Charles not Ada, Charles not Charles and Ada, just Charles…

The is an old saying in English, “if you’ve got an itch scratch it!” A medically more correct piece of advice is offered, usually by mothers in a loud stern voice, “Don’t scratch!”  I have had an itch since the start of December and have been manfully trying to heed the wise words of mother but have finally cracked and am going to have a bloody good scratch.

I actually don’t wish to dump on Lady Science, which I regard as a usually excellent website promoting the role of women in science, particularly in the history of science but the essay, Before Lovelace, that they posted 3 December 2020 is so full of errors concerning Ada Lovelace and Charles Babbage that I simply cannot ignore it. In and of itself the main point that the concept of the algorithm exists in many fields and did so long before the invention of the computer is interesting and of course correct. In fact, it is a trivial point, that is trivial in the sense of simple and obvious. An algorithm is just a finite, step by step procedure to complete a task or solve a problem, a recipe!

My objections concern the wildly inaccurate claims about the respective roles of Charles Babbage and Ada Lovelace in the story of the Analytical Engine. Let us examine those claims, the essay opens at follows:

Charles Babbage and Ada Lovelace loom large in the history of computing. These famous 19th-century figures are consistently cited as the origin points for the modern day computer: Babbage hailed as the “father of computing” and Lovelace as the “first computer programmer” Babbage was a mathematician, inventor, and engineer, famous for his lavish parties and his curmudgeonly attitude. Lady Augusta Ada King, Countess of Lovelace was a mathematician and scientist, introduced to Babbage when she was a teenager. The two developed a long professional relationship, which included their collaborative work on a machine called the Analytical Engine, a design for the first mechanical, programmable computer.

They might be cited as the origin points of the modern-day computer, but such claims are historically wrong. For all of Babbage’s ingenuity in the design and conception of his mechanical, programmable calculating machines they played absolutely no role in and had no influence on the later development of the computer in the twentieth century. They were and remain an interesting historical anomaly. Regular readers of this blog will know that I reject the use of the expression “the father of” for anything in #histSTM and that for very good reasons. They will also know that I reject Ada Lovelace being called the “first computer programmer” for the very simple reason that she wasn’t. (See addendum below) I am of the opinion that Ada Lovelace was not a mathematician in any meaningful sense of the word, and she was in absolutely no way a scientist. Ada Lovelace and Charles Babbage did not have a long professional relationship and did not collaborate on the design of the Analytical Engine, which was entirely the work of Charles Babbage alone, and in which Ada Lovelace played absolutely no part. Assigning co-authorship and co-development to Ada Lovelace for Babbage’s work is no different to saying that a journalist, who interviews a scientist about his research work and then write a puff piece about it, is the scientist’s co-researcher! The train-wreck continues:

Much of what we know about the Analytical Engine comes from Lovelace’s paper on the machine. In 1842, she published” A Sketch of the Analytical Engine, with notes by the Translator”,” a translation of an earlier article by mathematician Luigi Menabrea. Lovelace’s English translation of Menabrea’s article included her own extended appendix in which she elaborated on the machine’s design and proposed several early computer programs. Her notes were instrumental for Alan Turing’s work on the first modern computer in the 1930s. His work would later provide the basis for the Colossus computer, the world’s first large-scale programmable, electronic, digital computer, developed to assist with cryptography work during World War II. Machines like the Colossus were the precursors to the computers we carry around today in our pockets and our backpacks.

We actually know far more about the Analytical Engine from Babbage’s biography (see footnote 1) and his own extensive papers on it, which were collected and published by his son Henry, Babbage’s Calculating Engines: Being a Collection of Papers Relating to Them; Their History and Construction, Charles Babbage, Edited by Henry P. Babbage, CUP, 1889. The notes to the translation, which the author calls an appendix, we know to have been co-authored by Babbage and Lovelace and not as here stated written by Lovelace alone. There is only one computer program in the notes and that we know to have been written by Babbage and not Lovelace. (See addendum below) Her notes played absolutely no role whatsoever in Turing’s work in the 1930s, which was not on the first modern computer but on a problem in metamathematics, known as the Entscheidungsproblem (English: decision problem). Turing discussed one part of the notes in his paper on artificial intelligence, Computing Machinery and Intelligence, (Mind, October 1950). Turing’s 1930s work had nothing to do with the design of the Colossus, although his work on the use of probability in cryptoanalysis did. Colossus was designed and built by Tommy Flowers, who generally gets far too little credit for his pioneering work in computers. The Colossus played no role in the future development of computers because the British government dismantled or hid all of the Colossus computers from Bletchley Park after the war and closed access to the information on the Colossus for thirty years under the official secret act. We are not done yet:

With Babbage and Lovelace’s work as the foundation and the Turing Machine as the next step toward what we now think of as computers…

Babbage’s work, not Babbage’s and Lovelace’s, was not, as already stated above, the foundation and the Turing Machine was very definitely not the next step towards what we now think of as the computer. I really do wish that people would take the trouble to find out what a Turing Machine really is. It’s an abstract metamathematical concept that is useful for describing, on an abstract level, how a computer works and for defining the computing power or capabilities of a given computer. It played no role in the development of real computers in the 1940s and wasn’t even referenced in the computer industry before the 1950s at the very earliest. Small tip for future authors, if you are going to write about the history of the computer, it pays to learn something about that history before you start. We are approaching the finish line:

One part of the history of computing that is much less familiar is the role the textile industry played in Babbage and Lovelace’s plans for the Analytical Engine. In a key line from Lovelace’s publication, she observes, “we may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.” The Jacquard Loom was a mechanical weaving system controlled by a chain of punched cards. The punched cards were fed into the weaving loom and dictated which threads were activated as the machine wove each row. The result was an intricate textile pattern that had been “programmed” by the punch cards.

Impressed by the ingenuity of this automation system, Babbage and Lovelace used punched cards as the processing input for the Analytical Engine. The punched cards, Lovelace explains in her notes, contain “the impress of whatever special function we may desire to develop or to tabulate” using the machine.

Why is it that so many authors use ‘less familiar’ or ‘less well known’ about things that are very well known to those, who take an interest in the given topic? For those, who take an interest in Babbage and his computers, the fact that he borrowed the punch card concept from Jacquard’s mechanical, silk weaving loom is very well known. Once again, I must emphasise, Babbage and not Babbage and Lovelace. He adopted the idea of using punch cards to program the Analytical Engine entirely alone, Ada Lovelace was not in anyway involved in this decision.

Itch now successfully scratched! As, I said at the beginning the rest of the essay makes some interesting points and is well worth a read, but I really do wish she had done some real research before writing the totally crap introduction.

Addendum:

I have pointed out on numerous occasions that it was Babbage, who wrote the program for the Analytical Engine to calculate the Bernoulli numbers, as presented in Note G of the Lovelace memoir. He tells us this himself in his autobiography[1]. I have been called a liar for stating this and also challenged to provide evidence by people to lazy to check for themselves, so here are his own words in black and white (16-bit grayscale actually)

[1] Charles Babbage, Passages from the Life of a Philosopher, Longman, Green, Longman, Roberts, Green, London, 1864, p. 136

Christmas Trilogy 2019 Part 2: Babbage, Airy and financing the Difference Engine.

Charles Babbage first announced his concept for his first computer, the Difference Engine, in a Royal Astronomical Society paper, Note on the application of machinery to the computation of astronomical and mathematical tables in 1822.

Engraving of Charles Babbage dated 1833 Source: Wikimedia Commons

He managed to convince the British Government that a mechanical calculator would be useful for producing numerical tables faster, cheaper and more accurately and in 1823 they advance Babbage £1700 to begin construction of a full scale machine. It took Babbage and his engineer, Joseph Clements, nine years to produce a small working model but costs had spiralled out of control and the government suspended payment at around £17,000, in those days a small fortune, in 1833.

