After computers were made of bronze cogs but before they were made of integrated circuits, they were made of paper, they were found in books:
The figure pictured above is called a volvelle or wheel chart; it’s a series of circles held together that can be rotated in order to yield some string of information. On paper, the concept dates back to the 11th century Persia where it was used most frequently in astronomical texts to depict the movement of the planets and stars, or by astrologers to forecast the future in devices known as zairja. Based on its ability to yield calculations, however simple, the volvelle is considered an early example of a computer. But you can also find one that doesn’t compute anything on the album sleeve of Led Zeppelin III.
From East to West
Volvelles were imported into the West in the 1270s by Raymund Lull (1232-1315, also possibly the first European novelist). The ‘Quarta Figura’ pictured above is a printed version of his ‘Lullian Circle’. Lull marketed the idea as the Ars Magna or ‘General Art’, and provided a system of logic blending influences from Arabic mysticism, Egyptian hermeticism, and his own missions to Jews and Muslims, to power the movements of his little paper wheels. Ironically enough he had built a tool to debate Muslims – to debate the beliefs of the Arabic philosophers from whom he had poached the design concept.
Each letter of the circle represents a topic, and each circle represents one portion of a sentence: there are nine main subjects including God, Angels, and Man, each assigned a letter B-K. The same letters next are assigned to predicates: Goodness, Greatness, Duration, Power, Wisdom, Will, Virtue, Truth, and Glory. The relationship between these sets of terms is determined by three triangles in the middle that highlight their differences, similarities, and magnitudes of importance to one another. Sample statements include: “God is eternal” and “Angels are Wise”. Lull worked under the assumption that there were basic, indisputable truths, and that his ‘machine’ could produce all of them. The concept of truth here is pretty limited, but theoretically this early computer is not far in its ambitions from more recent models, and unsurprisingly someone has tried to make a computer program for it.
The Ultimate General Art caught on in manuscript, then print, and then came the commentaries and how-to guides to ensure some trickle-down longevity for scholars of the 16th and 17th centuries (click here for a meticulous list of Lullians through the ages). Henrich Cornelius Agrippa’s popular commentary on Lull’s art reached several editions from 1530 – 1605, so unlike me, his readers must have agreed the system was “easy to learn for schoolboys and old men alike” as he claims in the Preface. This is the book that crossed my desk last week and introduced me formally to Lull, and the long history of paper computing.
Agrippa provides broken down diagrams of the circles, descriptions of their components, and an exhaustive list of all possible letters combinations and their values (BK, BC, BD, BE, and so on up to four characters), but he does not provide the volvelles, although you could cut-and-paste together your own:
From Philosophy to Poetry
In ‘Raymund Lull’s Thinking Machine’, Borges’ main concern with the Lullian circle is that its terms are outdated, not the machine itself: “We (who are basically no less naïve than Llull) would load the machine differently, no doubt with the words Entropy, Time, Electrons, Potential Energy, Fourth Dimension, Relativity, Protons, Einstein. Or with Surplus Value, Proletariat, Capitalism, Class Struggle, Dialectical Materialism, Engels.”
In a sense that had already happened by the end of the 16th century: by Agrippa’s time, Lull’s combinatory art had already blended with poetic practices dating back the 4th century - centos comprised of cut and pasted fragments from poems and chance operations as with bibliomancy - and updating it to suit the latest tastes. Poetic ‘machines’ were used to piece together syllables into words, words into verse, proving that computer-generated poetry isn’t just a child of the 20th century.
The poems might not have been any good, but the adaptation of the paper machine to new pursuits meant new audiences. As a poetic system it had more formal uses: in 1651 Georg Philipp Harsdörffer, equal parts poet and linguist, used volvelles to compute the limits of the German language:
Georg Philipp Harsdörffer’s Fünffacher Denckring der Teutschen Sprache, or the Five-fold Thought-ring of the German Language (1651), is composed of five nesting paper discs, each of which is inscribed with a set of word parts along its edge. The innermost ring contains forty-eight prefixes; the next ring, fifty initial letters or diphthongs; the middle ring, twelve medial letters; then, 120 final letters or diphthongs; with the outermost ring storing twenty-four suffixes. When spun, this simple mechanism can generate German words, producing as many as 97,209,600 different combinations. (Source)
For more on Harsdörffer and the Lullian connection see Whitney Trettian’s dissertation: “Computers, Cut-Ups, and Combinatory Volvelles: An Archaeology of Text-Generating Mechanisms” which thoroughly covers the poetics in the age of mechanical reproduction and can be found here. It’s both an amazing resource for material on the history of paper computing, and a computing device in its own right – as it focuses on the use of volvelles to produce poetry, so it practices its preaching and allows you to produce your own textual ordering of the essay.
From Poetry to Mathematics
At the close of the 17th century, there were really only two roads a paper computer might follow: the satirical and the serious. Luckily there was enough paper and time to travel down both.
