Category Archives: History of science

Hyping the history of mathematics

A while back the Internet was full of reports about a sensational discovery in the history of mathematics. Two researchers had apparently proved that a well know Babylonian cuneiform clay tablet (Plimpton 322), which contains a list of Pythagorean triples, is in fact a proof that the Babylonians had developed trigonometry one thousand years before the Greeks and it was even a superior and more accurate system than that of the Greeks. My first reaction was that the reports contained considerably more hype than substance, a reaction that was largely confirmed by an excellent blog post on the topic by Evelyn Lamb.

Plimpton 322, Babylonian tablet listing pythagorean triples
Source: Wikimedia Commons

This was followed by an equally excellent and equally deflating essay by Eduardo A Escobar an expert on cuneiform tablets. And so another hyped sensation is brought crashing down into the real world. Both put downs were endorsed by Eleanor Robson author of Mathematics in Ancient Iraq: A Social History and a leading expert on Babylonian mathematics.

Last week saw the next history of mathematics press feeding frenzy with the announcement by the Bodleian Library in Oxford that an Indian manuscript containing a symbol for zero had been re-dated using radio carbon dating and was now considered to be from the third to fourth centuries CE rather than the eight century CE, making it the earliest known Indian symbol for zero. This is of course an interesting and significant discovery in the history of mathematics but it doesn’t actually change our knowledge of that history in any really significant way. I will explain later, but first the hype in the various Internet reports.

A leaf from the Bakhshali Manuscript, showing off Indian mathematical genius. A zero symbol has been highlighted in the image.
Courtesy of the Bodleian Library


We start off with Richard Ovenden from Bodleian Libraries who announced, “The finding is of “vital importance” to the history of mathematics.”

Bodleian Library Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol ‘zero’

The Guardian leads off with an article by Marcus Du Sautoy: Much ado about nothing: ancient Indian text contains earliest zero symbol. Who in a video film and in the text of his article tells us, “This becomes the birth of the concept of zero in it’s own right and this is a total revolution that happens out of India.”

The Science Museum’s article Illuminating India: starring the oldest recorded origins of ‘zero’, the Bakhshali manuscript, basically repeats the Du Sautoy doctrine, makes the fundamental mistake of entitling their contribution, The First Zero, although in the text they return to the wording, “the world’s oldest recorded origin of the zero that we use today.”

The BBC joins the party with another clone of the basic article, Carbon dating reveals earliest origins of zero symbol.

Entrepreneur Cecile G Tamura summed up the implicit and sometimes explicit message of all these reports with the following tweet, One of the greatest conceptual breakthroughs in mathematics has been traced to the Bakhshali manuscript dating from the 3rd or 4th century at a period even earlier than we thought. To which I can only reply, has it?

All of the articles, which are all basically clones of the original announcement state quite clearly that this is a placeholder zero and not the number concept zero[1] and that there are earlier recorded symbols for placeholder zeros in both Babylonian and Mayan mathematics. Of course it was only in Indian mathematics that the place-holder zero developed into the number concept zero of which the earliest evidence can be found in Brahmagupta’s Brahmasphuṭasiddhanta from the seven century CE. However, this re-dating of the Bakhshali manuscript doesn’t actually bring us any closer to knowing when, why or how that conceptual shift, so important in the history of mathematics, took place. Does it in anyway actually change the history of the zero concept within the history of mathematics? No not really.

Historians of mathematics have known for a long time that the history of the zero concept within Indian culture doesn’t begin with Brahmagupta and that it was certainly preceded by a long complex prehistory. They are well aware of zero concepts in Sanskrit linguistics and in Hindu philosophy that stretch back well before the turn of the millennium. In fact it is exactly this linguistic and philosophical acceptance of ‘nothing’ that the historian assume enabled the Indian mathematicians to make the leap to the concept of a number signifying nothing, whereas the Greeks with their philosophical rejection of the void were unable to spring the gap. Having a new earliest symbol in Indian mathematics for zero as a placeholder, as opposed to the earlier recorded words for the concept of nothingness doesn’t actually change anything fundamental in our historical knowledge of the number concept of zero.

There is a small technical problem that should be mentioned in this context. Due to the fact that early Indian culture tended to write on perishable organic material, such as the bark used here, means that the chances of our ever discovering manuscripts documenting that oh so important conceptual leap are relatively low.

I’m afraid I must also take umbrage with another of Richard Ovenden’s claims in the original Bodleian report:

 Richard Ovenden, head of the Bodleian Library, said the results highlight a Western bias that has often seen the contributions of South Asian scholars being overlooked. “These surprising research results testify to the subcontinent’s rich and longstanding scientific tradition,” he said.

Whilst this claim might be true in other areas of #histSTM, as far as the history of the so-called Hindu-Arabic numbers system and the number concept zero are concerned it is totally bosh. Pierre-Simon, marquis de Laplace (1749-1827) wrote the following:

“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”

I started buying general books on the history of mathematics more than 45 years ago and now have nine such volumes all of which deal explicitly with the Indian development of the decimal place value number system and the invention of the number concept zero. I own two monographs dedicated solely to the history of the number concept zero. I have four volumes dedicated to the history of number systems all of which deal extensively with the immensely important Indian contributions. I also own two books that are entirely devoted to the history of Indian mathematics. Somehow I can’t see in the case of the massive Indian contribution to the development of number systems that a Western bias has here overseen the contributions of South Asian scholars.

This of course opens the question as to why this discovery was made public at this time and in this overblown manner? Maybe I’m being cynical but could it have something to do with the fact that this manuscript is going on display in a major Science Museum exhibition starting in October?

