Category Archives: History of Mathematics

Emmy the student and Emmy the communist!

Emmy Noether’s birthday on 23 March saw her honoured with a Google Doodle, which of course led to various people posting brief biographies of Erlangen’s most famous science personality or drawing attention to existing posts in the Internet.

Emmy Google Doodle

Almost all of these posts contain two significant errors concerning Emmy’s career that I would like to correct here. For those interested I have written earlier posts on Emmy’s family home in Erlangen and the problems she went through trying to get her habilitation, the German qualification required to be able to teach at university.

The first oft repeated error concerns Emmy’s education and I quote a typical example below:

Today she is celebrated for her contributions to abstract algebra and theoretical physics, but in 20th-century Bavaria, Noether had to fight for every bit of education and academic achievement. Women were not allowed to enrol at the University of Erlangen, so Noether had to petition each professor to attend classes.

As a teenager Emmy displayed neither an interest nor a special aptitude for mathematics but rather more for music and dance. She attended the Städtische Höhere Töchterschule (the town secondary girls’ school), now the Marie-Therese-Gymnasium, and in 1900 graduated as a teacher for English and French at the girls’ school in Ansbach. In 1903 she took her Abitur exam externally at the Königlichen Realgymnasium in Nürnberg. The Abitur is the diploma from German secondary school qualifying for university admission or matriculation. Previous to this she had been auditing some mathematics courses in Göttingen as a guest student with the personal permission of the professors whose courses she visited, hence the claim above. However she had become ill and had returned home to Erlangen. In 1903 the laws were changed in Bavaria allowing women to register at university for the first time. Emmy registered as a regular student at the University of Erlangen in 1903 and graduated with a PhD in mathematics in 1907, under the supervision of Paul Gordon, in invariant theory. She was only the second woman in Germany to obtain a PhD in mathematics. In 1908 she became a member of the Circolo Matematico di Palermo and in 1909 a member of the Deutschen Mathematiker-Vereinigung. In 1909 Hilbert and Klein invited her to come to the University of Göttingen, as a post-doc researcher. It was here in 1915 that Hilbert suggested that she should habilitate with the well know consequences.

Emmy remained in Göttingen until the Nazis came to power in 1933. She held guest professorships in Moscow in 1928/29 and in Frankfort am Main in 1930. She was awarded the Ackermann-Teubner Memorial Prize for her complete scientific work in 1932 and held the plenary lecture at the International Mathematical Congress in Zurich also in 1932. In 1933 when the Nazis came to power she was expelled from her teaching position in Göttingen and it is here that the second oft repeated error turns up.

On coming to power the Nazis introduced the so-called Gesetz zur Wiederherstellung des Berufsbeamtentums, (The Law for the Restoration of the Professional Civil Service). This was a law introduced by the Nazis to remove all undesirables from state employment, this of course meant the Jews but also, socialists, communists and anybody else deemed undesirable by the Nazi Party. Like many of her colleges in the mathematics department at Göttingen Emmy was removed from her teaching position under this law. In fact the culling in the mathematics department was so extreme that it led to a famous, possibly apocryphal, exchange between Bernhard Rust (and not Hermann Göring, see comments) and David Hilbert.

Rust: “I hear you have some problems in the mathematics department at Göttingen Herr Professor”.

Hilbert: “No, there are no problems; there is no mathematics department in Göttingen”.

The Wikipedia article on the history of the University Göttingen gives the story as follows (in German)

Ein Jahr später erkundigte sich der Reichserziehungsminister Bernhard Rust anlässlich eines Banketts bei dem neben ihm platzierten Mathematiker David Hilbert ob das mathematische Institut in Göttingen durch die Entfernung der jüdischen, demokratischen und sozialistischen Mathematiker gelitten habe. Hilbert soll in seiner ostpreußischen Mundart (laut Abraham Fraenkel, Lebenskreise, 1967, S. 159) erwidert haben: „Jelitten? Dat hat nich jelitten, Herr Minister. Dat jibt es doch janich mehr.“

The source here is given as Abraham Fraenkel in his autobiography Lebenkreise published in 1967.

This translates as follows:

One year later [that is after the expulsions in 1933] the Imperial Education Minister Bernhard Rust, who was seated next to the mathematician David Hilbert at a banquet, inquired, whether the Mathematics Institute at Göttingen had suffered through the removal of the Jewish, democratic and socialist mathematicians. Hilbert is said to have replied in his East Prussian dialect” Suffered? It hasn’t suffered, Herr Minister. It doesn’t exist anymore”

It is usually claimed that Emmy lost her position because she was Jewish, a reasonable assumption but not true. Emmy lost her position, like many other in Göttingen, because the Nazis thought she was a communist. Like many European universities in the 1920s and 30s Göttingen was a hot bed of radical intellectual socialism. Emmy had been a member of a radical socialist party in the early twenties but changed later to the more moderate SPD, who were also banned by the Nazis. However it was her guest professorship in Moscow that proved her undoing. Because she reported positively on her year in Russia the Nazis considered her to be a communist and this was the reason for her expulsion from the university in 1933.

Initially Emmy, after her expulsion, actually applied for a position at the University of Moscow but the attempts by the Russian topologist Pavel Alexandrov to get her a position got bogged down in the Russian bureaucracy and so when, through the good offices of Hermann Weyl, she received the offer of a guest professorship in America at Bryn Mawr College she accepted. In America she taught at Bryn Mawr and the Institute of Advanced Studies in Princeton but tragically died of cancer of the uterus in 1935.

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Filed under History of Mathematics, Ladies of Science

A Swiss Clockmaker

We all have clichéd images in our heads when we hear the names of countries other than our own. For many people the name Switzerland evokes a muddled collection of snow-covered mountains, delicious superior chocolates and high precision clocks and watches. Jost Bürgi who was born in the small town of Lichtensteig, in the  Toggenburg region of the canton of St. Gallen on 28 February 1552 fills this cliché as the most expert clockmaker in the sixteenth century. However Bürgi was much more that just a Swiss clockmaker, he was also an instrument maker, an astronomer, a mathematician and in his private life a successful property owner and private banker, the last of course serving yet another Swiss cliché.

