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.

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?

Sliding to mathematical fame.

William Oughtred born on the 5^th March 1575, who Newton regarded along with Christopher Wren and John Wallis as one of the three best seventeenth-century English mathematicians, was the epitome of the so-called English School of Mathematics. The English School of Mathematics is a loose historical grouping of English mathematicians stretching over several generations in the sixteenth and seventeenth centuries who propagated and supported the spread of mathematics, mostly in the vernacular, through teaching and writing at a time when the established educational institutions, schools and universities, offered little in the way of mathematical tuition. These men taught each other, learnt from each other, corresponded with each other, advertised each other in their works, borrowed from each other and occasionally stole from each other building an English language mathematical community that stretched from Robert Recorde (c. 1512 – 1558) who is regarded as its founder to Isaac Newton at the close of the seventeenth century who can be regarded as a quasi member.  Oughtred who died in 1660 spanned the middle of this period and can be considered to be one of its most influential members.

Oughtred was born at Eton College where his father Benjamin was a writing master and registrar and baptised there on 5^th March 1575, which is reputedly also his birthdate. He was educated at Eton College and at King’s College Cambridge where he graduated BA in 1596 and MA in 1600. It was at Cambridge that he says he first developed his interest for mathematics having been taught arithmetic by his father.  Whilst still at Cambridge he also started what was to become his vocation, teaching others mathematics.  He was ordained priest in 1603 and appointed vicar of Shalford in Surry. In 1610 he was appointed rector of nearby Albury where he remained for the rest of his life. He married Christgift Caryll in 1606, who bore him twelve or possibly thirteen children, accounts differ. All in all Oughtred lived the life of a simple country parson and would have remained unknown to history if it had not been for his love of mathematics.

William Oughtred
by Wenceslas Hollar 1646

Oughtred’s first claim to fame as a mathematician was as a pedagogue. He worked as a private tutor and also wrote and published one of the most influential algebra textbooks of the century his Clavis Mathematicae first published in Latin in 1631. This was a very compact introduction to symbolic algebra and was one of the first such books to be written almost exclusively in symbols, several of which Oughtred was the first to use and which are still in use today. Further Latin edition appeared in 1648, 1652, 1667 and 1698 with an English translation appearing in 1647 under the title The Key to Mathematics.

The later editions were produced by a group of Oxford mathematicians that included Christopher Wren, Seth Ward and John Wallis. Seth Ward lived and studied with Oughtred for six months and Wallis, Wren and Jonas Moore all regarded themselves as disciples, although whether they studied directly with Oughtred is not known. Wallis probably didn’t but claimed to have taught himself maths using the Clavis.

Title page Clavis Mathematicae 5th ed 1698
Ed John Wallis

The Latin editions of the Clavis were read throughout Europe and Oughtred enjoyed a very widespread and very high reputation as a mathematician.

Although he always preached the importance of theory before application Oughtred also enjoyed a very high reputation as the inventor of mathematical instruments and it is for his invention of the slide rule that he is best remembered today. The international society for slide rule collectors is known as the Oughtred Society. I realise that in this age of the computer, the tablet, the smart phone and the pocket calculator there is a strong chance that somebody reading this won’t have the faintest idea what a slide rule is. I’m not going to explain although I will outline the historical route to the invention of the slide rule but will refer those interested to this website.

The Scottish mathematician John Napier and the Swiss clock and instrument maker Jobst Bürgi both invented logarithms independently of each other at the beginning of the seventeenth century although Napier published first in 1614. The basic idea had been floating around for sometime and could be found in the work of the Frenchman Nicolas Chuquet in the fifteenth century and the German Michael Stifel in the sixteenth. In other words it was an invention waiting to happen. Napier’s logarithms were base ‘e’ now called natural logarithms (that’s the ln key on your pocket calculator) and the English mathematician Henry Briggs (1561 – 1630), Gresham Professor of Geometry, thought it would be cool to have logarithms base 10 (that’s the log key on your pocket calculator), which he published in 1620. Edmund Gunter (1581 – 1626), Gresham Professor of Astronomy, who was very interested in cartography and navigation, produced a logarithmic scale on a ruler, known, not surprisingly, as the Gunter Scale or Rule, which could be read off using a pair of dividers to enable navigators to make rapid calculations on sea charts.

Briggs introduced his good friend Oughtred to Gunter, remember that bit above about teaching, learning etc. from each other, and it was Oughtred who came up with the idea of placing two Gunter Scales next to each other to facilitate calculation by sliding the one scale up and down against the other and thus the slide rule was born. Oughtred first published his invention in a pamphlet entitled The Circles of Proportion and the Horizontal Instrument in 1631, which actually describes an improved circular slide rule with the scales now on circular discs rotating about a central pin. This publication led to a very nasty dispute with Richard Delamain, a former pupil of Oughtred’s who claimed that he had invented the slide rule and not his former teacher. This led to one of those splendid pamphlet priority wars with both antagonists pouring invective over each other by the bucket load. Oughtred won the day both in his own time and in the opinion of the historians and is universally acknowledged as the inventor of the slide rule, which became the trusty companion of all applied mathematicians, engineers and physicist down the centuries. Even when I was at secondary school in the 1960s you would never see a physicist without his trusty slide rule.

