An hour forwards, an hour back

In my last post I talked about the Albrecht Dürer House that is at the end of my history of astronomy tour of Nürnberg. My tour starts under the rather spectacular sundial painted on the south side of the church of St Lorenz.

I start my tour by talking about the way the day was divided up in the past; the observing, quantifying and recording of the passage of time down the ages being a particular interest of mine. I mention that it was the ancient Egyptians who initially introduced the 24 hour day, first dividing the night into twelve segments based on the rising of stars and the by analogy the day was divided into twelve segments. Adopted by the rest of the ancient world this became the European norm.

However during the Middle Ages our equinoctial system in which all twenty-four hours are equally long was not used but one in which the day starts at dawn and ends at dusk meaning that the twelve daylight hours and the twelve night time hours vary continually in length throughout the year. Nürnberg had its own special system, the great Nürnberg clock, which I explained earlier in an extra post. The sundial on the church displays various system of calculating the hours including Nürnberg’s special system making it one of the most complex sundials in Europe.

Moving around the corner we come to two more sundials, one south facing and one fairly rare east facing one that only shows the afternoon hours. Here on my tour I explain that a sundial usually displays local time i.e. time measured from a midday that is marked by the sun being directly overhead. This was the way that time was recorded, almost universally, down to the end of the nineteenth century. This means that every settlement has its own time. One-degree difference in longitude means a difference of four minutes in time. Prague is 3° 20’ east of Nürnberg so on local time when it’s twelve noon in Nürnberg it’s already 13’ 20’’ past twelve in Prague.

It was the invention of the railways and the telegraph that required and made possible the standardisation of time. A train timetable between two towns some distance apart requires that both towns are on the same clock, so to speak. This necessity led to the introduction of our system of standardised time zones, which are in reality purely convenient fictions, although based around some point, whose twelve-midday is actually local solar time such as Greenwich for the UK’s time zone. This system was discussed at the 1884 Washington longitude conference and finally accepted in the early twentieth century. When the clocks change, as was the case a couple of weeks ago in the EU and last week in North America it is purely an arbitrary redefining of the twelve-midday point within that particular time zone, largely divorced from local solar time. Some countries actually operate outside of the time zone system. Spain, which geographically is in the GMT time zone, is in the CET time zone one hour to the east.

Having set the scene, what I’m now about to say will probably convince many of my readers that I lack a sense of humour but when I see cartoons of the following type during the clock change period I don’t find them funny I just think of them as being horribly wrong. The prejudices of the expert.

Repositioning the Stones at Stonehenge today ready for the end of British Summer Time this weekend.

This is how they change the clocks for summertime at the prehistoric Avebury Stone Circle in England

What’s the problem? Firstly the Neolithic stone circles such as Stonehenge and Avebury are not and never have been clocks. They probably are constructed along solar alignments. I say probably because although they almost certainly are, because the builders are long dead and we possess no construction plans we can never be one hundred per cent certain. Stonehenge appears to have been constructed to align not with the summer solstice but with the winter solstice. These alignments are based not on time zones but on local solar time.

Stonehenge Winter

This is actually a major problem for archeoastronomers searching for possible alignments in Neolithic and other ancient monuments because due to the precession of the equinox local solar time changes over time. From year to year the effect is almost undetectable but is noticeable over a period of several thousand years. What might have been well aligned in 3000 BCE is now 5000 years later a bit off.

All of this, means that the alignments of Neolithic monuments such as Stonehenge and Avebury, being based on local solar time, don’t actually change in anyway what so ever when we change our clocks arbitrarily in our artificial time zones. The so-called jokes display a fundamental misconception of the conventions that we apply to keep track of time.

One thing I did learn this year during the European time change is that The Maritime Museum in Greenwich has a modern sundial, the Dolphin Sundial that has changeable plates for GMT and BST. Cool! You can watch a video of somebody changing the plates here.








Filed under Uncategorized

The Albrecht Dürer or should that be the Bernhard Walther House?

