The Man from Nowhere

This post has nothing to do with the history of science, so if you come here just for that, you don’t need to read this.

I just had an exchange on the Internet with an acquaintance, who knows that I’m British (at least according to my passport) but had forgotten that I live in Germany. He suggested I would pay for something in pounds sterling and I pointed out that it would be Euro for me. His response was that many of us live away from home: he’s an Irishman who lives in America. This exchange reminded me of a post that I started to write but never finished and inspired me to finish it.

Recently the UK’s prime minister Theresa May said, “If you believe you’re a citizen of the world you’re a citizen of nowhere”. My immediate response, as a nominal British citizen, was the title of this post, because I have, I think, every reason to consider myself a citizen of the world. I will explain.

My father’s family were lowland Scots but he was born and brought up in London, although his parents made sure that he stayed in touch with his Scottish roots. My mother’s family were Northern Irish protestants but she was born in Rangoon in Burma, a third generation colonialist in British India, and spent the first thirty plus years of her life living in Burma and Northern India. Her family were tea planters. My brother, the eldest child of the family, was born in Lahore, at the time part of India today in Pakistan. My eldest sister was, like my mother, born in Rangoon, in fact in the same hospital. My father served in the Royal Indian Army during WWII, which is how he met my mother. She was the matron of the hospital where he was treated for malaria. After the war he became a civil servant and they settled down to life in India. However in 47/48, with independence they moved back to Britain, to Derbyshire. My younger sister was born in Buxton. In 1951 they moved to North-East Essex and I, for my sins, was born in Clacton-on Sea, although my parents lived in an agricultural village about seven miles inland, where I spent the first fifteen years of my life.

I then spent two years at boarding school in Colchester, Britain’s oldest city (or so they claim); living in central London in the school holidays. Having been thrown out of my boarding school, thank god, I spent one year living in central London and going to school in Holland Park. Having acquired a ropy set of A-levels I trundled off to Cardiff in Wales, which would be my main base for the next ten years. Whilst based in Cardiff I had periods of living in Brussels in Belgium and in Malmö in Southern Sweden. I have now lived in Middle Franconia in Southern Germany for thirty-seven years. Are you still paying attention at the back there?

I have a younger half sister (we share a father), who like her mother is Dutch, although her mother was born in Java and spent a substantial part of her childhood in a Japanese concentration camp. My half sister also has three mother tongues having grown up in England, Holland and Columbia. My step mother (not my half-sister’s mother), who is an fantastic lady and one of my best friends, is English but spent part of her childhood in the Middle East and as a young woman married an Indian and lived in Northern India for several years. Expelled from Burma following the war my mother’s family all moved to Western Australia where they thrived and prospered. I sometimes have the feeling that I’m related to half of the population of Perth. My brother’s daughter, my eldest niece, married an American, who she met in Munich when they were both working for Siemens, and now lives in Florida with her two charming American daughters.

I have lived in five different European countries – England, Wales (and don’t make the mistake of thinking England and Wales are the same country), Belgium, Sweden and Germany. Although I was born there, I was always regarded as an incomer in the conservative, rural, North-East Essex community where I grew up and after my mother died, when I was fifteen, I became effectively rootless, a vagabond whose home was wherever his bed was. In later life I have found a home in Middle Franconia, Erlangen is my Heimat, a German word, which is not really translatable; it means much more than simply home. However my true home for the last ten years has been the Internet and the readers of my blogs, the people I follow on social media and who follow me and the people I communicate with through comment columns and email come literally from all over the world. A day in which I converse with people from Australia, India, North and South America and half the countries of Europe is a normal day in my current life.

Although I now call Erlangen my Heimat, I still identify with North-East Essex where I grew up and first found my way in the world. I identify with the London of the late 1960s where I discovered sex and drugs and rock’n’roll. I identify with Cardiff and the ten years of my life that did most to shape the person that I am today. I identify with Brussels where I learnt for the first time what it means to live is a foreign culture, although I had a strong inkling of this from my time working with Welsh language theatre companies. I identify with Malmö, where I discovered both the philosophy of mathematics and the philosophy of science and for the first time set myself the aim of becoming a historian and philosopher of science; an aim of which this blog is the end product. Being a historian of the subjects has also taught me that the evolution of mathematics, science, medicine and technology has never respected national, cultural, religious or language boundaries. I am drawn to Asia not only because it is where my mother came from but also because my father was a lecturer for art and archaeology of South-East Asia and I grew up as much on anecdotes of lands such as Viet Nam and Indonesia as any tales of European countries.

