Conrad Gesner Day 2017

Anyone who pokes around long enough here at the Renaissance Mathematicus will realise that I have a fondness for polymaths. It is in fact interesting how many of the leading researcher in history were in fact polymaths. One of my favourites is the Swiss Renaissance physician, classicist, Hebraist, natural historian, bibliographer and mountaineer, Conrad Gesner.

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

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

Last year on the five hundredth anniversary of his birth I duly recycled my old Conrad Gesner post and discovered to my delight that I had a small but distinguished Gesner fan club on my Twitter stream. We spent a happy 24 plus hours tweeting and retweeting each other’s tributes to and admirations of the Swiss polymath. At some point in a flippant mood I suggested that we should celebrate an annual Conrad Gesner Day on, 26 March his birthday. The suggestion was taken up with enthusiasm by the others and so we parted.

A couple of months ago Gesner’s name came up again and I said I was serious about celebrating Conrad Gesner Day and all the others immediately responded that they were very much still up for it so it’s on. At the moment Biodiversity Heritage Library (BHL @BioDivLIbrary), Michelle Marshall (Historical SciArt (@HistSciArt), New York Academy of Medicine Center for History (@NYAMHistory), the rare book librarian at Smithsonian Libraries and I are committed to celebrating Conrad Gesner Day. What about you?

What is going to happen? That’s up to all those involved. You can post blog posts, post illustrations from Gesner’s works on Twitter, Facebook, Instagram, whatever, where ever. Post links to sites about Gesner. If you want to write something on Gesner but don’t have your own blog, contact me and I’ll post it here at the Renaissance Mathematicus. I will collect all the contributions and post a Whewell’s Gazette style links list here at RM on the Monday.

The aim is not to glorify Conrad Gesner but to raise peoples’ awareness of a fascinating and important figure in the history of Renaissance science. Join us! Make a contribution! We already have a hash tag .



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Filed under History of science, Renaissance Science

Not German but also not Polish

I recently wrote a post concerning the problems historians can and do face assigning a nationality to figures from the past that they are studying. In the history of science one of the most contentious figures in this sense was and apparently still is the Renaissance astronomer Nicolas Copernicus. The question of his nationality produced a massive war of words between Poland and Germany, both of whom claim him as their own, which started in the late eighteenth century and unfortunately still rumbles on today.

Nicolaus Copernicus portrait from Town Hall in Toruń - 1580 Source: Wikimedia Commons

Nicolaus Copernicus portrait from Town Hall in Toruń – 1580
Source: Wikimedia Commons

Today is Copernicus’ birthday (19 February 1473) and all over the Internet British and American posters are being, what they see as, scrupulously, politically correct and announcing today as the birthday of the Polish astronomer… All very well but it isn’t factually right.

Nicolas Copernicus was born in the city of Toruń, which is today in Poland but wasn’t at the time of his birth. The whole area in which Copernicus was born and in which he lived for all of his life, except when he was away studying at university, was highly dispute territory over which several wars were fought. Between 1454 and 1466 the Thirteen Years’ War was fought between the Prussian Confederation allied with the Crown of the Kingdom of Poland and the State of the Teutonic Knights. This war ended with the Second Peace of Toruń under which Toruń remained a free city now under the patronage of the Polish King.

As I pointed out in an earlier post Copernicus spent all of his adult life, after graduating from university, as a citizen of Ermland (Warmia), which was then an autonomous Prince Bishopric ruled by the Bishop of Frombork and the canons of the cathedral chapter, of which Copernicus was one.

All of this means that Copernicus was neither German nor Polish but was born a citizen of Toruń and died a citizen of Ermland. I realise that this doesn’t fit our neat modern concept of national states but that is the historical reality that people should learn to live with and to accept.




