to mark the passage of time. 

I said above that what distinguishes Orzel’s book is a strong emphasis on the physics of timekeeping. To this end, the book had not one, but two interrelated but separate narratives. There is the main historical narrative in language accessible to every non-expert reader describing forms of timekeeping, their origins, and developments. The second separate narrative, presented on pages with a grey stripe on the edge, takes the willing reader through the physics and technical aspects behind the timekeeping devices described in the historical narrative. Orzel is a good teacher with an easy pedagogical style, so those prepared to invest a little effort can learn much from his explanations. This means that the reader has multiple possibilities to approach the book. They can read it straight through taking in historical narrative and physics explication as they come, which is what I did. They can also skip the physics and just read the historical narrative and still win much from Orzel’s book. It would be possible to do the reverse and just read the physics, skipping the historical narrative, but I, at least, find it difficult to imagine someone doing this. Other possibilities suggest themselves, such as reading first the historical narrative, then going back and dipping into selected explanations of some of the physics. I find the division of the contents in this way a very positive aspect of the book. 

Orzel starts his journey through time and its measurement with the tick of the sun’s annual journey. He takes us back to the Neolithic and such monuments as the Newgrange chamber tomb and Stonehenge which display obvious solar orientations. The technical section of this first chapter is a very handy guide to all things to do with the solar orbit. The second chapter stays with astronomy and the creation of early lunar, lunar-solar and solar calendars. Here and in the following chapter which deals with the Gregorian calendar reform there are no technical sections. 

In Chapter 4, The Apocalypse That Wasn’t, Orzel reminds us of all the rubbish that was generated in the months leading up to the apocalypse supposedly predicted by the Mayan calendar in 2012. In fact, all it was the end of one of the various Mayan cycles of counting days. Orzel gives a very good description of the Mayan number system and their various day counting cycles. An excellent short introduction to the topic for any teacher. 

Leaving Middle America behind, in the next chapter we return to the Middle East and the invention of the water clock or clepsydra. He takes us from ancient Egypt and the simplest form of water clock to the giant tower clock of medieval China. The technical section deals with the physics of the various systems that were developed to produce a constant flow in a water clock. In the simplest form of water clock, a hole in the bottom of a cylinder of water, the rate of flow slows down as the mass of water in the cylinder decreases. 

Chapter 6 takes us to the real tick tock of the mechanical clock from its beginnings up to the pendulum clock. Interestingly there is a lot of, well explained, physics in the narrative section, but the technical section is historical. Orzel gives us a careful analysis of what exactly Galileo did or did not do, did or did not achieve with his pendulum experiments. The chapter closes with the story how the pendulum was used to help determine the shape of the earth.

The next three chapters take as deep into the world of astronomy. For obvious reasons astronomy and timekeeping have always been interwoven strands. We start with what is basically a comparison of Mayan astronomy, with the Dresden Codex observations of Venus, and European astronomy. In the European section, after a brief, but good, section on Ptolemy and his epicycle- deferent model, we get introduced to the work of Tycho Brahe.

The rules of the history of astronomy says that Kepler must follow Tycho and that is also the case here. After Kepler’s laws of planetary motion, we arrive at the invention of the telescope, the discovery of the moons of Jupiter and the determination of the speed of light. If you want a good, accurate, short guide to the history of European astronomy then this book is for you. 

Chapter nine starts with a very brief introduction to the world of Newtonian astronomy before taking the reader into the problem of determining longitude, a time difference problem, and the solution offered by the lunar distance method as perfected by Tobias Mayer. Here, the technical section explains why the determination of longitude is a time difference problem, how the lunar distance method works, and why it was so difficult to make it work.

Of course, in a book on the history of timekeeping, having introduced the longitude problem we now have John Harrison and the invention of the marine chronometer. I almost cheered when Orzel pointed out that although Harrison provided a solution, it wasn’t “the” solution because his chronometer was too complex and too expensive to be practical. The technical section is a brief survey of the evolution of portable clocks. The chapter closes with a couple of paragraphs in which Orzel muses over the difference between “geniuses” and master craftsmen, a category into which he places both Mayer and Harrison. I found these few lines very perceptive and definitely worth expanding upon. 

Up till now we were still in the era of local time determined by the daily journey of the sun. Orzel’s next chapter takes us into the age of railways, and telegraphs and the need for standardised time for train timetables and the introduction of our international time zone system. The technical section is a fascinating essay on the problems of synchronising clocks using the telegraph and having to account for the delays caused by the time the signal needs to travel from A to B. It’s a hell of a lot more complex than you might think.

We are now firmly in the modern age and the advent of the special theory of relativity. Refreshingly, Orzel does most of the introductory work here by following the thoughts of Henri Poincaré, the largely forgotten man of relativity. Of course, we get Albert too.  The technical section is about clocks on moving trains and will give the readers brains a good workout. 

Having moved into the world of modern physics Orzel introduces his readers to the quantum clock and timekeeping on a mindboggling level of accuracy. We get a user-friendly introduction to the workings of the atomic clock. This was the first part of the book that was completely new to me, and I found it totally fascinating. The technical section explains how the advent of the atomic clock has been used to provide a universal time for the world. The chapter closes with a brief introduction to GPS, which is dependent on atomic clocks.

Einstein returns with his general theory of relativity and a technical section on why and how exactly gravity bends light. A phenomenon that famously provided the first confirmation of the general theory.

Approaching the end, our narrative takes a sharp turn away from the world of twentieth century physics to the advent and evolution of cheap wrist and pocket watches. In an age where it is taken for granted that almost everyone can afford to carry an accurate timekeeper around with them, it is easy to forget just how recent this phenomenon is. The main part of this chapter deals with the quartz watch. A development that made a highly accurate timepiece available cheaply to everyone who desired it. Naturally, the technical section deals with the physics of the quartz clock. 

The book closes with a look at The Future of Time. One might be forgiven for thinking that modern atomic clocks were the non plus ultra in timekeeping, but physicists don’t share this opinion. In this chapter Orzel describes various project to produce even more accurate timepieces.

Throughout the book are scattered footnote, which are comments on or addition to the text. The book is illustrated with grey scale drawing and diagrams that help to explicate points being explained. There is a short list of just seven recommended books for further reading. I personally own six of the seven and have read the seventh and can confirm that they are all excellent. There is also a comprehensive index.

Chad Orzel is a master storyteller and despite the, at times, highly complex nature of the narrative he is spinning, he makes it light and accessible for readers at all levels. He is also an excellent teacher and this book, which was originally a course that he teaches, would make a first-class course book for anybody wishing to teach a course on the history of timekeeping from any level from say around middle teens upwards. Perhaps combined with Davis Rooney’s About TimeA History of Civilisation in Twelve Clocks, as I find that the two books complement each other perfectly. Orzel’s A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks is a first-rate addition to the literature on the topic and highly recommendable. 


[1] Chad Orzel, A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks, BenBella Books, Dallas, TX, 2022

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Filed under Book Reviews, History of Astronomy, History of Physics

A terrible fortnight for the HISTSCI_HULK

It’s been a tough two weeks for my old buddy the HISTSCI_HULK, who has now packed his bags and departed for pastures unknown screaming, “you can all kiss my posterior!” That not what he actually said but you get the message. 

So, what has upset the #histSTM pedant this time and what was the straw that finally broke the poor monsters back? It all started with Nicolaus Copernicus’ birthday on 19 February. As per usual this year, numerous people, including myself, posted on social media to mark the occasion. Our attention was drawn to the post on Twitter by the Smithsonian National Air and Space Museum, so we followed the link to their website and were less than happy about what we found there:

A rigid code of respect for ancient cultures and thought governed the early Renaissance, a period during which resistance to traditional concepts was met with hostility. Therefore, the Polish astronomer, Nicolaus Copernicus, whose ideas changed the course of astronomy forever, did not release his manuscript for publication until he was on his deathbed.

De revolutionibus Source: Wikimedia Commons

PIFFLE! snorted the HISTSCI_HULK, TOTAL PIFFLE! 

The early Renaissance was a period of lively scientific debate characterised by clashes of contrasting, conflicting, and even contradictory theories, and ideas. The debate in astronomy, to which Copernicus contributed, had been rumbling on since at least the middle of the fifteenth century. Also, it is not true that he “didn’t release his manuscript for publication until he was on his deathbed”. Rheticus published his Narratio Prima, as a trial balloon, in 1540. Following its relatively positive reception, Copernicus gave the manuscript of De revolutionibus to Rheticus to take to Petreius in Nürnberg to be published. At the time, as far as we known, he was still healthy. Printing and publishing a book takes time and by the time the book was finished, Copernicus had suffered a stroke and lay on his deathbed. Finally, the reason why Copernicus held De revolutionibus back for so long was because he couldn’t deliver. In the Commentariolus, Copernicus stated he would prove his hypothesis that the cosmos was heliocentric, but he had failed in this endeavour and so was reluctant to publish, a reluctance that was dissolved by the positive reception of the Narratio Prima.

Looking further on the Smithsonian National Air and Space Museum website, under Ancient Times and the Greeks, we find the following: 

Plato wondered why the starlike planets moved relative to the stars. Trying to answer the question was to occupy the attention of astronomers for many centuries.

Plato was more interested in the how rather than the why. Astronomers sought a mathematical explanation for the celestial movements. 

Under Ptolemy’s Planetary System we find the following

In the theory of Ptolemy, the planets moved in small orbits while revolving in large orbits about the Earth. This theory, although incorrect, could explain the apparent motions of the planets and also account for changes in their brightness.

This is an attempt to explain the deferent–epicycle model of planetary motion that Ptolemaeus presented. If one didn’t already know how Ptolemaeus’ system functioned, one certainly would have no idea after reading this. 

This is what is being described: The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). Source: Wikimedia Commons

The HISTSCI_HULK, COME ON SMITHSONIAN YOU CAN DO BETTER THAN THIS!

Already more than somewhat miffed the HISTSCI_HULK had the misfortune fourteen days later to view the article posted by the magazine History Today to acknowledge the birthday of Gerard Mercator on 5 March, he flipped out completely, thundering:

WHAT IS THIS HEAP OF ROTTING GARBAGE? WHY DOESN’T SOMEBODY FLUSH IT DOWN THE TOILET WITH ALL THE OTHER EXCREMENT?

Let us examine the offending object, the opening paragraph truly is a stinker:

The age of discovery that began with Christopher Columbus, along with Ferdinand Magellan’s conclusive demonstration that the Earth is round, created a demand for new maps and confronted cartographers with the problem of how to depict the spherical Earth on a flat surface. Of the various solutions, or ‘projections’, the one accepted as the best was that of Gerardus Mercator, which is still in use today. It was also Mercator who first used the term ‘atlas’ for a collection of maps.

In my opinion the age of discovery is an unfortunate misnomer, as I pointed out in a fairly recent blog post on the subject, preferring the term, Contact Period. It didn’t start with Columbus but was well underway by the time he found backing for his first voyage. 

… along with Ferdinand Magellan’s conclusive demonstration that the Earth is round …!!