It still seems strange to me that more than a whole generation has grown up with no idea what a slide rule is or what it could be used for and that Oughtred’s main claim to fame is slowly but surely sliding into the abyss of forgetfulness.

5 Brilliant Mathematicians – 4 Crappy Commentaries

I still tend to call myself a historian of mathematics although my historical interests have long since expanded to include a much wider field of science and technology, in fact I have recently been considering just calling myself a historian to avoid being pushed into a ghetto by those who don’t take the history of science seriously. Whatever, I have never lost my initial love for the history of mathematics and will automatically follow any link offering some of the same. So it was that I arrived on the Mother Nature Network and a blog post titled 5 brilliant mathematicians and their impact on the modern world. The author, Shea Gunther, had actually chosen 5 brilliant mathematicians with Isaac Newton, Carl Gauss, John von Neumann, Alan Turing and Benoit Mandelbrot and had even managed to avoid the temptation of calling them ‘the greatest’ or something similar. However a closer examination of his commentaries on his chosen subjects reveals some pretty dodgy not to say down right crappy claims, which I shall now correct in my usual restrained style.

He starts of fairly well on Newton with the following:

There aren’t many subjects that Newton didn’t have a huge impact in — he was one of the inventors of calculus, built the first reflecting telescope and helped establish the field of classical mechanics with his seminal work, “Philosophiæ Naturalis Principia Mathematica.” He was the first to decompose white light into its constituent colors and gave us, the three laws of motion, now known as Newton’s laws.

But then blows it completely with his closing paragraph:

We would live in a very different world had Sir Isaac Newton not been born. Other scientists would probably have worked out most of his ideas eventually, but there is no telling how long it would have taken and how far behind we might have fallen from our current technological trajectory.

This is the type of hagiographical claim that fans of great scientists tend to make who have no real idea of the context in which their hero worked. Let’s examine step by step each of the achievements of Newton listed here and see if the claim made in this final paragraph actually holds up.

Ignoring the problems inherent in the claim that Newton invented calculus, which I’ve discussed here, the author acknowledges that Newton was only co-inventor together with Leibniz and although Newton almost certainly developed his system first it was Leibniz who published first and it was his system that spread throughout Europe and eventually the world so no changes here if Isaac had not been born.

Newton did indeed construct the first functioning reflecting telescope but as I explained here it was by no means the first. It would also be fifty years before John Hadley succeeded in repeating Newton’s feat and finally making the commercial production of reflecting telescopes viable. However Hadley also succeeded in making working models of James Gregory’s reflecting telescope, which actually predated Newton’s and it was the Gregorian that, principally in the hands of James Short, became the dominant model in the eighteenth century. Although to be fair one should mention that William Herschel made his discoveries with Newtonians. Once again our author’s claim fails to hold water.

Sticking with optics for the moment it is a little know and even less acknowledge fact that the Bohemian physicus and mathematician Jan Marek Marci (1595 – 1667) actually decomposed white light into its constituent colours before Newton. Remaining for a time with optics, James Gregory, Francesco Maria Grimaldi, Christian Huygens and Robert Hooke were all on a level with Newton although none of them wrote such an influential book as Newton’s Optics on the subject. Now this was not all positive. Due to the influence won through the Principia, The Optics became all dominant preventing the introduction of the wave theory of light developed by Huygens and Hooke and even slowing down its acceptance in the nineteenth century when proposed by Fresnel and Young. If Newton hadn’t been born optics might even have developed and advance more quickly than it did.

This just leaves the field of classical mechanics Newton real scientific monument. Now, as I’ve pointed out several times before the three laws of motion were all borrowed by Newton from others and the inverse square law of gravity was general public property in the second half of the seventeenth century. Newton’s true genius lay in his mathematical combination of the various elements to create a whole. Now the question is how quickly might this synthesis come about had Newton never lived. Both Huygens and Leibniz had made substantial contribution to mechanics contemporaneously with Newton and the succeeding generation of French and Swiss-German mathematicians created a synthesis of Newton’s, Leibniz’s and Huygens’ work and it is this that is what we know as the field of classical mechanics. Without Newton’s undoubtedly massive contribution this synthesis might have taken a little longer to come into being but I don’t think the delay would have radically changed the world in which we live.

Like almost all great scientists Newton’s discoveries were of their time and he was only a fraction ahead of and sometimes even behind his rivals. His non-existence would probably not have had that much impact on the development of history.