I am a historian of astronomy and all those who have looked up to the stars, rather than down to their feet, have always been awed by the vastness of space. On a cosmic scale we cling to the surface of a very small lump of rock, circling a comparatively small star, on the edge of a not particularly big galaxy of which there are a couple of zillion out there. For me national boundaries, counties, continents and whatever dividing lines people think up, and they are all of them artificial constructs, have very little substantive meaning. I am a citizen of the world and if that makes me a nowhere man then it’s a label that I wear with pride.

Theresa May’s comment, which sparked this mild tirade, has the stench of the parochial, racist tinged, xenophobia that is so typical of a certain strain of English thought. It is something that my truly cosmopolitan parents made me aware of, and also warned me about, from a very early age. It is an aspect of English society that I detest and reject with all my heart. My parent taught me to embrace the world and they taught me well. In my youth I was for many years first a Cub and then a Boy Scout, it was one of the few social activities for children in the village where I grew up. One of the Scout laws is (was?), ‘a scout is a brother to every other scout, no mater to what country, class or creed the other may belong’. I have tried to live by an extended version of that law, ‘a human is a sibling to every other human, no mater to what country, class or creed the other may belong. We’s all just humans baby!




Filed under Autobiographical

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

A Renaissance artist-engineer icon – Vitruvian Man

Leonardo da Vinci’s drawing of Vitruvian Man is one of the most well known graphic images in the world. Many people don’t even know the title I have used for the image and of those that do, many have no idea why it’s so called. Even less people are aware that the image is not unique or original to Leonardo, although his rendition is probably the most beautiful and most powerful, but is in fact an iconic concept in the work of Renaissance artist-engineers.

The origin of the Vitruvian Man is to be found in Vitruvius, De architectura (Ten Books of Architecture).[1] Vitruvius lived in ancient Rome in the first century BCE and his Ten Books of Architecture is the only known full treatise on architecture that we have from classical antiquity. Almost nothing is known about Vitruvius himself and even the full name that tradition has accredited him with, Marcus Vitruvius Pollio, is questionable the name Vitruvius being the only part that is certain. Although the book is nominally about architecture more than half of the text is about things we would not normally associate with a textbook on architecture such as astronomy, geography and natural philosophy to quote Tomas Noble Howe, himself quoting Frank Brown, “…the mission of Vitruvius is to present architecture as a liberal art, based on a Hellenistic belief of the unity of knowledge.”

It is against this background that we find the passages referencing the dimensions of the human body, the origins of the iconic diagram, in Book 3: Temples Chapter 1: First Principles of Symmetry.

  1. The composition of a temple is based on symmetry, whose principles architects should take the greatest care to master Symmetry derives from proportion, which is called analogia in Greek. Proportion is the mutual calibration of each element of the work and of the whole, from which the proportional system is achieved. No temple can have any compositional system without symmetry and proportion, unless, as it were, it has an exact system of correspondence to the likeness of a well-formed human being.


  1. For Nature composed the human body in such a way that the face, from the chin to the top of the forehead and the lowest roots of the hairline should be one-tenth [of the total height of the body]; the palm of the hand from the wrist to the tip of the middle finger should measure likewise; the head from the chin to the crown, one-eighth; from the top of the chest to the hairline including the base of the neck, one-sixth; from the centre of the chest to the crown of the had, one-fourth. Of the height of the face itself, one-third goes from the base of the chin to the lowermost part of the nostrils, another third from the base of the nostrils to the point between the eyebrows, from that point to the hairline, the forehead also measures one-third. The foot should be one-sixth the height, the cubit, one-fourth, the chest also one-fourth. The other limbs, as well, have their own commensurate proportions, which the famous ancient painters and sculptors employed to attain great and unending praise.


I have quoted theses passages in full to make it very clear that for Vitruvius the form of the human body is quite literally the mass of all things. Symmetry and proportion is everything and the human body is the model for this claim. In his next paragraph Vitruvius delivers up the construction plan for Vitruvian Man.

  1. Similarly, indeed, the elements of holy temples should have dimensions for each individual part that agree with the magnitude of the work. So, too, for example, the centre and midpoint of the human body is the navel. For if a person is imagined lying back with outstretched arms and feet within a circle whose centre is at the navel, the fingers and toes will trace the circumference of this circle as they move about. But to whatever extent a circular scheme may be present in the body, a square design may also be discerned there. For if we measure from the soles of the feet to the crown of the head, and this measurement is compared with that of the outstretched hands, one discovers that this breadth equals the height, just as in areas which have been squared off by use of the set square.


