Why, FFS! why?

On Twitter this morning physicist and science writer Graham Farmelo inadvertently drew my attention to a reader’s letter in The Guardian from Sunday by a Collin Moffat. Upon reading this load of old cobblers, your friendly, mild mannered historian of Renaissance mathematics instantly turned into the howling-with-rage HISTSCI_HULK. What could possibly have provoked this outbreak? I present for your delectation the offending object.

I fear Thomas Eaton (Weekend Quiz, 12 October) is giving further credence to “fake news” from 1507, when a German cartographer was seeking the derivation of “America” and hit upon the name of Amerigo Vespucci, an obscure Florentine navigator. Derived from this single source, this made-up derivation has been copied ever after.

The fact is that Christopher Columbus visited Iceland in 1477-78, and learned of a western landmass named “Markland”. Seeking funds from King Ferdinand of Spain, he told the king that the western continent really did exist, it even had a name – and Columbus adapted “Markland” into the Spanish way of speaking, which requires an initial vowel “A-”, and dropped “-land” substituting “-ia”.

Thus “A-mark-ia”, ie “America”. In Icelandic, “Markland” may be translated as “the Outback” – perhaps a fair description.

See Graeme Davis, Vikings in America (Birlinn, 2009).

Astute readers will remember that we have been here before, with those that erroneously claim that America was named after a Welsh merchant by the name of Richard Ap Meric. The claim presented here is equally erroneous; let us examine it in detail.

…when a German cartographer was seeking the derivation of “America” and hit upon the name of Amerigo Vespucci, an obscure Florentine navigator.

It was actually two German cartographers Martin Waldseemüller and Matthias Ringmann and they were not looking for a derivation of America, they coined the name. What is more, they give a clear explanation as to why and how the coined the name and why exactly they chose to name the newly discovered continent after Amerigo Vespucci, who, by the way, wasn’t that obscure. You can read the details in my earlier post. It is of interest that the supporters of the Ap Meric theory use exactly the same tactic of lying about Waldseemüller and Ringmann and their coinage.

The fact is that Christopher Columbus visited Iceland in 1477-78, and learned of a western landmass named “Markland”.

Let us examine what is known about Columbus’ supposed visit to Iceland. You will note that I use the term supposed, as facts about this voyage are more than rather thin. In his biography of Columbus, Felipe Fernandez-Armesto, historian of Early Modern exploration, writes:

He claimed that February 1477–the date can be treated as unreliable in such a long –deferred recollection [from 1495]–he sailed ‘a hundred leagues beyond’ Iceland, on a trip from Bristol…

In “Christopher Columbus and the Age of Exploration: An Encyclopedia”[1] edited by the American historian, Silvio A. Bedini, we can read:

The possibility of Columbus having visited Iceland is based on a passage in his son Fernando Colón’s biography of his father. He cites a letter from Columbus stating that in February 1477 he sailed “a hundred leagues beyond the island of Til” (i.e. Thule, Iceland). But there is no evidence to his having stopped in Iceland or spoken with anyone, and in any case it is unlikely that anyone he spoke to would have known about the the Icelandic discovery of Vinland.

This makes rather a mockery of the letter’s final claim:

Seeking funds from King Ferdinand of Spain, he told the king that the western continent really did exist, it even had a name – and Columbus adapted “Markland” into the Spanish way of speaking, which requires an initial vowel “A-”, and dropped “-land” substituting “-ia”.

Given that it is a well established fact that Columbus was trying to sail westward to Asia and ran into America purely by accident, convinced by the way that he had actually reached Asia, the above is nothing more than a fairly tale with no historical substance whatsoever.

To close I want to address the question posed in the title to this brief post. Given that we have a clear and one hundred per cent reliable source for the name of America and the two men who coined it, why oh why do people keep coming up with totally unsubstantiated origins of the name based on ahistorical fantasies? And no I can’t be bothered to waste either my time or my money on Graeme Davis’ book, which is currently deleted and only available as a Kindle.

[1] On days like this it pays to have one book or another sitting around on your bookshelves.

Felipe Fernández-Armesto, Columbus, Duckworth, London, ppb 1996, p. 18. Christopher Columbus and the Age of Exploration: An Encyclopedia, ed. Silvio A. Bedini, Da Capo Press, New York, ppb 1992, p. 314

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The emergence of modern astronomy – a complex mosaic: Part XXI

A widespread myth in the popular history of astronomy is that Galileo Galilei (1564–1642) was the first or even the only astronomer to realise the potential of the newly invented telescope as an instrument for astronomy. This perception is very far from the truth. He was just one of a group of investigator, who realised the telescopes potential and all of the discoveries traditionally attributed to Galileo were actually made contemporaneously by several people, who full of curiosity pointed their primitive new instruments at the night skies. So why does Galileo usually get all of the credit? Quite simply, he was the first to publish.

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Galileo’s “cannocchiali” telescopes at the Museo Galileo, Florence

Starting in the middle of 1609 various astronomers began pointing primitive Dutch telescopes at the night skies, Thomas Harriot (1560–1621) and his friend and student William Lower (1570–1615) in Britain, Simon Marius (1573–1625) in Ansbach, Johannes Fabricius (1587–1616) in Frisia, Odo van Maelcote (1572–1615) and Giovanni Paolo Lembo (1570–1618) in Rome, Christoph Scheiner (1573 or 1575–1650) in Ingolstadt and of course Galileo in Padua. As far as we can ascertain Thomas Harriot was the first and the order in which the others took up the chase is almost impossible to determine and also irrelevant, as it was who was first to publish that really matters and that was, as already stated, Galileo.

Harriot made a simple two-dimensional telescopic sketch of the moon in the middle of 1609.

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Thomas Harriot’s initial telescopic sketch of the moon from 1609 Source: Wikimedia Commons

Both Galileo and Simon Marius started making telescopic astronomical observations sometime late in the same year. At the beginning Galileo wrote his observation logbook in his Tuscan dialect and then on 7 January 1610 he made the discovery that would make him famous, his first observation of three of the four so-called Galilean moons of Jupiter.

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It was on this page that Galileo first noted an observation of the moons of Jupiter. This observation upset the notion that all celestial bodies must revolve around the Earth. Source: Wikimedia Commons

Galileo realised at once that he had hit the jackpot and immediately changed to writing his observations in Latin in preparation for a publication. Simon Marius, who made the same discovery just one day later, didn’t make any preparations for immediate publication. Galileo kept on making his observations and collecting material for his publication and then on 12 March 1610, just two months after he first saw the Jupiter moons, his Sidereus Nuncius (Starry Messenger of Starry Message, the original Latin is ambiguous) was published in Padua but dedicated to Cosimo II de Medici, Fourth Grand Duke of Tuscany. Galileo had already negotiated with the court in Florence about the naming of the moons; he named them the Medicean Stars thus taking his first step in turning his discovery into personal advancement.