Moving on to Gauss we will have other problems. Our author again makes a good start:

Isaac Newton is a hard act to follow, but if anyone can pull it off, it’s Carl Gauss. If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever.

Very hyperbolic and hagiographic but if anybody could be called the greatest mathematician ever then Gauss would be a serious candidate. However in the next paragraph we go off the rails. The paragraph starts OK:

Carl Friedrich Gauss was born to a poor family in Germany in 1777 and quickly showed himself to be a brilliant mathematician. He published “Arithmetical Investigations,” a foundational textbook that laid out the tenets of number theory (the study of whole numbers).

So far so good but then our author demonstrates his lack of knowledge of the subject on a grand scale:

Without number theory, you could kiss computers goodbye. Computers operate, on a the most basic level, using just two digits — 1 and 0…

Here we have gone over to the binary number system, with which Gauss book on number theory has nothing to do, what so ever. In modern European mathematics the binary number system was first investigated in depth by Gottfried Leibniz in 1679 more than one hundred years before Gauss wrote his Disquisitiones Arithmeticae, which as already stated has nothing on the subject. The use of the binary number system in computing is an application of the two valued symbolic logic of George Boole the 1 and 0 standing for true and false in programing and on and off in circuit design. All of which has nothing to do with Gauss. Gauss made so many epochal contributions to mathematics, physics, cartography, surveying and god knows what else so why credit him with something he didn’t do?

Moving on to John von Neumann we again have a case of credit being given where credit is not due but to be fair to our author, this time he is probably not to blame for this misattribution.  Our author ends his von Neumann description as follows:

Before his death in 1957, von Neumann made important discoveries in set theory, geometry, quantum mechanics, game theory, statistics, computer science and was a vital member of the Manhattan Project.

This paragraph is fine and if Shea Gunther had chosen to feature von Neumann’s invention of game theory or three valued quantum logic I would have said fine, praised the writer for his knowledge and moved on without comment. However instead our author dishes up one of the biggest myths in the history of the computer.

…he went on to design the architecture underlying nearly every single computer built on the planet today. Right now, whatever device or computer that you are reading this on, be it phone or computer, is cycling through a series of basic steps billions of times over each second; steps that allow it to do things like render Internet articles and play videos and music, steps that were first thought up by John von Neumann.

Now any standard computer is called a von Neumann machine in terms of its architecture because of a paper that von Neumann published in 1945, First Draft of a Report on the EDVAC. This paper described the architecture of the EDVAC one of the earliest stored memory computers but von Neumann was not responsible for the design, the team led by Eckert and Mauchly were. Von Neumann had merely described and analysed the architecture. His publication caused massive problems for the design team because the information now being in the public realm it meant that they were no longer able to patent their innovations. Also von Neumann’s name as author on the report meant that people, including our author, falsely believed that he had designed the EDVAC. Of historical interest is the fact that Charles Babbage’s Analytical Engine in the nineteenth century already possessed von Neumann architecture!

Unsurprisingly we walk straight into another couple of history of the computer myths when we turn to Alan Turing.  We start with the Enigma story:

During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine.

There were various versions of the Enigma machine and various codes used by different branches of the German armed forces. The Polish Cipher Bureau were the first to break an Enigma code in 1932. Various other forms of the Enigma codes were broken by various teams at Bletchley Park without Turing. Turing was responsible for cracking the German Naval Enigma. The statement above denies credit to the Polish Cipher Bureau and the other 9000 workers in Bletchley Park for their contributions to encoding Enigma.

Besides helping to stop Nazi Germany from achieving world domination, Alan Turing was instrumental in the development of the modern day computer. His design for a so-called “Turing machine” remains central to how computers operate today.

I’ve lost count of how many times that I’ve seen variations on the claim in the above paragraph in the last eighteen months or so, all equally incorrect. What such comments demonstrate is that their authors actually have no idea what a Turing machine is or how it relates to computer design.

In 1936 Alan Turing, a mathematician, published a paper entitled On Computable Numbers, with an Application to the Entscheidungsproblem. This was in fact one of four contemporaneous solutions offered to a problem in meta-mathematics first broached by David Hilbert, the Entscheidungsproblem. The other solutions, which needn’t concern us here, apart from the fact that Post’s solution is strongly similar to Turing’s, were from Kurt Gödel, Alonso Church and Emil Post. Entscheidung is the German for decision and the Entscheidungsproblem asks if for a given axiomatic system whether it is also possible with the help of an algorithm to decide if a given statement in that axiom system is true or false. The straightforward answer that all four men arrived at by different strategies is that it isn’t. There will always be undecidable statements within any sufficiently complex axiomatic system.