The hype that I have outlined here in the recent history of mathematics has unfortunately become the norm in all genres of history and in the historical sciences such as archaeology or palaeontology. New discoveries are not presented in a reasonable manner putting them correctly into the context of the state of the art research in the given field but are trumpeted out at a metaphorical 140 decibel claiming that this is a sensation, a discipline re-defining, an unbelievable, a unique, a choose your own hyperbolic superlative discovery. The context is, as above, very often misrepresented to make the new discovery seem more important, more significant, whatever. Everybody is struggling to make themselves heard above the clamour of all the other discovery announcements being made by the competition thereby creating a totally false impression of how academia works and how it progresses. Can we please turn down the volume, cut out the hype and present the results of academic research in history in a manner appropriate to it and not to the marketing of the latest Hollywood mega-bucks, blockbuster?

[1] For those who are not to sure about these terms, a placeholder zero just indicates an empty space in a place value number system, so you can distinguish between 11 and 101, where here the zero is a placeholder. A number concept zero also fulfils the same function but beyond this is a number in its own right. You can perform the arithmetical operations of addition, subtraction and multiplication with it. However, as we all learnt at school (didn’t we!) you can’t divide by zero; division by zero is not defined.



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

The Great Man paradox – A coda: biographies

This is a follow up to my last post that was inspired by an interesting discussion on Twitter and by the comment on that post by Paul Engle, author of the excellent Conciatore: The Life and Times of 17th Century Glassmaker Antonio Neri.

It is clear to me that biographies, particular popular ones, play a very central roll in the creation of the great men and lone genius myths. Now don’t misunderstand me I am not condemning #histSTM biographies in general; I have one and a half metres of such biographies on my bookshelves and have consumed many, many more that I don’t own. What I am criticising is the way that many such biographies are written and presented and I am going to make some suggestions, with examples, how, in my opinion such biographies should be written in order to avoid falling into the great man and lone genius traps.

The problem as I see it is produced by short, single volume, popular biographies of #histSTM figures or the even shorter portraits printed in newspapers and magazines. Here the title figure is presented with as much emphasis as possible on the uniqueness, epoch defining, and world-moving importance of their contribution to the history of science, technology or medicine. Given the brevity and desired readability of such works the context in which the subject worked is reduced to a minimum and any imperfections in their efforts are often conveniently left out. In order to achieve maximum return on their investment publishers then hype the book in their advertising, in the choice of title and/or subtitle and in the cover blurbs. A good fairly recent example of this was the subtitle of David Loves Kepler biography, How One Man Revolutionised Astronomy, about which I wrote a scathing blog post.

The authors of such works, rarely themselves historian of science, also tend to ignore the painfully won knowledge of historians and prefer to repeat ad nauseam the well worn myths handed down by the generations – Newton and the apple, Galileo and the Tower of Pisa and so on and so forth.

#histSTM biography does not have to be like this. Individual biographies can be historically accurate, can include the necessary context, and can illuminate the failings and errors of their subjects. Good examples of this are Westfall’s Newton biography Never at Rest and Abraham Pais’ Einstein biography Subtle is the Lord. Unfortunately these are doorstep size, scholarly works that tend to scare off the non-professional reader. Are there popular #histSTM works that surmount this problem? I think there are and I think the solution lies in the multi-biography and the theme-orientated books with biographies.

A good example of the first is Laura J Snyder’s The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World. Despite the hype in the subtitle this book embeds its four principal biographies in a deep sea of context and because all four of them were polymaths, manages to give a very wide picture of Victorian science in the first half of the nineteenth century.

Another good example is Jenny Uglow’s The Lunar Men: The Friends Who made the Future, once again a terrible subtitle, but with its even larger cast of central characters and even wider spectrum of science and technology delivered by them we get a true panorama of science and technology in the eighteenth and nineteenth centuries. Neither book has any lone geniuses and far too many scrambling for attention for any of them to fit the great man schema.

Two good examples of the second type are both by the same author, Renaissance Mathematicus friend and Twitter sparring partner, Matthew the Mancunian Maggot Man, aka Matthew Cobb. Both his books, The Egg and Sperm Race: The Seventeenth Century Scientists Who Unravelled the Secrets of Sex, Life and Growth

and Life’s Greatest Secret: The Race to Crack the Genetic Code

deal with the evolution of scientific concepts over a relatively long time span. Both books contain accurate portraits of the scientists involved complete with all of their failings but the emphasis is on the development of the science not on the developers. Here, once again, with both books having a ‘cast of millions’ there is no place for lone geniuses or great men.

These, in my opinion, are the types of books that we should be recommending, quoting and even buying for friends and relatives not the single volume, one central figure biographies. If more such books formed the basis of peoples knowledge of #histSTM then the myths of the lone genius and the great man might actually begin to fade out and with luck over time disappear but sadly I don’t think it is going to happen any day soon.

Having mentioned it at the beginning I should say something about Paul Engle’s Conciatore.

This is a single volume, one central figure biography of the seventeenth-century glassmaker Antonio Neri, who was the first man to write and publish a book revealing the secrets of glassmaking. His revealing of the trade secrets of a craft marks a major turning point in the history of technology. Up till the seventeenth century trade secrets were just that, secret with severe punishment for those who dared to reveal them, including death. Later in the century Joseph Moxon would follow Neri’s example publishing a whole series of books revealing the secrets of a whole range of trades including the first ever textbook on book printing his Mechanical Exercises or the Doctrine of Handy-Works. Paul’s book is a biography of Neri but because of why he is writing about Neri it is more a history of glassmaking and so sits amongst my history of technology books and not with my collection of #histSTM biographies. Here the context takes precedence over the individual, another example of how to write a productive biography and a highly recommended one at that.





