The challenge of contingency and Leibniz’s cybernetic thinking

By guest contributor Audrey Borowski


Gottfried Wilhelm Leibniz, painted by Christoph Bernhard Francke

According to the philosopher of science Alexandre Koyré, the early modern period marked the passage ‘from the world of more-or-less to the universe of precision’. Not all thinkers greeted the mathematization of epistemology with the same enthusiasm: for the German philosopher Martin Heidegger, this marked a watershed moment when modern nihilism had taken root in the shape of the reduction of the world to calculation and recently culminated with the emergence of cybernetics. One of the main culprits of this trend was none other than the German mathematician and polymath Gottfried Leibniz (1646-1716), who in the late seventeenth century invented the calculus and envisaged a binary mathematical system. Crucially, Leibniz had concerned himself with the formalization and the mechanization of the thought process either through the invention of actual calculating machines or the introduction of a universal symbolic language – his so-called ‘Universal characteristic’– which relied purely on logical operations. Ideally, this would form the basis for a general science (mathesis universalis). According to this scheme, all disputes would be ended by the simple imperative ‘Gentlemen, let us calculate!’


A graphic representation of second-order cybernetics by Mark Côté

For having mechanized reasoning, cyberneticist Norbert Wiener touted Leibniz as a ‘patron saint for cybernetics’ (Wiener 1965, p. 12) in the ‘Introduction’ to his 1948 seminal work Cybernetics or Control and Communication in the Animal and the Machine. In it, he settled on the term ‘kybernetes’, the ‘steersman’ to describe a novel type of automatic and self-correcting reasoning which consisted in the deployment of mathematics, notably via a feedback mechanism, towards the domestication of contingency and unpredictability. Cybernetics does not ‘drive toward the ultimate truth or solution, but is geared toward narrowing the field of approximations for better technical results by minimizing on entropy––but never being able to produce a system that would be at an entropy of zero…. In all of this, [it] is dealing with data as part of its feedback mechanism for increasing the probability of a successful event in the future (or in avoiding unwanted events).’

Cybernetic applications are ubiquitous today from anti-aircraft systems to cryptography; an anti-aircraft system, for instance, receives input data on a moving target and delivers the navigation of bullet to the target as output after a computing process.  Cybernetics’ aim is first and foremost practical and its method probabilistic: through the constant refining of the precision of a prediction, it helps steer action through the selection between probabilities. Under those conditions, a constant process of becoming is subordinated to a weak form of determinism; real infinite complexity is deferred in favour of logical symbolism and ‘disorganization’, that ‘arch-enemy’ endemic to intense mutability as Nobert Wiener put it, gives way to ontological prediction.

In his works The Taming of Chance and The Emergence of Probability Ian Hacking traced the emergence of probabilistic thinking away from deterministic causation. In fact and against commonly-held positivist narratives of the triumph of objective rationality, historians of mathematics generally acknowledge that the seventeenth century witnessed the birth of both probability theory and modern probabilism perhaps most famously epitomized by Pascal’s Wager. With the emergence of contingency, the question of its conceptualization became all the more pressing.

Perhaps no thinker was more aware of this imperative than Leibniz. Leibniz is often portrayed as an arch-rationalist and yet he did not view pure deduction as sufficient for reasoning; the ‘statics’ inherent to his characteristic (Leibniz, 1677) were simply ill-suited to a constantly evolving practical reality. Finite calculation needed to be complemented by probabilistic reasoning (1975, p. 135) which would better embrace the infinite complexity and evolving nature of reality. Although the author of a conjectural history of the world, The Protogaea, Leibniz did not merely conjecture about the past, but also sought to come to grips with the future and the state of mutability of the world. To this end, he pioneered the collection of statistical data and probabilistic reasoning especially with regards to the advancement of the modern state or the public good (Taming of Chance, 18). Leibniz had pored over degrees of probability as early as his 1665 law degree essay De conditionibus and the ability to transmute uncertainty into (approximate) certainty in conditions of constant mutability remained a lifelong preoccupation. More specifically, he set out to meet the challenge of mutability with what appears as a cybernetic solution.