A portion of the difference engine. Woodcut after a drawing by Benjamin Herschel Babbage Source: Wikimedia Commons

Babbage and Clement had parted in dispute by this time. The next nine years saw Babbage negotiating with various government officials to try and get payment reinstated. Enter George Biddel Airy (1801–1892).

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

Airy entered Trinity College Cambridge in 1819, graduating Senior Wrangler and Smith Prize man in 1823. He was elected a fellow of Trinity in 1824 and Lucasian Professor of mathematics beating Babbage for the position in 1826. In 1828 he was elected Plumian Professor of astronomy and director of the new Cambridge Observatory. Babbage succeeded him as Lucasian Professor. Airy proved very competent and very efficient as the director of the observatory, which led to him being appointed Astronomer Royal at the Greenwich Observatory in 1835 and thus the leading state scientist and effectively the government scientific advisor. It was in this capacity that the paths of the two Cambridge mathematicians crossed once again[1].

In 1842 Henry Goulburn (1784–1856), Chancellor of the Exchequer in the cabinet of Sir Robert Peel (1788–1850) was asked by Peel to gather information on Babbage’s Difference Engine project, which he would have liked to ditch, preferable yesterday rather than tomorrow. Goulburn turned to Airy as the countries leading scientific civil servant and also because the Royal Observatory was responsible for producing many of the mathematical tables, the productions of which the Difference Engine was supposed to facilitate. Could Airy offer an opinion on the utility of the proposed mechanical calculator? Airy could and it was anything but positive:

Mr Babbage made the approval of the machine a personal question. In consequence of this, I, and I believe other persons, have carefully abstained for several years from alluding to it in his presence. I think he lives in a sort of dream as to its utility.

An absurd notion has been spread abroad, that the machine was intended for all calculations of every kind. This is quite wrong. The machine is intended solely for calculations which can be made by addition and subtraction in a particular way. This excludes all ordinary calculation.

Scarcely a figure of the Nautical Almanac could be computed by it. Not a single figure of the Geenwich Observations or the great human Computations now going on could be computed by it. Indeed it was proposed only for the computation of new Tables (as Tables of Logarithms and the like), and even for these, the difficult part must be done by human computers. The necessity for such new tables does not occur, as I really believe, once in fifty years. I can therefore state without the least hesitation that I believe the machine to be useless, and that the sooner it is abandoned, the better it will be for all parties[2].

Airy’s opinion was devastating Peel acting on Goulburn’s advice abandoned the financing of the Difference Engine once and for all. Even the personal appeals of Babbage directly to Peel were unable to change this decision. Airy’s judgement was actually based on common sense and solid economic arguments. The tables computed by human computers were comparatively free of errors and nothing could be gained here by replacing their labour with a machine that would probably prove more expensive. Also setting up the machine to compute any particular set of tables would first require human computers to determine the initially values for the algorithms and to determine that the approximations delivered by the difference series remained within an acceptable tolerance range. Airy could really see no advantages in employing Babbage’s machine rather than his highly trained human computers. Also any human computers employed to work with the Difference Engine would, by necessity, also need first to be trained for the task.

Airy’s views on the utility or rather lack thereof of mechanical calculators was shared by the Swedish astronomer Nils Seelander (1804–1870) also used the same arguments against the use of mechanical calculators in 1844 as did Urbain Le Verrier (1811–1877) at the Paris Observatory.

Babbage was never one to take criticism or defeat lying down and in 1851 when the working model of the Difference Engine No. 1 was on display at the Great Exhibition he launched a vicious attack on Airy in his book The Exposition of 1851: Views of The Industry, The Science and The Government of England.

Babbage was not a happy man. By 1851 Airy was firmly established as a leading European scientist and an exemplary public servant and could and did publically ignore Babbage’s diatribe. Privately he wrote a parody of the rhyme This is the House that Jack Built mocking Babbage’s efforts to realise his Difference Engine. Verse seven of This is the Engine that Charles Built reads as follows:

There are Treasury lords, slightly furnished with sense,

Who the wealth of the nation unfairly dispense:

They know but one man, in the Queen’s vast dominion,

Who in things scientific can give an opinion:

And when Babbage for funds for the Engine applied,

The called upon Airy, no doubt, to decide:

And doubtless adopted, in apathy slavish,

The hostile suggestions of enmity knavish:

The powers of official position abused,

And flatly all further advances refused.

For completing the Engine that Charles built.[3]

Today Charles Babbage is seen as a visionary in the history of computers and computing, George Airy very clearly did not share that vision but he was no Luddite opposing the progress of technology out of principle. His opposition to the financing of Babbage’s Difference Engine was based on sound mathematical and financial principles and delivered with well-considered arguments.

[1] The following account is based almost entirely on Doran D. Swade’s excellent paper, George Biddell Airy, Greenwich and the Utility of Calculating Engines in Mathematics at the Meridian: The History of Mathematics at Greenwich, de. Raymond Flood, Tony Mann & Mary Croarken, CRC Press, Boca Raton, London New York, 2019 pp. 63–81. A review of the entire, excellent volume will follow some time next year.

[2] All three quotes are from Airy’s letter to Goulburn 16 September 1842 RGO6–427, f. 65. Emphasis original. Quoted by Swade p. 69.

[3] Swade p. 74 The whole poem can be read in Appendix I of Doran David Swade, Calculation and Tabulation in the Nineteenth Century: Airy versus Babbage, Thesis submitted for the degree of PhD, University College London, 2003, which of course deals with the whole story in great depth and detail and is available here on the Internet.

Christmas Trilogy 2018 Part 2: A danseuse and a woven portrait

I had decided some time ago to give up my attempts to rescue Charles Babbage’s reputation from the calumnies of the acolytes of Saint Ada, as a lost cause. However, the recent attempt by said acolytes to heave her onto the planned new British £50 banknote combined with the vast amounts of crap posted all over the Internet on her birthday on 10 December this year convinced me to return to the foray. I shan’t be writing about Ada per see but analysing two quotes that he supporters claim show her superior understanding of the potential of the computer over the, in their opinion, pitifully inadequate Babbage.

Two things should be born in mind when assessing the Notes to the translation of Menabrea’s essay on the Analytical Engine. Firstly, everything that Lovelace knew about the Analytical Engine she had learnt from Babbage and secondly, it is an established fact that Babbage co-authored those notes. The supporters of Lovelace as some sort of computing prophet always state, without giving any sort of proof for their claim, that Babbage was only interested in his Analytical Engine as a sort of super number cruncher and that anything that goes beyond that must per definition come from Lovelace. One should never forget that any computer is in fact just a super number cruncher; everything that one does on a computer, typing this post for example, has first to be translated in mathematical algorithms in binary code so that the computer can understand them. Babbage was, of course, first and foremost interested in producing a machine or automata capable of reading and carrying out the widest possible range of mathematical functions to give it maximum flexibility.

We now turn to one of the favourite Ada fan club quotes:

[The Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine…Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

It would not be false to claim that music is in fact applied mathematics. Both rhythm and pitch can be and are expressed by mathematical functions. For about two thousand years music was part of the mathematical curriculum, as one of the four disciplines of the quadrivium. That a mathematician of Babbage’s stature wouldn’t think of the possibility of programming his computer to play or even create music is asking a lot. However, we have very direct proof that Babbage was well aware of the relationship between music and automata.