Filed under Book Reviews, History of science, Myths of Science

School days

It is the middle of August and also the middle of what in German is known as Saure-Gurken-Zeit, in English as the silly season and in American as the dog days. It’s that time when parliaments are in recess, the politicians on holiday and the press is full of silly man bites dog stories. Even the history of science community is in a sort of half sleep with little happening and many of its members conspicuous by their absence. This being the case I though I would write a somewhat frivolous post this week before I too disappear off on holiday or a gathering of the clan in the beautiful city of Bath to be more precise.

It is common practice for schools to boast about the famous politicians, sports persons and show business celebrities who once, as snotty nosed kids, ran screaming through their corridors but what about the scientists? Which notable or significant scientist got their education at the pedagogical institution where you acquired the ability to write grammatical sentences and to find the derivatives of simple trigonometrical functions? To start the ball rolling I shall tell you of my historical scientific school chums and I hope you will tell me of yours in the comments.

I will admit to having an advantage as the grammar school that I attended has a somewhat more than eight hundred year history giving them lots of time to have educated one or other scientific luminary. From September 1963 till July 1969 I was a pupil of Colchester Royal Grammar School (CRGS) for boys, one of England’s most elite state schools; the first four years as a day boy, the last to as a boarder. Founded at the beginning of the thirteenth century, 1206 to be precise, and adorned with not one but two royal charters, Henry VIII (1539) and Elizabeth I (1584), it has boasted one of the highest Oxbridge entrance rates and best A-level averages almost every year since the WWII. It would be very surprising if this august educational institution had not thrown up a notable scientist over the centuries and in fact it can boast at least three.

School House CRGS pre-1908. The first floor window to the left of the main entrance in the middle was my bedroom for two years.
Source Wikimedia Commons

CRGS’s first and possibly most famous scientist (if you’ll excuse the anachronistic use of the term) was William Gilbert (1544–1603). Born in Colchester he followed his time at the school by becoming one of those Oxbridge statistics in 1558, St. John’s College Cambridge to be precise, where he graduated BA in 1561, MA in 1564 and MD in 1569. He moved to London where he followed a successful medical career. Elected a Fellow of the Royal College of Physicians he became their president in 1600. He became personal physician to Elizabeth I in 1601 and to James IV and I and 1603 the year of his death.

William Gilbert (1544–1603) artist unknown.
Source: Wellcome Library via Wikimedia Commons

Gilbert is of course most famous for his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth) published in London in 1600, regarded as one of the first ‘modern’ science books. This legendary scientific publication was much admired in its time and exercised a great influence on the development of experimental physics in the first half of the seventeenth century. Galileo praised it but thought it had too little mathematics and Kepler based his theory of a planetary force holding/driving the planets in their orbits on a magnetic monopole theory derived from Gilbert’s book. Based on his false belief that a terrella (a spherical magnet) revolves on its axis and his correct assumption that the earth is a large spherical magnet, Gilbert hypothesised a diurnal rotation for the earth. His theory had a major influence on the acceptance of a helio-geocentric system with diurnal rotation (as opposed to one without) in the first half of the seventeenth century.

There is a certain irony in the fact that although Gilbert is thought to have attended CRGS, as his name is attached to another school in Colchester, The Gilberd School. Gilberd is an alternative spelling of the family name.

We fast-forward almost a century to CRGS’s next scientific luminary, Francis Hauksbee (1660-1730). Not as famous as Gilbert, Hauksbee is still a notable figure in the history of science. Also a born Colcestrian, Hauksbee original apprenticed as a draper to his older brother in 1678 but at some point he became an assistant to Isaac Newton. In 1703 he became Robert Hooke’s successor as curator, experimentalist and instrument maker at the Royal Society.

From 1705 onwards he concentrated his experimental efforts on the phenomenon of electricity, a word coined by Gilbert in his De Magnete, publishing his investigations in his Physico-Mechanical Experiments on Various Subjects in 1709. In 1708 he independently discovered Charles’s law of gasses. Being something of an unsung hero of science it is fitting that in 2009 the Royal Society created the Hauksbee Awards to recognise “the unsung heroes of science, technology, engineering and maths for their work and commitment.”

We now spring into the nineteenth century to a scientist who whilst probably not as well known as Gilbert was truly one of the giants of science in his time, George Biddle Airy (1801– 1892).

George Biddell Airy (1801-1892)
John Collier / 1883
Source: Wikimedia Commons

Born in Alnwick in Northumberland he attended CRGS after an elementary school in Hereford. Like Gilbert he went up to Cambridge University, in his case Trinity College, in 1819. He graduated senior wrangler in in 1823, became a fellow of Trinity in 1824 and became Lucasian professor of mathematics, Newton’s chair, in 1826. He moved to the Plumian chair of astronomy in 1828 and was appointed director of the new Cambridge observatory. The list of Airy’s appointments and scientific achievements is too long for this light summer post – he published 518(!) scientific papers in his long live – but he was most notably Astronomer Royal from 1835 until his retirement in 1881.

George Biddell Airy caricatured by Ape in Vanity Fair Nov 1875
Source: Wikimedia Commons

As you can see CRGS can boast a trio of notable scientist in its long history, what about your alma mater? I do have to admit that I was expelled from CRGS in 1969 and finished my schooling at Holland Park Comprehensive in the school year 69–70. Much younger than CRGS, Holland Park was in my time as famous as the older establishment, as the flag ship educational establishment in the Labour government’s scheme to turn the English school system into a comprehensive one. I must admit that I know of no famous scientists who have emerged from Holland Park and my own memories of my one year there are largely of getting stoned and dropping acid; come on it was the late 60s and Notting Hill Gate!