Where to start? 1) Nobody of significance in Europe need a demonstration that the Earth was round in 1521, it had been an accepted fact for around a thousand years by then. 2) Ferdinand Magellan didn’t demonstrate anything, he died on route on the island of Mactan, waging imperialist war against the indigenous inhabitants. 3) Any nineteenth century flat earther would counter the claim that he “conclusive demonstration that the Earth is round” by stating that he merely sailed in a circle around the flat Earth disc.

… created a demand for new maps and confronted cartographers with the problem of how to depict the spherical Earth on a flat surface.

This statement would have historians of mapmaking and map projection tearing their hair out, that’s if they have any to tear out. The problem of how to project a spherical earth onto a flat surface had been extensively discussed by Ptolemaeus in his Geographia in the second century CE, a book that re-entered Europe at the beginning of fifteenth century more than one hundred years before Magellan undertook his fateful voyage. 

Of the various solutions, or ‘projections’, the one accepted as the best was that of Gerardus Mercator, which is still in use today.

Ignoring for a moment that “accepted as the best” is total rubbish, which of Mercator’s projections? He used at least two different ones and his son a third. Our author is, of course, referring to the so-called Mercator Projection. First off there is no such thing as “the best projection.” All projections have their strengths and weaknesses and, which projection one uses is dependent, or should be, on the task in hand. The Mercator projection allows a mariner to plot a course of constant compass bearing as a straight line on a sea chart. 

Yes, it was Mercator who first used the term atlas for a collection of maps. Our author at least got that right.

The next paragraph is a potted biography, which is OK but is littered with small inaccuracies:

He was born Gerhard Kremer at Rupelmonde in Flanders (now in Belgium), the seventh and last child of an impoverished German family which had recently moved there. His father was a cobbler, but the surname meant ‘merchant’ and Gerhard turned it into Latin as Mercator after his father and mother died when he was in his teens. A great-uncle who was a priest made sure that he got a good education and after graduating from the University of Louvain in 1532 he studied mathematics, geography and astronomy under Gemma Frisius, the Low Countries’ leading figure in these fields. He learned the craft of engraving from a local expert called Gaspar Van der Heyden and the three men worked together in the making of maps, globes and astronomical instruments for wealthy patrons, including the Holy Roman Emperor Charles V.

When Mercator was born his parents were only visiting his uncle or great-uncle, it is not known for certain whether he was the brother or uncle of Mercator’s father, in Rupelmonde. Following his birth, they returned to Gangelt in the Duchy of Jülich. Whether the family was German, or Flemish is not known for certain. They first moved permanently to Rupelmonde when Mercator was six years old. He adopted the Latin name of Mercator, meaning merchant as does Kremer, not when his parents died but when his uncle/great-uncle sent him to a Latin school. In the school he became Gerardus Mercator Rupelmundanus. After graduating MA on the liberal arts faculty of the University of Louvain in 1532, he left the university and only returned two years later, in 1534, to study geography, mathematics, and astronomy under the guidance of Gemma Frisius. He learnt the art of globe making when he assisted Frisius and Gaspar Van der Heyden to construct a terrestrial globe in 1535. This is followed by another paragraph of biography:

In 1538 Mercator produced a map of the world on a projection shaped like a pair of hearts. His inability to accept the Bible’s account of the universe’s creation got him into trouble with the Inquisition in 1544 and he spent some months in prison on suspicion of heresy before being released. John Dee, the English mathematician, astrologer and sage, spent time in Louvain from 1548 and he and Mercator became close friends.

The sentences about the cordiform projection (heart shaped, devised by Johannes Stabius before Magellan “sailed around the world” by the way) world maps and about John Dee are OK.  Why he refers to Dee as an astrologer but not Frisius or Mercator, who were both practicing astrologers, puzzles me. I’m also not sure why he calls Dee a sage, or what it’s supposed to mean. However, his account of Mercator’s arrest on suspicion of heresy is simply bizarre. He was arrested in 1543 on suspicion of being a Lutheran. Whilst in prison he was accused of suspicious correspondence with the Franciscan friars of Mechelen. No evidence was found to support either accusation, and he was released after four months without being charged. Nothing to do with, “His inability to accept the Bible’s account of the universe’s creation.”

We are now on the home straight with the final paragraph. Mostly harmless biography but it contains a real humdinger!

In 1552 Mercator moved to Duisburg in the Duchy of Cleves in Germany, where he enjoyed the favour of the duke. He set up a cartographic workshop there with his staff of engravers and perfected the Mercator projection, which he used in the map of the world he created in 1569. It employed straight lines spaced in a way that provided an accurate ratio of latitude and longitude at any point and proved a boon to sailors, though he never spent a day at sea himself [my emphasis]. In the 1580s he began publishing his atlas, named after the giant holding the world on his shoulders in Greek mythology, who was now identified with a mythical astronomer-king of ancient times. Strokes in the early 1590s partly paralysed Mercator and left him almost blind. A final one carried him off in 1594 at the age of 82 and he was buried in the Salvatorkirche in Duisburg.

I studied mathematics at university and have been studying/teaching myself the history of map projections for maybe the last thirty years and I have absolutely no idea what the phrase, straight lines spaced in a way that provided an accurate ratio of latitude and longitude at any point, is supposed to mean. I’m certain the author, when he wrote it, didn’t have the faintest clue what he was saying and tried to bluff. I also pity any reader who tries to make any sense out of it. It’s balderdash, hogwash, gobbledygook, poppycock, mumbo-jumbo, gibberish, baloney, claptrap, prattle, or just plain total-fucking-nonsense! What it definitively isn’t, in anyway whatsoever, is a description of the Mercator projection.

This wonderful piece of bullshit caused the HISTSCI_HULK to flip out completely. Imitating Charles Atlas, he tore his facsimile edition of the Mercator-Hondius Atlas in half with his bare hands and threw it out of the window. It’s a hard back by the way.

The term Atlas, as used by Mercator had nothing to do with the mythological Greek Titan Atlas, who by the way, holds the cosmos on his shoulders and not the Earth, but rather bizarrely the equally mythical King Atlas of Mauritania, who according to legend was a wise philosopher, mathematician, and astronomer, who is credited with having produced the first celestial globe. As Mercator explains: “I have set this man Atlas, so notable for his erudition, humaneness, and wisdom as a model for my imitation.”

Bizarrely, the article is illustrated, not by Mercator’s 1569 world map based on his projection, but the double planisphere world map from 1587 created by his son Rumold Mercator (1541–1599), which was based on it, and which first appeared in Isaac Casaubon’s edition of Strabo’s Geographia, published in Geneva. It was incorporated into later editions of the Atlas. 

Source: Wikimedia Commons

History Today is a popular English monthly history magazine, which according to Wikipedia, and I quote, “presents serious and authoritative history to as wide a public as possible.” Judging by this article, you could have fooled me. History Today has more than 300,000 followers on Twitter, that’s more than 300,000 potential readers for this garbage. The article was written by Richard Cavendish (1930–2016), an Oxford graduate, who specialised in medieval studies. Most well known as a historian of the occult his work, quoting Wikipedia once more, “is highly regarded for its depth of research and agnostic stance towards its sometimes controversial subject matter,” and, “He also wrote regularly for the British journal History Today.” The article was written in 2012, but the editor, Paul Lay, who considered it “serious and authoritative history” then, is the same editor, who thought it suitable to trot out again in 2022. 

Having within a fortnight been confronted by two horrible examples of how not to write popular #histSTM, the HISTSCI_HULK was more than somewhat mentally fragile when he stumbled on the offending object that finally caused him to snap, pack his bag, and depart, vowing never to read another word ever again. The offending object? A page from the book of the four-year-old daughter of a historian, who I know on Twitter:

THAT’S BLEEDIN’ INDOCTRINATION, THAT IS, SCREECHED THE HISTSCI_HULK AS HE SLAMMED THE DOOR SHUT ON HIS WAY OUT

“He made an amazing discovery.” As we obviously have to do with Galileo’s telescopic discoveries, there were more than one, we will restrict ourselves to those. All of Galileo’s telescopic discoveries were made independently, in the same time period, by other astronomers and they were also confirmed by the Jesuit astronomers of the Collegio Romano, so in fact anybody, who had anything to say on the topic, not only believed him but also congratulated him for having made them. 

“Galileo changed how people think about the Sun and Earth.” If any single person is going to be given credit for that then surely it should be Copernicus. In fact, it is, in my opinion, wrong to credit any single person with this. The shift in perception from a geocentric cosmos to a heliocentric one was a gradual accumulative process to which a fairly number of people contributed.

“He built a new telescope to study space.” I have difficulties with the new in this sentence. Galileo, like quite a large number of people built a so-called Dutch telescope with which to make astronomical observations. He was by no means unique in doing this and not even the first to do so. What should be expressed here is that Galileo was one of a number of people, who constructed telescopes, after it was invented in 1608, in order to make astronomical observations.

“He proved that Earth travels around the Sun.” Apart from the fact that the sentence isn’t even grammatically correct, it should read “the Earth”, it’s simple false. The problem that faced all the early supporters of a heliocentric model of the cosmos was that they simply couldn’t prove the hypothesis.

“People thought it was the other way around.” Of course, they did because that’s what our senses tell us. We all have to learn that it’s not true!

I have a very simple question. Why do people present young, impressionable children with garbage like this?

In case anybody is concerned, I’m sure the HISTSCI_HULK will return when he’s calmed down.  

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Filed under History of Astronomy, History of Cartography, Myths of Science

Renaissance science – XXVIII

In the last episode of this series, we explored the history of the magnetic compass in Europe and marine cartography from the Portolan chart to the Mercator Projection. We will now turn our attention to the other developments in navigation at sea in the Renaissance. As already stated in the last episode, the need to develop new methods of navigation and the instruments to carry them out was driven by what I prefer to call the Contact Period, commonly called the Age of Discovery or Age of Exploration. The period when the Europeans moved out into the rest of the world and exploited it. 

This movement in turn was motivated by various factors. Curiosity about lands outside of Europe was driven both by travellers’ tales such as The Travels of Marco Polo c. 1300 and The Travels of Sir John Mandeville, which first appeared around 1360, both of which were highly popular throughout Europe, and also by new cartographical representation of the know world, known to the Europeans that is, in particular Ptolemaeus’ Geographia, which first became available in the early fifteenth century. Another development was technological, the development by the Portuguese, who as we shall see led the drive out of Europe into the rest of the world, of a new type of ship, the caravel, which was more manoeuvrable than existing vessels and because of its lateen sails was capable of sailing windward, making it more suitable for long ocean voyages, as opposed to coastal sailing.

The Portuguese invention of the caravel, which was maneuverable and able to undertake ocean voyages, was essential to European maritime exploration. The present image shows the “Caravela Vera Cruz“, navigating the Tagus river, Lisboa. Source: Wikipedia Commons
Depending on the situation, different intervals between tacking can be used. This does not influence the total distance travelled (though may impact the time required). Sailing from point A to point B, path P1 involves more turns but only requires a narrow channel. Path P2 involves fewer turns but a wider channel. Path P3 requires only a single turn but covers comparatively the widest channel. Source: Wikimedia Commons

The final and definitely most important factor was trade or perhaps more accurately greed. The early sailors, who set out to investigate the world outside of Europe, were not the romantic explorers or discoverers, we get taught about in school, but hard-headed businessmen out to make a profit by trade or if necessary, theft. 

