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Measure for measure

The Brexit vote in the UK has produced a bizarre collection of desires of those Leavers eager to escape the poisonous grasp of the Brussels’ bureaucrats. At the top of their list is a return of the death penalty, a piece of errant stupidity that I shall leave largely uncommented here. Not far behind is the wish to abandon the metric system and to return to selling fruit and vegetables in pounds and ounces. This is particularly strange for a number of reasons. Firstly the UK went metric in 1965, six years before it joined the EU. Secondly EU regulations actually allows countries to use other systems of weights and measures parallel to the metric system, so there is nothing in EU law stopping greengrocers selling you a pound of carrots or bananas. Thirdly the country having gone metric in 1965, anybody in the UK under the age of about fifty is going to have a very hard time knowing what exactly pounds and ounces are.

Most readers of this blog will have now gathered that I have spent more than half my life living in Germany. Germany is of course one of the founding states of the EU and as such has been part of it from the very beginning in 1957. The various states that now constitute Germany also went metric at various points in the nineteenth century, the earliest in 1806-15, and the latest in 1868. However the Germans are a very pragmatic folk and I can and do buy my vegetables on the market place in Erlangen in pounds and half pounds. The Germans like most Europeans used variation of the predecessors to the so-called Imperial system of weights and measures and simple re-designated the pound (Pfund in German) to be half a kilo. The Imperial pound is actually approximately 454 grams and for practical purposes when buying potatoes or apples the 46-gram difference if negligible. Apparently the British are either too stupid or too inflexible to adopt such a pragmatic solution.

At the beginning of the month Tory dingbat and wanna be journalist Simon Heffer wrote an article in The Telegraph with the glorious title, Now that we are to be a sovereign nation again, we must bring back imperial units. I haven’t actually read it because one has to register in order to do so and I would rather drink bleach than register with the Torygraph. I shall also not link to the offending article, as it will only encourage them. Heffer charges into the fray thus:

But I know from my postbag that there is another infliction from the decades of our EU membership that many would like to be shot of, and that was the imposition of the metric system on large parts of our life. 

Consumer resistance ensured that our beer is still served in pints (though not in half-pint and pint bottles when bought in supermarkets: brewers please note), and that our signposts are still marked in miles.

As pointed out above it was not the EU who imposed the metric system on British lives but the British government before the UK joined the EU. According to EU regulations you can serve drinks in any quantities you like just as long as the glasses are calibrated, so keeping the traditional pint glasses and mugs in British pubs was never a problem. Alcohol is sold in Germany in a bewildering range of different size glasses depending on the local traditions. My beer drinking German friends (the Germans invented the stuff, you know) particularly like pints of beer because they say that they contain a mouthful more beer that a half litre glass. Sadly many bars in Franconia have gone over to selling beer in 0.4litre glasses to increase their profits, but I digress.

UK signposts are still marked in miles because the government could not afford the cost of replacing all of them when the UK went metric. Expediency not national pride was the motivation here.

Just before Heffer’s diatribe disappears behind the registration wall he spouts the following:

But we have been forced on to the Celsius temperature scale, which is less precise than Fahrenheit

When I read this statement I went back to check if the article had been published on 1 April, it hadn’t! Is the international scientific community aware of the fact that they have been conned into using an inaccurate temperature scale? (I know that scientist actually use the Kelvin temperature scale but it’s the same as the Celsius scale with a different zero point, so I assume by Heffer’s logic(!) it suffers from the same inaccuracy). Will all of those zillions of experiments and research programmes carried out using the Celsius/Kelvin scale have to be repeated with the accurate Fahrenheit scale? Does Simon Heffer actually get paid for writing this crap?


Anders Celcius Portrait by Olof Arenius Source: Wikimedia Commons


Daniel Gabriel Fahrenheit

Like myself on being confronted with the bring back imperial weights and measures madness lots of commentators pointed out that the UK went metric in 1965 but is this true? No, it isn’t! The UK actually went metric, by act of parliament over one hundred years earlier in 1864! The nineteenth century contains some pretty stirring history concerning the struggles between the metric and imperial systems and we will now take a brief look at them.

As soon as it became in someway necessary for humans to measure things in their environment it was fairly obvious that they would use parts of their body to do so. If we want a quick approximate measure of something we still pace it out or measure it with the length of an arm or the span of our fingers. So it was natural that parts of the body became the units of measurement, the foot, the forearm, the arm span and so on and so forth. This system of course suffers from the fact that we are not all the same size. My foot is shorter than yours; my forearm is longer than my partners. This led cultures with a strong central bureaucracy to develop standard feet and forearms. The various Fertile Crescent cultures developed sophisticated weights and measures systems, as did the Roman Empire and it is the latter that is the forefather of the imperial system. The Roman foot was between 29.5 and 30 cm, the pace was 2.5 feet and the Roman mile was 5000 feet. The word mile comes from the Latin for thousand, mille. The Roman military, which was very standardised, carried the Roman system of weights and measures to large parts of Europe thus establishing their standards overall.

With the collapse of the Roman Empire their standardised system of weights and measures slowly degenerated and whilst the names were retained their dimensions varied from district to district and from town to town. In the eighth and ninth centuries Karl der Große (that’s Charlemagne for the Brits) succeeded in uniting a substantial part of Europe under his rule. Although he was uneducated and illiterate he was a strong supporter of education and what passed at the time for science and amongst his reforms he introduced a unified system of weights and measures for his entire empire, another forefather of the imperial system. Things are looking quite grim for the anti-European supporters of the imperial system; it was born in Rome the birthplace of the EU and was reborn at the hands of a German, nothing very British here.