An example of Leibniz’s diagrammatic reasoning

In a series of lesser-known texts Leibniz explored the limits and potentially dangerous ramifications of finite cognition, and the necessity for flexible and recursive reasoning. In 1693 Leibniz penned The Horizon of the Human Doctrine, a thought experiment which he subtitled: ‘Meditation on the number of all possible truths and falsities, enunciable by humanity such as we know it to be; and on the number of feasible books. Wherein it is demonstrated that these numbers are finite, and that it is possible to write, and easy to conceive, a much greater number. To show the limits of the human spirit [l’esprit humain], and to know the extent to these limits’. Building on his enduring fascination with combinatorial logic that had begun as a teenager in 1666 with his De Arte Combinatoria and had culminated ten years later with his famous ‘Universal Characteristic’, he set out to ‘show the limits of the human spirit, and to know the extent to these limits’. Following in the footsteps of Clavius, Mersenne and Guldin, Leibniz reached the conclusion that, through the combination of all 23 letters of the alphabet, it would be possible to calculate the number of all possible truths. Considering their prodigious, albeit ultimately finite number, there would inevitably come a point in time when all possible variations would have been exhausted and the ‘horizon’ of human doctrine would be reached and when nothing could be said or written that had not been expressed before (nihil dici, quod non dictum sit prius) (p. 52). The exhaustion of all possibilities would give way to repetition.

In his two later treatments on the theme of apokatastasis, or ‘universal restitution’, Leibniz took this reasoning one step further by exploring the possible ramifications of the limits of human utterability for reality.  In them, he extended the rule of correspondence between possible words to actual historical events. For instance, since ‘facts supply the matter for discourse’ (p. 57), it would seem, by virtue of this logic, that events themselves must eventually exhaust all possible combinations. Accordingly, all possible public, as well as individual histories, would be exhausted in a number of years, inevitably incurring a recurrence of events, whereby the exact same circumstances would repeat themselves, returning ‘such as it was before.’ (p.65):

‘[S]uppose that one day nothing is said that had not already been said before; then there must also be a time when the same events reoccur and when nothing happens which did not happen before, since events provide the matter for words.’

In a passage he later decided to omit, Leibniz even muses about his own return, writing once again the same letters to the same friends.

Now from this it follows: if the human race endured long enough in its current state, there would be a time when the same life of certain individuals would return in detail through the very same circumstances. I myself, for example, would be living in a city called Hanover situated on the river Leine, occupied with the history of Brunswick, and writing letters to the same friends with the same meaning. [Fi 64]

Leibniz contemplated the doctrine of Eternal Return, but it was incompatible with his metaphysical understanding of the world. Ultimately, he reasserted the primacy of the infinite complexity of the world over finite combinatorics. Beneath the superficial similarity of events – and thus of description- lay a trove of infinite differences which superseded any finite number of combinations: paradoxically, ‘even if a previous century returns with respect to sensible things or which can be described by books, it will not return completely in all respects: since there will always be differences although imperceptible and such that could not be sufficiently described in any book however long it is.’. [Fi 72]’   Any repetition of event was thus only apparent; each part of matter contained the ‘world of an infinity of creatures’ which ensured that truths of fact ‘could be diversified to infinity’ (p. 77).

To this epistemological quandary Leibniz opposed a ‘cybernetic’ solution whereby the analysis of the infinite ‘detail’ of contingent reality would open up a field of constant epistemological renewal which lay beyond finite combinatorial language, raising the prospect of an ‘infinite progress in knowledge’ for those spirits ‘in search of truth.’ (p. 59) The finite number of truths expressible by humans at one particular moment in time would be continuously updated to adapt itself to the mutability and progress of the contingent world. ‘Sensible truths’ could ‘always supply new material and new items of knowledge, i.e. in theorems increasing in length’ in this manner permitting knowledge to approach reality asymptotically. In this manner, the theoretical limits which had been placed upon human knowledge could be indefinitely postponed, in the process allowing for incrementally greater understanding of nature through constant refinement.

Leibniz thus set forth an ingenious solution in the shape of a constantly updated finitude which would espouse the perpetually evolving infinity of concrete reality. By adopting what may be termed a ‘cybernetic’ solution avant la lettre, he offered a model, albeit linear and continuous, which could help reconcile determinism and probabilism, finite computation and infinite reality and freedom and predictability. Probabilism here served to induce and sustain a weak form of determinism, one which, in keeping with the nature of contingency itself as defined by Leibniz, ‘inclined’ rather than ‘necessitated’.

Audrey Borowski is a historian of ideas at the University of Oxford.