Turing’s solution to the Entscheidungsproblem is simple, elegant and ingenious. He hypothesised a very simple machine that was capable of reading a potentially infinite tape and following instruction encoded on that tape. Instruction that moved the tape either right or left or simply stopped the whole process. Through this analogy Turing was able to show that within an axiomatic system some problems would never be Entscheidbar or in English decidable. What Turing’s work does is, on a very abstract level, to delineate the maximum computability of any automated calculating system. Only much later, in the 1950s, after the invention of electronic computers a process in which Turing also played a role did it occur to people to describe the computational abilities of real computers with the expression ‘Turing machine’.  A Turing machine is not a design for a computer it is term used to described the capabilities of a computer.

To be quite open and honest I don’t know enough about Benoit Mandelbrot and fractals to be able to say whether our author at least got that one right, so I’m going to cut him some slack and assume that he did. If he didn’t I hope somebody who knows more about the subject that I will provide the necessary corrections in the comments.

All of the errors listed above are errors that could have been easily avoided if the author of the article had cared in anyway about historical accuracy and truth. However as is all to often the case in the history of science or in this case mathematics people are prepared to dish up a collection of half baked myths, misconceptions and not to put too fine a point on it crap and think they are performing some sort of public service in doing so. Sometimes I despair.

 

Christmas Trilogy 2012 Part II: Charles and Ada: A tale of genius or of exploitation?

This year Ada Lovelace Day, a celebration of women in STEM (science, technology, engineering and mathematics) fuelled by the Finding Ada website and twitter account took off big time. Now I have nothing against this celebration and have actively supported it on this blog for the last three years; writing about Emmy Noether in 2010, a quartet of lady astronomers in 2011 and the first female professor at a European university, Laura Brassi, in 2012. I have also posted on other women in the history of science on other occasions. This year I, by chance, also attended, but did not participate in, the edit-thron for STEM women on Wikipedia held at the Royal Society. As I have already said I have nothing against this celebration but as a historian of mathematics and computing each time I do so I have very major misgivings about the organisers choice of figurehead, Ada Lovelace. These qualms were strengthened this month on the tenth, Ada’s birthday, as an echo of Ada Lovelace Day set off a flurry of biographical posts throughout the Intertubes, some of them old and merely linked, others freshly written for the occasion. All of them however had one thing in common, they were not written from original or even well researched secondary sources but simply regurgitated older fundamentally flawed largely mythical short biographies. There is nothing new in what I’m going to say now, in fact I’ve blogged about it before as has one of The Guardian’s excellent lady historians of science Rebekah “Becky” Higgitt. Even the much-maligned Wikipedia gets it largely right in its Ada Lovelace article. All of the short biographies state clearly that Ada was a mathematician and “the first computer programmer”.  Both statements are wrong. So what is the truth?

Ada, the daughter of Annabelle Milbanke and George Byron, was motivated to learn mathematics as a child (unusually for a women in the nineteenth century) by her mathematics fan mother to try to prevent her growing up to be like her “mad, bad and dangerous to know” poetic father. A stultifying logical education rather than a stimulating poetic one! Ada had various maths tutors in her youth including the aging radical reformer William Frend, Augustus De Morgan’s father in law and her mother’s old childhood tutor. None of these really managed to instil any real enthusiasm or ability for mathematics in the young Ada. Later as a young lady she became acquainted with both Mary Somerville, the mathematical translator and science populariser and Charles Babbage and became fascinated with the mathematical sciences. She received some informal tuition from Somerville who became her mentor and role model. Later determined to finally get to grips with the discipline she succeeded in persuading De Morgan, she was acquainted through his wife Sophia, Frend’s daughter, to become her maths tutor in an informal correspondence course. The surviving letters of their mathematical correspondence clearly show that although Ada is obviously the possessor of a bright and inquisitive mind she never really grasped several important fundamental mathematical concepts and her acquisition of the secrets of mathematics never progressed beyond that of a failed first year undergraduate. To call Ada a mathematician is a perversion by any stretch of the imagination. As Dorothy Stein, who has analysed the De Morgan – Ada mathematical correspondence in detail, puts it in her excellent biography Ada:  A Life and a Legacy (1985):

At twenty-eight, […] and after ten years of intermittent but sometimes intensive study, Ada was still a promising “young beginner”.

Having failed to master mathematics Ada now turned her attention to the occupation of Mary Somerville, her mentor, scientific translating. Quoting Stein again:

Translation was a good way to begin, whether or not original contributions were to follow. Mary Somerville, De Morgan and Babbage himself had all begun their published careers as translators. There was no reason why she could not proceed on a course at least as successful and rewarding as those of Mary Somerville and her mother’s friends Harriet Martineau and Anna Jameson.