As we all too many figures, who made significant contributions to science and technology in the Renaissance we know next to nothing about Bürgi’s origins or background. There is no known registration of his birth or his baptism; his date of birth is known from the engraving shown below from 1592, in which the portrait was added in 1619 but which was first published in 1648. That the included date is his birthday was confirmed by Bürgi’s brother in law.

Bramer1648

His father was probably the locksmith Lienz Bürgi but that is not known for certain. About his education or lack of it nothing is known at all and just as little is known about where he learnt his trade as clockmaker. Various speculations have been made by historians over the years but they remain just speculations. The earliest documentary proof that we have of Bürgi’s existence is his employment contract when he entered the service of the Landgrave Wilhelm IV of Hessen-Kassel as court clockmaker, already twenty-seven years old, on 25 July 1579. Wilhelm was unique amongst the German rulers of the Renaissance in that he was not only a fan or supporter of astronomy but was himself an active practicing astronomer. In his castle in Kassel he constructed, what is recognised as, the first observatory in Early Modern Europe.

Wilhelm IV. von Hessen-Kassel Source: Wikimedia Commons

Wilhelm IV. von Hessen-Kassel
Source: Wikimedia Commons

He also played a major role in persuading the Danish King Frederick II, a cousin, to supply Tycho Brahe with the necessary land and money to establish an observatory in Denmark. In the 1560s Wilhelm was supported in his astronomical activities by Andreas Schöner, the son of the famous Nürnberger cartographer, globe and instrument maker, astronomer, astrologer and mathematician Johannes Schöner. He also commissioned the clockmaker Eberhard Baldewein (1525-1593) to construct two planet clocks and a mechanical globe.

 

Eberhart Baldewein Planet clock 1661 Source: Wikimedia Commons

Eberhart Baldewein Planet clock 1661
Source: Wikimedia Commons

The planet clock shows the positions of the sun, moon and the planets, based on Peter Apian’s Astronomicom Caessareum, on its various dials.

 

Eberhard Baldewein Mechanical Celestial Globe circa 1573

Eberhard Baldewein Mechanical Celestial Globe circa 1573 The globe, finished by Heinrich Lennep in 1693, was used to record the position of the stars mapped by Wilhelm and his team in their observations.

These mechanical objects were serviced and maintained by Baldewein’s ex-apprentice, Hans Bucher, who had helped to build them and who had been employed by Wilhelm, for this purpose, since 1560. When Bucher died in 1578-1579 Bürgi was employed to replace him, charged with the maintenance of the existing objects on a fixed, but very generous salary, and commissioned to produce new mechanical instruments for which he would be paid extra. Over the next fifty years Bürgi produced many beautiful and highly efficient clocks and mechanical globes both for Wilhelm and for others.

Bürgi Quartz Clock 1622-27 Source: Swiss Physical Society

Bürgi Quartz Clock 1622-27
Source: Swiss Physical Society

 

 

 

 

 

Bürgi Mechanical Celestial Globe 1594 Source: Wikimedia Commons

Bürgi Mechanical Celestial Globe 1594
Source: Wikimedia Commons

 

 

Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock made 1585 in Kassel, now at Nordiska Museet in Stockholm. Source Wikimedia Commons

Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock made 1585 in Kassel, now at Nordiska Museet in Stockholm.
Source Wikimedia Commons

Bürgi was also a highly inventive clockmaker, who is credited with the invention of both the cross-beat escapement and the remontoire, two highly important improvements in clock mechanics. In the late sixteenth century the average clocks were accurate to about thirty minutes a day, Bürgi’s clock were said to be accurate to less than one minute a day. This amazing increase in accuracy allowed mechanical clocks to be used, for the first time ever, for timing astronomical observations. Bürgi also supplied clocks for this purpose for Tycho’s observatory on Hven. In 1592 Wilhelm presented his nephew Rudolph II, the German Emperor, with one of Bürgi’s mechanical globes and Bürgi was sent to Prague with the globe to demonstrate it to Rudolph. This was his first contact with what would later become his workplace. Whilst away from Kassel Bürgi’s employer, Wilhelm died. Before continuing the story we need to go back and look at some of Bürgi’s other activities.

As stated at the beginning Bürgi was not just a clockmaker. In 1584 Wilhelm appointed the Wittenberg University graduate Christoph Rothmann as court astronomer. From this point on the three, Wilhelm, Rothmann and Bürgi, were engaged in a major programme to map the heavens, similar to and just as accurate, as that of Tycho on Hven. The two observatories exchanged much information on instruments, observations and astronomical and cosmological theories. However all was not harmonious in this three-man team. Although Wilhelm treated Bürgi, whom he held in high regard, with great respect Rothmann, who appears to have been a bit of a snob, treated Bürgi with contempt because he was uneducated and couldn’t read or write Latin, that Bürgi was the better mathematician of the two might have been one reason for Rothmann’s attitude.

In the 1580s the itinerant mathematician and astronomer Paul Wittich came to Kassel from Hven and taught Bürgi prosthaphaeresis, a method using trigonometric formulas, of turning multiplication into addition, thus simplifying complex astronomical calculations. The method was first discovered by Johannes Werner in Nürnberg at the beginning of the sixteenth century but he never published it and so his discovery remained unknown. It is not known whether Wittich rediscovered the method or learnt of it from Werner’s manuscripts whilst visiting Nürnberg. The method was first published by Nicolaus Reimers Baer, who was then accused by Tycho of having plagiarised the method, Tycho claiming falsely that he had discovered it. In fact Tycho had also learnt it from Wittich. Bürgi had expanded and improved the method and when Baer also came to Kassel in 1588, Bürgi taught him the method and how to use it, in exchange for which Baer translated Copernicus’ De revolutionibus into German for Bürgi. This was the first such translation and a copy of Baer’s manuscript is still in existence in Graz. Whilst Baer was in Kassel Bürgi created a brass model of the Tychonic geocentric-heliocentric model of the cosmos, which Baer claimed to have discovered himself. When Tycho got wind of this he was apoplectic with rage.

