Category Archives: History of Mathematics

Well no, actually he didn’t.

Ethan Siegel has written a reply to my AEON Galileo opinion piece on his Forbes blog. Ethan makes his opinion very clear in the title of his post, Galileo Didn’t Invent Astronomy, But He DID Invent Mechanical Physics! My response is also contained in my title above and no, Galileo did not invent mechanical physics. For a change we’ll start with something positive about Galileo, his inclined plane experiments to determine the laws of fall, the description of which form the bulk of Ethan’s post, are in fact one of the truly great pieces of experimental physics and are what makes Galileo justifiably famous. However the rest of Ethan’s post leaves much to be desired.

Ethan starts off by describing the legendary Leaning Tower of Pisa experiment, in which Galileo supposedly dropped two ball of unequal weight of the tower and measured how long they took to fall. The major problem with this is that Galileo almost certainly never did carry out this experiment, however both John Philoponus in the sixth century CE and Simon Stevin in 1586 did so, well before Galileo considered the subject. The laws of fall were also investigated theoretically by the so-called Oxford Calculatores, who developed the mean speed theory, the foundation of the laws of fall, and the Paris Physicists, who represented the results graphically, both in the fourteenth century CE. Galileo knew of the work of John Philoponus, the Oxford Calculatores and the Paris Physicists, even using the same graph to represent the laws of fall in his Two New Sciences, as Oresme had used four hundred years earlier. In the sixteenth centuries the Italian mathematician Tartaglia investigated the path of projectiles, publishing the results in his Nova Scientia, his work was partially validated, partially refuted by Galileo. His landsman Benedetti anticipated most of Galileo’s results on the laws of fall. With the exception of Stevin’s work Galileo knew of all this work and built his own researches on it thus rather challenging Ethan’s claim that Galileo invented mechanical physics.

Galileo’s central achievement was to provide empirical proof of the laws of fall with his ingenious ramp experiments but even here there are problems. Galileo’s results are simply too good, not displaying the expected experimental deviations, leading Alexander Koyré, the first great historian of Galileo’s work, to conclude that Galileo never did the experiments at all. The modern consensus is that he did indeed do the experiments but probably massaged his results, a common practice. The second problem is that any set of empirical results requires confirmation by other independent researchers. Mersenne, a great supporter and propagator of Galileo’s physics, complains of the difficulties of reproducing Galileo’s experimental results and it was first Riccioli, who finally succeeded in doing so, publishing the results in 1651.

A small complaint is Ethan’s claim that Galileo’s work on the laws of fall “was the culmination of a lifetime of work”. In fact although Galileo first published his Two New Sciences in 1638 his work on mechanics was carried out early in his life and completed well before he made his telescopic discoveries.

The real problem with Ethan’s post is what follows the quote above, he writes:

…and the equations of motion derived from Newton’s laws are essentially a reformulation of the results of Galileo. Newton indeed stood on the shoulders of giants when he developed the laws of gravitation and mechanics, but the biggest titan of all in the field before him was Galileo, completely independent of what he contributed to astronomy.

This is quite simply wrong. After stating his first two laws of motion in the Principia Newton writes:

The principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds. By means of the first two laws and the first two corollaries Galileo found that the decent of heavy bodies is the squared ratio of the time that the motion of projectiles occurs in a parabola, as experiment confirms, except insofar as these motion are somewhat retarded by the resistance of the air.

As Bernard Cohen points out, in the introduction to his translation of the Principia from which I have taken the quote, this is wrong because, Galileo certainly did not know Newton’s first law. As to the second law, Galileo would not have known the part about change in momentum in the Newtonian sense, since this concept depends on the concept of mass which was invented by Newton and first made public in the Principia.

I hear Galileo’s fans protesting that Newton’s first law is the law of inertia, which was discovered by Galileo, so he did know it. However Galileo’s version of the law of inertia is flawed, as he believes natural unforced motion to be circular and not linear. In fact Newton takes his first law from Descartes who in turn took it from Isaac Beeckman. Newton’s Principia, or at least his investigation leading up to it, are in fact heavily indebted to the work of Descartes rather than that of Galileo and Descartes in turn owes his greatest debts in physics to the works of Beeckman and Stevin and not Galileo.

An interesting consequence of Newton’s false attribution to Galileo in the quote above is that it shows that Newton had almost certainly never read Galileo’s masterpiece and only knew of it through hearsay. Galileo’s laws of fall are only minimally present in the Principia and then only mentioned in passing as asides, whereas the parabola law occurs quite frequently whenever Newton is resolving forces in orbits but then only as Galileo has shown.

One small irony remains in Ethan’s post. He loves to plaster his efforts with lots of pictures and diagrams and videos. This post does the same and includes a standard physics textbook diagram showing the force vectors of a heavy body sliding down an inclined plane. You can search Galileo’s work in vain for a similar diagram but you will find an almost identical one in the work of Simon Stevin, who worked on physical mechanics independently of and earlier than Galileo. Galileo made some very important contributions to the development of mechanical physics but he certainly didn’t invent the discipline.

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Filed under History of Mathematics, History of Physics, Myths of Science, Newton

The Reformation, Astrology, and Mathematics in Schools and Universities.

It is one of the ironies of the medieval universities that mathematics played almost no role in undergraduate education. It is ironical because the curriculum was nominally based on the seven liberal arts of which the mathematical sciences – arithmetic, geometry, music and astronomy – formed one half, the quadrivium. Although the quadrivium was officially a large part of the curriculum in reality the four mathematical disciplines were paid little attention and hardly taught at all. This only began to change in the fifteenth century with the rise of astro-medicine or iatromathematics, to give it its formal name. With the rise of this astrology-based medicine the humanist universities of Northern Italy and Kraków introduced chairs of mathematics to teach astrology to their students of medicine. This of course entailed first teaching mathematics and then astronomy in order to be able to do astrology and thus mathematics gained a first foothold in the European universities. Ingolstadt became the first German university to introduce a chair for mathematics, also for teaching astrology to medical students, in the 1470s. It became an important centre for seeding new chairs at other universities with its graduates. Stabius and Stiborius going from there to Vienna with Celtis, for example. However there was no systematic introduction of mathematics into the university curriculum as of yet, this would first come as a result of the Reformation and the educational reforms of Philip Melanchthon.