On Saturday I did my history of astronomy tour of Nürnberg for some readers of this blog who were visiting the city[1]. As usually it ended at Nürnberg’s biggest tourist attraction the Albrecht Dürer House. There are of course good reasons for including Nürnberg’s most famous artist in such a tour, as readers of this blog should know. He wrote and published the very first printed maths book in German and was the artist involved in creating the first every printed European star maps. However this is another reason for including this building in a history of astronomy tour. Before it became the Albrecht Dürer House it had been the Bernhard Walther House and this was one of the reasons that motivated Dürer to purchase it. But who, I hear you say, was Bernhard Walther?

Bernhard Walther (Albrecht Dürer) House on Tiergärtentor Nürnberg
Photo: Monica Weidemann
Source: Wikipedia Commons

Bernhard Walther was born in Memmingen in Bavaria in 1430. The first really reliable fact we have about his life is when he became a citizen of Nürnberg in 1467; remember Nürnberg was an independent city-state in the fifteenth century. He was the general manager of the Nürnberg trading post of the Memmingen merchant traders the Vöhlin-Welser-Company. When Regiomontanus came to Nürnberg in 1471, he and Walther became friends and Walther became his astronomical assistant and companion. The accounts that claim that Walther was Regiomontanus’ patron are false, as are also the claims that the two of them built an observatory financed by Walther. They carried out their astronomical observations with portable instruments out in the streets. As well as astronomy Walther apparently learnt Greek from Regiomontanus, who had learnt the language whilst a member of Cardinal Bessarion’s household in Italy. We know of Walther’s abilities in the ancient language because they are mentioned in an ode that Conrad Celtis, the so-called arch humanist, wrote in his honour.

Regiomontanus had come to Nürnberg, according to his own account, to reform astronomy in two ways; firstly by starting a new programme of astronomical observations to replace those of Ptolemaeus corrupted by centuries of copying and recopying in manuscripts and secondly by printing and publishing new editions of the astronomical literature cleared of their errors through careful philological editing. Regiomontanus had chosen Nürnberg for his programme because the city made the best scientific instruments and because of its extensive communications network being aware of the fact that his programme was only achievable with the active assistance of other European astronomers. In an age without postal services, Nürnberg, as a major European trading city, had a private communications system second only to that of Venice.

Walther assisted Regiomontanus in both of his reform endeavours but they had only succeeded in publishing nine items, including the publishing house’s ambitious publication programme, when Regiomontanus again left Nürnberg in the direction of Rome to answer the Pope’s call to work on a calendar reform in 1475. Regiomontanus never returned from that journey, dying in Rome in 1476, presumable during some sort of epidemic. Walther did not continue the publishing endeavour, although he bought up Regiomontanus extensive collection of manuscripts, but he did carry on making a series of basic simple astronomical observations for the next almost thirty years. This was the first such series of astronomical observations carried out in Early Modern Europe, making Walther to an important if minor figure in the history of astronomy.

As the general manager of the trading company Walther occupied a house on the West side of the market place in Nürnberg, today Market Place No. 11. The original hose was destroyed in the Second World War.

Walther’s trading depot was on the west side of the Nürnberg market place, next door to the right of where the Körn & Berg bookshop now stands.

When he finally retired, seventy years old, he sold the house on the market place and bought the house on Tiergärtentor (The Zoo Gate) in 1501, which is now known as the Albrecht Dürer House. Walther substantially rebuilt the house adding the whole of what is now the top floor. He also had a small window let into the south gable with a stone window ledge; he used this window to make his astronomical observations resting his observing instruments on that stone ledge, this was his observatory. We know that Walther had this window constructed because in the document with which the city council gave permission for its construction, Walther had to give a guarantee that he wouldn’t empty his chamber pot out on to the roof of the neighbouring building.

Walther House with Observatory Window in the south gable
Photo: Nora Reim
Source: Astronomie in Nürnberg

Walther’s observation programme was comparatively simple and consisted largely of regularly determining the altitude of the Sun, observing eclipses and determining the positions of the planets during conjunctions etc. The latter set of observations leads to the assumption that the observations were principally for use by astrologers. This is not surprising as Regiomontanus was a practicing astrologer, with a very good reputation, whose stated intention in reforming astronomy was in order to improve astrological predictions. He claimed that such predictions were often wrong because the astronomical data on which they were based was inaccurate. Three of Walther’s observations found their way into Copernicus’ De revolutionibus, although we don’t know how they got there. Copernicus falsely attributes part of the used data to Johannes Schöner. In 1544 Schöner did publish Regiomontanus’ and Walther’s observations in his Scripta clarissimi Mathematici M. Joannis Regiomontani. Walther’s observation were, for their time, highly accurate only to be first superceded by those of Tycho Brahe at the end of the century.