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

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

The vexed problem of nationality in the history of science

People seem to like/want/need heroes in sport, culture, politics, in fact in almost every area of life including the history of science. In particular for many people this desire for heroes is closely tied to feelings of national pride – a great Argentinian footballer, a great German composer, a great American boxer, a great English physicist and so on and so forth. This identification of people, whatever their field of activity, with their nationality is problematic for historians of science both geographically and historically

The earth did not come into existence about four and a half billion years ago with the borders of the national states stamped into its surface. In fact even within the one hundred to two hundred thousand years that Homo sapiens have occupied the earth the concept of a nation state is, in historical terms, a very recent one. Also within the time since nation states have existed their borders have not been static but have ebbed and flowed like the tide; states coming into and going out of existence down the centuries.

Brabant and Savoy, two important European states that existed in the High Middle Ages and Early Modern Period have long since disappeared into the mists of history. Looking at the modern map of Europe, The Netherlands only came into existence in the late sixteenth century, whilst its neighbour Belgium was created in 1815. Germany only really became a nation state following the fall of Hitler and the Nazis in 1945 and was for several decades two nation states, East and West, which only became finally united on 3 October 1990.

Duchy of Brabant 1477 Source Wikimedia Commons

Duchy of Brabant 1477
Source Wikimedia Commons

The early years of Wikipedia saw several epic battles over the nationality of scientific heroes, the most notorious being over Nicolaus Copernicus, which became so vitriolic that it was a news item on BBC Radio 4’s flagship news magazine, The Today Programme. The Poles and Germans carrying on a dispute that dates back to the late eighteenth century; a dispute that is totally barmy, as he was actually neither Polish nor German, as I explained in an earlier post. The nationality of the Islamic mathematician Muḥammad ibn Mūsā al-Khwārizmī, who gave algebra and the algorithm their names, is also disputed between Persia and Uzbekistan. The astronomer Johannes Hevelius, a native of Danzig, or should that be Gdańsk, is like Copernicus claimed by both Germany and Poland. The Jesuit mathematician, astronomer and physicist Ruđer Josip Bošković (English: Roger Joseph Boscovich) is claimed by Croatia, Serbia and Italy, although it should be noted he became a naturalised French citizen and the end of his life. Anther astronomer with dual nationality is the Italian Giovanni Domenico Cassini who ended his life as the Frenchman Jean-Dominique Cassini. Although it is debateable whether it is correct to call Cassini an Italian, as Italy only became a united national state in 1861, about one hundred and fifty years after his death

The latest case of, potentially, disputed nationality that caught my eye and generated this post occurred in an article on the BBC News website, The Irish novel that seduced the USSR, the story of the novel The Gadfly by Ethel Voynich. Don’t Panic! The Renaissance Mathematicus has not metamorphosed overnight into a blog for literature criticism, you might understand when I say that Ethel Voynich was born Ethel Lilian Boole the youngest of the five daughters of the mathematician and logician George Boole and his wife the proto-feminist and educationalist Mary Everest-Boole. What provoked this post was that the article describes Ethel Voynich as an Irish writer.

Ethel Lilian Voynich née Boole

Ethel Lilian Voynich née Boole

Ethel Lilian Boole was born 11 May 1864 in the city of Cork in the Irish province of Munster, so she is Irish, right? Well, maybe not. My eldest sister was born in Rangoon in Burma, so she is Burmese, right? Actually she isn’t, she was born British and has remained British all of her life. Likewise, my brother was born in Lahore, so he’s Pakistani, right. Once again no, he was born British and remained British up to his death two years ago. Both of them were born in what was then British India of British parents, although my mother like my sister was born in Rangoon, and so both of them were automatically British citizens. My bother’s potential nationality is made even more complex by the fact that when he was born Lahore was in India but is now in Pakistan.

Let’s take a closer look at Ethel Lilian. At the time of her birth Ireland was part of the United Kingdom of Britain and Ireland, a country ruled by a single government in Westminster, London. Her father, George Boole, was born in Lincoln and was thus English.

Georg Boole Source: Wikimedia Commons

Georg Boole
Source: Wikimedia Commons

Her mother Mary Everest, the niece of Georg Everest for whom the mountain is named, was born in Wickwar in Gloucestershire and so was also English, although her family is Welsh. The family name, by the way, is pronounced Eve-rest and not Ever-est.