Coming to Terms with the Cybernetic Age

by guest contributor Jamie Phillips

Rare the conference attracting a crowd on a cold December Saturday morning, but such happened recently at NYU’s Remarque Institute. Space filled out early for the conclusion of a two-day conference on Cybernetics and the Human Sciences (PDF). The turnout bore out the conference’s contention of a renewed historiographical and philosophical interest in cybernetics, the science of “control and communication in the animal and the machine,” as Norbert Wiener subtitled his 1948 work that gave the interdisciplinary movement its name. As Leif Weatherby, co-organizer of the conference along with Stefanos Geroulanos, noted in his introductory remarks, the twentieth century was a cybernetic century, and the twenty-first must cope with its legacy. Even as the name has faded, Weatherby suggested, cybernetics remains everywhere in our material and intellectual worlds. And so for two days scholars came to cope, to probe that legacy, to trace its contours and question its ramifications, to reevaluate the legacy of cybernetics as a history of the present.

The range of presenters proved particularly well-suited to such a reevaluation, with some working directly on cybernetics itself, while others approached the subject more obliquely, finding, as it were, the cybernetic in their work even where it had not been named. Ronald R. Kline, author of the recent The Cybernetics Moment: Or Why We Call Our Age the Information Age, set the tone early in emphasizing the disunity of cybernetics. Despite the claims of some of its advocates and latter-day commentators, Kline contended, cybernetics never was one thing. On this point general consensus emerged the conference tended to eschew a search for definitions or classifications in favor of a wide-ranging exploration of the many faces of cybernetics’ legacy. And wide-ranging it indeed was as papers and discussion touched on topics from international relations theory and the restrainer of the Antichrist, to Soviet planning in Novosibirsk, the manufacture of telephones, brain implants and bullfights, Voodoo death, and starfish embryos.

A number of papers spoke to the pre-history (or rather pre-histories) of cybernetics. Mara Mills emphasized the importance of the manufacturing context for the emergence of ideas of quality control, as a crucial site for the development of cybernetic conceptions of feedback. Geroulanos addressed physiological theories of organismic integration, stemming from WWI studies of wound shock and concerns with the body on the verge of collapse, and leading to Walter B. Cannon’s concept of homeostasis, so pivotal for early cyberneticians. Other papers spoke to the varying trajectories of cybernetics in different national contexts. Diana West discussed the appeal of cybernetics in the Soviet Union in the 1970s and 1980s as offering promise of a more dynamic form of large-scale regional planning, a promise expressed in abstract theoretical modeling and premised on a computing power that never came. Isabel Gabel explored the intersections of biology, embryology and metaphysics in the work of French philosopher Raymond Ruyer. Jacob Krell gave an entertaining appraisal of the strange humanist engagement with cybernetics by the heterogeneous “Groupe des dix” in post-68 France, while Danielle Carr spoke to the anxious reaction against visions of human mind control in the Cold War United States, through the work of José Manuel Rodriguez Delgado. Other papers still, particularly those of Weatherby and Luciana Parisi, directly confronted a cybernetic metaphysics, and between them they raised questions concerning its novelty and significance with respect to the history of philosophy and contemporary media theory.


Stefanos Geroulanos

Taken together, the papers compellingly demonstrated the ubiquity and diversity of the cybernetic across disciplines, decades, and geographical and political contexts. Taken together, however, they also raised a question that has long been posed to cybernetics itself. Here we might cite the words of Georges Boulanger, president of the International Association of Cybernetics, who asked, in 1969: “But after all what is cybernetics? Or rather what is it not, for paradoxically the more people talk about cybernetics the less they seem to agree on a definition” (quoted in Kline, The Cybernetics Moment, 7). Indeed, just as cybernetics itself declined as it expanded into everything, there is perhaps a risk that in finding cybernetics everywhere we lose hold of the object itself. To push the point further, we might echo the frustration of one of the interviewees cited by Diana West in her talk (and here I paraphrase): ‘They promised us cybernetics, but they never gave us cybernetics.’

Over two days, the conference answered this challenge through the productive discussion it generated. The more people talked about cybernetics, the more they seemed to find common ground for engagement.. Beyond the numerous schematics that served as the immediate graphic markers of the cybernetic imagination (see image), conversation coalesced around a loose conceptual vocabulary—of information, of feedback and system, of mechanism and organism, of governance, error and self-organization—that effectively bridged topics and disciplines, and that gave promise of discerning a certain conceptual coherence in the cybernetic age.