Filed under Autobiographical, History of Astronomy, History of Physics, History of science

The House of Blaeu vs.The House of Hondius – The Battle of the Globes and Atlases

There is a South to North trajectory in the evolution of the modern mathematical cartography in Europe over the two hundred years between fourteen hundred and sixteen hundred. Ptolemaic mathematical cartography re-entered Europe in Northern Italy with the first translation into Latin of his Geographia by Jacobus Angulus in 1406. Following this the first modern first modern cartographers, including Paolo dal Pozzo Toscanelli, were also situated in Northern Italy. By the middle of the fifteenth century the main centre of cartographical activity had moved north to Vienna and was centred around Kloster-Neuburg and the University with its First Viennese School of Mathematics, Georg von Peuerbach and Johannes Regiomontanus. Towards the end of the century printed editions of Ptolemaeus’ work began to appear both north and south of the Alps. The beginning of the sixteenth century saw the main centres of cartographic development in the Southern German sphere. Two principle schools are identifiable, the Nürnberg-Vienna school, whose main figures are Johannes Stabius, Peter Apian and Johannes Schöner, and the South-Western school with Waldseemüller and Ringmann in Saint-Dié-des-Vosges and Sebastian Münster in Basel. Again by the middle of the century the centre had once again moved northwards to Leuven and the Flemish school founded by Gemma Frisius and including the two great atlas makers Abraham Ortelius and Gerard Mercator. At the start of the seventeenth century the final step northwards had been taken and the new state of The United Provinces (The Netherlands) had taken the lead in modern cartography. This final step is the subject of this post.

Willem Janszoon Blaeu was born into a prosperous herring trading family in Alkmaar or Uitgeest in 1471. As would have been expected he was sent at an early age to Amsterdam to learn the family trade but it did not appeal to him and he worked instead as a carpenter and clerk in the office of his cousin. In late 1595 his life took a radical turn when he travelled to Hven to study astronomy under Tycho Brahe. It is not known what level of foreknowledge Blaeu took to Hven with him but he spent six months there studiously learning astronomy, instrument making, geodesy and cartography with Tycho and his staff. When he started his observing marathon Tycho had had a large brass globe constructed on which he, over the years, engraved the positions of all the stars that he had measured. Blaeu was given permission to transfer this data to a globe of his own. In 1596 he returned to Alkmaar and his wife Maertgen Cornilisdochter who bore his eldest son Joan on 21 September. On 21 February 1598 Blaeu in Alkmaar and Tycho in Hamburg both observed a lunar eclipse to determine the relative longitude of the two cities.

Portrait of Willem Janszoon Blaeu Artist unknown

Sometime in 1598/9 Blaeu took his family to Amsterdam and set up shop as a printer, instrument maker, globe maker and cartographer; making his first celestial globe, 34 cm diameter, for Adriaan Anthoniszoon, using Tycho’s data; this was the first publication of that data. However Blaeu’s new career was not going to be simple as he had an established competitor, Jocodus Hondius.

Jocodus Hondius was born Joost de Hondt in Wakken and grew up in Ghent, both now in Belgium, on 14 October 1563. He received an education in mathematics and learnt engraving, drawing and calligraphy. He had already established himself as a successful engraver when he was forced by the Spanish, as a Calvinist, to flee to London in 1584. In London he worked for and with Richard Hakluyt and Edward Wright and expanded his knowledge of geography and cartography through contact with the English explorers Francis Drake, Thomas Cavendish and Walter Raleigh. Around 1589 he published a wall map in London showing Drake’s voyage around the world. In 1593 he moved back to The Netherlands, establishing himself in Amsterdam.

Self-portrait of Jodocus Hondas taken from one of his maps

Portrait of Francis Drake by Jodocus Hondas from his Drake world map

He formed an alliance with the Plantin printing house in Leiden for who he made several globes. In 1602 he matriculated at the University of Leiden to study mathematics. In 1604 he made the most important decision of his career in that he bought the copper printing plates of the of both Mercator’s edition of Ptolemaeus’ Geographia and Mercator’s Atlas from his heirs.He published a new edition of Mercator’s Ptolemaeus, Claudïï Ptolemaeï Alexandrini geographicae libri octo graecog latini, in the same year. He set up his own publishing house in Amsterdam in December 1604. In the sixteenth century Mercator’s Atlas had failed to establish itself in a market dominated by Ortelius’ Theatum Orbis Terrarum, however Hondius republished it in 1606 with 36 new maps and it became a best seller.

Atlas sive Cosmographiae Meditationes de Fabrica Mundi et Frabicati Figura
Mercator (left) and Hondius (right) shown working together on tittle page of 1630 Atlas
Slightly ironical as they never met and both were dead by then.

Meanwhile Blaeu had established himself as a globe maker and astronomer. Following the tradition established by Johannes Schöner and continued by Mercator Blaeu issued a pair of 23.5 cm globes, terrestrial and celestial, in 1602. His rival Hondius introduced the southern constellation on a celestial globe produced in cooperation with the astronomer-cartographer Petrus Plancius in 1598. Blaeu followed suite in 1603. Hondius produced a pair of 53.5 cm globes in 1613; Blaeu countered with a pair of 68 cm globes in 1616, which remained the largest globes in production for over 70 years.