Karl’s attempt to impose a unified system of weights and measures on his empire was not a great success and soon after his death each district and town went back to their own local standards, if they ever left them. Throughout the Middle Ages and deep into the Early Modern Period traders had to live with the fact that a foot in Liège was not the same as a foot in Venice and a pound in Copenhagen was not a pound in Vienna.

This chaos provided work for the reckoning masters producing tables of conversions or actually doing the conversions for the traders, as well as running reckoning schools for the apprentice traders where they taught the arithmetic and algebra necessary to do the conversions, writing the textbooks for the tuition as well. The lack of unity in currency and mensuration in medieval Europe was a major driving force in the development algebra – the rule of three ruled supreme.

At the beginning of the seventeenth century Simon Stevin and Christoph Clavius introduced decimal fractions and the decimal point into European mathematics, necessary requirements for a decimal based metric system of mensuration. Already in the middle of the seventeenth century just such a system emerged and not from the dastardly French but from a true blue English man, who was an Anglican bishop to boot, polymath, science supporter, communicator, founding member of the Royal Society and one of its first secretaries, John Wilkins (1614–1672).

Greenhill, John, c.1649-1676; John Wilkins (1614-1672), Warden (1648-1659)

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Asked by the society to devise a universal standard of measure he devoted four pages of his monumental An Essay towards a Real Character and a Philosophical Language (1668) to the subject.


Title Page Source: Wikimedia Commons

He proposed a decimal system of measure based on a universal measure derived from nature for use between ‘learned men’ of various nations. He considered atmospheric pressure, the earth’s meridian and the pendulum as his universal measure, rejecting the first as susceptible to variation, the second as immeasurable and settled on the length of the second pendulum as his measure of length. Volume should be the cubic of length and weight a cubic standard of water. To all extents and purposes he proposed the metric system. His proposal fell, however, on deaf ears.


European units of length in the first third of the 19th century Part 1


European units of length in the first third of the 19th century Part 2

As science developed throughout the seventeenth and eighteenth century it became obvious that some sort of universal system of measurement was a necessity and various people in various countries addressed to subject. In 1790 the revolutionary Assemblée in France commissioned the Académie to investigate the topic. A committee consisting of Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and Nicolas de Condorcet, all leading scientific figures, recommended the adoption of a decimal metric system based on one ten-millionth of one quarter of the Earth’s circumference. The proposal was accepted by the Assemblée on 30 March 1791. Actually determining the length of one quarter of the Earth circumference turned into a major project fraught with difficulties, which I can’t do justice to here in an already overlong blog post, but if you are interested then read Ken Adler’s excellent The Measure of All Things: The Seven-Year Odyssey That Transformed The World.


Standard meter on the left of the entrance of the french Ministère de la Justice, Paris, France. Source: Wikimedia Commons

However Britain needed a unified system of mensuration, as they still had the problem that every town had different local standards for foot, pound etc. John Herschel the rising leading scientific figure wanted a new decimal imperial system based on the second pendulum but in the end parliament decide to stick with the old imperial system taking a physical yard housed in the Houses of Parliament as the standard for the whole of the UK. Unfortunately disaster struck. The Houses of Parliament burnt down in 1834 and with it the official standard yard. It took the scientists several years to re-establish the length of the official yard and meanwhile a large number were still advocating for the adoption of the metric system.


The informal public imperial measurement standards erected at the Royal Observatory, Greenwich, London, in the 19th century: 1 British yard, 2 feet, 1 foot, 6 inches, and 3 inches. The inexact monument was designed to permit rods of the correct measure to fit snugly into its pins at an ambient temperature of 62 °F (16.66 °C) Source: Wikimedia Commons

The debate now took a scurrile turn with the introduction of pyramidology! An English writer, John Taylor, developed the thesis that the Great Pyramid was constructed using the imperial system and that the imperial system was somehow divine. Strangely his ideas were adopted and championed by Charles Piazzi Smyth the Astronomer Royal of Scotland and even received tacit and indirect support from John Herschel, who rejected the pyramidology aspect but saw Taylor’s pyramid inch as the natural standard of length.

However wiser heads prevailed and the leaders of the British Victorian scientific community made major contributions to the expansion of the metric system towards the SI system, used internationally by scientists today. They applied political pressure and in 1864 the politicians capitulated and parliament passed the Metric (Weights and Measures) Act. This permitted the use of weights and measures in Britain. Further acts followed in 1867, 1868, 1871 and 1873 extending the permitted use of the metre. However the metric system could be used for scientific purposes but not for business. For that, Britain would have to wait another one hundred and one years!

Interestingly, parallel to the discussion about systems of mensuration in the nineteenth century, a discussing took place about the adoption of a single prime meridian for cartographical, navigational, and time purposes. In the end the two main contenders were the observatories in Paris and Greenwich. Naturally neither Britain nor France was prepared to concede to the other. To try and solve the stalemate it was suggested that in exchange for Paris accepting Greenwich as the prime meridian London should adopt the metric system of measurement. By the end of the nineteenth century both countries had nominally agreed to the deal without a formal commitment. Although France fulfilled their half of this deal sometime early in the twentieth century, Britain took until 1965 before they fulfilled their half.

Should the Leavers get their wish and the UK returns to the imperial system of measurement then they will be joining an elite group consisting of the USA, Myanmar and Liberia, the only countries in the world that don’t have the metric system as their national system of measurement for all purposes.


Filed under History of Mathematics, History of Navigation, History of science, Uncategorized

A birthday amongst the stars

Readers will probably be aware that as well as writing this blog I also hold, on a more or less regular basis, semi-popular, public lectures on the history of science. These lectures are as diverse as this blog and have been held in a wide variety of places. However I have, over the years, held more lectures in the Nürnberg Planetarium than anywhere else and last Thursday I was once again under the dome, this time not to hold a lecture but to help celebrate the ninetieth birthday of this august institution.