Another little known Nürnberg astronomer, Conrad Heinfogel, referred to himself as a pupil of Bernard Walther and it was Heinfogel who provided the astronomical knowledge for Dürer’s star maps.

Largely forgotten today Walther was well known and highly regarded by his contemporaries and the astronomical community down to Tycho and Kepler, Tycho using Walther’s observations to check against his own. Walther died in 1504 and in 1509 Albrecht Dürer bought the house on the Tiergärtentor, partially because being himself a big fan of the mathematical sciences he desired to own Walther’s house. At the same time he also acquired ten manuscripts out of the Regiomontanus/Walther collection including an Elements of Euclid.

If you are ever in Nürnberg go round to the back of the Dürer house and you can see Walther’s observatory for yourself. However please be quite when doing so as the people who live next door get really pissed off with the tourists and the noise that they make.

[1] Any readers of the blog who visit Nürnberg are welcome to the same tour, you just need to arrange it in advance; all you have to do is buy me lunch at the end of it. A low price of a highly entertaining and educational tour that lasts between three and four hours!


Filed under History of Astrology, History of Astronomy, History of science, Renaissance Science, Uncategorized

Men of Mathematics

This is something that I wrote this morning as a response on the History of Astronomy mailing list; having written it I have decided to cross post it here.

John Briggs is the second person in two days, who has recommended Eric Temple Bell’s “Men of Mathematics”. I can’t remember who the first one was, as I only registered it in passing, and it might not even have been on this particular mailing list. Immediately after John Briggs recommended it Rudi Lindner endorsed that recommendation. This series of recommendations has led me to say something about the role that book played in my own life and my view of it now.

“Men of Mathematics” was the first book on the history of science and/or mathematics that I ever read. I was deeply passionate fan of maths at school and my father gave me Bell’s book to read when I was sixteen years old. My other great passion was history and I had been reading history books since I taught myself to read at the age of three. Here was a book that magically combined my two great passions. I devoured it. Bell has a fluid narrative style and the book is easy to read and very stimulating.

Bell showed me that the calculus, that I had recently fallen in love with, had been invented/discovered (choose the verb that best fits your philosophy of maths), something I had never even considered before. Not only that but it was done independently by two of the greatest names in the history of science, Newton and Leibniz, and that this led to one of the most embittered priority and plagiarism disputes in intellectual history. He introduced me to George Boole, whom I had never heard of before and whose work and its reception in the 19th century I would seriously study many years later in a long-year research project into the history of formal or mathematical logic, my apprenticeship as a historian of science.

Bell’s tome ignited a burning passion for the history of mathematics in my soul, which rapidly developed into a passion for the whole of the history of science; a passion that is still burning brightly fifty years later. So would I join the chorus of those warmly recommending “Men of Mathematics”? No, actually I wouldn’t.

Why, if as I say Bell’s book played such a decisive role in my own development as a historian of mathematics/science, do I reject it now? Bell’s florid narrative writing style is very seductive but it is unfortunately also very misleading. Bell is always more than prepared to sacrifice truth and historical accuracy for a good story. The result is that his potted biographies are hagiographic, mythologizing and historically inaccurate, often to a painful degree. I spent a lot of time and effort unlearning a lot of what I had learnt from Bell. His is exactly the type of sloppy historiography against which I have taken up my crusade on my blog and in my public lectures in my later life. Sorry but, although it inspired me in my youth, I think Bell’s book should be laid to rest and not recommended to new generations.



Filed under Book Reviews, History of Logic, History of Mathematics, History of science, Myths of Science

Getting names right is rather important in the history of science

“Have you seen my new Rolls Royce?”

“But that’s not a Rolls Royce; it’s a Fiat Bambino!”

“It’s got four wheels, an internal combustion engine and it gets you from a to b so it’s a Rolls Royce, isn’t it?”

“Well, no it isn’t.”

