The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time

The title of this post is the subtitle of Dava Sobel’s Longitude, her mega bestselling account of the life and work of the eighteenth-century clock maker John Harrison; probably the biggest selling popular #histSTM book of all time.

I’m quite happy to admit that when I first read it I was very impressed by her account of a man I didn’t know from a period of history with which I was not particularly well acquainted. However, because I was very impressed, I went looking for more information about the history of John Harrison and the marine chronometer. I found and read quite a lot of academic literature on both topics and came to the realisation that Sobel’s account was not really the true story and that she had twisted the facts to make for a more exciting story but quite far removed from the true narrative.

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

The next segment of the subtitle is also not true. Harrison was supported and encouraged in his endeavours by George Graham, possibly the greatest eighteenth-century English clockmaker, and James Short, almost certainly the greatest telescope maker in the world in the eighteenth century. Both men were important and highly influential figures in the scientific and technological communities of the period. Their support of Harrison rather gives the lie to the claim that Harrison was a lone genius.

George Graham
Source: Wikimedia Commons

The final segment of the subtitle is also highly inaccurate. The problem that Harrison and others were working on in the eighteenth century was a reliable method of determining longitude at sea. They were trying to solve a technological problem not a scientific one. The scientific problem had already been solved in antiquity. Scholars in ancient Greece already knew that to determine the difference in longitude between two locations, one ‘merely’ had to determine the local time difference between them; knowing this the problem was how to determine that time difference, as I said a technological problem.

In antiquity and up to the early modern period cartographers and astronomers (usually the same person) used astronomical phenomena such as solar or lunar eclipses. Observers determined the local time of the occurrence of a given astronomical phenomenon at two different locations and it was then possible to determine their longitudinal difference. Unfortunately eclipses are not very frequent occurrences and so this method has rather limited usefulness. Something else had to be developed.

In the early seventeenth century both Galileo Galilei and Simon Marius discovered the four largest moons of Jupiter and Galileo realised that the orbits of these moons and their appearances and disappearances as the circled Jupiter could, if tabulated accurately enough, be used as a clock to determine longitude. Towards the end of the seventeenth century Giovanni Domenico Cassini and Ole Rømer succeeded in producing the necessary tables and Galileo’s idea could be put into practice. Whilst this method was very successful for cartographers on land, on a rolling ship it was not possible to observe the Jupiter moons accurately enough with a telescope to be able to apply this method; something else had to be used.

The two solutions that came to be developed in the eighteenth century and form the backbone of Sobel’s book, the lunar distance method (lunars) and the marine chronometer, were both first suggested in the sixteenth century, the former by Johannes Werner and the latter by Gemma Frisius. Other methods were suggested but proved either impractical or downright impossible. For lunars you need accurate lunar orbit tables and an accurate instrument to determine the position of the moon. Tobias Mayer provided the necessary tables and John Hadley the instrument with his sextant. For the clock method you require a clock that has a high level of accuracy over a long period of time and which retains that accuracy under the often very adverse conditions of a sea voyage; this is the technological problem that Harrison solved. Sobel presents the two methods as in competition but for navigators they are in fact complimentary and they were both used. As my #histsci soul sister Rebekah ‘Becky’ Higgitt constantly repeats, with the marine chronometer you can carry longitude with you, but if you chronometer breaks down you can’t find it, whereas with lunars you can find longitude, as James Cook did in fact do on one of his voyages.

As I said above, I began to seriously doubt the veracity of Sobel’s account through my own study of the academic accounts of the story, these doubts were then confirmed as I began to follow the blog of the Longitude Board research project set up by Cambridge University and the Maritime Museum in Greenwich, of which Becky Higgitt was one of the lead researchers. For a more balanced and accurate account of the story I recommend Finding Longitude the book written by Becky and Richard Dunn to accompany the longitude exhibition at the Maritime Museum, one of the products of the research project.

Recently I have become fully aware of another aspect of the Harrison story that Sobel does not cover. I say fully aware because I already knew something of it before reading David S. Landes’ excellent Revolution in Time: Clocks and the making of the Modern World (Harvard University Press, 1983). Landes covers the whole history of the mechanical clock from the Middle Ages through to the quartz wristwatch. One of his central themes is the increasing accuracy of clocks down the ages in which the invention of the marine chronometer played a central role, so he devotes a whole chapter to Harrison’s endeavours.

Landes quite correctly points out that after a lifetime of experimentation and ingenious invention John Harrison did indeed produce a solution to the technological problem of determining longitude with a clock. An astute reader with a feel for language might have noticed that in the previous sentence I wrote ‘a solution’ and not ‘the solution’ and therein lies the rub. Over the years that he worked on the problem Harrison produced many ingenious innovations in clock making in order to achieve his aim, an accurate, reliable, highly durable timepiece, however the timepiece that he finally produced was too complex and too expensive to be practicable for widespread everyday service at sea. Harrison had, so to speak, priced himself out of the market.

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

Harrison was by no means the only clock maker working on a viable marine chronometer in the eighteenth century and it is actually his competitors who in the end carried away the laurels and not Harrison. Two clockmakers who made important contributions to the eventual development of a mechanically and financially viable marine chronometer were the Frenchman Pierre Le Roy and Swiss Ferdinand Berthoud, who were bitter rivals.