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Title page of Sidereus nuncius, 1610, by Galileo Galilei (1564-1642). *IC6.G1333.610s, Houghton Library, Harvard University Source: Wikimedia Commons

What exactly did Galileo discover with his telescope, who else made the same discoveries and what effect did they have on the ongoing astronomical/cosmological debate? We can start by stating quite categorically that the initial discoveries that Galileo published in his Sidereus Nuncius neither proved the heliocentric hypothesis nor did they refute the geocentric one,

The first discovery that the Sidereus Nuncius contains is that viewed through the telescope many more stars are visible than to the naked-eye. This was already known to those, who took part in Lipperhey’s first ever public demonstration of the telescope in Den Haag in September 1608 and to all, who subsequently pointed a telescope of any sort at the night sky. This played absolutely no role in the astronomical/cosmological debate but was worrying for the theologians. Christianity in general had accepted both astronomy and astrology, as long as the latter was not interpreted deterministically, because the Bible says  “And God said, Let there be lights in the firmament of the heaven to divide the day from night; and let them be for signs, and for seasons, and for days, and years:” (Gen 1:14). If the lights in the heavens are signs from God to be interpreted by humanity, what use are signs that can only be seen with a telescope?

Next up we have the fact that some of the nebulae, indistinct clouds of light in the heavens, when viewed with a telescope resolved into dense groups of stars. Nebulae had never played a major role in Western astronomy, so this discovery whilst interesting did not play a major role in the contemporary debate. Simon Marius made the first telescopic observations of the Andromeda nebula, which was unknown to Ptolemaeus, but which had already been described by the Persian astronomer, Abd al-Rahman al-Sufi (903–986), usually referred to simply as Al Sufi. It is historically interesting because the Andromeda nebula was the first galaxy to be recognised outside of the Milky Way.

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Al Sufi’s drawing of the constellation Fish with the Andromeda nebula in fount of it mouth

Galileo’s next discovery was that the moon was not smooth and perfect, as required of all celestial bodies by Aristotelian cosmology, but had geological feature, mountains and valleys, just like the earth i.e. the surface was three-dimensional and not two-dimensional, as Harriot had sketched it. This perception of Galileo’s is attributed to the fact that he was a trained painter used to creating light and shadows in paintings and he thus recognised that what he was seeing on the moons surface was indeed shadows cast by mountains.

As soon as he read the Sidereus Nuncius, Harriot recognised that Galileo was correct and he went on to produce the first real telescopic map of the moon.

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Thomas Harriot’s 1611 telescopic map of the moon Source: Wikimedia Commons

Galileo’s own washes of the moon, the most famous illustrations in the Sidereus Nuncius, are in fact studies to illustrate his arguments and not accurate illustrations of what he saw.

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Galileo’s sketches of the Moon from Sidereus Nuncius. Source: Wikimedia Commons

That the moon was earth like and for some that the well-known markings on the moon, the man in the moon etc., are in fact a mountainous landscape was a view held by various in antiquity, such as Thales, Orpheus, Anaxagoras, Democritus, Pythagoras, Philolaus, Plutarch and Lucian. In particular Plutarch (c. 46–c. 120 CE) in his On the Face of the Moon in his Moralia, having dismissed other theories including Aristotle’s wrote:

Just as our earth contains gulfs that are deep and extensive, one here pouring in towards us through the Pillars of Herakles and outside the Caspian and the Red Sea with its gulfs, so those features are depths and hollows of the Moon. The largest of them is called “Hecate’s Recess,” where the souls suffer and extract penalties for whatever they have endured or committed after having already become spirits; and the two long ones are called “the Gates,” for through them pass the souls now to the side of the Moon that faces heaven and now back to the side that faces Earth. The side of the Moon towards heaven is named “Elysian plain,” the hither side, “House of counter-terrestrial Persephone.”

So Galileo’s discovery was not so sensational, as it is often presented. However, the earth-like, and not smooth and perfect, appearance of the moon was yet another hole torn in the fabric of Aristotelian cosmology.

Of course the major sensation in the Sidereus Nuncius was the discovery of the four largest moons of Jupiter.

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Galileo’s drawings of Jupiter and its Medicean Stars from Sidereus Nuncius. Image courtesy of the History of Science Collections, University of Oklahoma Libraries. Source: Wikimedia Commons

This contradicted the major premise of Aristotelian cosmology that all of the celestial bodies revolved around a common centre, his homo-centricity.  It also added a small modicum of support to a heliocentric cosmology, which had suffered from the criticism, if all the celestial bodies revolve around the sun, why does the moon continue to revolve around the earth. Now Jupiter had not just one but four moons, or satellites as Johannes Kepler called them, so the earth was no longer alone in having a moon. As already stated above Simon Marius discovered the moons of Jupiter just one day later than Galileo but he didn’t publish his discovery until 1614. A delay that would later bring him a charge of plagiarism from Galileo and ruin his reputation, which was first restored at the end of the nineteenth century when an investigation of the respective observation data showed that Marius’ observations were independent of those of Galileo.

The publication of the Sidereus Nuncius was an absolute sensation and the book quickly sold out. Galileo went, almost literally overnight, from being a virtually unknown, middle aged, Northern Italian, professor of mathematics to the most celebrated astronomer in the whole of Europe. However, not everybody celebrated or accepted the truth of his discoveries and that not without reason. Firstly, any new scientific discovery needs to be confirmed independently by other. If Simon Marius had also published early in 1610 things might have been different but he, for whatever reasons, didn’t publish his Mundus Jovialis (The World of Jupiter) until 1614. Secondly there was no scientific explanation available that explained how a telescope functioned, so how did anyone know that what Galileo and others were observing was real? Thirdly, and this is a very important point that often gets ignored, the early telescopes were very, very poor quality suffering from all sorts of imperfections and distortions and it is almost a miracle that Galileo et al discovered anything with these extremely primitive instruments.

As I stated in the last episode, the second problem was solved by Johannes Kepler in 1611 with the publication of his Dioptrice.

