Galileo’s the 12th most influential person in Western History – Really?

Somebody, who will remain nameless, drew my attention to a post on the Presidential Politics for America blog shortly before Christmas in order to provoke me. Anybody who knows me and my blogging will instantly recognise why I should feel provoked if they just read the opening paragraph.

Despite the paradigm-shifting idea of our #28 Nicolaus Copernicus, for nearly a century afterward his heliocentric theory twisted in the solar wind. It took another man to confirm Copernicus’s daring theory. That alone would make this other man an all-time great contributor to Western science, but he gifted us so much more than merely confirming someone else’s idea. He had a series of inventions, discoveries, and theories that helped modernize science. His accomplishments in mechanics were without precedent. His telescope observed what was once unobservable. Perhaps most importantly, he embodied, furthered, and inspired a growing sentiment that truth is a slave to science and facts, not authority and dogma.

This man was Galileo Galilei, and he’s the 12thmost influential person in Western History.

Before I start on my usually HistSci_Hulk demolition job to welcome the New Year I should point out that this crap was written by somebody claiming to be a history teacher; I feel for his student.

This post is part of a long-term series on The Top 30 Most Influential Western European Figures in History; I kid you not! Sorry, but I’m not a fan of rankings in general and to attempt to rank the historical influence of Western Europeans is in my opinion foolhardy at best and totally bonkers at worst.

We turn our attention to his #11 Galileo Galilei. We start with the very obvious false claim, the very first one in fact, Galileo did not ‘confirm Copernicus’s daring theory.’ Next up we have the statement: ‘He had a series of inventions, discoveries, and theories that helped modernize science.’

Only in his teens, he identified the tautochronic curve that explains why the pendulum behaves as it does. This discovery laid the groundwork for Christian [sic] Huygens to create the world’s first pendulum clock, which became the most accurate method of keeping time into the twentieth century. 

It is Christiaan not Christian Huygens. Galileo discovered the isochronal principle of the pendulum but the earliest record of his researches on the pendulum is in a letter to his patron Guidobaldo del Monte dated 2 November 1602, when he was 38 years old. The story that he discovered the principle, as a teenager was first propagated posthumously by his first biographer Viviani and to be taken with a pinch of salt. He didn’t discover that the free circular pendulum swing is not isochronal but only the tautochrone curve is; this discovery was actually made by Huygens. There is no evidence that Galileo’s design of a never realised pendulum clock had any connections with or influence on Huygens’ eventually successfully constructed pendulum clock. That pendulum clocks remained the most accurate method of keeping time into the twentieth century is simply wrong.

The precocious Galileo also invented thethermoscope…

 It is not certain that Galileo invented the thermoscope; it is thought that his friend Santorio Santorio actually invented it; he was certainly the first during the Renaissance to publish a description of it. The invention was attributed to Galileo, Santorio, Robert Fludd and Cornelius Drebble. However, the principle on which it was based was used in the Hellenic period and described even earlier by Empedocles in book On Nature in 460 BCE. This is part of a general pattern in the Galileo hagiography, inventions and discoveries that were made by several researchers during his lifetime are attributed solely to Galileo even when he was not even the first to have made them.

At just 22, he published a book onhydrostatic balance, giving him his first bit of fame.

 This ‘book’, La Bilancetta or The Little Balance was actually a booklet or pamphlet and only exists in a few manuscripts so during his lifetime never printed. He used it together with another pamphlet on determining centres of gravity to impress and win patrons within the mathematical community such as Guidobaldo del Monte and Christoph Clavius; in this he was successful.

He attended medical school but, for financial reasons, he had to drop out and work as a tutor. Nevertheless, he eventually became chair of the mathematics department at theUniversity of Pisa.

He studied medicine at the University of Pisa because that was the career that his father had determined for him. He dropped out, not for financial reasons but because he wanted to become a mathematician and not a physician. He studied mathematics privately in Florence and having established his abilities with the pamphlets mentioned above was, with the assistance of his patrons, appointed to teach mathematics in Pisa. However, due to his innate ability to piss people off his contract was terminated after only three years. His patrons now helped him to move to the University of Padua.

He taught at Padua for nearly 20 years, and it’s there where he turned from reasonably well-known Galileo Galilei to Galileo[emphasis in original]. Like the great Italian artists of his age, he became so talented and renowned that soon just his first name sufficed.

This is simply rubbish. He remained virtually unknown outside of Padua until he made his telescopic discoveries in 1610. He turned those discoveries into his exit ticket and left Padua as soon as possible. As for his name, he is, for example, known in English as Galileo but in German as Galilei.

We now turn to mechanics the one field in which Galileo can really claim more than a modicum of originality. However, even here our author drops a major clangour.

Through experimentation, he determined that a feather falls slower than a rock not because of the contrasting weight but because of the extra friction caused by the displacement of Earth’s atmosphere on the flatter object. 

Through experimentation! Where and when did Galileo build his vacuum chamber? Our author missed an opportunity here. This was, of course, Galileo’s most famous thought experiment in which he argues rationally that without air resistance all objects would fall at the same rate. In fact Galileo’s famous use of thought experiments doesn’t make an appearance in this account at all.

Galileo built on this foundation a mathematical formula that showed the rate of acceleration for falling objects on Earth. Tying math to physics, he essentially laid the groundwork for later studies of inertia. These mechanical discoveries provided a firm launching point for Isaac Newton’s further modernization of the field.

It is time for the obligatory statement that the mean speed formula the basis of the mathematics of free fall was known to the Oxford Calculatores and the Paris Physicists in the fourteenth century and also the laws of free fall were already known to Giambattista Benedetti in the sixteenth century. As to inertia, Galileo famously got it wrong and Newton took the law of inertia from Descartes, who in turn had it from Isaac Beeckman and not Galileo. In the late sixteenth and early seventeenth centuries several researchers tied mathematics to physics, many of them before Galileo. See comment above about attributing the work of many solely to Galileo. We now turn to astronomy!