Pierre Le Roy (1717–1785)
Source: Wikimedia Commons

Plans of Le Roy chronometer
Source: Wikimedia Commons

Ferdinand Berthoud (1727–1807)
Source: Wikimedia Commons

Berthoud marine clock no.2, with motor spring and double pendulum wheel, 1763
Source: Wikimedia Commons

Neither of them can be said to have solved the problem but the work of both of them in different ways led in the right direction. Another contributor was George Graham’s one time apprentice, Thomas Mudge, his highly praised marine chronometer suffered from the same problem as Harrison’s too complex and thus too expensive to manufacture.

The two English clock makers, who actually first solved the problem of a viable marine chronometer were John Arnold and Thomas Earnshaw, who also became bitter rivals. This rivalry involved accusations of theft of innovations and disputes over patents. In the end it was John Arnold and Thomas Earnshaw, who became the most successful of the early clock makers, who worked on the development of the marine chronometer.

Chronometer-maker John Arnold (1736–1799) (attributed to Mason Chamberlin, ca. 1767)
Source: Wikimedia Commons

Thomas Earnshaw (!749–1829)
Source: Wikimedia Commons

Earnshaw chronometer No. 506
Source: Wikimedia Commons

I don’t intend to go into the details of which innovations in clock manufacture each of the man listed above contributed to the development of the marine chronometer that would go on to become an essential navigation tool in the nineteenth century. What I wish to make clear is exactly the same point as my essay on the history of the reflecting telescope for AEON made. From its first conception by Gemma Frisius in the sixteenth century, through the failure of Christiaan Huygens to realise it with his pendulum clock in the late seventeenth century (not discussed here), over its first successful realisation by John Harrison and on to the creation of a viable model by a succession of eighteenth-century clock makers, the marine chronometer was not the product of a single man’s (John Harrison’s) genius but a tool that evolved through the endeavours of a succession of dedicated inventors and innovators. Scientific and technological progress is teamwork.

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

Why doesn’t he just shut up?

Neil deGrasse Tyson (NdGT), probably the most influential science communicator in the world, spends a lot of time spouting out the message that learning science allows you to better detect bullshit, charlatans, fake news etc. etc. However it apparently doesn’t enable you to detect bullshit in the history of science, at least judging by NdGT’s own record on the subject. Not for the first time, I was tempted recently to throw my computer through the window upon witnessing NdGT pontificating on the history of science.

On a recent video recorded for Big Think, and also available on Youtube and already viewed by 2.6 million sycophants, he answers the question “Who’s the greatest physicist in history?” His answer appears under the title My Man, Sir Isaac Newton. Thoughtfully, Big Think have provided a transcription of NdGT’s blathering that I reproduce below for your delectation before I perform a Hist_Sci Hulk autopsy upon it.

Question: Who’s the greatest physicist in history?DeGrasse Tyson:    Isaac Newton.  I mean, just look… You read his writings.  Hair stands up… I don’t have hair there but if I did, it would stand up on the back of my neck.  You read his writings, the man was connected to the universe in ways that I never seen another human being connected.  It’s kind of spooky actually.  He discovers the laws of optics, figured out that white light is composed of colors.  That’s kind of freaky right there.  You take your colors of the rainbow, put them back together, you have white light again.  That freaked out the artist of the day.  How does that work?  Red, orange, yellow, green, blue, violet gives you white.  The laws of optics.  He discovers the laws of motion and the universal law of gravitation.  Then, a friend of his says, “Well, why do these orbits of the planets… Why are they in a shape of an ellipse, sort of flattened circle?  Why aren’t… some other shape?”  He said, you know, “I can’t… I don’t know.  I’ll get back to you.”  So he goes… goes home, comes back couple of months later, “Here’s why.  They’re actually conic sections, sections of a cone that you cut.”  And… And he said, “Well, how did find this out?  How did you determine this?”  “Well, I had to invent integral and differential calculus to determine this.”  Then, he turned 26.  Then, he turned 26.  We got people slogging through calculus in college just to learn what it is that Isaac Newtown invented on a dare, practically.  So that’s my man, Isaac Newton. 


Let us examine the actual history of science content of this stream of consciousness bullshit. We get told, “He discovers the laws of optic…!” Now Isaac Newton is indeed a very important figure in the history of physical optics but he by no means discovered the laws of optics. By the time he started doing his work in optics he stood at the end of a two thousand year long chain of researchers, starting with Euclid in the fourth century BCE, all of whom had been uncovering the laws of optics. This chain includes Ptolemaeus, Hero of Alexandria, al-Kindi, Ibn al-Haytham, Ibn Sahl, Robert Grosseteste, Roger Bacon, John Pecham, Witelo, Kamal al-Din al-Farisi, Theodoric of Freiberg, Francesco Maurolico, Giovanni Battista Della Porta, Friedrich Risner, Johannes Kepler, Thomas Harriot, Marco Antonio de Dominis, Willebrord Snellius, René Descartes, Christiaan Huygens, Francesco Maria Grimaldi, Robert Hooke, James Gregory and quite a few lesser known figures, much of whose work Newton was well acquainted with. Here we have an example of a generalisation that is so wrong it borders on the moronic.