Melanchthon in 1526: engraving by Albrecht Dürer Translation of Latin caption: «Dürer was able to draw Philip’s face, but the learned hand could not paint his spirit». Source: Wikimedia Commons

Melanchthon in 1526: engraving by Albrecht Dürer Translation of Latin caption: «Dürer was able to draw Philip’s face, but the learned hand could not paint his spirit».
Source: Wikimedia Commons

Melanchthon was born Philip Schwartzerdt in Bretten near Karlsruhe on 16 February 1497. A great nephew of Johann Reuchlin a leading humanist scholar Philip changed his name to Melanchthon, a literal Greek translation of his German name, which means black earth, at Reuchlin’s suggestion. Melanchthon was a child prodigy who would grow up to be Germany’s greatest humanist scholar. He studied at Heidelberg University where he was denied his master degree in 1512 on account of his youth. He transferred to Tübingen where he came under the influence of Johannes Stöffler, one of those Ingolstadt graduates, a leading and highly influential mathematician/astrologer.

Johannes Stöffler Source Wikimedia Commons

Johannes Stöffler
Source Wikimedia Commons

The cosmograph Sebastian Münster was another of Stöffler’s famous pupils. Stöffler also has a great influence on several of the Nürnberger mathematician-astronomers, especial Johannes Schöner and Georg Hartmann. Under Stöffler’s influence Melanchthon became a passionate supporter of astrology.

On Reuchlin’s recommendation Melanchthon became professor of Greek at Luther’s University of Wittenberg at the age of twenty-one and thus a central figure in the Reformation. One of the major problems faced by the reformers was the fact that the education system was totally in the hands of the Catholic Church, which meant that they had to start from scratch and create their own school and university system; this task was taken on by Melanchthon, who became Luther’s Preceptor Germania, Germany’s Schoolmaster.

Because of his own personal passion for astrology Melanchthon introduced mathematics into the curriculum of all the Lutheran schools and universities. He invented a new type of school on a level between the old Church Latin schools and the universities that were devised to prepare their pupils for a university education. The very first of these was the Eigidien Oberschule in Nürnberg, which opened in 1526 with Johannes Schöner, as its first professor for mathematics.

Johannes_Schoner_Astronomer_01

These type of school created by Melanchthon would become the Gymnasium, still today the highest level secondary schools in the German education system.

In Wittenberg he appointed Johannes Volmar (1480-1536) professor for the higher mathematic, music and astronomy, and Jakob Milich (1501- 1559) professor for the lower mathematic, arithmetic and geometry, in 1525. Their most famous students were Erasmus Reinhold, who followed Volmar on the chair for higher mathematics when he died in 1536, and Georg Joachim Rheticus, who followed Milich on the chair for lower mathematics, in the same year when Milich became professor for medicine. Schöner, Reinhold and Rheticus were not the only mathematicians supported by Melanchthon, who played an important role in the dissemination of the heliocentric astronomy. Although following Melanchthon’s lead these Protestant mathematicians treated the heliocentric hypothesis in a purely instrumentalist manner, i.e. it is not true but is mathematically useful, they taught it in their university courses alongside the geocentric astronomy.

As a result of Melanchthon’s passion for astrology the Lutheran Protestant schools and universities of Europe all had departments for the study of mathematics headed by qualified professors. The Catholic schools and universities would have to wait until the end of the sixteenth century before Christoph Clavius did the same for them, although his motivation was not astrology. Sadly Anglican England lagged well behind the continent with Oxford first appointing professors for geometry and astronomy in the 1620s at the bequest of Henry Savile, who had had to go abroad to receive his own mathematical education. Cambridge only followed suit with the establishment of the Lucasian Chair in 1663, whose first occupant was Isaac Barrow followed by that other Isaac, Newton. In 1705 John Arbuthnot could still complain in an essay that there was not one single school in England that taught mathematics.

 

 

 

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Filed under History of Astrology, History of Astronomy, History of Mathematics, History of science, Renaissance Science, University History

Christoph and the Calendar

The first substantive history of science post that I wrote on this blog was about the Jesuit mathematician and astronomer Christoph Clavius. I wrote this because at the time I was preparing a lecture on the life and work of Clavius to be held in his hometown Bamberg. Clavius is one of my local history of science celebrities and over the years I have become the local default Clavius expert and because of his involvement in the Gregorian calendar reform of 1572 I have also become the local default expert on that topic too.

Christoph Clavius

Christoph Clavius

All of this means that I have become very sensitive to incorrect statements about either Clavius or the Gregorian calendar reform and particularly sensitive to false statements about Clavius’ involvement in the latter. Some time back the Atlas Obscura website had a ‘time week’ featuring a series of blog post on the subject of time one of which, When The Pope Made 10 Days Disappear, was about the Gregorian calendar reform and contained the following claim:

The new lead astronomer on the project, Jesuit prodigy Christopher Clavius, considered this and other proposals for five years.

The brief statement contains three major inaccuracies, the most important of which, is that Clavius as not the lead astronomer, or lead anything else for that matter, on the project. This is a very widespread misconception and one to which I devote a far amount of time when I lecture on the subject, so I thought I would clear up the matter in a post. Before doing so I would point out that I have never come across any other reference to Clavius as a prodigy and there is absolutely nothing in his biography to suggest that he was one. That was the second major inaccuracy for those who are counting.

Before telling the correct story we need to look at the wider context as presented in the article before the quote I brought above we have the following:

A hundred years later, Pope Gregory XIII rolled up his sleeves and went for it in earnest. After a call for suggestions, he was brought a gigantic manuscript. This was the life’s work of physician Luigi Lilio, who argued for a “slow 10-day correction” to bring things back into alignment, and a new leap year system to keep them that way. This would have meant that years divisible by 100 but not by 400 (e.g. 1800, 1900, and 2100) didn’t get the extra day, thereby shrinking the difference between the solar calendar and the Earthly calendar down to a mere .00031 days, or 26 seconds.

Luigi LIlio Source: Wikimedia Commons

Luigi LIlio
Source: Wikimedia Commons

This is correct as far as it goes, although there were two Europe wide appeals for suggestions and we don’t actually know how many different suggestions were made as the relevant documents are missing from the Vatican archives. It should also be pointed out the Lilio was a physician/astronomer/astrologer and not just simply a physician. Whether or not his manuscript was gigantic is not known because it no longer exists. Having decided to consider Lilio’s proposal this was not simply passed on to Christoph Clavius, who was a largely unknown mathematicus at the time, which should be obvious to anybody who gives more than five minutes thought to the subject.