Enter Jonathan Swift. On his travels, Gulliver is given a tour of the Academy of Lagado, and taken to the department of “Speculative Learning” where a professor aims to enable ”the most ignorant person…[to] write books in philosophy, poetry, politics, laws, mathematics, and theology, without the least assistance from genius or study” using a giant ‘machine’ ridiculous yet imaginative, adding wire and iron to the paper works:
It was twenty feet square, placed in the middle of the room. The superfices was composed of several bits of wood, about the bigness of a die, but some larger than others. They were all linked together by slender wires. These bits of wood were covered, on every square, with paper pasted on them; and on these papers were written all the words of their language….The pupils, at his command, took each of them hold of an iron handle, whereof there were forty fixed round the edges of the frame; and giving them a sudden turn, the whole disposition of the words was entirely changed. He then commanded six-and-thirty of the lads, to read the several lines softly, as they appeared upon the frame; and where they found three or four words together that might make part of a sentence, they dictated to the four remaining boys, who were scribes.
Did anything worthwhile happen other than what Jonathan Swift thought worth making fun of? Probably not. But if he acknowledged ”My main purpose in everything I do is rather to enrage than to amuse,” he also documented change. In this case, change of possibilities for the ‘thinking machines’: from religious debate and poetry to any field of knowledge, from a fixed set of 9 subjects to words on 40 six-sided cubes. Such a heightening of the stakes made the device, for all its absurdity, more recognisable as a computing machine, one that has to grapple with randomness and in terms of information science, one that makes a whole lotta noise.
It’s no coincidence Swift lambasts a machine that mostly produces random babbling: it was an idea he had criticized over a decade before he wrote Gulliver in “A Tritical Essay Upon the Faculties of the Mind” (1711):
[H]ow can the Epicureans Opinion be true, that the Universe was formed by a fortuitous concourse of Atoms, which I will no more believe, then that the accidental jumbling of the Letters in the Alphabet would fall by chance into a most ingenius and learned Treatise of Philosophy…
Swift’s scepticism happens to form the basis for one early articulation of the infinite-monkey theorem - “that a half-dozen monkeys provided with typewriters would, in a few eternities, produce the works of Shakespeare” – traced by Borges in his essay “The Total Library”. But his preoccupation with accidental jumbling is no accident: a few countries over it had been put to serious practice by Gottfried Wilhelm Leibniz.
There is too much to say about Leibniz. What a guy. You should probably just read Maria Antognazza’s Intellectual Biography and in the meantime his Wikipedia page. Funny that Swift complained about a ‘fortuitous concourse of Atoms’ and the ‘accidental jumbling of letters’ in the same breath: Leibniz’s doctoral dissertation on the Art of Combining (1666) had discussed just that, drawing a parallel between the random yet meaningful combination of the atoms of the universe into matter, and the particles of speech that comprise words and sentences. He concludes that language and the universe are similar in that they are the work of the same acts of mixing and re-mixing. Leibniz applied Lull’s combinatory art to the idea of a universal human language, what he called an ‘alphabet of human thought’, the inspiration for which was drawn from Harsdörffer’s German language wheel. He wanted to reduce all thought to a series of characters (like hieroglyphs), and a computer to order these characters in every possible combination. This would mean that the system would produce all possible ideas, old and new. Such a machine would eliminate the unknown.
Unfortunately he never elaborated on the actual alphabet he had in mind, although it is thought he imagined it to be a kind of algebraic language. By 1714 he had abandoned the project and distanced himself from his schoolboy ambitions, but not without reflecting on the merits of his resources for the in a letter to Nicholas Raymond:
“When I was young, I found some pleasure in the Lullian art, yet I thought also that I found some defects in it, and I said something about these in a little schoolboyish essay called On the Art of Combinations, published in 1666, and later reprinted without my permission. But I do not readily disdain anything—except the arts of divination, which are nothing but pure cheating—and I have found something valuable, too, in the art of Lully…”
He might have dropped the idea of universal language, but he kept the idea of a machine that could compute the language into each possible combination. The calculator. The value in ‘the art of Lully’ was that it contributed to the calculator Leibniz invented in 1694: the Stepped Reckoner. It was the first to be able to add, subtract, multiply, and divide (Blaise Pascal’s calculator could not multiply and divide automatically). So from Arabic Astrology to Raymond Lull, Religious Debate to Poetic Composition and Language study, revolving paper wheels were finally put to the task of solving math problems, leading to the calculator, and setting the foundations for computing instruments of the 19th and 20th centuries - c.f. The Universal Computer: The Road from Leibniz to Turing.
All of this adds just another dimension of the relationship between book and computer. More than containers that sometimes compete for the same information, they are on the family tree of a daunting ambition to compute and compile all that can be known. Each in their own time are the best-fit materials for the job, and the complexity of harnessing that ideal in some material form is as troublesome for Lull’s paper machine as it is in digital terms.
If we look at these two technologies based on the loftiest ideals they’re meant to serve, a universal library being one of them, things seem a little less tense. Thinking about each as instruments to aid and abet in that (as-of-today) impossible goal is one way of arguing on behalf of both, because neither serve the purpose. Both have failed so far. So one has not trumped the other. Like the majority of sibling rivalries, it produces all kinds of anxieties and behaviours that never truly resolve themselves but are never as life threatening as they seem.