What comes next is on safer ground, “…figured out that white light is composed of colors…” Newton did in fact, in a series of groundbreaking experiment, do exactly that. However NdGT, like almost everybody else is apparently not aware that Newton was by no means the first to make this discovery. The Bohemian Jesuit scholar Jan Marek (or Marcus) Marci (1595–1667) actually made this discovery earlier than Newton but firstly his explanation of the phenomenon was confused and largely wrong and secondly almost nobody knew of his work so the laurels go, probably correctly, to Newton.

NdGT’s next statement is for a physicist quite simply mindboggling he says, “That freaked out the artist of the day.  How does that work?  Red, orange, yellow, green, blue, violet gives you white.” Apparently NdGT is not aware of the fact that the rules for mixing coloured light and those for mixing pigments are different. I got taught this in primary school; NdGT appears never to have learnt it.

Up next are Newton’s contributions to mechanics, “He discovers the laws of motion and the universal law of gravitation.  Then, a friend of his says, “Well, why do these orbits of the planets… Why are they in a shape of an ellipse, sort of flattened circle?  Why aren’t… some other shape?”  He said, you know, “I can’t… I don’t know.  I’ll get back to you.”  So he goes… goes home, comes back couple of months later, “Here’s why.  They’re actually conic sections, sections of a cone that you cut.””

Where to begin? First off Newton did not discover either the laws of motion or the law of gravity. He borrowed all of them from others; his crowing achievement lay not in discovering them but in the way that he combined them. The questioning friend was of course Edmond Halley in what is one of the most famous and well document episodes in the history of physics, so why can’t NdGT get it right? What Halley actually asked was, assuming an inverse squared law of attraction what would be the shape of aa planetary orbit? This goes back to a question posed earlier by Christopher Wren in a discussion with Halley and Robert Hooke, “would an inverse squared law of attraction lead to Kepler’s laws of planetary motion?” Halley could not solve the problem so took the opportunity to ask Newton, at that time an acquaintance rather than a friend, who supposedly answered Halley’s question spontaneously with, “an ellipse.” Halley then asked how he knew it and Newton supposedly answered, “I have calculated it.” Newton being unable to find his claimed calculation sent Halley away and after some time supplied him with the nine-page manuscript De motu corporum in gyrum, which in massively expanded form would become Newton’s Principia.

NdGT blithely ignoring the, as I’ve said, well documented historical facts now continues his #histsigh fairy story, “And he said, “Well, how did find this out?  How did you determine this?”  “Well, I had to invent integral and differential calculus to determine this.”” This is complete an utter bullshit! This is in no way what Newton did and as such he also never claimed to have done it. In fact one of the most perplexing facts in Newton’s biography is that although he was a co-discoverer/co-inventor of the calculus (we’ll ignore for the moment the fact that even this is not strictly true, read the story here) there is no evidence that he used calculus to write Principia.

NdGT now drops his biggest historical clangour! He says, “Then, he turned 26.  Then, he turned 26.  We got people slogging through calculus in college just to learn what it is that Isaac Newtown invented on a dare, practically.  So that’s my man, Isaac Newton.” Newton was twenty-six going on twenty seven when he carried out the optics research that led to his theory of colours in 1666-67 but the episode with Halley concerning the shape of planetary orbits took place in 1682 when he was forty years old and he first delivered up De motu corporum in gyrum two years later in 1684. NdGT might, as an astro-physicist, be an expert on a telescope but he shouldn’t telescope time when talking about historical events.


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

“One man takes the credit, one man takes the blame…”

Er war einst groß in Spiel mit den Symbolen,

War viele Künste, viele Sprachen Meister,

War ein weltkundiger, ein weit gereister,

Berühmter Mann, gekannt bis zu den Polen,

Umgeben stets von Schülern und Kollegen.

Ein Fragment von den Gedichten des jungen Josef K.[1]


In my blog anniversary post yesterday I explained how I came to live in Germany; today in what is a sort of continuation of that post, I will explain how I came to evolve from a rank amateur deeply interested in the histories of mathematics and science into a full blown quasi-professional historian of science. This post is a tribute to the man who is responsible for that evolution, my friend, mentor and teacher Christian Thiel, who celebrates his eightieth birthday today.


I tell a joke that when I first came to Germany I could only speak six words of German: ja, nein, bitte, danke, Bier and Scheiße. In reality this was almost the truth, so the first task I set myself, when I decided to stay, was to learn the language. As well as buying teach-yourself books, I also started attending German courses at the adult education evening classes in Nürnberg. These were actually very good but were, as far as I was concerned, far too slow and so I began to look around for alternatives. Somebody told me that the local university in Erlangen ran courses in German as a foreign language, so I trundled off to investigate. It turned out that to register for these courses I needed to apply for a place as a normal student at the university. Now I had dropped out of university in Cardiff ten years earlier, with the intention of returning to higher education when I had sorted out what it was that I really wanted to study, so I thought why not. I registered to become a maths student and was thus admitted to the German as a foreign language course.

I now spent a year learning German at the university in the mornings and working as an industrial cleaner in the afternoons. The course was very intensive, as the students are expected to be capable of taking a degree course in any academic subject in German at the end of it. To my own surprise I passed the course with flying colours and was now qualified to start my studies as a student of mathematics.