Before the twentieth century the term planetarium was a synonym for orrery, a mechanical model, which demonstrates the movements of the planets in the solar system. The beginnings of the planetarium in the modern sense was as Walther Bauersfeld, an engineer of the German optics company Zeiss, produced the plans for the construction of a planetarium projector based on earlier concepts. In 1923 the world’s first planetarium projector, the Zeiss Mark I, was demonstrated in the Zeiss factory in Jena and two months later on 21 October in the Deutschen Museum in Munich. Following further developments the first planetarium was opened in the Deutschen Museum on 7 May 1925.

Zeiss Mark I Planetarium Projector

Various German town and cities followed suit and the city council of Nürnberg signed a contract with Zeiss for a planetarium projector on 12 February 1925. The contract called for the city council to pay Zeiss 150, 000 Reichsmark ( a small fortune) in three instalments and 10% of the takings from the public shows. In a building on Rathenauplatz designed by Otto Ernst Schweizer the Nürnberg planetarium opened ninety years ago on 10 April 1927.

Original Nürnberg Planetarium

Fitted out with a new Zeiss Mark II projector the first of the so-called dumbbell design projectors with a sphere at each end for the north and south hemispheres. It was the world’s ninth planetarium.

Zeiss Mark II Planetarium Projector

From the very beginning the planetarium was born under a bad sign as the NSDAP (Nazi) city councillor, Julius Streicher, (notorious as the editor of the anti-Semitic weekly newspaper Der Stürmer) vehemently opposed the plans of the SPD council to build the planetarium. On 30 January 1933 the NSDAP seized power in Germany and the days of the planetarium were numbered. In November the planetarium director was ‘persuaded’ to recommend closing the planetarium and at the beginning of December it was closed. There were discussions about using the building for another purpose but Streicher, now Gauleiter (district commissioner) of Franconia was out for revenge. In March 1934 the planetarium was demolished on Streicher’s orders, with the argument that it looked too much like a synagogue! However the projector, and all the technical equipment, was rescued and put into storage.

Historischer Kunstbunker Entrance: There are guided tours

During the Second World War the projector was stored together with the art treasures of the city in the Historischer Kunstbunker (historical art bunker), a tunnel under the Castle of Nürnberg.

Following the war, in the 1950s, as Nürnberg was being rebuilt the city council decided to rebuild the planetarium and on 11 December 1961 it was reopened on the new site on the Plärrer, with an updated Zeiss Mark III. During the celebrations for the five hundredth anniversary of the death of Nicolaus Copernicus in 1973, whose De revolutionibus was printed and published in Nürnberg, the planetarium became the Nicolaus-Copernicus-Planetarium. In 1977 the Mark III projector was replaced with a Mark V, which is still in service and in 2010 the planetarium entered the twenty-first century with a digital Full-Dome projector.

Nicolaus-Copernicus-Planetarium am Plärrer in Nürnberg (2013)

The Zeiss Mark V Planetarium Projector in Nürnberg

Since the 1990’s the planetarium has been part of the City of Nürnberg’s adult education complex and alongside the planetarium programme it is used extensively for STEM lectures. I shall be holding my next lecture there on 28 November this year about Vannevar Bush, Claude Shannon, Robert H Goddard and William Shockley- Four Americans Who Shaped the Future (in German!) and if you’re in the area you’re welcome to come and throw peanuts.





Filed under Autobiographical, History of Astronomy, History of Optics, History of science, Uncategorized

Happy Birthday Conrad – #GesnerDay 2017

This is a rolling post collating all the contribution made today to celebrate the 501st birthday of the Swiss polymath Conrad Gesner.

Conrad’s birthday has ended and with it this rolling blog closes. We thank all of those who contributed to #GesnerDay 2017 and made it a great birthday party for Switzerland’s best loved polymath. We hope you will all be back at the same time next year for #GesnerDay 2018.


Conrad Gesner based on a painting by Tobias Stimmer (1539–1584)


Celebrating Gesner at the Smithsonian: Behind the scenes tour video

The Guardian: 16th century ‘zoological goldmine’ discovered – in pictures


Spiky blowfish Gessner had this image drawn in Frankfurt from a dried blowfish. Such dried fish decorated the shops of many European apothecaries at the time. Gessner used this drawing as the model for a printed full-page illustration in the fish volume (1558) of his Historia Animalium, but he made a subtle change. While a hook (from which the fish can be hung) pulls up the dried skin into a bump, that hook disappeared in the printed illustration. In this way he turned a portrait of an individual dried fish into a scientific representation of a fish species. Photograph: Special Collections of the University of Amsterdam

The Renaissance Mathematicus: Putting the lead in your pencil


The first ever published illustration of a pencil from Conrad Gesner’s De rerum fossilium


Dracones (from Gesner’s 1587 »Historiae Animalium Liber V, qui est de Serpentium natura«) h/t Patrick J Burns


Shark teeth depicted in C. Gesner´s “De Rerum fossilium…[]”. Such figures made it possible for other naturalists to compare their fossils with specimens of other collectors or hosted in private, non easily accessible, collections. However the quality of the used wood cuts was still poor and were soon replaced by copper engravings, with a higher reproduction quality.