In 1840 Babbage held a series of public lectures before an audience of eminent Italian philosophers and men of science on his Analytical Engine in Turin. This was a publicity exercise and Babbage’s plan was that the most eminent attendee, Baron Plana, should publish an account of the lectures creating much needed publicity for his cash strapped project. Plana declined and Babbage had to content himself with an account written in French by the young unknown military engineer, Captain Luigi Menabrea (who in a strange twist of fate would later become prime minister of Italy).  It was this document, which Ada, a long-time fan of Babbage’s calculating machines, chose at the suggestion of Charles Wheatstone, Babbage’s friend, as her first (and last) scientific translation project. (As a historian of science and a big fan of polymaths I find it fascinating that the physicist Wheatstone universally known by school kids studying physics for his Wheatstone Bridge (which he didn’t invent) was the inventor of the English Concertina.)

When he became aware, after the event, of Ada’s translation Babbage, never one to miss a trick, realised he had a great opportunity for a publicity stunt and suggested that Ada should garnish her work, in the manner of Somerville’s Laplace translation, with her own notes on the Analytical Engine; a suggestion that the flattered young lady grasped with alacrity. It is obvious from the extensive correspondence that Babbage controlled and supervised every single point and comma of the infamous Lovelace notes and it difficult to say how much of them is original Ada and how much Babbage expressed through a mouthpiece. Even some of the more interesting speculative ideas contained in the notes can be shown to be paraphrases of ideas first muted mooted in earlier Babbage publications such as his Economy of Machinery and Manufactures (1832) and his Ninth Bridgewater Treatise (1837).

On the question of who the first computer programmer was, there is no confusion what so ever and it was not Ada Lovelace. The Menabrea Memoir that Ada had translated already contained examples of programmes for the Analytical Engine that Babbage had used to illustrate his Turin lectures and had actually developed several years before. The notes contain further examples from the same source that Babbage supplied to the authoress. The only new programme example developed for the notes was the one to determine the so-called Bernoulli numbers. Quite who contributed what to this programme is open to dispute. In his autobiography, written several years after Ada’s death, Babbage claims that Ada suggested the programme, which he then wrote, although noting that she had spotted a serious error in the original. The correspondence suggests that Ada was much more actively involved in the development of the programme and should perhaps be given more credit than Babbage allowed her. Whatever the truth of the matter Ada Lovelace was neither a mathematician nor the first computer programmer.

Ada was not some sort of mathematical genius who conceived the first computer programme but was rather an intelligent but rather confused young lady who was exploited by Charles Babbage to gain publicity for his out of control megalomaniac computer project. However Ada’s annotated translation was elegantly written, as she, despite her mother’s best efforts, seems to have inherited some of her father’s poetic genius. It would in no way be amiss to describe Ada as a female science populariser or science communicator however if one were to choose one of these as a role model for women in STEM careers then Mary Somerville would be a much more obvious choice as her annotated Laplace translation was much more significant and immensely more influential than Ada’s memoir.

In general I find it sad that the organisers of Ada Lovelace Day didn’t choose one of the many real women mathematician and scientists out of history as their figurehead rather than a woman who was neither.

 

The Cult of St Alan of Bletchley Park

I realise that to rail against anything published in the Daily Fail is about as effective as pissing against the wind in a force 8 gale but this article on Alan Turing got so up my nose that I have decided to strap on my bother-boots of historical criticism and give the author a good kicking if only to assuage my own frustration. It won’t do any good but it might make me feel better.

Before I start in on a not so subtle demolition job, I should point out that I’m actually a Turing fan who has read and absorbed Andrew Hodges’ excellent Turing biography[1] as well as many books and articles on and by Turing. I have seriously studied his legendary paper on the Entscheidungsproblem[2], I have a copy sitting on my bookshelf, which I understand thoroughly including its significance for Hilbert’s Programme, which the Mail’s journalist almost certainly does not. If I here seem to be seriously challenging Turing’s claims to scientific sainthood it is only in the interests of historical accuracy and not out of any sense of antipathy to the man himself, who would definitely be one of my heroes if I went in for them.

The Mail article opens with a real humdinger of a claim that is so wrong it’s laughable:

Own a laptop, a smartphone or an iPad? If so, you owe it to a man many of us have never heard of – a genius called Alan Turing. ‘He invented the digital world we live in today,’ says Turing’s biographer David Leavitt in a new Channel 4 drama-documentary about the brilliant mathematician.