The little dialogue above would probably seem pretty ridiculous to any of my readers but today BBC News achieved something similar concerning scientific instruments. On the BBC website they posted a story with the following title, Astrolabe: Shipwreck find ‘earliest navigation tool’

The story is about the find of a scientific instrument found by marine archaeologists in 2014, in the wreck of a Portuguese ship that sank in 1503. Not just in the title, but also throughout the article the discovered instrument is simply referred to as an astrolabe. The article went on to say that astrolabes are relatively rare, and this is the only the 108th to be confirmed catalogued. It is also the earliest known example by several decades.

As it stood this was patent rubbish. There are more than 900 hundred known astrolabes between the earliest known dated instrument from 927 CE and 1900 CE. However the problem is not in the historical accuracy but in the name. The instrument that had been discovered is not an astrolabe but a mariner’s astrolabe a more than somewhat different instrument.

Astrolabe Renners Arsenius 1569
Source: Wikimedia Commons

Mariner’s Astrolabe Francisco de Goes 1608 Source: Istituto e Museo di Storia della Scienza, Firenze

As I explained to someone on Twitter, as I had just corrected the tweet linking to the article for about the zillionth time, a mariner’s astrolabe is a very simplified form of the astrolabe specifically made for use on ships with just one function, the measuring of the altitude of a star or the sun in order to determine latitude. The astrolabe, however, is a very complex instrument with hundreds of different function in astronomy, chronology and surveying.

Following my protests, and those of others, the article has been changed very slightly for the majority of the article it still refers to the instrument as an astrolabe but about three quarters of the way through, the sentence that I have quoted above now starts “Mariners’ astrolabes” instead of simply astrolabes. So everything is now OK? Well, actually no.

All of the references to astrolabe should have been changed to mariner’s astrolabe and above all the click bait title should have been changed, as it also has a second major problem. It states, shipwreck find ‘earliest navigation tool’. This is complete rubbish. Mariner’s astrolabes are quite late developments in the history of navigation and there are many navigation tools that predate it, such as the quadrant, the sea chart, the compass etc. etc. This blatant hyperbolic error is corrected in the subtitle, which reads: An artefact excavated from a shipwreck off the coast of Oman has been found to be the oldest know example of a type of navigation tool [my emphasis]. But of course by now the damage has been done for the casual reader who just glances at the title.

This article is a mess and a lousy piece of history of science communication for which there is absolutely no excuse whatsoever.


Filed under History of Navigation

History of science that had this (pedantic) historian grinding his teeth in the last week.

On 11 October, The American Astronomical Society had an article on its website by Teresa Wilson (Michigan Technological University) title, This Month in Astronomical History: The Invention of the Telescope that is liberally strewn with easily avoidable errors.

We start off with:

The inventor of the refracting telescope is unknown, but the accomplishment is often attributed to the man who first filed a patent for it: Hans Lippershey (or Lipperhey), a 16th century Dutch eyeglass maker and inventor from Middelburg.

Pierre Borel – De vero telescopii inventore
Source: Wikimedia Commons

Although both variations turn up in the literature, historians of the telescope are clear that the man’s name was Lipperhey and not Lippershey, however he was German, born in Wessel, and not Dutch although he lived in Middelburg in the Dutch province of Zeeland. We continue:

Incidentally, the stories of his inspiration for building the instrument vary and tend to discredit his originality. In one scenario, two children were playing with optical lenses in his shop and he overheard them remark that a distant weather vane appeared closer when they looked through a pair of different lenses. In others, he took credit for the work of his assistant, or stole the idea from a third party altogether.

All of the above are fairy stories, which have no basis in history so why bother to mention them at all? And further:

Regardless of how events transpired, Lippershey filed for a 30-year patent from the States General of the Netherlands on 2 October 1608, creating the first written record for an instrument “for seeing things far away as if they were near.”

The first written record of the telescope is in the letter of introduction written for Lipperhey by the Council of Zeeland to Zeeland’s delegates at the States General, dated 25 September 1608. The quoted description of his telescope is actually from this letter.

Only weeks later, a lens maker from Alkmaar in North Holland, Jacob Metius, applied for a patent on a similar design. Zacharias Jansen, another eyeglass maker from Middelburg and purported inventor of the compound microscope, is also claimed to have invented the telescope.