In 1590 Rothmann disappeared off the face of the earth following a visit to Hven and for the last two years of Wilhelm’s life Bürgi took over as chief astronomical observer in Kassel, proving to be just as good in this work as in his clock making.

Following Wilhelm’s death his son Maurice who inherited the title renewed Bürgi’s contract with the court.

 

Kupferstich mit dem Porträt Moritz von Hessen-Kassel aus dem Werk Theatrum Europaeum von 1662 Source: Wikimedia Commons

Kupferstich mit dem Porträt Moritz von Hessen-Kassel aus dem Werk Theatrum Europaeum von 1662
Source: Wikimedia Commons

However Maurice did not share his father’s love of astronomy investing his spare time instead in the study of alchemy. Bürgi however continued to serve the court as clock and instrument maker. Over the next eight years Bürgi made several visits to the Emperor’s court in Prague and in 1604 Rudolph requested Maurice to allow him to retain Bürgi’s services on a permanent basis. Maurice acquiesced and Bürgi moved permanently to Prague although still remaining formally in service to Maurice in Kassel. Rudolph gave Bürgi a very generous contract paying him 60 gulden a month as well as full board and lodging. As in Kassel all clocks and globes were paid extra. To put that into perspective 60 gulden was a yearly wage for a young academic starting out on his career!

In Prague Bürgi worked closely with the Imperial Mathematicus, Johannes Kepler. Kepler, unlike Rothmann, respected Bürgi immensely and encouraged him to publish his mathematical works. Bürgi was the author of an original Cos, an algebra textbook, from which Kepler says he learnt much and which only saw the light of day through Kepler’s efforts. Kepler was also responsible for the publication of Bürgi’s logarithmic tables in 1620.

 

Bürgi's Logarithmic Tables Source: University of Graz

Bürgi’s Logarithmic Tables
Source: University of Graz

This is probably Bürgi’s greatest mathematical achievement and he is considered along side of John Napier as the inventor of logarithms. In many earlier historical works Bürgi is credited with having invented logarithms before Napier. Napier published his tables in 1614 six years before Bürgi and is known to have been working on them for twenty years, that is since 1594. Bürgi’s fan club claim that he had invented his logarithms in 1588 that is six years earlier than Napier. However modern experts on the history of logarithms think that references to 1588 are to Bürgi’s use of prosthaphaeresis and that he didn’t start work on his logarithms before 1604. However it is clear that the two men developed the concept independently of each other and both deserve the laurels for their invention. It should however be pointed out that the concept on which logarithms are based was known to Archimedes and had already been investigated by Michael Stifel earlier in the sixteenth century in a work that was probably known to Bürgi.

Through his work as clock maker Bürgi became a very wealthy man and invested his wealth with profit in property deals and as a private banker lending quite substantial sums to his customers. In 1631 Bürgi, now 80 years old, retired and returned ‘home’ to Kassel where he died in January of the following year shortly before his 81st birthday. His death was registered in the Church of St Martin’s on the 31 January 1632. Although now only known to historians of science and horology, in his own time Bürgi was a well-known and highly respected, astronomer, mathematician and clock maker who made significant and important contributions to all three disciplines.

 

 

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

Preach truth – serve up myths.

Over Christmas I poked a bit of fun at Neil deGrasse Tyson for tweeting that Newton would transform the world by the age of 30, pointing out he was going on forty-five when he published his world transforming work the Principia. The following day NdGT posted a short piece on Face Book praising his own tweet and its success. Here he justified his by the age of thirty claim but in doing so rode himself deeper into the mire of sloppy #histsci. You might ask why this matters, to which the answer is very simple. NdGT is immensely popular especially amongst those with little idea of science and less of the history of science and who hang on his every utterance. Numerous historians of science labour very hard to dismantle the myths of science and to replace them with a reasonable picture of how science evolved throughout its long and convoluted history. NdGT disdains those efforts and perpetuates the myths leading his hordes of admirers up the garden path of delusion. Let us take a brief look at his latest propagation of #histmyth.

NdGT’s post starts off with the news that his Newton birthday tweet is the most RTed tweet he has every posted citing numbers that lesser mortals would not even dare to dream about. This of course just emphasises the danger of NdGT as disseminator of false history of science, his reach is wide and his influence is strong. Apparently some Christians had objected to NdGT celebrating Newton’s birthday on Christ’s birthday and NdGT denies that his tweet was intended to be anti-Christian but then goes on to quote the tweet that he sent out in answer to those accusations:

“Imagine a world in which we are all enlightened by objective truths rather than offended by them.”

Now on the whole I agree with the sentiment expressed in this tweet, although I do have vague vision of Orwellian dystopia when people from the scientism/gnu atheist camp start preaching about ‘objective truth’. Doesn’t Pravda mean truth? However I digress.

I find it increasing strange that NdGT’s craving for objective truth doesn’t stretch to the history of science where he seems to much prefer juicy myths to any form of objectivity. And so also in this case. In his post he expands on the tweet I had previously poked fun at. He writes:

Everybody knows that Christians celebrate the birth of Jesus on December 25th.  I think fewer people know that Isaac Newton shares the same birthday.  Christmas day in England – 1642.  And perhaps even fewer people know that before he turned 30, Newton had discovered the laws of motion, the universal law of gravitation, and invented integral and differential calculus.  All of which served as the mechanistic foundation for the industrial revolution of the 18th and 19th centuries that would forever transform the world.