In those days the first degree in mathematics at the university of Erlangen was a diploma, equivalent of a master’s degree at an English university. Alongside the main subject students had to choose a subsidiary subject. In the 1970s I had become very interested in the philosophy of science and so I thought I would take a shot at that. One chair in the philosophy department was also offering a seminar in constructive geometry for the coming semester. I had no idea what constructive geometry was but it was an added incentive to choose philosophy as my subsidiary. The chair in question was one specialising in history and philosophy of science; I decided to go take a look see.

I found out when the professor held his office hours and went along at the appointed time. He wasn’t there. Knocking on his secretary’s door I asked when the professor would be there. She very kindly rang the professor and said that if I could wait, he would be along soon. I had waited maybe a quarter of an hour when I then met Christian Thiel for the first time. What I didn’t know was that it was not only my first semester as a student at the university but it was also Christian Thiel’s first semester as occupant of that chair. He, an Erlanger, had studied in Erlangen, taken his doctorate and his habilitation there but had then gone away to a chair elsewhere, as was normal in the German academic system. He was now returning to Erlangen to occupy the chair of his own mentor, Paul Lorenzen. What I also didn’t know at the time was that the department secretary had warned Christian Thiel that there was a ‘dangerous looking man’ waiting to see him. I was wearing a complete set of black motorcycle leathers, had my long hair tied back in a ponytail and sported three very prominent silver earrings, dangerous?

Christian Thiel wasn’t at all fazed by my dangerous appearance. We got on from the very first moment and were soon deep in a conversation about maths and the philosophy of science. In the time (ten years!) that I spent studying at Erlangen University more than fifty per cent of the courses that I took were with Christian Thiel. I think I learnt more from him than all of the other teachers that I have had in my life put together. He formed me, any abilities that I might possess as a historian of science I owe largely to Christian Thiel.

The maths department in Erlangen, when I studied, was not interested in the history of mathematics, my main motivation for studying the subject, Christian Thiel, however, was a historian of mathematics and mathematical logic, so after a time I dropped maths and became a student of philosophy with English philology and history as my subsidiaries. This move was also motivated by the fact that very early in my studies Christian Thiel, who obviously saw something in me that I couldn’t see in myself, offered me, to my surprise, a position in a major research project into the social history (read external history) of formal logic. I learnt so much in that research project, probably more than in my official studies and it is here that I really became a genuine historian of science. I can’t say how much being offered that chance, as a student, to do real cutting edge historical research meant to me. Without it I would not be sitting here now writing this blog post.

As the title of this blog post says, ‘one man takes the credit, one man takes the blame’ and that man is Christian Thiel and I am very pleased to be able to write this brief tribute to him on my blog on the occasion of his eightieth birthday.

I should point out that this is not the first tribute that I have written to Christian Thiel. The German quote that opens this post is taken from my essay in the Festschrift[2] published in honour of his retirement twelve years ago. This in turn is loosely based on the speech I held at the conference in his honour in Altdorf in 2005. Nearly all of the lectures at the conference related to Christian Thiel as an academic researcher, I had the privilege of honouring Christian Thiel the teacher. There is not a little irony in this. Over the years Christian Thiel has taught many, many successful students, postgraduates and postdocs, I, however, am, so to speak, one of his failures, falling at the final fence and failing to graduate. I closed my speech and my essay with a simple phrase, which I’m going to repeat once again here.


“Thanks Chris, you have been a bloody good teacher.”


[1] A couple of words about the title and the opening quote to this post. The title is a line from Tom Lehrer’s song Lobachevsky. I would like to point out that whilst the title hero of the song has inspired the narrator to plagiarise, Christian Thiel actually taught me and all of his students the exact opposite. I chose the quote because a love of Tom Lehrer and of Hermann Hesse the source of the opening quote are two of the many things that I and Christian Thiel have in common. Das Glasperlenspiel, the source of the opening quote, is my favourite novel and when I set out to learn German, one of my aims was  to be able to read it in German one day. In Germany to become a professor a scholar has to do a sort of second doctorate called a habilitation. When the habilitation thesis has been graded and accepted the potential habilitant then has to hold a habilitation lecture in front of an audience of all of the habilitanten of his faculty. Thiel’s habilitation lecture was on Das Glasperlenspiel.

[2] Thony Christie, The Teacher in G. Löffladt (Hrsg), Mathematik – Logik – Philosophie: Ideen und ihre historischen Wechselwirkungen, Verlag Harri Deutsch, Frankfurt am Main, 2012

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“I went on holiday and I haven’t gone back home yet”

Today is the eighth anniversary of the founding of The Renaissance Mathematicus and, as on a couple of similar occasions in the past, I have decided to regale you with something biographical[1]. This is quite literally a tale of sex and drugs and rock’n’roll, so if you have any objections, moral or otherwise, to reading about such things or to the people who indulge or have indulged in them then I suggest you stop reading now.

In what follows I intend to tell the tale of how I came to live in Germany, where I have substantially now spent more than half of my life and where, all things being equal, I shall probably die. You might ask what my coming to live in Germany has to do with my blogging about the history of science but the connection is really quite direct. If I hadn’t come to Germany in 1980, I wouldn’t have ended up studying the history and philosophy of science, as a mature student, at Erlangen University and although I never completed my master’s degree, due to mental health problems, going on to become a sort of semi-professional historian of science and then a history of science blogger. But back to the beginning.

It all started in the summer 1977 when I moved back to Cardiff from Malmö in Sweden (that’s another story!). D (all the other people in this story will only be identified by their initials) had started constructing a yurt or ger, the round tents used as dwellings by the nomads of Central Asia, most notably the Mongolians.

