Category Archives: Uncategorized

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


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Christmas Trilogy 2016 Part 1: Is Newtonian physics Newton’s physics?

Nature and nature’s laws lay hid in night;

God said “Let Newton be” and all was light.

Isaac Newton's Tomb in Westminster Abbey Photo: Klaus-Dieter Keller Source: Wikimedia Commons

Isaac Newton’s Tomb in Westminster Abbey
Photo: Klaus-Dieter Keller
Source: Wikimedia Commons

Alexander Pope’s epitaph sets the capstone on the myth of Newton’s achievements that had been under construction since the publication of the Principia in 1687. Newton had single-handedly delivered up the core of modern science – mechanics, astronomy/cosmology, optics with a side order of mathematics – all packed up and ready to go, just pay at the cash desk on your way out. We, of course, know (you do know don’t you?) that Pope’s claim is more than somewhat hyperbolic and that Newton’s achievements have, over the centuries since his death, been greatly exaggerated. But what about the mechanics? Surely that is something that Newton delivered up as a finished package in the Principia? We all learnt Newtonian physics at school, didn’t we, and that – the three laws of motion, the definition of force and the rest – is all straight out of the Principia, isn’t it? Newtonian physics is Newton’s physics, isn’t it? There is a rule in journalism/blogging that if the title of an article/post is in the form of a question then the answer is no. So Newtonian physics is not Newton’s physics, or is it? The answer is actually a qualified yes, Newtonian physics is Newton’s physics, but it’s very qualified.

Newton's own copy of his Principia, with hand-written corrections for the second edition Source: Wikimedia Commons

Newton’s own copy of his Principia, with hand-written corrections for the second edition
Source: Wikimedia Commons

The differences begin with the mathematics and this is important, after all Newton’s masterwork is The Mathematical Principles of Natural Philosophy with the emphasis very much on the mathematical. Newton wanted to differentiate his work, which he considered to be rigorously mathematical, from other versions of natural philosophy, in particular that of Descartes, which he saw as more speculatively philosophical. In this sense the Principia is a real change from much that went before and was rejected by some of a more philosophical and literary bent for exactly that reason. However Newton’s mathematics would prove a problem for any modern student learning Newtonian mechanics.

Our student would use calculus in his study of the mechanics writing his work either in Leibniz’s dx/dy notation or the more modern F’(x) = f(x) notation of the French mathematician, Lagrange (1736–1813). He won’t be using the dot notation developed by Newton and against which Babbage, Peacock, Herschel and the Analytical Society campaigned so hard at the beginning of the nineteenth century. In fact if our student turns to the Principia, he won’t find Newton’s dot notation calculus there either, as I explained in an earlier post Newton didn’t use calculus when writing the Principia, but did all of his mathematics with Euclidian geometry. This makes the Principia difficult to read for the modern reader and at times impenetrable. It should also be noted that although both Leibniz and Newton, independently of each other, codified a system of calculus – they didn’t invent it – at the end of the seventeenth century, they didn’t produce a completed system. A lot of the calculus that our student will be using was developed in the eighteenth century by such mathematicians as Pierre Varignon (1654–1722) in France and various Bernoullis as well as Leonard Euler (1707­1783) in Switzerland. The concept of limits that are so important to our modern student’s calculus proofs was first introduced by Bernard Bolzano (1781–1848), Augustin-Louis Cauchy (1789–1857) and above all Karl Theodor Wilhelm Weierstrass (1815–1897) in the nineteenth century.

Turning from the mathematics to the physics itself, although the core of what we now know as Newtonian mechanics can be found in the Principia, what we actually use/ teach today is actually an eighteenth-century synthesis of Newton’s work with elements taken from the works of Descartes and Leibniz; something our Isaac would definitely not have been very happy about, as he nursed a strong aversion to both of them.

A notable example of this synthesis concerns the relationship between mass, velocity and energy and was brought about one of the very few women to be involved in these developments in the eighteenth century, Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, the French aristocrat, lover of Voltaire and translator of the first French edition of the Principia.