What we are being served up here is a slightly milder version of the ‘annus mirabilis’ myth. This very widespread myth claims that Newton did all of the things NdGT lists above in one miraculous year, 1666, whilst abiding his time at home in Woolsthorpe, because the University of Cambridge had been closed down due to an outbreak of the plague. NdGT allows Newton a little more time, he turned 30 in 1672, but the principle is the same, look oh yee of little brain and tremble in awe at the mighty immaculate God of science Sir Isaac Newton! What NdGT the purported lover of objective truth chooses to ignore, or perhaps he really is ignorant of the facts, is that a generation of some of the best historians of science who have ever lived, Richard S. Westfall, D. T. Whiteside, Frank Manuel, I. Bernard Cohen, Betty Jo Teeter Dobbs and others, have very carefully researched and studied the vast convolute of Newton’s papers and have clearly shown that the whole story is a myth. To be a little bit fair to NdGT the myth was first put in the world by Newton himself in order to shoot down all his opponents in the numerous plagiarism disputes that he conducted. If he had done it all that early then he definitely had priority and the others were all dastardly scoundrels out to steal his glory. We now know that this was all a fabrication on Newton’s part.

Newton was awarded his BA in 1665 and in the following years he was no different to any highly gifted postgraduate trying to find his feet in the world of academic research. He spread his interests wide reading and absorbing as much of the modern science of the time as he could and making copious notes on what he read as well as setting up ambitious research programmes on a wide range of topics that were to occupy his time for the next thirty years. In the eighteen months before being sent down from Cambridge because of the plague he concentrated his efforts on the new analytical mathematics that had developed over the previous century. Whilst reading widely and bringing himself up to date on material that was not taught at Cambridge he simultaneously extended and developed what he was reading laying the foundations for his version of the calculus. It was no means a completed edifice as NdGT, and unfortunately many others, would have us believe but it was still a very notable mathematical achievement. Over the decades he would return from time to time to his mathematical researches building on and extending that initial foundation. He also didn’t ‘invent’ integral and differential calculus but brought together, codified and extended the work of many others, in particular, Descartes, Fermat, Pascal, Barrow and Wallace, who in turn looked back upon two thousand years of history on the topic.

In the period beginning in 1666 he left off with mathematical endeavours and turned his attention to mechanics mostly addressing the work of Descartes. He made some progress and even wondered, maybe inspired by observing a falling apple in his garden in Woolsthorpe, if the force which causes things to fall the Earth is the same as the force which prevents the Moon from shooting off at a tangent to its orbit. He did some back of an envelope calculations, which showed that they weren’t, due to faulty data and he dropped the matter. He didn’t discover the laws of motion and as he derived the law of gravity from Huygens’ law of centripetal force that was first published in 1673 he certainly didn’t do it before he was thirty. In fact most of the work that went into Newton’s magnum opus the Principia was done in an amazing burst of concentrated effort in the years between 1684 and 1687 when Newton was already over forty.

What Newton did do between 1666 and 1672 was to conduct an extensive experimental programme into physical optics, in particular what he termed the phenomenon of colour. This programme resulted in the construction of the first reflecting telescope and in 1672 Newton’s legendary first paper A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; Containing His New Theory about Light and Colors published in the Philosophical Transactions of the Royal Society. Apparently optics doesn’t interest NdGT. Around 1666 Newton also embarked on perhaps his most intensive and longest research programme to discover the secrets of alchemy, whilst starting his life long obsession with the Bible and religion. The last two don’t exactly fit NdGT’s vision of enlightened objective truth.

Newton is without doubt an exceptional figure in the history of science, who has few equals, but like anybody else Newton’s achievements were based on long years of extensive and intensive work and study and are not the result of some sort of scientific miracle in his young years. Telling the truth about Newton’s life and work rather than propagating the myths, as NdGT does, gives students who are potential scientists a much better impression of what it means to be a scientist and is thus in my opinion to be preferred.

As a brief addendum NdGT points out that Newton’s birthday is not actually 25 December (neither is Christ’s by the way) because he was born before the calendar reform was introduced into Britain so we should, if we are logical, be celebrating his birthday on 4 January. NdGT includes the following remark in his explanation, “But the Gregorian Calendar (an awesomely accurate reckoning of Earth’s annual time), introduced in 1584 by Pope Gregory, was not yet adopted in Great Britain.” There is a certain irony in his praise, “an awesomely accurate reckoning of Earth’s annual time”, as this calendar was developed and introduced for purely religious reasons, again not exactly enlightened or objective.

 

 

 

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Filed under History of Astronomy, History of Mathematics, History of Physics, History of science, Myths of Science, Renaissance Science

Mega inanity

Since the lead up to the Turing centennial in 2012 celebrating the birth of one of the great meta-mathematicians of the twentieth century, Alan Mathison Turing, I have observed with increasing horror the escalating hagiographic accounts of Turing’s undoubted historical achievements and the resulting perversion of the histories of twentieth-century science, mathematics and technology and in particular the history of computing.

This abhorrence on my part is not based on a mere nodding acquaintance with Turing’s name but on a deep and long-time engagement with the man and his work. I served my apprenticeship as a historian of science over many years in a research project on the history of formal or mathematical logic. Formal logic is one of the so-called formal sciences the others being mathematics and informatics (or computer science). I have spent my whole life studying the history of mathematics with a special interest in the history of computing both in its abstract form and in its technological realisation in all sorts of calculating aids and machines. I also devoted a substantial part of my formal study of philosophy to the study of the philosophy of mathematics and the logical, meta-logical and meta-mathematical problems that this discipline, some would say unfortunately, generates. The history of all of these intellectual streams flow together in the first half of the twentieth century in the work of such people as Leopold Löwenheim, Thoralf Skolem, Emil Post, Alfred Tarski, Kurt Gödel, Alonso Church and Alan Turing amongst others. These people created a new discipline known as meta-mathematics whilst carrying out a programme delineated by David Hilbert.

