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 18thand early 19thcenturies 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


Filed under History of Computing, History of Mathematics

3 responses to “Christmas Trilogy 2018 Part 2: A danseuse and a woven portrait

  1. Whilst I have some shared concerns about the hagiographic treatment of Ada and have argued with my women-in-engineering pals that we should not be pressing her case just because of her association with the Babbage engine (I favour Dorothey Hodgkin for the banknote), it has to be recognised that her glamour has been helpful in drawing girls towards engineering and computing. Yes, I know that the word ‘glamour’ originally meant faerie-dust delusions, more or less, but either way her story is attractive even if her contribution to programming is toned down!
    Thanks for your treats as always.

    • Gavin Moodie

      Yes, of course we should do all we can to encourage girls into engineering and computing. But if it is based on false ‘evidence’ or on a false interpretation of evidence it betrays the core principle of all scholarship.

      Science has many disappointments. Let us not add to those misleading historical concoctions.

      Perhaps an accurate account of Lovelace’s involvement with science offers a different useful lesson: that even if one is not exceptional at science one may be involved with science and one may contribute to science,

  2. Thony, It really heartens me to see that others, such as you, also do battle with mass delusions, even while knowing that we may fail in the shorter term. Cheers, and Happy New Year.

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