Decoding the Heavens
Page 14
Meanwhile, Michael Wright used his skills as a mechanic to deduce how the gearwheels must have worked, and to build a reconstruction. He had been fascinated by mechanical devices since he was a boy, when his parents would bring him to the Science Museum and let him loose with no instruction except that when the museum closed he should go down the road to find his uncle, who was an assistant keeper at the Natural History Museum. Back then the Science Museum was filled with old instruments in cases, like an enchanted forest of glass and metal. He’d invariably get lost, but always learned something new finding his way out.
At home and at school he had loved taking things apart to see how they worked, even if they didn’t always go back together again. Soon he was building models: aeroplanes, trains, even working clocks. Like Price, he had studied physics at university, but his job now was to look after the exhibits in the museum’s echoing energy hall – especially the hulking coal-burning steam engines that had powered Britain’s Industrial Revolution.
He also took an interest in the museum’s old clocks, including the stunning astronomical pieces that decorated Europe from the fourteenth century onwards. He was particularly fond of the museum’s replica of one of the most impressive examples, completed by Giovanni de’ Dondi in Padua, Italy, in 1364. One hundred and seven gearwheels drove seven golden dials showing the position in the zodiac of the Sun, Moon and five known planets: Saturn, Jupiter, Mars, Venus and Mercury. Wright came to know all the little tricks inside these clocks, and like Price he saw how the complexities of the gearing they used to model the planets turned up later in the steam-powered mills and looms of the Industrial Revolution.
Now, reconstructing the Byzantine sundial in his home workshop, he applied his skills to an artefact that no one had seen (or built) in many centuries. Some parts of the puzzle were missing, but he felt his way around the pieces, noting a scratch mark there, some asymmetrical wear here, trying to reconstruct how the device must have been put together. He quickly realised that despite the 500-year gap, the four surviving gearwheels had been part of a simple calendar very like the eight-wheeled one described by al-Biruni.
The gear ratios and layout of the Byzantine instrument were slightly different – and attached to a sundial rather than an astrolabe – but otherwise the principle was the same. Wright’s reconstruction had a knob sticking up through the centre of the seven-headed dial, around which gods representing the Sun, Moon and five known planets stood guard over the seven days of the week. The ratchet, with seven lobed teeth, fitted directly underneath – clicking on exactly one day at a time as the knob was turned. As it rotated, a little wheel with seven teeth on the same axle drove the larger 59-tooth wheel, so that it turned one tooth for every day, and so that the numbers around its edge showed up one at a time in a little window on the missing back face of the disc – the day of the month. The two penny-sized holes in the 59-tooth wheel would have been filled with a black material, perhaps wax or dark wood. As the wheel turned, they moved under a circular hole on the back face to display the changing phases of the Moon. The missing wheels drove dials showing the positions of the Sun and Moon in the zodiac. The calendar was a nice little addition to the sundial, and clicking the ratchet on each day would have provided the date for setting the gnomon.
Once he had worked out the mechanism, Wright perfected two models of it. He filed the gear teeth until the wheels turned smoothly, then lovingly carved the Moon goddess’s curls and topped both dials with fixing pins in the shape of horses’ heads. The results were satisfyingly heavy in the palm of his hand as he ran his little solar systems through their paces, the latest in a long line of instrument-makers throughout history who have tried to catch the Moon in a box. Then he sent one of his models to his sons Gabriel and Caleb, who proudly showed it off to their friends at boarding school as the winter sun slanted over the playing fields (the horsehead pin, dropped and never found, is probably still there in the mud).
Wright had never been sure that he was doing the right thing with his life – he had ended up at the Science Museum more by accident than design. But now he felt a new purpose. Few of his colleagues as curators and historians could actually do what they studied and wrote about. He would combine his knowledge of ancient mechanisms with his practical skill as a craftsman to bring something unique to the field. By understanding the instruments from the maker’s point of view he could glean insights that would be lost to a purely academic investigator. Maybe he was only a self-taught museum curator, but as a practical man he could still uncover things that the university professors might never see.