Mary Everest Boole Source: Wikimedia Commons

Mary Everest Boole
Source: Wikimedia Commons

To complicate matters, George Boole died 8 December 1864 just seven months after Ethel Lilian’s birth and Mary immediately returned to England with her five daughters. Ethel Lilian grew up in England and never returned to Ireland and identified as English not Irish. Given her parentage it is doubtful whether she should be referred to as Irish at all, despite having been born in Cork.

It is even more of a stretch to call The Gadfly an Irish novel. Ethel Lilian travelled extensively throughout Europe, as an adult and the novel, which is set in Italy and features an English hero, was first published in New York and then London before being translated into Russian, whereupon it became a mega best seller in Russia. To call it an Irish novel purely because of Ethel Lilian’s birth and seven-month residency in Cork is in my opinion a bridge too far.

Cover of the first publication of E. L. Vojnich's novel «The Gadfly» Source: Wikimedia Commons

Cover of the first publication of E. L. Vojnich’s novel «The Gadfly»
Source: Wikimedia Commons

All five of Boole’s daughters led fascinating and historically significant lives. You can read a short account of Those Amazing Boole Girls on my friend Pat’s Blog or for a fuller account I heartily recommend Desmond MacHale’s excellent biography, The Life and Work of George Boole: A Prelude to the Digital Age. The family history is dealt with even more fully in Gerry Kennedy’s The Booles and the Hintons: Two Dynasties That Helped Shape the Modern World, which I haven’t read yet (it’s on the infinite reading list) but which has received excellent reviews.








Filed under History of science


When I dropped out of academia (for the second time in my life) in the early 1990s, because of serious (mental) health problems, I throttled back my life-long interest in the history of science, giving my energy instead to recovering my mental equilibrium. When, after a break of several years, I returned to an intensive engagement with the history of science, one of the first things I did was to take part in a seminar at the university on Copernicus’ De revolutionibus. This led me to the question, why was De revolutionibus published in Nürnberg? Regular readers will know that I live just down the road from Nürnberg, so this a fairly natural question for me to ask. My attempts to find an answer led to an in depth study of the life and work of Johannes Petreius, the printer publisher who published De revolutionibus and to the early history of the printed book, as Petreius stood in a direct line of descent from Gutenberg through his Basler relatives who had learnt the black art directly from its inventor.

The more general question of the influence of the printed book on the evolution of modern science led quite naturally to a deepened interest in the early history of scientific book publication in which Nürnberg again played a role through Regiomontanus the first printer publisher of scientific books.

Curiously Nürnberg was also the site of the first paper mill north of the Alps, paper being an essentially ingredient in mass production of printed books and this fact led to a strong interest in the history of paper making and to the materials that preceded paper as a medium for transmitting the written word.

Another seminar that I took part in at the university, following my return to the history of science, concerned the history of illustrations in scientific texts, which awakened my interest in the various methods of illustration reproduction and their histories. Another Nürnberger, Albrecht Dürer, played a significant role in that history.

Over the years I acquired a deep interest, and a modicum of knowledge of the histories of all the various aspects of recording knowledge in word and picture, so it was not surprising that my interest was drawn almost magnetically to a fairly recent new publication with the title, The Book: A Cover to Cover Exploration of the Most Powerful Object of Our Times. An interest made even stronger by the fact that the author of this tome is Keith Houston, the author of both the book Shady Characters: The Secret Life of Punctuation, Symbols & Other Typographical Marks, a serious candidate for ultimate geek bedtime reading, and of the blog of the same name. Unable to resist temptation I acquired a copy of The Book.


Having delved deeply into the subject over a number of years I expected to be entertained, Houston is a witty writer, but not really to learn much that was new. I was mistaken, even though I consider myself well informed on the topic I took away much that was new from Houston’s excellent study of the topic.