The two commodities most desired by these traders, were precious metals, principally gold but also silver and copper, and spices. The metal ore mines of Middle Europe could not fill the demands for precious metals, so other sources must be found. This is perhaps best illustrated by the search in South America, by the Spanish, for the mythical city of gold, El Dorado, during the sixteenth century. Spices had been coming into Europe from the East over the Indian Ocean and then overland, brought by Arab traders, to the port cities of Northern Italy, principally Venice and Genoa, from where there were distributed overland throughout Europe since the eleventh century. The new generation of traders thought they could maximise profits by cutting out the middlemen and going directly to the source by the sea route. This was the motivation of both Vasco da Gama (c. 1460–1524), sailing eastwards, and Christopher Columbus (1451–1506), sailing westward. Their voyages are, however, one end point of a series of voyages, which began with the Portuguese capture of Ceuta, in North Africa, from the Arabs, in 1415.

Having established a bridgehead in North Africa the Portuguese, who were after all situated on the Atlantic coast of the Iberian Peninsula, argued that they could bypass the middleman, their trading partners the Arabs, and sail down the coast to Sub-Saharan West Africa and fetch for themselves, the gold and the third great trading commodity of the Contact Period, slaves, who they had previously bought from Arab traders. It is fair to ask why other countries, further north, with Atlantic coasts did not lead the expansion into unknown territory? The first decades of the Portuguese Atlantic ventures were still very much coastal sailing progressively further down the African coast; other northern European countries, such as Britain did sail north and south along the Atlantic coast, but their journeys remained within Europe. 

Starting in 1520, Portuguese expeditions worked their way down the west coast of Africa until the end of the sixteenth century.

The gradual Portuguese progress down the West Coast of Africa Source: Wikipedia Commons

The Nürnberger Martin Behaim (1459–1507), responsible for the creation of the oldest surviving terrestrial globe and member of the Portuguese Board of Navigation (to which we will return), claimed to have sailed with Diogo Cão, who made two journeys in the 1480s, which is almost certainly a lie. At the time of Cão’s first voyage along the African coast Behaim is known to have been in Antwerp. On his second voyage Cão erected pillars at all of his landing places naming all of the important members of the crew, who were on the voyage, Martin Behaim is not amongst them. 

The two most significant Portuguese expedition were that of Bartolomeu Dias (c. 1450–1500) in 1488, which was the first to round the Cape of Good Hope, actually Diogo Cão’s aim on his two voyages, which he failed to achieve, and, of course, Vasco da Gama’s voyage of 1497, which took him not only up the east African coast but all the way to India with the help of a local navigator. The two voyages also showed that the Indian Ocean was open to the south, whereas Ptolemaeus had shown it to be a closed sea in his Geographia. 

Much earlier in the century the Portuguese had ventured out into the Atlantic and when blown off course by a storm João Gonçalves Zarco (c. 1390 –1471) and Tristão Vaz Teixeira (c. 1395–1480) discovered the archipelago of Madeira in 1420 and one expedition discovered the Azores, 1,200 km from the Portuguese coast in 1427. The Canaries had already been discovered in the early fourteenth century and were colonised by the Spanish in 1402. The Cap Verde archipelago was discovered around 1456. The discovery of the Atlantic islands off the coasts of the Iberian Peninsula and Africa was important in two senses. Firstly, there developed myths about other islands further westward in the Atlantic, which encouraged people to go and look for them. Secondly, by venturing further out into the Atlantic sailors began to discover the major Atlantic winds and currents,, known as gyres essential knowledge for successful expeditions.

The Atlantic Gyres influenced the Portuguese discoveries and trading port routes, here shown in the India Run (“Carreira da Índia“), which would be developed in subsequent years. Source: Wikipedia Commons

Dias could only successfully round the Cape because he followed the prevailing current in a big loop almost all the way to South America and then back past the southern tip of Africa. Sailors crossing the Indian Ocean between Africa and India had long known about the prevailing winds and currents, which change with the seasons, which they had to follow to make successful crossings. The Spanish and the Portuguese would later discover the currents they needed to follow to successfully sail to the American continent and back.

The idea of island hopping to travel westwards in the Atlantic that the discoveries of the Azores and the other Southern Atlantic islands suggested was something already been followed in the North Atlantic by fishing fleets sailing out of Bristol in Southwest England in the fifteenth century. They would sail up the coast of Ireland going North to the Faroe Islands, settled by the Vikings around 800 CE and then onto Iceland, another Viking settlement, preceding to Greenland and onto the fishing grounds off the coast of Newfoundland. This is the route that Sebastian Cabot (c. 1474–c. 1557) would follow on his expedition to North America in the service of Henry VIII. It is also probable that Columbus got his first experience of navigating across the Atlantic on this northern route. 

Columbus famously made his first expedition to what would be erroneously named America in 1492, in an attempt to reach the Spice Islands of Southeast Asia by sailing westward around the globe. This expedition was undertaken on the basis of a series of errors concerning the size of the globe, the extent of the oikumene, the European-Asian landmass known to the Greek cartographers, and the distance of Japan from the Asian mainland. Columbus thought he was undertaking a journey of about 3,700 km from the Canary Islands to Japan instead of the actual 19,600 km! If he hadn’t bumped into America, he and his entire crew would have starved to death on the open sea. Be that as it may, he did bump into America and succeeded in returning safely, if only by the skin of his teeth. With Columbus’ expedition to America and da Gama’s to India, the Europeans were no longer merely coastal sailors but established deep sea and new approaches to navigation had to be found.

The easiest way to locate something on a large open area is to use a geometrical coordinate system with one set of equally spaced lines running from top to bottom and a second set from side to side or in the case of a map from north to south and east to west. We now call such a grid on a map or sea chart, lines of longitude also called meridians, north to south, and lines of latitude also called parallels, east to west. The earliest know presentation of this idea is attributed to the Greek polymath Eratosthenes (c. 276­–c. 195 BCE).

A perspective view of the Earth showing how latitude (𝛟) and longitude (𝛌) are defined on a spherical model. The graticule spacing is 10 degrees.

The concept was reintroduced into Early Modern Europe by the discovery of Ptolemaeus’ Geographia. It’s all very well to have a location grid on your maps and charts but it’s a very different problem to determine where exactly you are on that grid when stuck in the middle of an ocean. However, before we consider this problem and its solutions I want to return to the Portuguese Board of Navigation, which I briefly mentioned above.

Both the Portuguese and the Spanish realised fairly early on as they began to journey out onto the oceans that they needed some way of collecting and collating new geographical and navigation relevant information that their various expeditions brought back with them and also a way of imparting the relevant information and techniques to navigators due to set out on new expeditions. Both countries established official institutions to fulfil these tasks and also appointed official cosmographers to lead these endeavours. Pedro Nunes (1502–1578), who we met in the first episode on navigation, as the discoverer of the loxodrome, was appointed Portugal’s Royal Cosmographer in 1529 and Chief Royal Cosmographer in 1547, a post he held until his death.

Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons

The practice of establishing official organisations to teach cartography and navigation, as well as the mathematics they needed to carry them out to seamen was followed in time by France, Holland, and Britain as they too began to send out deep sea marine expeditions. 

To determine latitude and longitude are two very different problems and I will start with the easier of the two, the determination of latitude. For the determination of longitude or latitude you first need a null point, for latitude this is the equator. In the northern hemisphere your latitude is how many degrees you are north of the equator. You can determine your latitude using either the Sun during the day or the North Star at night. At night you need to observe the North Star with some sort of angle measuring device then measure the angle that makes to the horizon and that angle is your latitude in degrees. During the day you need to observe the Sun at exactly noon with an angle measuring device then the angle to makes with a vertical plumb line is your latitude. This is only strictly true for the date of the two equinoxes. For other days of the year, you have to calculate an adjustment using tables. For these observations mariners initially used either a quadrant,

Geometric quadrant with plumb bob. Source: Wikimedia Commons

which had been in use since antiquity or a Jacob’s Staff or Cross Staff, the invention of which is attributed to the French astronomer Levi Ben Gershon (1268–1344).

A sailor uses a ‘Jacob’s Staff’ to calculate the angle between a star and the horizon Source

Contrary to many claims, astrolabes were never used on ships for this purpose. However, around the end of the fifteenth century a much-simplified version of the astrolabe, the mariner’s astrolabe began to be used for this purpose. 

Mariner’s astrolabe Source: Wikimedia Commons

Because looking directly into the Sun is not good for the eyes, the backstaff was developed over time. With a backstaff the mariner stands with his back to the Sun and a shadow is cast onto the angle measuring scale. Thomas Harriot (c. 1560–1621) is credited with being the originator of the concept. The mariner John Davis (c. 1550–1605) introduced the double quadrant or Davis quadrant in his book on practical navigation, The Seaman’s Secrets in 1594, a device that evolved over time.

Davis quadrant, made in 1765 by Johannes Van Keulen. On display at the Musée national de la Marine in Paris. Source: Wikimedia Commons
How a Davis Quadrant is used Source includes a video of how to use one

In 1730, John Hadley invented the reflecting octant, which incorporated a mirror to reflect the image of the Sun, whilst the user observed the horizon.

John Hadley Source: Wikimedia Commons
Hadley Octant Source includes video

This evolved into the sextant the device still used today to “shoot the Sun” as it is called. Here we see an evolution of instruments used to fulfil a specific function.

The determination of longitude at sea is a much more difficult problem. First, there is no natural null point, and any meridian can be and indeed was used until the Greenwich Meridian was chosen as the international null point for the determination of longitude at the International Meridian Conference in Washington in 1884. Because the Earth revolves once in twenty-four hours the determination of the difference in longitude between two locations is equivalent to the difference in local time between them, one degree of longitude equals four minutes of time difference, so the determination of longitude is basically the determination of time differences, which is easy to state but much more difficult to carry out.

The various European sea going nations–Spain, Portugal, France, Holland, Britain–all offered financial awards to anybody who could come up with a practical solution for determining longitude at sea. 

In antiquity, the difference in longitude between two locations was determined by calculating the difference in the observation times of major astronomical events such as lunar or solar eclipses. Then, if one had determined the difference in longitude between two given locations and their respective distances from a third location, it was possible to calculate the difference in longitude for the third location geometrically. Using these methods, astronomers, and cartographers gradually built-up tables of longitude for large numbers of towns and cities such as the one found in Ptolemaeus’ Geographia. This method is, of course, not practical for mariners at sea.

Starting in the early sixteenth century, various methods were suggested for determining time differences in order to determine longitude. The Nürnberger mathematicus Johannes Werner (1468 – 1522) in his In hoc opere haec continentur Nova translatio primi libri geographiae Cl’ Ptolomaei … (Nürnberg 1514) proposed the so-called lunar distance method. In this method an accurate table of the position of the Moon relative to a given set of reference stars for a given location for the entire year needs to be created.