In the early 1600s, despite Copernicus’s elegant heliocentric model of the solar system having debuted more than a half-century earlier, skeptics remained. Indeed, there was an ongoing divide among astronomers; some favored the Copernican model while others clung to the traditional Ptolemaic premise adopted by the Catholic Church, which put the earth at the universe’s center. Even Tycho Brahe, a leading post-Copernican astronomer, favored geocentrism, though his Tychonic system did make some allowances for Copernicus’s less controversial ideas. Brahe’s position helped him avoid the fate of heliocentrist Giordano Bruno who was burned at the stake by the Catholic Inquisition in 1600. This heated astronomical climate awaited Galileo Galilei.

There is nothing particularly elegant about Copernicus’ heliocentric model of the solar system. In fact it’s rather clunky due to his insistence, after removing the equant point, of retaining the so-called Platonic axiom of uniform circular motion. His model was in fact more cluttered and less elegant than the prevailing geocentric model from Peuerbach. Sceptics didn’t remain, as our author puts it, implying in this and the following sentences that there was no reason other than (religious) prejudice for retaining a geocentric model. Unfortunately, as I never tire of repeating, Copernicus’ model suffered from a small blemish, a lack of proof. In fact the vast majority of available empirical evidence supported a geocentric system. You know proof is a fundamental element of all science, including astronomy. If I were playing mythology of science bingo I would now shout full house with the introduction of Giordano Bruno into the mix. No, Giordano was not immolated because he was a supporter of heliocentricity.

Like Bruno, Galileo knew Copernicus was right, and he set out to prove it. Early in the seventeenth century, he received word about a new invention created by the German-Dutch spectacle-makerHans Lippershey In 1608, Lippershey used his knowledge of lenses to make a refracting telescope, which used lenses, an eye piece, and angular strategies to bend light, allowing in more of it. More light could clarify and magnify a desired object, and Lippershey’s rudimentary design could make something appear about three times bigger. Galileo, though he never saw a telescope in person nor even designs of one, heard a basic description of it, checked the information against his brain’s enormous database, realized it could work, and built one of his own. A better one.

Comparing Bruno with Galileo is really something one should avoid doing. Our author’s description of how a refracting telescope works is, I admit, beyond my comprehension, as the function of a refracting telescope is apparently beyond his. The claim that Galileo never saw a telescope, which he made himself, has been undermined by the researches of Mario Biagioli, who argues convincingly that he probably had seen one. I love the expression “checked the information against his brain’s enormous database.” I would describe it not so much as hyperbole as hyperbollocks!

With his improved telescope he could magnify objects thirty times, and he immediately pointed it to the once unknowable heavens and transformed astronomy in numerous ways:

I will start with the general observation that Galileo was by no means the only person pointing a telescope at the heavens in the period between 1609 and 1613, which covers the discoveries described below. He wasn’t even the first that honour goes to Thomas Harriot. Also, all of the discoveries were made independently either at roughly the same time or even earlier than Galileo. If Galileo had never heard of the telescope it would have made virtually no difference to the history of astronomy. He had two things in his favour; he was in general a more accurate observer that his competitors and he published first. Although it should be noted that his principle publication, the Sidereus Nuncius, is more a press release that a scientific report. The first telescope Galileo presented to the world was a 9X magnification and although Galileo did build a 30X magnification telescope most of his discoveries were made with a 20X magnification model. The competitors were using very similar telescopes. “…the once unknowable heavens” we actually already knew quite a lot about the heavens through naked-eye observations.

  • It was assumed that the moon, like all the heavenly spheres, was perfectly smooth. Galileo observed craters and mountains. He inferred, accurately, that all celestial objects had blemishes of their own.

This was actually one of Galileo’s greatest coups. Thomas Harriot, who drew telescopic images of the moon well before Galileo did not realise what he was seeing. After seeing Galileo’s drawings of the moon in the Sidereus Nuncius, he immediately realised that Galileo was right and changed his own drawing immediately. One should, however, be aware of the fact that throughout history there were those who hypothesised that the shadows on the moon were signs of an uneven surface.

  • Though Jupiter had been observed since the ancient world, what Galileo was the first to discover was satellites orbiting around it — the Jovian System. In other words, a planet other than the Earth had stuff orbiting it. It was another brick in Copernicus’s “we’re not that important” wall.

And as I never tire of emphasising, Simon Marius made the same discovery one day later. I have no idea what Copernicus’s “we’re not that important” wall is supposed to be but the discovery of the moons of Jupiter is an invalidation of the principle in Aristotelian cosmology that states that all celestial bodies have a common centre of rotation; a principle that was already violated by the Ptolemaic epicycle-deferent model. It says nothing about the truth or lack of it of either a geocentric or heliocentric model of the cosmos.

  • Pointing his telescope at the sun, Galileo observed sunspots. Though the Chinese first discovered them in 800 BC, as Westerners did five hundred years later, no one had seen or sketched them as clearly as Galileo had. It was another argument against the perfect spheres in our sky.

Telescopic observations of sunspots were first made by Thomas Harriot. The first publication on the discovery was made by Johannes Fabricius. Galileo became embroiled in a meaningless pissing contest with the Jesuit astronomer, Christoph Scheiner, as to who first discovered them. The best sketches of the sunspots were made by Scheiner in his Rosa Ursina sive Sol (Bracciano, 1626–1630).

  • Galileo also discovered that Venus, like the moon, has phases (crescent/quarter/half, waxing/waning, etc.). This was a monumental step in confirming Copernicus’s theory, as Venusian phases require certain angles of sunlight that a geocentric model does not allow.

The phases of Venus were discovered independently by at least four observers, Thomas Harriot, Simon Marius, Galileo and the Jesuit astronomer Paolo Lembo. The astronomers of the Collegio Romano claimed that Lembo had discovered them before Galileo but dating the discoveries is almost impossible. In a geocentric model Venus would also have phases but they would be different to the ones observed, which confirmed that Venus, and by analogy Mercury, whose phases were only observed much later, orbits the Sun. Although this discovery refutes a pure geocentric system it is still compatible with a Capellan system, in which Venus and Mercury orbit the Sun in a geocentric model, which was very popular in the Middle ages and also with any of the Tychonic and semi-Tychonic models in circulation at the time so it doesn’t really confirm a heliocentric model

  • The observable hub of the Milky Way galaxy was assumed to be, just as it looks to us, a big, milky cloud. Galileo discovered it was not a cloud, but a huge cluster of stars. (We now know it numbers in the billions.)