A cybernetic schematic: “A Functional Diagram of Information Flow in Foreign Policy Decisions,” from Karl Deutch’s 1963 The Nerves of Government (courtesy of Stefanos Geroulanos)

This proved true even when (or perhaps especially when) understandings of the cybernetic seemed to point in very different directions. A panel of papers by David Bates and Nicolas Guilhot was particularly exemplary in this regard. Bates and Guilhot brought contrasting approaches to the question of the political in the cybernetic age. Bates presented his paper in the form of a question—on the face of it paradoxical, or simply unpromising—of whether we might think a concept of the political in the cybernetic age through the work of Carl Schmitt. Referring to Schmitt’s concept of the katechon (from his post-war work The Nomos of the Earth) as the Restrainer of the Anti-Christ, Bates proposed thinking the political as a deferral of chaos, a notion he linked to the idea of an open system that maintains itself through constant disequilibration, and to an organism that establishes its norms through states of exception. Recalling, through Schmitt, Hobbes’ conception of the Leviathan as an artificial man in which sovereignty is an artificial soul, Bates argued for a concept of the political that would enable us to think mechanism and organism together, that could recover the human without abandoning technology.


Nicolas Guilhot, David Bates, and Alexander Arnold (courtesy of Stefanos Geroulanos)

Guilhot, by contrast, looked at the place of cybernetics in international relations theory and the work of political theorists in the 1960s and 1970s. Cybernetics, Guilhot suggested, here offered the promise of an image of the political that was not dependent on sovereign actors and judgment, one that could do away with decision making in favor of structure, system, and mechanistic process. Where Bates expressed concern that the technical had overrun the capacity of humans to participate in their own systems, for Guilhot’s theorists this was precisely the appeal: coming at a moment of a widely perceived crisis of democracy, cybernetics promised to replace politics with governance as such. For Guilhot here too, though, there was a critical intervention at stake: the image of the political as a system does not remove decision making, he contended, but rather obfuscates it. Prompted by the panel chair to respond to each other directly, Bates and Guilhot agreed that their papers were indeed complementary, with Bates speaking to an earlier moment of concern in the history of cybernetics that had subsequently been lost. The lively discussion that ensued served as proof of the productive engagement that can come from bringing it to the fore again.

Seen in this light, it was a fitting—if unwitting—coda to the conference as a whole that the menu at the post-conference lunch that Saturday afternoon rendered the title of the conference as “Cybernetics and the Human Services” (see image). One might take this as an occasion to think about the flow of information, about the place of error in systems of control and communication. But for present purposes, and for the present author, this fortuitous transposition of ‘human sciences’ into ‘human services’ serves rather to bring to the fore the question implicit in the conference’s agenda: how does the effort to reevaluate the legacy of cybernetics as a single history of the present change our possibilities for understanding and acting within it. What service, in short, can the human sciences render?


(© Jamie Phillips)

In his paper that concluded the conference, Weatherby referred to an occasion at one of the Macy Conferences where the participants, considering the question of whether the brain was digital, confronted the further problem of defining the digital itself. Here, Weatherby suggested, they suffered from a lack of contribution from the humanities—no participant could themselves help the group to arrive upon a definition of cybernetics, what it does, how it works. Such is the work, it seems, that awaits the return to cybernetics. As the conference amply demonstrated, this will not and cannot be simply a matter of narrow definition: any attempt to come to terms with the cybernetic age and our continued place within it must pay heed to the pluralities, the disunities, the dispersed and intertwined trajectories that constitute that legacy; for all its own promise to unify the sciences, cybernetics was never one thing. At the same time, coming to terms with the cybernetic age will entail an effort to find a commonality in the plurality: if cybernetics indeed saturates the human and social sciences, how can we distill it; if it is everywhere without being named, what does it mean to name it, and what does it allow us to see. In this respect, one hopes, the menu will not be the last word, but will point rather to the urgency of continuing the ongoing reevaluation. An edited volume, I am told, is in the works.

Jamie Phillips is a Ph.D. candidate in modern European history at NYU. His dissertation examines the history of psychoneurology as a total science of the human in early twentieth century Russia, and its relation to the project of creating a ‘New Man.’