The Renaissance Mathematicus: Friends

Fraumünster and the Münster close on the altarpiece of Hans Leu the Older (1460-1507) Where Conrad Gesner and Georg Joachim Rheticus went to school and became friends Source: Wikimedia Commons

University of Glasgow Library: Conrad Gesner: Illustrated Inventories with the use of Wonderful Woodcuts

Conrad Gesner ‘Tiger’ (Sp Coll Hunterian A.a.1.2)

Hyper allergic: The 16th-Century Fossil Book that First Depicted the Pencil


Frontispiece image from Conrad Gessner’s ‘De Rerum Fossilium Lapidum et Gemmarum Maxime, Figuris et Similitudinibus Liber’ (1565)

Jeff Ollerton’s Biodiversity Blog: Celebrating Conrad Gesner Day 2017

Gessner House Zürich
Photo: Jeff Ollerton 2008





Today is Conrad Gesner’s 501st birthday! Explore his publications in Biodiversity Heritage Library




Gesner’s (born 1516) “Historia Animalium”  is full of monsters. Why? Monsters Are Real


Scorpions (Order Scorpiones). Conrad Gesner, Historia Animalium, Liber 2 (1586) in @BioDivLibrary: h/t Historical SciArt  

NYAM Blog: Happy Bird-day, Conrad Gesner


SciHi Blog: Conrad Gessner’s Truly Renaissance Knowledge


The Pachyderm, from Conrad Gesner ‘Historiae animalium‘ (1551-58)



Happy B-day, Conrad Gesner! G’s #marginalia re bison in his copy of Icones 1560 #GesnerDay #histSTM @ZBZuerich h/t Michal Choptiany   


Peacock (Genus Pavo). Conrad Gesner, Historia Animalium, Liber 3 (1585) in @BioDivLibrary: h/t Historial SciArt


Gurnard (Dactylopterus volitans?). Conrad Gesner, Historia Animalium, Liber 2 (1586) in @BioDivLibrary h/t Historical SciArt   

Renaissance Quarterly: Ann Blair: The 2016 Josephine Waters Bennett Lecture: Humanism and Printing in the Work of Conrad Gessner


Anglerfish (Order Lophiiformes). Conrad Gesner, Historia Animalium, Liber 2 (1586) in @BioDivLibrary: h/t Historical SciArt  


Sea Monsters for #GesnerDay! Conrad Gesner, Historia Animalium, Liber 2 (1586) in @BioDivLibrary: h/t Historical SciArt  


The naturalist’s library. Conducted by Sir William Jardine: MEMOIR OF GESNER h/t William Ulate  


h/t William Ulate   


Until next year, #GesnerDay! Here’s your #MondayMotivationOwl! Explore more of Gesner’s works in @BioDivLibrary: h/t Historical SciArt





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Friends – #GesnerDay

It is very common in the history of science, particularly in popular presentations, to describe the life and work of scientists as if they existed in some sort of bubble cut off from the rest of humanity. This type of presentation is also a form of distortion of the history of science; scientists are almost always parts of a network of thinkers, researchers, critics all exchanging information and constantly reviewing, criticising and praising each other work. Sometimes scientists form deep friendships with other researchers that go beyond the scientific level into the personal. As my contribution to this year’s Conrad Gesner Day I would like to sketch one such personal friendship.

Georg Joachim Iserin was born 16 February 1514 in Feldkirch in present day Austria, the son of the town physician Georg Iserin and his wife Thomasina de Porris, a minor Italian aristocrat. In 1528 Georg Iserin was convicted of having stolen money and belonging from his patients and was executed. As part of his punishment the family name was banned and his fourteen year-old son became Georg Joachim de Porris. Following his father’s death the boy was sent to the school of the Fraumünster collegiate church in Zurich in 1528. It was here that he first made the acquaintance of Conrad Gesner.[1]

Fraumünster and the Münster Close on the altarpiece of Hans Leu the Older (1460-1507)
Source: Wikimedia Commons

Conrad Gesner was born on either 16 or 26 March 1516 in Zurich one of the eight children of the furrier Urs Gesner and his wife Agathe Frick. The family was destitute and when he was five years old Conrad went to live with his great-uncle Johannes Frick a chaplain, in whose garden he first developed his love of botany. Frick sent his nephew to the Fraumünster, school in 1526.

In their first mutual year at the cathedral school, Georg Joachim and Conrad both lived in the house of the teacher Oswald Myconius. Myconius (1488–1552), who was born Geißhüsler, was a friend of both Ulrich Zwingli, the Swiss Reformer, and the humanist scholar Erasmus of Rotterdam, who supposedly gave him the humanist name Myconius. Myconius was a significant religious and educational reformer and he exercised a strong influence on both Georg Joachim and Conrad. From Myconius Georg Joachim probably learnt his love of mathematics and Conrad got his grounding in Hebrew, subjects, which both of them would go on to teach as university professors later in life. The two young men only shared their school life for three years, but they would remain close friends for life.

Oswald Mycosis
Source: Wikimedia Commons

In 1532 Georg Joachim returned to Feldkirch where Achilles Pirmin Gasser, who later became town physician in Feldkirch, took over his education and sent him off to his own alma mater the University of Wittenberg, where he adopted the toponym Rheticus and became a protégé of Philip Melanchthon, who had been Gasser’s teacher. Conrad left for Strasbourg where he was to deepen his knowledge of Hebrew.

Rheticus graduated MA in 1536 and was appointed to the chair of lower mathematics (arithmetic and geometry) at Wittenberg by Melanchthon. As is well known in 1538 Rheticus took a sabbatical, armed with a letter of recommendation from Melanchthon, and visited Nürnberg, Tübingen and possibly Ingolstadt before returning to Feldkirch, from where he set out on his history making journey to Frombork to meet Nicolaus Copernicus. Here Rheticus persuaded Copernicus to finally publish his opus magnum, De revolutionibus, and took the manuscript to the printer-publisher Johannes Petreius in Nürnberg in 1542. Melanchthon now put pressure on Rheticus to take up his new appointment as professor of mathematics in Leipzig, which he duly did.