The problem with the calendar, as far as the Church was concerned, was that they were celebrating Easter the most important doctrinal festival in the Church calendar on the wrong date. This was not a problem that could be decided by a mere mathematicus, at a time when the social status of a mathematicus was about the level of a bricklayer, it was far too important for that. This problem required a high-ranking Church commission and one was duly set up. This commission did not consider the proposal for five years but for at least ten and possibly more, again we are not sure due to missing documents. It is more than likely that the membership of the commission changed over the period of its existence but because we don’t have the minutes of its meetings we can only speculate. What we do have is the signatures of the nine members of the commission who signed the final proposal that was presented to the Pope at the end of their deliberations. It is to these names that we will now turn our attention.

The names fall into three distinct groups of three of which the first consists of the high-ranking clerics who actually lead this very important enquiry into a fundamental change in Church doctrinal practice. The chairman of the committee was of course a cardinal,Guglielmo Sirleto (1514–1584) a distinguished linguist and from 1570 Vatican librarian.

Cardinal Guglielmo Sirleto Source: Wikimedia Commons

Cardinal Guglielmo Sirleto
Source: Wikimedia Commons

The vice chairman was Bishop Vincenzo Lauro (1523–1592) a Papal diplomat who was created cardinal in 1583. Next up was Ignatius Nemet Aloho Patriarch of Antioch and head of the Syriac Orthodox Church till his forced resignation in 1576. Ignatius was like his two Catholic colleagues highly knowledgeable of astronomy and was brought into the commission because of his knowledge of Arabic astronomy and also to try to make the reform acceptable to the Orthodox Churches. The last did not function as the Orthodox Churches initially rejected the reform only adopting it one after the other over the centuries with the exception of the Russian Eastern Orthodox Churches, whose church calendar is still the Julian one, which is why they celebrate Christmas on 6 7 January.

Our second triplet is a mixed bag. First up we have Leonardo Abela from Malta who functioned as Ignatius’ translator, he couldn’t speak Latin, and witnessed his signature on the commissions final report. He is followed by Seraphinus Olivarius an expert lawyer, whose role was to check that the reform did not conflict with any aspects of cannon law. The third member of this group was Pedro Chacón a Spanish mathematician and historian, whose role was to check that the reform was in line with the doctrines of the Church Fathers.

Our final triplet consists of what might be termed the scientific advisors. Heading this group is Antonio Lilio the brother of Luigi and like his brother a physician and astronomer. He was here to elucidate Luigi’s plan, as Luigi was already dead. The lead astronomer, to use the Atlas Obscura phase, was the Dominican monk Ignazio Danti (1536–1582) mathematician, astronomer, cosmographer, architect and instrument maker.

Ignazio Danti Source: Wikimedia Commons

Ignazio Danti
Source: Wikimedia Commons

In a distinguished career Danti was cosmographer to Cosimo I, Duke of Tuscany whilst professor of mathematics at the university of Pissa, professor of mathematics at the University of Bologna and finally pontifical mathematicus in Rome. For the Pope Danti painted the Gallery of Maps in the Cortile del Belvedere in the Vatican Palace and deigned and constructed the instruments in the Sundial Rome of the Gregorian Tower of Tower of Winds above the Gallery of Maps.

Map of Italy, Corsica and Sardinia - Gallery of Maps - Vatican Museums. Source: Wikimedia Commons

Map of Italy, Corsica and Sardinia – Gallery of Maps – Vatican Museums.
Source: Wikimedia Commons

After the calendar reform the Pope appointed him Bishop of Altari. Danti was one of the leading mathematical practitioners of the age, who was more than capable of supplying all the scientific expertise necessary for the reform, so what was the role of Christoph Clavius the last signer of the commission’s recommendation.

The simple answer to this question is that we don’t know; all we can do is speculate. When Clavius (1538–1612) first joined the commission he was, in comparison to Danti, a relative nobody so his appointment to this high level commission with its all-star cast is somewhat puzzling. Apart from his acknowledged mathematical skills it seems that his membership of the Jesuit Order and his status as a Rome insider are the most obvious reasons. Although relative young the Jesuit Order was already a powerful group within the Church and would have wanted one of theirs in such a an important commission. The same thought concerns Clavius’ status as a Rome insider. The Church was highly fractional and all of the other members of the commission came from power bases outside of Rome, whereas Clavius, although a German, as professor at the Collegio Romano counted as part of the Roman establishment, thus representing that establishment in the commission. It was probably a bit of all three reasons that led to Clavius’ appointment.

Having established that Clavius only had a fairly lowly status within the commission how did the very widespread myth come into being that he was somehow the calendar reform man? Quite simply after the event he did in fact become just that.

When Pope Gregory accepted the recommendations of the commission and issued the papal bull Inter gravissimas on 24 February 1582, ordering the introduction of the new calendar on 4 October of the same year,

Inter-grav

he granted Antonio Lilio an exclusive licence to write a book describing the details of the calendar reform and the modifications made to the process of calculating the date of Easter. The sales of the book, which were expected to be high, would then be the Lilio family’s reward for Luigi Lilio having created the mathematical basis of the reform. Unfortunately Antonio Lilio failed to deliver and after a few years the public demand for a written explanation of the reform had become such that the Pope commissioned Clavius, who had by now become a leading European astronomer and mathematician, to write the book instead. Clavius complied with the Pope’s wishes and wrote and published his Novi calendarii romani apologia, Rome 1588, which would become the first of a series of texts explaining and defending the calendar reform. The later was necessary because the reform was not only attacked on religious grounds by numerous Protestants, but also on mathematical and astronomical grounds by such leading mathematicians as François Viète and Michael Maestlin. Over the years Clavius wrote and published several thousand pages defending and explicating the Gregorian calendar reform and it is this work that has linked him inseparably with the calendar reform and not his activities in the commission.

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Filed under History of Astronomy, History of Mathematics, History of science, Local Heroes, Renaissance Science

The Arch-Humanist

The name Conrad Celtis is not one that you’ll find in most standard books on the history of mathematics, which is not surprising as he was a Renaissance humanist scholar best known in his lifetime as a poet. However, Celtis played an important role in the history of mathematics and is a good example of the fact that if you really wish to study the evolution of the mathematical sciences it is necessary to leave the narrow confines of the mathematics books.

