In his last novel, The Glass Bead Game (1943), Hermann Hesse (1877–1962) regarded the seventeenth-century German philosopher and polymath Gottfried Wilhelm Leibniz (1646–1716) as one of the the precursors of the Glass Bead Game.
The choice was perhaps even more appropriate than Hesse imagined. Both men yearned for utopias in which extraordinary machines would have a central role. The utopias differ.
Leibniz’s, unlike Hesse’s, is an intensification and perfection of certain features of his world rather than a radical break with it; and his utopian machine, instead of being presented whole, has, in effect, to be assembled by the Leibniz scholar from some of the philosopher’s pet projects. But both Leibniz and Hesse were Good Europeans in Nietzsche’s antichauvinistic sense, and both stood for a planetary culture consistent with the universal spiritual and humanistic traditions of the West.
Moreover, Leibniz’s and Hesse’s utopian machines both bear some striking similarities to the modem computer, and these will be noted, not only because they are intrinsically interesting to the twentieth century mind but also because they should shed more light on the operations and uses of the utopian machines in question.
Leibniz’s Universal Characteristic is probably the most ambitious new method (organe noveau) ever conceived. Meant to displace all others, it had two immediate purposes: first to ascertain the veracity of what people took for knowledge and second to serve as a means for discovering new truths. Leibniz advanced the idea, reminiscent of Plato, that the principles of all branches of knowledge either were or participated in “truths of reason,” a realm which encompassed rational theology, metaphysics, logic, and pure mathematics. The veracity of a concept was to be demonstrated by analyzing it into its simple components, or predicates, and 1 ien seeing whether these components and their relations gave an adequate, noncontradictory account of it, and if the concept was a “mixed truth,” i.e., at once a truth of reason and a truth of fact-as the principles of the sciences would be-the criteria of veracity would have to include observation and experimentation. Indeed, testing truths of the mixed variety would serve as a guide to making observations and designing experiments.* Once matters of fact were agreed upon, disputes ranging from those in metaphysics through those in the sciences to those in jurisprudence would be resolved not by fruitless, and often acrimonious, debate, but by the injunction “Let’s calculate!”; for at the heart of the Universal Characteristic lay the assumption that its logical operations could be performed by the rules and signs of a new arithmetic that Leibniz tried to invent intermittently over the course of his life.
By the late 1670s Leibniz conceived of this arithmetic as an ingenious code of numbers and letters. The simple components of concepts were to be assigned prime numbers and then combined by multiplication into products that stood for complex ideas, which, in turn, could be analyzed back into their prime numbers or simple components. The prime numbers and their products would automatically be relegated to certain numerical categories, on the basis of which each number would be converted into one or more vowels, consonents, or diphthongs.
This transformation of numerical expressions into syllables was to produce the words of a new kind of universal writing (écriture universelle), more precisely, of a new, universal language of logic with its own dictionary and grammar. The language could be based on a living tongue or on an artificial one of invented signs. Preferring the latter, Leibniz made repeated efforts to invent a “grammar” for it, in the course of which he became a precursor of symbolic logic. And since logic forms the basis of mathematics, he became more convinced than ever that the rules of mathematics could serve as a model for those needed to organize, analyze, judge, and discover ideas. This is what he meant in 1696 when he said that mathematics was the real foundation of the Universal Characteristic.
Mathematics relies on numbers. These need not be decentary. Already in the 1690s Leibniz found a way to translate ordinary numbers into the binary notation of 0’s and 1’s. It stands to reason that a philosopher who formally posed the question of why something exists rather than nothing should be fascinated by a notation that symbolizes in the starkest and simplest way the antinomy between being and nothingness. That the system could serve as an ideal code for expressing and manipulating ideas became apparent to him through the mediation of a member of the Jesuits’ China Mission, Fr. Joachim Bouvet. Leibniz had shared his understanding of the binary system in a letter to Bouvet after the Jesuit had persuaded him that the hexagrams of the I Ching were a simple and natural representation of the principles of all the sciences as well as of a perfect metaphysics that the Chinese had forgotten before the advent of Confucius. Bouvet in his reply perceived a connection between the binary system and the hexagrams, and he included a woodcut of a hexagramic arrangement attributed to Fu-Hsi, the mythical founder of ancient Chinese culture. Leibniz, convinced, interpreted the broken lines in these hexagrams as 0’s and the full lines as 1’s. Leibniz believed that they summarized metaphysical and scientific principles, and he was certain Fu-Hsi had nothing less in mind than biblical creation when he invented the trigrams from which the hexagrams were formed. Soon Leibniz was elaborating upon these views in an essay for the French Academy of the Sciences and in a discourse on the natural theology of the Chinese. That he was wrong about Fu-Hsi in particular and Chinese hexagrams in general pales before the fact that he used binary numbers to express some of the concepts meant to be manipulated by the Universal Characteristic. […]
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ANTOSIK, Stanley, 1992. Utopian Machines: Leibniz’s “Computer” and Hesse’s Glass Bead Game. The Germanic Review: Literature, Culture, Theory. 1 January 1992. Vol. 67, no. 1, p. 35–45. DOI 10.1080/00168890.1992.9936543.