Chapter three of Babbage’s autobiography opens thus:

“During my boyhood my mother took me to several exhibitions of machinery. I well remember one of them in Hanover Square, by a man who called himself Merlin. I was so greatly interested in it, that the Exhibiter remarked the circumstance, and after explain some of the objects to which the public had access, proposed to my mother to take me up to his workshop. Where I would see still more wonderful automata. We accordingly ascended to the attic. There were two uncovered female figures of silver, about twelve inches high.

[…]

The other silver figure was an admirable danseuse, with a bird on the fore finger of her right hand, which wagged its tail, flapped its wings, and opened its beak. This lady attitudinized in a most fascinating manner. Her eyes were full of imagination, and irresistible.[1]

Following Merlin’s death in 1803, his automata were acquired by another showman Thomas Weeks, who in turn having gone out of business died in 1834. Babbage, now a grown man and very wealthy, attended the auction of Week’s possessions and for £35 acquired the danseuse. He restored the model and having had clothes made for her displayed the danseuse on a glass pedestal in his salon[2]. Babbage’s passion, and it was truly a passion, for machines was sparked by a musical automata, his silver danseuse, an image somewhat far from that of the boring mathematician only interested in numbers. In fact many of the most famous model produced in the golden age of automata in the late 18^thand early 19^thcenturies were musical, something which Babbage, who became a great expert if not ‘the great expert’ on, would have well aware of. That Babbage probably did play with the thought of his super automata, his Analytical Engine, producing music is a more than plausible concept.

The all time favourite quote of the Ada acolytes that they flourish like a hand of four aces in poker is:

“The Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.”

Here the turn of phrase might well be Ada’s but the concept is with certainty Babbage’s. Anybody who thinks otherwise has never read anything by or on Babbage or the Analytical Engine or even the Notes supposedly written alone by Ada. Babbage’s greatest stroke of genius in his conception of his Analytical Engine was the idea of programming it with punch cards; an idea that he borrowed from Joseph Marie Jacquard 1752–1834), who had used it to program his silk weaving loom.

Detail of Jaquard loom at TextielMuseum Tilburg showing punch cards Source: Wikimedia Commons

Jacquard in turn had borrowed from Jacques de Vaucanson (1709–1782), arguably the greatest of the automata builders in that great age of automata. Vaucanson produced two famous musical automata, a flute player with a repertoire of twelve tunes and a tambourine player. The role of the punch cards and their origin are discussed extensively in the Notes. Turning once again to Babbage’s autobiography we find the following:

It is a known fact that the Jacquard loom is capable of weaving any design which the imagination of man may conceive. It is also the constant practice for skilled artists to be employed by manufacturers in designing patterns. These patterns are then sent to a peculiar artist, who, by means of a certain machine, punches holes in a set of pasteboard cards in such a manner that when the cards are placed in a Jacquard loom, it will then weave upon its produce the exact pattern designed by the artist.

Now the manufacturer may use, for the warp and weft of his work, threads which are all of the same colour; let us suppose them to be unbleached or white threads. In this case the cloth will be woven all of one colour; but there will be a damask pattern upon it such as the artist designed.

But the manufacturer might use the same cards, and put into the warp threads of any other colour. Every thread might even be of a different colour, or of a different shade of colour; but in all these cases the form of the pattern will be precisely the same—the colours only will differ.

The Analogy of the Analytical Engine with this well-known process is nearly perfect.

[…]

Every formula which the Analytical Engine can be required to compute consists of certain algebraic operations to be performed upon given letters, and of certain other modifications depending on the numerical values assigned to those letters.

There are therefore two sets of cards, the first to direct the nature of the operations to be performed—these are called operation cards: the other to direct the particular variable on which those cards are required to operate—these latter are called variable cards

[…]

Under this arrangement, when any formula is required to be computed, a set of operation cards must be strung together, which contain the series of operations in the order in which they occur. Another set of cards must then be strung together, to call in the variables into the mill, the order in which they are required to be acted upon.

[…]

Thus the Analytical Engine will possess a library of its own. Every set of cards once made will at any future time reproduce the calculations for which it was first arranged. The numerical value of its constants may then be inserted[3].

 

This may not have the poetical elegance of Ada’s pregnant phrase but Babbage here clearly elucidates (I’ve left out a lot of the details) how the Analytical Engine will weave algebraical patterns.

Of interest in the whole story of the punch cards, the Jacquard loom and the Analytical Engine is the story of the portrait. As a demonstration of the versatility of his system, in 1839 a portrait of Jacquard was woven in silk on a Jacquard loom; it required 24,000 punch cards to create.

Portrait of Jacquard woven in silk Source: Science Museum via Wikimedia Commons

Charles Babbage acquired one of these woven portraits for the then enormous sum of £800 and displayed it in his salon along with his silver danseuse and the ‘miracle performing’ unit of his Difference Engine. Having astounded his guests with performances of the danseuse and his Difference Engine he would then unveil the portrait and challenge his guests to guess how it had been produced. Babbage was as much a showman as he was a mathematician.

[1]Charles Babbage, Passages from The Life of a Philosopher, Longman, Green, Longman, Roberts, & Green, London, 1864 p. 17

[2]For the full story of Merlin, Weeks and much more see Simon Schaffer, Babbage’s Dancer

[3]Babbage, Passages, pp. 116–118

Don’t criticise what you don’t understand!

I was pleasantly surprised by the level of positive support my latest anti-Ada polemic received on Twitter, I had expected much more negative reaction to be honest. But I did receive two attacks that I would like to comment on more fully here. The first came from a certain Yael Moussaieff (@sachaieff) and reads as follows:

 

It still blows my mind how convinced mediocre men are that they’re not mediocre and that their opinions are in fact urgent and needed.

I’m not really sure in what sense here I am supposedly mediocre: my intelligence, my expertise, my abilities, all three, in all aspects of my existence? And how does Ms Moussaieff (I assume she is a she) know this, never having met me, on the basis of one, what I consider to be a fairly reasonably argued, blog post on the evaluation of the contributions of one Victorian woman to computer science. If she had brought some counter arguments to demonstrate the mediocrity of my thought processes or the mediocrity of my understanding of the historical period or the mediocrity of my abilities as a historian of computing (and I am one, see the reply to the next comment) then perhaps I could understand the intension or meaning of her criticism but for the moment I remain perplexed. Maybe my inability to comprehend is, in itself, a sign of my mediocrity.

Peter Robinson (@PeterRobinson76) chose a different line of attack:

We also love to put down anyone that dares to have popularity. Even long dead women.

To which I spontaneously responded:

There is a difference between a put down and a reasoned argument based on facts. I formally studied and researched both Babbage and Lovelace long before the current Lovelace hagiography started, as a professional historian of logic and computing. What are your qualifications?

For his benefit I would like to elucidate and explain my claim to professionalism in this matter. Some or even most of what I am now going to relate ought to be already known to those who have been reading this blog for a number of years for newer readers it might prove instructive.

Throughout the 1980s and the early 1990s I studied as a mature student at the Friedrich-Alexander University of Erlangen & Nürnberg. The first two and a half years I studied mathematics with philosophy as my subsidiary. I then changed to philosophy with English philology and history as my subsidiaries. The emphasis of my studies was always on the history and philosophy of science. During this time I worked for ten years as a paid research assistant in a major research project into the history of formal/symbolic/mathematical logic under the supervision of one of the world’s leading logic historians. This means that somebody, who is considered knowledgeable in these things, thought me competent enough to appoint me to this position. The fact that I was still there ten years later shows that he still believed in my competence. Possibly because I was the only English native speaker in the research team, my main area of research was nineteenth century British algebraic logics, which means I was researching Boole, Jevons, De Morgan, Venn, Cayley, McColl and others including the Americans working together with Peirce. Because algebraic logic was just a small part of the much wider field of abstract algebras emerging in the nineteenth century, I also researched Peacock, John Herschel, Babbage, Cayley, Sylvester, William Rowan Hamilton and various others. Calculating machines was also a part of our remit so Babbage and his computers along with the good Countess Lovelace came in for extensive study on my part.