He also started thinking more and more about the Antikythera mechanism. Price had suggested that there was a continuing tradition of geared instruments in the Hellenistic world and that this had been transmitted to Islamic culture. However, he had found no direct evidence to support either of those claims. Knowledge of astronomy and other subjects was certainly transmitted from the Greeks to the Arabs, but directly linking the Antikythera mechanism with a geared astrolabe from such a different world was a huge leap of intuition. Yet here out of nowhere was a stepping stone across a thousand years of history – a single shining drop of evidence that Price was right.
It now became clear that the Islamic clockwork calendars had not been invented from scratch. Their similarity to the one in Wright’s sundial showed that they must have been influenced by the Byzantine tradition. And although the sundial calendar was much simpler than the Antikythera mechanism, its Greek inscriptions suggested that it was itself descended from Hellenistic instruments. What’s more the workmanship – plain brass, without any traces of gold or silver, and gear teeth that were accurate but not excessively neat – suggested that this was an everyday object, not a rare luxury. There could have been hundreds, if not thousands, of these things all across the Byzantine world. In some simple form, at least, the tradition begun by the Antikythera mechanism of using gearwheels to model the movement of the heavens had survived.
But the more Wright studied Price’s work, the more the details of it worried him. He was now ten years older and wiser than when he first read Gears from the Greeks, and he realised that many of Price’s arguments just didn’t make sense. In several places Price had cited the results of Karakalos’ tooth counts only to reject them. For a gearwheel labelled E5, for example, Karakalos had estimated 50–52 teeth, but Price settled on 48 as more ‘appropriate’. And for wheel G2, Karakalos counted 54 or 55 teeth, but Price had dismissed this as ‘too small for any simple or meaningful interpretation of the gear train’ and suggested 60 instead. Again and again, Price had changed the numbers for no obvious reason except that he needed to make them fit the gear trains already in his mind. He seemed to pull his ideas out of nowhere, and he made liberal use of supposedly practical arguments that to Wright, who had so much experience in making clockwork mechanisms, made no sense at all.
There was his old question of why the maker of the Antikythera mechanism would have used a complicated differential gear to work out the phase of the Moon when it could be done much more easily with a simple fixed gear train – as in the Byzantine sundial, for example. Wright also found Price’s suggested function for the back dials ridiculously simple compared to the obvious sophistication of the device. Price had thought that the upper back dial showed a four-year cycle. But why would anyone go to all that trouble – a train involving seven gearwheels and a dial of five concentric rings – just to show a pointer that went round four times for every turn of the main wheel?
And then there was the big four-spoked wheel, the most striking feature of the whole mechanism. Why was it so big and sturdy compared to the other wheels in the device? By grandly calling it the ‘Main Drive Wheel’ Price had given the impression that it was big and strong because it drove all of the mechanism’s gear trains. But all that the wheel actually did in Price’s reconstruction was to transfer its motion to a much smaller wheel turning around the same shaft, which then drove all the other trains from there.
Price’s paper was certainly a stunning piece of detective work, but Wright felt he saw some sleight of hand in it as well. Even Price’s name for the device – a ‘calendar computer’ – seemed designed to distract attention from the fact that his reconstruction of the mechanism corresponded to no known instrument, and didn’t have any obvious practical use. For all of Price’s insights, it was clear that he had barely begun to understand what the device was capable of. Wright wished he could discuss his questions with Price. The two men had briefly met, when Price had called at the Science Museum to see the newly discovered Byzantine sundial during his visit to London in 1983. But that was before Wright started studying the Antikythera mechanism in earnest, and within a fortnight of that meeting Price was dead.
Wright knew what he had to do. He would go to Athens to study the mechanism for himself and pick up where Price had left off. He would study the fragments, read the inscriptions, X-ray them for himself if necessary, and find out what the device really was.