Once again a multiple discovery made by everybody who pointed a telescope at the heavens beginning with Lipperhey.

Galileo not only confirmed Copernicus’s heliocentric theory, but he allowed the likes of Johannes Kepler to more accurately plot out the planets’ orbits, Isaac Newton to explain how it was happening, and Albert Einstein to explain why. It was such a colossal step forward for the observable universe that some people didn’t even believe what they were seeing in the telescope, electing to instead remain skeptical of Galileo’s “sorcery.”

Galileo did not in any way confirm Copernicus’ heliocentric theory. In fact heliocentricity wasn’t confirmed until the eighteenth century. First with Bradley’s discovery of stellar aberration in 1725 proving the annual orbit around the sun and then the determination of the earth’s shape in the middle of the century indirectly confirming diurnal rotation. The telescopic observations made by Galileo et al had absolutely nothing to do with Kepler’s determination of the planetary orbits. Newton’s work was based principally on Kepler’s elliptical system regarded as a competitor to Copernicus’ system, which Galileo rejected/ignored, and neither Galileo nor Copernicus played a significant role in it. How Albert got in here I have absolutely no idea. Given the very poor quality of the lenses used at the beginning of the seventeenth century and the number of optical artifacts that the early telescopes produced, people were more than justified in remaining skeptical about the things apparently seen in telescopes.

Ever the watchdog on sorcery, it was time for the Catholic Church to guard its territory. Protective of geocentrism and its right to teach us about the heavens, the Church had some suggestions about exactly where the astronomer could stick his telescope. In 1616, under the leadership of Pope Paul V, heliocentrism was deemed officially heretical, and Galileo was instructed “henceforth not to hold, teach, or defend it in any way.”

The wording of this paragraph clearly states the author’s prejudices without consideration of historical accuracy. Galileo got into trouble in 1615/16 for telling the Catholic Church how to interpret the Bible, a definitive mistake in the middle of the Counter Reformation. Heliocentrism was never deemed officially heretical. The injunction against Galileo referred only to heliocentrism as a doctrine i.e. a true theory. He and everybody else were free to discuss it as a hypothesis, which many astronomers preceded proceeded to do.

A few years later, a confusing stretch of papal leadership got Galileo into some trouble. In 1623,Pope Urban VIII took a shine to Galileo and encouraged his studies by lifting Pope Paul’s ban. A grateful Galileo resumed his observations and collected them into his largest work, 1632’s “Dialogue Concerning the Two Chief World Systems” In it, he sums up much of his observations and shows the superiority of the newer heliocentric model. The following year, almost as if a trap were set, the Catholic Inquisition responded with a formal condemnation and trial, charging him with violating the initial 1616 decree. Dialogue was placed on the Church’s Index of Prohibited Books.

Maffeo Barberini, Pope Urban VIII, had been a good friend of Galileo’s since he first emerged into the limelight in 1611 and after he was elected Pope did indeed show great favour to Galileo. He didn’t, however, lift Paul V’s ban. It appears that he gave Galileo permission to write a book presenting the geocentric and heliocentric systems, as long as he gave them equal weight. This he very obviously did not do; Galileo the master of polemic skewed his work very, very heavily in favour of the heliocentric system. He had badly overstepped the mark and got hammered for it.  He, by the way, didn’t resume his observations; the Dialogo is based entirely on earlier work. One is, by the way, condemn after being found guilty in a trial not before the trial takes place when one is charged or accused.

Galileo’s popularity, combined with a sheepish Pope Urban, limited his punishment to a public retraction and house arrest for his remaining days. At nearly 70, he didn’t have the strength to resist. Old, tired, and losing his vision after years of repeatedly pointing a telescope at the brightest object in the solar system, he accepted his sentence. Blind and condemned, his final years were mostly spent dictating “Two New Sciences,” which summarized his 30 years of studying physics.

Galileo’s popularity would not have helped him, exactly the opposite. People who were highly popular and angered the Church tended to get stamped on extra hard, as an example to the masses. Also, Urban was anything but sheepish. The public retraction was standard procedure for anyone found guilty by the Inquisition and the transmission of his sentence from life imprisonment to house arrest was an act of mercy to an old man by an old friend. Whether Galileo’s telescopic observations contributed to his blindness is disputed and he hadn’t really made many observations since about 1613. The work summarised in the Discorsi was mostly carried out in the middle period of his life between 1589 and 1616.

The author now veers off into a discussion, as to who is the father or founder of this or that and why one or other title belongs to Copernicus, Newton, Aristotle, Bacon etc. rather than Galileo. Given his belief that one can rank The Top 30 Most Influential Western European Figures in History, it doesn’t surprise me that he is a fan of founder and father of titles. They are, as regular readers will already know, in my opinion a load of old cobblers. Disciplines or sub-disciplines are founded or fathered over several generations by groups of researchers not individuals.

His article closes with a piece of hagiographical pathos:

Moreover, Galileo’s successes were symbolic of a cornerstone in modern science. His struggle against the Church embodied the argument that truth comes from experience, experiments, and the facts — not dogma. He showed us authority and knowledge are not interchangeable. Though the Inquisitors silenced him in 1633, his discoveries, works, and ideas outlived them. For centuries, he has stood as an inspiration for free thinkers wrestling against ignorant authority.

This is typical exaggerated presentation of the shabby little episode that is Galileo’s conflict with the Catholic Church. It wasn’t really like that you know. Here we have the heroic struggle of scientific truth versus religious dogma, a wonderful vision but basically pure bullshit. What actually took place was that a researcher with an oversized ego, Galileo, thought he could take the piss out of the Pope and the Catholic Church. As it turned out he was mistaken.

Being a history teacher I’m sure our author would want me to grade his endeavours. He has obviously put a lot of work into his piece so I will give him an E for effort. However, it is so strewn with errors and falsities that I can only give him a F for the content.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

Halley & Hevelius

The Smithsonian website has a post about the seventeenth-century, Danzig astronomer Johannes Hevelius entitled, The 17th-Century Astronomer Who Made the First Atlas of the Moon. The article is OK as far as it goes but one sentence in it disturbs me:

Johannes_Hevelius(close-up)

Johannes Hevelius, portrait by Daniel Schultz Source: Wikimedia Commons

Esteemed visitors such as Edmond Halley, whose many accomplishments include predicting the return of the comet that bears his name, came to visit and meet with Hevelius, hundreds of miles from other epicenters of astronomy in Paris and London.