Hondas celestial globe 1600
Source: Linda Hall Library

A matching pair of Blaeu globes

As an astronomer Blaeu discovered the star P Cygni, only the third variable star to be discovered. In 1617 Willebrord Snellius published his Eratosthenes Batavus (The Dutch Eratosthenes) in which he described his measurement of a meridian arc between Alkmaar and Bergen op Zoom. This was done in consultation with Blaeu, who had learnt the art of triangulation from Tycho, using a quadrant, with a radius of more than 2 metres, constructed by Blaeu. Blaeu specialised in publishing books on navigation beginning in 1605 with his Nieuw graetbouck and established himself as the leading Dutch publisher of such literature.

Source: Wikimedia Commons

Title page
Source: Wikimedia Commons

Quadrant constructed by Blaeu for Snellius now in Museum Boerhaave in Leiden
Source: Wikimedia Commons

Jodocus Hondius died in 1612 and his sons Jodocus II and Henricus took over the publish house later going into partnership with Jan Janszoon their brother in law. They continued to publish new improved version of the Mercator-Hondius Atlas. Blaeu had already established himself as the successful publisher of wall maps when he began planning a major atlas to rival that of the house of Hondius. That rivalry is also reflected in a name change that Blaeu undertook in 1617. Up till then he had signed his work either Guilielmus Janssonius or Willem Janszoon, now he started add the name Blaeu to his signature probably to avoid confusion with Jan Janszoon (Janssonius), his rival.

Jan Janszoon Original copperplate from his Atlas Novus 1647

In 1630 the strangest episode in the battle of the globes and atlases took place when Jodocus II’s widow sold 37 of the copper plates of the Mercator-Hondius Atlas to Willem Blaeu. He published them together with maps of his own in his Atlantic Appendix in 1631. In 1636 Blaeu published the first two volumes of his own planned world atlas as Atlas Novus or Theatrum Orbis Terrarum, thus reviving the old Ortelius name.

In 1633 the States General (the government of the United Provinces) appointed Blaeu mapmaker of the Republic. In the same year he was appointed cartographer and hydrographer of the Vereenighde Oostindische Compagnie (VOC) – The Dutch East India Company. His son Joan inherited the VOC position, as did his grandson Joan II; The Blaeu family held this prestigious position from 1633 till 1712.

Willem Blaeu had great plans to publish several more volumes of his world atlas but he didn’t live to see them realised, dying 21 October 1638. The publishing house passed to his two sons Joan (1596-1673) and Cornelis (c.1610-1644). The last two volumes prepared by Willem appeared in 1640 and 1645. Joan completed his father’s atlas with a sixth volume in 1655.

Along with all his other achievements Willem Janszoon Blaeu made a substantial improvement to the mechanical printing press by adding a counter weight to the pressure bar in order to make the platen rise automatically. This ‘Blaeu’ or ‘Dutch’ press became standard throughout the low countries and was also introduced into England. The first printing press introduced into America in 1639 was a Blaeu press.

Although he held a doctorate in law, Joan devoted his life to the family cartographic publishing business. In 1662 he set the high point of the atlas battle with the House of Hondius with the publication of the Atlas Maior; containing 600 double page maps and 3,000 pages of text it was the most spectacular atlas of all time. Along with its lavish maps the Atlas Maior contained a map of Hven and pictures of the house and stellar observatory on the island where Willem Janszoon Blaeu first learnt his trade. Whereas Willem was careful not to take sides in the dispute between the different systems for the cosmos – geocentric, heliocentric, geo-heliocentric – in the Atlas Maior, Joan committed to heliocentricity.

Joan Blaeu. By J.van Rossum
Source: Wikimedia Commons

Blaeu Atlas Maior 1662-5, Volume 1
Nova Et Accvratissima Totius Terrarvm Orbis Tabvla
Source: National Library of Scotland

The rivalry between the Houses of Hondius and Blaeu, pushing each other to new heights of quality and accuracy in their maps and globes led to them totally dominating the European market in the first half of the sixteenth century, particularly in the production of globes where they almost had a monopoly. Globes in the period, which weren’t from one of the Amsterdam producers, were almost always pirated copies of their products.

As an interesting footnote, as with all things mathematical England lagged behind the continent in cartography and globe making. Although there had been earlier single globes made in on the island, England’s first commercial producer of terrestrial and celestial globes, Joseph Moxon, learnt his trade from Willem Janszoon Blaeu in Amsterdam. In 1634 Blaeu had published a manual on how to use globes, Tweevoudigh onderwijs van de Hemelsche en Aerdsche globen (Twofold instruction in the use of the celestial and terrestrial globes). In the 1660s, Moxon published his highly successful A Tutor to Astronomie and Geographie. Or an Easie and speedy way to know the Use of both the Globes, Cœlestial and Terrestrial : in six Books, which went through many editions, however the first edition was just an English translation of Blaeu’s earlier manual.

The Dutch painter Jan Vermeer often featured globes and maps in his paintings and it has been shown that these are all reproductions of products from the Blaeu publishing house.

Vermeer’s Art of Painting or The Allegory of Painting (c. 1666–68)
With Blaeu Wall Map
Google Art Project Source: Wikimedia Commons

Jan Vermeer The Astronomer with Blaeu celestial globe and right on the wall a Blaeu wall map
Source: Wikimedia Commons

Jan Vermeer The Geographer with Blaeu terrestrial globe and again right a Blaeu wall map
Source: Wikimedia Commons

The Blaeu wall map used in Vermeers’ The Astronomer and The Geographer

We tend to emphasise politicians, artists and big name scientists, as the people who shape culture in any given age but the cartographic publishing houses of Hondius and Blaeu made significant contributions to shaping the culture of The United Provinces in the so-called Dutch Golden Age and deserve to be much better known than they are.