Source: Wikimedia Commons

The mariner then has to observe the position of the Moon relative to the reference stars for his local time and then calculate the time difference to the given location from the tables. Unfortunately, because the Moon is pulled all over the place by the gravitational influence of both the Sun and the Earth, its orbit is highly irregular and the preparation of such tables proved beyond the capabilities of sixteenth century astronomers and indeed of seventeenth century astronomers, when the method was proposed again by Jean-Baptiste Morin (1583–1656). There was also the problem of an instrument accurate enough to measure the position of the Moon on a moving ship. It was Tobias Mayer (1723–1762), who first managed to produce accurate tables and Hadley’s octant or rather the sextant that evolved out of it solved the instrument problem. The calculations necessary to determine longitude having measured the lunar distance proved to be too complex and too time consuming for seamen and so Neville Maskelyne produced the Nautical Almanac containing the results pre-calculated in the form of tables and published for the first time in 1766.

Portrait of Nevil Maskelyne by Edward Scriven Source: Wikimedia Commons
Source: Library of Congress Washington

The next solution to the problem of determining longitude suggested during the Renaissance by Gemma Frisius (1508–1555) was the clock, published in his De principiis astronomiae et cosmographiae. (Antwerp, 1530).

Gemma Frisius 17th C woodcut by E. de Boulonois Source: Wikimedia Commons

The mariner should take a clock, capable of maintaining accurate time over a long period under the conditions that prevail on a ship on the high seas, set to the time of the point of departure. By comparing local time with the clock time, the longitude difference could then be calculated. The problem was that although mechanical clocks had been around for a couple of centuries when Gemma Frisius made his suggestion, they were incapable of maintaining the required accuracy on land, let alone on a ship at sea. Jean-Baptiste Morin thought it would never be possible, “I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try.” A view apparently shared by Isaac Newton, when he sat on the English Board of Longitude.

Only when Christiaan Huygens (1629–1695) had the first pendulum clock constructed by Salomon Coster (c. 1620–1659) accord his design in 1657 that Frisius’ idea began to seem realistic.

Christiaen Huygens II (1629-1695) signed C.Netscher / 1671 Source: Wikimedia Commons
Spring-driven pendulum clock, designed by Huygens and built by Salomon Coster (1657),  with a copy of the Horologium Oscillatorium (1673), at Museum Boerhaave, Leiden. Source: Wikimedia Commons

One of Huygens’ clocks was actually sent on sea trials but failed the test. In what is, thanks to Dava Sobel[1], probably the most well-known story in the history of technology John Harrison (1693–1776)

P. L. Tassaert’s half-tone print of Thomas King’s original 1767 portrait of John Harrison, located at the Science and Society Picture Library, London Source: Wikimedia Commons

finally succeeded in producing a clock capable of fulfilling the demands with his H4 in 1761, slightly later than the successful fulfilment of the lunar distance method. In one sense the problem was still not really solved because the H4 was too complex and too expensive for it to be mass produced at a reasonable cost for use in sea transport. It was only really in the nineteenth century, after further developments in clock technology, that the marine chronometer became a real solution to the longitude problem.

Harrison’s “sea watch” No.1 (H4), with winding crank Source: Wikimedia Commons

Back tacking, at the beginning of the seventeenth century with the discovery of the four largest moons of Jupiter another method suggested itself. These moons, Io, Europa, Ganymede, and Callisto, have orbital periods of respectively, 1.77, 3.55, 7.15, and 16.6 days.

A montage of Jupiter and its four largest moons (distance and sizes not to scale) Source: Wikimedia Commons

This means that one or other of them is being fairly often eclipsed by Jupiter. Galileo argued that is one could calculate the orbits accurately enough they could be used as a clock to determine longitude. He tried to sell the idea to the governments of both Spain and the Netherlands without success. The principal problem was the difficulty of observing them with a telescope on a moving ship. Galileo worked on an idea of an observing chair with the telescope mounted on a helmet, but the idea never made it off the paper. Later in the seventeenth century Jean-Dominique Cassini (1625–1712) produced tables of the orbits accurate enough for them to be used to determine longitude and he and Jean Picard (1620–1682) used the method on land to accurately determine the borders of France, leading Louis XVI to famously quip that he had lost more territory to the cartographers than he ever lost to his enemies.

Map showing both old and new French coastlines Source: Wikimedia Commons

In the first part of this account of navigation I described the phenomenon of magnetic variations or declination, which is the fact that that a compass does not point to true north but to magnetic north, which is somewhat removed from true north. I also mentioned that magnetic declination is not constant but varies from location to location. This led to the thought that if one were to map the magnetic inclination for the entire Atlantic one could use the data to determine longitude, whilst at sea. Edmond Halley (1556–1742) did in fact create such a map on a voyage from1699 to 1700. However, this method of determining longitude was never really utilised. 

Portrait of Halley (c. 1690) by Thomas Murray Source: Wikimedia Commons
Halley’s 1701 map showing isogonic lines of equal magnetic declination in the Atlantic Ocean. Source: Wikimedia Commons

Although the methods eventually developed to determine longitude on the high seas all came to fruition long after the Renaissance, they all have their roots firmly planted in the practical science of the Renaissance. This brief sketch also displays an important aspect of the history of science and technology. A lot of time can pass, and very often does, between the recognition of a problem, the suggestion of one or more solutions to that problem, and the realisation or fulfilment of those solutions.

Having gone to great lengths to describe the principal methods suggested and eventually realised for determining longitude, there were others ranging from the sublime to the ridiculous that I haven’t described, there remains the question, how did mariners navigate when far away from the coast during the Early Modern Period? There are two answers firstly latitude sailing and secondly dead reckoning. In latitude sailing, instead of, for example, trying to cross the Atlantic by the most direct course from A to B, the navigator first sails due north or south along the coast until he reaches the latitude of his planned destination. They then turn their ship through ninety degrees and maintain a course along that latitude. This, of course, nearly always means a much longer voyage but one with less risk of getting lost. 

In dead reckoning, the navigator, starting from a fixed point, measures the speed and direction of his ship over a given period of time transferring this information mathematically to a sea chat to determine their new position. The direction is determined with the compass, but the determination of the ship’s speed is at best an approximation, which was carried out in the following manner. A log would be thrown overboard at the front of the ship and the mariners would measure how long it took for the ship to pass the log, and the result recorded in a book, which became known as the logbook. The term logbook expanded to include all the information recorded on a voyage on a sip and then later on planes and even lorries. Of note, the word blog is an abbreviation of the term weblog, a record of web or internet activity, but I’m deviating from the topic.

An example of dead reckoning Columbus’ return voyage Source

The process of measuring the ships speed evolved over time. The log was thrown overboard attached to a long line and using an hourglass, the time how long the line needed to pay out was recorded. Later the line was knotted at regular intervals and the number of knots were recorded for a given time period. This is, of course, the origin of the term knots for the speed of ships and aircraft. Overtime the simple log of wood was replaced with a so-called chip-log, which became standardised:

The shape is a quarter circle, or quadrant with a radius of 5 inches (130 mm) or 6 inches (150 mm), and 0.5 inches (13 mm) thick. The logline attaches to the board with a bridle of three lines that connect to the vertex and to the two ends of the quadrant’s arc. To ensure the log submerges and orients correctly in the water, the bottom of the log is weighted with lead. This provides more resistance in the water, and a more accurate and repeatable reading. The bridle attaches in such a way that a strong tug on the logline makes one or two of the bridle’s lines release, enabling a sailor to retrieve the log. (Wikipedia)

Model of chip log and associated kit. The reel of log-line is clearly visible. The first knot, marking the first nautical mile is visible on the reel just below the centre. The timing sandglass is in the upper left and the chip log is in the lower left. The small light-coloured wooden pin and plug form a release mechanism for two lines of the bridle. From the Musée de la Marine, Paris. Source: Wikimedia Commons

The invention of the log method of determining a ship’s speed is attributed to the Portuguese mariner Bartolomeu Crescêncio at the end of the fifteenth century. The earliest known published account of using a log to determine a ship’s speed was by William Bourne (c. 1535–1582) in his A regiment of the Sea in 1574, which went through 11 English editions up to 1631 and at least 3 Dutch edition from 1594. 

Dead reckoning is a process that is prone to error, as it doesn’t take into account directional drift caused by wind and currents. Another problem was that not all mariners processed the necessary mathematical knowledge to transfer the data to a sea chart. Those mariners, who disliked and rejected the mathematical approach used a traverse board, which uses threads and pegs to record direction and speed of a ship. William Bourne writing in 1571 said:

I have known within these 20 years that them that were ancient masters of shippes hathe derided and mocked them that have occupied their cards and plattes and also the observation of the Altitude of the Pole saying; that they care not for their sheepskinne for he could keepe a better account upon a board.

This blog post is already far too long, so I’ll skip a detailed description of the traverse board, but you can read one here.

We have one last Renaissance contribution to the art of navigation from the English mathematical practitioner, Edmund Gunter (1581–1626), who we have already met as the inventor of the standard English surveyor’s chain in the episode on surveying. Gunter invented the Gunter scale or rule, simply known as the “gunter” by mariners, which he published in his Description and Use of the Sector, the Crosse-staffe and other Instrumentsin 1623. Developed shortly after the invention of logarithms, the scale is usually somewhat more than a half metre long and about 40 mm broad. It is engraved on both sides with various scales or lines. Usually, on the one side are natural line, chords, sines, tangents, rhumbs etc., and on the other scales of the logarithms of those functions. Navigational mathematical problems were then worked through using a pair of compasses. 

Gunter scale front
Gunter scale back Source

Despite its drawbacks, uncertainties, and errors dead reckoning was used for centuries by European mariners to crisscross the oceans and circumnavigate the globe. It continued to be used well into the nineteenth century, long after the perfection of the marine chronometer and the lunar distance method. 

This over long blog post is but a sketch of the contributions made by the Renaissance mathematical practitioners to the development of methods of deep-sea navigation required by the European mariners during the Contact Period, when they swarmed out to investigate the world beyond Europe and exploit it. Those contributions were in the form of theories, publications, instruments, charts, and practical instruction (which I haven’t really expanded upon here). For a more detailed version of the story, I heartily recommend Margaret Scotte’s excellent Sailing School: Navigation Science and Skill, 1550–1800 (Johns Hopkins University Press, 2019).


[1] Sobel’s account of the story is somewhat less than historically accurate and as always, I recommend instead Dunne and Higgitt, Finding LongitudeHow ships, clocks and stars helped solve the longitude problem (Collins, 2014)

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Filed under Early Scientific Publishing, History of Astronomy, History of Mathematics, History of Navigation, Renaissance Science

WRONG, WRONG, WRONG…

I think the Internet has finally broken the HISTSCI_HULK; he’s lying in the corner sobbing bitterly and mumbling wrong, wrong, wrong… like a broken record. What could have felled the mighty beast? 

29 January was the anniversary of the birth (1611) and death (1687) of the Danzig astronomer Johannes Hevelius and numerous people, including myself, posted or reposted articles about him on the Internet. One of those articles was the 2018 article, The 17th-Century Astronomer Who Made the First Atlas of the Moon by Elizabeth Landau, with the lede Johannes Hevelius drew some of the first maps of the moon, praised for their detail, from his homemade rooftop observatory in the Kingdom of Poland, in the Smithsonian Magazine.