Since the work of Huib Zuidervaart made public in 2008 and published in The Origins of the Telescope (2010) we know that Zacharias Jansen was not a potential inventor of the telescope.

Accounts disagree on whether Lippershey’s original instrument was made with a convex and a concave lens providing an upright image, or two concave [sic] lenses  providing an inverted image, but they agree that the instrument provided three-times magnification of distant objects.

This is no disagreement whatsoever; Lipperhey’s telescope had one convex (objective) and one concave (eyepiece) lens. One couldn’t construct a telescope with two concave lenses, which is obviously a fatal, given the context, typo for two convex lenses.

 Word reached Italy in 1609 and Galileo created his own modified version. By the end of the year, he had built a telescope that could magnify 20 times. He was the first to turn it skyward for a concerted series of astronomical observations. With his new instrument, Galileo discovered Jupiter’s four largest moons, observed a supernova, verified the phases of Venus, and observed sunspots.

The only difference between Lipperhey’s telescope and Galileo’s was the focal length of the lenses; I’m not really sure that qualifies as modified. Galileo was not the first to turn it skywards for a concerted series of astronomical observations; this honour definitely goes to Thomas Harriot and it is possible that Simon Marius also preceded Galileo in telescopic astronomical observations. Galileo did not observe a supernova with his telescope. The last supernova observable in Europe was in 1604 that is four years before the telescope was invented.

What makes all these errors even more embarrassing is that if the author had actually read the literature that she lists at the end of her article then she could have written a factually accurate article.

Inspired by this years 250th anniversary of the Mason-Dixon line I took down my tsundoku*** copy of Edwin Danson’s Drawing the Line: How Mason and Dixon Surveyed the Most Famous Border in America from the geodesy and surveying section of my humble home library.

From the beginning, whilst reading I was irritated by minor historical errors and an aggressive promotion of the Dava Sobel warped version of the longitude story. However my irritation boiled over when I read the following:

In 1753, Johann Tobias Mayer (1723–1762), the Swiss astronomer and professor of geography at Göttingen published a table of lunar distances…

The man who made the lunars method of determining longitude viable was Tobias Mayer; Johann Tobias Mayer (1752–1830) was his son, who after studying in Göttingen became professor of mathematics in Altdorf in 1780. Tobias Mayer was born in Marbach and grew up in Esslingen, which makes him thoroughly German and not Swiss. Lastly he was professor of economics in Göttingen not geography. I those days there was a department of economics and mathematics at the university and it was the latter, which Mayer actually taught.

Slightly earlier in the text a statement that almost set me off was:

The clarity of Auzout lenses, mirrors and telescopes enabled Huygens to improve the observing accuracy of Jovian eclipses and to discover the rings of Saturn.

The observing accuracy of Jovian eclipses was due to Giovanni Domenico Cassini, here falsely called Gian Domenico, and not to Huygens. Huygens did not use the lenses and telescopes of Adrian Auzout but famously constructed his own together with his older brother Constantijn. Huygens also did not discover the rings of Saturn but correctly hypothesised their existence by analysing all of the earlier records of the observations of this particular phenomenon.

Earlier than this Danson, a surveyor, makes the standard error of attributing the invention of triangulation to Willebrord Snel van Royen instead of Gemma Frisius. All of this would normally have had this mild mannered historian of science hurling this volume at the wall but on this occasion I persevered.

As I said above Danson aggressively promotes Sobel’s warped version of the longitude story including the myth that the Board of Longitude discriminated in favour of Maskelyne against Harrison because the latter was working class, whereas Maskelyne was a gentleman scholar. This is patent rubbish, as almost all of the eighteenth-century British instrument makers, regarded as the best in the world, were working class and were highly respected and honoured by the scientific community. Danson, when introducing Maskelyne, sets up this supposed class rivalry as follows:

With the start of the Michaelmas term [1755], Maskelyne returned to his college [Trinity] to take Holly Orders, a prerequisite for a Cambridge fellowship in the eighteenth century. In the tower above Trinity College, the inventor of the chronometer, John Harrison, was busy installing one of his famous turret clocks, oblivious of Maskelyne, his future adversary, strolling around the quad bellow.

