The eccentric engineer: How the strange world of Mediaeval paper computers.

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 Valverde. The Colville derives its name from the Latin Colville – 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. Medieval valveless usually consisted of parchment circles set into a book, the center is 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 Lull: ‘Ar's Generals Ultimo’ from 1308. It included a table with two moveable figures of parchment, attached through the center by a thread. L lull was a missionary, scholar, and mystic at the court of the Kingdom of Majorca, but where he had got the idea for valveless 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 valveless 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 the too 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, L lull has been compared to the great analog computer inventor who has graced these pages before – Vannevar Bush. Sadly for L lull, not everyone was appreciative. His valveless were suspected as instruments of black magic, perhaps due to their predictive qualities – whether astronomical or astrological (it was all much the same to L lull). His use of paper computers to address theological problems drew the attention of the 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 Colville. 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 of. 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 unraveled, so a valveless known as ‘Equatorial’ was developed to demonstrate the motions of the celestial spheres without the need for complex mathematical calculation. As educational tools, Equatorial 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 Apia. Apia was a mathematician at the court of the Holy Roman Emperor, and a contemporary of Copernicus. His 1524 ‘tomographic’, complete with three Colville, proved so popular that it was translated into four languages and went through at least 45 editions. This was followed by his ‘Astronomical Caesar’, which included 21 Colville 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 modeling the epicycles theories of Ptolemy, with silken reference lines and tiny pearl position markers. As a fragile but essential teaching tool, Colville survived the Renaissance and the early modern world, reaching the modern era. Even today you’ll find valveless in use for mileage calculation, color calibration, radiation exposure, and much more.