Conrad Celtis: Gedächtnisbild von Hans Burgkmair dem Älteren, 1507 Source: Wikimedia Commons

Conrad Celtis: Gedächtnisbild von Hans Burgkmair dem Älteren, 1507
Source: Wikimedia Commons

Born Konrad Bickel or Pyckell, (Conrad Celtis was his humanist pseudonym) the son of a winemaker, in Franconian Wipfield am Main near Schweinfurt on 1 February 1459, he obtained his BA at the University of Cologne in 1497. Unsatisfied with the quality of tuition in Cologne he undertook the first of many study journeys, which typified his life, to Buda in 1482, where he came into contact with the humanist circle on the court of Matthias Corvinus, the earlier patron of Regiomontanus. 1484 he continued his studies at the University of Heidelberg specialising in poetics and rhetoric, learning Greek and Hebrew and humanism as a student of Rudolf Agricola, a leading Dutch early humanist scholar. Celtis obtained his MA in 1485. 1486 found him underway in Italy, where he continued his humanist studies at the leading Italian universities and in conversation with many leading humanist scholars. Returning to Germany he taught poetics at the universities of Erfurt, Rostock and Leipzig and on 18 April 1487 he was crowned Poet Laureate by Emperor Friedrich III in Nürnberg during the Reichstag. In Nürnberg he became part of the circle of humanists that produced the Nürnberger Chronicle to which he contributed the section on the history and geography of Nürnberg. It is here that we see the central occupation of Celtis’ life that brought him into contact with the Renaissance mathematical sciences.

During his time in Italy he suffered under the jibes of his Italian colleges who said that whilst Italy had perfect humanist credentials being the inheritors of the ancient Roman culture, Germany was historically a land of uncultured barbarians. This spurred Celtis on to prove them wrong. He set himself the task of researching and writing a history of Germany to show that its culture was the equal of Italy’s. Celtis’ concept of history, like that of his Renaissance contemporaries, was more a mixture of our history and geography the two disciplines being regarded as two sides of the same coin. Geography being based on Ptolemaeus’ Geographia (Geographike Hyphegesis), which of course meant cartography, a branch of the mathematical sciences.

Continuing his travels in 1489 Celtis matriculated at the University of Kraków specifically to study the mathematical sciences for which Kraków had an excellent reputation. A couple of years later Nicolaus Copernicus would learn the fundamentals of mathematics and astronomy there. Wandering back to Germany via Prague and Nürnberg Celtis was appointed professor of poetics and rhetoric at the University of Ingolstadt in 1491/92. Ingolstadt was the first German university to have a dedicated chair for mathematics, established around 1470 to teach medical students astrology and the necessary mathematics and astronomy to cast a horoscope. When Celtis came to Ingolstadt there were the professor of mathematics was Andreas Stiborius (born Stöberl 1464–1515) who was followed by his best student Johannes Stabius (born Stöberer before 1468­–1522) both of whom Celtis convinced to support him in his cartographic endeavours.

In 1497 Celtis received a call to the University of Vienna where he established a Collegium poetarum et mathematicorum, that is a college for poetry and mathematics, with Stiborius, whom he had brought with him from Ingolstadt, as the professor for mathematics. In 1502 he also brought Stabius, who had succeeded Stiborius as professor in Ingolstadt, and his star student Georg Tanstetter to Vienna. Stiborius, Stabius and Tanstetter became what is known, to historians of mathematics, as the Second Viennese School of Mathematics, the First Viennese School being Johannes von Gmunden, Peuerbach and Regiomontanus, in the middle of the fifteenth century. Under these three Vienna became a major European centre for the mathematical sciences producing many important mathematicians the most notable being Peter Apian.

Although not a mathematician himself Conrad Celtis, the humanist poet, was the driving force behind one of the most important German language centres for Renaissance mathematics and as such earns a place in the history of mathematics. A dedicated humanist, wherever he went on his travels Celtis would establish humanist societies to propagate humanist studies and it was this activity that earned him the German title of Der Erzhumanist, in English the Arch Humanist. Celtis died in 1508 but his Collegium poetarum et mathematicorum survived him by twenty-two years, closing first in 1530

 

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

Christmas Trilogy 2015 Part 3: Roll out the barrel.

The village master taught his little school

The village all declared how much he knew,

‘Twas certain he could write, and cipher too;

Lands he could measure, times and tides presage,

And e’en the story ran that he could gauge

Oliver Goldsmith – The Deserted Village

As I have commented on a number of occasions in the past, although most people only know Johannes Kepler, if they have heard of him at all, as the creator of his eponymous three laws of planetary motion in fact he published more than eighty books and pamphlets in his life covering a very wide range of scientific and mathematical subjects. One of those publications, which often brings a smile to the faces of those not aware of its mathematical significance, is his Nova stereometria doliorum vinariorum (which translates as The New Art of Measuring the Contents of Wine Barrels) published in 1615. A whole book devoted to determining the volume of wine barrels! Surely not a suitable subject for a man who determined the laws of the cosmos and helped lay the foundations of modern optics, had the good Johannes taken to drink in the face of his personal problems?

Title page of Kepler's 1615 Nova stereometria doliorum vinariorum (image used by permission of the Carnegie Mellon University Libraries)

Title page of Kepler’s 1615 Nova stereometria doliorum vinariorum (image used by permission of the Carnegie Mellon University Libraries)

Because he is now regarded as one of the earliest ‘modern’ mathematicians people tend to forget that Kepler lived not in the age of the mathematician but in that of the mathematical practitioner. This means that as district mathematician in Graz, and later in Linz, Kepler would have been expected to carry out a large range of practical mathematical tasks including surveying, cartography, dialling (that is the design and construction of sundials), writing astrological prognostica, almanacs and calendars and gauging amongst others. We know that Kepler carried out a lot of these tasks but as far as I know he was never employed as a gauger, that is a man responsible for measuring and/or calculating the volume of barrels and their contents.

Nowadays with the wooden barrel degraded to the role of garden ornament in the forecourts of kitschy country pubs it is hard for people to imagine that for more than half a millennium the art of gauging and the profession of the gauger were a widespread and important part of the political and business life of Europe. Wooden barrels first made their appearance during the iron age, that is sometime during the first millennium BCE, iron making it possible to make tools with which craftsmen could work and shape the hard woods used to make barrels. It seems that we owe the invention of the barrel to the Celtic peoples of Northern Europe, who were making wooden barrels at least as early as five hundred BCE, although wooden buckets go back much earlier, with the earliest known one being from Egypt, 2690 BCE. The early wooden buckets were carved from single blocks of wood unlike barrels that are made from staves assembled and held together with hoops of saplings, rope or iron.

Source: Wood, Whiskey and Wine: A History of Barrels by Henry H. Work

Source: Wood, Whiskey and Wine: A History of Barrels by Henry H. Work

The ancient Greeks and Romans used large clay vessels called amphora to transport goods, in particular liquids such a wine and oil.