But by this time the atmosphere at the Science Museum had begun to change. It was under new management, which argued that the museum needed to focus less on studying obscure artefacts and more on pleasing its visitors or ‘customers’ as they became known. And Wright had a new supervisor who didn’t approve of a curator spending valuable museum time on his own research projects. Wright’s job was to look after the museum’s exhibits – to maintain them, ensure they were displayed to best advantage and answer any public enquiries about them. Where, his boss asked him, did the job description say anything about flying off to Athens on a nice holiday to check out some obscure relic in the back room of a Greek museum? Wright’s request for research time was turned down flat.
Kept busy on other projects, he dreamed instead. He was forbidden from spending any time on the Antikythera mechanism during work hours, but in his spare time he read up on ancient astronomy and technology, and brushed up on the Greek he had learned at school. When he finally got to Athens to see the mechanism for himself, he would be ready.
And then a bearded ball of energy rolled into Wright’s office. His name was Allan G. Bromley.
Probing the nature of interstellar dust clouds was how Bromley had started his career, as an astrophysicist at the University of Sydney in Australia. That research got him interested in high-performance computing, and so he had become a lecturer in the computer science department. But he also had a keen interest in mechanical calculators, in fact anything to do with the history of computation and measurement. In his small house in the Sydney suburb of Dulwich Hill, he had a garage full of adding machines, bits of clocks and giant analogue computers, one of them so heavy that it crushed the bricks on his driveway when he brought it home.
Bromley had first entered the Science Museum in 1979 on a year’s sabbatical to study the notebooks and drawings of Charles Babbage, popularly known as the ‘grandfather of computing’. The museum held the biggest collection of Babbage’s papers, mostly abstract representations of his designs, such as logic diagrams and flow charts, and notebooks (‘scribbling books’, as Babbage called them) totalling thousands of pages. The scrawled notes were jumbled and fiendishly complicated, but Bromley was a worthy match for them. He knew the theory of computing inside out and had an excellent memory and insatiable desire for detail. He soon made himself a world authority on Babbage and became the first man to decode the diagrams since the author himself.
Babbage was famous for his attempts to build a machine that would construct whole sets of mathematical tables automatically. He, too, was inspired by a desire to predict the movements of the heavens. One day in 1821, at his house in Devonshire Street, London, he was proofreading hand-calculated astronomical tables with his friend, the astronomer John Herschel. He became frustrated by the numerous errors they found, and supposedly burst out: ‘I wish to God these calculations had been executed by steam!’
‘It is quite possible,’ Herschel calmly replied. This got the 29-year-old mathematician thinking and within days he had come up with the idea for his Difference Engine. It took advantage of the fact that the path of any astronomical body can be calculated relatively simply by breaking it down into small chunks and adding the difference necessary to get from one step to the next – much like the arithmetic progressions used centuries earlier by the Babylonian astronomers. The resulting design was a huge contraption, involving hundreds of bronze gears, levers and wheels. Each digit of a number had its own wheel and the value of the digit was represented by the amount by which the wheel rotated. Babbage came up with a series of designs, culminating in the even more sophisticated and flexible Analytical Engine, which could multiply and divide, as well as add and subtract, store numbers, and even be programmed using punchcards. If it had ever been finished, it would have been the world’s first programmable computer.
The British government paid Babbage £17,000 – a fortune at the time – to build his machines. Sailors relied on astronomical tables for navigation, so having a more accurate way to produce them would have been invaluable for a nation that relied for so much of its wealth on overseas trade, not to mention saving countless lives. But quarrels with his engineer and an inability to stop tinkering with his designs meant that Babbage never completed a single working machine. He died a bitter man.
After Bromley’s sabbatical was over he visited London whenever he could to continue his studies of Babbage’s papers, mostly in the British winter when his students were on summer vacation. His short stature, along with his bushy beard, rosy cheeks and yellow waistcoat (knitted by his mother), he became a familiar sight at the museum, as well as in London’s flea markets, which he regularly scoured for antique mechanical calculators and measuring devices that he shipped back home to his collection in Sydney.