Conrad Gesner continued his studies at a series of European universities, at times also teaching, before he finally completed his doctorate in medicine at the University of Basel in 1541, when he returned to Zurich and became professor for the natural sciences on the Collegium Carolinum. In 1545 he published his Bibliotheca universalis, an attempt to catalogue all the books published since to invention of book printing. This was the start of his extraordinary career as a true polymath. It is from the Bibliotheca that we know of the shared school experiences of the young Conrad and Georg Joachim.

Collegium Carolinum on the Grossmünster in Zürich
Source: Wikimedia Commons

It can be assumed that the two young friends, who, like most of their contemporaries, where energetic letter writers, wrote to each other over the years, but if they did none of their correspondence has survived. Both went their way and established their academic careers and it was in 1547 that they first met up again but this time not as school comrades but as teacher and pupil.

In 1545 Rheticus set out on another long journey, this time to Italy where he visited the physician, mathematician and astrologer Girolamo Cardano. In 1547 Rheticus on his way back from Italy stopped in Lindau, where he appears to have suffered some sort of mental breakdown. When he finally recovered from his illness, which had lasted several months, instead of returning to Leipzig, where he was long overdue and was neglecting his duties, he decamped to Konstanz having first despatched a letter to Gesner in Zürich, which is no longer extant. After teaching mathematics and astronomy in Konstanz for several months he made his way to his old school friend in Zürich in December 1547.

In Zürich Rheticus took up the study of medicine as Gesner’s student. It was common practice for professors of mathematics to study for a doctorate in medicine parallel to their teaching duties. During the Renaissance astro-medicine was a dominant direction in school medicine and mathematicians were best equipped to cast and interpret the necessary horoscopes used in diagnosis and treatment. However they usually did this at their own universities and not hundreds of miles away at another university. The university in Leipzig demanded that he return but he wrote back in May that he was still suffering from his illness and did not return until September 1548. During the time that Rheticus was studying under Gesner, the latter published his Pandectarum, save Partitionum universalium (Zürich 1548), which contained a work by Rheticus on the division of the scales on a triquetrum an astronomical instrument.

Nicolaus Copernicus’ Triquetrum
Source: Wikimedia Commons

After Rheticus’ departure from Zürich the two friends did not meet again and, as already mentioned, any correspondence between the two of them has not survived. Gesner died in Zürich in 1565. Having fled the university of Leipzig in 1552 following a scandal, Rheticus wandered around Europe completing his medical studies before settling in Kraków, where he made a successful career as a physician and astrologer.

One wonders if those two unfortunate teenage boys, the one having just lost his father under traumatic circumstances and the other from a family so poor that they couldn’t afford to feed him, who became friends in Zürich in 1528 ever dreamed that they would both be famous in the history of science five hundred years into the future; Rheticus as the midwife of Copernicus’ heliocentric astronomy and Gesner as one of the founders of modern zoology.

[1] There are no known portraits of Georg Joachim Rheticus so out of a sense of fairness I have decided not to include any of Conrad Gesner in this post.

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Prelude to Conrad Gesner Day

Conrad Gessner memorial at the Old Botanical Garden, Zürich
Source: Wikimedia Commons

Tomorrow Friday 24 March 2017 Smithsonian Libraries (@SILibraries)will be holding a prelude to Sunday’s Conrad Gesner Day. There will be a live Facebook tour of Gesner’s Books held by the library at 1:30 pm ET (6:30 CET). #GesnerDay 


CHNDM Library Reading Room in the Carnegie Mansion

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The problem with Jonathan Jones and #histSTM

It cannot be said that I am a fan of Jonathan Jones The Guardian’s wanna be art critic but although I find most of his attempts at art criticism questionable at best, as a historian of science I am normal content to simply ignore him. However when he strays into the area of #histSTM I occasionally feel the desire to give him a good kicking if only a metaphorical one. In recent times he has twice committed the sin of publicly displaying his ignorance of #histSTM thereby provoking this post. In both cases Leonard da Vinci plays a central role in his transgressions, so I feel the need to make a general comment first. Many people are fascinated by Leonardo and some of them feel the need to express that fascination in public. These can be roughly divided into two categories, the first are experts who have seriously studied Leonardo and whose utterances are based on knowledge and informed analysis, examples of this first group are Matin Kemp the art historian and Monica Azzolini the Renaissance historian. The second category could be grouped together under the title Leonardo groupies and their utterances are mostly distinguished by lack of knowledge and often mind boggling stupidity. Jonathan Jones is definitely a Leonardo groupie.

Jones’ first foray into the world of #histSTM on 28 January with a piece entitled, The charisma droids: today’s robots and the artists who foresaw them, which is a review of the new major robot exhibition at the Science Museum. What he has to say about the exhibition doesn’t really interest me here but in the middle of his article we stumble across the following paragraph:

So it is oddly inevitable that one of the first recorded inventors of robots was Leonardo da Vinci, consummate artist and pioneering engineer [my emphasis]. Leonardo apparently made, or at least designed, a robot knight to amuse the court of Milan. It worked with pulleys and was capable of simple movements. Documents of this invention are frustratingly sparse, but there is a reliable eyewitness account of another of Leonardo’s automata. In 1515 he delighted Francois I, king of France, with a robot lion that walked forward towards the monarch, then released a bunch of lilies, the royal flower, from a panel that opened in its back.