Roman Amphorae Source: Wikimedia Commons

Roman Amphorae
Source: Wikimedia Commons

However by about two hundred to three hundred CE the Romans, to whom we owe our written knowledge (supported by archaeological finds) of the Celtic origins of barrel making, were transporting wine in barrels. Wooden barrels appear to be a uniquely European invention appearing first in other parts of the world when introduced by Europeans.

By the Middle Ages wooden barrels had become ubiquitous throughout Europe used for transporting and storing a bewildering range of both dry and wet goods including books and corpses, the latter conserved in alcohol. With the vast increase in trade, both national and international, came the problem of taxes and custom duties on borders or at town gates. Wine, beer and spirits were taxed according to volume and the tax officials were faced with the problem of determining the volumes of the diverse barrels that poured daily across borders or through town gates, enter the gauger and the gauging rod.

Gauger with gauging rod Source:

Gauger with gauging rod
Source:

The simplest method of determining the volume of liquid contained in a barrel would be to pour out contents into a measuring vessel. This was of course not a viable choice for tax or customs official, so something else had to be done. Because of its shape determining the volume of a barrel-shaped container is not a simple geometrical exercise like that of determining the volume of a cylinder, sphere or cube so the mathematicians had to find another way. The solution was a gauging rod. This is a rod marked with a scale that was inserted diagonally into the barrel through the bung hole and by reading off the number on the scale the gauger could then calculate a good approximation of the volume of fluid in the barrel and then calculate the tax or custom’s duty due. From some time in the High Middle ages through to the nineteenth century gaugers and their gauging rods and gauging slide rules were a standard part of the European trade landscape.

A gauging slide rule Source

A gauging slide rule
Source

The mathematical literature on the art of gauging, particularly from the Early Modern Period is vast. As a small side note Antonie van Leeuwenhoek, the famous seventeenth-century microscopist, also worked for a time as gauger for the City of Delft.

A Cooper Jan Luyken Source

A Cooper Jan Luyken
Source

However after this brief excursion into the history of barrels and barrel gauging it is time to turn attention back to Kepler and his Nova stereometria doliorum vinarioru. In 1613, now living in Linz, Kepler purchased some barrels to lay in a supply of wine for his family. The wine dealer filled the casks and proceeded to measure the volume they contained using a gauging rod. Kepler being a notoriously exacting mathematician was horrified by the inaccuracy of this method of measurement and set about immediately to see if he produce a better mathematical method of determining the volume of barrels. Returning to the Eudoxian/Archimedian method of exhaustion that he had utilized to determine his second law of planetary motion he presented the volume of the barrel as the sum of a potentially infinite sum of a series of slices through the barrels. In modern terminology he used integral calculus to determine the volume. Never content to do half a job Kepler extended his mathematical investigations to determining the volumes of a wide range of three-dimensional containers and his efforts developed into a substantial book. Because he lacked the necessary notions of limits and convergence when summing infinite series, Kepler’s efforts lack mathematical rigour, as had his determination of his second law, a fact that Kepler was more than aware of. However, as with his second law he was prepared to sacrifice rigour for a practical functioning solution and to leave it to prosperity posterity to clean up the mess.

Having devoted so much time and effort to the task Kepler decided to publish his studies and immediately ran into new problems. There was at the time no printer/publisher in Linz so Kepler was forced to send his manuscript to Markus Welser, rich trader and science patron from Augsburg, who initiated the sunspot dispute between Galileo and Christoph Scheiner, to get his book published there. Unfortunately none of the printer/publishers in Augsburg were prepared to take on the risk of publishing the book and when Welser died in 1614 Kepler had to retrieve his manuscript and make other arrangements. In 1615 he fetched the printer Johannes Plank from Erfurt to Linz and paid him to print the book at his own cost. Unfortunately it proved to be anything but a best seller leaving Kepler with a loss on his efforts. In order to make his new discoveries available to a wider audience Kepler edited a very much simplified German edition in the same year under the title Ausszug auss der Vralten Messkunst Archimedis (Excerpts from the ancient art of mensuration by Archimedes). This book is important in the history of mathematics for provided the first German translations of numerous Greek and Latin mathematical terms. Plank remained in Linz and became Kepler’s house publisher during his time there.

Ausszug auss der Vralten Messkunst Archimedis title page Source

Ausszug auss der Vralten Messkunst Archimedis title page
Source

Although not one of his most successful works Kepler’s Nova stereometria doliorum is historically important for two different reasons. It was the first book to present a systematic study of the volumes of barrels based on geometrical principles and it also plays an important role in the history of infinitesimal calculus.

 

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Filed under History of Computing, History of Mathematics

Hans Holbein and the Nürnberg–Ingolstadt–Vienna Renaissance mathematical nexus.

There is a strong tendency, particularly in the popular history of science, to write about or present scientists as individuals. This leads to a serious distortion of the way that science develops and in particular propagates the lone genius myth. In reality science has always been a collective endeavour with its practitioners interacting in many different ways and on many different levels. In the Renaissance, when travelling from one end of Europe to the other would take weeks and letters often even longer, one might be excused for thinking that such cooperation was very low level but in fact the opposite was the truth, with scholars in the mathematical sciences exchanging information and ideas throughout Europe. A particularly strong mathematical nexus existed in the Southern German speaking area between the cities of Nürnberg, Ingolstadt and Vienna in the century between 1450 and 1550. Interestingly two of the paintings of the Northern Renaissance artist Hans Holbein the Younger open a door into this nexus.

Holbein (c. 1497–1543) was born in Augsburg the son of the painter and draughtsman Hans Holbein the Elder. As a young artist he lived and worked for a time in Basel where he became acquainted with Erasmus and worked for the printer publisher Johann Froben amongst others. Between 1526 and 1528 he spent some time in England in the household of Thomas More and it is here that he painted the second portrait I shall be discussing. The next four years find him living in Basel again before he returned to England in 1532 where he became associated with the court of Henry VIII, More having fallen out of favour. It was at the court that he painted, what is probably his most well know portrait, The Ambassadors in 1533.

Hans Holbein The Ambassadors Source: Wikimedia Commons

Hans Holbein The Ambassadors
Source: Wikimedia Commons

The painting shows two courtiers, usually identified as the French Ambassador Jean de Dinteville and Georges de Selve, Bishop of Lavaur standing on either side of a set of shelves laden with various books and instruments. There is much discussion was to what the instruments are supposed to represent but it is certain that, whatever else they stand for, they represent the quadrivium, arithmetic, geometry music and astronomy, the four mathematical sciences taught at European medieval universities. There are two globes, on the lower shelf a terrestrial and on the upper a celestial one. The celestial globe has been positively identified, as a Schöner globe and the terrestrial globe also displays characteristics of Schöner’s handwork.