Edmund_Halley

Edmond Halley portrait by Thomas Murray Source: Wikimedia Commons

Now Halley did indeed go to Danzig to visit Hevelius but when he did so he was not that esteemed and still a long way from predicting the return of what is now know as Comet Halley; he was in fact only twenty-three years old and had barely begun he long and distinguished career. He was already slightly notorious having dropped out of Oxford in 1676, at the age of twenty, to travel to St. Helena to map the stars of the Southern Hemisphere, returning to England first in 1678.

In 1679 the Royal Society sent him to Danzig to settle the dispute between Hevelius, a member of the Royal Society, and Robert Hooke over the use of telescopic sights on his observing instruments; Hevelius preferred not to use them. The author mentions this dispute in their article but does not connect it with Halley’s visit:

Hevelius’s strong feelings about naked-eye astronomy led to a famous debate with famed English polymath Robert Hooke and the first Astronomer Royal, John Flamsteed. Specifically, an instrument of the day called a sextant, which measured angles between celestial objects or the horizon, had a “sight” or aiming device on each arm. Hooke and Flamsteed argued that using telescopes for sights would make measurements more accurate, while Hevelius disagreed.

However this is not the principle reason why the sentence about Halley’s visit disturbs me. As I said, in 1679 Halley was only twenty-three years old and had almost his entire career before him; even his catalogue of 341 of the stars of the southern skies, Catalogus Stellarum Australium, was first published after his return from Danzig in 1679. This meant that the young man, who turned up on Hevelius’ doorstep in Danzig was effectively a nobody and anything but an esteemed visitor. Whilst there, Halley indulged in some observing with Hevelius and both convinced himself of the very high accuracy of Hevelius’ naked-eye observations and impressed his host with his own observational skills.

My problem is one that occurs far too oft in historical articles, in my opinion, and it is the presentation of historical figures in the full glory of their lifetime achievements in historical situations where those achievements still lie in the future. The man who visited Hevelius was a young, unknown beginner in the world of Early Modern astronomy and not the famous multi-talent who became England’s second Astronomer Royal. If the author had written, “the young Edmond Halley, who would later go on to make a distinguished career in astronomy, visited Hevelius in Danzig in 1679”, I would have no problems.

Some might think that I’m making a mountain out of a molehill but I think it is important when writing history of science to introduce the participants, as they were at the time under discussion and not as they became years or even in some cases decades later. Scientific researchers are not born famous but evolve and grow over time and our descriptions and discussions of them must reflect this fact. The Halley who discussed with Hevelius in 1679 was not the Halley who twenty-six years later published the results of his long-year comet research, Synopsis Astronomia Cometicae.

This failure to acknowledge the development in a researcher’s life occurs all too often in my opinion and is one of those things that should be avoided when writing history of science. Just to mention one other example that unfortunately occurs very often. In 1697 Peter the Great, Tsar of Russia, went on an incognito tour of The Netherlands and England to study the latest developments in shipbuilding and other innovations in technology and science. During his time in England he became friends with Halley and visited Isaac Newton, already famous as the author of his Principia: I’ve lost count of how many times I have read that Peter visited Sir Isaac Newton. Newton wasn’t knighted until seven years after Peter’s visit!

 

 

 

 

 

 

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Christmas Trilogy 2018 Part 3: Johannes’ battle with Mars

It would be entirely plausible to claim the Johannes Kepler’s Astronomia Nova was more important to the eventual acceptance of a heliocentric view of the cosmos than either Copernicus’ De revolutionibus or Galileo’s Sidereus Nuncius. As with most things in Kepler’s life the story of the genesis of 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 anything but simple.

Astronomia_Nova

Astronomia Nova title page Source: Wikimedia Commons

From his studies at Tübingen University Kepler was sent, in 1594, by the Lutheran Church to Graz as mathematics teacher in the local Lutheran school and as district mathematicus, responsible for surveying, cartography and above all yearly astrological prognostica. His situation in Graz, a predominantly Catholic area, was anything but easy and as the Counter Reformation gained pace the Lutheran school was closed and the Protestants were given the choice of converting to Catholicism or leaving the area. Largely because of the success of his prognostica Kepler was granted an exemption. However, by 1600 things got very tight even for him and he was desperately seeking a way out. All of his efforts to obtain employment failed, including, somewhat surprisingly, an appeal to his teacher Michael Mästlin in Tübingen.

During his time in Graz he had published his first book, Mysterium Cosmographicum (The Cosmographic Mystery), in which he attempted to prove, the for us today bizarre hypothesis, that in a heliocentric cosmos there were and could only be six planets because their obits were separated by the ratios of the volumes of the five regular Platonic solids. He realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. However, when he actually did the maths he realised that although he had a good approximation, it wasn’t good enough; he blamed the failing accuracy on the poor quality of the data he had available. He needed to obtain better data.

Kepler-solar-system-1

Kepler’s Platonic solid model of the solar system, from Mysterium Cosmographicum (1596) Source: Wikimedia Commons

Kepler was well aware of the fact that, for the last thirty years or so, Tycho Brahe had been accumulating vast quantities of new, comparatively accurate data, so he decided to go visit the Danish aristocratic astronomer in Prague, maybe there was also a chance of employment. There was, however, a small problem with this plan. As a young, first time author, he had sent complimentary copies of his publication to all of the leading European astronomers. This had led to the first correspondence with Galileo, who had received his copy rather more by accident than by design but also to a very tricky situation with Tycho. Kepler had sent a copy to Nicolaus Reimers Baer (1551–1600), also called Ursus, at the time Tycho’s predecessor as Imperial Mathematicus to the Emperor Rudolph II; this was accompanied by the usual highly flattering Renaissance letter of introduction. Ursus was engaged in a very bitter priority dispute with Tycho about the so-called Tychonic system, Tycho had accused him of having stolen it during a visit to Hven, and Ursus printed Kepler’s flattering letter in a highly insulting answer to Tycho’s accusations. Kepler was very definitely not Tycho’s favourite astronomer, as a result. Despite all of this Tycho, also in desperate need of new assistants since moving to Prague, actually invited the young Kepler to come and visit him. By a strange twist of fate the letter of invitation arrived after Kepler had already left Graz for Prague.