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A book that Galileo, always rather arrogant, dismissed as unreadable. This was his triumph and nobody else was going to muscle in on his glory. The third problem was one that only time and improvements in both glass making and the grinding and polishing of lenses would solve. In the intervening years there were numerous cases of new astronomical discoveries that turned out to be artefacts produced by poor quality instruments.

The first problem was the major hurdle that Galileo had to take if he wanted his discoveries to be taken seriously. Upon hearing of Galileo discoveries, Johannes Kepler in Prague immediately put pen to paper and fired off a pamphlet, Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) congratulating Galileo, welcoming his discoveries and stating his belief in their correctness, which he sent off to Italy. Galileo immediately printed and distributed a pirate copy of Kepler’s work, without even bothering to ask permission, it was after all a confirmation from the Imperial Mathematicus and Kepler’s reputation at this time was considerably bigger than Galileo’s.

Johannes Kepler, Dissertatio cum Nuncio sidereo… (Frankfurt am Main, 1611)

A reprint of Kepler’s letter to Galileo, originally issued in Prague in 1610

However, Kepler’s confirmations were based on faith and not personal confirmatory observations, so they didn’t really solve Galileo’s central problem. Help came in the end from the Jesuit astronomers of the Collegio Romano.

Odo van Maelcote and Giovanni Paolo Lembo had already been making telescopic astronomical observations before the publication of Galileo’s Sidereus Nuncius. Galileo also enjoyed good relations with Christoph Clavius (1538–1612), the founder and head of the school of mathematics at the Collegio Romano, who had been instrumental in helping Galileo to obtain the professorship in Padua. Under the direction of Christoph Grienberger (1561–1636), soon to be Clavius’ successor as professor for mathematics at the Collegio, the Jesuit astronomers set about trying to confirm all of Galileo’s discoveries. This proved more than somewhat difficult, as they were unable, even with Galileo’s assistance via correspondence, to produce an instrument of sufficient quality to observe the moons of Jupiter. In the end Antonio Santini (1577–1662), a mathematician from Venice, succeeded in producing a telescope of sufficient quality for the task, confirmed for himself the existence of the Jupiter moons and then sent a telescope to the Collegio Romano, where the Jesuit astronomers were now also able to confirm all of Galileo’s discovery. Galileo could not have wished for a better confirmation of his efforts, nobody was going to doubt the word of the Jesuits.

In March 1611 Galileo travelled to Rome, where the Jesuits staged a banquet in his honour at which Odo van Maelcote held an oration to the Tuscan astronomer. Galileo’s strategy of dedicating the Sidereus Nuncius to Cosimo de Medici and naming the four moons the Medicean Stars paid off and he was appointed court mathematicus and philosophicus in Florence and professor of mathematics at the university without any teaching obligations; Galileo had arrived at the top of the greasy pole but what goes up must, as we will see, come down.

 

 

 

 

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Mathematical aids for Early Modern astronomers.

Since its very beginnings in the Fertile Crescent, European astronomy has always involved a lot of complicated and tedious mathematical calculations. Those early astronomers described the orbits of planets, lunar eclipses and other astronomical phenomena using arithmetical or algebraic algorithms. In order to simplify the complex calculations needed for their algorithms the astronomers used pre-calculated tables of reciprocals, squares, cubes, square roots and cube roots.

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Cuniform reciprocal table Source

The ancient Greeks, who inherited their astronomy from the Babylonians, based their astronomical models on geometry rather than algebra and so needed other calculation aids. They developed trigonometry for this work based on chords of a circle. The first chord tables are attributed to Hipparkhos (c. 190–c. 120 BCE) but they did not survive. The oldest surviving chord tables are in Ptolemaeus’ Mathēmatikē Syntaxis written in about 150 CE, which also contains a detailed explanation of how to calculate such a table in Chapter 10 of Book I.

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Ptolemaeus’ Chord Table taken from Toomer’s Almagest translation. The 3rd and 6th columns are the interpolations necessary for angles between the given ones

Greek astronomy travelled to India, where the astronomers replaced Ptolemaeus’ chords with half chords, that is our sines. Islamic astronomers inherited their astronomy from the Indians with their sines and cosines and the Persian astronomer Abū al-Wafāʾ (940–998 CE) was using all six of the trigonometrical relations that we learnt at school (didn’t we!) in the tenth century.

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Abū al-Wafāʾ Source: Wikimedia Commons

Astronomical trigonometry trickled slowly into medieval Europe and Regiomontanus (1536–1576)  (1436–1476) was the first European to produce a comprehensive work on trigonometry for astronomers, his De triangulis omnimodis, which was only edited by Johannes Schöner and published by Johannes Petreius in 1533.

Whilst trigonometry was a great aid to astronomers calculating trigonometrical tables was time consuming, tedious and difficult work.

A new calculating aid for astronomers emerged during the sixteenth century, prosthaphaeresis, by which, multiplications could be converted into additions using a series of trigonometrical identities:

Prosthaphaeresis appears to have first been used by Johannes Werner (1468–1522), who used the first two formulas with both sides multiplied by two.

However Werner never published his discovery and it first became known through the work of the itinerant mathematician Paul Wittich (c. 1546–1586), who taught it to both Tycho Brahe (1546–1601) on his island of Hven and to Jost Bürgi (1552–1632) in Kassel, who both developed it further. It is not known if Wittich learnt the method from Werner’s papers on one of his visits to Nürnberg or rediscovered it for himself. Bürgi in turn taught it to Nicolaus Reimers Baer (1551–1600) in in exchange translated Copernicus’ De revolutionibus into German for Bürgi, who couldn’t read Latin. This was the first German translation of De revolutionibus. As can be seen the method of prosthaphaeresis spread throughout Europe in the latter half of the sixteenth century but was soon to be superceded by a superior method of simplifying astronomical calculations by turning multiplications into additions, logarithms.

As is often the case in the histories of science and mathematics logarithms were not discovered by one person but almost simultaneously, independently by two, Jost Bürgi and John Napier (1550–1617) and both of them seem to have developed the idea through their acquaintance with prosthaphaeresis. I have already blogged about Jost Bürgi, so I will devote the rest of this post to John Napier.

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John Napier, artist unknown Source: Wikimedia Commons

John Napier was the 8th Laird of Merchiston, an independently owned estate in the southwest of Edinburgh.

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Merchiston Castle from an 1834 woodcut Source: Wikimedia Commons

His exact date of birth is not known and also very little is known about his childhood or education. It is assumed that he was home educated and he was enrolled at the University of St. Andrews at the age of thirteen. He appears not to have graduated at St. Andrews but is believed to have continued his education in Europe but where is not known. He returned to Scotland in 1571 fluent in Greek but where he had acquired it is not known. As a laird he was very active in the local politics. His intellectual reputation was established as a theologian rather than a mathematician.