Terrestrial Globe The Ambassadors Source Wikimedia Commons

Terrestrial Globe The Ambassadors
Source Wikimedia Commons

Celestial Globe The Ambassadors Source Wikimedia Commons

Celestial Globe The Ambassadors
Source Wikimedia Commons

Johannes Schöner (1477–1547) was professor for mathematics at the Egidienöberschule in Nürnberg, the addressee of Rheticus’ Narratio Prima, the founder of the tradition of printed globe pairs, an editor of mathematical texts for publication (especially for Johannes Petreius the sixteenth centuries most important scientific publisher) and one of the most influential astrologers in Europe. Schöner is a central and highly influential figure in Renaissance mathematics.

On the left hand side of the lower shelf is a copy of Peter Apian’s Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen (published in Ingolstadt in 1527) held open by a ruler. This is a popular book of commercial arithmetic, written in German, typical of the period. Peter Apian (1495–1552) professor of mathematics at the University of Ingolstadt, cartographer, printer-publisher and astronomer was a third generation representative of the so-called Second Viennese School of Mathematics. A pupil of Georg Tannstetter (1482–1535) a graduate of the University of Ingolstadt who had followed his teachers Johannes Stabius and Andreas Stiborious to teach at Conrad Celtis’ Collegium poetarum et mathematicorum, of which more later. Together Apian and Tannstetter produced the first printed edition of the Optic of Witelo, one of the most important medieval optic texts, which was printed by Petreius in Nürnberg in 1535. The Tannstetter/Apian/Petreius Witelo was one of the books that Rheticus took with him as a present for Copernicus when he visited him in 1539. Already, a brief description of the activities of Schöner and Apian is beginning to illustrate the connection between our three cities.

Apian's Arithmetic Book The Ambassadors Source: Wikimedia Commons

Apian’s Arithmetic Book The Ambassadors
Source: Wikimedia Commons

When Sebastian Münster (1488–1552), the cosmographer, sent out a circular requesting the cartographers of Germany to supply him with data and maps for his Cosmographia, he specifically addressed both Schöner and Apian by name as the leading cartographers of the age. Münster’s Cosmographia, which became the biggest selling book of the sixteenth century, was first published by Heinrich Petri in Basel in 1544. Münster was Petri’s stepfather and Petri was the cousin of Johannes Petreius, who learnt his trade as printer publisher in Heinrich’s printing shop in Basel. The Petri publishing house was also part of a consortium with Johann Amerbach and Johann Froben who had employed Hans Holbein in his time in Basel. Wheels within wheels.

The, mostly astronomical, instruments on the upper shelf are almost certainly the property of the German mathematician Nicolaus Kratzer (1487–1550), who is the subject of the second Holbein portrait who will be looking at.

Nicolas Kratzer by Hans Holbein Source: Wikimedia Commona

Nicolas Kratzer by Hans Holbein
Source: Wikimedia Commona

Born in Munich and educated at the universities of Cologne and Wittenberg Kratzer, originally came to England, like Holbein, to become part of the Thomas More household, where he was employed as a tutor for More’s children. Also like Holbein, Kratzer moved over to Henry VIII’s court as court horologist or clock maker, although the clocks he was responsible for making were more probably sundials than mechanical ones. During his time as a courtier Kratzer also lectured at Oxford and is said to have erected a monumental stone sundial in the grounds of Corpus Christi College. One polyhedral sundial attributed to Kratzer is in the Oxford Museum for the History of Science.

Polyhedral Sundial attributed to Nicolas Kratzer Source: MHS Oxford

Polyhedral Sundial attributed to Nicolas Kratzer
Source: MHS Oxford

In 1520 Kratzer travelled to Antwerp to visit Erasmus and here he met up with Nürnberg’s most famous painter Albrecht Dürer, who regular readers of this blog will know was also the author of a book on mathematics. Dürer’s book contains the first printed instructions, in German, on how to design, construct and install sundials, so the two men will have had a common topic of interest to liven there conversations. Kratzer witnessed Dürer, who was in Antwerp to negotiate with the German Emperor, painting Erasmus’ portrait and Dürer is said to have also drawn a portrait of Kratzer that is now missing. After Kratzer returned to England and Dürer to Nürnberg the two of them exchanged, at least once, letters and it is Kratzer’s letter that reveals some new connections in out nexus.

Albrecht Dürer selfportrait Source: Wikimedia Commons

Albrecht Dürer selfportrait
Source: Wikimedia Commons

In his letter, from 1524, Kratzer makes inquires about Willibald Pirckheimer and also asks if Dürer knows what has happened to the mathematical papers of Johannes Werner and Johannes Stabius who had both died two years earlier.

Willibald Pirckheimer (1470–1530) a close friend and patron of Dürer’s was a rich merchant, a politician, a soldier and a humanist scholar. In the last capacity he was the hub of a group of largely mathematical humanist scholars now known as the Pirckheimer circle. Although not a mathematician himself Pirckheimer was a fervent supporter of the mathematical sciences and produced a Latin translation from the Greek of Ptolemaeus’ Geōgraphikḕ or Geographia, Pirckheimer’s translation provided the basis for Sebastian Münster’s edition, which was regarded as the definitive text in the sixteenth century. Stabius and Werner were both prominent members of the Pirckheimer circle.

Willibald Pirckheimer by Albrecht Dürer Source: Wikimedia Commons

Willibald Pirckheimer by Albrecht Dürer
Source: Wikimedia Commons

The two Johanneses, Stabius (1450–1522) and Werner (1468–1522), had become friends at the University of Ingolstadt where the both studied mathematics. Ingolstadt was the first German university to have a dedicated chair for mathematics. Werner returned to his hometown of Nürnberg where he became a priest but the Austrian Stabius remained in Ingolstadt, where he became professor of mathematics. The two of them continued to correspond and work together and Werner is said to have instigated the highly complex sundial on the wall of the Saint Lorenz Church in Nürnberg, which was designed by Stabius and constructed in 1502.