A ger sits on the Steppes near Mandalgovi
Source: Wikimedia Commons

Why D had decided to construct a yurt I never quite fathomed but it was a typical D project. D had a good degree in biology but had decided instead of becoming a biologist, to smoke dope and indulge in moderately crazy projects. The projects were financed by the collective’s dope dealing activities. The collective consisted of those who lived in number 24, where D was at home, a rotating group of about twelve and various friends and acquaintances, of which I was one, bringing the total to somewhere around thirty. Many members of the collective were musicians. One member of the collective would buy dope in wholesale quantities and then others would distribute it at low profit margins to a relatively large network throughout the city. The professional dealers didn’t like us because we seriously undercut their prices but we had the protection of the big guys, who found our ‘socialist’ dealing somehow charming. I was a distributer, my only profit being my own not inconsiderable consumption. I got to smoke for free and my ‘customers’ enjoyed low priced dope. Everybody was happy. The central profits were used to finance projects like the yurt or the collective’s long wheel based Land Rover.

In the evenings members of the collective would come together in the large ground flour living room in number 24, get totally wasted and then indulge in long musical jam sessions, playing blues, folk, rock and often long open-ended snake dance instrumental jams. K & C were a couple who were both excellent guitarists who also sang and C, an American medical student, who had a beautiful voice like Joanie Mitchell also played flute. A, who had a degree in philosophy but who had gone off the rails and now ran a whole food shop, played saxophone and clarinet. Both B and JC were professional base players and were also excellent guitarists. B had a double music degree in classical guitar and composition. I played blues harp and jaw harp and almost everyone played percussion. Those sessions often ran for hours. There was also a formal house band built around K & C, which would occasionally play public gigs.

Various members of the collective, including me, were involved in constructing the wooden frame of the yurt and N, who worked as a theatre company seamstress sewed the roof and wall coverings out of lorry tarpaulins on an industrial sewing machine. We road tested the yurt on a very stoned, long weekend in Mid Wales in autumn during the magic mushroom season. It proved to be very reliable.

Mongolian Ger: starting to place roof poles
Source: Wikimedia Commons

In 1979 we decided to take yurt, house band and whoever wanted to come to the summer solstice free festival at Stonehenge. We loaded the yurt onto the Land Rover together with a lot of serious camping equipment, saws, axes, cooking pots etc. and set off for the full tens days of sex and drugs and rock’n’roll on Salisbury Plain. All together we were about thirty people, the yurt was big enough to sleep up to twenty and several people, myself included, took their own tents.

Surprisingly several of this bunch of dope smoking hippies had been boy scouts in their youth, including me, and we set a very professional camp site with a large fire pit on which we not only cooked food for all of our own group, funded from a communal kitty, but cooked and sold food to other attendees. A lot of drugs were consumed and a lot of music was played. On the afternoon before the solstice A and I took off across the festival site selling some first class acid that we had acquired. In the evening A, B and I dropped some acid and taking our respective instruments went off to a tepee with a generator to take part in an amplified jam session. We played raga rock, flying on acid for several hours until the generator ran out of petrol.

I wound my way back to our campsite in the early hours of the solstice dawn to join a fairly large gathering that had assembled around our fire pit to greet the solstice. One of those sitting around the glowing embers was a young German lady, AZ. We got into conversation and as the party wound down we retired to my tent. The following day AZ moved on in her Interrail trip around Britain but not before we had exchanged addresses. Over the next year we exchanged occasional letters and postcards.

Your author at Stonehenge Free Festival 1979 sawing firewood courtesy of AZ
I have no idea who the young lady on the right is!

In the summer of 1980 I was at something of a lose end in my personal life that didn’t seem to be going anywhere in particular. I was busy rewiring the photo and graphics studio of a friend one afternoon when I decided that what I needed was a holiday. Due to the work I was doing I knew that I would have some funds and fell to thinking where I could possibly go. The first two thoughts I had were that I could visit AZ in Germany or I could take a trip to Morocco, the destination of choice of various of my traveller friends at the time. Travellers were people who would work for six months or a year saving as much of their earnings as possible and then set off with a rucksack and sleeping bag to parts exotic for as long as they could make the money last. I had several such friends in those days but I wasn’t a traveller. When I got home to my flat on that evening there was a postcard from AZ who was on holiday in Morocco! I kid you not this really did happen.

Never one to ignore a wink of fate, in particular not one that obvious, I set off in September to hitch to Morocco via Southern Germany. I took a ferry to Hoek van Holland because I wanted to visit a friend who had moved there. Nobody had his address but I was assured by his brother that he was in the local telephone book. If he was, I couldn’t find him and so I set out to hitch down to Nürnberg in the vicinity of which AZ was living. It took two days including a night spent sleeping on the periphery of Frankfurt Airport. Not a quiet night. I had intended to stay just a couple of days in Franconia but ended up staying two weeks and getting to know a great crowd of people. When I started out again I hitched down through Austria to Florence in Northern Italy. From here I moved across Italy into Southern France winding my way across the south into Spain. Here I got picked up by a group of French Canadians with whom I spent a couple of crazy days. Working my way further south at snails pace, Spain was not a good country for hitch hiking in those days, I finally arrived in Algeciras and took the ferry to Ceuta, where I met a Swiss hippy who offered a sort of unofficial taxi service down to Marrakesh, which I took.