Attempts to provide a solid foundation for mathematics using set theory and logic had run into serious problems with paradoxes. Hilbert thought the solution lay in developing each mathematical discipline as a strict axiomatic systems and then proving that each axiomatic system possessed a set of required characteristics thus ensuring the solidity and reliability of a given system. This concept of proving theories for complete axiomatic systems is the meta- of meta-mathematics. The properties that Hilbert required for his axiomatic systems were consistency, which means the systems should be shown to be free of contradictions, completeness, meaning that all of the theorems that belong to a particular discipline are deductible from its axiom system, and finally decidability, meaning that for any well-formed statement within the system it should be possible to produced an algorithmic process to decide if the statement is true within the axiomatic system or not. An algorithm is like a cookery recipe if you follow the steps correctly you will produce the right result.

The meta-mathematicians listed above showed by very ingenious methods that none of Hilbert’s aims could be fulfilled bringing the dream of a secure foundation for mathematics crashing to the ground. Turing’s solution to the problem of decidability is an ingenious thought experiment, for which he is justifiably regarded as one of the meta-mathematical gods of the twentieth century. It was this work that led to him being employed as a code breaker at Bletchley Park during WW II and eventually to the fame and disaster of the rest of his too short life.

Unfortunately the attempts to restore Turing’s reputation since the centenary of his birth in 2012 has led to some terrible misrepresentations of his work and its consequences. I thought we had reach a low point in the ebb and flow of the centenary celebrations but the release of “The Imitation Game”, the Alan Turing biopic, has produced a new series of false and inaccurate statements in the reviews. I was pleasantly pleased to see several reviews, which attempt to correct some of the worst historical errors in the film. You can read a collection of reviews of the film in the most recent edition of the weekly histories of science, technology and medicine links list Whewell’s Gazette. Not having seen the film yet I can’t comment but I was stunned when I read the following paragraph from the abc NEWS review of the film written by Alyssa Newcomb. It’s so bad you can only file it under; you can’t make this shit up.

The “Turing Machine” was the first modern computer to logically process information, running on interchangeable software and essentially laying the groundwork for every computing device we have today — from laptops to smartphones.

Before I analyse this train wreck of a historical statement I would just like to emphasise that this is not the Little Piddlington School Gazette, whose enthusiastic but slightly slapdash twelve-year-old film critic got his facts a little mixed up, but a review that appeared on the website of a major American media company and as such totally unacceptable however you view it.

The first compound statement contains a double whammy of mega-inane falsehood and I had real problems deciding where to begin and finally plumped for the “first modern computer to logically process information, running on interchangeable software”. Alan Turing had nothing to do with the first such machine, the honour going to Konrad Zuse’s Z3, which Zuse completed in 1941. The first such machine in whose design and construction Alan Turing was involved was the ACE produced at the National Physical Laboratory, in London, in 1949. In the intervening years Atanasoff and Berry, Tommy Flowers, Howard Aikin, as well as Eckert and Mauchly had all designed and constructed computers of various types and abilities. To credit Turing with the sole responsibility for our digital computer age is not only historically inaccurate but also highly insulting to all the others who made substantial and important contributions to the evolution of the computer. Many, many more than I’ve named here.

We now turn to the second error contained in this wonderfully inane opening statement and return to the subject of meta-mathematics. The “Turing Machine” is not a computer at all its Alan Turing’s truly genial thought experiment solution to Hilbert’s decidability problem. Turing imagined a very simple machine that consists of a scanning-reading head and an infinite tape that runs under the scanning head. The head can read instructions on the tape and execute them, moving the tape right or left or doing nothing. The question then reduces to the question, which set of instructions on the tape come eventually to a stop (decidable) and which lead to an infinite loop (undecidable). Turing developed this idea to a machine capable of computing any computable function (a universal Turing Machine) and thus created a theoretical model for all computers. This is of course a long way from a practical, real mechanical realisation i.e. a computer but it does provide a theoretical measure with which to describe the capabilities of a mechanical computing device. A computer that is the equivalent of a Universal Turing Machine is called Turing complete. For example, Zuse’s Z3 was Turing complete whereas Colossus, the computer designed and constructed by Tommy Flowers for decoding work at Bletchley Park, was not.

Turing’s work played and continues to play an important role in the theory of computation but historically had very little effect on the development of real computers. Attributing the digital computer age to Turing and his work is not just historically wrong but is as I already stated above highly insulting to all of those who really did bring about that age. Turing is a fascinating, brilliant, and because of what happened to him because of the persecution of homosexuals, tragic figure in the histories of mathematics, logic and computing in the twentieth century but attributing achievements to him that he didn’t make does not honour his memory, which certainly should be honoured, but ridicules it.

I should in fairness to the author of the film review, that I took as motivation from this post, say that she seems to be channelling misinformation from the film distributors as I’ve read very similar stupid claims in other previews and reviews of the film.

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

The Queen of Science – The woman who tamed Laplace.

In a footnote to my recent post on the mythologizing of Ibn al-Haytham I briefly noted the inadequacy of the terms Arabic science and Islamic science, pointing out that there were scholars included in these categories who were not Muslims and ones who were not Arabic. In the comments Renaissance Mathematicus friend, the blogger theofloinn, asked, Who were the non-muslim “muslim” scientists? And (aside from Persians) who were the non-Arab “arab” scientists? And then in a follow up comment wrote, I knew about Hunayn ibn Ishaq and the House of Wisdom, but I was not thinking of translation as “doing science.” From the standpoint of the historian of science this second comment is very interesting and reflects a common problem in the historiography of science. On the whole most people regard science as being that which scientists do and when describing its history they tend to concentrate on the big name scientists.