Now ten plus years might seem a rather long time to study as a student but as I said I was a mature student without grant or parental support, which meant I had to earn money to do silly things like pay the rent or even on occasions eat and the pittance paid to research assistants in those days did not cover my daily living costs, so I also worked outside of the university. I had virtually finished my studies with just my master thesis to complete and my final exams to write–not a very big deal, as there was in those days a strong emphasis on continual assessment–when I crashed out with serious mental health problems. You can only burn the candle at both ends for a limited period of time until the two flames meet in the middle. Coming out of the loony bin I chucked my studies because being a qualified historian of science was never going to pay those pesky bills.

When I quit I had completed the entire research for both my master’s thesis and my doctoral thesis. I had written about 50–70% of my master’s thesis and a complete, highly detailed outline for my doctoral thesis. Now it might seem strange that I was writing both theses at the same time but my original master’s thesis, a wide-ranging study of the entire English speaking nineteenth century algebraic logic community, had grown far too big to be a master’s thesis, so I had cut out one section, on the life and work of Hugh McColl, to be my master’s thesis and turned the main project into a potential doctoral thesis. I recently, whilst clearing out some old cartons, came across all the material for that doctoral thesis. I was stunned at how far I had got with it, having in the intervening years forgotten most of the work I had invested. I sat and stared at it for three days then threw it all away.

So you see, if I say that I have researched and studied Babbage and Lovelace in a professional capacity it is simply the truth. I should point out that if I write about either of them now, I don’t rely on my memory of work done long ago but go back and read the original sources that I sorted out and studied then, modifying if necessary my views, as my knowledge has grown over the intervening years. In more recent years I have been paid by reputable, educational institutions to hold public lectures on Mr Babbage and his computing engines, so yes through preparing those lectures my knowledge has grown.

Let us return to my critics. Over the years battling the Ada hagiography I have come to the conclusion that the majority of her acolytes don’t actually bother to look at the sources at all. It seems some of them have read a blog post or an article in a non-academic Internet magazine, highly biased and based on dubious secondary sources rather than primary ones (and yes I am aware of the irony of writing that on a blog post). The rest have only ever read a short précis of those blog posts/articles posted on one or other of the Internet’s social media, which parrot the inaccurate accounts of their sources. This majority continue to parrot this ‘fake news’ without bothering to check whether it is historical accurate. The result is that we now have a major Ada myth industry.

If I had the chance to discuss with Yael, Peter or any of the acolytes who have criticised and attacked me over the years I would ask them the following questions:

Which Ada biography have you read?

 I have read five of which I have what I regard as the two best ones standing on my bookshelf.

What about Babbage? Have you read his autobiography?

It’s actually a fascinating piece of literature covering much more than the computing engines for which Babbage is famous.

Maybe you have instead read the more modern and objective biography contained in Laura Snyder’s “The Philosophical Breakfast Club”?

A wonderful book, as I wrote in my review of it for the journal Endeavour

Have you read his 9^thBridgewater Treatise, in which Babbage discusses religion and expands on his theory that one could explain miracles by unexpected changes in computer programmes?

An interesting if slightly bizarre  argument.

Or perhaps, you have read his On the Economy of Machinery Manufactures, the result of his extensive research into automation?

Babbage’s interest in automation drove much of his studies including his work on computing and computers. His On the Economy was a highly influential book in the nineteenth century.

Maybe you have read his unpublished writings on abstract algebra, now in the British Library, that are thought to have inspired George Peacock’s “Treatise on Algebra”?

 I will admit that I haven’t but it’s on my bucket list. I have however read Peacock’s book, fascinating and an important milestone in the history of mathematics,

Maybe you’ve read up on the Analytical Society, the student group Babbage and Herschel created in Cambridge to convince the university to introduce continental methods of analysis to replace Newton?

I stumbled across this intriguing piece of maths history during my research; it shows the dynamic that drove Babbage even from an early age.

This might seem like an intellectual pissing contest but if you wish to criticise me and maybe show me that I have erred, that I am mistaken or that I’m just plain wrong then I expect you to at least do the leg work. I actually like being shown that I am wrong because it means that I have learnt something new and I love to learn, to improve and to expand my knowledge of a subject. It is what I live for. I am a historian of science with a good international reputation that I have worked very hard to earn. I also work very hard to get my facts right. If you criticise me and hold a different opinion on some topic that I have written about but treat me with respect then I will treat you with respect even if I know that you are wrong. If, however, you just gratuitously insult me, as, in my opinion, Yael and Peter have done then I will treat you with disdain and if the mood suits me with a generous portion of sarcasm.

 

 

 

NO, SIMPLY NO!

I realise that in writing this blog post I am banging my head against a reinforced concrete wall, pissing against a hurricane, crying into the void and definitely not going to do my reputation any good with a certain class of feminist historians of science, but I cannot stay silent.

The Bank of England has announced that there is going to be a new British £50 banknote and that it will be graced with the portrait of a notable British scientist. To this end they have invited the great British public, renowned for their forethought and wisdom, see for example Brexit, to nominate potential candidates for this great honour. The only rules are that the nominated scientist must be British and dead! Upon this announcement going public Internet social media became an instant hotbed of wishes, suggestions, claims, counterclaims and sure-fire certs.

Unfortunately, the acolytes of Augusta Ada King, Countess of Lovelacewere immediately out in force shouting their, in their minds indisputable, claims from the rooftops and proclaiming their, in their minds unchallengeable, right to this honour for their saintly heroine in the highways and byways of the Internet. Unfortunately, the only criterion by which she qualifies is that she is dead. She was in no way by any meaningful definition of the term a scientist. Some have, however, pled that the honour should in fact not be awarded to a scientist at all but to a mathematician and that she would thus be an eminently suitable candidate. However, she was in no way by any meaningful definition of the term a mathematician and none of the recent published research on the topic does anything whatsoever to change this fact.

Although I have addressed this subject on a number of occasions on this blog let us briefly recap the largely mythical claims made on behalf of the good Countess. Indisputable is the fact that she translated, from the original French, at the suggestion of Charles Wheatstone, a memoir on Charles Babbage’s planned Analytical Engine written by Luigi Menabrea and based on a series of talks that Babbage had given on his planned computer in Turin in 1840. She was also asked by Babbage to expand on Menabrea’s original essay with an appended series of long notes. Indisputable is also the fact that these note were not compiled by Lovelace alone but in extensive cooperation with Babbage.

Note G of these appended notes contains the outline of a programme for the Analytical Engine to calculate the so-called Bernoulli numbers. On the basis of this note Lovelace has been incorrectly dubbed the first computer programmer. I say incorrectly, as Babbage had already demonstrated several programs for the Analytical Engine during his talks in Turin, some of which are outlined by Menabrea in his published memoir that Lovelace translated. If this were not enough Babbage actually states very clearly in his autobiography that although Countess Lovelace suggested the topic for Note G, he actually wrote the programme. In order to maintain their dubious claim on behalf of the Countess her acolytes either simply ignore this statement by Babbage or accuse him of lying. One interesting variant is to claim that the actual real first computer programme is the tabular presentation of the Bernoulli number programme that is appended to Note G and that this is alone the work of Lovelace. There are no such tabular representations of the programmes in Menabrea’s memoir. Again, unfortunately, in her correspondence Lovelace remarks on this subject that her table is an improvement on Babbage’s version. In what sense she improved it–simplified, made more readable, attractive, clearer–is not known, but this correspondence clearly shows that the tabular presentation also was originated by Babbage.