It is not known how and when he became interested in mathematics but there is evidence that this interest was already established in the early 1570s, so he may have developed it during his foreign travels. It is thought that he learnt of prosthaphaeresis through John Craig (d. 1620) a Scottish mathematician and physician, who had studied and later taught at Frankfurt an der Oder, a pupil of Paul Wittich, who knew Tycho Brahe. Craig returned to Edinburgh in 1583 and is known to have had contact with Napier. The historian Anthony à Wood (1632–1695) wrote:

one Dr. Craig … coming out of Denmark into his own country called upon John Neper, baron of Murcheston, near Edinburgh, and told him, among other discourses, of a new invention in Denmark (by Longomontanus as ’tis said) to save the tedious multiplication and division in astronomical calculations. Neper being solicitous to know farther of him concerning this matter, he could give no other account of it than that it was by proportionable numbers. [Neper is the Latin version of his family name]

Napier is thought to have begum work on the invention of logarithms about 1590. Logarithms exploit the relation ship between arithmetical and geometrical series. In modern terminology, as we all learnt at school, didn’t we:

Am x An = Am+n

Am/An = Am-n

These relationships were discussed by various mathematicians in the sixteenth century, without the modern notation, in particularly by Michael Stefil (1487–1567) in his Arithmetica integra (1544).

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Michael Stifel Source: Wikimedia Commons

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Michael Stifel’s Arithmetica Integra (1544) Source: Wikimedia Commons

What the rules for exponents show is that if one had tables to convert all numbers into powers of a given base then one could turn all multiplications and divisions into simple additions and subtractions of the exponents then using the tables to covert the result back into a number. This is what Napier did calling the result logarithms. The methodology Napier used to calculate his tables is too complex to deal with here but the work took him over twenty years and were published in his Mirifici logarithmorum canonis descriptio… (1614).

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Napier coined the term logarithm from the Greek logos (ratio) and arithmos (number), meaning ratio-number. As well as the logarithm tables, the book contains seven pages of explanation on the nature of logarithms and their use. A secondary feature of Napier’s work is that he uses full decimal notation including the decimal point. He was not the first to do so but his doing so played an important role in the acceptance of this form of arithmetical notation. The book also contains important developments in spherical trigonometry.

Edward Wright  (baptised 1561–1615) produced an English translation of Napier’s Descriptio, which was approved by Napier, A Description of the Admirable Table of Logarithmes, which was published posthumously in 1616 by his son Samuel.

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Gresham College was quick to take up Napier’s new invention and this resulted in Henry Briggs (1561–1630), the Gresham professor of geometry, travelling to Edinburgh from London to meet with Napier. As a result of this meeting Briggs, with Napier’s active support, developed tables of base ten logarithms, Logarithmorum chilias prima, which were publish in London sometime before Napier’s death in 1617.

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He published a second extended set of base ten tables, Arithmetica logarithmica, in 1624.

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Napier’s own tables are often said to be Natural Logarithms, that is with Euler’s number ‘e’ as base but this is not true. The base of Napierian logarithms is given by:

NapLog(x) = –107ln (x/107)

Natural logarithms have many fathers all of whom developed them before ‘e’ itself was discovered and defined; these include the Jesuit mathematicians Gregoire de Saint-Vincent (1584–1667) and Alphonse Antonio de Sarasa (1618–1667) around 1649, and Nicholas Mercator (c. 1620–1687) in his Logarithmotechnia (1688) but John Speidell (fl. 1600–1634), had already produced a table of not quite natural logarithms in 1619.

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Napier’s son, Robert, published a second work by his father on logarithms, Mirifici logarithmorum canonis constructio; et eorum ad naturales ipsorum numeros habitudines, posthumously in 1619.

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This was actually written earlier than the Descriptio, and describes the principle behind the logarithms and how they were calculated.

The English mathematician Edmund Gunter (1581–1626) developed a scale or rule containing trigonometrical and logarithmic scales, which could be used with a pair of compasses to solve navigational problems.

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Table of Trigonometry, from the 1728 Cyclopaedia, Volume 2 featuring a Gunter’s scale Source: Wikimedia Commons

Out of two Gunter scales laid next to each other William Oughtred (1574–1660) developed the slide rule, basically a set of portable logarithm tables for carry out calculations.

Napier developed other aids to calculation, which he published in his Rabdologiae, seu numerationis per virgulas libri duo in 1617; the most interesting of which was his so called Napier’s Bones.

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These are a set of multiplication tables embedded in rods. They can be used for multiplication, division and square root extraction.

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An 18th century set of Napier’s bones Source: Wikimedia Commons

Wilhelm Schickard’s calculating machine incorporated a set of cylindrical Napier’s Bones to facilitate multiplication.

The Swiss mathematician Jost Bürgi (1552–1632) produced a set of logarithm tables independently of Napier at almost the same time, which were however first published at Kepler’s urging as, Arithmetische und Geometrische Progress Tabulen…, in 1620. However, unlike Napier, Bürgi delivered no explanation of the how his table were calculated.

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Tables of logarithms became the standard calculation aid for all those making mathematical calculations down to the twentieth century. These were some of the mathematical tables that Babbage wanted to produce and print mechanically with his Difference Engine. When I was at secondary school in the 1960s I still carried out all my calculations with my trusty set of log tables, pocket calculators just beginning to appear as I transitioned from school to university but still too expensive for most people.

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Not my copy but this is the set of log tables that accompanied me through my school years

Later in the late 1980s at university in Germany I had, in a lecture on the history of calculating, to explain to the listening students what log tables were, as they had never seen, let alone used, them. However for more than 350 years Napier’s invention served all those, who needed to make mathematical calculations well.

 

 

 

 

 

 

 

 

 

 

 

 

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Robert Hunter (June 23 1941–September 23 2019)

If you don’t like the Grateful Dead then don’t read this. The Grateful Dead and especially the songs of Jerry Garcia and Robert Hunter have been the soundtrack of my life for the last fifty years. Those songs have given me hope when I was down and transported me to the stars when I was up. They have accompanied me through all the up and downs, along the twisting and turning highway that has been my life, the strange diversions and dead ends. They were always there a mental bedrock to which I could cling whatever happened.