This attitude is a highly mistaken one that creates a falsified picture of scientific endeavour. Science is a collective enterprise in which the ‘scientists’ are only one part of a collective consisting of scientists, technicians, instrument designers and makers, and other supportive workers without whom the scientist could not carry out his or her work. This often includes such ignored people as the secretaries, or in earlier times amanuenses, who wrote up the scientific reports or life partners who, invisible in the background, often carried out much of the drudgery of scientific investigation. My favourite example being William Herschel’s sister and housekeeper, Caroline (a successful astronomer in her own right), who sieved the horse manure on which he bedded his self cast telescope mirrors to polish them.

Translators very definitely belong to the long list of so-called helpers without whom the scientific endeavour would grind to a halt. It was translators who made the Babylonian astronomy and astrology accessible to their Greek heirs thus making possible the work of Eudoxus, Hipparchus, Ptolemaeus and many others. It was translators who set the ball rolling for those Islamic, or if you prefer Arabic, scholars when they translated the treasures of Greek science into Arabic. It was again translators who kicked off the various scientific Renaissances in the twelfth and thirteenth-centuries and again in the fifteenth-century, thereby making the so-called European scientific revolution possible. All of these translators were also more or less scientists in their own right as without a working knowledge of the subject matter that they were translating they would not have been able to render the texts from one language into another. In fact there are many instances in the history of the transmission of scientific knowledge where an inadequate knowledge of the subject at hand led to an inaccurate or even false translation causing major problems for the scholars who tried to understand the texts in the new language. Translators have always been and continue to be an important part of the scientific endeavour.

The two most important works on celestial mechanics produced in Europe in the long eighteenth-century were Isaac Newton’s Philosophiæ Naturalis Principia Mathematica and Pierre-Simon, marquis de Laplace’s Mécanique céleste. The former was originally published in Latin, with an English translation being published shortly after the author’s death, and the latter in French. This meant that these works were only accessible to those who mastered the respective language. It is a fascinating quirk of history that the former was rendered into French and that latter into English in each case by a women; Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet translated Newton’s masterpiece into French and Mary Somerville translated Laplace’s pièce de résistance into English. I have blogged about Émilie de Châtelet before but who was Mary Somerville? (1)

 

Mary Somerville by Thomas Phillips

Mary Somerville by Thomas Phillips

She was born Mary Fairfax, the daughter of William Fairfax, a naval officer, and Mary Charters at Jedburgh in the Scottish boarders on 26 December 1780. Her parents very definitely didn’t believe in education for women and she spent her childhood wandering through the Scottish countryside developing a lifelong love of nature. At the age of ten, still semi-illiterate, she was sent to Miss Primrose’s boarding school at Musselburgh in Midlothian for one year; the only formal schooling she would ever receive. As a young lady she received lessons in dancing, music, painting and cookery. At the age of fifteen she came across a mathematical puzzle in a ladies magazine (mathematical recreation columns were quite common in ladies magazines in the 18th and 19th-centuries!) whilst visiting friends. Fascinated by the symbols that she didn’t understand, she was informed that it was algebra, a word that meant nothing to her. Later her painting teacher revealed that she could learn geometry from Euclid’s Elements whilst discussing the topic of perspective. With the assistance of her brother’s tutor, young ladies could not buy maths-books, she acquired a copy of the Euclid as well as one of Bonnycastle’s Algebra and began to teach herself mathematics in the secrecy of her bedroom. When her parents discovered this they were mortified her father saying to her mother, “Peg, we must put a stop to this, or we shall have Mary in a strait jacket one of these days. There is X., who went raving mad about the longitude.” They forbid her studies, but she persisted rising before at dawn to study until breakfast time. Her mother eventually allowed her to take some lessons on the terrestrial and celestial globes with the village schoolmaster.

In 1804 she was married off to a distant cousin, Samuel Grieg, like her father a naval officer but in the Russian Navy. He, like her parents, disapproved of her mathematical studies and she seemed condemned to the life of wife and mother. She bore two sons in her first marriage, David who died in infancy and Woronzow, who would later write a biography of Ada Lovelace. One could say fortunately, for the young Mary, her husband died after only three years of marriage in 1807 leaving her well enough off that she could now devote herself to her studies, which she duly did. Under the tutorship of John Wallace, later professor of mathematics in Edinburgh, she started on a course of mathematical study, of mostly French books but covering a wide range of mathematical topic, even tacking Newton’s Principia, which she found very difficult. She was by now already twenty-eight years old. During the next years she became a fixture in the highest intellectual circles of Edinburgh.

In 1812 she married for a second time, another cousin, William Somerville and thus acquired the name under which she would become famous throughout Europe. Unlike her parents and Samuel Grieg, William vigorously encouraged and supported her scientific interests. In 1816 the family moved to London. Due to her Scottish connections Mary soon became a member of the London intellectual scene and was on friendly terms with such luminaries as Thomas Young, Charles Babbage, John Herschel and many, many others; all of whom treated Mary as an equal in their wide ranging scientific discussions. In 1817 the Somervilles went to Paris where Mary became acquainted with the cream of the French scientists, including Biot, Arago, Cuvier, Guy-Lussac, Laplace, Poisson and many more.

In 1824 William was appointed Physician to Chelsea Hospital where Mary began a series of scientific experiments on light and magnetism, which resulted in a first scientific paper published in the Philosophical Transactions of the Royal Society in 1826. In 1836, a second piece of Mary’s original research was presented to the Académie des Sciences by Arago. The third and last of her own researches appeared in the Philosophical Transactions in 1845. However it was not as a researcher that Mary Somerville made her mark but as a translator and populariser.