Kepler duly arrived in Prague and one of the most fateful meetings in the history of astronomy took place. That first meeting was a monumental disaster. Kepler took umbrage and departed to sulk in a Prague hotel, convinced that his journey to Prague had been in vain. However, thanks to the diplomatic efforts of the Bohemian physician Johannes Jessenius (1566–1621) the two hot heads settled their differences and Tycho offered Kepler at least temporary employment. Having no better offers Kepler agreed, returned to Graz, packed up his home and together with his wife and children returned to Prague.

Unfortunately, there was no way that Tycho was going to trust a comparative stranger with the accumulated treasures of thirty years of observations and Kepler had to be satisfied with the tasks that Tycho gave him. First of all, maybe as a form of punishment, Tycho set him to work writing a vindication of Tycho’s claims against Ursus. Although Kepler did not produce the stinging condemnation of Ursus that Tycho wanted, he did produce a fascinating philosophical analysis of the role of hypothesis in the history of astronomy, A Defence of Tycho against Ursus, which was not published at the time but which historian Nicholas has described in the title of his scholarly edition of the work as ‘the birth of history and philosophy of science.[1]’ On the astronomical front, Tycho gave Kepler what would prove to be a task of immeasurable importance in the history of astronomy, the determination of the orbit of Mars.

When Kepler initially arrived in Prague to work with Tycho, Longomontanus, Tycho’s chief assistant, was working on the orbit of Mars. With Kepler’s arrival Tycho moved Longomontanus onto his model of the Moon’s orbit and put Kepler onto Mars. When first assigned Kepler famously claimed that he would knock it off in a couple of weeks, in the end he took the best part of six years to complete the task. This fact out of Kepler’s life often gets reported, oft with the false claim that he took ten years, but what the people almost never add is that in those six years the Astronomia Novawas not the only thing that occupied his time.

Not long after Kepler began his work Tycho died and he inherited the position of Imperial Mathematicus. This, however, had a major snag. Tycho’s data, the reason Kepler had come to Prague, was Tycho’s private property and that inherited his children including his daughter Elizabeth and her husband Frans Gansneb genaamd Tengnagel van de Camp. Being present when Tycho had died, Kepler secured the data for himself but was aware that it didn’t belong to him. There followed long and weary negotiations between Kepler and Frans Tengnagel, who claimed that he intended to continue Tycho’s life’s work. However, Tengnagel was a diplomat and not an astronomer, so in the end a compromise was achieved. Kepler could retain the data and utilise it but any publications that resulted from it would have Tengnagel named as co-author! In the end he contributed a preface to the Astronomia Nova. Kepler also spent a lot of time and effort haggling with the bureaucrats at Rudolph’s court, attempting to get his salary paid. Rudolph was good at appointing people and promising a salary but less good at paying up.

Apart from being distracted by bureaucratic and legal issues during this period Kepler also produced some other rather important scientific work. In 1604 he published his Astronomiae Pars Optica, written in 1603, which was the most important work in optics published since the Middle Ages and laid the foundations for the modern science. 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. The latter was confirmed empirically by Christoph Scheiner.

C0194687-Kepler_s_Astronomiae_Pars_Optica_1604_

Astronomiae Pars Optica title page

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.

The Astronomia Nova is almost unique amongst major scientific publications in that it appears to outline in detail the work Kepler undertook to arrive at his conclusions, including all of the false turnings he took, the mistaken hypotheses he used and then abandoned and the failures he made in his calculations. Normally scientific researchers leave these things in their notebooks, sketchpads and laboratory protocols; only presenting to their readers a sanitised version of their results and the calculations or experiments necessary to achieve them. Why did Kepler act differently with his Astronomia Nova going into great detail on his six-year battle with Mars? The answer is contained in my ‘it appears’ in the opening sentence of this paragraph. Kepler was to a large extent pulling the wool over his readers’ eyes.

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 real physical cause. Of course, he couldn’t really prove this but he did his best to con his readers into thinking he could. He actually road tested his arguments for this literary tour de force in a long-year correspondence with the Frisian astronomer David Fabricius. Fabricius was a first class astronomer and a convinced Tychonic i.e. he accepted Tycho’s geo-heliocentric model of the cosmos. Over the period of their correspondence Kepler would present Fabricius with his arguments and Fabricius would criticise them to the best of his ability, which was excellent. In this way Kepler could slowly build up an impression of what he needed to do in order to convince people of his central arguments. This was the rhetoric that he then used to write the final version of Astronomia Nova[2].

To a large extent Kepler failed in both his main aims when the book was published in 1609. In fact it would not be an exaggeration to say that it was initially a flop. People weren’t buying either his heliocentricity or his physical cause arguments. But the book contains two gems that in the end would prove very decisive in the battle of the cosmological systems, his first and second 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, that 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. Today school kids learn the first two laws together with the third one, discovered thirteen years later when Kepler was working on his opus magnum the Harmonice mundi, but they rarely learn of the years of toil that Kepler invested in their discovery during his battle with Mars.

[1]Nicholas Jardine, The Birth of History and Philosophy of Science: Kepler’s ‘A Defence of Tycho against Ursus’ with Essays on its Provenance and Significance, CUP, ppb. 2009

[2]For an excellent account of the writing of Astronomia Novaand in particular the Kepler-Fabricius correspondence read James R. Voelkel, The Composition of Kepler’s Astronomia Nova, Princeton University Press, 2001

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

Christmas Trilogy 2018 Part 2: A danseuse and a woven portrait

I had decided some time ago to give up my attempts to rescue Charles Babbage’s reputation from the calumnies of the acolytes of Saint Ada, as a lost cause. However, the recent attempt by said acolytes to heave her onto the planned new British £50 banknote combined with the vast amounts of crap posted all over the Internet on her birthday on 10 December this year convinced me to return to the foray. I shan’t be writing about Ada per see but analysing two quotes that he supporters claim show her superior understanding of the potential of the computer over the, in their opinion, pitifully inadequate Babbage.