In the frontispiece to Voltaire's book on Newton's philosophy, du Châtelet appears as Voltaire's muse, reflecting Newton's heavenly insights down to Voltaire. Source: Wikimedia Commons

In the frontispiece to Voltaire’s book on Newton’s philosophy, du Châtelet appears as Voltaire’s muse, reflecting Newton’s heavenly insights down to Voltaire.
Source: Wikimedia Commons

One should remember that mechanics doesn’t begin with Newton; Simon Stevin, Galileo Galilei, Giovanni Alfonso Borelli, René Descartes, Christiaan Huygens and others all produced works on mechanics before Newton and a lot of their work flowed into the Principia. One of the problems of mechanics discussed in the seventeenth century was the physics of elastic and inelastic collisions, sounds horribly technical but it’s the physics of billiard and snooker for example, which Descartes famously got wrong. Part of the problem is the value of the energy[1] imparted upon impact by an object of mass m travelling at a velocity v upon impact.

Newton believed that the solution was simply mass times velocity, mv and belief is the right term his explanation being surprisingly non-mathematical and rather religious. Leibniz, however, thought that the solution was mass times velocity squared, again with very little scientific justification. The support for the two theories was divided largely along nationalist line, the Germans siding with Leibniz and the British with Newton and it was the French Newtonian Émilie du Châtelet who settled the dispute in favour of Leibniz. Drawing on experimental results produced by the Dutch Newtonian, Willem Jacob ‘s Gravesande (1688–1742), she was able to demonstrate the impact energy is indeed mv2.

Willem Jacob 's Gravesande (1688-1745) Portrait by Hendrik van Limborch (1681-1759) Source: Wikimedia Commons

Willem Jacob ‘s Gravesande (1688-1745) Portrait by Hendrik van Limborch (1681-1759)
Source: Wikimedia Commons

The purpose of this brief excurse into eighteenth-century physics is intended to show that contrary to Pope’s epitaph not even the great Isaac Newton can illuminate a whole branch of science in one sweep. He added a strong beam of light to many beacons already ignited by others throughout the seventeenth century but even he left many corners in the shadows for other researchers to find and illuminate in their turn.





[1] The use of the term energy here is of course anachronistic


Filed under History of Physics, History of science, Myths of Science, Newton, Uncategorized

Never say Never!

In the past I’ve blogged about various terms and phrases that people writing about the history of science should refrain from using or better still ban from their vocabularies completely, such as ‘the greatest’ or ‘the father of’. Today I want to add another to the list­ – ‘you’ve never heard of’. This dubious claim almost always turns up, mostly in titles, in combination with other phrases that should be avoided such as ‘the most important’, ‘the greatest’, ‘the most significant’ or other such empty superlatives, as the writer never actually clears up greatest/most in relation to what. These titles are in end effect just click bait designed to ensnare the unwary reader into reading the proffered article or post, which is almost inevitably about some scientist about whom there have only been a couple of zillion similar articles/post in the not too distant past. The particular article that triggered this post was one written by a Steven Poole in the New York Magazine to advertise his forthcoming book, Rethink: The Surprising History of New Ideas, entitled Grace Hopper: The Most Important Computer Pioneer You’ve Never Heard Of.

Grace Hopper working on the Harvard Mark I Source: Harvard Gazette

Grace Hopper working on the Harvard Mark I
Source: Harvard Gazette

Now I’m prepared to bet big money that Grace Hopper is one of the most well known figures for people interested in the history of computing, programming, information theory etc, etc. If you Google her name you get over half a million hits in about one quarter of a second. Now I realise that this is not very many in comparison to #histsci big hitters like Einstein (104 million in 0.68 sec) or Galileo (44 million in 0.39 sec) but the history of computing is not really one of the glamour subject in the popular history of science. Beyond Alan Turing (somewhat more than 2 million in 0.49 sec) and Johnny von Neumann (nearly 5 million in 0.75 sec) none of the major players in the history of computing since the Second World War are exactly household names. John Mauchly, one half of the team, which designed the first really influential electronic computers, ENIAC & UNIVAC, only manages 220 thousand hits in 0,51 sec. His partner John Presper Eckert a meagre 133 thousand in 0.62 sec. John Backus the developer of FORTRAN, an equivalent role to Hopper’s work on COBOL, manages a halfway respectable 430 thousand in 0.49 sec.