In 1827 Henry Lord Brougham and Vaux requested Mary to translate Laplace’s Mécanique céleste into English for the Society for the Diffusion of Useful Knowledge. Initially hesitant she finally agreed but only on the condition that the project remained secret and it would only be published if judged fit for purpose, otherwise the manuscript should be burnt. She had met Laplace in 1817 and had maintained a scientific correspondence with him until his death in 1827. The translation took four years and was published as The Mechanism of the Heavens, with a dedication to Lord Brougham, in 1831. The manuscript had been refereed by John Herschel, Britain’s leading astronomer and a brilliant mathematician, who was thoroughly cognisant with the original, he found the translation much, much more than fit for the purpose. Laplace’s original text was written in a style that made it inaccessible for all but the best mathematicians, Mary Somerville did not just translate the text but made it accessible for all with a modicum of mathematics, simplifying and elucidating as she went. This wasn’t just a translation but a masterpiece. The text proved too vast for Brougham’s Library of Useful Knowledge but on the recommendation of Herschel, the publisher John Murray published the book at his own cost and risk promising the author two thirds of the profits. The book was a smash hit the first edition of 750 selling out almost instantly following glowing reviews by Herschel and others. In honour of the success the Royal Society commissioned a bust of Mrs Somerville to be placed in their Great Hall, she couldn’t of course become a member!

At the age of fifty-one Mary Somerville’s career as a science writer had started with a bang. Her Laplace translation was used as a textbook in English schools and universities for many years and went through many editions. Her elucidatory preface was extracted and published separately and also became a best seller. If she had never written another word she would still be hailed as a great translator and science writer but she didn’t stop here. Over the next forty years Mary Somerville wrote three major works of semi-popular science On the Connection of the Physical Sciences (1st ed. 1834), Physical Geography (1st ed. 1848), (she was now sixty-eight years old!) and at the age of seventy-nine, On Molecular and Microscopic Science (1st ed. 1859). The first two were major successes, which went through many editions each one extended, brought up to date, and improved. The third, which she later regretted having published, wasn’t as successful as her other books. Famously, in the history of science, William Whewell in his anonymous 1834 review of On the Connection of the Physical Sciences first used the term scientist, which he had coined a year earlier, in print but not, as is oft erroneously claimed, in reference to Mary Somerville.

Following the publication of On the Connection of the Physical Sciences Mary Somerville was awarded a state pension of £200 per annum, which was later raised to £300. Together with Caroline Herschel, Mary Somerville became the first female honorary member of the Royal Astronomical Society just one of many memberships and honorary memberships of learned societies throughout Europe and America. Somerville College Oxford, founded seven years after her death, was also named in her honour. She died on 28 November 1872, at the age of ninety-one, the obituary which appeared in the Morning Post on 2 December said, “Whatever difficulty we might experience in the middle of the nineteenth century in choosing a king of science, there could be no question whatever as to the queen of science.” The Times of the same date, “spoke of the high regard in which her services to science were held both by men of science and by the nation”.

As this is my contribution to Ada Lovelace day celebrating the role of women in the history of science, medicine, engineering, mathematics and technology I will close by mentioning the role that Mary Somerville played in the life of Ada. A friend of Ada’s mother, the older women became a scientific mentor and occasional mathematics tutor to the young Miss Byron. As her various attempts to make something of herself in science or mathematics all came to nought Ada decided to take a leaf out of her mentor’s book and to turn to scientific translating. At the suggestion of Charles Wheatstone she chose to translate Luigi Menabrea’s essay on Babbage’s Analytical Engine, at Babbage’s suggestion elucidating the original text as her mentor had elucidated Laplace and the rest is, as they say, history. I personally would wish that the founders of Ada Lovelace Day had chosen Mary Somerville instead, as their galleon figure, as she contributed much, much more to the history of science than her feted protégée.

(1) What follows is largely a very condensed version of Elizabeth  C. Patterson’s excellent Somerville biography Mary Somerville, The British Journal for the History of Science, Vol. 4, 1969, pp. 311-339

 

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Filed under History of Astronomy, History of Mathematics, History of Physics, History of science, Ladies of Science

Henry and Isaac invade Oxford.

There is subject well known to all blog owners that I have never talked about, spam; I get two different varieties here at The Renaissance Mathematicus. The first is spam comments, which turn up in a never ending stream but which mostly end up in Word Press’ apparently efficient spam filter. Very occasionally one or two get through and I have to weed these out from underneath whichever post they have chosen to enrich with their presence. Otherwise the only real problem I have is remembering to regularly check the spam filter for non-spam and send the rest of its contents off to rot in cyber-hell until that day dawns when the Internet is turned off forever. Maybe I shouldn’t say this but I think that the spammers might be more successful if they didn’t have email addresses such as purchase@cheapviagra.com, just a thought.

The second type of spam I receive as a blogger is in the form of emails. These are emails from people trying to get me to either let them advertise or publish something on my blog or link something to it. Again these people might be more successful if the things that they were offering and which they are so convinced that I will find interesting were actually related in anyway to the content of my blog, they never are. As a blogger I get another type of email, ones that are invariably addressed to Professor or Doctor or even in German style to Professor Doctor. I wouldn’t mind them awarding me illusionary titles that I don’t possess, and almost certainly never will, if only they would show a little imagination in addressing me, after all professors and doctors are two a penny. Were I to get an email addressed to Our Glorious, Benevolent, Gracious, Omniscient and Wise Leader in this Age of Darkness I might just be tempted to respond, but they never do and so I don’t. The emails addressing me with imaginary academic titles usually invite me to contribute articles to their prestigious academic journal that well-known rival to Nature and Science, The East Krakatoa Journal for Island Approaches to the Philosophy of Renaissance Mathematics. Dear editors, to paraphrase Groucho Marx, “I would never submit an article to a journal that would publish anything written by me”. All of these spam emails get dispatched forthwith to cyber-hell unread, unanswered and with all links left strictly unlinked. I can spread my own viruses, thank you.