Not content with declaring her to be the first computer programmer, her acolytes moved on to making the, quite frankly ludicrous, claim that the appended notes show that she clearly understood the potential of the computer and computing much better than its inventor, Charles Babbage. Whilst anybody who can read must freely acknowledge that Lovelace can write considerable better than Babbage, whose prose tends to be rather turgid, whereas she has a poetic turn of phrase, such a claim can only be made by someone who simply ignores Babbage’s own extensive writings on the topic of the Analytical Engine. There is not a single idea or concept on the computer or computing in the Notes that cannot be found either in Babbage’s published writings, his masses of unpublished notes or his correspondence before Lovelace even became involved in the promotion of his project. At best she is a tech journalist and at worst Babbage’s sock puppet used by him to popularise his project and try to get financial backing for it.

Let us be generous and take the first option, this would make Ada Lovelace a female nineteenth century science writer, of which there were quite a few notable examples. It is not unusual that an intelligent, literate science writer can express the ideas of a scientist or inventor better for the lay reader than the originator of those ideas. That does not make the science writer a scientist or co-inventor, merely a communicator of concepts and ideas. If I, as a non-physicist, wish to acquire an understanding of the current state of quantum physics then I stand a better chance of doing so if I read Philip Ball’s Beyond Weird, than if I try to plough through the original papers published by the physicists who created the discipline. Ada Lovelace was perhaps a talented science writer but she was definitely neither a scientist nor a mathematician and thus although dead does not qualify as a potential candidate to adorn the new British £50 banknote.

I am personally totally in favour of a female scientist being chosen to adorn the new piece of British currency and a host of eminently good suggestions have already been made on social media from Dorothy Hodgkin, Britain’s only female Nobel Laureate, and inevitably Rosalind Franklin for her contributions to the discovery of the structure of DNA, to Jonathan Healey’s charming suggestion of Margaret Cavendish, as well as a whole host more of highly deserving and often neglected female scientists. So let us all nominate one of these genuine female scientists and not Ada Lovelace.

 

The first calculating machine

 

Even in the world of polymath, Renaissance mathematici Wilhelm Schickard (1592–1635) sticks out for the sheer breadth of his activities. Professor of both Hebrew and mathematics at the University of Tübingen he was a multi-lingual philologist, mathematician, astronomer, optician, surveyor, geodesist, cartographer, graphic artist, woodblock cutter, copperplate engraver, printer and inventor. Born 22 April 1592 the son of the carpenter Lucas Schickard and the pastor’s daughter Margarete Gmelin he was probably destined for a life as a craftsman. However, his father died when he was only ten years old and his education was taken over by various pastor and schoolteacher uncles. Following the death of his father he was, like Kepler, from an impoverished background, like Kepler he received a stipend from the Duke of Württemburg from a scheme set up to provided pastors and teachers for the Protestant land. Like Kepler he was a student of the Tübinger Stift (hall of residence for protestant stipendiaries), where he graduated BA in 1609 and MA in 1611. He remained at the university studying theology until a suitable vacancy could be found for him. In 1613 he was considered for a church post together with another student but although he proved intellectually the superior was not chosen on grounds of his youth. In the following period he was appointed to two positions as a trainee priest. However in 1614 he returned to the Tübinger Stift as a tutor for Hebrew.

Wilhelm Schickard, artist unknown Source: Wikimedia Commons

Here we come across the duality in Schickard’s personality and abilities. Like Kepler he had already found favour, as an undergraduate, with the professor for mathematics, Michael Maestlin, who obviously recognised his mathematical talent. However, another professor recognised his talent for Hebrew and encouraged him to follow this course of studies. On his return to Tübingen he became part of the circle of scholars who would start the whole Rosicrucian movement, most notably Johann Valentin Andreae, the author of the Chymical Wedding of Christian Rosenkreutz, who also shared Schickard’s interest in astronomy and mathematics.

Johann Valentin Andreae Source: Wikimedia Commons

Although Schickard appear not to have been involved in the Rosicrucian movement, the two stayed friends and correspondents for life. Another member of the group was the lawyer Christian Besold, who would later introduce Schickard to Kepler.

Christopher Besold etching by Schickard 1618

This group was made up of the brightest scholars in Tübingen and it says a lot that they took up Schickard into their company.

In late 1614 Schickard was appointed as a deacon to the parish of Nürtingen; in the Lutheran Church a deacon is a sort of second or assistant parish pastor. His church duties left him enough time to follow his other interests and he initially produced and printed with woodblocks a manuscript on optics. In the same period he began the study of Syriac. In 1617 Kepler came to Württtemburg to defend his mother against the charge of witchcraft, in which he was ably assisted by Christian Besold, who as already mentioned introduced Schickard to the Imperial Mathematicus. Kepler was much impressed and wrote, “I came again and again to Mästlin and discussed with him all aspects of the [Rudolphine] Tables. I also met an exceptional talent in Nürtingen, a young enthusiast for mathematics, Wilhelm Schickard, an extremely diligent mechanicus and also lover of the oriental languages.” Kepler was impressed with Schickard’s abilities as an artist and printer and employed him to provide illustrations for both the Epitome Astronomiae Copernicanae and the Harmonice Mundi. The two would remain friends and correspondents for life.

3D geometrical figures from Kepler’s Hamonice Mundi by Schickard

In 1608 Schickard was offered the professorship for Hebrew at the University of Tübingen; an offer he initially rejected because it paid less than his position as deacon and a university professor had a lower social status than an on going pastor. The university decided to appoint another candidate but the Duke, whose astronomical advisor Schickard had become, insisted that the university appoint Schickard at a higher salary and also appoint him to a position as student rector, to raise his income. On these conditions Schickard accepted and on 6 August 1619 he became a university professor. Schickard subsidised his income by offering private tuition in Chaldean, Rabbinic, mathematic, mechanic, perspective drawing, architecture, fortification construction, hydraulics and optics.

Page from a manuscript on the comets of 1618 written and illustrated by Schickard for the Duke of Württemberg

The Chaldean indicates his widening range of languages, which over the years would grow to include Ethiopian, Turkish, Arabic and Persian and he even took a stab at Malay and Chinese later in life. Schickard’s language acquisition was aimed at reading and translating text and not in acquiring the languages to communicate. Over the years Schickard acquired status and offices becoming a member of the university senate in 1628 and a school supervisor for the land of Württemberg a year later.  In 1631 he succeeded his teacher Michael Mästlin as professor of mathematics retaining his chair in Hebrew. He had been offered this succession in 1618 to make the chair of Hebrew chair more attractive but nobody had thought that Mästlin, then almost 70, would live for another 12 years after Schickard’s initial appointment.

Michael Mästlin portrait 1619 the year Schickard became professor for Hebrew (artist unknown)

In 1624 Schickard set himself the task of producing a new, more accurate map of the land of Württemberg. Well read, he used the latest methods as described by Willebrord Snell in his Eratosthenes Batavus (1617).

This project took Schickard many more years than he originally conceived. In 1629 he published a pamphlet in German describing how to carry out simple geodetic surveys in the hope that others would assist him in his work. Like Sebastian Münster’s similar appeal his overture fell on deaf ears. Later he used his annual school supervision trips to carry out the necessary work.

Part of Schickard’s map of Württemberg

Schickard established himself as a mathematician-astronomer and linguist with a Europe wide reputation. As well as Kepler and Andreae he stood in regular correspondence with such leading European scholars as Hugo Grotius, Pierre Gassendi, Élie Diodati, Ismaël Boulliau, Nicolas-Claude Fabri de Peiresc, Jean-Baptiste Morin, Willem Janszoon Blaeu and many others.