Sorry folks Alan Turing did not invent the digital world we live in today. In the 1930s Turing was one of several meta-mathematicians who laid the theoretical foundations for computability and although his contributions were, viewed from a technical standpoint, brilliant we would still have had the computer revolution if Alan Turing as an undergraduate had turned his undoubted talents to deciphering ancient Sumerian clay tablets instead of to solving meta-logical problems. The German computer pioneer Konrad Zuse designed and built functioning digital computers in the 1930s and 40s without, as far I know, ever having heard of Turing. Zuse was an engineer and not a mathematician and approached the problem from a purely practical point of view. The American engineer Vannevar Bush built a highly advanced analogue computer, his Differential Analyser, to solve differential equations in 1927 when Turing was still at school. Claude Shannon who laid the foundations of digital circuit design was one of Bush’s graduate students. All three American groups, which developed digital computers in the late 193os and early 1940s, Atanasoff and Berry in Iowa, Aiken in Harvard and Eckert and Mauchly in Pennsylvania all referenced Bush when describing their motivations saying they wished to construct an improved version of his Differential Analyser. As far as I know none of them had read Turing’s paper, which is not surprising as Turing himself claimed that in the 1930’s only two people had responded to his paper. The modern computer industry mainly developed out of the work of these three American groups and not from anything produced by Turing.

Turing did do work on real digital computers at Bletchley Park in the 1940s but this work was kept secret by the British government after the war and so had no influence on the civil development of computing in the 1950s and 60s. Turing like many other of the computer pioneers from Bletchley started again from scratch after the war but due to their delayed start and underfunding they never really successfully competed with the Americans. We now turn to Bletchley Park and Turing’s contribution to the Allied war effort. The Mail writes:

Ironically, the same society that hounded him to his death owed its survival to him. For during the Second World War it was Turing who pioneered the cracking of Nazi military codes at Bletchley Park, allowing the Allies to anticipate every move the Germans made.

The first sentence is a reference to Turing’s suicide caused by his mistreatment as a homosexual, which I’m not going to discuss here other than to say that it’s a very black mark against my country and my countrymen. We now come to a piece of pure hagiography. The cracking of the Germany military codes was actually pioneered by the Poles before Bletchley Park even got in on the act. It should also be pointed out that Turing was one of nine thousand people working in Bletchley by the end of the War. Also he was only in charge of one team working on one of the codes in use, the navel naval Enigma, there were several other teams working on the other German codes. Turing was one cog in a vast machine, an important cog but a long way from being the whole show. The Mail next addresses Turing’s famous paper:

‘While still a student at Cambridge he wrote a paper called Computing Machinery, in which all the developments of modern computer science are foretold. If you take an iPhone to pieces, all the parts in there were anticipated by Turing in the 1930s.’

He wasn’t a student but a postgraduate fellow of his college. The title of the paper is On Computable Numbers, with an Application to the Entscheidungsproblem. It outlines some of the developments of modern computing but not all and no he didn’t anticipate all of the parts of an iPhone. Apart from that the paragraph is correct.

Turing’s outstanding talents were recognised at the outbreak of war, when he was plucked from academic life at Cambridge to head the team at Bletchley Park, codenamed Station X. They were tasked with breaking the German codes, transmitted on complex devices called Enigma machines, which encrypted words into as many as 15 million million possible combinations.

‘Turing took one look at Enigma and said, “I can crack that,”’ says Sen. ‘And he did.’ Part of Turing’s method was to develop prototype computers to decipher the Enigma codes, enabling him to do in minutes what would take a team of scientists months to unravel. It was thanks to him that the movements of German U-boats could be tracked and the battle for control of the Atlantic was won, allowing supplies to reach Britain and saving us from starvation.

Turing was not “plucked from academic life”; interested in the mathematics of cryptology Turing started working for the Government Code and Cypher School already in 1938 and joined the staff of Bletchley Park at the outbreak of war. The department he headed was called Hut 8. With reference to the computers developed in Bletchley, as I have already said in an earlier post Turing was responsible for the design of special single purpose computer, the Bombe, which was actually a development from the earlier Polish computer the Bomba and had nothing to do with the much more advance and better known Bletchley invention, the Colossus. The second paragraph is largely correct.

The life and work of Alan Turing and the role of Bletchley Park in the war effort are both important themes in the histories of science, mathematics and technology and can certainly be used as good examples on which to base popular history but nobody is served by the type of ignorant, ill-informed rubbish propagated by the Daily Fail and obviously by the Channel 4 documentary that they are reporting on, which is obviously being screened tonight. My recommendation don’t watch it!

 

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[1] Andrew Hodges, Alan Turing: The Enigma, Simon & Schuster, 1983.

[2] Alan M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, 2 ser. vol. 42, (1936 – 37), pp. 230 – 265.

Ich bin a Gastblogger III: Drinking from the same well

I’m an alien

I’m a legal alien

I’m an Englishman in Nürnberg¹

 

As an English historian of mathematics living in Germany another question that I have had put to me several times by those with somewhat more knowledge of the history of mathematics is, “who invented logarithms the Scottish aristocrat John Napier or the Swiss instrument maker Jost Bürgi?”…..

 

A Christmas Trinity II: Charlie, Ivor, Robert and me.