Today I received an unsolicited email asking me to advertise something, help with publicizing was the actual phrase used, and I’m actually going to do so, a first as far as I can remember here at RM. The email came from David Norbrook, Merton Professor of English Literature at the University of Oxford and he asked me very nicely to spread the word about his up coming conference Scholarship, Science, and Religion in the Age of Isaac Casaubon (1559-1614) and Henry Savile (1549-1622) at the T. S. Eliot Theatre, Merton College, Tuesday 1st – Thursday 3rd July 20124

For those not in the know Henry and Isaac are two of the Renaissance scholars who make you turn green with envy. Each of them was brainy enough to win a round of University Challenge on their own without teammates and each of them mastered enough academic disciplines to fill a small encyclopaedia on his own.

Isaac Casaubon was a French Huguenot classical scholar, philologist, historian and theologian born to refugee parents in Geneva. Home educated until he entered the University of Geneva aged seventeen were he studied Greek and was recommended for the chair in Greek only four years later. He was a consummate classical scholar and philologist whose main occupation was the translation, editing and publication of classical Greek text. He worked most of his life in Switzerland and France torn and troubled by the religious conflicts of the age. Regarded at his intellectual peak as one of the most learned men in the whole of Europe the Catholics, Lutherans, Calvinists and Anglicans all competed with offers of jobs, money and other inducements to win him as a propagandist for their cause. The situation has strong similarities to the attempts today of leading European football clubs to induce a star striker to sign for them and not one of their rivals. During the religious upheaval in Europe in the Early Modern Period a star polemicist was regarded as a good catch by the rival religious communities. In the end the political pressure in France caused him to move to England in 1610 were he died four years later. As a historian of science my main interest in Casaubon is his De rebus sacris et ecclesiasticis exercitationes XVI published in 1614 in which he proved by philological analysis that the Corpus Hermeticus, one of the most influential collection of texts in the Renaissance, was not as ancient as claimed but was in fact a product of late antiquity. This was a key moment in the evolution of the discipline of history, applying scientific, philological analysis to texts to determine their age.

I can’t leave even this brief account of Isaac Casaubon without mentioning his son Méric, who was the man responsible for ruining John Dee’s reputation. Despite all of the misfortunes that befell him in later life, in the early seventeenth-century Dee still enjoyed a good reputation in England for his work in the mathematical sciences. Around 1650 more and more people were starting to question the existence of ghosts, witches and other aspects of the occult. Deeply religious people, of whom Méric was one, were worried that this was the thin edge of the wedge that would inevitably lead to atheism. To counter this tendency Méric published John Dee’s Angel Diaries, his account of his conversations with angels, which up till then had remained largely unknown. Méric’s intention was that Dee’s accounts should act as a proof, from a reputable scholar, that the world of spirits is real and not to be questioned. Méric’s attempt backfired ruining Dee’s reputation causing people to forget the mathematicus and only remember the notorious Renaissance magus that he now became for the next four hundred years down to the present day.

Henry Savile was educated at Oxford and, self-taught, began to lecture there on astronomy at the age of 21 in 1570. He not only lectured on Ptolemaeus but also on the works of Regiomontanus and Copernicus, real cutting edge at the time. In 1578 he went on a grand tour of Europe meeting with and learning from the leading continental mathematicians; a necessary move for anyone interested in the mathematical sciences in England at that time as England was an intellectual backwater in terms of mathematics. On his return to England, in 1582, Savile was appointed Greek tutor to Queen Elizabeth. Later he became both Warden of Merton College Oxford and Provost of Eaton. Like Casaubon, with whom he was acquainted, Savile was a classical scholar and philologist but it is for his contributions to mathematics that he is best remembered. Appalled by the primitive level of mathematics teaching in England in comparison to the continent he established the first two university chairs for the mathematical sciences in England in 1619, the Savilian Chairs for Geometry and Astronomy at Oxford. In the seventeenth-century many of England’s leading mathematicians occupied one or other of these chairs including such figures as Henry Briggs, John Wallis and Edmund Halley, whose adventures sailing around the Atlantic you can follow on Twitter (@HalleysLog).

Both Casaubon and Savile are fascinating figures, who lived in and contributed to a period of great intellectual change in European history and I’m sure the Merton College conference on these two intellectual giants will be a stimulating and informative experience. If I had the time and the money, and I don’t have either, I personally would love to take part and I can only recommend that those who do have the time and the money to do so.

Unfortunately, I only got the information on the conference today and if you want to take advantage of the early booker rebate you only have until tomorrow to do so!

 

 

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Filed under History of Mathematics, Renaissance Science, University History

Oh please!

The latest move in the canonisation of Alan Turing is an opera, or whatever, written by the Pet Shop Boys, which is being heavily promoted by a PR campaign launched yesterday. As part of this press onslaught this magazine cover appeared on my Twitter stream today.

BmDT0wnCIAAeAwH.jpg-large

For the record, as a fan and one time student of meta-mathematics I was aware of and to some extent in awe of Alan Turing long before most of the people now trying to elevate him into Olympus even knew he existed. He was without a shadow of a doubt one of the most brilliant logicians of the twentieth-century and he along with others of his ilk, such as Leopold Löwenheim, Thoralf Skolem, Emil Post, Kurt Gödel, Alonzo Church etc. etc., who laid the theoretical foundations for much of the computer age, all deserve to be much better known than they are, however the attempts to adulate Turing’s memory have become grotesque. The Gay Man Who Saved the World is hyperbolic, hagiographic bullshit!

Turing made significant contributions to the work of Bletchley Park in breaking various German codes during the Second World War. He was one of nine thousand people who worked there. He did not work in isolation; he led a team that cracked one version of the Enigma Code. To what extent the work of Bletchley Park contributed to the eventual Allied victory is probably almost impossible to assess or quantify.

Alan Turing made significant contributions to the theories of meta-mathematics and an equally significant contribution to the British war effort. He did not, as is frequently claimed by the claqueur, invent the computer and he most certainly did not “save the world”. Can we please return to sanity in our assessment of our scientific heroes?

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