The last years of Schickard’s life were filled with tragedy. Following the death of Gustav Adolf in the Thirty Years War in 1632, the Protestant land of Württemberg was invaded by Catholic troops. Along with chaos and destruction, the invading army also brought the plague. Schickard’s wife had born nine children of which four, three girls and a boy, were still living in 1634. Within a sort time the plague claimed his wife and his three daughters leaving just Schickard and his son alive. The invading troops treated Schickard with respect because they wished to exploit his cartographical knowledge and abilities. In 1635 his sister became homeless and she and her three daughters moved into his home. Shortly thereafter they too became ill and one after another died. Initially Schickard fled with his son to escape the plague but unable to abandon his work he soon returned home and he also died on 23 October 1635, just 43 years old, followed one day later by his son.

One of the great ironies of history is that although Schickard was well known and successful throughout his life, today if he is known at all, it is for something that never became public in his own lifetime. Schickard is considered to be the inventor of the first mechanical calculator, an honour that for many years was accorded to Blaise Pascal. The supporters of Schickard and Pascal still dispute who should actually be accorded this honour, as Schickard’s calculator never really saw the light of day before the 20^thcentury. The story of this invention is a fascinating one.

Inspired by Kepler’s construction of his logarithm tables to simplify his astronomical calculation Schickard conceived and constructed his Rechenuhr (calculating clock) for the same purpose in 1623.

Source

The machine could add or subtract six figure numbers and included a set of Napier’s Bones on revolving cylinders to carry out multiplications and divisions. We know from a letter that a second machine he was constructing for Kepler was destroyed in a workshop fire in 1624 and here the project seems to have died. Knowledge of this fascinating invention disappeared with the deaths of Kepler and Schickard and Pascal became credited with having invented the earliest known mechanical calculator, the Pascaline.

A Pascaline signed by Pascal in 1652 Source: Wikimedia Commons

The first mention of the Rechenuhr was in Michael Gottlieb Hansch’s Kepler biography from 1718, which contained two letters from Schickard in Latin describing his invention. The first was just an announcement that he had made his calculating machine:

Further, I have therefore recently in a mechanical way done what you have done with calculation and constructed a machine out of eleven complete and six truncated wheels, which automatically reckons together given numbers instantly: adds, subtracts, multiplies and divides. You would laugh out loud if you were here and would experience, how the position to the left, if it goes past ten or a hundred, turns entirely by itself or by subtraction takes something away.

The second is a much more detailed description, which however obviously refers to an illustration or diagram and without which is difficult or even impossible to understand.

Schickard’s priority was also noted in the Stuttgarter Zeitschrift für Vermessungswesen in 1899. In the twentieth century Franz Hammer found a sketch amongst Kepler’s papers in the Pulkowo Observatory in St Petersburg that he realised was the missing diagram to the second Schickard letter.

The Rechenuhr sketch from Pulkowow from a letter to Kepler from 24 February 1624

Returning to Württemberg he found a second sketch with explanatory notes in German amongst Schickard’s papers in the Würtemmberger State Library in Stuttgart.

Hammer made his discoveries public at a maths conference in 1957 and said that Schickard’s drawings predated Pascal’s work by twenty years. In the following years Hammer and Bruno von Freytag-Löringhoff built a replica of Schickard’s Rechenuhr based on his diagrams and notes, proving that it could have functioned as Schickard had claimed.

Schickard’s Rechenuhr. Reconstruction by Bruno Baron von Freytag-Löringhoff and Franz Hammer

Bruno von Freytag-Löringhoff travelled around over the years holding lectures on and demonstrations of his reconstructed Schickard Rechenuhr and thus with time Schickard became acknowledged as the first to invent a mechanical calculator, recognition only coming almost 450 years after his tragic plague death.

 

Christmas Trilogy 2017 Part 2: Charles takes a trip to Turin

Charles Babbage wrote a sort of autobiography, Passages From The Life of a Philosopher.

One of its meandering chapters is devoted to his ideas about and work on his Analytical Engine. In one section he describes explaining to his friend the Irish physicist and mathematician James MacCullagh (1809–1847), who did important work in optics and was awarded the Royal Society’s Copley Medal in 1842,

James MacCullagh artist unknown
Source: Wikimedia Commons

how the Analytical Engine could be fed subroutines to evaluate trigonometrical or logarithmic functions, whilst working on algebraic operations. He goes on to explain that three or four days later Carl Gustav Jacob Jacobi (1804–1851) and Friedrich Wilhelm Bessel (1784–1846), two of Germany’s most important 19^th century mathematicians, were visiting and discussing the Analytical Engine when MacCullagh returned and he completed his programming explanation. Which historian of 19^th century mathematician wouldn’t give their eyeteeth to listen in on that conversation?

Having dealt with the problem of subroutines for the Analytical Engine Babbage moves on to another of his mathematical acquaintances, he tells us:

In 1840 I received from my friend M. Plana a letter pressing me strongly to visit Turin at the then approaching meeting of Italian Philosophers. In that letter M. Plana stated that he had inquired anxiously of many of my countrymen about the power and mechanism of the Analytical Engine.

Plana was Giovanni Antonio Amedeo Plana (1781–1864) mathematician and astronomer, a pupil of the great Joseph-Louis Lagrange (1736–1813), who was appointed to the chair of astronomy in Turin in 1811.

Giovanni Antonio Amedeo Plana
Source: Wikimedia Commons

Plana worked in many fields but was most famous for his work on the motions of the moon for which he was awarded the Copley Medal in 1834 and the Gold Medal of the Royal Astronomical Society in 1840. The meeting to which he had invited Babbage took place in the Turin Accademia delle Scienze. This august society was founded in 1757 by Count Angelo Saluzzo di Monesiglio, the physician Gianfrancesco Cigna and Joseph-Louis Lagrange as a private society. In 1759 it founded its own journal the Miscellanea philosophico mathematica Societatis privatae Taurinensis still in print today as the Memorie della Accademia delle Scienze. In 1783 having acquired an excellent international reputation it became the Reale Accademia delle Scienze, first as the Academy of Science of the Kingdom of Sardinia and later of the Kingdom of Italy. In 1874 it lost this status to the newly reconstituted Accademia dei Lincei in Rome. It still exists as a private academy today.

Rooms of the Turin Accademia delle Scienze

The meeting to which Babbage had been invited to explain his Analytical Engine was the second congress of Italian scientists. Babbage’s invitation in 1840 was thus recognition of his work at the highest international levels within the scientific community.

Babbage did not need to be asked twice, packed up his plans, drawings and descriptions of the Analytical Engine and accompanied by MacCullagh set of for Turin.

A general plan of the Analytical Engine from 1840

This was not just your usual conference sixty-minute lecture with time for questions. Babbage spent several days ensconced in his apartments in Turin with the elite of the Turin scientific and engineering community. Babbage writes, “M. Plana had at first planned to make notes, in order to write an outline of the principles of the engine. But his own laborious pursuits induced him to give up this plan, and to transfer this task to a younger friend of his, M. Menabrea, who had already established his reputation as a profound analyst.”

Luigi Federico Menabrea (1809–1896) studied at the University of Turin and was an engineer and mathematician. A professional soldier he was professor at both the military academy and at the university in Turin. Later in life he entered politics first as a diplomat and then later as a politician serving as a government minister. He served as prime minister of Italy from 1867 to 1869.