Robert Hunter was one of the truly great lyricists of the rock era, with all of the literary and high art implications that lyricist rather than simple songwriter carries. The breadth and depth of emotional colours that his words could and do magic into existence are seemingly infinite. The music and words of Garcia and Hunter are attuned to my soul in a way no other music is, was or ever will be and I own and listen to a very wide spectrum of music. Robert Hunter’s lyrics melded perfectly with Jerry Garcia’s liquid gold guitar lines.

I listen to music when I write and about eighty per cent of the time it’s the Grateful Dead. Hundred Year Hall, to which Hunter wrote some very beautiful sleeve notes, is blasting out of the stereo system, as I write these inadequate words.

I cried when I heard that Jerry Garcia had died fourteen years ago, something that surprised more than a little but which I accepted. I’m crying now having heard of the passing of Robert Hunter. I, and I suspect many others, own him an unpayable debt for all of the joy, sustenance in dark times and peace of mind that he has given me through his wonderful songs.

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The emergence of modern astronomy – a complex mosaic: Part XX

It is not an exaggeration to say that the invention of telescope was a very major turning point in the general history of science and in particular the history of astronomy. Basic science is fundamentally empirical; people investigating the world make observations with their senses–taste, sight, touch, smell, hearing–then try to develop theories to describe and explain what has been observed and recorded. The telescope was the first ever instrument that was capable of expanding or strengthening one of those senses that of sight. The telescope made it possible to see things that had never been seen before.

The road to the telescope was a long one and one of the questions is why it wasn’t invented earlier. There are various legends or myths about devices to enable people to see things at a distance throughout antiquity and various lens shaped objects also from the distant past that might or might not have been lenses. Lenses in scientific literature in antiquity and the early middle ages were burning lenses used to focus sunlight to ignite fires. The first definite use of lenses to improve eyesight were the so-called reading stones, which emerged around 1000 CE, approximately hemispherical lenses, placed on documents to help those suffering from presbyopia, weakening of the ability of the eye to focus due to aging.

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Source: Zeiss

Reading glasses utilising plano-convex lenses first appeared around 1290.

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The earliest pictorial evidence for the use of eyeglasses is Tommaso da Modena’s 1352 portrait of the cardinal Hugh de Provence reading in a scriptorium Source: Wikimedia Commons

The current accepted theory of the discovery of simple lenses is that in the Middle Ages monks cutting gems to decorate reliquary discovered the simple magnifying properties of the gemstones they were grinding and polishing.

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Reliquary Cross, French, c. 1180 Source: Wikimedia Commons

By the middle of the fifteenth century eye glasses utilising both convex and concave lenses were being manufactured and traded, so why did it take until 1608 before somebody successfully combined a concave lens and convex lens to create a simple so-called Dutch telescope?

There are in fact earlier in the sixteenth century in the writings of Girolamo Fracastoro (ca. 1476–1553) and Giambattista della Porta (1532–1615) descriptions of the magnifying properties of such lens combinations but these are now thought to refer to special eyeglasses rather than telescopes.

Della Porta Telescope Sketch

The early lenses were spherical lenses, which were hand ground and polished and as a result were fairly inaccurate in their form tending to deviate from their ideal spherical form the further out one goes from the centre.  These deformations caused distortions in the images formed and combining lenses increased the level of distortion making such combinations next to useless. It is now thought that the breakthrough came through the use of a mask to stop down the diameter of the eyepiece lens cutting out the light rays from the periphery, restricting the image to the centre of the lens and thus massively reducing the distortion. So who made this discovery? Who first successfully developed a working telescope?

This question has been hotly discussed and various claims just as hotly disputed since at least the middle of the seventeenth century. However, there now exists a general consensus amongst historian of optics.

[To see the current stand on the subject read the bog post that I wrote at this time last year, which I don’t intend to repeat here]

Popular accounts of the early use of the telescope in astronomy almost always credit Galileo Galilei, at the time a relatively unknown professor for mathematics in Padua, with first recognising the potential of the telescope for astronomy; this is a myth.

As can be seen from the quote from the French newsletter AMBASSADES DV ROY DE SIAM ENVOYE’ A L’ECELence du Prince Maurice, arriué à la Haye le 10. Septemb.1608., recording the visit of the ambassador of the King of Siam (Thailand), who was also present at the first demonstration of the telescope the potential of this new instrument, as a tool for astronomy was recognised from the very beginning:

even the stars which normally are not visible for us, because of the scanty proportion and feeble sight of our eyes, can be seen with this instrument.

In fact the English polymath Thomas Harriot (1560–1621) made the earliest known telescopic, astronomical observations but, as with everything else he did, he didn’t publish, so outside of a small group of friends and acquaintances his work remained largely unknown. Also definitely contemporaneous with, if not earlier than, Galileo the Franconian court mathematicus, Simon Marius (1573–1625), began making telescopic observations in late 1609. However, unlike Galileo, who as we will see published his observations and discoveries as soon as possible, Marius didn’t publish until 1614, which would eventually bring the accusation of having plagiarised Galileo.  At the Collegio Romano, the Jesuit University in Rome, Odo van Maelcote (1572–1615) and Giovanni Paolo Lembo (1570–1618) were also making telescopic observations within the same time frame. There were almost certainly others, who didn’t make their observations public.

Before we turn to the observations and discoveries that these early telescopic observers made, we need to look at a serious technical problem that tends to get ignored by popular accounts of those discovery, how does a telescope work? In 1608 when the telescope first saw the light of day there existed absolutely no scientific explanation of how it worked. The group of early inventors almost certainly discovered its magnifying effect by accident and the first people to improve it and turn it into a viable scientific instrument, again almost certainly, did so by trial and error. At this point the problem is not to find the optical theory needed to develop better telescopes systematically but to find the optical theory necessary to justify the result the telescope produced. Using any sort of instrument in science requires a scientific explanation of how those results are achieved and as already stated at the beginning no such theory existed. The man, who came to the rescue, was Johannes Kepler in the second of his major contributions to the story of heliocentric astronomy.

Already in 1604 in his Ad Vitellionem Paralipomena Astronomiae pars optica, Kepler had published the first explanation of how lenses focus light rays and how eyeglasses work to compensate for short and long sightedness so he already had a head start on explaining how the telescope functions.

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Source

Francesco Maurolico (1494–1575) had covered much of the same ground in his Theoremata de lumine et umbra earlier than Kepler but this work was only published posthumously in 1611, so the priority goes to Kepler.