Having spent several days in Marrakesh I moved on to Meknes, which at that time had the only functioning mosque that one could visit as a non-Muslim. Here I had two very nice experiences. In order to visit the mosque you have to be shown round by a guide. I got shown round, together with two German tourists, by a young Moroccan student. The student only spoke French and the Germans only spoke English so I ended up acting as translator, because of this a got my guided tour for free, the student being thankful for my services. The student then took me to a student café where I spent the evening in the company of about twenty young Moroccans, mostly students, dinking mint tea and smoking kief. The young students made me feel very much at home and those were the happiest hours that I spent in Morocco.

In classic style my money began to run out and I got sick, some sort of flu like virus, so I began to head back to Europe. I was feeling shit and was very, very low on funds by the time I reached Madrid and was wondering how I could get back home when I met a German who had been deported from Morocco and had a one-way train ticket to Munich paid for by the German Embassy in Morocco. He sold me his train ticket for most of the cash that I had left and I rode the train back to Germany getting off in Nürnberg and going back to AZ’s.

My plan was to get well, find some casual work and earn enough money to get back to the UK. Having recovered my health, speaking no German I went down the honoured George Orwell route and got a job as a dishwasher in a local hotel. Here I had the best name-dropping experience of my entire life. The hotel manager was rather chuffed at having a genuine white British dishwasher, all of my colleagues where Indians, and would come and practice his English on me. One day I came into work at 7 am and he rushed to meet me asking if I knew who had slept in his hotel that night? I of course had no idea and playing the required role of straight man responded, no who? He burst out excitedly, “Roy Jenkins, President of the European Commission!” I, without thinking at all about what I was saying, “Oh, I went to school with his children”. His face dropped a mile, trumped by a mere dishwasher. He turned and walked away without saying a word.

In December I decided that I was going to stay in Germany and I’m still here thirty-seven years later. If people ask how I came to live in Germany I always answer, as I said above, “I went on holiday and I haven’t gone back home yet”, which is the simple truth.



[1] This also fulfils a request made by some commentators on my 2016 Winter Solstice post.


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Open shelved serendipity

One of my favourite radio science programmes is BBC Radio 4’s Science Stories presented by Philip Ball and Naomi Alderman. Yesterday was the first episode of the fifth series of this excellent piece of popular history of science broadcasting. Last week whilst advertising the new series on Twitter Philip Ball let drop the fact that next weeks episode would be about the medieval theologian and scholar Robert Grosseteste, featuring the physicist of the fascinating interdisciplinary University of Durham research project Ordered Universe, Thom McLeish. This brief Internet exchange awoke in me memories of my own first encounter with the medieval Bishop of Lincoln.

14th-Century Portrait of Robert Grosseteste, Bishop of Lincoln by unknown scribe
Source: Wikimedia Commons

I studied mathematics, philosophy, English philology and history with a strong emphasis on the history and philosophy of science, as a mature student, at the University of Erlangen between 1981 and 1991. It was this period of my life that converted me from an enthusiastic amateur into a university educated and trained researcher into the history of science (For more on this see my post next Monday). When I started this decade of formal studies I held a fairly standard, conservative view of the Scientific Revolution; this started with the publication of Copernicus’ De revolutionibus in 1543 and was completed with the publication of Newton’s Principia Mathematica in 1687. What disrupted, one could even say exploded, this idealised picture was my first encounter with Grosseteste.

Erlangen University is a comparatively large university and its main library is, like that of almost all such institutions, closed shelf. However the department libraries are almost all open shelf and as a student I developed the habit of browsing library bookshelves with no particular aim in view. The Bavarian State university library system has for book purchases an emphasis policy. Each Bavarian university library has a collecting emphasis so that specialist books in a particular discipline are only bought/collected by one university but are available to all the others through the interlibrary loan system. This is a method of making the available funds go further. Erlangen’s collection emphasis is philosophy, including the history and philosophy of science, so the philosophy department library is particularly well stocked in this direction.

One day fairly early in my time as a student in Erlangen I was cruising the history and philosophy of science bookshelves in the philosophy department library when my eyes chanced upon a rather unimposing, fairly weighty book by some guy called Alistair Crombie (I had know idea who he was then) with the title Robert Grosseteste and the origins of experimental science: 1100 – 1700. I have no idea what motivated me to take that volume home with me but I did and once I started reading didn’t stop until I had reached the end. This was a whole new world to me, the world of medieval science, of whose existence I had been blissfully unaware up until that point in time. Reading Crombie’s book radically changed my whole understanding of the history of science.

Here was this twelfth/thirteenth century cleric, lecturer at Oxford University (and possibly for a time chancellor of that august institution), who went on to become Bishop of Lincoln, teaching what amounted to empirical mathematical science.

Grosseteste’s Tomb and Chapel in Lincoln Cathedral
Source: Wikimedia Commons

It should be pointed out that whilst Grosseteste was strong on mathematical empirical science in theory, his work was somewhat lacking in the practice of that which he preached. Crombie has Grosseteste standing at the head of a chain of scholars that include Roger Bacon in the thirteenth century, the Oxford Calculators (about whom there is a good podcast from History of Philosophy without any gaps) and the Paris Physicists in the fourteenth century and so on down to Isaac Newton at the end of the seventeenth century. Unknown to me at the time Crombie was presenting a modernised version of the Duhem Thesis that the scientific revolution took place in the thirteenth and fourteenth centuries and not as the standard model has it, and as I had believed up till I read Crombie’s book, in the sixteenth and seventeenth centuries.