Now I have no doubts that amongst his many other accomplishments Leonardo turned his amazingly fertile thoughts to the subject of automata, after all he, like his fellow Renaissance engineers, was a fan of Hero of Alexandria who wrote extensively about automata and also constructed them. Here we have the crux of the problem. Leonardo was not “one of the first recorded inventors of robots”. In fact by the time Leonardo came on the scene automata as a topic of discussion, speculation, legend and myth had already enjoyed a couple of thousand years of history. If Jones had taken the trouble to read Ellie Truitt’s (@MedievalRobots) excellent Medieval Robots: Mechanism, Magic, Nature and Art (University of Pennsylvania Press, 2015) he would have known just how wrong his claim was. However Jones is one of those who wish to perpetuate the myth that Leonardo is the source of everything. Actually one doesn’t even need to read Ms. Truitt’s wonderful tome, you can listen to her sketching the early history of automata on the first episode of Adam Rutherford’s documentary The Rise of the Robots on BBC Radio 4, also inspired by the Science Museums exhibition. The whole series is well worth a listen.

On 6 February Jones took his Leonardo fantasies to new heights in a piece, entitled Did the Mona Lisa have syphilis? Yes, seriously that is the title of his article. Retro-diagnosis in historical studies is a best a dodgy business and should, I think, be avoided. We have whole libraries of literature diagnosing Joan of Arc’s voices, Van Gough’s mental disorders and the causes of death of numerous historical figures. There are whole lists of figures from the history of science, including such notables as Newton and Einstein, who are considered by some, usually self declared, experts to have suffered from Asperger’s syndrome. All of these theories are at best half way founded speculations and all too oft wild ones. So why does Jonathan Jones think that the Mona Lisa had syphilis? He reveals his evidence already in the sub-title to his piece:

Lisa del Giocondo, the model for Leonardo’s painting, was recorded buying snail water – then considered a cur for the STD: It could be the secret to a painting haunted by the spectre of death.

That’s it folks don’t buy any snail water or Jonathan Jones will think that you have syphilis.

Let’s look at the detail of Jones’ amazingly revelatory discovery:

Yet, as it happens, a handful of documents have survived that give glimpses of Del Giocondo’s life. For instance, she is recorded in the ledger of a Florentine convent as buying snail water (acqua di chiocciole) from its apothecary.

Snail water? I remember finding it comical when I first read this. Beyond that, I accepted a bland suggestion that it was used as a cosmetic or for indigestion. In fact, this is nonsense. The main use of snail water in pre-modern medicine was, I have recently discovered, to combat sexually transmitted diseases, including syphilis.

So she bought some snail water from an apothecary, she was the female head of the household and there is absolutely no evidence that she acquired the snail water for herself. This is something that Jones admits but then casually brushes aside. Can’t let ugly doubts get in the way of such a wonderful theory. More importantly is the claim that “the main use of snail water snail water in pre-modern medicine was […] to combat sexually transmitted diseases, including syphilis” actually correct? Those in the know disagree. I reproduce for your entertainment the following exchange concerning the subject from Twitter.

Greg Jenner (@greg_jenner)

Hello, you may have read that the Mona Lisa had syphilis. This thread points out that is probably bollocks

 Dubious theory – the key evidence is her buying “snail water”, but this was used as a remedy for rashes, earaches, wounds, bad eyes, etc…

Greg Jenner added,

Seen this ‪@DrAlun ‪@DrJaninaRamirez ? What say you? I’ve seen snail water used in so many different Early Modern remedies

Alun Withey (@DrAlun)

I think it’s an ENORMOUS leap to that conclusion. Most commonly I’ve seen it for eye complaints.

Greg Jenner

‪@DrAlun @DrJaninaRamirez yeah, as I thought – and syphilis expert @monaob1 agrees

 Alun Withey

‪@greg_jenner @DrJaninaRamirez @monaob1 So, the burning question then, did the real Mona Lisa have sore eyes? It’s a game-changer!

Mona O’Brian (@monaob1)

‪@DrAlun @greg_jenner @DrJaninaRamirez interested to hear the art historical interpretation on the ‘unhealthy’ eyes comment!

Alun Withey

‪@monaob1 @greg_jenner @DrJaninaRamirez doesn’t JJ say in the article there’s a shadow around her eyes? Mystery solved. *mic drop*

Greg Jenner

‪@DrAlun @monaob1 @DrJaninaRamirez speaking as a man who recently had to buy eye moisturiser, eyes get tired with age? No disease needed

 Mona O’Brian

@greg_jenner Agreed! Also against the pinning of the disease on the New World, considering debates about the disease’s origin are ongoing

Jen Roberts (@jshermanroberts)

‪@greg_jenner I just wrote a blog post about snail water for @historecipes –common household cure for phlegmy complaints like consumption.

Tim Kimber (@Tim_Kimber)

‪@greg_jenner Doesn’t the definite article imply the painting, rather than the person? So they’re saying the painting had syphilis… right?

Minister for Moths (@GrahamMoonieD)

‪@greg_jenner but useless against enigmatic smiles

Interestingly around the same time an advert was doing the rounds on the Internet concerning the use of snail slime as a skin beauty treatment. You can read Jen Roberts highly informative blog post on the history of snail water on The Recipes Project, which includes a closing paragraph on modern snail facials!




Filed under History of medicine, History of Technology, Renaissance Science, Uncategorized

The widespread and persistent myth that it is easier to multiply and divide with Hindu-Arabic numerals than with Roman ones.