Charles Babbage, who was born on 26^th December 1791¹, is famous as a pioneer in the history of the computer, a fame that is to some extent exaggerated as his work, although spectacular (his analytical engine was a full von Neumann machine more than a century before von Neumann became famous for defining the same), had no real influence on the later actual development of the computer, the later inventors only becoming aware of Babbage’s work after the fact.

However Babbage is significant in the history of science and technology not only for his calculating engines. He was for a number of years the holder of the Lucasian Chair for mathematics at Cambridge, whose current holder is Michael Green the string theorist and whose previous occupants include Stephan Hawking the cosmologist, the physicists Paul Dirac and Gabriel Stokes, the astronomer and optical physicist George Biddell Airy (a friend of Babbage), its original occupant Isaac Barrow and his successor Isaac Newton. Babbage was also instrumental in the founding of a number of scientific societies most notably the Royal Astronomical Society and the British Society for the Advancement of Science.

As well as working on his calculating engines he worked as a scientific advisor to governments and rulers throughout Europe and distinguished himself as an inventor. One Internet site has the following list of his inventions, “the dynamometer, standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, heliograph ophthalmoscope. He also had an interest in cyphers and lock-picking.” For me the most fascinating fact is that he also invented that essential stage prop of Hollywood westerns the cowcatcher! This was actually conceived to push aside small obstacles on the tracks and not cows!

Over the years Babbage has gained a reputation as an English eccentric based largely on his own autobiography Passages from the Life of a Philosopher (1864) and in particular for the often-quoted chapter XXVI therein Street nuisances, which he even published as a separate pamphlet. Here Babbage complains bitterly about the noise pollution produced by street musicians and street criers, to quote just one such passage:

It is difficult to estimate the misery inflicted upon thousands of persons and the absolute pecuniary penalty imposed upon multitudes of intellectual workers by the loss of their time, destroyed by organ-grinders and other similar nuisances.

He is here complaining the he and others like him are unable to work because of the noise produced by street musicians. Such passages and others like them from this chapter are quoted as evidence that Babbage was at best an eccentric and at worst a loony. I beg to differ.

Another noted British eccentric of more recent vintage was the Scottish poet, musician, storyteller and educationalist Ivor Cutler whose quirky humour and fascinating ditties enriched my childhood and my youth. I still own and love his wonderful LP Ludo. Cutler was much loved by John Peel and played a role in the Beatles Magical Mystery Tour film. He is said to be probably the only artist to have loyal audiences on BBC Radios 1, 2, 3 and 4. Cutler was notorious for his many eccentricities and in particular for his passionate support of the Noise Abatement Society. He would ask to see the manager in cafes and bars with background music and complain that the sound was hurting his sensitive ears. He always won and got the offending sound system turned off. In supermarkets with music systems he would also summon the manager and complain that he was unable to think about what he wished to purchase because of the intruding noise of the background music.

Robert Fripp legendary guitarist of King Crimson is another Englishman who has been labelled an eccentric. A man whose scorching lead solos have graced no only his own music but also such classics as Bowie’s Heroes or the new Grinderman single defies the etiquette for rock lead guitarists and plays sitting down. In a business whose public image in defined by the catchphrase “sex and drugs and rock and roll” Fripp is an abstinent intellectual who read the Financial Times and pontificates on the morals of the music business. Fripp writes a very entertaining Internet road diary and here he comments sarcastically on the Noise Pollution Units (music systems) at the breakfast troughs in the hotels where he stays whilst underway. He has taken to carrying his so-called noisebusters, an ipod loaded with suitable classical music of his own choosing.

I too have a local reputation as an English eccentric, an aging English hippie living in Franconia who is accompanied everywhere by a large shaggy mongrel dog. I too like my fellow British eccentrics intensely dislike being barraged by other people’s choice of music in bars, cafes, restaurants, shops, on the streets and even today in medical practices. I love music and even call myself a music junkie. I spent a large part of my life earning my living as a concert promoter, concert manager and live concert sound technician. I have an obscenely large record collection (an expression that dates me especially considering the fact that the majority of the music I own is now actually on CD). My favourite occupation is listening to music both live and recorded but I want to listen to the music of my choice in a space conceived for intensive listening. I do not want to be forced to listen to somebody else’s choice of music when I’m drinking a coffee, buying my groceries, having dental surgery (I once got very dirty looks in a dental clinic when I requested that they turn off the aural pollution) or just simply strolling down the street.

Today, Green politicians are very active about environmental pollution and astronomers about light pollution I think more people should take an active stand with Charlie, Ivor Robert and me on noise pollution!

1) This should have been posted yesterday but real life intervened.

Weaving the computer age.