I must admit that I was mildly excited when I read that, what a fascinating historical coincidence, if it’s true, but is it true? I had never come across this claim before, maybe it’s in Sobel’s book, but I don’t remember it, I read it many years ago. Stimulated by the claim I did what I always do in such circumstances, I went looking for evidence.

The Trinity College Tower Clock is quite famous so I was reasonably certain that I could dig up something on its history fairly easily and I was right. On the Trinity website we have a webpage titled, The College Clock. This tells us that the clock was constructed by one Richard Holdfield in 1610. A new clock and dial-plate was put in place under the Mastership of Richard Bentley in 1726-27. No clock maker in named but Harrison was still in Yorkshire at the time and it’s also not 1755. The clock was renewed once more in 1910 long after Harrison was deceased. Had Danson completely invented this episode, he had proved to be a bad historian, but falsifying a whole story? I dug deeper.

Tower or turret clocks need regular maintenance and repair and on the Cambridge University Digital Library website we find a drawing of a turret clock escapement, which was designed by John Harrison for a turret clock at Trinity College, Cambridge, dated 1755. Not a whole clock but at least part of one. Danson’s honour as an author is restored or is it?

The entry goes on:

Though designed by Harrison, the escapement was actually made by another clockmaker, William Smith, something which was far from unusual in the extensive sub-contracting system which was fundamental to the production of time-keeping devices in the eighteenth century.

Made and one can reasonably assume installed by William Smith, so no close encounter of Maskelyne and Harrison in Trinity College in 1755.

Later in the text we are in America surveying with Mason and Dixon when Danson informs us that:

For their mathematical and trigonometric calculations, the surveyors used seven-figure logarithmic tables. John Napier invented logarithms, a tabular method for multiplication and division, in 1614; in 1624 his colleague, Henry Briggs, published a set of natural logarithms (log tables), and later developed tables of trigonometrical logarithmic functions (trig tables). The slide rule had also been invented and perfected between 1654 and 1683 by Seth Partridge and Henry Coggeswall.

Where to begin? Napier did invent logarithms in 1614 and published the first log tables, which are often falsely called natural logarithms (i.e. logarithms base e), although they are closely related to natural logarithms. In 1624 Henry Briggs published the first tables of common or base 10 logarithms and not natural logarithms. John Speidell had published the first table of what were effectively naturel logarithms based on Napier’s work in 1619. The first description of natural logarithms was by Nicholas Mercator in 1668. Tables of trigonometrical logarithmic functions are not trig tables. Surprisingly, trig tables are tables of trigonometrical functions. The slide rule was invented by William Oughtred in 1630. Seth Partridge developed the moving slide/fixed stock principle in 1657. Henry Coggeshall developed the so-called carpenter’s slide rule for measuring the dimensions of timber in 1677.

All of this leads me to ask in John Wiley & Sons Inc., a large and successful academic publishing company, the publishers of Danson’s tome, have actually heard of fact checking or if they just don’t care. The mistakes that I have picked up on here are all fairly elementary history of science errors and make me as a reader of the book wonder how much of the other information in the book is trust worthy. If I was doing anything formal on Mason and Dixon I would be very wary of quoting anything from Danson’s book before checking it thoroughly against other sources.

The sloppiness of both Wilson’s article on the telescope and Danson’s book on the Mason-Dixon line make me angry because with a small modicum of effort on the part of the respective authors the mistakes they have made could easily have been avoided.





Filed under Uncategorized

Did Isaac leap or was he pushed?

In 2016 2017 it would not be too much to expect a professor of philosophy at an American university to have a working knowledge of the evolution of science in the seventeenth century, particularly given that said evolution had a massive impact on the historical evolution of philosophy. One might excuse a freshly baked adjunct professor at a small liberal arts college, in his first year, if they were not au fait with the minutiae of the history of seventeenth-century astronomy but one would expect better from an established and acknowledged expert. Andrew Janiak is just that, an established and acknowledged expert. Creed C. Black Professor of Philosophy and Chair of Department at Duke University; according to Wikipedia, “Duke is consistently included among the best universities in the world by numerous university rankings”. Janiak is also an acknowledge expert on Isaac Newton and author of Isaac Newton in the Blackwell Great Minds series, so one is all the more dumbfounded to read the following in his article entitled Newton’s Leap on the Institute of Arts and Ideas: Philosophy for our times website:


Isaac Newton 1677 after Peter Lely Source: Wikimedia Commons Comment from CJ Schilt (a Newton expert) on Facebook: On another note, that picture is probably not Newton, despite what Finegold thinks.