Last Sunday the eminent British historian of the twentieth century, Richard Evans, tweeted the following:

Let’s remember we use Arabic numerals – 1, 2, 3 etc. Try dividing MCMLXVI by XXXIX ­– Sir Richard Evans (@Richard Evans36)

There was no context to the tweet, a reply or whatever, so I can only assume that he was offering a defence of Islamic or Muslim culture against the widespread current attacks by drawing attention to the fact that we appropriated our number system along with much else from that culture. I would point out, as I have already done in my nineteenth-century style over long title, that one should call them Hindu-Arabic numerals, as although we appropriated them from the Islamic Empire, they in turn had appropriated them from the Indians, who created them.

As the title suggests, in his tweet Evans is actually guilty of perpetuating a widespread and very persistent myth concerning the comparative utility of the Hindu-Arabic number system and the Roman one when carrying out basic arithmetical calculations. Although I have taken Professor Evans’ tweet as incentive to write this post, I have thought about doing so on many occasions in the past when reading numerous similar comments. Before proving Professor Evans wrong I will make some general comments about the various types of number system that have been used historically.

Our Hindu-Arabic number system is a place-value decimal number system, which means that the numerals used take on different values depending on their position within a given number if I write the Number of the Beast, 666, the three sixes each represents a different value. The six on the far right stands for six times one, i.e. six, its immediate neighbour on the left stands for six time ten, i.e. sixty, and the six on the left stands for six times one hundred, i.e. six hundred, so our whole number is six hundred and sixty six. It is a decimal (i.e. ten) system going from right to left the first numeral is a multiple of 100 (for those who maths is a little rusty, anything to the power of zero is one), the second numeral is a multiple of 101, the third is a multiple of 102, the forth is a multiple of 103, the fifth is a multiple of 104, and so on and so fourth. If we have a decimal point the first numeral to the right of it is 10-1 (i.e. one tenth), the second 10-2 (i.e. one hundredth), the third 10-3 (i.e. one thousandth), and so on and so forth. This is a very powerful system of writing numbers because it comes out with just ten numerals, one to nine and zero making it very economical to write.

The Hindu-Arabic number system developed sometime in the early centuries CE and our first written account of it is from the Indian mathematician, Brahmagupta, in his Brāhmasphuṭasiddhānta (“Correctly Established Doctrine of Brahma“) written c. 628 CE. It came into Europe via Al-Khwārizmī’s treatise, On the Calculation with Hindu Numerals from 825 CE, which only survives in the 12th-century Latin translation, Algoritmi de numero Indorum. After its initial introduction into Europe in the high Middle Ages the Hindu-Arabic system was only really used on the universities to carry out computos, that is the calculation of the dates on which Easter falls. Various medieval scholars such as Robert Grosseteste John of Sacrobosco wrote elementary textbooks explaining the Hindu-Arabic system and how to use it. The system was reintroduced for trading purposes by Leonard of Pisa, who had learnt it trading with Arabs in Spain, in his book the Liber Abbaci in the thirteenth century but didn’t really take off until the introduction of double-entry bookkeeping in the fourteenth century.

The Hindu-Arabic system was not the earliest place-value number system. That honour goes to the Babylonians, who developed a place-value system about 1700 2100* BCE but was not a decimal system but a sexagesimal system, that is base sixty, so the first numeral is a multiple of 600, the second a multiple of 601, the third a multiple of 602, and so on and so fourth. Fractions work the same, sixtieths, three thousand six-hundredths (!), and so on and so fourth. Mathematically a base sixty system is in some senses superior to a base ten one. The Babylonian system suffered from the problem that it did not have distinct numerals but a stroke list system with two symbols, one for individual stroke and a second one for ten stokes:

Babylonian Numerals Source: Wikimedia Commons

Babylonian Numerals
Source: Wikimedia Commons

The Babylonian system also initially suffered from the fact that it possessed no zero. This meant that to take the simple case, apart from context there was no way of knowing if a single stroke stood for one, sixty, three thousand six hundred or whatever. The problem gets even more difficult for more complex numbers. Later the Babylonians developed a symbol for zero. However the Babylonian zero was just a placeholder and not a number as in the Hindu-Arabic system.

The Babylonian sexagesimal system is the reason why we have sixty minutes in an hour, sixty seconds in a minute, sixty minutes in a degree and so forth. It is not however, contrary to a widespread belief the reason for the three hundred and sixty degrees in a circle; this comes from the Egyptian solar years of twelve thirty day months projected on to the ecliptic, a division that the Babylonian then took over from the Egyptians.

The Greeks used letters for numbers. For this purpose the Greek alphabet was extended to twenty-seven letters. The first nine letters represented the numbers one to nine, the next nine the multiples of ten from ten to ninety and the last nine the hundreds from one hundred to nine hundred. For the thousands they started again with alpha, beta etc. but with a superscript subscript prime mark. So twice through the alphabet takes you to nine hundred thousand nine hundred and ninety-nine. If you need to go further you start at the beginning again with two subscript primes. Interestingly the Greek astronomers continued to use the Babylonian sexagesimal system, a tradition in the astronomy that continued in Europe down to the Renaissance.

We now turn to the Romans, who also have a simple stroke number system with a cancelled stroke forming an X as a bundle of ten strokes. The X halved horizontally through the middle gives a V for a bundle of five. As should be well known L stands for a bundle of fifty, C for a bundle of one hundred and M for a bundle of one thousand given us the well known Roman numerals. A lower symbol placed before a higher one reduces it by one, so LX is sixty but XL is forty. Of interest is the well-known IV instead of IIII for four was first introduced in the Middle Ages. The year of my birth 1951 becomes in Roman numerals MCMLI.