With this post I’m going to lose whatever reputation I might have with all the feminist and politically correct denizens of the blogahedron. Why, because I intend to explode one of the greatest myths in the history of the computer. It is universally claimed that Ada Lady Lovelace was the world’s first programmer, the US Department of Defence even named a computer programme after her to celebrate this fact; this claim is total rubbish. Already in the 19^th century Babbage’s son pointed out that the credit given to Lovelace for her memoir on his fathers Analytical engine was due to his father and not to her. Lovelace has the role of a populariser, deliberately exploited by Babbage to help him in his never ending search for financing of his computer projects. The programme that Lovelace describes for generating Bernoulli numbers was created by Babbage and not by her.

This portrait of Jacquard was woven in silk on a Jacquard loom and required 24,000 punched cards to create (1839). It was only produced to order. One of these portraits in the possession of Charles Babbage inspired him in using perforated cards in his analytical engine. It is in the collection of the Science Museum in London, England. Source: Wikimedia Commons

So Charles Babbage is the first programmer and not Ada Lovelace, well, actually no Babbage borrowed the concept for programming his analytical engine from today’s birthday boy the French silk weaver, Joseph Maria Jacquard, 7^th July 1752. Jacquard developed the idea of using punch cards to programme the weaving patterns on his power weaving looms. If anybody should receive the credit for being the first programmer then it’s Joseph Jacquard and not Ada Lovelace.

The Colossus is not a computer!

Having bashed the Americans yesterday for ignoring Konrad Zuse, I will take the opportunity today to bash the Germans, or more precisely Horst Zuse, Konrad’s son, and at the same time correct a commonly held myth.

23^rd June is the birthday of another computer pioneer, Alan Turing. Turing of course means Bletchley Park and the breaking of the Enigma code. Now Bletchley also means one of the early computers, Colossus an electronic, binary, programmable non-Turing complete, special purpose computer designed and built in order to help the Bletchley code breakers. In a lot of popular sources Turing and Colossus are brought together as if it were obvious, Turing = computer expert, Colossus = computer, 1+1 = 3! Before the war Turing wrote one of the most important theoretical works on computing in the history of mathematics and after the War he worked on two major computer projects but in Bletchley he was responsible for the Bombe a very specialised and primitive form of computer but he was not involved in the design and construction of Colossus.

What does all this have to do with Horst Zuse? Horst is a professor for informatics who also specialises in the history of his father’s work. In one of his excellent lectures on his father’s computers, at which I was present, somebody asked him about the Colossus, his answer: “The Colossus was not a computer”. It would appear that Horst Zuse is as blind to his father’s competitors as the Americans to theirs.

Z3 or not Z3 that is the question.

Anyone who reads this blog regularly is probably aware of the fact that the history of computing has more than a passing interest for me. I should add that the history of computing is for me not just the history of the machine on which I am typing this post but covers the whole history of computing in the true meaning of the word i.e. the calculating with numbers starting with people cutting notches in bones tens of thousands of years in the past and going up to the present. This post however concerns the history of the modern computer as the machine with which you are reading this post.

Now as I have already pointed out in a post about Charles Babbage the question as to who invented the computer depends on how you define computer. Do you mean mechanical, electro-mechanical or electronic, special purpose or general purpose, programmable or not programmable, Turning complete or not, binary or decimal and so on and so forth. Beyond this list of technical problems it would appear that there is a certain national element involved in the answer to this question. If you visit the normally excellent Stanford Encyclopaedia of Philosophy and read the History of Modern Computing article you will find discussions of Babbage, Turing, Atanasoff and many others but you wont find a single word about Konrad Zuse who was born 100 years ago on 22^nd June 1910. Some of you might ask so what? The answer in really quite simple according to the Germans, and not only the Germans, Konrad Zuse invented the computer.

Konrad Zuge 1992 Source: Wikimedia Commons

Konrad Zuse was a German engineer who built his first machine the Z1, a mechanical computer, in 1938. Built with massive steel components that Zuse cut out with a jigsaw the Z1 was never very reliable and Zuse transferred his concept to the Z2 a prototype that functioned with electrical relays in 1939. This he developed further and produced his Z3 in 1941. This was a fully programmable, binary, Turing complete general purpose electro-mechanical computer. Apart from the fact that it was electro-mechanical and not electronic Zuse’s Z3 was in every aspect a modern computer. Unfortunately for him the Z3 was destroyed in an air raid so after the war the honours for inventing the computer went to Eckert’s and Mauchly’s ENIAC although later an American judge in a strange ruling awarded this honour to Atanasoff and Berry, strange because the ABC never actually functioned.

Reconstruction of Zuse Z3 im Deutschen Museum in München Source: Wikimedia Commons

After WW II Zuse built his first electronic computer the Z4 and this went into production, my university here in Erlangen had a Z4 as its first computer and it’s still here in their museum of computing and is still functioning. Today Zuse is generally recognised as the inventor of the computer for his Z3 but apparently not in America.