Johannes Hevelius by Daniel Schultz Source: Wikimedia Commons

I suppose that I’m really to blame because I let him read it. He was chugging along quite happily, nodding his head, and burbling to himself, on the lookout, as always, for history of science errors and howlers, when he let out a piercing scream, NOOOOOO!!!!!! And collapsed in a sobbing heap on the floor. I’ve tried everything but I haven’t been able to console the poor beast.

So, what was it that caused this total breakdown? The first six paragraphs of the article are harmless enough, with only some very minor questionable statements, not really worth bothering about, but then comes this monstrosity:

Mapping the moon was one of Hevelius’s first major undertakings. The seafaring nations at the time were desperately searching for a way to measure longitude at sea, and it was thought that the moon could provide a solution. The idea was that during a lunar eclipse, if sailors observed the shadow of the moon crossing a particular point on the surface at 3:03 p.m., but they knew that in another location, such as Paris, the same crossing would occur at 3:33 p.m., then they could calculate their degrees of longitude away from the known location of the city. More accurate lunar charts, however, would be required for the technique to be possible (and due to the practical matters of using a large telescope on a rolling ship, a truly reliable way to calculate longitude at sea would not be achieved until the invention of the marine chronometer).

One can only assume that it is an attempt to describe the lunar distance method for determining longitude but apart from the word moon, it has absolutely nothing in common with the actual lunar distance method. Put very mildly it is a complete travesty that should never have seen the light of day, let alone been published. 

Lunar eclipses had already been used for many centuries to determine the longitude difference between two locations, but you don’t need either a map of the moon or a telescope to do so. Two observers, in their respective locations, merely record the local time of the beginning and/or the end of the eclipse (initial and final contacts) and the resulting time difference gives the difference in longitude. Lunar eclipses are impractical as a method of determining longitude for navigation, as they occur too infrequently; there will only be a total of 230 lunar eclipses in the whole of the twenty-first century, of which only eighty-five will be total lunar eclipses. For example, if you were sitting in the middle of the Atlantic Ocean on 6 June 2022 and wished to determine your longitude, you would have to wait until 8 November for the next total lunar eclipse. After that you would have to wait until 14 March 2025 for the next total lunar eclipse, although there are a couple of partial and penumbral eclipses in between. 

Early Modern explorers did use solar and lunar eclipses combined with an ephemeris, a book of astronomical tables, to determine longitude on land, to establish their location and to draw maps. Columbus, famously, used his knowledge of the total lunar eclipse on 1 March 1504, taken from an ephemeris, to intimidate the natives on the island of Jamaica into continuing to feed his hungry stranded crew.

The lunar distance method of determining longitude is something completely different. It was first proposed by the Nürnberger mathematicus, Johannes Werner (1468–1522) in his Latin translation of Ptolemaeus’ GeographiaIn Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, published in Nürnberg in 1514 and then discussed by Peter Apian (1495–1552) in his Cosmographicus liber, published in Landshut in 1524. For reasons that I will explain in a minute, it was found impractical, but was proposed again in 1634 by the French astronomer Jean-Baptiste Morin (1586–1656), but once again rejected as impractical. 

The lunar distance method relies on determining the position of the Moon relative to a given set of reference stars, a unique constellation for every part of the Moon’s orbit. Then using a set of tables to determine the timing of a given constellation for a given fixed point. Having determined one’s local time, it is then possible to calculate the time difference and thus the longitude. Because it is pulled hither and thither by both the Sun and the Earth the Moon’s orbit is extremely erratic and not the smooth ellipse suggested by Kepler’s three laws of planetary motion. This led to the realisation that compiling the tables to the necessary accuracy was beyond the capabilities of those sixteenth century astronomers and their comparatively primitive instruments, hence the method had not been realised. 

We now turn our attention to Landau’s closing statement in this horror paragraph:

More accurate lunar charts, however, would be required for the technique to be possible (and due to the practical matters of using a large telescope on a rolling ship, a truly reliable way to calculate longitude at sea would not be achieved until the invention of the marine chronometer).

Historically, tables of the necessary accuracy were produced by Tobias Meyer (1723–1762) in 1755. However, the calculations necessary to determine longitude having measured the lunar distance proved to be too complex and too time consuming for seamen and so Neville Maskelyne (1732–1811) produced the Nautical Almanac containing the results pre-calculated in the form of tables and published for the first time in 1766. One does not need a telescope to make the necessary observations. A sextant is sufficient to measure the distance between the moon and the reference stars and that had been invented by John Hadley (1682–1744) in 1731. The lunar distance method was in fact ready for practical use before the marine chronometer. 

One question that I have, is did Landau extract this heap of nonsense out of her own posterior or is she paraphrasing somebody else’s description? Throughout her article she gives links to various books with the information she is using, so did she take this abomination from another source? If so, it is still out there somewhere creating confusion for anybody unlucky enough to read it. On the question of sources, Dava Sobel’s Longitude, which, despite her prejudices against it, contains a correct description of the lunar distance method was published in 2005 and the much better Finding Longitude by Rebekah Higgitt and Richard Dunn was published in 2014, so there is no real excuse for Landau’s load of bovine manure in 2018. 

I don’t know how many people have subscriptions to the Smithsonian Magazine, but it has over 300,000 followers on Twitter. If we look at the Wikipedia article on the Smithsonian Institutions it starts thus, “The Smithsonian Institution, or simply, the Smithsonian, is a group of museums and education and research centers, the largest such complex in the world, created by the U.S. government for the increase and diffusion of knowledge (my emphasis), so why is the Smithsonian Magazine diffusing crap?

I’m hoping that with plenty of sweet tea and digestive biscuits, I’ll be able to restore the HISTSCI_HULK to his normal boisterous self. 

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Filed under History of Astronomy, History of Navigation, Myths of Science

The black sheep of the Provence-Paris group

I continue my sketches of the seventeenth century group pf mathematicians and astronomers associated with Nicolas-Claude Fabri de Peiresc (1580-1637) in Provence and Marin Mersenne (1588–1648) in Paris with Jean-Baptiste Morin (1583–1656), who was born in Villefranche-sur-Saône in the east of France.

Jean-Baptiste Morin Source: Wikimedia Commons

He seems to have come from an affluent family and at the age of sixteen he began his studies at the University of Aix-en-Provence. Here he resided in the house of the Provencal astronomer Joseph Gaultier de la Valette (1564–1647), vicar general of Aix and Peiresc’s observing partner. For the last two years of his time in Aix, the young Pierre Gassendi, also lived in Gaultier de la Valette’s house and the two became good friends and observing partners.

In 1611, Morin moved to the University of Avignon, where he studied medicine graduating MD in 1613. For the next eight years, until 1621, he was in the service of Claude Dormy (c.1562–1626) the Bishop of Boulogne, in Paris, who paid for him to travel extensively in Germany, Hungary and Transylvania to study the metal mining industry. As well as serving Dormy as physician, he almost certainly acted as his astrologer, this was still in the period when astro-medicine or iatromathematics was the mainstream medical theory.

The tomb of Claude Dormy Source

From 1621 to 1629 he served Philip IV, King of Spain, and Duke of Luxembourg, also probably as astrologer. 

In 1630, he was indirectly asked by Marie de’ Medici, the Queen Mother, to cast a horoscope for her son, Louis XIII, who was seriously ill and whose doctor had predicted, on his own astrological reading, that he would die. Morin’s astrological analysis said that Louis would be severely ill but would survive. Luckily for Morin, his prediction proved accurate, and Marie de’ Medici used her influence to have him appointed professor for mathematics at the Collège Royal in Paris, a position he held until his death in 1656.

Marie de Médici portrait by Frans Pourbus, the Younger Source: Wikimedia Commons

In Paris, Morin he took up his friendship with Gassendi from their mutual student days and even continued to make astronomical observations with him in the 1630s, at the same time becoming a member of the group around Mersenne. However, in my title I have labelled Morin the black sheep of the Provence-Paris group and if we turn to his scholarly activities, it is very clear why. Whereas Peiresc, Mersenne, Boulliau, and Gassendi were all to one degree or another supporters of the new scientific developments in the early seventeenth century, coming to reject Aristotelean philosophy and geocentric astronomy in favour of a heliocentric world view, Morin stayed staunchly conservative in his philosophy and his cosmology.

Already in 1624, Morin wrote and published a defence of Aristotle, and he remained an Aristotelian all of his life. He rejected heliocentricity and insisted that the Earth lies at the centre of the cosmos and does not move. Whereas the others in the group supported the ideas of Galileo and also tried to defend Galileo against the Catholic Church, Morin launched an open attack on Galileo and his ideas in 1630, continuing to attack him even after his trial and house arrest. In 1638, he also publicly attacked René Descartes and his philosophy, not critically like Gassendi, but across-the-board, without real justification. He famously wrote that he knew that Descartes philosophy was no good just by looking at him when they first met. This claim is typical of Morin’s character, he could, without prejudice, be best described as a belligerent malcontent. Over the years he managed to alienate himself from almost the entire Parisian scholarly community. 

It would seem legitimate to ask, if Morin was so pig-headed and completely out of step with the developments and advances in science that were going on around him, and in which his friends were actively engaged, why bother with him at all? Morin distinguished himself in two areas, one scientific the other pseudo-scientific and it is to these that we now turn.

The scientific area in which made a mark was the determination of longitude. With European seamen venturing out into the deep sea for the first time, beginning at the end of the fifteenth century, navigation took on a new importance. If you are out in the middle of one of the Earth’s oceans, then being able to determine your exact position is an important necessity. Determining one’s latitude is a comparatively easy task. You need to determine local time, the position of the Sun, during the day, or the Pole Star, during the night and then make a comparatively easy trigonometrical calculation. Longitude is a much more difficult problem that relies on some method of determining time differences between one’s given position and some other fixed position. If one is one hour time difference west of Greenwich, say, then one is fifteen degrees of longitude west of Greenwich. 

Finding a solution to this problem became an urgent task for all of the European sea going nations, including France, and several of them were offering substantial financial rewards for a usable solution. In 1634, Morin suggested a solution using the Moon as a clock. The method, called the lunar distance method or simply lunars, was not new and had already suggested by the Nürnberger mathematicus, Johannes Werner (1468–1522) in his Latin translation of Ptolemaeus’ GeographiaIn Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, published in Nürnberg in 1514 and then discussed by Peter Apian (1495–1552) in his Cosmographicus liber, published in Landshut in 1524.

The lunar distance method relies on determining the position of the Moon relative to a given set of reference stars, a unique constellation for every part of the Moon’s orbit. Then using a set of tables to determine the timing of a given constellation for a given fixed point. Having determined one’s local time, it is then possible to calculate the time difference and thus the longitude. Because it is pulled hither and thither by both the Sun and the Earth the Moon’s orbit is extremely erratic and not the smooth ellipse suggested by Kepler’s three laws of planetary motion. This led to the realisation that compiling the tables to the necessary accuracy was beyond the capabilities of those sixteenth century astronomers and their comparatively primitive instruments, hence the method had not been realised. Another method that was under discussion was taking time with you in the form of an accurate clock, as first proposed by Gemma Frisius (1508–1555), Morin did not think much of this idea:

“I do not know if the Devil will succeed in making a longitude timekeeper but it is folly for man to try.”