Filed under Early Scientific Publishing, History of Astronomy, History of Cartography, History of Navigation, History of science, Renaissance Science

Why doesn’t he just shut up?

Neil deGrasse Tyson (NdGT), probably the most influential science communicator in the world, spends a lot of time spouting out the message that learning science allows you to better detect bullshit, charlatans, fake news etc. etc. However it apparently doesn’t enable you to detect bullshit in the history of science, at least judging by NdGT’s own record on the subject. Not for the first time, I was tempted recently to throw my computer through the window upon witnessing NdGT pontificating on the history of science.

On a recent video recorded for Big Think, and also available on Youtube and already viewed by 2.6 million sycophants, he answers the question “Who’s the greatest physicist in history?” His answer appears under the title My Man, Sir Isaac Newton. Thoughtfully, Big Think have provided a transcription of NdGT’s blathering that I reproduce below for your delectation before I perform a Hist_Sci Hulk autopsy upon it.

Question: Who’s the greatest physicist in history?DeGrasse Tyson:    Isaac Newton.  I mean, just look… You read his writings.  Hair stands up… I don’t have hair there but if I did, it would stand up on the back of my neck.  You read his writings, the man was connected to the universe in ways that I never seen another human being connected.  It’s kind of spooky actually.  He discovers the laws of optics, figured out that white light is composed of colors.  That’s kind of freaky right there.  You take your colors of the rainbow, put them back together, you have white light again.  That freaked out the artist of the day.  How does that work?  Red, orange, yellow, green, blue, violet gives you white.  The laws of optics.  He discovers the laws of motion and the universal law of gravitation.  Then, a friend of his says, “Well, why do these orbits of the planets… Why are they in a shape of an ellipse, sort of flattened circle?  Why aren’t… some other shape?”  He said, you know, “I can’t… I don’t know.  I’ll get back to you.”  So he goes… goes home, comes back couple of months later, “Here’s why.  They’re actually conic sections, sections of a cone that you cut.”  And… And he said, “Well, how did find this out?  How did you determine this?”  “Well, I had to invent integral and differential calculus to determine this.”  Then, he turned 26.  Then, he turned 26.  We got people slogging through calculus in college just to learn what it is that Isaac Newtown invented on a dare, practically.  So that’s my man, Isaac Newton. 


Let us examine the actual history of science content of this stream of consciousness bullshit. We get told, “He discovers the laws of optic…!” Now Isaac Newton is indeed a very important figure in the history of physical optics but he by no means discovered the laws of optics. By the time he started doing his work in optics he stood at the end of a two thousand year long chain of researchers, starting with Euclid in the fourth century BCE, all of whom had been uncovering the laws of optics. This chain includes Ptolemaeus, Hero of Alexandria, al-Kindi, Ibn al-Haytham, Ibn Sahl, Robert Grosseteste, Roger Bacon, John Pecham, Witelo, Kamal al-Din al-Farisi, Theodoric of Freiberg, Francesco Maurolico, Giovanni Battista Della Porta, Friedrich Risner, Johannes Kepler, Thomas Harriot, Marco Antonio de Dominis, Willebrord Snellius, René Descartes, Christiaan Huygens, Francesco Maria Grimaldi, Robert Hooke, James Gregory and quite a few lesser known figures, much of whose work Newton was well acquainted with. Here we have an example of a generalisation that is so wrong it borders on the moronic.

What comes next is on safer ground, “…figured out that white light is composed of colors…” Newton did in fact, in a series of groundbreaking experiment, do exactly that. However NdGT, like almost everybody else is apparently not aware that Newton was by no means the first to make this discovery. The Bohemian Jesuit scholar Jan Marek (or Marcus) Marci (1595–1667) actually made this discovery earlier than Newton but firstly his explanation of the phenomenon was confused and largely wrong and secondly almost nobody knew of his work so the laurels go, probably correctly, to Newton.

NdGT’s next statement is for a physicist quite simply mindboggling he says, “That freaked out the artist of the day.  How does that work?  Red, orange, yellow, green, blue, violet gives you white.” Apparently NdGT is not aware of the fact that the rules for mixing coloured light and those for mixing pigments are different. I got taught this in primary school; NdGT appears never to have learnt it.

Up next are Newton’s contributions to mechanics, “He discovers the laws of motion and the universal law of gravitation.  Then, a friend of his says, “Well, why do these orbits of the planets… Why are they in a shape of an ellipse, sort of flattened circle?  Why aren’t… some other shape?”  He said, you know, “I can’t… I don’t know.  I’ll get back to you.”  So he goes… goes home, comes back couple of months later, “Here’s why.  They’re actually conic sections, sections of a cone that you cut.””

Where to begin? First off Newton did not discover either the laws of motion or the law of gravity. He borrowed all of them from others; his crowing achievement lay not in discovering them but in the way that he combined them. The questioning friend was of course Edmond Halley in what is one of the most famous and well document episodes in the history of physics, so why can’t NdGT get it right? What Halley actually asked was, assuming an inverse squared law of attraction what would be the shape of aa planetary orbit? This goes back to a question posed earlier by Christopher Wren in a discussion with Halley and Robert Hooke, “would an inverse squared law of attraction lead to Kepler’s laws of planetary motion?” Halley could not solve the problem so took the opportunity to ask Newton, at that time an acquaintance rather than a friend, who supposedly answered Halley’s question spontaneously with, “an ellipse.” Halley then asked how he knew it and Newton supposedly answered, “I have calculated it.” Newton being unable to find his claimed calculation sent Halley away and after some time supplied him with the nine-page manuscript De motu corporum in gyrum, which in massively expanded form would become Newton’s Principia.