The illustrations are Thomas Noble Howe’s modern reconstructions but we have good reason to believe that manuscripts of Vitruvius’ work in antiquity would have had illustration.[2]

Given his unified approach to art, science, design, engineering and metaphysics it comes as no surprise that Vitruvius served as a major role model for the Renaissance artist-engineers and that his Ten Books of Architecture served them as a bible. We already find the Florentine artist Lorenzo Ghiberti (1378–1455), an acknowledged forerunner to the artist-engineers, quoting Vitruvius in his potted history of linear perspective; the humanist scholar Poggio Bracciolini having ‘rediscovered’ Vitruvius in 1406.

Vitruvian man emerged in the works of the so-called Sienese engineers. The first of these was Mariano di Jacopo (1382–1543) known as Taccola. Taccola an engineer produced two annotated manuscripts of drawings of machines De ingeneis (Concerning engines)

Machines, by Taccola, De ingeneis

and De machinis (Concerning machines).

Paddle boat system, by Taccola, De machinis (1449)

In his notes we find his rendition of Vitruvian Man, not an artistic one like Leonardo’s but the simple diagrammatic version of an engineer.

Taccola Vitruvian Man

Taccola was the major influence on a second Sienese engineer Francesco di Giorgio Martini (1493–1501), whose studies of machines are almost all based on those of Taccola.

Extract from a notebook of Francesco di Giorgio Martini, 1470


However unlike Taccola he was also a painter, a sculptor and a leading architect. His rendition of the Vitruvian Man is very simplistic

Trattato di architettura di Francesco di Giorgio Martini

He, however, went one stage further incorporating inscribed human bodies into the architectural drawings of his ‘temples’, the churches he designed.

Trattato di architettura di Francesco di Giorgio Martini

Trattato di architettura di Francesco di Giorgio Martini

Both Taccola and Francesco di Giorgio influenced Leonardo who processed manuscripts of the work of both men; his manuscript of di Giorgio being particularly heavily annotated.

Although Luca Pacioli (1445–1517) doesn’t include a version of the Vitruvian Man in his De divina proportioni (Venice, 1509), famously illustrated by Leonardo, the second part of the book Trattato dell’architettura (Treatise on Architecture) is a twenty chapter discussion of the theories of Vitruvius comparing the proportions of the human body to those of artificial structures.

Having considered the right arrangement of the human body, the ancients proportionedall their work, particularly the temples, in accordance with it. In the human body the discovered the two main figures without which it is impossible to achieve anything, namely the perfect circle and the square.

Luca Pacioli De divina proportione

Naturally the early printed editions of De architectura contain illustrations of the Vitruvian Man. The first printed and illustrated edition of De architecture edited by Italian architect and scholar, Fra. Giovanni Giocondo, in 1511 contained images for both square and circle:

The first Italian edition by Cesare Cesariano in 1521 also contains two images


Another edition from 1525 edited by Francesco Giorgi contains only one image of the circle.


The artist who spread the Italian concepts of linear perspective north of the Alps, Albrecht Dürer, was also obsessed with the idea of the perfect mathematical proportions of the human body and devoted a large part of his life to writing his magnum opus Vier Bücher von Menschlicher Proportion (Four Books on Human Proportion), published posthumously in 1528. Followed in 1532 by a Latin edition. Of interest is the fact that as he had almost completed his book he realised that the mathematics it contained was too difficult for the apprentice painters for whom he was writing so he wrote an introductory geometry book, Underweysung der Messung mit dem Zirkel und Richtscheyt (Instruction in Measurement with Compass and Straightedge). Dürer’s book does not contain a Vitruvian Man but contains many diagrams demonstrating the mathematical proportions of the human body.

Dürer Vier bücher von menschlicher Proportion

In the middle of the sixteenth century another Renaissance polymath, physician, astronomer, astrologer, mathematician and philosopher, Girolamo Cardano, wrote in his De subtilitate rerum (1552) that Vitruvius was one of the twelve persons who he supposes to have excelled all men in the force of genius and invention; and would not have scrupled to have given him the first place, if it could be imagined that he had delivered nothing but his own discoveries.

Since the ‘rediscovery’ of Leonardo in the eighteenth century his version of Vitruvian Man has been used, modified and parodied in a thousand different images, diagrams, adverts, poster and whatever. By a strange coincidence as I was preparing this post Monica Azzolini, Renaissance historian and Leonardo expert, posted two modern parodies of Leonardo’s Vitruvian Man on Facebook, which caught my fancy and I offer them for your amusement.


From the Uncyclopedia

 And of course a Ninja Turtle Leonardo Vitruvian Man

[1] All references to Vitruvius, Ten Books of Architecture are taken from the English translation edited by Ingrid D. Rowland (translator) and Thomas Noble Howe (illustrator), CUP, pb 2001

[2] On the subject of illustrations in scientific works in antiquity see: Alfred Stückelberger, Bild und Work: Das illustrierte Fachbuch in der antiken Naturwissenschaft, Medizin und Technik


Filed under Renaissance Science

Has The Renaissance Mathematicus gone over to the dark side?