The Book is divided into four sections, The Page, The Text, Illustrations and Form. The first deals with the history of writing material from papyrus over parchment to paper and the progress from hand-made paper to modern industrial paper production. The second deals with methods of bringing writing onto that material starting with Babylonian cuneiform symbols impressed into clay tablets, outlining the history of ink and moving on to the history of moveable type printing. Once again covering the arc from the cradle of civilisation to the twentieth century. Part three does the same for pictures on the page. The final part deals with the forms that books have taken over the centuries from the papyrus roles to the codex and the various sizes and forms that the codex has adopted down the years. We also get a detailed history of the evolution of bookbinding.

Houston has researched his topic exceedingly well and delivers his cornucopia of information in a well-digested and easily accessible form for the reader, with a healthy portion of humour. One aspect of the book that appealed to me as a history of science myth buster is Houston’s use of multiple layers of historical story telling. For example, he takes a topic and tells his readers how its history was understood and presented in the nineteenth century. Then he explains how modern research showed this to be wrong and represents the history from this standpoint. Having gone into great detail he then explodes this version by showing why it can’t be true. I’m not going to go here into any great detail, as it would spoil the fun for future readers, and it really is fun, but Houston gives his readers a useful lesson in the evolution of the historiography of his subject.

One thing that has to be said is that The Book is beautifully produced with much obvious loving care for detail. It is printed with a very attractive typeface on lovely paper both of which make it a real pleasure to hold and to read. It comes bound in heavy light-grey carton boards joined together by dark read spinal binding tape. Its gatherings are, as befits a book about the history of the book, stitched and not glued. Throughout the book, starting with the cover, all of the bits and pieces that a book consists of are bracketed and labelled with their corrected technical terms. The book is beautifully illustrated, each illustration possessing an extensive explanatory text of its own. There are a helpful further reading list, extensive endnotes (as always I would have preferred footnotes) and an equally extensive index. Despite being just over 400 pages long, and being a high quality, beautifully produced, bound book it retails at a ridiculously low price. The publishers offer it at $29.95 but it can be had for less than twenty pounds, euro or dollar depending on your location.

If you have any interest in the history of the book as an object or the history of moveable type printing then I can only recommend acquiring a copy of Keith Houston’s wonderful book on the book.



Filed under Book Reviews, Early Scientific Publishing

Why Mathematicus?

“The Renaissance Mathematiwot?”

“Mathematicus, it’s the Latin root of the word mathematician.”

“Then why can’t you just write The Renaissance Mathematician instead of showing off and confusing people?”

“Because a mathematicus is not the same as a mathematician.”

“But you just said…”

“Words evolve over time and change their meanings, what we now understand as the occupational profile of a mathematician has some things in common with the occupational profile of a Renaissance mathematicus but an awful lot more that isn’t. I will attempt to explain.”

The word mathematician actually has its origins in the Greek word mathema, which literally meant ‘that which is learnt’, and came to mean knowledge in general or more specifically scientific knowledge or mathematical knowledge. In the Hellenistic period, when Latin became the lingua franca, so to speak, the knowledge most associated with the word mathematica was astrological knowledge. In fact the terms for the professors[1] of such knowledge, mathematicus and astrologus, were synonymous. This led to the famous historical error that St. Augustine rejected mathematics, whereas his notorious attack on the mathematici[2] was launched not against mathematicians, as we understand the term, but against astrologers.

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome Source: Wikimedia Commons

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome
Source: Wikimedia Commons

However St. Augustine lived in North Africa in the fourth century CE and we are concerned with the European Renaissance, which, for the purposes of this post we will define as being from roughly 1400 to 1650 CE.

The Renaissance was a period of strong revival for Greek astrology and the two hundred and fifty years that I have bracketed have been called the golden age of astrology and the principle occupation of our mathematicus is still very much the casting and interpretation of horoscopes. Mathematics had played a very minor role at the medieval universities but the Renaissance humanist universities of Northern Italy and Krakow in Poland introduced dedicated chairs for mathematics in the early fifteenth century, which were in fact chairs for astrology, whose occupants were expected to teach astrology to the medical students for their astro-medicine or as it was known iatro-mathematics. All Renaissance professors of mathematics down to and including Galileo were expected to and did teach astrology.