NdGT blithely ignoring the, as I’ve said, well documented historical facts now continues his #histsigh fairy story, “And he said, “Well, how did find this out?  How did you determine this?”  “Well, I had to invent integral and differential calculus to determine this.”” This is complete an utter bullshit! This is in no way what Newton did and as such he also never claimed to have done it. In fact one of the most perplexing facts in Newton’s biography is that although he was a co-discoverer/co-inventor of the calculus (we’ll ignore for the moment the fact that even this is not strictly true, read the story here) there is no evidence that he used calculus to write Principia.

NdGT now drops his biggest historical clangour! He says, “Then, he turned 26.  Then, he turned 26.  We got people slogging through calculus in college just to learn what it is that Isaac Newtown invented on a dare, practically.  So that’s my man, Isaac Newton.” Newton was twenty-six going on twenty seven when he carried out the optics research that led to his theory of colours in 1666-67 but the episode with Halley concerning the shape of planetary orbits took place in 1682 when he was forty years old and he first delivered up De motu corporum in gyrum two years later in 1684. NdGT might, as an astro-physicist, be an expert on a telescope but he shouldn’t telescope time when talking about historical events.


Filed under History of Optics, History of science, Myths of Science, Newton

Open shelved serendipity

One of my favourite radio science programmes is BBC Radio 4’s Science Stories presented by Philip Ball and Naomi Alderman. Yesterday was the first episode of the fifth series of this excellent piece of popular history of science broadcasting. Last week whilst advertising the new series on Twitter Philip Ball let drop the fact that next weeks episode would be about the medieval theologian and scholar Robert Grosseteste, featuring the physicist of the fascinating interdisciplinary University of Durham research project Ordered Universe, Thom McLeish. This brief Internet exchange awoke in me memories of my own first encounter with the medieval Bishop of Lincoln.

14th-Century Portrait of Robert Grosseteste, Bishop of Lincoln by unknown scribe
Source: Wikimedia Commons

I studied mathematics, philosophy, English philology and history with a strong emphasis on the history and philosophy of science, as a mature student, at the University of Erlangen between 1981 and 1991. It was this period of my life that converted me from an enthusiastic amateur into a university educated and trained researcher into the history of science (For more on this see my post next Monday). When I started this decade of formal studies I held a fairly standard, conservative view of the Scientific Revolution; this started with the publication of Copernicus’ De revolutionibus in 1543 and was completed with the publication of Newton’s Principia Mathematica in 1687. What disrupted, one could even say exploded, this idealised picture was my first encounter with Grosseteste.

Erlangen University is a comparatively large university and its main library is, like that of almost all such institutions, closed shelf. However the department libraries are almost all open shelf and as a student I developed the habit of browsing library bookshelves with no particular aim in view. The Bavarian State university library system has for book purchases an emphasis policy. Each Bavarian university library has a collecting emphasis so that specialist books in a particular discipline are only bought/collected by one university but are available to all the others through the interlibrary loan system. This is a method of making the available funds go further. Erlangen’s collection emphasis is philosophy, including the history and philosophy of science, so the philosophy department library is particularly well stocked in this direction.

One day fairly early in my time as a student in Erlangen I was cruising the history and philosophy of science bookshelves in the philosophy department library when my eyes chanced upon a rather unimposing, fairly weighty book by some guy called Alistair Crombie (I had know idea who he was then) with the title Robert Grosseteste and the origins of experimental science: 1100 – 1700. I have no idea what motivated me to take that volume home with me but I did and once I started reading didn’t stop until I had reached the end. This was a whole new world to me, the world of medieval science, of whose existence I had been blissfully unaware up until that point in time. Reading Crombie’s book radically changed my whole understanding of the history of science.

Here was this twelfth/thirteenth century cleric, lecturer at Oxford University (and possibly for a time chancellor of that august institution), who went on to become Bishop of Lincoln, teaching what amounted to empirical mathematical science.

Grosseteste’s Tomb and Chapel in Lincoln Cathedral
Source: Wikimedia Commons

It should be pointed out that whilst Grosseteste was strong on mathematical empirical science in theory, his work was somewhat lacking in the practice of that which he preached. Crombie has Grosseteste standing at the head of a chain of scholars that include Roger Bacon in the thirteenth century, the Oxford Calculators (about whom there is a good podcast from History of Philosophy without any gaps) and the Paris Physicists in the fourteenth century and so on down to Isaac Newton at the end of the seventeenth century. Unknown to me at the time Crombie was presenting a modernised version of the Duhem Thesis that the scientific revolution took place in the thirteenth and fourteenth centuries and not as the standard model has it, and as I had believed up till I read Crombie’s book, in the sixteenth and seventeenth centuries.

This was the start of a long intellectual journey for me during which I read the works of not only Crombie but of Edward Grant, Marshal Clagett, John Murdoch, David Lindberg, A. Mark Smith, Toby Huff and many other historians of medieval science. This journey also took me into the fascinating world of Islamic science, which in turn led me to the histories of both Indian and Chinese science although I still have the impression that in all these areas medieval European science, Islamic science, and Indian and Chinese science I have till now barely scratched the surface.

