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The eccentric engineer: the strange world of Mediaeval paper computers

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Our medieval forebears used paper devices known as volvelles to perform complex astronomical calculations, to plan medical treatments and much more.

One of the more delicate areas of engineering must be paper engineering – from pop-up books to origami it brings solid physical process and design into the realm of the ephemeral. But beyond delighting children and calming adults, paper engineering has a long history of guiding scientific progress, not least through a small paper device called a volvelle.

The volvelle derives its name from the Latin volvere – to turn. It is a paper device of one or more moveable circles, surrounded by other graduated circles used to calculate various mathematical processes, from the rising of the sun and the state of the tide, to cryptographic code generation and standards conversions. In short, they were paper machines, which could turn the illuminated manuscripts of the Middle Ages into computers.

Mediaeval volvelles usually consisted of parchment circles set into a book, the centre being held in place with a silk thread so the circles could revolve. Who originally came up with the idea remains open to debate, but the first surviving book containing them is by artist and writer Ramón Llull: ‘Ars Generalis Ultima’ from 1308. It included a table with two movable figures of parchment, attached through the centre by a thread. Llull was a missionary, scholar, and mystic at the court of the Kingdom of Majorca, but where he had got the idea for volvelles is unknown. What is known is that he was deeply immersed in the Arabic scholastic traditions, having bought a Muslim slave (his only possession at the time) to teach him Arabic.

His hopes for his volvelles were nothing if not ambitious. Through his paper machines, he hoped to unravel the secrets of complex combinatorial problems, from decoding the nine names of God, to calculating the time at night using the stars and discovering the most propitious times for administering medicines to the sick.

Some of these intentions might seem a little fantastical today, but the astronomical devices genuinely worked, providing a cheap, if fragile alternative to the expensive brass astronomical and navigational instruments of the day and providing a form of artificial memory and algorithmic processing that might reasonably be compared to a modern computer. Indeed, Llull has been compared to the great analogue computer inventor who has graced these pages before – Vannevar Bush.

Sadly for Llull, not everyone was appreciative. His volvelles were suspected as instruments of black magic, perhaps due to their predictive qualities – whether astronomical or astrological (it was all much the same to Llull). His use of paper computers to address theological problems drew the attention of that most inflexible of medieval institutions, the Church, and his work was banned by Pope Gregory XI in 1376.

Thankfully, this was not the end for the volvelle. The medieval world was a world of spheres and explaining their interconnection on a two-dimensional page was simply too good an idea to let go.

Explaining the movements of celestial bodies, and certainly teaching them to students, required more than just tables and words if the geometry was ever to be unravelled, so volvelles known as ‘equatoria’ were developed to demonstrate the motions of the celestial spheres without the need for complex mathematical calculation.

As educational tools, equatoria proved invaluable and began to regularly appear in manuscripts, reaching the height of their sophistication in the 16th century in the extraordinary books of Peter Apian. Apian was a mathematician at the court of the Holy Roman Emperor, and a contemporary of Copernicus. His 1524 ‘Cosmographia’, complete with three volvelles, proved so popular that it was translated into four languages and went through at least 45 editions. This was followed by his ‘Astronomicum Caesareum’, which included 21 volvelles covering problems from calculating planetary orbits and eclipses, to discovering the most dangerous moments in the course of an illness. One of these paper machines consisted of a full six moveable dials modelling the epicyclic theories of Ptolemy, with silken reference lines and tiny pearl position markers.

As a fragile but essential teaching tool, volvelles survived the Renaissance and the early modern world, reaching the modern era. Even today you’ll find volvelles in use for mileage calculation, colour calibration, radiation exposure and much more. Portable, cheap and battery-free, these paper wonders still put the power of medieval computing in our pockets.

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