Luigi Federico Menabrea
Source: Wikimedia Commons

After another lengthy explanation of the programming of the Analytical Engine, Babbage writes:

It was during these meetings that my highly valued friend, M. Menabrea, [in reality Babbage had almost certainly never heard of Menabrea before he met him in Turin] collected the materials for that lucid and admirable description which he subsequently published in the Bibli. Uni. de Genève, t. xli. Oct. 1842.

 This is of course the famous document that Ada Lovelace would translate from the original French into English and annotate. Babbage writes of the two documents:

These two memoires taken together furnish, for those who are capable of understanding the reasoning, a complete demonstration—That the whole of the developments and operations of analysis are now capable of being executed by machinery. [emphasis in original]

That he was never able to realise his dreams of the Analytical Engine must have been very bitter for Babbage and now that we can execute the whole of the developments and operations of analysis with machinery, which even a Charles Babbage could not have envisaged in the 19^th century, we should take a moment to consider just how extraordinary his vision of an Analytical Engine was.

Juggling information

One of the parlour games played by intellectuals and academic, as well as those who like to think of themselves as such, is which famous historical figures would you invite to a cocktail or dinner party and why. One premise for the game being, which historical figure or figures would you most like to meet and converse with. As a historian of mostly Early Modern science I am a bit wary of this question, as many of the people I study or have studied in depth have very unpleasant sides to their characters, as I have commented in the past in more than one blog post. However in my other guise, as a historian of formal or mathematical logic and the history of the computer there is actually one figure, who I would have been more than pleased to have met and that is the mathematician and engineer, Claude Shannon.

A young Claude Shannon
Source: Wikimedia Commons

For those who might not know who Claude Shannon was, he was a man who made two very major contributions to the development of the computers on which I am typing this post and on which you are reading it. The first was when he at the age of twenty-one, in what has been described as the most important master’s thesis written in the twentieth century, combined Boolean algebra with electric circuit design thus rationalising the whole process and simplifying the design of complex circuitry beyond measure. The second was sixteen years later when he in his A Mathematical Theory of Communication, building, it should be added, on the work of others, basically laid the foundations of our so-called information age. His work laid out how to transmit digital signals through circuitry without loss of information. He is regarded as the über-guru of information theory, to quote Wikipedia:

 Information theory studies the quantification, storage, and communication of information. It was originally proposed by Claude E. Shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper entitled “A Mathematical Theory of Communication”.

Given that the period we live in is called both the computer age and the information age, it is somewhat surprising that the first full-length biography of Shannon, A Mind at Play,[1] only appeared this year. Having somewhat foolishly said that I would hold a public lecture in November on Vannevar Bush, who was Shannon’s master’s thesis supervisor, and Shannon, I have been reading Soni’s and Goodman’s Shannon biography, which I have to say I enjoyed immensely.

 

This is a full length, full width biography that covers both the live of the human being as well as the intellectual achievements of the engineer-mathematician. Shannon couldn’t decide which to study as an undergraduate so he did a double BSc in both engineering and mathematics. This dual course of studies is what led to that extraordinary master’s thesis. Having studied Boolean algebra in his maths courses Shannon realised that he could apply it to rationalise and simplify electrical switching when working, as a postgrad, on the switching circuits for Bush’s analogue computer, the differential analyser. It’s one of those things that seems obvious with hindsight but required the right ‘prepared mind’, Shannon’s, to realise it in the first place. It is a mark of his character that he shrugged off any genius on his part in conceiving the idea, claiming that he had just been lucky.

Shannon’s other great contribution, his treatise on communication and information transmission, came out of his work at Bell Labs as a cryptanalyst during World War II. The analysis of language that he developed in order to break down codes led him to a more general consideration of the transmission of information with languages out of which he then laid down the foundations of his theories on communication and information.

Soni’s and Goodman’s and volume deals well with the algebraic calculus for circuit design and I came away with a much clearer picture of a subject about which I already knew quite a lot. However I found myself working really hard on their explanation of Shannon’s information theory but this is largely because it is not the easiest subject in the world to understand.

The rest of the book contains much of interest about the man and his work and I came away with the impression of a fascinating, very deep thinking, modest man who also possessed a, for me, very personable sense of humour. One aspect that appealed to me was that Shannon was a unicyclist and a juggler, who also loved toys, hence the title of my review. As I said at the beginning Claude Shannon is a man I would have liked to have met for a long chat over a cup of tea.

An elder Claude Shannon
Source: Wikimedia Commons

On the whole I found the biography well written and light to read, except for the technical details of Shannon information theory, and it contains a fairly large collection of black and white photos detailing all of Shannon’s life. As far as the notes are concerned we have the worst of all possible solutions, hanging endnotes; that is endnotes, with page numbers, to which there is no link or reference in the text. There is an extensive and comprehensive bibliography as well as a good index. This is a biography that I would whole-heartedly recommend to anybody who might be interested in the man or his area of work or both.

 

 

[1] Jimmy Soni & Rob Goodman, A Mind at Play: How Claude Shannon Invented the Information Age, Simon & Shuster, New York etc., 2017

Journalists getting the facts wrong in the 19th century

One of the joys of having an extensive twitter stream is the unexpected titbits that it throws up from time to time. Recently Lee Jackson[1] (@VictorianLondon) posted this small newspaper cutting from The Times for the 2^nd May 1862.

This is an excerpt from an account of the 1862 Great London Exposition not to be confused with the more famous Crystal Palace Exhibition of 1851. This Exposition was held in a building especially constructed for the purpose in South Kensington, where the Natural History Museum now stands.

Panoramic view of the International Exhibition of 1862 in South Kensington, London
Source: Wikimedia Commons

A twenty-one acre construction designed by Captain Francis Fowke (1823–1865) of the Royal Engineers, it was supposed to be a permanent structure but when parliament refused to buy the building after the Exposition closed it was demolished and the materials used to build Alexandra Palace. The building cost £300,000 paid for out the profits of the 1851 Exhibition. Fowke also produced the original plans for the Natural History Museum but died before they could be realised. His plans were modified by Alfred Waterhouse, the new architect, when the museum was finally constructed in 1870.

Francis Fowke (1823-1865)
Source: Victoria & Albert Museum

The main aim of the Exposition, which ran from 1 May to 15 November attracting over six million visitors, was to present the latest technological advances of the industrial revolution, hence the presence an engine of Charles Babbage as described in the cutting. However the author of the piece has got his facts wonderfully mixed up.

The author introduces Charles Babbage by way of his notorious disputes with the street musicians of London for which he was better known than for his mathematical and technical achievements and which I blogged about several years ago. We then get told that the Exposition is displaying “Mr Babbage’s great calculating machine, which will work quadrations and calculate logarithms up to seven places of decimals.” All well and good so far but then he goes on, “It was the account of this invention written by the late Lady Lovelace – Lord Byron’s daughter –…” Anybody cognisant with the calculating engines designed by Charles Babbage will have immediately realised that the reporter can’t tell his Difference Engines from his Analytical Engines.

The calculating machine capable of calculating logarithms to seven places of decimals, of which a demonstration module was indeed displayed at the 1862 Exposition, was Babbage’s Difference Engine. The computer described by Lady Lovelace in her notorious memoire from 1842 was Babbage’s Analytical Engine of which he only constructed a model in 1871, nine years after the Exposition. This brings us to Messrs Scheutz of Stockholm.

Difference Engine No. 1, portion,1832
Source: Science Museum London

Analytical Engine, experimental model, 1871
Source: Science Museum London

Per Georg Scheutz (1785-1873) was a Swedish lawyer and inventor, who invented the Scheutzian calculation engine in 1837 based on the design of Babbage’s Difference Engine.