A Renaissance Horoscope Kepler's Horoskop für Wallenstein Source: Wikimedia Commons

A Renaissance Horoscope
Kepler’s Horoskop für Wallenstein
Source: Wikimedia Commons

Of course, to teach astrology they also had to practice and teach astronomy, which in turn required the basics of mathematics – arithmetic, geometry and trigonometry – which is what our mathematicus has in common with the modern mathematician. Throughout this period the terms Astrologus, astronomus and mathematicus – astrologer, astronomer and mathematician ­– were synonymous.

A Renaissance mathematicus was not just required to be an astronomer but to quantify and describe the entire cosmos making him a cosmographer i.e. a geographer and cartographer as well as astronomer. A Renaissance geographer/cartographer also covered much that we would now consider to be history, rather than geography.

The Renaissance mathematicus was also in general expected to produce the tools of his trade meaning conceiving, designing and manufacturing or having manufactured the mathematical instruments needed for astronomer, surveying and cartography. Many were not just cartographers but also globe makers.

Many Renaissance mathematici earned their living outside of the universities. Most of these worked at courts both secular and clerical. Here once again their primary function was usually court astrologer but they were expected to fulfil any functions considered to fall within the scope of the mathematical science much of which we would see as assignments for architects and/or engineers rather than mathematicians. Like their university colleagues they were also instrument makers a principle function being horologist, i.e. clock maker, which mostly meant the design and construction of sundials.

If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.

This very wide range of functions fulfilled by a Renaissance mathematicus leads to a common historiographical problem in the history of Renaissance mathematics, which I will explain with reference to one of my favourite Renaissance mathematici, Johannes Schöner.

Joan Schonerus Mathematicus Source: Wikimedia Commons

Joan Schonerus Mathematicus
Source: Wikimedia Commons

Schöner who was a school professor of mathematics for twenty years was an astrologer, astronomer, geographer, cartographer, instrument maker, globe maker, textbook author, and mathematical editor and like many other mathematici such as Peter Apian, Gemma Frisius, Oronce Fine and Gerard Mercator, he regarded all of his activities as different aspects or facets of one single discipline, mathematica. From the modern standpoint almost all of activities represent a separate discipline each of which has its own discipline historians, this means that our historical picture of Schöner is a very fragmented one.

Because he produced no original mathematics historians of mathematics tend to ignore him and although they should really be looking at how the discipline evolved in this period, many just spring over it. Historians of astronomy treat him as a minor figure, whilst ignoring his astrology although it was this that played the major role in his relationship to Rheticus and thus to the publication of Copernicus’ De revolutionibus. For historians of astrology, Schöner is a major figure in Renaissance astrology although a major study of his role and influence in the discipline still has to be written. Historians of geography tend to leave him to the historians of cartography, these whilst using the maps on his globes for their studies ignore his role in the history of globe making whilst doing so. For the historians of globe making, and yes it really is a separate discipline, Schöner is a central and highly significant figure as the founder of the long tradition of printed globe pairs but they don’t tend to look outside of their own discipline to see how his globe making fits together with his other activities. I’m still looking for a serious study of his activities as an instrument maker. There is also, as far as I know no real comprehensive study of his role as textbook author and editor, areas that tend to be the neglected stepchildren of the histories of science and technology. What is glaringly missing is a historiographical approach that treats the work of Schöner or of the Renaissance mathematici as an integrated coherent whole.

Western hemisphere of the Schöner globe from 1520. Source: Wikimedia Commons

Western hemisphere of the Schöner globe from 1520.
Source: Wikimedia Commons

The world of this blog is at its core the world of the Renaissance mathematici and thus we are the Renaissance Mathematicus and not the Renaissance Mathematician.

[1] That is professor in its original meaning donated somebody who claims to possessing a particular area of knowledge.

[2] Augustinus De Genesi ad Litteram,

Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant. II, xvii, 37


Filed under History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of science, History of Technology, Renaissance Science