This was the start of a long intellectual journey for me during which I read the works of not only Crombie but of Edward Grant, Marshal Clagett, John Murdoch, David Lindberg, A. Mark Smith, Toby Huff and many other historians of medieval science. This journey also took me into the fascinating world of Islamic science, which in turn led me to the histories of both Indian and Chinese science although I still have the impression that in all these areas medieval European science, Islamic science, and Indian and Chinese science I have till now barely scratched the surface.

As I said above this journey started with Crombie’s book and Robert Grosseteste discovered whilst aimlessly browsing the shelves in the department library. This is by no means the only important and influential book that I have discovered for myself by this practice of browsing in open shelf department libraries. On one occasion I went looking for one specific book on map projection in the geography department library and, after a happy hour or two of browsing, left with an armful of books on the history of cartography. On another occasion I discovered, purely by accident, The Life and Letters of Sir Henry Wotton edited by Logan Pearsall Smith in the English Department Library. Wotton a sixteenth/seventeenth century English diplomat was a passionate fan of natural philosophy, who sent the first copies of Galileo’s Sidereus Nuncius, fresh off the printing press to London on its day of publication in 1610.

There are many other examples of the scholarly serendipity that my habit of browsing open shelf library shelves has brought me over the years but I think I have already made the point that I wanted to when I set out to write this post. Libraries are full of wonderful, vista opening books, so don’t wait for somebody to recommend them to you but find an open shelf library and go and see what chance throws you way, it might just change your life.







Filed under Autobiographical, History of science, Mediaeval Science

Recipes in the Wild By Paul Engle June 1, 2017

The Recipes Project blog is, starting today, running a Virtual Conversation on the theme, “What is a Recipe?” I featured this in the editorial of the latest edition of Whewells Gazette the Weekly #histSTM Links List. Inspired by a comparison that I made between algorithms and recipes and a question that I posed, Paul Engle, author of the very excellent Conciatore: The Life and Times of 17th Century Glassmaker Antonio Neri and writer of the Conciatore Blog, sent me the following essay stating, “Feel free to do with it what you will.” So what I will is to post it here as a very welcome guest blog post from an excellent historian of technology who really knows what a recipe is.  

It has been suggested at Whewell’s Gazette in a recent editorial that in considering recipes, particularly technical recipes and their relation to algorithms, that, “the two words are in their essence synonyms and there isn’t really a difference.” [1] With all due respect to the author of this passage, I do not think that is quite right.

A recipe is much more than an algorithm, in fact I propose that while algorithms are quite powerful tools, they occupy a rather distinct niche in the universe of recipes. We do agree on some things however,

“For me a recipe is quite simply a set of instructions, which describe how to complete successfully a given task. The task does not necessarily have to have anything to do with cooking, the first thought that pops up when we hear the word recipe.” [2]

I have thirty-odd years of empirical experience writing and following technical recipes in a laboratory setting; I have several shelves full of them that I am looking at right now. I have been programming computers and dealing with algorithms, dare I say it, since the days of punch cards and paper tape. This is a subject particularly dear to me and besides, I sense an irresistible opportunity to make a fool of myself, so here goes.

In the realms of mathematics and computer science, an algorithm is a set of instructions that enjoy several conditions favorable over recipes; a well-defined environment where it does not matter if it is raining or sunny outside and an output or result that is usually unambiguous. For recipes, not so much; even the lowly baker known that on humid days, a prized and tested bread recipes must be adjusted to produce an edible product. These adjustments do not always take a form that can easily be measured or quantified and this starts to get at the heart of the matter.

Any day of the week, rain or shine, a computer running a straightforward algorithm can generate the first million digits of pi, (yes, the millionth digit is 1). While there may be a certain amount of difficulty in verifying a result, it is something that is done quite routinely. While some simple recipes fall into this form, many others do not. Consider that some technical recipes seem to work even if we do not know how. Others require “experienced” practitioners, not because of anything magical going on, but simply because the most reliable results are obtained by one who has done it before. Even with seemingly simple, well-documented tasks like polishing a material, there can be an enormous number of variables involved, some unknown, others that are not practical or possible to control.

An algorithm generally lives in an artificially constructed, tightly controlled environment, recipes, on the other hand, operate in the wild. An aspect of technical recipes often missed by outsiders is the level of attention that must be paid to the interaction of your “product” with its environment. This may mean frequent observation and testing, or, in the kitchen, it may mean tasting the gumbo every few minutes and making appropriate adjustments. No matter if the result is a well-polished sample in a materials laboratory, or a well-seasoned bowl of soup in the French Quarter, what makes the result “good” is not necessarily easy to define. We can calibrate our equipment and take great care with our materials. We can scrutinize the results, and take measurements until the cows come home, but in many instances, this is only a starting point; learning to perform a recipe “well” can be like a mini-education. Writing that down stepwise can be like trying to capture everything you learned at cooking school.