Enough of the boring Google results, Grace Hopper has a major Wikipedia article that includes a long and very impressive list of the honours she has received[1], can be found in quite a few Youtube videos including an appearance on Letterman, has articles about her life and work in numerous major newspapers and magazines and biographies on almost every major history of science and history of technology biography site. She is also the subject of several book length biographies. If anybody who takes an interest in the history of computers and computing has not heard of Grace Hopper they have been living at the bottom of a murky pond with their head stuck under a weed covered boulder for the last ten years. Grace Hopper is computer royalty and a much honoured and celebrated figure in computing circles. However as things stand, that the man behind the computerised cash-desk in you local neighbourhood supermarket has probably never heard of Grace Hopper, unless he’s an unemployed computer science graduate, is not the criterion under which one should be writing history of technology articles.

Interestingly, as I said above, the titles that use this device, ‘you’ve never heard of’, are almost always written by people trying to jump on the band wagon of a supposedly neglected figure in #histSTM when the band wagon is coming round the block for at least the tenth time, a fact that makes more than a mockery of the title.

All of this of course raises the question, at least in my mind, as to just how well known figures in #histSTM should be, who should they be known to and what do we mean by well known? I often have the feeling that historians in general and historians of science in particular live in a sort of scholarly echo chamber. We think that just because some historical figure is significant to our own work or line of research that everybody else should be aware of and acknowledge that significance. We express this view within the community of our fellow historians and receive lots of echoes back supporting that view. Of course they should! Oh I totally agree with you, they deserve to be much better known. Etc, etc… Of course there are also those who give faint support whilst loudly disclaiming that their latest discovery in their field deserve to be even better known than your chosen candidate. However in general we all agree, in a heady torrent of unanimity, that the history of our whole discipline and its practitioners should be much, much better known, but should it? Dare I express the heretical thought that we exaggerate the importance of our endeavours for the general public, the masses, or whatever cliché you prefer for describing the vast majority of humanity who are not historians (of science).

This is a problem that is by no means unique to #histSTM and its subject matter but one that exists in all branches of history, even in the often over emphasised political history that still builds the core of school historical teaching. To take just one simple example, I am relatively certain that if I went out onto the high street of Erlangen, a town with an extremely high average level of education – it largely consists of a big university and the research and development centre of Siemens – and were to ask the people who or what is Fürst Metternich then the vast majority would not answer, an important 19th-century European diplomat who was largely responsible for shaping the map of modern Europe at the Congress of Vienna in 1815 but would instead say, oh it’s a popular brand of German sparkling wine. History, of whatever sort, is not very important to the majority of non-historians even in an age where historical novels are extremely popular.

I both hold and also attend semi-popular public history lectures, and not just of science, and the audiences are mostly fairly small, one hundred attendees would be a lot, and to a large extent consist of retirees, who have the time and the desire to indulge in a little light education to while away the last years of their lives. Rather like the rock and pop concerts by the dinosaurs of the sixties music boom very few young people find their way to such lectures being more concerned with living in the here and now.

The next problem is who really should be better known? #histSTM is littered with literally thousands of practitioners, who have contributed to its evolution over the last four thousand years. How many of those should an average educated person know about and which ones. The Greeks of course, says one classicist very firmly. Stop being so Eurocentric says another historian breaking a lance for the Chinese, whilst his colleague along the corridor wants you to turn your attention to India. Islamic science does not get the attention it deserves shouts the Middle Eastern historian whilst, the feminist, quite correctly, bemoans the lack of attention paid to women in #histSTM. The historian of chemistry points out that the history of physics gets far too much attention paid to it at the expense of the other scientific disciplines. A not unjustified claim. Meanwhile the historians of all the other multitude of scientific disciplines are lining up to get their fair share of limelight, whatever that might be.

I became a passionate fan of the histories of mathematics and science as a teenager and have devoted nearly fifty years of study to that passion. I have studied both widely and deeply and am blessed with an elephantine memory, a prerequisite I think for any historian, but I still constantly stumble across new scholars, who I don’t know and who on closer examination appear to me to deserve to be much better known. Five years ago I had never heard the name Stephen Hales, but after stumbling across him whilst following my interest in the history of gasses in the seventeenth and eighteenth centuries I began to delve deeper into his activities and discovered a man who made substantial contributions to a number of areas in chemistry and the life sciences and certainly, in my opinion deserves to be better known and so I wrote a blog post about him. Quite a few of my biographical blog post arise in this way.