Two things should be born in mind when assessing the Notes to the translation of Menabrea’s essay on the Analytical Engine. Firstly, everything that Lovelace knew about the Analytical Engine she had learnt from Babbage and secondly, it is an established fact that Babbage co-authored those notes. The supporters of Lovelace as some sort of computing prophet always state, without giving any sort of proof for their claim, that Babbage was only interested in his Analytical Engine as a sort of super number cruncher and that anything that goes beyond that must per definition come from Lovelace. One should never forget that any computer is in fact just a super number cruncher; everything that one does on a computer, typing this post for example, has first to be translated in mathematical algorithms in binary code so that the computer can understand them. Babbage was, of course, first and foremost interested in producing a machine or automata capable of reading and carrying out the widest possible range of mathematical functions to give it maximum flexibility.

We now turn to one of the favourite Ada fan club quotes:

[The Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine…Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

It would not be false to claim that music is in fact applied mathematics. Both rhythm and pitch can be and are expressed by mathematical functions. For about two thousand years music was part of the mathematical curriculum, as one of the four disciplines of the quadrivium. That a mathematician of Babbage’s stature wouldn’t think of the possibility of programming his computer to play or even create music is asking a lot. However, we have very direct proof that Babbage was well aware of the relationship between music and automata.

Chapter three of Babbage’s autobiography opens thus:

“During my boyhood my mother took me to several exhibitions of machinery. I well remember one of them in Hanover Square, by a man who called himself Merlin. I was so greatly interested in it, that the Exhibiter remarked the circumstance, and after explain some of the objects to which the public had access, proposed to my mother to take me up to his workshop. Where I would see still more wonderful automata. We accordingly ascended to the attic. There were two uncovered female figures of silver, about twelve inches high.

[…]

The other silver figure was an admirable danseuse, with a bird on the fore finger of her right hand, which wagged its tail, flapped its wings, and opened its beak. This lady attitudinized in a most fascinating manner. Her eyes were full of imagination, and irresistible.[1]

Following Merlin’s death in 1803, his automata were acquired by another showman Thomas Weeks, who in turn having gone out of business died in 1834. Babbage, now a grown man and very wealthy, attended the auction of Week’s possessions and for £35 acquired the danseuse. He restored the model and having had clothes made for her displayed the danseuse on a glass pedestal in his salon[2]. Babbage’s passion, and it was truly a passion, for machines was sparked by a musical automata, his silver danseuse, an image somewhat far from that of the boring mathematician only interested in numbers. In fact many of the most famous model produced in the golden age of automata in the late 18thand early 19thcenturies were musical, something which Babbage, who became a great expert if not ‘the great expert’ on, would have well aware of. That Babbage probably did play with the thought of his super automata, his Analytical Engine, producing music is a more than plausible concept.

The all time favourite quote of the Ada acolytes that they flourish like a hand of four aces in poker is:

“The Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.”

Here the turn of phrase might well be Ada’s but the concept is with certainty Babbage’s. Anybody who thinks otherwise has never read anything by or on Babbage or the Analytical Engine or even the Notes supposedly written alone by Ada. Babbage’s greatest stroke of genius in his conception of his Analytical Engine was the idea of programming it with punch cards; an idea that he borrowed from Joseph Marie Jacquard 1752–1834), who had used it to program his silk weaving loom.

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Detail of Jaquard loom at TextielMuseum Tilburg showing punch cards Source: Wikimedia Commons

Jacquard in turn had borrowed from Jacques de Vaucanson (1709–1782), arguably the greatest of the automata builders in that great age of automata. Vaucanson produced two famous musical automata, a flute player with a repertoire of twelve tunes and a tambourine player. The role of the punch cards and their origin are discussed extensively in the Notes. Turning once again to Babbage’s autobiography we find the following:

It is a known fact that the Jacquard loom is capable of weaving any design which the imagination of man may conceive. It is also the constant practice for skilled artists to be employed by manufacturers in designing patterns. These patterns are then sent to a peculiar artist, who, by means of a certain machine, punches holes in a set of pasteboard cards in such a manner that when the cards are placed in a Jacquard loom, it will then weave upon its produce the exact pattern designed by the artist.

Now the manufacturer may use, for the warp and weft of his work, threads which are all of the same colour; let us suppose them to be unbleached or white threads. In this case the cloth will be woven all of one colour; but there will be a damask pattern upon it such as the artist designed.

But the manufacturer might use the same cards, and put into the warp threads of any other colour. Every thread might even be of a different colour, or of a different shade of colour; but in all these cases the form of the pattern will be precisely the same—the colours only will differ.

The Analogy of the Analytical Engine with this well-known process is nearly perfect.

[…]

Every formula which the Analytical Engine can be required to compute consists of certain algebraic operations to be performed upon given letters, and of certain other modifications depending on the numerical values assigned to those letters.

There are therefore two sets of cards, the first to direct the nature of the operations to be performed—these are called operation cards: the other to direct the particular variable on which those cards are required to operate—these latter are called variable cards

[…]

Under this arrangement, when any formula is required to be computed, a set of operation cards must be strung together, which contain the series of operations in the order in which they occur. Another set of cards must then be strung together, to call in the variables into the mill, the order in which they are required to be acted upon.

[…]

Thus the Analytical Engine will possess a library of its own. Every set of cards once made will at any future time reproduce the calculations for which it was first arranged. The numerical value of its constants may then be inserted[3].

 

This may not have the poetical elegance of Ada’s pregnant phrase but Babbage here clearly elucidates (I’ve left out a lot of the details) how the Analytical Engine will weave algebraical patterns.

Of interest in the whole story of the punch cards, the Jacquard loom and the Analytical Engine is the story of the portrait. As a demonstration of the versatility of his system, in 1839 a portrait of Jacquard was woven in silk on a Jacquard loom; it required 24,000 punch cards to create.

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Portrait of Jacquard woven in silk Source: Science Museum via Wikimedia Commons

Charles Babbage acquired one of these woven portraits for the then enormous sum of £800 and displayed it in his salon along with his silver danseuse and the ‘miracle performing’ unit of his Difference Engine. Having astounded his guests with performances of the danseuse and his Difference Engine he would then unveil the portrait and challenge his guests to guess how it had been produced. Babbage was as much a showman as he was a mathematician.

