“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.


Filed under Uncategorized

In history getting labels right is important

This is a post about history in general but it applies just as much to the history of science. I have over the years written several posts about the problems of attributing nationalities or even countries of origins to historical figures and this post discusses another example of this, where the attributions are about ahistorical as you can get. What is it this time that has piqued my ire? It was the title of an article in The Guardian that contains historical attributions that are ahistorical, anachronistic and quite frankly xenophobic.

Did Dutch hordes kill off the early Britons who started Stonehenge?

Strong words, strong claims, so what is wrong with this title? The article is about the spread into Britain from the continent of the so-called Beaker folk, a European wide Neolithic-Bronze Age culture that existed from around 2900 BCE to 1800 BCE. Archaeologists and prehistorians define cultures through characteristic behaviours or artefacts. The Beaker culture is so named because of the habit of burying their dead with distinctive ceramic pots or beakers. This cultural group moved into Britain around 2500 BCE and the article claims that DNA analysis has shown that the previous inhabitants disappear out of the genetic record to be replaced by the newcomers. All well and good so what’s my beef?

First off, the title suggests that the original population were killed off by invading Europeans but the previous population were, like the Beaker people, themselves European immigrants, as had and have been all of the inhabitants of the British Isles. It is not known when exactly the Neolithic culture that started building Stonehenge arrived in Britain but they were with certainty not Britons! One moment there! If they are living in Britain they are Britons, right? Wrong!

The name Britons for inhabitants of this island derives from the reports of the fourth-century Greek explorer Pytheas of Massalia (that’s Marseille). Pytheas supposedly circumnavigated the island and referred to its inhabitants as Pretani and the island as Prettanikē; these are the origins of the words Briton and Britain. The words he is using are thought to be transliterations into Greek of the names used by the inhabitants that Pytheas met, who are not even Beaker people but members of a later wave of immigrants the Celts. We don’t have a name for the Neolithic folk who started building Stonehenge but they were not Britons.

We have the same problem with the Beaker people being called Dutch in the title. There were settlements of the Beaker people all over Europe but they thought to have originated in what is now Spain. The group that crossed the Channel onto the British Island are said by the historical geneticists to have come from what is now the Northern Netherlands but that in no way makes them Dutch.

The Dutch are, like the English, a Low German dialect speaking Germanic folk. They originated in what is today Southern Scandinavia and Northern Germany and because of climate change moved southwards into the Netherlands between 850 and 750 BCE so once again long after the Beaker culture had died out.

What we actually have is one wave of immigrants from the European continent being supplanted by another wave of immigrants from the European continent. The former are not Britons and the latter are not Dutch and to claim that they were, is a massive historical distortion and has, as I said at the beginning a strong stench of xenophobia. The British Isles has on and off, since about 42,000 years BP (before the present), been occupied by successive waves of immigrants from the European continent the last being the Normans, a Norse culture residing in France, in 1066 CE.

Almost all areas in the world have similar histories of habitation and historians or people writing historical articles should be very, very careful when attaching labels to peoples or geographical areas in their writings.


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Perpetuating the myths addendum – ‘The Copernican Shock

Frequent Renaissance Mathematicus commentator (comment-writer, commenter, commentor), Phillip Helbig, sent me an interesting email in response to my previous blog post. In skewering the Nadlers’ comic book I didn’t actually comment on every single detail of everything that was wrong with it, one of the things I left out was Galileo saying:

It is not the center of the cosmos it is a planet just like the others and they all orbit the sun.

As Phillip correctly pointed out in the Ptolemaic-Aristotelian geocentric model of the cosmos the Earth was not viewed as the centre of the cosmos but rather as the bottom. I wrote a brief post long ago quoting a wonderful passage by Otto von Guericke, the inventor of the vacuum pump on exactly this topic:

Since, however, almost everyone has been of the conviction that the earth is immobile since it is a heavy body, the dregs, as it were, of the universe and for this reason situated in the middle or the lowest region of the heaven

Otto von Guericke; The New (So-Called) Magdeburg Experiments of Otto von Guericke, trans. with pref. by Margaret Glover Foley Ames. Kluwer Academic Publishers, Dordrecht/Boston/London, 1994, pp. 15 – 16. (my emphasis)

Phillip then asks, “So what was the “shock” of the Copernican Revolution (how many even get that pun?)?  Was it demoting humanity from the centre of the universe, or promoting the Earth to be on par with the other heavenly bodies?”