But wait a minute: what could be more amazing than a young man discovering a fundamental force of nature while sitting under a tree? For starters, we have to recognize how foreign Newton’s ultimate idea about gravity was to philosophers, astronomers and mathematicians in the era of the Scientific Revolution. Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space. [my emphasis]That seems so obvious to us, it’s hard to imagine that for centuries, the world’s leading thinkers, from Aristotle to Ptolemy and onwards, did not have that idea at all. Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were. [my emphasis] The question of what caused the planetary orbits was not even on the table for astronomers in those days. [my emphasis] Down on earth, apples fell from trees throughout history just as they do now. But philosophers and mathematicians didn’t have any reason to think that whatever causes apples to fall to the ground might somehow be connected to anything going on in the heavens. After all, the heavens were thought to be the home of everlasting motions, of perfect circles, and were therefore nothing like the constantly changing, messy world down below, where worms eat through apples as they rot on the ground.

So what is wrong with this piece of #histSTM prose? Let us start with the second of my bold emphasised segments:

Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were.

Whilst it is true that, following Empedocles, Western culture adopted the so-called Platonic axioms, which stated that celestial motion was uniform and circular, it is not true that they claimed this motion to be without cause. Aristotle, whose system became dominant for a time in the Middle Ages, hypothesised a system of nested crystalline spheres, which working from the outside to the centre drove each other through direct contact; a system that probably would not have worked due to friction. His outer-most sphere was moved by the unmoved mover, who remained unnamed, making the theory very attractive for Christian theologians in the High Middle Ages, who simple called the unmoved mover God. Interestingly the expression love makes the world go round originates in the Aristotelian belief that that driving force was love. In the Middle Ages we also find the beliefs that each of the heavenly bodies has a soul, which propels it through space or alternatively an angel pushing it around its orbit.

All of this is all well and good but of course doesn’t have any real relevance for Newton because by the time he came on the scene the Platonic axioms were well and truly dead, killed off by one Johannes Kepler. You might have heard of him? Kepler published the first two of his planetary laws, number one: that the planetary orbits are ellipses and that the sun is at one focus of the ellipse and number two: that a line connecting the sun to the planet sweeps out equal areas in equal time periods in 1609, that’s thirty-three years before Newton was born. Somewhat later Cassini proved with the support of his teachers, Riccioli and Grimaldi, using a heliometer they had constructed in the San Petronio Basilica in Bologna, that the earth’s orbit around the sun or the sun’s around the earth, (the method couldn’t decide which) was definitely elliptical.

Part of the San Petronio Basilica heliometer.
The meridian line sundial inscribed on the floor at the San Petronio Basilica in Bologna, Emilia Romagna, northern Italy. An image of the Sun produced by a pinhole gnomon in the churches vaults 66.8 meters (219 ft) away fills this 168×64 cm oval at noon on the winter solstice.
Source Wikimedia Commons

By the time Newton became interested in astronomy it was accepted by all that the planetary orbits were Keplerian ellipses and not circles. Kepler’s first and third laws were accepted almost immediately being based on observation and solid mathematics but law two remained contentious until about 1670, when it was newly derived by Nicholas Mercator. The dispute over alternatives to Kepler’s second law between Ismaël Boulliau and Seth Ward was almost certainly Newton’s introduction to Kepler’s theories.

Turning to the other two bold emphasised claims we have:

 Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space.


The question of what caused the planetary orbits was not even on the table for astronomers in those days.

I’m afraid that Herr Kepler would disagree rather strongly with these claims. Not only had he asked this question he had also supplied a fairly ingenious and complex answer to it. Also quite famously his teacher Michael Maestlin rebuked him quite strongly for having done so. Kepler is usually credited with being the first to reject vitalist explanations of planetary motion by souls, spirits or angels (anima) and suggest instead a non-vitalist force (vir). His theory, based on the magnetic theories of Gilbert, was some sort of magnetic attraction emanating from the sun that weakened the further out it got. Kepler’s work started a debate that wound its way through the seventeenth century.