As I said above this journey started with Crombie’s book and Robert Grosseteste discovered whilst aimlessly browsing the shelves in the department library. This is by no means the only important and influential book that I have discovered for myself by this practice of browsing in open shelf department libraries. On one occasion I went looking for one specific book on map projection in the geography department library and, after a happy hour or two of browsing, left with an armful of books on the history of cartography. On another occasion I discovered, purely by accident, The Life and Letters of Sir Henry Wotton edited by Logan Pearsall Smith in the English Department Library. Wotton a sixteenth/seventeenth century English diplomat was a passionate fan of natural philosophy, who sent the first copies of Galileo’s Sidereus Nuncius, fresh off the printing press to London on its day of publication in 1610.

There are many other examples of the scholarly serendipity that my habit of browsing open shelf library shelves has brought me over the years but I think I have already made the point that I wanted to when I set out to write this post. Libraries are full of wonderful, vista opening books, so don’t wait for somebody to recommend them to you but find an open shelf library and go and see what chance throws you way, it might just change your life.







Filed under Autobiographical, History of science, Mediaeval Science

Recipes in the Wild By Paul Engle June 1, 2017

The Recipes Project blog is, starting today, running a Virtual Conversation on the theme, “What is a Recipe?” I featured this in the editorial of the latest edition of Whewells Gazette the Weekly #histSTM Links List. Inspired by a comparison that I made between algorithms and recipes and a question that I posed, Paul Engle, author of the very excellent Conciatore: The Life and Times of 17th Century Glassmaker Antonio Neri and writer of the Conciatore Blog, sent me the following essay stating, “Feel free to do with it what you will.” So what I will is to post it here as a very welcome guest blog post from an excellent historian of technology who really knows what a recipe is.  

It has been suggested at Whewell’s Gazette in a recent editorial that in considering recipes, particularly technical recipes and their relation to algorithms, that, “the two words are in their essence synonyms and there isn’t really a difference.” [1] With all due respect to the author of this passage, I do not think that is quite right.

A recipe is much more than an algorithm, in fact I propose that while algorithms are quite powerful tools, they occupy a rather distinct niche in the universe of recipes. We do agree on some things however,

“For me a recipe is quite simply a set of instructions, which describe how to complete successfully a given task. The task does not necessarily have to have anything to do with cooking, the first thought that pops up when we hear the word recipe.” [2]

I have thirty-odd years of empirical experience writing and following technical recipes in a laboratory setting; I have several shelves full of them that I am looking at right now. I have been programming computers and dealing with algorithms, dare I say it, since the days of punch cards and paper tape. This is a subject particularly dear to me and besides, I sense an irresistible opportunity to make a fool of myself, so here goes.

In the realms of mathematics and computer science, an algorithm is a set of instructions that enjoy several conditions favorable over recipes; a well-defined environment where it does not matter if it is raining or sunny outside and an output or result that is usually unambiguous. For recipes, not so much; even the lowly baker known that on humid days, a prized and tested bread recipes must be adjusted to produce an edible product. These adjustments do not always take a form that can easily be measured or quantified and this starts to get at the heart of the matter.

Any day of the week, rain or shine, a computer running a straightforward algorithm can generate the first million digits of pi, (yes, the millionth digit is 1). While there may be a certain amount of difficulty in verifying a result, it is something that is done quite routinely. While some simple recipes fall into this form, many others do not. Consider that some technical recipes seem to work even if we do not know how. Others require “experienced” practitioners, not because of anything magical going on, but simply because the most reliable results are obtained by one who has done it before. Even with seemingly simple, well-documented tasks like polishing a material, there can be an enormous number of variables involved, some unknown, others that are not practical or possible to control.

An algorithm generally lives in an artificially constructed, tightly controlled environment, recipes, on the other hand, operate in the wild. An aspect of technical recipes often missed by outsiders is the level of attention that must be paid to the interaction of your “product” with its environment. This may mean frequent observation and testing, or, in the kitchen, it may mean tasting the gumbo every few minutes and making appropriate adjustments. No matter if the result is a well-polished sample in a materials laboratory, or a well-seasoned bowl of soup in the French Quarter, what makes the result “good” is not necessarily easy to define. We can calibrate our equipment and take great care with our materials. We can scrutinize the results, and take measurements until the cows come home, but in many instances, this is only a starting point; learning to perform a recipe “well” can be like a mini-education. Writing that down stepwise can be like trying to capture everything you learned at cooking school.

It is in this setting, where there are many variables to keep track of, many unknowns, and even the results may be hard to characterize, that we step into the realm of “art.” A successful outcome depends as much on what you bring to the table as what is written on the page. A recipe becomes like a roadmap for threading your way through a complex maze of decision points. Here is where I get passionate about my subject. Practicing a recipe, in a sense, can be viewed as the purest form of empirical science. And this can take place in a laboratory or in a kitchen. If science is the study of the way the world actually behaves, then going through a series of steps and paying close attention to what is happening, is as good as it gets. It is not a matter of imposing ones will on the world, but of interacting with nature and moving toward a result given the constraints of reality; there is a give and take. A scientific experiment can be viewed as the act of developing a new recipe toward a specific result. Writing that recipe down is an exercise in determining the important variables to pay attention to and capturing a method in a way that is repeatable by others.

As computer algorithms move into the realms of artificial intelligence, driverless cars and the like, they will start to encounter the same difficulties as our baker does on a humid day. Perhaps a true test of machine intelligence will be how well an algorithm negotiates real-world recipes.

[1] Christie, Thony 2017. Whewell’s Ghost blog, “Editorial, Whewell’s Gazette: Year 03, Vol. #41” 31 May 2017.
[2] Op. Cit.


Filed under History of science, History of Technology