As the ultimate anti-establishment, indie rock band, The Grateful Dead, was inducted into the Rock and Roll Hall of fame, lead guitarist, Jerry Garcia, commented something along the lines of, it’s like the neighbourhood whore, if she stands on the corner long enough then eventually she becomes part of the establishment. And so it has came to pass than your friendly neighbourhood indie, anti-establishment, arse kicking, history of science blogger, The Renaissance Mathematicus, got asked, no, not asked, invited to submit an article to the latest edition[1] of the British Society for the History of Science online journal Viewpoints! He, being the publicity whore that he is, putting aside all thoughts of tarnishing his brand or weakening his reputation accepted with alacrity. And so it is that you, dear readers, can peruse his words of wisdom in the latest edition of that honourable establishment publication. For those that brave of vicissitudes of this dubious blog at regular intervals there is nothing in the latest outpourings of the #histsci hooligan that will be new to you but there are, with certainty, many other good and worthy things to read in this excellent journal, so why don’t you just stroll on over and indulge in some first class history of science story telling.

[1] When I originally wrote this post it was the latest edition of Viewpoint but I couldn’t find a link so I never posted this. Now that I have found a link it’s still the latest issue but no longer dew fresh.


Filed under Autobiographical, History of science, Myths of Science

Something personal – Yevgeny Yevtushenko

Back in the 1970s I was for a time the manager (read general dogsbody) of the black box theatre space in the local arts centre. Early one morning we got asked if we could put on a poetry reading by the Russian poet Yevgeny Yevtushenko on the same evening, the performance would be advertised during the day on the local BBC radio and by word of mouth on the culture grapevine. The theatre was free so I had no objections, they would have been overruled if I had had any. So it was agreed that we would go ahead with this almost spontaneous event.

Yevgeny Yevtushenko

My preparations were not arduous, light the stage with some general background lighting and set up a couple of microphones. Come the afternoon and the great man appeared for a quick technical run through. As we met Yevgeny greeted me extremely warmly proclaiming, “You look just like my good friend Gary Snyder!” For those who don’t know, Gary Snyder is a Zen Buddhist Beat Poet and environmentalist who featured heavily in some of Jack Kerouac’s autobiographical novels. I was a big Kerouac and Gary Snyder fan and felt very chuffed by this warm greeting.

Come the evening the theatre was sold out and the poetry reading went without a hitch. Yevgeny would read, or better said perform one of his poems in Russian, he was a very expressive reader, and his lady translator, and bed partner, would then read her English translation. This was done with one exception; Yevgeny performed his own English translation of the poem The City of Yes and The City of No. An incredibly powerful performance.

Following the poetry reading the self appointed cultural elite of the city had organised a party to celebrate Yevgeny’s visit. I was grudgingly invited (you don’t invite the servants!), I suspect at Yevgeny’s insistence, and we all trooped off to the house of one of the literati. Now Yevgeny was not interested in being buttonholed by any of the literary groupies eager to have a conversation with the great poet, so he grabbed a glass of wine and proceeded to start an animated conversation with me about god and the world. And so the night continued, Yevgeny and I got wonderfully drunk and chewed the cud like long lost friends, whilst the literary groupies hovered, hoping to get at least a couple of words with the great man. When Yevgeny had drunk enough he made his excuses and left and I wended my way home, happily drunk, followed I suspect by the curses of the city’s self appointed cultural elite. That should have been the end of the story, one of many happy memories in a chaotic life full of weird turns and unexpected diversions, but…

Fast-forward forty years. In the small village where I live in Southern Germany one of my neighbours is a Russian lady (a nuclear submarine engineer, I kid you not!) who I got to know because we travelled into town on the same bus everyday. We became good friends and one day I discovered that she went to university with one of Yevgeny’s granddaughters and had often been in his apartment and knew him well. It is truly a small world as the cliché has it.

All of this means that I was saddened to learn this morning that Yevgeny Yevtushenko had died yesterday; another small element of my youth has gone.


Filed under Autobiographical

On an excursion

If you wish to read the latest words of wisdom, this time on the conception and invention of the reflecting telescope, then you will have to take an excursion to AEON magazine, where you can peruse:

How many great minds does it take to invent a telescope?

Isaac Newton’s reflecting telescope of 1671. Photo ©The Royal Society, London


Filed under History of Astronomy, History of Optics, History of Technology, Newton