Morin was well aware of the difficulties involved and suggested a comprehensive plan to overcome them. Eager to win the offered reward money, Morin put his proposal to Cardinal Richelieu (1585–1642), Chief Minister and most powerful man in France. Morin suggested improved astronomical instruments fitted out with vernier scales, a recent invention, and telescopic sights, also comparatively new, along with improvements in spherical trigonometry. He also suggested the construction of a national observatory, with the specific assignment of collected more accurate lunar data. Richelieu put Morin’s proposition to an expert commission consisting of Étienne Pascal (1588–1651), the father of Blaise, Pierre Hérigone (1580–1643), a Parisian mathematics teacher, and Claude Mydorge (1585–1647), optical physicist and geometer. This commission rejected Morin’s proposal as still not practical, resulting in a five year long dispute between Morin and the commission. It would be another century before Tobias Mayer (1723–1762) made the lunar distance method viable, basically following Morin’s plan.

Although his proposal was rejected, Morin did receive 2000 livre for his suggestion from Richelieu’s successor, Cardinal Mazarin (1602–1661) in 1645. Mazarin’s successor Jean-Baptiste Colbert (1619–1683) set up both the Académie des sciences in 1666 and the Paris Observatory in 1667, to work on the problem. This led, eventually to Charles II setting up the Royal Observatory in Greenwich, in 1675 for the same purpose.

Today, Morin is actually best known as an astrologer. The practice of astrology was still acceptable for mathematicians and astronomers during Morin’s lifetime, although it went into steep decline in the decades following his death. Although an avid astronomer, Peiresc appears to have had no interest in astrology. This is most obvious in his observation notes on the great comet of 1618. Comets were a central theme for astrologers, but Peiresc offers no astrological interpretation of the comet at all. Both Mersenne and Gassendi accepted the scientific status of astrology and make brief references to it in their published works, but neither of them appears to have practiced astrology. Boulliau also appear to have accepted astrology, as amongst his published translations of scientific texts from antiquity we can find Marcus Manilius’ Astronomicom (1655), an astrological poem written about 30 CE, and Ptolemaeus’ De judicandi jacultate (1667). Like Mersenne and Gassendi he appears not to have practiced astrology.

According to Morin’s own account, he initially thought little of astrology, but around the age of thirty he changed his mind and then spent ten years studying it in depth.

Jean-Baptiste Morin’s with chart as cast by himself

He then spent thirty years writing a total of twenty-six volumes on astrology that were published posthumously as one volume of 850 pages in Den Hague in 1661, as Astrologia Galllica (French Astrology). Like Regiomontanus, Tycho Brahe, and Kepler before him, he saw astrology as in need of reformation and himself as its anointed reformer. 

Source: Wikimedia Commons

The first eight volumes of Astrologia Galllica hardly deal with astrology at all but lay down Morin’s philosophical and religious views on which he bases his astrology. The remaining eighteen volumes then deal with the various topics of astrology one by one. Central to his work is the concept of directio in interpreting horoscopes. This is a method of determining the times of major events in a subject’s life that are indicated in their birth horoscope. Originally, to be found in Ptolemaeus’ Tetrabiblos, it became very popular during the Renaissance. The standard text was Regiomontanus’ Tabulae Directionum, originally written in 1467, and large numbers of manuscripts can still be found in libraries and archives. It was published in print by Erhard Ratdolt in Augsburg in 1490 and went through eleven editions, the last being published in 1626. Aware of Kepler’s rejection of both the signs of the zodiac and the system of houses, Morin defends both of them.

Coming, as it did at a time when astrology was in decline as an accepted academic discipline, Morin’s Astrologia Galllica had very little impact in the seventeenth century, but surprisingly, in English translation, it enjoys a lot of popularity amongst modern astrologers.

Morin was cantankerous and belligerent, which cost him most of his contacts with the contemporary scholars in Paris and his adherence to Aristotelian philosophy and a geocentric world view put him out of step with the rest of the Provence-Paris group, but he certainly didn’t suffer from a lack of belief in his own abilities as he tells us in this autobiographical quote:

“… I am excessively inclined to consider myself superior to others on account of my intellectual endowments and scientific attainments, and it is very difficult for me to struggle against this tendency, except when the realization of my sins troubles me, and I see myself a vile man and worthy of contempt. Because of all this my name has become famous throughout the world.”

 

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Filed under History of Astrology, History of Astronomy, History of medicine, History of Navigation

STOMP. STOMP, STOMP … KEPLER DID WOT!

I really shouldn’t but the HISTSCI_HULK is twisting my arm and muttering dark threats, so here goes. A week ago, we took apart Vedang Sati’s post 10 Discoveries By Newton That Changed The World. When I copied it to my blog, I removed the links that Sati had built into his post. I then made the mistake of following his link to his post on Kepler, so here we go again. 

Johannes Kepler Source: Wikimedia Commons

7 Ways In Which Johannes Kepler Changed Astronomy

Johannes Kepler was a German astronomer who discovered the three laws of planetary motion. Apart from his contributions to astronomy, he is also known to have pioneered the field of optics. In this post, let’s read some amazing facts about Kepler and his work. 

He obviously doesn’t rate Kepler as highly as he rates Newton, so the introduction is less hagiographic this time. However, it does contain one quite extraordinary claim, when he writes, “he is also known to have pioneered the field of optics.” Optics as a scientific discipline was pioneered by Euclid, who lived in the fourth century BCE, so about two thousand years before Kepler. There were also quite a few people active in the field in the two millennia in between.

Early Affliction

He suffered from small pox at a very early age. The disease left him with weak eyesight. Isn’t  it wonderful then how he went on to invent eyeglasses for near-eye and far-eye sightedness.

Kepler did indeed suffer from smallpox sometime around the age of four, which almost cost him his life and did indeed leave him with damaged eyesight. However, Kepler did not invent spectacles of any type whatsoever. The first spectacles for presbyopia, far-sightedness occurring in old age, began to appear in the last decades of the thirteenth century CE. Spectacles for myopia, short-sightedness, were widely available by the early fifteenth century. What Kepler actually did was to publish the first scientific explanation of how lenses function to correct defects in eyesight in his Astronomiae Pars Optica (The Optical Part of Astronomy), in 1604. Francesco Maurolico (1494–1574) actually gave the correct explanation earlier than Kepler in his Photismi de lumine et umbra but this was only published posthumously in 1611, so the credit for priority goes to Kepler

Astronomiae Pars Optica Source: Wikimedia Commons

Introduction to Astronomy

Kepler’s childhood was worsened by his family’s financial troubles. At the age of 6, Johannes had to drop out of school so to earn money for the family. He worked as a waiter in an inn.

As Kepler first entered school at the age of seven, it would have been difficult for his schooling to have been interrupted when he was six. His primary schooling was in fact often interrupted both by illness and the financial fortunes of the family. 

In the same year, his mother took him out at night to show him the Great Comet of 1577 which aroused his life-long interest in science and astronomy. 

Yes, she did!

Copernican Supporter

At a time when everyone was against the heliocentric model of the universe, Kepler became its outspoken supporter. He was the first person to defend the Copernican theory from a scientific and a religious perspective.

Not everyone was opposed to the heliocentric model of the universe, just the majority. Poor old Georg Joachim Rheticus (1514–1574), as the professor of mathematics, who persuaded Copernicus to publish De revolutionibus, he would be deeply insulted by the claim that Kepler was the “first person to defend the Copernican theory from a scientific and a religious perspective.” Rheticus, of course, did both, long before Kepler was even born, although his religious defence remained unpublished and was only rediscovered in the twentieth century. Rheticus was not the only supporter of Copernicus, who preceded Kepler there were others, most notably, in this case, Michael Mästlin (1550–1631), who taught Kepler the Copernican heliocentrism. 

Contemporary of Galileo

Galileo was not a great supporter of Kepler’s work especially when Kepler had proposed that the Moon had an influence over the water (tides). It would take an understanding many decades later which would prove Kepler correct and Galileo wrong.

It is indeed very true that Galileo rejected Kepler’s theory of the tides, when promoting his own highly defective theory, but that is mild compared to his conscious ignoring of Kepler’s laws of planetary motion, which were at the time the most significant evidence for a heliocentric cosmos.

Pioneer of Optics

Kepler made ground-breaking contributions to optics including the formulation of inverse-square law governing the intensity of light; inventing an improved refracting telescope; and correctly explaining the function of the human eye.

Kepler’s contributions to the science of optics were indeed highly significant and represent a major turning point in the development of the discipline. His Astronomiae Pars Optica does indeed contain the inverse square law of light intensity and the first statement that the image is created in the eye on the retina and not in the crystal lens.

However, that he invented an improved telescope is more than a little problematic. When Galileo published his Sidereus Nuncius in 1610, the first published account of astronomical, telescopic discoveries, there was no explanation how a telescope actually functions, so people were justifiably sceptical. Having written the book on how lenses function with his Astronomiae Pars Optica in 1604, Kepler now delivered a scientific explanation how the telescope functioned with his Dioptrice in 1611. 

Kepler Dioptrice Source: Wikimedia Commons

This contained not just a theoretical explanation of the optics of a Dutch or Galilean telescope, with a convex objective and a concave eyepiece, but also of a telescope with convex objective and convex eyepiece, which produces an inverted image, now known as a Keplerian or astronomical telescope, also one with three convex lenses, the third lens to right the inverted image, now known as a field telescope, and lastly, difficult to believe, the telephoto lens. Kepler’s work remained strictly theoretical, and he never constructed any of these telescopes, so is he really the inventor? The first astronomical telescope was constructed by Christoph Grienberger (1561–1636) for Christoph Scheiner (c. 1573–1650) as his heliotropic telescope, for his sunspot studies. 

Heliotropic telescope on the left. On the right Scheiner’s acknowledgement that Grienberger was the inventor

Is the astronomical telescope an improved telescope, in comparison with the Dutch telescope? It is very much a question of horses for courses. If you go to the theatre or the opera then your opera glasses, actually a Dutch telescope, will be much more help in distinguishing the figure on the stage than an astronomical telescope. Naturally, the astronomical telescope, with its wider fields of vision, is, as its name implies, much better for astronomical observations than the Dutch telescope once you get past the problem of the inverted image. This problem was solved with the invention of the multiple lens eyepiece by Anton Maria Schyrleus de Rheita (1604–1660), announced in Oculus Enoch et Eliae published in 1645, although he had already been manufacturing them together with Johann Wiesel (1583–1662) since 1643.

Helped Newton

His planetary laws went on to help Sir Isaac Newton derive the inverse square law of gravity. Newton had famously acknowledged Kepler’s role, in a quote: “If I have seen further, it is by standing on the shoulders of giant(s).

Sati is not alone in failing to give credit to Kepler for his laws of planetary motion in their own right, but instead regarding them merely as a stepping-stone for Newton and the law of gravity. Kepler’s laws of planetary motion, in particular his third law, are the most significant evidence for a heliocentric model of the cosmos between the publication of De revolutionibus in 1543 and Principia in 1687 and deserve to be acknowledged and honoured in their own right! 