When compared with the Hindu-Arabic number system the Greek and Roman systems seem to be cumbersome and the implied sneer in Professor Evans’ tweet seems justified. However there are two important points that have to be taken into consideration before forming a judgement about the relative merits of the systems. Firstly up till the Early Modern period almost all arithmetic was carried out using a counting-board or abacus, which with its columns for the counters is basically a physical representation of a place value number system.

Rechentisch/Counting board (engraving probably from Strasbourg) Source: Wikimedia Commons

Rechentisch/Counting board (engraving probably from Strasbourg)
Source: Wikimedia Commons

The oldest surviving counting board dates back to about 300 BCE and they were still in use in the seventeenth century.

An early photograph of the Salamis Tablet, 1899. The original is marble and is held by the National Museum of Epigraphy, in Athens. Source: Wikimedia Commons

An early photograph of the Salamis Tablet, 1899. The original is marble and is held by the National Museum of Epigraphy, in Athens.
Source: Wikimedia Commons

A skilful counting-board operator can not only add and subtract but can also multiply and divide and even extract square roots using his board so he has no need to do written calculation. He just needed to record the final results. The Romans even had a small hand abacus or as we would say a pocket calculator. The words to calculate, calculus and calculator all come from the Latin calculi, which were the small pebbles used as counters on the counting board. In antiquity it was also common practice to create a counting-board in a sand tray by simply making parallel groves in the sand with ones fingers.

A reconstruction of a Roman hand abacus, made by the RGZ Museum in Mainz, 1977. The original is bronze and is held by the Bibliothèque nationale de France, in Paris. This example is, confusingly, missing many counter beads. Source: Wikimedia Commons

A reconstruction of a Roman hand abacus, made by the RGZ Museum in Mainz, 1977. The original is bronze and is held by the Bibliothèque nationale de France, in Paris. This example is, confusingly, missing many counter beads.
Source: Wikimedia Commons

Moving away from the counting-board to written calculations it would at first appear that Professor Evans is correct and that multiplication and division are both much simpler with our Hindu-Arabic number system than with the Roman one but this is because we are guilty of presentism. In order to do long multiplication or long division we use algorithms that most of us spent a long time learning, often rather painfully, in primary school and we assume that one would use the same algorithms to carry out the same tasks with Roman numerals, one wouldn’t. The algorithms that we use are by no means the only ones for use with the Hindu-Arabic number system and I wrote a blog post long ago explaining one that was in use in the early modern period. The post also contains links to the original post at Ptak Science books that provoked my post and to a blog with lots of different arithmetical algorithms. My friend Pat Belew also has an old blog post on the topic.

I’m now going to give a couple of simple examples of long multiplication and long division both in the Hindu-Arabic number system using algorithms I learnt I school and them the same examples using the correct algorithms for Roman numerals. You might be surprised at which is actually easier.


My example is 125×37



875 Here we have multiplied the top row by 7

3750 Here we have multiplied the top row by 3 and 10

4625 We now add our two partial results together to obtain our final result.

To carry out this multiplication we need to know our times table up to nine times nine.

Now we divide 4625 : 125

4625 : 125 = 37





First we guestimate how often 125 goes into 462 and guess three times and write down our three. We then multiply 125 by three and subtract the result from 462 giving us 87. We then “bring down” the 5 giving us 875 and once again guestimate how oft 125 goes into this, we guess seven times, write down our seven, multiply 125 by 7 and subtract the result from our 875 leaving zero. Thus our answer is, as we already knew 37. Not exactly the simplest process in the world.


How do we do the same with CXXV times XXXVII? The algorithm we use comes from the Papyrus Rhind an ancient Egyptian maths textbook dating from around 1650 BCE and is now known as halving and doubling because that is literally all one does. The Egyptian number system is basically the same as the Roman one, strokes and bundles, with different symbols. We set up our numbers in two columns. The left hand number is continually halved down to one, simple ignoring remainders of one and the right hand is continually doubled.


You now add the results from the right hand column leaving out those where the number on the left is even i.e. rows 2, 4 and 5. So we have CXXV + D + MMMM = MMMMDCXXV. All we need to carry out the multiplication is the ability to multiply and divide by two! Somewhat simpler than the same operation in the Hindu-Arabic number system!

Division works by an analogous algorithm. So now to divide 4625 by 125 or MMMMDCXXV by CXXV


We start with 1 on the left and 125 on the right and keep doubling both until we reach a number on the right that when doubled would be greater than MMMMDCXXV. We then add up those numbers on the left whose sum on the right equal MMMMDCXXV, i.e. rows 1, 3 and 6, giving us I+IIII+XXXII = XXXIIIIIII = XXXVII or 37.

Having explained the method we will now approach Professor Evan’s challenge


Adding rows 6, 3 and 2 on the right we get MCCXLVIII+CLVI+LXXVIII=MCML i.e. MCMLXVI less XVI so our result is XXXII+XVI+II = L remainder XVI

6 + 5 + 2 = MCCXLVIII+DCXXIIII+LXXVIII = 1950 + 16(reminder) is the correct value for the given example (MCMLXVI) Thanks to Lucas (see Comments!)

Now that wasn’t that hard was it?

Interestingly the ancient Egyptian halving and doubling algorithms for multiplication and division are, in somewhat modified form, how modern computers carry out these arithmetical operations.

* Added 13 February 2017: I have been criticised on Twitter, certainly correctly, by Eleanor Robson, a leading expert on Cuneiform mathematics, for what she calls a sloppy and outdated account of the sexagesimal number system.  For those who would like a more up to date and anything but sloppy account then I suggest they read Eleanor Robson’s (not cheap) Mathematics in Ancient IraqA Social History, Princeton University Press, 2008


Filed under Uncategorized