Dr Stephen Hales FRS (1677-1761) Source

Dr Stephen Hales FRS (1677-1761)

How much #histSTM should people, that is non-historians of science, be expected to know and which bits of it? When should it be taught? In primary/grade schools? In high schools? Only at college level? And what should be taught? This post is more an attempt to clarify some question that have been rattling around in my head, in what passes for a brain, for quite sometime and I personally don’t really have any structured answers to my own questions. However I do sincerely believe that all people working within the field of #histSTM should seriously address these question, putting aside all personal prejudices in favour of their own research, and try to reach an honest answer.

Before I close I can’t help taking a pot shot at one statement in Poole’s article about another famous computer pioneer, Johnny von Neumann. Poole writes:

In 1944, Grace Hopper, a 37-year-old math Ph.D., joined the Navy as a lieutenant and was assigned to that lab. Her group also included the soon-to-be famous mathematician John von Neumann

In 1944 von Neumann was not soon-to-be famous but was already one of the most renowned mathematician in the world, which is why he was working on the Manhattan Project and came to Harvard in 1944 to run programs on the Mark I concerned with his work in Los Alamos. Grace Hoppers group did not include John von Neumann, she was an unknown associate professor from Vassar and von Neumann was a mathematical VIP.

John von Neumann and the Harvard Mark I Source

John von Neumann and the Harvard Mark I


[1] Whilst I have been writing this blog post it has been announced that Grace Hopper has been posthumously award the Presidential Medal of Freedom


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New lecturing attire

I have acquired a new T-shirt from the good folks at the History of Alchemy Podcasts, which will be worn with pride whilst lecturing on the history of alchemy (and other topics).

The elegant piece of attire can be witnessed below modelled by the lecturer in person on the market place in Erlangen this very Saturday.


Should you wish to also acquire such an elegant object of haut-couture and thereby support the excellent work of the History of Alchemy Podcasts then you can do so here. If you don’t already listen to the History of Alchemy Podcasts you should!

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Some rather strange history of maths

Scientific American has a guest blog post with the title: Mathematicians Are Overselling the Idea That “Math Is Everywhere, which argues in its subtitle: The mathematics that is most important to society is the province of the exceptional few—and that’s always been true. Now I’m not really interested in the substantial argument of the article but the author, Michael J. Barany, opens his piece with some historical comments that I find to be substantially wrong; a situation made worse by the fact that the author is a historian of mathematics.

Barany’s third paragraph starts as follows:

In the first agricultural societies in the cradle of civilization, math connected the heavens and the earth. Priests used astronomical calculations to mark the seasons and interpret divine will, and their special command of mathematics gave them power and privilege in their societies.

We are taking about the area loosely known as Babylon, although the names and culture changed over the millennia, and it is largely a myth, not only for this culture, that astronomical calculations were used to mark the seasons. The Babylonian astrologers certainly interpreted the divine will but they were civil servants who whilst certainly belonging to the upper echelons of society did not have much in the way of power or privilege. They were trained experts who did a job for which they got paid. If they did it well they lived a peaceful life and if they did it badly they risked an awful lot, including their lives.

Barany continues as follows:

As early economies grew larger and more complex, merchants and craftsmen incorporated more and more basic mathematics into their work, but for them mathematics was a trick of the trade rather than a public good. For millennia, advanced math remained the concern of the well-off, as either a philosophical pastime or a means to assert special authority.

It is certainly true that merchants and craftsmen in advanced societies – Babylon, Greece, Rome – used basic mathematics in their work but as these people provide the bedrock of their societies ­– food, housing etc. – I think it is safe to say that their maths based activities were in general for the public good. As for advanced maths, and here I restrict myself to European history, it appeared no earlier than 1500 BCE in Babylon and had disappeared again by the fourth century CE with the collapse of the Roman Empire, so we are talking about two millennia at the most. Also for a large part of that time the Romans, who were the dominant power of the period, didn’t really have much interest in advance maths at all.

With the rebirth of European learned culture in the High Middle ages we have a society that founded the European universities but, like the Romans, didn’t really care for advanced maths, which only really began to reappear in the fifteenth century. Barany’s next paragraph contains an inherent contradiction:

The first relatively widespread suggestions that anything beyond simple practical math ought to have a wider reach date to what historians call the Early Modern period, beginning around five centuries ago, when many of our modern social structures and institutions started to take shape. Just as Martin Luther and other early Protestants began to insist that Scripture should be available to the masses in their own languages, scientific writers like Welsh polymath Robert Recorde used the relatively new technology of the printing press to promote math for the people. Recorde’s 1543 English arithmetic textbook began with an argument that “no man can do any thing alone, and much less talk or bargain with another, but he shall still have to do with number” and that numbers’ uses were “unnumerable” (pun intended).

