Ada enjoyed her moments in the royal gaze. She curtsied to the king and his wife Queen Adelaide. Ada was also introduced to various foreign dignitaries who happened to be visiting the king and queen.
Lady Byron described the event in a letter to a friend:
Ada wore white satin & tulle. She was amused by seeing for the first time – the Duke of Wellington – Talleyrand [the famous then seventy-nine-year-old French diplomat] – and the Duke of Orléans [the French king’s oldest son, who was five years older than Ada]. She liked the straightforwardness of the first – the second gave her the idea of an ‘old monkey’ – the third she thought very pleasing.
One might have thought the pomp and glamour of the royal court whose Empire straddled the world and a handsome prince would have dazzled a sheltered eighteen-year-old. But to Dr King, Lady Byron noted with obvious approval that her daughter was more impressed with meeting scientists on Wednesday, June 5, 1833, rather than royalty. In particular Ada greatly enjoyed meeting the forty-four-year-old Charles Babbage:
Ada was more pleased with a party she was at on Wednesday than with any of the assemblage in the grand monde. She met there a few scientific people – amongst them Babbage with whom she was delighted. I think her power of enjoying such society is in a great measure owing to your kindness in conversing with and reading with her on philosophical subjects.
Babbage, as prone to exuberant enthusiasm as Ada, told mother and daughter about his Difference Engine, in effect a machine to make calculations:
Babbage was full of animation and talked of his wonderful machine (which he is to shew us) as a child does of its plaything.
The Difference Engine was indeed a remarkable machine. Babbage wasn’t the first inventor to try to build a machine for carrying out reliable calculation, but in the nineteenth century he was the one who got closest to making the dream of reliable mechanical calculation come true.
In 1642, the French scientist and philosopher Blaise Pascal had tried to make an adding machine to aid him in computations for his father’s business accounts. The machine consisted of a train of number wheels whose positions could be observed through windows in the cover of a box that enclosed the mechanism. Numbers were entered by means of dial wheels. But Pascal’s machine turned out to be unreliable and it never made any impact in mechanising calculation.
The German mathematician, Gottfried Wilhelm Leibniz, saw Pascal’s machine while on a visit to Paris and worked to develop a more advanced version. Pascal’s device was only able to count, whereas the instrument Leibniz developed was designed to multiply and divide, and could even extract square roots. He completed a model of the machine in 1673 and exhibited it at the Royal Society, but Leibniz’s device did not work properly either and was never anything more than a curiosity.
Pascal’s and Leibniz’s machines differed in one vitally important respect from the device Babbage planned to make. Theirs were manual devices, but Babbage was adamant from the outset that his own calculation machine would be automatic. Unlike Pascal’s and Leibniz’s attempts, which required meticulous human intervention every stage of the way, the first calculation machine Babbage conceived – his Difference Engine – was designed to produce results automatically, with the operator only having to turn the handle that powered the machine. Even the handle-turning process could have been mechanised: there was indeed no reason why a small steam engine could not have been connected to the machine to do the job.
It wasn’t just science enthusiasts such as Annabella and Ada who were intrigued by Babbage. In 1832, the need for such a calculating machine was becoming urgent. The more extensive the role technology played in society, the more serious the problem of potentially inaccurate mathematical tables became.
If you were using inaccurate logarithmic tables to carry out an important calculation, your calculation was doomed from the start. Even worse, you had no way of knowing exactly where an inaccuracy in the mathematical tables might be found. John Herschel, writing in 1842 would observe: ‘An undetected error in a logarithmic table is like a sunken rock at sea yet undiscovered, upon which it is impossible to say what wrecks may have taken place.’ If properly designed, a mechanical calculator would sidestep any human errors and as science seeped more and more into the economy, the huge potential benefits it could offer became more obvious even to those with little interest in pure mathematics.
An especially painful illustration of the problem would be seen in the work of the English mathematician William Shanks. In 1853, Shanks announced that he had successfully calculated, to an astounding total of 530 decimal places, the basic mathematical ratio. This, the ratio between the circumference of a circle and its diameter, is a special number in mathematics that begins 3.14159 and proceeds with a never-ending series of decimal places. Shanks devoted the next twenty years of his life to extending the approximation further to try to take the evaluation into new and undiscovered realms of mathematical achievement. But unfortunately for Shanks, an error in the 528th place meant that his subsequent life’s work was entirely wasted. (Shanks was spared the anguish of this knowledge as the error was only discovered after his death.)
Ada and Annabella’s excitement about meeting Babbage was due to the fact that in December 1832, he, his chief engineer Joseph Clement and a team of workmen finished building the only mechanical device in the world that, in its day, challenged the Jacquard loom in complexity: the demonstration piece of his calculating machine, or the Difference Engine, as he called it, on which he had been working for the past twelve years interrupted only by the death of his wife in 1827. The demonstration piece quickly became the talk of scientific London. Babbage, who was always something of a showman, loved talking about the device to guests and putting it through its paces in front of an audience.