It is in this setting, where there are many variables to keep track of, many unknowns, and even the results may be hard to characterize, that we step into the realm of “art.” A successful outcome depends as much on what you bring to the table as what is written on the page. A recipe becomes like a roadmap for threading your way through a complex maze of decision points. Here is where I get passionate about my subject. Practicing a recipe, in a sense, can be viewed as the purest form of empirical science. And this can take place in a laboratory or in a kitchen. If science is the study of the way the world actually behaves, then going through a series of steps and paying close attention to what is happening, is as good as it gets. It is not a matter of imposing ones will on the world, but of interacting with nature and moving toward a result given the constraints of reality; there is a give and take. A scientific experiment can be viewed as the act of developing a new recipe toward a specific result. Writing that recipe down is an exercise in determining the important variables to pay attention to and capturing a method in a way that is repeatable by others.

As computer algorithms move into the realms of artificial intelligence, driverless cars and the like, they will start to encounter the same difficulties as our baker does on a humid day. Perhaps a true test of machine intelligence will be how well an algorithm negotiates real-world recipes.

[1] Christie, Thony 2017. Whewell’s Ghost blog, “Editorial, Whewell’s Gazette: Year 03, Vol. #41” 31 May 2017.
[2] Op. Cit.


Filed under History of science, History of Technology

Telling the time at night

The first humans almost certainly followed a pattern of being active during daylight and resting or sleeping during the night, if the latter with one eye open, because of potential danger. As humanity developed it also began to develop the potential for tracking time. During the day following the path of the sun is the first step and this eventually leads to the use of shadows to track and to express times. However at night the sun is no longer visible and it is rare for the moon to be bright enough cast shadows and these are fairly useless for tracking time. So how do you track time at night?

If you look into a clear night sky the heavens are full of stars, still visible in the days before the invention of street lighting and light pollution. At first there seems to be no order to this extensive panorama of bight points but for those living in the northern hemisphere if you look due north you will eventually perceive that there is one star, Polaris the North or Pole Star[1], that appears to remain stationary whilst the stars and groups of stars surrounding it appear to circle it as the night proceeds. As we know, the stars are stationary it is the earth that is revolving on its axis. The stars and groups of stars closest to Polaris appear to circle it completely but those further away rise up over the horizon cross the sky and then set under the horizon on the other side of the heavens.

A time exposure showing the path of the circumpolar star with Polaris in the centre
Photo: Ashley Dace
Source: Wikimedia Commons

The ancient Egyptians used this phenomenon of the rising stars and groups of stars, (known as heliacal rising wrong see comments!) to tell the time at night. They identified thirty-six stars or groups of stars, known as the Decans (because a new one appeared over the horizon every ten days), for this purpose to cover the whole year, because of the tilt of the earth’s axis different stars or groups of stars rise on different nights. On any given night twelve of these chosen stars or groups of stars rose over the horizon at regular interval during the night giving the Egyptian astronomer/priests a clock with which to divide the night into twelve periods. Again, because of the tilt of the earth’s axis and the varying seasons the length of the nights varies and with them the length of the divisions. With time the Egyptians also divided the daytime into twelve segments giving us our twenty-four hour day.

Diagonal star table’ from the late 11th Dynasty coffin lid; found at Asyut, Egypt. Roemer- und Pelizaeus-Museum Hildesheim
Source: Wikimedia Commons

Later cultures measured the hours of the night using other methods such as water clocks (or clepsydra) and candle clocks. These of course because of their imperfections only give approximate hourly divisions but this was more than accurate enough for those using them, who did not yet possess our obsession of living by the clock.

An early 19th-century illustration of Ctesibius’s (285–222 BC) clepsydra from the 3rd century BCE. The hour indicator ascends as water flows in. Also, a series of gears rotate a cylinder to correspond to the temporal hours.
The illustrator was probably John Farey, Jr. (1791–1851).
Source: Wikimedia Commons


Al-Jazari’s candle clock in 1206
Source: Wikimedia Commons

However others, like the ancient Egyptians, continued to use star clocks. Mariners who regularly sailed the same routes grew to know the night sky and could by observing the position of a given circumpolar star or group of stars approximately determine the hours of the night. This form of using the circumpolar stars as the hands of a clock was put into use in the Middle Ages by the invention of an astronomical instrument known as a nocturnal or nocturlabium.

Girolamo della Volpaia (ca. 1530-1614)
Nocturnal and horary quadrant, 1568
Florence, Istituto e Museo di Storia della Scienza, inv. 2503
The horary quadrant is used to determine the time during daylight

The nocturnal is a circular, usually brass, instrument with a hole in the middle. It has two discs or dials and an indicator arm or pointer that sticks out beyond the outer dial. The outer dial is marked with the months of the year and the inner dial with the hours of the day. The inner dial also has a pointer. Nocturnals are constructed and calibrated for a specific circumpolar star. To tell the time the inner disc is rotated until its pointer points at the right month. Then the instrument is raised to the observer’s eye and the Pole Star is sighted through the central hole. The pointer or indicator arm is then adjusted until it lies on the position of the calibrated star or star group. The time can now be read off on the inner dial. Small nocturnals are usually only calibrated in hours, larger instruments are accurate to a quarter of an hour.

Medieval diagram explaining how to use a nocturnal. Peter Apian I think!
Source Wikimedia Commons

[1] Because the stars are actually moving very slowly relative to the earth the star that has been perceived as the Pole Star over the millennia has actually changed.


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