Ismaël Boulliau, a Keplerian, in his Astronomia philolaica from 1645 discussed Kepler’s theory of planetary force, which he rejected but added that if it did exist it would be an inverse-square law in analogy to Kepler’s law of the propagation of light. Newton was well aware of Boulliau’s suggestion of an inverse-square law. In 1666 Giovanni Alfonso Borelli, a disciple of Galileo, published his Theoricae Mediceorum planetarum ex causis physicis deductae in which he suggested that planetary motion was the result of three forces.

Famously in 1684 in a London coffee house Christopher Wren posed the question to Robert Hooke and Edmond Halley, if the force driving the planets was an inverse-square force would the orbits be Keplerian ellipses, offering a book token as prize to the first one to solve the problem. This, as is well known, led to Halley asking Newton who answered in the positive and wrote his Principia to prove it; in the Principia Newton shows that he is fully aware of both Kepler’s and Borelli’s work on the subject. What Newton deliberately left out of the Principia is that in an earlier exchange it had in fact been Hooke who first posited a universal force of gravity.

As this all too brief survey of the history shows, far from Newton providing an answer to a question that hadn’t been asked yet, he was, so to speak, a Johnny-come-lately to a debate that when he added his contribution was already eighty years old.

The Institute of Arts and Ideas advertises itself as follows:

So the IAI seeks to challenge the notion that our present accepted wisdom is the truth. It aims to uncover the flaws and limitations in our current thinking in search of alternative and better ways to hold the world.

Personally I don’t see how having a leading philosopher of science propagating the lone genius myth by spouting crap about the history of science fulfils that aim.







Filed under History of Astronomy, History of science, Myths of Science, Newton

Can we please stop (mis)quoting Albert on Emmy, it’s demeaning?

Emmy Noether, whom I’ve blogged about a couple of times in the past, is without any doubt one of the greats in the history of mathematics, as is well documented by the testimonials written by some of the greatest contemporary mathematicians and physicists and collected in Auguste Dick’s slim but well research biography, Emmy Noether: 1882–1935.

Emmy Noether c. 1930
Source:Wikimedia Commons

Yesterday was World Maths Day and the Royal Society tweeted portraits of mathematicians with links to articles all day, one of those tweets was about Emmy Noether. The tweet included a paraphrase of a well known quote from Albert Einstein, after all what could be better than a quote from old Albert the greatest of the great? Well almost anything actually, as the Einstein quote is highly demeaning. As given informally by the Royal Society it read as follows:

Emmy Noether was described by Einstein as the most important woman in the history of mathematics.

What Einstein actually wrote in a letter to the New York Times on the occasion of her death in 1935 was the following:

In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered, methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians.

In the same year, but before she died, Norbert Wiener wrote:

Miss Noether is… the greatest woman mathematician who has ever lived; and the greatest woman scientist of any sort now living, and a scholar at least on the plane of Madame Curie.

Now I’m sure that the Royal Society, Albert Einstein and Norbert Wiener all meant well, but take a step back and consider what all of them said in their different ways, Emmy Noether was pretty good for a woman [my emphasis].

Emmy Noether was one of the greatest mathematicians of the twentieth century, male or female, man or woman, about that there is absolutely no doubt, to qualify that praise with the term woman is quite simple demeaning.

In my mind it triggers the text of Melanie Safka’s mega pop hit from 1971, Brand New Key:

I ride my bike, I roller skate, don’t drive no car

Don’t go too fast, but I go pretty far

For somebody who don’t drive

I been all around the world

Some people say, I done all right for a girl [my emphasis]

On twitter, space archaeologist, Alice Gorman (@drspacejunk) took it one stage further, in my opinion correctly, and asked, “Dare I cite Samuel Johnson’s aphorism about the talking dog?” For those who are not up to speed on the good doctor’s witticisms:

I told him I had been that morning at a meeting of the people called Quakers, where I had heard a woman preach. Johnson: “Sir, a woman’s preaching is like a dog’s walking on his hind legs. It is not done well; but you are surprised to find it done at all.” – Boswell: Life

Can we please in future when talking about Emmy Noether resist the temptation to quote those who affix their praise of her mathematical talents with the term woman and just acknowledge her as a great mathematician?



Filed under History of Mathematics, Ladies of Science