The carriage mechanism was and is fantastically ingenious (it is today in the Science Museum, London). It is enacted by a column of helically arranged arms, situated on each of the three tiers of wheels that are visible at the back of the machine. These rotate during each calculation cycle and pull each of the figure wheels in turn to see if there is a carry to be taken into account from the last addition. The carriage mechanism, clearly visible at the back of the device when the demonstration piece is being operated, creates a remarkably beautiful oscillation of the helically arranged arms, which has the appearance of endlessly changing and rippling waves.
The demonstration piece was able to carry out some calculations, though not a sufficient amount of them to have the commercial application of the fully working Difference Engine, which Babbage knew would transform the creation of mathematical tables. The demonstration piece was built of bronze and steel and stood about two and a half feet high, two feet wide and the same amount deep. Today it still works exactly as Babbage planned. It can produce calculations for mathematical tables, extract roots and undertake additions, subtractions, multiplications and divisions.
While only representing part of the Difference Engine that Babbage planned, the demonstration piece was immensely impressive. By June 1833, it resided in the drawing-room of Babbage’s home, and he greatly enjoyed showing it to visitors, hence his invitation to show it to Ada and her mother, who keenly accepted.
9
The Thinking Machine
Ada and Lady Byron visited Babbage at his home at number one Dorset Street on Monday, June 17, 1833, just twelve days after they first met him. Babbage lived there on his own after the death, in 1827, of his beloved wife Georgiana, in childbirth.* He had made a desultory attempt to remarry after a year-long tour of the Continent, then had thrown himself into his work and building the Difference Engine, a fiendishly expensive project even for a relatively well-off man as Babbage.
In 1823, following a desperate application by Babbage to the Government, he had originally been given a grant of £1,500, about £150,000 today. This money was awarded, as the Government put it, ‘to bring to perfection a machine invented by him for the construction of numerical tables.’ But i
t was a fraction of what was needed. The grant helped to accelerate development on the demonstration piece, but Babbage and Joseph Clement, his chief engineer, regularly quarrelled. A major reason for the tension between them was that Babbage insisted on treating Clement as a servant rather than a colleague, though it didn’t help that Clement often sent Babbage invoices considerably larger than what had been agreed.
After 1827, Babbage had redoubled his efforts. The Duke of Wellington – Prime Minister from January 22, 1828, to November 16, 1830, and also for a little less than a month late in 1834 – had taken a personal interest and by 1833 Babbage had received about £17,500 (maybe £17.5 million today) from the British government as a grant to help him build the Difference Engine. This was a fabulous sum, enough, in Babbage’s day, to pay for two battleships, but all Babbage had to show for the money was the demonstration piece. Babbage had spent too much of the Government’s grant on continually refining the design of these components. The machine required the production of several thousand cogwheels to precise specifications. It has been argued that the engineering of his day could not make cogwheels to the specification he required. This however is not true; modern research demonstrates that Babbage actually specified levels of precision that were greater than those he required.
In the summer of 1833, despite Babbage having built a portion of his beloved engine and being the talk of London, his project was, in truth, at a dead end. He was getting nowhere with his plan to build the whole machine. There was no precision metal industry in the 1820s, and so the only way of making these cogwheels was laboriously by hand, which was also extremely expensive. Besides, precise cogwheels and the other parts could only be made very slowly, and Babbage needed many thousands of cogwheels. While he was rich – his difficult father had died as well in 1827, leaving him a fortune of £100,000 – his funds were not unlimited.
So Babbage welcomed the distraction afforded by the visit of Ada and Lady Byron’s and demonstrated to them the one-seventh portion of the Difference Engine that had been built at the expense of so much money and heartache.
Lady Byron described her visit with Ada to Babbage’s home in a letter she wrote to Dr King four days after the visit.
There are many remarkable things about this letter. One is Lady Byron’s apparently casual description of the Difference Engine as the ‘thinking machine,’ which will seem to us today a reasonable enough description of Babbage’s device, but in 1833 is a highly original and exciting way of describing a machine.
As Lady Byron writes:
We both went to see the thinking machine (for such it seems) last Monday. It raised several Nos. to the 2nd and 3rd powers, and extracted the root of a quadratic equation. I had but faint glimpses of the principles by which it worked. Babbage said it had given him notions with respect to general laws which were never before presented to his mind. For instance, the Machine would go on counting regularly, 1, 2, 3, 4 &c to 10,000 and then pursue its calculation according to a new ratio … He said, indeed, that the exceptions which took place in the operation of his Machine, & which were not to be accounted for by any errors or derangement of structure, would follow a greater number of uniform experiences than the world has known of days & nights. There was a sublimity in the views thus opened of the ultimate results of intellectual power.
But Ada’s response was different. She saw more than just the whirring, beautifully moving cogwheels of Babbage’s machine that brought mathematics to life in an exciting elegant way. Many years later, Sophia Frend, the daughter of Ada’s and Lady Byron’s former mathematics tutor, claimed in her memoirs to have been present on the evening when Lady Byron and Ada saw the demonstration piece of the Difference Engine in action for the first time.