Barany says, “that anything beyond simple practical math ought to have a wider reach…” and then goes on to suggest that this was typified by Robert Recorde with his The Grounde of Artes from 1543. Recorde’s book is very basic arithmetic; it is an abbacus or reckoning book for teaching basic arithmetic and book keeping to apprentices. In other words it is a book of simple practical maths. Historically what makes Recorde’s book interesting is that it is the first such book written in English, whereas on the continent such books had been being produced in the vernacular as manuscripts and then later as printed books since the thirteenth century when Leonardo of Pisa produced his Libre Abbaci, the book that gave the genre its name. Abbaci comes from the Italian verb to calculate or to reckon.

What however led me to write this post is the beginning of Barany’s next paragraph:

Far more influential and representative of this period, however, was Recorde’s contemporary John Dee, who used his mathematical reputation to gain a powerful position advising Queen Elizabeth I. Dee hewed so closely to the idea of math as a secret and privileged kind of knowledge that his detractors accused him of conjuring and other occult practices.

Barany is contrasting Recorde, man of the people bringing mathematic to the masses in his opinion with Dee an elitist defender of mathematics as secret and privileged knowledge. This would be quite funny if it wasn’t contained in an essay in Scientific American. Let us examine the two founders of the so-called English School of Mathematics a little more closely.

Robert Recorde who obtained a doctorate in medicine from Cambridge University was in fact personal physician to both Edward VI and Queen Mary. He served as comptroller of the Bristol Mint and supervisor of the Dublin Mint both important high level government appointments. Dee acquired a BA at St John’s College Cambridge and became a fellow of Trinity College. He then travelled extensively on the continent studying in Leuven under Gemma Frisius. Shortly after his return to England he was thrown into to prison on suspicion of sedition against Queen Mary; a charge of which he was eventually cleared. Although consulted oft by Queen Elizabeth he never, as opposed to Recorde, managed to obtain an official court appointment.

On the mathematical side Recorde did indeed write and publish, in English, a series of four introductory mathematics textbooks establishing the so-called English School of Mathematics. Following Recorde’s death it was Dee who edited and published further editions of Recorde’s mathematics books. Dee, having studied under Gemma Frisius and Gerard Mercator, introduced modern cartography and globe making into Britain. He also taught navigation and cartography to the captains of the Muscovy Trading Company. In his home in Mortlake, Dee assembled the largest mathematics library in Europe, which functioned as a sort of open university for all who wished to come and study with him. His most important pupil was his foster son Thomas Digges who went on to become the most important English mathematical practitioner of the next generation. Dee also wrote the preface to the first English translation of Euclid’s Elements by Henry Billingsley. The preface is a brilliant tour de force surveying, in English, all the existing branches of mathematics. Somehow this is not the picture of a man, who hewed so closely to the idea of math as a secret and privileged kind of knowledge. Dee was an evangelising populariser and propagator of mathematics for everyman.

It is however Barany’s next segment that should leave any historian of science or mathematics totally gobsmacked and gasping for words. He writes:

In the seventeenth century’s Scientific Revolution, the new promoters of an experimental science that was (at least in principle) open to any observer were suspicious of mathematical arguments as inaccessible, tending to shut down diverse perspectives with a false sense of certainty.

What can I say? I hardly know where to begin. Let us just list the major seventeenth-century contributors to the so-called Scientific Revolution, which itself has been characterised as the mathematization of nature (my emphasis). Simon Stevin, Johannes Kepler, Galileo Galilei, René Descartes, Blaise Pascal, Christiaan Huygens and last but by no means least Isaac Newton. Every single one of them a mathematician, whose very substantial contributions to the so-called Scientific Revolution were all mathematical. I could also add an even longer list of not quite so well known mathematicians who contributed. The seventeenth century has also been characterised, by more than one historian of mathematics as the golden age of mathematics, producing as it did modern algebra, analytical geometry and calculus along with a whole raft full of other mathematical developments.

The only thing I can say in Barany’s defence is that he in apparently a history of modern, i.e. twentieth-century, mathematics. I would politely suggest that should he again venture somewhat deeper into the past that he first does a little more research.


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