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In 1611 Kepler published his very quickly written Dioptrice, in which he covered the path of light rays through single lenses and then through lens combinations. In this extraordinary work he covers the Dutch or Galilean telescope, convex objective–concave eyepiece, the astronomical or Keplerian telescope, convex objective–convex eyepiece, the terrestrial telescope, convex objective–convex eyepiece–convex–field–lens to invert image, and finally for good measure the telephoto lens! Galileo’s response to this masterpiece in the history of geometrical optics was that it was unreadable!

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Source: Wikimedia Commons

In the next section we will turn to the discoveries that the various early telescopic astronomical observers made and the roles that those various discoveries played in the debates on, which was the correct astronomical model of the cosmos. A much more complicated affair than it is often presented.

 

 

 

 

 

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The role of celestial influence in the complex structure of medieval knowledge.

My entire life has followed a rather strange and at time confusing path that bears no relationship to the normal career path of a typical, well educated, middle class Englishman. It has taken many twists and turns over the years but without doubt one of the most bizarre was how I got to know historian of astrology Darrel Rutkin. We met on a bus, when he a total stranger commented that he knew the author of the book that I was reading, Monica Azzolini’s excellent, The Duke and the Stars: Astrology and Politics in Renaissance Milan. You can read the story in full here. At the time Darrel was a fellow at the International Consortium for Research in the Humanities: Fate, Freedom and Prognostication. Strategies for Coping with the Future in East Asia and Europe in Erlangen, where he was working on his book on the history of European astrology. Darrel and I became friends, talking about Early Modern science and related topics over cups of coffee and he twice took part in my History of Astronomy tour of Nürnberg. Before he left Erlangen he asked me if I would be interested in reading and reviewing his book when he finished writing it. I, of course, said yes. Some weeks ago I received my review copy of H. Darrel Rutkin, Sapientia Astrologica: Astrology, Magic and Natural Knowledge, ca. 1250–1800: I.Medieval Structures (1250–1500): Conceptual, Institutional, Socio-Political, Theologico-Religious and Cultural and this is my review.

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As should be obvious from the impressive title this is not in anyway a popular or even semi-popular presentation but a very solid piece of hard-core academic research. What I have, and will discuss here, is just volume one of three, which weighs in at over six hundred pages. In his work Rutkin present two theses the first of which he explicates in Volume I of his epos and the second of which forms the backbone of the two future volumes. The central thesis of Volume I is summed up in the slightly intimidating twelve-word term “astrologizing Aristotelian natural philosophy with its geometrical-optical model of celestial influences.” A large part of the book is devoted to constructing this object and I will now attempt to produce a simplified description of what it means and how it operated in medieval Europe.

It is common in the history of astrology to treat it as a separate object, as if it had little or nothing to do with the rest of the contemporary knowledge complex. It is also very common to lump astrology together with magic and the other so-called occult sciences. For the High Middle Ages, the period that his book covers, Rutkin rejects both of these approaches and instead proposes that astrology was an integral and important part of the accepted scientific knowledge of the period. His book is divided into five sections each of which I will now outline.

The first section is an eighty-nine-page introduction, which contains a detailed road map of the author’s intentions including a brief summary of what he sees as the current situation in various aspects of the study of the subject under investigation. This also includes an excursion: Astrological Basics: Horoscopes and Practical Astrology. This section is not based on the author’s own work but on that of Roger Bacon, one of the central figures of the book, so if you want to know how a leading medieval astrologer set up and worked with a horoscope then this is the right place to come.

The first section of the book proper deals with the relationship between astrology and natural philosophy in the thirteenth century and it is this section that defines and explains our intimidating twelve-word term from above. Rutkin’s analysis is based on four primary sources; these are an anonymous astrological text the Speculum Astronomiae, written around 1260 and often attributed to Albertus Magnus, an attribution that Rutkin disputes, the writings of Albertus Magnus (before 1200–1280), those of Thomas Aquinas (1225–1274) and those of Roger Bacon (ca. 1220­–1292), as well as numerous other sources from antiquity, and both the Islamic and Christian Middle Ages. In this first section he first presents those writings of Aristotle that contain his thoughts on celestial influence, which form the philosophical foundations for the acceptance of astrology as a science. He then demonstrates how the Speculum Astronomiae, Bacon and Albertus expanded Aristotle’s thoughts to include the whole of horoscope astrology and imbedded it into medieval Aristotelian natural philosophy, this is our “astrologizing Aristotelian natural philosophy.” He also shows how Thomas, whilst not so strongly astrological, as the others, also accepts this model. The technical astrology that is considered here is a highly mathematical, read geometrical, one based on the radiation theories of the Arabic scholar al-Kindi in his De radiis stellarum, as originally introduced into European thought by Robert Grosseteste (1175–1253) in his optical theories and adopted by Bacon. This explains how every geographical point on the earth at every point in time has a unique horoscope/astrological celestial influence: the “geometrical-optical” part of our intimidating twelve-word term. This also ties in with Aristotle’s geographical theories of the influence of place on growth and change. What comes out of this analysis is an astrological-geographical-mathematical-natural philosophical model of knowledge based on Aristotle’s natural philosophy, Ptolemaeus’ astronomy and astrology, and al-Kindi’s radiation theory at the centre of thirteenth century thought.

Rutkin does not simple state an interpretation of Albertus’, Bacon’s or Aquinas’ views but analyses their actual writings in fine detail. First he outlines one step in a given thought process then he quotes a paragraph from their writings in English translation, with the original in the footnotes, including original terms in brackets in the translation if they could possible be considered ambiguous. This is followed by a detailed analysis of the paragraph showing how it fits into the overall argument being discussed. He proceeds in this manner paragraph for paragraph cementing his argument through out the book. This makes hard work for the reader but guarantees that Rutkin’s arguments are as watertight as possible.

The second section of the book proper deals with the subject of theology, a very important aspect of the medieval knowledge complex. Rutkin shows that both Albertus and Thomas accepted astrology within their theology but were careful to show that celestial influence did not control human fate, providence or free will these being the dominion of their Christian God. This is of course absolutely central for the acceptance of astrology by Christian theologians. Bacon’s attitude to astrology and theology is completely different; he builds a complete history of the world’s principle religions based on the occurrence of planetary conjunctions, explaining why, as a result, Christianity is the best religion and addressed to the Pope, for whom he is writing, how one needs to combat the religion of the Anti-Christ.

The third section of the book proper now turns to the vexed question of the relationship between astrology and magic. Rutkin shows that both the Speculum Astronomiae and Albertus in his writing accept that astrology can be used to create magical images or talisman for simple tasks such as killing snakes. However, this is the limit of the connection between the two areas, other aspects of magic being worked by evil spirits or demons. Thomas, not surprisingly rejects even this very circumscribed form of astrological magic regarding all of magic to have its roots in evil. Bacon is much more open to a wider range of connections between the areas of astrology and magic.