By the mid-1980s Bromley was formulating a plan: the Science Museum would build one of Babbage’s machines for the bicentenary of his birth in 1991. Bromley was convinced that the inventor’s designs would work, but he had been looking at them from the point of view of a computer scientist. He understood the logic and the theory behind them, but he wanted to know more about how the parts of the mechanism would have been made and put together. He asked the museum staff if anyone there knew about making geared mechanisms. The answer came without hesitation: ‘Michael Wright.’
And so Bromley ended up in Wright’s office. He came often, whenever he was over from Sydney, chatting to Wright over his sandwiches and learning about the practicalities of nineteenth-century planing machines and treadle lathes. He put together a proposal, which he handed to the museum’s senior curator of computing, Doron Swade, in May 1985. It would be one of the most ambitious scientific reconstructions ever attempted, likely to cost at least a quarter of a million pounds. But persuasion was one of Bromley’s talents. Under Swade’s supervision and with the help of some industry sponsorship, Difference Engine No. 2 was duly built. It carried out its first calculation on 29 November 1991, a month short of the bicentenary.
Over their lunches, however, Bromley and Wright didn’t just talk about Babbage. They covered the whole world of mechanical marvels and out of their conversations grew friendship. Wright told Bromley about his growing interest in the Antikythera mechanism and his dream of going to Athens to study it. He showed him Price’s papers, explained where he could see that Price had gone wrong, and the two swapped ideas about how the device might have worked.
The Antikythera mechanism piqued Bromley’s interest immediately. Babbage’s designs belonged to the line of digital calculators and computers, in which calculations are converted into numerical equations and the answer is given as a string of digits. This idea is familiar to us now because it’s the method used by modern electronic computers. But the Antikythera mechanism is part of a tradition of analogue computing,1 in which problems are modelled more directly and the output is continuous, for instance as a dial on a scale. If you’re trying to solve a problem of trigonometry, for example, the digital method would be to derive the
appropriate equation and work out the answer on a pocket calculator. But you could instead make a scale drawing of the triangle in question and simply measure the answer. That would be the analogue approach.
A slide rule is a simple example of an analogue computer, as is the astrolabe. Slightly more complex were the mechanical gun-aimers used during the Second World War. They had two metal arms to represent the angle above the horizon and the distance to the target aircraft, so once they had been set appropriately you could read off the height and horizontal distance to the target.
The first programmable analogue computer was the Totalisator – an Australian invention first installed at Newcastle Racecourse in New South Wales in 1913. It used banks of differential gears to calculate the amount of money to be paid to winning punters from a pool. Bromley had one of the earliest models in his garage, but he had never heard of anything like this strange Greek clockwork device. This mysterious machine represented the very beginning of the computing tradition, digital or analogue – it was the first known example of an object that people had built to think for them, to work through mathematical equations and display the answer on a numerical scale. Instantly, Bromley was mentally converting its gear trains into circuit diagrams and a new plan began to form in his mind. He would be the man to solve the Antikythera mechanism.
In particular, Bromley had a theory that the device couldn’t have been driven by the slow-moving big wheel – there just wouldn’t have been enough power to drive all the subsequent gear trains. He tweaked the gears and came up with his own variant, which was driven by the much faster moving turntable – the same one that carried Price’s differential gear. Back in Sydney, he tried out a rough model of the mechanism using Meccano gears, then worked with a clockmaker called Frank Percival to build a proper reconstruction. They had terrible trouble getting the sharp, triangular teeth to mesh properly, but after rounding them off at the edges it worked sweetly – much better than Price’s model. Wright, meanwhile, was rapidly losing faith that any part of Price’s reconstruction could be trusted. The only way to find out for sure was to go and study the fragments.