Lady Byron’s contemporary correspondence with Dr King makes no reference to Sophia, or indeed to anyone else, being there except Ada, Lady Byron and Babbage. It’s possible that Sophia (who says other visitors were there) had heard about the impression the Difference Engine had made on Ada the first time Ada saw it. But Sophia’s remarks are worth quoting, because even if she wasn’t there she would most likely have heard from a first-hand source, perhaps even from Ada or Lady Byron, just how entranced Ada was by the machine:
While other visitors gazed at the working of this beautiful instrument with the sort of expression, and I dare say the sort of feeling, that some savages are said to have shown on first seeing a looking-glass or hearing a gun … Miss Byron, young as she was, understood its working, and saw the great beauty of the invention.
Unlike Lady Byron, Ada understood how Babbage’s brilliant innovation linked the world of mathematics to a physical machine. At its heart, lay his decision to build his machine from cogwheels. Babbage had made this important practical decision about the technology that drove his planned calculation machine early on in his deliberations. Although we don’t know exactly what drove his decision, it isn’t difficult to guess the reasoning as it was the only technology available.
Babbage’s conception of the Difference Engine was based on the idea that teeth on individual cogwheels (described as ‘figure wheels’ by Babbage) would stand for numbers. The machine’s operation would be based around meshing independently moving cogwheels arranged in vertical columns with each other. This meshing process would carry out an arithmetical calculation.
Babbage decided to use our familiar, everyday counting system of base 10 for his machine. This derives purely from the fact that the normal human allocation of fingers and toes is ten of each. He arranged things so that the cogwheel at the bottom of a vertical column would represent the units, the cogwheel second from the bottom the tens, the cogwheel third from the bottom the hundreds, and so on.
For example, the setting of a four-digit number such as ‘6,538’ would require the bottom cogwheel to be turned eight teeth to represent ‘8’: the second cogwheel from the bottom to be turned three teeth to represent ‘3’; the third cogwheel from the bottom to be turned five teeth to represent ‘5’; and the fourth figure wheel from the bottom to be turned six teeth to represent ‘6.’ All the figure wheels above the fourth wheel would all be set to zero. The value of any number was therefore capable of being set in the machine in a vertical stack of cogwheels as long as there were enough wheels in the vertical stack to cover the tens, thousands, tens of thousands, hundreds of thousands, millions, etc. that were required to evaluate the calculation.
Babbage had christened his first calculating machine the Difference Engine because its entire operation was based on a mathematical concept called the ‘Method of Differences.’ This method was a technique for calculating mathematical tables by repeated regular additions of the ‘differences’ between successive items in a mathematical series. A mathematical series is a set of numbers (terms) in ordered succession, the value of each being determined by a specific relation to the preceding number. To take a simple example, the numbers 1, 2, 3, 4, 5 and so on to infinity comprise the series with a formula that requires 1 to be added to each previous number.
The beauty of the Method of Differences is that it simplifies the process of calculating a long and complex mathematical series. It allows otherwise difficult multiplications to be replaced by numerous straightforward but monotonous additions. But of course, if a machine is carrying them out, their monotony does not matter.
And the beauty of Babbage’s numbered cogwheels was that they could be made to do these additions because, firstly, a cogwheel is, by definition, a gearwheel. It facilitates the meshing with another cogwheel. Secondly, and equally important, a cogwheel allows the transmission of energy in defined, incremental steps. It’s precisely this attribute that makes cogwheels essential in ‘counting time’ in mechanical clocks. They are an essential part of the escapement: the device in a clock or watch that alternately checks and releases the train (i.e. the connected elements of the mechanism) by a fixed amount and transmits a periodic impulse from the spring to the balance wheel or pendulum.
Thus the machine had a
ll the ingredients that excited Ada; it showed how one could one day fly through mathematical formulas. Despite their many differences, not least their age, class and wealth, Ada and Babbage were fascinated by the same problems but approached them from different angles.
Babbage, like many of the intellectuals of his time, was interested close to the point of obsession by ideas of fate and predestination. He was also intrigued by the puzzle of how to reconcile the increasingly important influence of machines, which did what man wanted, with a belief in a God who, according to the theology adhered to by many people at the time, was supposed to look down on the human world like a sort of senior judge and intervene on occasions when he saw fit.
He was especially intrigued by the regularity and reliability of machines and got deep satisfaction from watching properly calibrated ones going through their paces, their mechanism invariably reaching the same point in the cycle after precisely the same interval as the previous time. Unlike Ada, he saw machines essentially as mechanised servants of mankind rather than as a new area of discovery with its own mysteries. His scientific imagination was ultimately more prosaic and less incandescent than hers.
While gregarious like Ada, Babbage could also be singularly eccentric, and he had a tendency to be gruff, morose and occasionally a show-off and know-it-all. In addition to this, he had a bizarre habit of talking about the most commonplace events as if they were mathematical phenomena. It made him a guaranteed attraction for fashionable society, who delighted in having Babbage in its midst. Hosts and hostesses were always extremely pleased to be able to inform their prospective guests that Mr Babbage would be attending. In an age when much social chit-chat involved exchanging mere superficial pleasantries, a lunch, supper or soirée with Babbage present was certainly never boring.
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