Having set up the place of astrology in the medieval knowledge complex of the thirteenth century, the fourth and final section of the book proper takes brief looks at the evidence for its use in various fields within Europe in the period up to 1500. Fields sketched rather than covered in great detail included mathematics, medicine, teaching in the various faculties at the universities, annual prognostications at the universities and to close astrology in society, politics and culture.

Does Rutkin succeed in proving his central thesis for this his first volume? History is not like mathematics and does not deliver conclusive proofs but Rutkin’s thesis is argued in great detail with an impressive array of very convincing evidence. His work is rock solid and anybody wishing to refute his thesis is going to have their work cut out for them. That is not to say that with time, new research and new evidence his thesis will not undergo modification, refinement and improvement but I think its foundations will stand the test of time.

His second main thesis, which will be presented in the two future volumes of his work, is to explain how and why the medieval, mathematics based (read mathematical astrology), Aristotelian natural philosophy that had been created in the High Middle Ages came to replaced by a very different mathematics based, system of natural philosophy in the seventeenth and eighteenth centuries. Having ploughed my way through Volume I, I very much look forward to reading both future volumes.

It goes without saying that the book has an impressively long bibliography of both primary and secondary sources that the author has consulted. I consider myself reasonably well read on the history of European astrology but if I were to sit down and read all of the new, interesting titles I discovered here, I would be very busy for a number of years to come. There is also a first class index and I’m very happy to report that the book also has excellent footnotes, many of which I consulted whilst reading, rather than the unfortunately ubiquitous endnotes that plague modern publishing.

Before I move to a conclusion I wish to point out a second way to read this book. As it stands this is not a book that I would necessarily dump on an undergraduate or a historian, whose interest in the fine detail of Rutkin’s argument was peripheral but that is not necessary or at least not in its totality. I have already mentioned that the introduction contains a detailed road map to the whole volume and as well as this, each of the four sections has an introduction outlining what the section sets out to show and a conclusion neatly summarising what has been demonstrated in the section. By reading main introduction and the introductions and conclusions to the sections a reader could absorb the essence of Rutkin’s thesis without having to work through all of the documentary proof that he produces.

In general I think that Rutkin has set standards in the historiography of medieval astrology and that his book will become a standard work on the topic, remaining one for a long time. I also think that anybody who wishes to seriously study medieval European astrology and/or medieval concepts of knowledge will have to read and digest this fundamental and important work.

I’m posting this today, having pulled it up from the back of a list of planned blog posts because today Darrel’s book is being formally presented at the University of Venice, where he is currently working in a research project, this afternoon with Monica Azzolini as one of those discussing the book and so a circle closes. I shall be there with them in spirit.

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The emergence of modern astronomy – a complex mosaic: Part XIX

Tycho and Kepler was one of the most important partnerships in the history of Early Modern science and a good counter example to those who mistakenly believe in the lone genius myth. Tycho the observational astronomer with an obsession for accuracy, who produced an unequalled volume of raw data

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Tycho Brahe Source: Wikimedia Commons

and Kepler the theoretical astronomer with an equal obsession for accuracy, who would come to turn that data into a completely new heliocentric model of the cosmos.

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Johannes Kepler Source: Wikimedia Commons

Superficially a marriage made in heaven but when the two men first met in Prague their future cooperation almost ended before it even started. Arriving in February 1600 at Tycho’s new home in Benátky Castle Kepler was initially welcomed as a guest and observer.

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Benátky Castle Source: Wikimedia Commons

He was impressed by Tycho’s setup and his data collection to which he hoped to gain access to fine tune his Platonic solids model of the cosmos. Tycho was impressed by the young theoretician but, suspicious of possible plagiarism, was not prepared to make his data freely available. Kepler was of course desperate for paid employment and after two months entered negotiations with Tycho over some sort of fixed employment. The young, working class, German mathematician took umbrage at the arrogant attitude of the Danish aristocrat and in a strop broke off the talks, departing for Prague. Interestingly Tycho, needing fresh workers, proved himself surprisingly conciliatory and through the diplomatic efforts of the Bohemian physician Jan Jesenius (1566–1621) Kepler was persuaded to return to Benátky, where conditions of employment for him were eventually arranged.

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Jan Jesenius

Kepler, who had left his family in Graz, now returned there and after a failed attempt to obtain employment from Archduke Ferdinand in August 1600 he finally set off for Prague with household and family. Initially he was employed directly by Tycho his first task being to write an account of the plagiarism dispute between Tycho and Ursus, probably as a punishment for having supplied Ursus with munitions in that dispute, and naturally he was expected to find in Tycho’s favour. This work, which turned out to be very impressive, was never published in Tycho’s or Kepler’s lifetimes and much more significant was the first real astronomical work that Tycho assigned to him.

When Kepler had first arrived in Benátky, Christen Longomontanus (1562–1647), who had returned to the fold having initially left Tycho’s circus when he quit Denmark, was working on the raw data for the orbit of Mars.

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Christen Longomontanus

Tycho now removed him from this work, assigning him instead to the Moon’s orbit, and gave the task instead to Kepler under Longomontanus’ supervision. This turned out to be one of the most fateful decisions in the entire history of astronomy. Kepler initially thought that he could knock off this task in a couple of weeks but in fact it took him six years to complete but as well as the mathematical difficulties involved there were extenuating circumstances. Before turning to the results of what Kepler called his war with Mars, a play upon the fact that Mars was the Roman god of war, we need to take a look at some of those circumstances.

Tycho’s financial resources were stretched so he negotiated with Rudolf, the Emperor, for Kepler to be appointed directly to the court in order to produce a new set of planetary tables, using Tycho’s data, to replace the existing Prutenic Tables of Erasmus Reinhold and to be named, of course, after the Emperor. What seemed like a step up for Kepler proved to be very problematic, as Rudolf, always strapped for cash, was very bad at paying his staff.