Before I answer his question I would point out that the idea that Copernicus had demoted the Earth from the centre of the cosmos first emerged much later, sometime in the late eighteenth or early nineteenth century, as an explanation for the supposed irrational rejection of the heliocentric hypothesis. Of course as is now well known, or at least should be, the initial rejection of the heliocentric hypothesis was not irrational but was based on solid common sense and the available empirical scientific evidence nearly all of which spoke against it. For a lot, but by no means all, of the astronomical arguments read Chris Graney’s excellent Setting Aside All Authority.

So back to Phillip’s question, what was the real Copernican shock? The answer is as simple as it is surprising, there wasn’t one. The acknowledgement and acceptance of the heliocentric hypothesis was so gradual and spread out over such a long period of time that it caused almost no waves at all.

First up, there was nothing very new in Copernicus suggesting a heliocentric cosmos. As should be well known it had already been proposed by Aristarchus of Samos in the third century BCE and Ptolemaeus’ Syntaxis Mathematiké (Almagest) contains a long section detailing the counter arguments to it, which were well known to all renaissance and medieval astronomers. Also in the centuries prior to Copernicus various scholars such as Nicholas of Cusa had extensively discussed both geocentric models with diurnal rotation and full heliocentric ones. All that was new with Copernicus was an extensive mathematical model for a heliocentric cosmos.

At first this was greeted with some enthusiasm as a purely hypothetical model with the hope that it would deliver better predictions of the heavenly movements than the geocentric models for use in astrology, cartography, navigation etc. However it soon became apparent that Copernicus was not really any better than the older models, as it was based on the same inaccurate and oft corrupted data as Ptolemaeus, so the interest waned, although it was these inaccuracies in both model that inspired Tycho Brahe to undertake his very extensive programme of new astronomical observations on which Kepler would base his models.

As Robert Westman pointed out, in a now legendary footnote, between the publication of De revolutionibus in 1543 and 1600 there were only ten people in the whole world, who accepted Copernicus’ heliocentric cosmology, not exactly earth shattering. Even after 1600 the acceptance of a heliocentric worldview only increased very slowly and in gradual increments as the evidence for it accumulated.

The first two factors are the work of Kepler and the early telescopic discoveries. Because Kepler couldn’t or rather didn’t deal with the physical problems of a moving earth his work initially fell on deaf ears. The early telescopic discoveries only refuted a pure Ptolemaic geocentric model but were consistent with a Tychonic geo-heliocentric one and as this had a stationary earth, it became the model of choice. Of interest, and I think up till now not adequately explained, a Tychonic model with diurnal rotation, i.e. a spinning earth, became the preferred variation. A partial step in the right direction. Kepler’s publication of the Rudolphine Tables in 1627 led to an acceptance of his elliptical astronomy at least for calculations if not cosmologically. Then Cassini, with the help of Riccioli, demonstrated with a heliometer in the San Petronio Basilica in Bologna that the sun’s orbit around the earth or the earth’s orbit around the sun was indeed a Keplerian ellipse, but couldn’t determine which of the two possibilities was the right one. Another partial step in the right direction.

Both Kepler’s first and third laws, solidly empirical, were now accepted but his second law still caused problems. Around 1670 Nicholas Mercator provided a new solid proof of Kepler’s second law and it is about then that the majority of European astronomers finally accepted heliocentricity, although it was Kepler’s elliptical astronomy and not Copernicus’ model; the two models were regarded as competitors; also there was still a distinct lack of empirical proof for a heliocentric cosmos.

The developments in physics over the seventeenth century combined with the discovery of the physical reality of the atmosphere and Newton’s gravitation law finally solved the problems of why, if the earth is moving various disasters don’t occur: high winds, atmosphere blowing away etc., all of those arguments already listed by Ptolemaeus. The final empirical proofs of the annual orbit, Bradley and stellar aberration in 1727, and diurnal rotation, measuring the shape of the earth, around 1750, were delivered in the eighteenth century.

As can been seen by this very brief outline of the acceptance and confirmation of heliocentrism it was a process that took nearly two hundred years and proceeded in small increments so there was never anything that could possibly be described as a shock. As already stated above the concept that the ‘Copernican Revolution’ caused consternation or was a shock is a myth created sometime in the late eighteenth or early nineteenth century to explain something that never took place. One might even call it fake news!

Addendum: A lot of the themes touched on here are dealt with in greater detail in my The transition to heliocentricity: The Rough Guides series of blog posts


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