St Lorenz Church Nürnberg Sundial 1502 Source: Astronomie in Nürnberg

St Lorenz Church Nürnberg Sundial 1502
Source: Astronomie in Nürnberg

It was also Werner who first published Stabius’ heart shaped or cordiform map projection leading to it being labelled the Werner-Stabius Projection. This projection was used for world maps by Peter Apian as well as Oronce Fine, France’s leading mathematicus of the sixteenth century and Gerard Mercator, of whom more, later. The network expands.

Mercator cordiform world map 1538 Source: American Geographical Society Library

Mercator cordiform world map 1538
Source: American Geographical Society Library

In his own right Werner produced a partial Latin translation from the Greek of Ptolemaeus’ Geographia, was the first to write about prosthaphaeresis (a trigonometrical method of simplifying calculation prior to the invention of logarithms), was the first to suggest the lunar distance method of determining longitude and was in all probability Albrecht Dürer’s maths teacher. He also was the subject of an astronomical dispute with Copernicus.

Johannes Werner Source: Wikimedia Commons

Johannes Werner
Source: Wikimedia Commons

Regular readers of this blog will know that Stabius co-operated with Albrecht Dürer on a series of projects, including his famous star maps, which you can read about in an earlier post here.

Johannes Statius Portrait by Albrecht Dürer Source: Wikimedia Commons

Johannes Statius Portrait by Albrecht Dürer
Source: Wikimedia Commons

An important non-Nürnberger member of the Pirckheimer Circle was Conrad Celtis (1459–1508), who is known in Germany as the arch-humanist. Like his friend Pirckheimer, Celtis was not a mathematician but believed in the importance of the mathematical sciences. Although already graduated he spent time in 1489 on the University of Kraków in order to get the education in mathematics and astronomy that he couldn’t get at a German university. Celtis had spent time at the humanist universities of Northern Italy and his mission in life was to demonstrate that Germany was just as civilised and educated as Italy and not a land of barbarians as the Italians claimed. His contributions to the Nuremberg Chronicle can be viewed as part of this demonstration. He believed he could achieve his aim by writing a comprehensive history of Germany including, as was common at the time its geography. In 1491/92 he received a teaching post in Ingolstadt, where he seduced the professors of mathematics Johannes Stabius and Andreas Stiborius (1464–1515) into turning their attention from astrology for medicine student, their official assignment, to mathematical cartography in order to help him with his historical geography.

Conrad Celtis Source: Wikimedia Commons

Conrad Celtis
Source: Wikimedia Commons

Unable to achieve his ends in Ingolstadt Celtis decamped to Vienna, taking Stabius and Stiborius with him, to found his Collegium poetarum et mathematicorum as mentioned above and with it the so-called Second Viennese School of Mathematics; the first had been Peuerbach and Regiomontanus in the middle of the fifteenth century. Regiomontanus spent the last five years of his life living in Nürnberg, where he set up the world’s first scientific publishing house. Stiborius’ pupil Georg Tannstetter proved to be a gifted teacher and Peter Apian was by no means his only famous pupil.

The influence of the Nürnberg–Ingolstadt–Vienna mathematicians reached far beyond their own relatively small Southern German corridor. As already stated Münster in Basel stood in contact with both Apian and Schöner and Stabius’ cordiform projection found favour with cartographers throughout Northern Europe. Both Apian and Schöner exercised a major influence on Gemma Frisius in Louvain and through him on his pupils Gerard Mercator and John Dee. As outlined in my blog post on Frisius, he took over editing the second and all subsequent editions of Apian’s Cosmographia, one of the most important textbooks for all things astronomical, cartographical and to do with surveying in the sixteenth century. Frisius also learnt his globe making, a skill he passed on to Mercator, through the works of Schöner. Dee and Mercator also had connections to Pedro Nunes (1502–1578) the most important mathematicus on the Iberian peninsular. Frisius had several other important pupils who spread the skills in cosmography, and globe and instrument making that he had acquired from Apian and Schöner all over Europe.

Famously Rheticus came to Nürnberg to study astrology at the feet of Johannes Schöner, who maintained close contacts to Philipp Melanchthon Rheticus patron. Schöner was the first professor of mathematics at a school designed by Melanchthon. Melanchthon had learnt his mathematics and astrology at the University of Tübingen from Johannes Stöffler (1452–1531) another mathematical graduate from Ingolstadt.

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica Source: Wikimedia Commons

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica
Source: Wikimedia Commons

Another of Stöffler’s pupils was Sebastian Münster. During his time in Nürnberg Rheticus became acquainted with the other Nürnberger mathematicians and above all with the printer-publisher Johannes Petreius and it was famously Rheticus who brought the manuscript of Copernicus’ De revolutionibus to Nürnberg for Petreius to publish. Rheticus says that he first learnt of Copernicus’s existence during his travels on his sabbatical and historians think that it was probably in Nürnberg that he acquired this knowledge. One of the few pieces of astronomical writing from Copernicus that we have is the so-called Letter to Werner. In this manuscript Copernicus criticises Werner’s theory of trepidation. Trepidation was a mistaken belief based on faulty data that the rate of the precession of the equinoxes is not constant but varies with time. Because of this highly technical dispute amongst astronomers Copernicus would have been known in Nürnberg and thus the assumption that Rheticus first heard of him there. Interestingly Copernicus includes observations of Mercury made by Bernhard Walther (1430–1504), Regiomontanus partner, in Nürnberg; falsely attributing some of them to Schöner, so a connection between Copernicus and Nürnberg seems to have existed.

In this brief outline we have covered a lot of ground but I hope I have made clear just how interconnected the mathematical practitioners of Germany and indeed Europe were in the second half of the fifteenth century and the first half of the sixteenth. Science is very much a collective endeavour and historians of science should not just concentrate on individuals but look at the networks within which those individual operate bringing to light the influences and exchanges that take place within those networks.

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

A double bicentennial – George contra Ada – Reality contra Perception

The end of this year sees a double English bicentennial in the history of computing. On 2 November we celebrate the two hundredth anniversary of the birth of mathematician and logician Georg Boole then on 10 December the two hundredth anniversary of the birth of ‘science writer’ Augusta Ada King, Countess of Lovelace. It is an interesting exercise to take a brief look at how these two bicentennials are being perceived in the public sphere.