Per Georg Schutz
Source: Wikimedia Commons

This was constructed by his son Edvard and finished in 1843. An improved model was created in 1853 and displayed at the World Fair in Paris in 1855. This machine was bought by the British Government in 1859 and was in fact displayed at the 1862 Exposition but had apparently been removed by the time the Time’s reporter paid his visit to South Kensington. Scheutz’s machine gives a lie to those who claim that Babbage’s Difference Engine was never realised. Scheutz constructed a third machine in 1860, which was sold to the American Government.

The third Difference engine (Scheutz No. 2) built by Per Georg Scheutz, Edvard Scheutz and Bryan Donkin
Source: Science Museum London

It would seem that journalist screwing up their accounts of scientific and technological advances has a long history.

 

 

 

[1] You should read his excellent Dirty Old London: The Victorian Fight Against Filth, Yale University Press, Reprint 2015

Christmas Trilogy 2016 Part 2: What a difference an engine makes

Charles Babbage is credited with having devised the first ever special-purpose mechanical computer as well as the first ever general-purpose mechanical computer. The first claim seems rather dubious in an age where there is general agreement that the Antikythera mechanism is some sort of analogue computer. However, Babbage did indeed conceive and design the Difference Engine, a special purpose mechanical computer, in the first half of the nineteenth century. But what is a Difference Engine and why “Difference”?

Both Babbage and John Herschel were deeply interested in mathematical tables – trigonometrical tables, logarithmic tables – when they were still students and Babbage started collecting as many different editions of such tables as he could find. His main object was to check them for mistakes. Such mathematical tables were essential for navigation and errors in the figures could lead to serious navigation error for the users. Today if I want to know the natural logarithm of a number, let’s take 23.483 for example, I just tip it into my pocket calculator, which cost me all of €18, and I instantly get an answer to nine decimal places, 3.156276755. In Babbage’s day one would have to look the answer up in a table each value of which had been arduously calculated by hand. The risk that those calculations contained errors was very high indeed.

Babbage reasoned that it should be possible to devise a machine that could carryout those arduous calculations free of error and if it included a printer, to print out the calculated answer avoiding printing errors as well. The result of this stream of thought was his Difference Engine but why Difference?

The London Science Museum’s reconstruction of Difference Engine No. 2
Source: Wikimedia Commons

Babbage needed to keep his machine as simple as possible, which meant that the simplest solution would be a machine that could calculate all the necessary tables with variations on one algorithm, where an algorithm is just a step-by-step recipe to solve a mathematical problem. However, he needed to calculate logarithms, sines, cosines and tangents, did such an algorithm exist. Yes it did and it had been discovered by Isaac Newton and known as the method of finite differences.

The method of finite differences describes a property shared by all polynomials. If it has been a while since you did any mathematics, polynomials are mathematical expressions of the type x²+5x-3 or 7x⁵-3x³+2x²-3x+6 or x²-2 etc, etc. If you tabulate the values of a given polynomial for x=0, x=1, x=2, x=3 and so on then subtract the first value from the second, the second from the third and so on you get a new column of numbers. Repeating the process with this column produces yet another column and so on. At some point in the process you end up with a column that is filled with a numerical constant. Confused? OK look at the table below!

 

x	x3-3x2+6	xn+1-xn	diff(1)n+1 –diff(1)n	diff(2)n+1 – diff(2)n
0	6	-2	0	6
1	4	-2	6	6
2	2	4	12	6
3	6	16	18
4	22	34
5	56
6

 

As you can see this particular polynomial bottoms out, so to speak, with as constant of 6. If we now go back into the right hand column and enter a new 6 in the first free line then add this to its immediate left hand neighbour repeating this process across the table we arrive at the polynomial column with the next value for the polynomial. See below:

 

x	x3-3x2+6	xn+1-xn	diff(1)n+1 –diff(1)n	diff(2)n+1 – diff(2)n
0	6	-2	0	6
1	4	-2	6	6
2	2	4	12	6
3	6	16	18	6
4	22	34
5	56
6

 

x	x3-3x2+6	xn+1-xn	diff(1)n+1 –diff(1)n	diff(2)n+1 – diff(2)n
0	6	-2	0	6
1	4	-2	6	6
2	2	4	12	6
3	6	16	18	6
4	22	34	24
5	56
6

 

x	x3-3x2+6	xn+1-xn	diff(1)n+1 –diff(1)n	diff(2)n+1 – diff(2)n
0	6	-2	0	6
1	4	-2	6	6
2	2	4	12	6
3	6	16	18	6
4	22	34	24
5	56	58
6

 

x	x3-3x2+6	xn+1-xn	diff(1)n+1 –diff(1)n	diff(2)n+1 – diff(2)n
0	6	-2	0	6
1	4	-2	6	6
2	2	4	12	6
3	6	16	18	6
4	22	34	24
5	56	58
6	114

This means that if we set up our table and calculate enough values to determine the difference constant then we can by a process of simple addition calculate all further values of the polynomial. This is exactly what Babbage designed his difference engine to do.

If you’ve been paying attention you might notice that the method of finite differences applies to polynomials and Babbage wished to calculate were logarithmic and trigonometrical functions. This is however not a serious problem, through the use of other bits of higher mathematics, which we don’t need to go into here, it is possible to represent both logarithmic and trigonometrical functions as polynomials. There are some problems involved with using the method of finite differences with these polynomials but these are surmountable and Babbage was a good enough mathematician to cope with these difficulties.

Babbage now had a concept and a plan to realise it, all he now needed was the finances to put his plan into action. This was not a problem. Great Britain was a world power with a large empire and the British Government was more than ready to cough up the readies for a scheme to provide reliable mathematical tables for navigation for the Royal Navy and Merchant Marine that serviced, controlled and defended that empire. In total over a period of about ten years the Government provided Babbage with about £17, 000, literally a fortune in the early nineteen hundreds. What did they get for their money, in the end nothing!

Why didn’t Babbage deliver the Difference Engine? There is a widespread myth that Babbage’s computer couldn’t be built with the technology available in the first half of the nineteenth century. This is simply not true, as I said a myth. Several modules of the Difference Engine were built and functioned perfectly. Babbage himself had one, which he would demonstrate at his scientific soirées, amongst other things to demonstrate his theory of miracles.

The Difference Engine model used by Babbage for his demonstrations of his miracle theory
Source: Wikimedia Commons

Other Difference Engines modules were exhibited and demonstrated at the Great Exhibition in Crystal Palace. So why didn’t Babbage finish building the Difference Engine and deliver it up to the British Government? Babbage was not an easy man, argumentative and prone to bitter disputes. He became embroiled in one such dispute with Joseph Clement, the engineer who was actually building the Difference Engine, about ownership of and rights to the tools developed to construct the engine and various already constructed elements. Joseph Clement won the dispute and decamped together with said tools and elements. By now Babbage was consumed with a passion for his new computing vision, the general purpose Analytical Engine. He now abandoned the Difference Engine and tried to convince the government to instead finance the, in his opinion, far superior Analytical Engine. Having sunk a fortune into the Difference Engine and receiving nothing in return, the government, not surprisingly, demurred. The much hyped Ada Lovelace Memoire on the Analytical Engine was just one of Babbage’s attempts to advertise his scheme and attract financing.

However, the story of the Difference Engine didn’t end there. Using knowledge that he had won through his work on the Analytical Engine, Babbage produced plans for an improved, simplified Difference Engine 2 at the beginning of the 1850s.

Per Georg Schutz
Source: Wikimedia Commons

The Swedish engineer Per Georg Scheutz, who had already been designing and building mechanical calculators, began to manufacture difference engines based on Babbage’s plans for the Difference Engine 2 in 1855. He even sold one to the British Government.

Scheutz Difference Engine No. 2. (1859) Maschine im Science Museum, London
Source: Wikimedia Commons