[1]Charles Babbage, Passages from The Life of a Philosopher, Longman, Green, Longman, Roberts, & Green, London, 1864 p. 17

[2]For the full story of Merlin, Weeks and much more see Simon Schaffer, Babbage’s Dancer

[3]Babbage, Passages, pp. 116–118

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Christmas Trilogy 2018 Part 1: The Harmonic Isaac

Isaac Newton is often referred to, as the ‘father’ of modern science but then again so is Galileo Galilei. In reality modern science has many fathers and some mothers as well. Those who use this accolade tend to want to sweep his theological studies and his alchemy under the carpet and pretend it doesn’t really count. Another weird aspect of Newton’s intellectual universe was his belief in prisca theology. This was the belief that in the period following the creation humankind had perfect knowledge of the natural world that got somehow lost over the centuries. This meant for Isaac that in his own scientific work he wasn’t making discoveries but rediscovering once lost knowledge. Amongst, what we would now regard as his occult beliefs, Isaac also subscribed to the Pythagorean belief in Harmonia (harmony), as a unifying concept in the cosmos.

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Robert Fludd’s Pythagorean Monocord

Although he was anything but a fan of music, he was a dedicated student of Harmonia, the mathematical theory of proportions that was part of the quadrivium. According to the legend Pythagoras was the first to discover that musical interval can be expressed as simple ratios of whole numbers related to a taut string: 1:1 (unison), 2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). Unfortunately, anybody who has studied the theory of music knows these ratios don’t quite work. If you start on a given tone and move up in steps of a perfect fifth you don’t actually arrive back at the original tone seven octaves higher after twelve fifths but slightly off. This difference is known as the Pythagorean comma. This disharmony was well known and in the sixteenth and seventeenth centuries a major debate developed on how to ‘correctly’ divide up musical scale to avoid this problem. The original adversaries were Gioseffo Zarlino (1570–1590) and Vincenzo Galilei (1520–1591) (Galileo’s father) and Kepler made a contribution in his Harmonice Mundi; perhaps the most important contribution being made by Marin Mersenne (1588–1648) in his Harmonie universelle, contenant la théorie et la pratique de la musique.

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Harmonie Universelle title page

Here he elucidated Mersenne’s Laws:

Frequency is:

  1. Inversely proportional to the length of the string (this was known to the ancients; it is usually credited toPythagoras)
  2. Proportional to the square root of the stretching force, and
  3. Inversely proportional to the square root of the mass per unit length.
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Source: Gouk p. 115

As a student Newton took up the challenge in one of his notebooks and we don’t need to go into his contribution to that debate here, however it is the first indication of his interest in this mathematics, which he would go on to apply to his two major scientific works, his optics and his theory of gravity.

After he graduated at Cambridge Newton’s first serious original research was into various aspects of optics. This led to his first published paper:

A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; Containing His New Theory about Light and Colors: Sent by the Author to the Publishee from Cambridge, Febr. 6. 1671/72; In Order to be Communicated to the R. Society

In which he described his experiments with a prism that showed that white light consists of blended coloured light and that the spectrum that one produces with a prism is the splitting up of the white light into its coloured components. Previous theories had claimed that the spectrum was produced by the dimming or dirtying of the white light by the prism. Newton wrote an extensive paper expanding on his optical research, An hypothesis explaining the properties of light, but due to the harsh criticism his first paper received he withheld it from publication. This expanded work only appeared in 1704 in his book, Opticks: A Treatise of the Reflections, Refractions, Inflections & Colours of Light. Here we can read:

In the Experiments of the fourth Proposition of the first Part of this first Book, when I had separated the heterogeneous Rays from one another, the Spectrum ptformed by the separated Rays, did in the Progress from its End p, on which the most refrangible Rays fell, unto its other End t, on which the most refrangible Rays fell, appear tinged with this Series of Colours, violet, indigo, blue, green, yellow, orange, red, together with all their intermediate Degrees in a continual Succession perpetually varying . So that there appeared as many Degrees of Colours, as there were sorts of Rays differing in Refrangibility.

This is of course the list of seven colours that we associate with the rainbow today. Before Newton researchers writing about the spectrum listed only three, four or at most five colours, so why did he raise the number to seven by dividing the blue end of the spectrum into violet, indigo and blue? He did so in order to align the number of colours of the spectrum with the notes on the musical scales. In the Queries that were added at the end of the Opticks over the years and the different editions we find the following:

Qu. 13. Do not several sorts of Rays make Vibrations of several bigness, which according to their bignesses excite Sensations of several Colours, much after the manner that the Vibrations of the Air, according to their several bignesses excite Sensations of several Sounds? And particularly do not Vibrations for making a Sensation of deep violet, the least refrangible the largest for making a Sensation of deep red, and several intermediate sorts of Rays, Vibrations of several intermediate bignesses to make Sensations of the several intermediate Colours?

Qu. 14. May not the harmony and discord of Colours arise from the proportions of the Vibrations propagated through the Fibres of the optick Nerves into the Brain, as the harmony and discord of Sounds arise from the proportions of the Vibrations of the Air? And some Colours, if they be view’d together, are agreeable to one another, as those of Gold and Indigo and other disagree.

In the An Hypothesis, Newton published a diagram illustrated the connection he believed to exist between the colours of the spectrum and the notes of the scale.

mersenne003

Source: Gouk p. 118

Interestingly Voltaire presented Newton’s theory in his Elemens de la philosophie de Newton (1738), again as a diagram.

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Source: Gouk p. 119

Turning now to Newton’s magnum opus we find the even more extraordinary association between his theory of gravity and the Pythagorean theory of harmony. Newton’s Law of Gravity is probably the last place one would expect to meet with Pythagorean harmony but against all expectations one does. In unpublished scholia on Proposition VIII of Book III of the Principia(the law of gravity) Newton claimed that Pythagoras had known the inverse square law. He argued that Pythagoras had discovered the inverse-square relationship in the vibration of strings (see Mersenne above) and had applied the same principle to the heavens.