Newton’s famous quote, actually a much-used phrase in one form or another in the Early Modern period, originated with Bernard of Chartres (died after 1124) in the twelfth century. Newton used it in a letter to Robert Hooke on 5 February 1675, so twelve years before the publication of his Principia and definitively not referencing Kepler:

What Des-Cartes [sic] did was a good step. You have added much several ways, & especially in taking the colours of thin plates into philosophical consideration. If I have seen further it is by standing on the sholders [sic] of Giants.

Kepler’s Legacy

There is a mountain range in New Zealand named after the famous astronomer. A crater on the Moon is called Kepler’s crater. NASA paid tribute to the scientist by naming their exo-planet telescope, Kepler.

Given the vast number of things named after Kepler, particularly in Germany, Sati’s selection is rather bizarre, in particular because it is a mountain hiking trail in New Zealand that is named after Kepler and not the mountain range itself.

Once again, we are confronted with a collection of half facts and straight falsehoods on this website, whose author, as I stated last time has nearly 190,000 followers on Facebook. 

Me: I told you that we couldn’t stop the tide coming in

HS_H: You’re not trying hard enough. You’ve gotta really STOMP EM!

Me: #histsigh

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Filed under History of Astronomy, History of Optics, Myths of Science

Renaissance science – XXVI

I wrote a whole fifty-two-part blog post series on The Emergence of Modern Astronomy, much of which covered the same period as this series, so I’m not going to repeat it here. However, an interesting question is, did the developments in astronomy during the Humanist Renaissance go hand in hand with humanism and to what extent, or did the two movements run parallel in time to each other without significant interaction? 

The simple answer to my own questions is yes, humanism and the emergence of modern astronomy were very closely interlinked in the period between 1400 and the early seventeenth century. This runs contrary to a popular conception that the Humanist Renaissance was purely literary and in no way scientific. In what follows I will briefly sketch some of that interlinking. 

To start, two of the driving forces behind the desire to renew and improve astronomy, the rediscovery of Ptolemaic mathematics-based cartography and the rise in importance of astrology were very much part of the Humanist Renaissance, as I have already documented in earlier episodes of this series. It is not a coincidence that many of the leading figures in the development of modern astronomy were also involved, either directly or indirectly, in the new cartography. Also, nearly all of them were active astrologers. 

Turning to the individual astronomers, the man, who kicked off the debate on the astronomical status of comets, a debate that, I have shown, played a central role in the evolution of modern astronomy, Paolo dal Pozzo Toscanelli (1397–1482) a member of the Florentine circle of prominent humanist scholars that included Filippo Brunelleschi, Marsilio Ficino, Leon Battista Alberti and Cardinal Nicolaus Cusanus, all of whom have featured in earlier episodes of this series.

Paolo dal Pozzo Toscanelli Source: Wikimedia Commons

Toscanelli, who is best known as the cosmographer, who supplied Columbus with a misleading world map, was one of those who met the Neoplatonic philosopher Georgius Gemistus Pletho (c. 1355–c. 1452) at the Council of Florence. Pletho introduced Toscanelli to the work of the Greek geographer Strabo (c. 64 BCE–c. 24 CE), which was previously unknown in Italy. 

Turning to the University of Vienna and the so-called First Viennese School of Mathematics, already during the time of Johannes von Gmunden (c. 1380–1442) and Georg Müstinger (before 1400–1442), Vienna had become a major centre for the new cartography as well as astronomy. However, it is with the next generation that we find humanist scholars at work. Toscanelli’s unpublished work on comets might have remained unknown if it hadn’t been for Georg von Peuerbach (1423–1461). As a young man Peuerbach had travelled extensively in Italy and become acquainted with the circle of humanists to which Toscanelli belonged. He shared an apartment in Rome with Cusanus and personally met and exchanged ideas with Toscanelli. Returning to Vienna he lectured on poetics and took a leading role in reviving classical Greek and Latin literature, a central humanist concern. Today he is, of course, better known for his work as an astronomer and as the teacher of Johannes Müller, better known Regiomontanus.

First page of Peuerbach’s Theoricae novae planetarum in the Manuscript Krakau, Biblioteca Jagiellońska, Ms. 599, fol. 1r (15th century) Source: Wikimedia Commons

Regiomontanus (1436–1476) became a member of the familia (household) of the leading Greek humanist scholar Basilios Bessarion (1403–1472), a pupil of Pletho. He travelled with Bessarion through Italy, working as his librarian finding and copying Latin and Greek manuscripts on astronomy, astrology and mathematics for Bessarion’s library. Bessarion had taught him Greek for this purpose. Leaving Bessarion’s service Regiomontanus served as librarian for the humanist scholars, János Vitéz Archbishop of Esztergom (c. 1408–1472) a friend of Peuerbach’s and then Matthias Corvinus (1443–1490) King of Hungary. 

Regiomontanus woodcut from the 1493 Nuremberg Chronicle Source: Wikimedia Commons

When Regiomontanus left Hungary for Nürnberg he took a vast collection of Geek and Latin manuscripts with him, with the intention of printing them and publishing them. At the same time applying humanist methods of philology to free them of their errors accumulated through centuries of copying and recopying. A standard humanist project as was the Epitome of Ptolemaeus that he and Peuerbach produced under the stewardship of Bessarion.

The so-called Second Viennese School of mathematics was literally founded by a humanist, when Conrad Celtis (1459–1508) took the professors of mathematics Andreas Stiborius (1464–1515) and Johann Stabius (before 1468–1522), along with the student Georg Tanstetter (1482–1535) from Ingolstadt to Vienna, where he founded his Collegium poetarum et mathematicorum, that is a college for poetry and mathematics, in 1497. Ingolstadt had established the first ever German chair for mathematics to teach astrology to medical students, also basically a humanist driven development.

Conrad Celtis: In memoriam by Hans Burgkmair the Elder, 1507
Source: Wikimedia Commons

The wind of humanism was strong in Vienna, where Peter Apian (1495–1552) was Tanstetter’s star pupil becoming like his teacher a cosmographer, returning to Ingolstadt, where his star pupil was his own son Philipp (1531–1589), like his father a cosmographer. Philipp became professor in Tübingen, where he was Michael Mästlin’s teacher, instilling him with the Viennese humanism. As should be well known Mästlin was Kepler’s teacher.

Source: Wikimedia Commons

Back-tracking, we must consider the central figure of the emergence of modern astronomy, Nicolaus Copernicus (1473–1543). There are no doubts about Copernicus’ humanist credentials.

Copernicus holding lily-of-the-valley: portrait in Nicolaus Reusner’s Icones (1587) Source: Wikimedia Commons

He initially studied at the University of Krakow, the oldest humanist university in Europe north of the Italian border. He continued his education at various North Italian humanist universities, where he continued to learn his astronomy from the works of Peuerbach and Regiomontanus (as he had already done in Krakow) under the supervision of Domenico Maria da Novara (1454–1504) a Neoplatonist, who regarded himself as a student of Regiomontanus.

Domenico Maria da Novara Source Museo Galileo

In Northern Italy Copernicus received a full humanist education even learning Greek and some Hebrew. Establishing his humanist credentials, Copernicus published a Latin translation from the Greek of a set of 85 brief poems by the seventh century Byzantine historian Theophylact Somicatta, as Theophilacti scolastici Simocati epistolae morales, rurales et amatoriae interpretatione Latina in 1509. He also wrote some Greek poetry himself.

Source

Copernicus is often hailed as the first modern astronomer but as many historians have pointed out, his initial intention, following the lead of Regiomontanus, was to restore the purity of Greek astronomy, a very humanist orientated undertaking. He wanted to remove the Ptolemaic equant point, which he saw as violating the Platonic ideal of uniform circular motion. De revolutionibus was modelled on Ptolemaeus’ Mathēmatikē Syntaxis, or more accurately on the Epytoma in almagesti Ptolemei of Peuerbach and Regiomontanus.

Tycho Brahe (1546–1601) was also heavily imbued with the humanist spirit. His elaborate, purpose-built home, laboratory, and observatory on the island of Hven, Uraniborg, was built in the style of the Venetian architect Andrea Palladio (1508–1580),

Portrait of Palladio by Alessandro Maganza Source: Wikimedia Commons

the most influential of the humanist architects, and was one of the earliest buildings constructed in the Renaissance style in Norther Europe.

Source:

All of the Early Modern astronomers from Toscanelli down to at least Tycho, and very much including Copernicus, were dedicated to the humanist ideal of restoring what they saw as the glory of classical astronomy from antiquity. Only incidentally did they pave a road that led away from antiquity to modern astronomy. 

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Filed under History of Astronomy, History of Cartography, Renaissance Science

The Epicurean mathematician

Continuing our look at the group of mathematician astronomers associated with Nicolas-Claude Fabri de Peiresc (1580-1637) in Provence and Marin Mersenne (1588–1648) in Paris, we turn today to Pierre Gassendi (1592–1655), celebrated in the world of Early Modern philosophy, as the man who succeeded in making Epicurean atomism acceptable to the Catholic Church. 

Pierre Gassendi Source: Wikimedia Commons

Pierre Gassendi was born the son of the peasant farmer Antoine Gassend and his wife Fançoise Fabry in the Alpes-de-Haute-Provence village of Champtercier on 22 January 1592. Recognised early as something of a child prodigy in mathematics and languages, he was initially educated by his uncle Thomas Fabry, a parish priest. In 1599 he was sent to the school in Digne, a town about ten kilometres from Champtercier, where he remained until 1607, with the exception of a year spent at school in another nearby village, Riez. 

In 1607 he returned to live in Champtercier and in 1609 he entered the university of Aix-en-Provence, where his studies were concentrated on philosophy and theology, also learning Hebrew and Greek. His father Antoine died in 1611. From 1612 to 1614 his served as principle at the College in Digne. In 1615 he was awarded a doctorate in theology by the University of Avignon and was ordained a priest in 1615. From 1614 he held a minor sinecure at the Cathedral in Digne until 1635, when he was elevated to a higher sinecure. From April to November in 1615 he visited Paris for the first time on Church business. 

Cathédrale Saint-Jérome de Digne Source: Wikimedia Commons

In 1617 both the chair of philosophy and the chair of theology became vacant at the University of Aix; Gassendi applied for both chairs and was offered both, one should note that he was still only twenty-four years old. He chose the chair for philosophy leaving the chair of theology for his former teacher. He remained in Aix for the next six years. 

When Gassendi first moved to Aix he lived in the house of the Provencal astronomer Joseph Gaultier de la Valette (1564–1647), vicar general of Aix and Peiresc’s observing partner. Whilst living in Gaultier’s house he got to know Jean-Baptiste Morin (1583–1556), who was also living there as Gaultier’s astronomical assistant. Although, in later years, in Paris, Gassendi and Morin would have a major public dispute, in Aix the two still young aspiring astronomers became good friends. It was also through Gaultier that Gassendi came to the attention of Peiresc, who would go on to become his patron and mentor. 

Jean-Baptiste Morin Source: Wikimedia Commons

For the next six years Gassendi taught philosophy at the University of Aix and took part in the astronomical activities of Peiresc and Gaultier, then in 1623 the Jesuits took over the university and Gassendi and the other non-Jesuit professors were replaced by Jesuits. Gassendi entered more than twenty years of wanderings without regular employment, although he still had his sinecure at the Cathedral of Digne.