As I have pointed out in several earlier posts Ada was a member of the minor aristocracy, who, although she never knew her father, had a wealthy well connected mother. She had access to the highest social and intellectual circles of early Victorian London. Despite being mentored and tutored by the best that London had to offer she failed totally in mastering more than elementary mathematics. So, as I have also pointed out more than once, to call her a mathematician is a very poor quality joke. Her only ‘scientific’ contribution was to translate a memoire on Babbage’s Analytical Engine from French into English to which are appended a series of new notes. There is very substantial internal and external evidence that these notes in fact stem from Babbage and not Ada and that she only gave them linguistic form. What we have here is basically a journalistic interview and not a piece of original work. It is a historical fact that she did not write the first computer programme, as is still repeated ad nauseam every time her name is mentioned.

However the acolytes of the Cult of the Holy Saint Ada are banging the advertising drum for her bicentennial on a level comparable to that accorded to Einstein for the centenary of the General Theory of Relativity. On social media ‘Finding Ada’ are obviously planning massive celebrations, which they have already indicated although the exact nature of them has yet to be revealed. More worrying is the publication of the graphic novel The Thrilling Adventures of Lovelace and Babbage: The (Mostly) True Story of the First Computer (note who gets first billing!) by animator and cartoonist Sydney Padua. The Analytical Engine as of course not the first computer that honour goes to Babbage’s Difference Engine. More important Padua’s novel is not even remotely ‘mostly’ true but largely fictional. This wouldn’t matter that much if said book had not received major media attention. Attention that compounded the error by conveniently forgetting the mostly. The biggest lie in the work of fiction is the claim that Ada was somehow directly involved in the conception and construction of the Analytical engine. In reality she had absolutely nothing to do with either its conception or its construction.

This deliberate misconception has been compounded by a, in social media widely disseminated, attempt to get support for a Lovelace, Babbage Analytical Engine Lego Set. The promoter of this enterprise has written in his blurb:

Ada Lovelace (1815-1852) is widely credited as the first computer scientist and Charles Babbage (1791-1871) is best remembered for originating the concept of a programmable computer. Together they collaborated on Babbage’s early mechanical general-purpose computer, the Analytical Engine.

Widely credited by whom? If anybody is the first computer scientist in this set up then it’s Babbage. Others such as Leibniz speculated on what we now call computer science long before Ada was born so I think that is another piece of hype that we can commit to the trashcan. Much more important is the fact that they did not collaborate on the Analytical Engine that was solely Babbage’s baby. This factually false hype is compounded in the following tweet from 21 July, which linked to the Lego promotion:

Historical lego [sic] of Ada Lovelace’s conception of the first programmable computer

To give some perspective to the whole issue it is instructive to ask about what in German is called the ‘Wirkungsgeschichte’, best translated as historical impact, of Babbage’s efforts to promote and build his computers, including the, in the mean time, notorious Menabrea memoire, irrespective as to who actually formulated the added notes. The impact of all of Babbage’s computer endeavours on the history of the computer is almost nothing. I say almost because, due to Turing, the notes did play a minor role in the early phases of the post World War II artificial intelligence debate. However one could get the impression from the efforts of the Ada Lovelace fan club, strongly supported by the media that this was a highly significant contribution to the history of computing that deserves to be massively celebrated on the Lovelace bicentennial.

Let us now turn our attention to subject of our other bicentennial celebration, George Boole. Born into a working class family in Lincoln, Boole had little formal education. However his father was a self-educated man with a thirst for knowledge, who instilled the same characteristics in his son. With some assistance he taught himself Latin and Greek and later French, German and Italian in order to be able to read the advanced continental mathematics. His father went bankrupt when he was 16 and he became breadwinner for the family, taking a post as schoolmaster in a small private school. When he was 19 he set up his own small school. Using the library of the local Mechanics Institute he taught himself mathematics. In the 1840s he began to publish original mathematical research in the Cambridge Mathematical Journal with the support of Duncan Gregory, a great great grandson of Newton’s contemporary James Gregory. Boole went on to become one of the leading British mathematicians of the nineteenth century and despite his total lack of formal qualifications he was appointed Professor of Mathematics at the newly founded Queen’s College of Cork in 1849.

Although a fascinating figure in the history of mathematics it is Boole the logician, who interests us here. In 1847 Boole published the first version of his logical algebra in the form of a largish pamphlet, Mathematical Analysis of Logic. This was followed in 1854 by an expanded version of his ideas in his An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probability. These publications contain the core of Boolean algebra, the final Boolean algebra was actually produced by Stanley Jevons, only the second non-standard algebra ever to be developed. The first non-standard algebra was Hamilton’s quaternions. For non-mathematical readers standard algebra is the stuff we all learned (and loved!) at school. Boolean algebra was Boole’s greatest contribution to the histories of mathematics, logic and science.

When it first appeared Boole’s logic was large ignored as an irrelevance but as the nineteenth century progressed it was taken up and developed by others, most notably by the German mathematician Ernst Schröder, and provided the tool for much early work in mathematical logic. Around 1930 it was superseded in this area by the mathematical logic of Whitehead’s and Russell’s Principia Mathematica. Boole’s algebraic logic seemed destined for the novelty scrap heap of history until a brilliant young American mathematician wrote his master’s thesis.

Claude Shannon (1916–2001) was a postgrad student of electrical engineering of Vannevar Bush at MIT working on Bush’s electro-mechanical computer the differential analyzer. Having learnt Boolean algebra as an undergraduate Shannon realised that it could be used for the systematic and logical design of electrical switching circuits. In 1937 he published a paper drawn from his master’s thesis, A Symbolic Analysis of Relay and Switching Circuits. Shannon switching algebra, applied Boolean algebra, would go on to supply the basis of the hardware design of all modern computers. When people began to write programs for the computers designed with Shannon’s switching algebra it was only natural that they would use Boole’s two-valued (1/0, true/false, on/off) algebra to write those programs. Almost all modern computers are both in their hardware and there software applied Boolean algebra. One can argue, as I have actually done somewhat tongue in cheek in a lecture, that George Boole is the ‘father’ of the modern computer. (Somewhat tongue in cheek, as I don’t actually like the term ‘father of’). The modern computer has of course many fathers and mothers.

In George Boole, as opposed to Babbage and Lovelace, we have a man whose work made a massive real contribution to history of the computer and although both the Universities of Cork and Lincoln are planning major celebration for his bicentennial they have been, up till now largely ignored by the media with the exception of the Irish newspapers who are happy to claim Boole, an Englishman, as one of their own.

The press seems to have decided that a ‘disadvantaged’ (she never was, as opposed to Boole) female ‘scientist’, who just happens to be Byron’s daughter is more newsworthy in the history of the computer than a male mathematician, even if she contributed almost nothing and he contributed very much.

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Filed under History of Computing, History of Mathematics, Ladies of Science, Myths of Science