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Rudolf II Portrait by Martino Rota Source: Wikimedia Commons

The next major event was the death of Tycho on 24 October1601 barely a year after Kepler had started working with him. For Kepler this was both good and bad. Already appointed to produce planetary tables for Rudolph, he now inherited Tycho’s title as Imperial Mathematicus, as the obvious candidate Longomontanus had left Benátky and Tycho’s service the previous year. This was truly a major step up but with the same caveat that Rudolf was extremely bad at paying salaries. Kepler was, of course, now in physical possession of all of Tycho’s data but unfortunately not in legal possession. Although he had been Imperial Mathematicus, Tycho’s data did not belong to Rudolf but was his own private property and was on his death inherited by his family. Kepler was faced with the problem of negotiating with Tycho’s son in law Frans Gansneb genaamd Tengnagel van de Camp over the use of the data. Frans Tengnagel initially claimed that he would work with the data but he was a diplomat and not an astronomer or mathematician and in the end a compromise was reached in that Kepler could use the data but that Fans Tengnagel would be named as co-author in any resulting publications. In fact, in the end Frans Tengnagel’s only contribution was a preface to the Astronomia nova.

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Frans Gansneb genaamd Tengnagel van de Camp

Even though he now possessed the desired data Kepler did not sit down solely to finish calculating the orbit of Mars. In 1604 he published his Astronomia Pars Optica, the most important work in optics since the Middle Ages, which laid the foundations of the modern science of optics.

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Astronomiae Pars Optica

It included the first explanations of how lenses work to correct short and long sight and above all the first-ever correct explanation of how the image is formed in the eye. This work would, as will see, proved extremely important following the invention of the telescope at the end of the decade. Also in 1604 a supernova appeared in the skies and Kepler systematically observed it, confirmed it was definitively supralunar (i.e. above the moon’s orbit) and wrote up and published his findings, De Stella nova in pede Serpentarii, in Prague in 1606. This of course confirmed what had already been demonstrated in the 1570s that the heavens were not incorruptible, driving another nail into the coffin of Aristotelian cosmology.

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Stella nova in pede Serpentarii title page

During this period Kepler also finished his determination of the orbit of Mars, in the course of which he changed the course of astronomy forever. Published in 1609 the Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ seu physica coelestis, tradita commentariis de motibus stellae Martis ex observationibus G.V. Tychonis Brahe, to give it its full title, is without any doubt whatsoever one of the most important books in the whole history of astronomy, although it was not recognised as such until long after it appeared.

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Astronomia Nova title page Source: Wikimedia Commons

Unique amongst major scientific publications the book appears to outline in great detail the path that the author took in his determination of the Planet’s orbit, including all the false paths he followed, the errors that he made and even his calculating mistakes. Normally scientists leave all of this out of their published work presenting only the successful conclusions of their battles with the evidence and data. So why did Kepler include all of his six years of strife in his finished product. The answer lies in the statement above, appears to outline. In fact the account presented is to some extent, to use an actual term, fake news. Kepler is deliberately misleading his readers but why?

Kepler was a convinced Copernicaner in a period where the majority of astronomers were either against heliocentricity, mostly with good scientific reasons, or at best sitting on the fence. Kepler was truly revolutionary in another sense, he believed firmly in a physical cause for the structure of the cosmos and the movement of the planets. This was something that he had already propagated in his Mysterium Cosmographicum and for which he had been strongly criticised by his teacher Mästlin. The vast majority of astronomers still believed they were creating mathematical models to save the phenomena, irrespective of the actually physical truth of those models. The true nature of the cosmos was a question to be answered by philosophers and not astronomers. Kepler structured the rhetoric of the Astronomia Nova to make it appear that his conclusions were inevitable; he had apparently no other choice, the evidence led him inescapably to a heliocentric system with a real physical cause. Of course, he couldn’t really prove this but he did his best to con his readers into thinking he could.

Kepler tested and refined his arguments in one of the most fascinating correspondences in the history of astronomy, which took place with the Frisian amateur astronomer David Fabricius (1564–1617) over a total of eight years; a correspondence that also makes a mockery of the lone genius myth. Fabricius was a Protestant pastor and a passionate amateur astronomer. He first emerged on the European astronomical scene when he took up contact with Jost Bürgi (1552–1632) in Kassel in 1592 to request his advice on constructing astronomical instruments. In 1596 having, as the first astronomer to do so, observed the variable star Mira he wrote a letter to Tycho Brahe in Hven describing his discovery. This was the start of an extensive correspondence between the two that lasted until Tycho’s death in 1601. In that year he visited Tycho in Prague, where he met Simon Marius (1573–1625) with whom he would also correspond but not Kepler who was in Austria on family business. The letters that Kepler and Fabricius exchanged were more in the nature of academic papers often running to forty or fifty pages.

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Monument to David Fabricius & his son Johannes in the church yard in Osteel his parish Source: Wikimedia Commons

Fabricius was neither a geocentrist nor a heliocenrist but a solid supporter of Tycho’s geo-heliocentric compromise and so was an ideal sparing partner for Kepler. Kepler would outline his latest heliocentric theories and Fabricius would do his best to demolish them and his best was very good indeed. This meant that over the years of their correspondence Kepler could really develop and refine the complex arguments that he would then finally present in the Astronomia nova. Probably frustrated by his failure to convert Fabricius to his way of thinking, Kepler rather abruptly broke off the correspondence in 1609. Fabricius, who Kepler acknowledge as the best observational astronomer in Europe following Tycho’s demise, died tragically in 1617, beaten to death with a spade by a local farmer, who thought Fabricius had accused him of being a thief in a sermon.

Despite Kepler’s best efforts the Astronomia nova was largely a flop when first published. Those who read it largely rejected his argument for heliocentricity. The book however contains two of the most important discoveries in the history of astronomy, Kepler’s first two laws of planetary motion:

1) That planets orbit the Sun on elliptical paths with the Sun situated at one focus of the ellipse

2) That a line connecting the planet to the Sun sweeps out equal areas in equal periods of time.

Kepler actually developed the second law first using it as his primary tool to determine the actually orbit of Mars. The formulation of this law went through an evolution, which he elucidates in the book, before it reached its final form. The first law was in fact the capstone of his entire endeavour. He had known for sometime that the orbit was oval and had even at one point considered an elliptical form but then rejected it. When he finally proved that the orbit was actually an ellipse he knew that his battle was over and he had won.

Although, at the time, Kepler had temporarily lost the public battle in the larger war for the recognition that the cosmos, as it was then known, was indeed heliocentric the publication of the Astronomia nova represents one of the most important steps towards the final victory in that war. This would not remain Kepler’s only contribution to that war but before we look at his further efforts we need to turn to what was possibly the most important event in the history of Early Modern astronomy, the invention of the telescope.

[Attentive readers of this blog might have noticed that I have ‘plagiarised’ my own post on the Astronomia nova from December last year. I simply couldn’t be bothered to find new ways of expressing things that I had already expressed to my own satisfaction.]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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