In 1623, Gassendi left Aix for Paris, where he was introduced to Marin Mersenne by Peiresc. The two would become very good friends, and as was his wont, Mersenne took on a steering function in Gassendi’s work, encouraging him to engage with and publish on various tropics. In Paris, Gassendi also became part of the circle around Pierre Dupuy (1582–1651) and his brother Jacques (1591–1656), who were keepers of the Bibliothèque du Roi, today the Bibliothèque nationale de France, and who were Ismael Boulliau’s employers for his first quarter century in Paris.

Pierre Dupuy Source: Wikimedia Commons

The Paris-Provence group Peiresc (1580–1637), Mersenne (1588–1648), Morin (1583–1656), Boulliau (1605–1694), and Gassendi (1592–1655) are all members of the transitional generation, who not only lived through the transformation of the scientific view of the cosmos from an Aristotelian-Ptolemaic geocentric one to a non-Aristotelian-Keplerian heliocentric one but were actively engaged in the discussions surrounding that transformation. When they were born in the late sixteenth century, or in Boulliau’s case the early seventeenth century, despite the fact that Copernicus’ De revolutionibus had been published several decades earlier and although a very small number had begun to accept a heliocentric model and another small number the Tychonic geo-heliocentric one, the geocentric model still ruled supreme. Kepler’s laws of planetary motion and the telescopic discoveries most associated with Galileo still lay in the future. By 1660, not long after their deaths, with once again the exception of Boulliau, who lived to witness it, the Keplerian heliocentric model had been largely accepted by the scientific community, despite there still being no empirical proof of the Earth’s movement. 

Given the Church’s official support of the Aristotelian-Ptolemaic geocentric model and after about 1620 the Tychonic geo-heliocentric model, combined with its reluctance to accept this transformation without solid empirical proof, the fact that all five of them were devout Catholics made their participation in the ongoing discussion something of a highwire act. Gassendi’s personal philosophical and scientific developments over his lifetime are a perfect illustration of this. 

During his six years as professor of philosophy at the University of Aix, Gassendi taught an Aristotelian philosophy conform with Church doctrine. However, he was already developing doubts and in 1624 he published the first of seven planned volumes criticising Aristotelian philosophy, his Exercitationes paradoxicae adversus aristoteleos, in quibus praecipua totius peripateticae doctrinae fundamenta excutiuntur, opiniones vero aut novae, aut ex vetustioribus obsoletae stabiliuntur, auctore Petro Gassendo. Grenoble: Pierre Verdier. In 1658, Laurent Anisson and Jean Baptiste Devenet published part of the second volume posthumously in Den Hague in 1658. Gassendi seems to have abandoned his plans for the other five volumes. 

To replace Aristotle, Gassendi began his promotion of the life and work of Greek atomist Epicurus (341–270 BCE). Atomism in general and Epicureanism in particular were frowned upon by the Christian Churches in general. The Epicurean belief that pleasure was the chief good in life led to its condemnation as encouraging debauchery in all its variations. Atomists, like Aristotle, believed in an eternal cosmos contradicting the Church’s teaching on the Creation. Atomist matter theory destroyed the Church’s philosophical explanation of transubstantiation, which was based on Aristotelian matter theory. Last but no means least Epicurus was viewed as being an atheist. 

In his biography of Epicurus De vita et moribus Epicuri libri octo published by Guillaume Barbier in Lyon in 1647

and revival and reinterpretation of Epicurus and Epicureanism in his Animadversiones in decimum librum Diogenis Laertii: qui est De vita, moribus, placitisque Epicuri. Continent autem Placita, quas ille treis statuit Philosophiae parteis 3 I. Canonicam, …; – II. Physicam, …; – III. Ethicam, … and his Syntagma philosophiae Epicuri cum refutationibus dogmatum quae contra fidem christianam ab eo asserta sunt published together by Guillaume Barbier in Lyon in 1649,

Gassendi presented a version of Epicurus and his work that was acceptable to Christians, leading to both a recognition of the importance of Epicurean philosophy and of atomism in the late seventeenth and early eighteenth centuries. 

Gassendi did not confine himself to work on ancient Greek philosophers. In 1629,  pushed by Mersenne, the scientific agent provocateur, he wrote an attack on the hermetic philosophy of Robert Fludd (1574–1637), who famously argued against mathematics-based science in his debate with Kepler. Also goaded by Mersenne, he read Descartes’ Meditationes de prima philosophia (Meditations on First Philosophy) (1641) and published a refutation of Descartes’ methodology. As a strong scientific empiricist, Gassendi had no time for Descartes’ rationalism. Interestingly, it was Gassendi in his Objections (1641), who first outlined the mind-body problem, reacting to Descartes’ mind-body dualism. Descartes was very dismissive of Gassendi’s criticisms in his Responses, to which Gassendi responded in his Instantiae (1642). 

Earlier, Gassendi had been a thorn in Descartes side in another philosophical debate. In 1628, Gassendi took part in his only journey outside of France, travelling through Flanders and Holland for several months, although he did travel widely throughout France during his lifetime. Whilst in Holland, he visited Isaac Beeckman (1588–1637) with whom he continued to correspond until the latter’s death. Earlier, Beeckman had had a massive influence on the young Descartes, introducing him to the mechanical philosophy. In 1630, Descartes wrote an abusive letter denying any influence on his work by Beeckman. Gassendi, also a supporter of the mechanical philosophy based on atomism, defended Beeckman.

Like the others in the Mersenne-Peiresc group, Gassendi was a student and supporter of the works of both Johannes Kepler (1571–1630) and Galileo Galilei (1564–1642) and it is here that he made most of his contributions to the evolution of the sciences in the seventeenth century. 

Having been introduced to astronomy very early in his development by Peiresc and Gaultier de la Valette, Gassendi remained an active observational astronomer all of his life. Like many others, he was a fan of Kepler’s Tabulae Rudolphinae (Rudolphine Tables) (1627) the most accurate planetary tables ever produced up till that time. Producing planetary tables and ephemerides for use in astrology, cartography, navigation, etc was regarded as the principal function of astronomy, and the superior quality of Kepler’s Tabulae Rudolphinae was a major driving force behind the acceptance of a heliocentric model of the cosmos. Consulting the Tabulae Rudolphinae Gassendi determined that there would be a transit of Mercury on 7 November 1631. Four European astronomers observed the transit, a clear proof that Mercury orbited the Sun and not the Earth, and Gassendi, who is credited with being the first to observe a transit of Mercury, published his observations Mercvrivs in sole visvs, et Venvs invisa Parisiis, anno 1631: pro voto, & admonitione Keppleri in Paris in 1632.

He also tried to observe the transit of Venus, predicted by Kepler for 6 December 1631, not realising that it was not visible from Europe, taking place there during the night. This was not yet a proof of heliocentricity, as it was explainable in both the Capellan model in which Mercury and Venus both orbit the Sun, which in turn orbits the Earth and the Tychonic model in which the five planets all orbit the Sun, which together with the Moon orbits the Earth. But it was a very positive step in the right direction. 

In his De motu impresso a motore translato. Epistolæ duæ. In quibus aliquot præcipuæ tum de motu vniuersè, tum speciatim de motu terræattributo difficulatates explicantur published in Paris in 1642, he dealt with objections to Galileo’s laws of fall.

Principally, he had someone drop stones from the mast of a moving ship to demonstrate that they conserve horizontal momentum, thus defusing the argument of those, who claimed that stones falling vertically to the Earth proved that it was not moving. In 1646 he published a second text on Galileo’s theory, De proportione qua gravia decidentia accelerantur, which corrected errors he had made in his earlier publication.

Like Mersenne before him, Gassendi tried, using a cannon, to determine the speed of sound in 1635, recording a speed of 1,473 Parian feet per second. The actual speed at 20° C is 1,055 Parian feet per second, making Gassendi’s determination almost forty percent too high. 

In 1648, Pascal, motivated by Mersenne, sent his brother-in-law up the Puy de Dôme with a primitive barometer to measure the decreasing atmospheric pressure. Gassendi provided a correct interpretation of this experiment, including the presence of a vacuum at the top of the tube. This was another indirect attack on Descartes, who maintained the assumption of the impossibility of a vacuum. 

Following his expulsion from the University of Aix, Nicolas-Claude Fabri de Peiresc’s house became Gassendi’s home base for his wanderings throughout France, with Peiresc helping to finance his scientific research and his publications. The two of them became close friends and when Peiresc died in 1637, Gassendi was distraught. He preceded to mourn his friend by writing his biography, Viri illvstris Nicolai Clavdii Fabricii de Peiresc, senatoris aqvisextiensis vita, which was published by Sebastian Cramoisy in Paris in 1641. It is considered to be the first ever complete biography of a scholar. It went through several edition and was translated into English.

In 1645, Gassendi was appointed professor of mathematics at the Collège Royal in Paris, where he lectured on astronomy and mathematics, ably assisted by the young Jean Picard (1620–1682), who later became famous for accurately determining the size of the Earth by measuring a meridian arc north of Paris.

Jean Picard

Gassendi only held the post for three years, forced to retire because of ill health in 1648. Around this time, he and Descartes became reconciled through the offices of the diplomat and cardinal César d’Estrées (1628–1714). 

Gassendi travelled to the south for his health and lived for two years in Toulon, returning to Paris in 1653 when his health improved. However, his health declined again, and he died of a lung complaint in 1655.

Although, like the others in the group, Gassendi was sympathetic to a heliocentric world view, during his time as professor he taught the now conventional geo-heliocentric astronomy approved by the Catholic Church, but also discussed the heliocentric systems. His lectures were written up and published as Institutio astronomica juxta hypotheseis tam veterum, quam Copernici et Tychonis in 1647. Although he toed the party line his treatment of the heliocentric was so sympathetic that he was reported to the Inquisition, who investigated him but raised no charges against him. Gassendi’s Institutio astronomica was very popular and proved to be a very good source for people to learn about the heliocentric system. 

As part of his campaign to promote the heliocentric world view, Gassendi also wrote biographies of Georg Peuerbach, Regiomontanus, Copernicus, and Tycho Brahe. It was the only biography of Tycho based on information from someone, who actually knew him. The text, Tychonis Brahei, eqvitis Dani, astronomorvm coryphaei vita, itemqve Nicolai Copernici, Georgii Peverbachii & Ioannis Regiomontani, celebrium Astronomorum was published in Paris in 1654, with a second edition appearing in Den Hague in the year of Gassendi’s death, 1655. In terms of historical accuracy, the biographies are to be treated with caution.

Gassendi also became engaged in a fierce dispute about astronomical models with his one-time friend from his student days, Jean-Baptiste Morin, who remained a strict geocentrist. I shall deal with this when I write a biographical sketch of Morin, who became the black sheep of the Paris-Provencal group.

Like the other members of the Paris-Provencal group, Gassendi communicated extensively with other astronomers and mathematician not only in France but throughout Europe, so his work was well known and influential both during his lifetime and also after his death. As with all the members of that group Gassendi’s life and work is a good example of the fact that science is a collective endeavour and often progresses through cooperation rather than rivalry. 

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