…consequently by comparing those weights with the weights of the planets , and the lengths of the strings with the distances of the planets, he understood by means of the harmony of the heavens that the weights of the planets towards the Sun were reciprocally as the squares of their distances from the Sun.[1]

Although Newton never published this theory David Gregory (1661–1708) did. David Gregory was a nephew of the physicist James Gregory who in 1684 became professor of mathematics at the University of Edinburgh, where he became “the first to openly teach the doctrines of the Principia, in a public seminary…in those days this was a daring innovation.”[2]

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Davis Gregory bust Source: Wikimedia Commons

In 1691, with Newton’s assistance, he was appointed Savilian Professor of Astronomy at Oxford going on to become an important mathematician, physicist and astronomer. He worked together with Newton on the planned second edition of the Principia, although he did not edit it, dying in 1708; the second edition appearing first in 1713 edited by Richard Bentley. In his Astronomiae physicae et geometricae elementa, a semi-popular presentation of Newton’s theories first published in Latin in 1702

2221a

Gregory wrote the following:

The Elements of Astronomy, Physical and Geometrical By David Gregory M.D. SavilianProfessor of Astronomy at Oxfordand Fellow of the Royal Society (1615)

The Author’sPreface

As it is manifest that the Ancients were apprized of, and had discover’d the Gravity of all Bodies towards one another, so also they were not unacquainted with the Law and Proportion which the action of Gravity observ’d according to the different Masses and Distances. For that Gravity is proportional to the Quantity of Matter in the heavy Body, Lucretiusdoes sufficiently declare, as also that what we call light Bodies, don’t ascend of their own accord, but by action of a force underneath them, impelling them upwards, just as a piece of Wood is in Water; and further, that all Bodies, as well the heavy as the light, do descend in vacuo, with an equal celerity. It will be plain likewise, from what I shall presently observe, that the famous Theorem about the proportion whereby Gravity decreases in receding from the Sun, was not unknown at least to Pythagoras. This indeed seems to be that which he and his followers would signify to us by the Harmony of the Spheres: That is, they feign’d Apolloplaying on a Harp of seven Strings, by which Symbol, as it is abundantly evident from Pliny, Macrobiusand Censorinus, they meant the Sun in Conjunction with the seven planets, for they made him the leader of that Septenary Chorus, and Moderator of Nature; and thought that by his Attractive force he acted upon the Planets (and called it Jupiter’s Prison, because it is by this Force that he retains and keeps them in their Orbits, from flying off in Right Lines) in the Harmonical ration of their Distances. For the forces, whereby equal Tensions act upon Strings of different lengths (being equal in other respects) are reciprocally as the Squares of the lengths of the Strings.

I first came across this theory, as elucidated by Gregory, years ago in a book, which book I have in the meantime forgotten, where it was summarised as follows:

Gravity is the strings upon which the celestial harmony is played.

 

 

 

 

 

 

 

 

[1]Quoted from Penelope Gouk, The harmonic roots of Newtonian science, in John Fauvel, Raymond Flood, Michael Shortland & Robin Wilson eds., Let Newton Be: A new perspective on his life and works, OUP, Oxford, New York, Tokyo, ppb. 1989 The inspiration and principle source for this blog post.

[2]Quoted from Significant Scots: David Gregory

https://www.electricscotland.com/history/other/gregory_david.htm

 

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Filed under History of Astronomy, History of Mathematics, History of Optics, History of science, Newton

Christmas at the Renaissance Mathematicus – A guide for new readers

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Being new to the Renaissance Mathematicus one might be excused if one assumed that the blogging activities were wound down over the Christmas period. However, exactly the opposite is true with the Renaissance Mathematicus going into hyper-drive posting its annual Christmas Trilogy, three blog posts in three days. Three of my favourite scientific figures have their birthday over Christmas–Isaac Newton 25thDecember, Charles Babbage 26thDecember and Johannes Kepler 27thDecember–and I write a blog post for each of them on their respective birthdays. Before somebody quibbles I am aware that the birthdays of Newton and Kepler are both old style, i.e. on the Julian Calendar, and Babbage new style, i.e. on the Gregorian Calendar but to be honest, in this case I don’t give a shit. So if you are looking for some #histSTM entertainment or possibly enlightenment over the holiday period the Renaissance Mathematicus is your number one address. In case the new trilogy is not enough for you:

The Trilogies of Christmas Past

Christmas Trilogy 2009 Post 1

Christmas Trilogy 2009 Post 2

Christmas Trilogy 2009 Post 3

Christmas Trilogy 2010 Post 1

Christmas Trilogy 2010 Post 2

Christmas Trilogy 2010 Post 3

Christmas Trilogy 2011 Post 1

Christmas Trilogy 2011 Post 2

Christmas Trilogy 2011 Post 3

Christmas Trilogy 2012 Post 1

Christmas Trilogy 2012 Post 2

Christmas Trilogy 2012 Post 3

Christmas Trilogy 2013 Post 1

Christmas Trilogy 2013 Post 2

Christmas Trilogy 2013 Post 3

Christmas Trilogy 2014 Post 1

Christmas Trilogy 2014 Post 2

Christmas Trilogy 2014 Post 3

Christmas Trilogy 2015 Post 1

Christmas Trilogy 2015 Post 2

Christmas Trilogy 2015 Post 3

Christmas Trilogy 2016 Post 1

Christmas Trilogy 2016 Post 2

Christmas Trilogy 2016 Post 3

Christmas Trilogy 2017 Post 1

Christmas Trilogy 2017 Post 2

Christmas Trilogy 2017 Post 3

 

 

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It’s Solstice Time Again!

We are deep in what is commonly called the holiday season. For personal reasons I don’t celebrate Christmas and as I explained in this post starting the New Year on 1 January on the Gregorian Calendar is/was a purely arbitrary decision. I wrote there that I consider the winter solstice to be the best choice to celebrate the end and beginning of a solar cycle in the northern hemisphere.

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Stonehenge Winter Solstice

Today at 22:23 UTC the sun will turn at the Tropic of Capricorn and begin its journey northwards to the Tropic of Cancer and the summer solstice.  Tropic comes from the Latin tropicus “pertaining to a turn,” from Greek tropikos “of or pertaining to a turn or change.”

I wish all of my readers a happy solstice and may the next 365 days, 5 hours, 48 minutes and 45 seconds bring you much light, joy, peace and wisdom. We can only hope that they will be better than the last 365 days, 5 hours, 48 minutes and 45 seconds (length of the mean tropical or solar year).

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Filed under Autobiographical, Odds and Ends, Uncategorized