How might we detect or measure the acceleration of the world? When pundits, alarmists, and dystopians declare that the world is moving too fast for us to keep track, how is it that they are estimating rates of cultural change and how do they establish that these changes are too fast for individuals and society to respond? We all know the answer: plotting a few exponentials, sprinkling around the word “singularity,” and neglecting the science of adaptation.

It is a curious fact of evolution that every organism that measures acceleration — that possesses a working accelerometer — does so in more or less the same way. Each organism contains an organ in which a “proof mass” is suspended on a mechanosensory hair in a fluid-filled chamber. The proof mass is inertial, and upon movement, it lags behind the basement membrane to which the hair is attached. The strain in the hair generates receptor potentials by opening ion channels, which are processed into an estimate of acceleration.

All evolved accelerometers face a series of unavoidable physical trade-offs. The minimum acceleration is bounded by a thermal noise floor: the smaller the proof mass, the harder it is to distinguish real motion from thermal fluctuations. This leads to a design choice through a bandwidth-sensitivity trade-off: For a small mass to counter noise, it needs to be suspended on a very stiff hair, and this limits the ability to detect low-frequency variation. This is why the semicircular canals in the human ear, using relatively massive otoliths, can detect low-frequency rotational acceleration on the order of 0.1Hz, whereas tiny insect campaniform cells can only detect changes two orders of magnitude higher. And all evolved accelerometers need to deal with viscous regimes — where the proof mass is strongly coupled to the surrounding fluid medium and fails to provide any evidence of relative motion.

We can extend these insights in a fairly straightforward way to knowledge and culture. Let’s treat the quantity of accumulated and connected cultural knowledge — all of those ideas that are coordinated into a correlated system of verified belief — as analogous to proof mass. Any paradigm change in a field induces a rate of change in the epistemic environment, and this is the acceleration we would like any “cultural accelerometer” to detect.

Just as with evolved accelerometers, there is a need to distinguish noise (misinformation, rumor, error) from signal. We know from Bayes’ rule that the prior plays the role of the proof mass: the greater the accumulated evidence for the incumbent beliefs, the greater the inertia in the system. And, we know the rate of updating maps to the stiffness of the mechanoreceptor: a commitment to the status quo reduces sensitivity to genuine signals for change but increases resistance to noise. Additionally, viscous regimes are those in which the zeitgeist is absolutely dominant — social pressures of various kinds induce a lock-step between individual and collective knowledge flow.

Just as insects detect high-frequency impulses at low sensitivity, and mammals detect low-frequency impulses with high sensitivity — a binding trade-off no life form can overcome — human society, with its high proof mass, has evolved to detect low-frequency changes with high sensitivity. Technologies offer the possibility for an invertebrate complement, responsive to high-frequency changes. And yet we have been building AI systems with fixed weights that are, in effect, an extreme version of the mammalian otoconial layer — mineralized once and rarely replaced. The proof mass doesn’t just resist change — it cannot change until retraining.

Now might be the right time to learn from the adaptive capabilities of crustaceans. The crustacean proof mass — statolith — is discarded at every molt and replaced. Each individual picks up sand grains and places them in the statocyst to rebuild its proof mass. If you give a shrimp iron filings instead of sand, it builds a ferromagnetic statolith and then orients to a magnet instead of gravity. The proof mass is expendable, replaceable, and reconstructed from environmental materials. The crustacean doesn’t carry its reference frame across molts — it rebuilds it from whatever the current environment provides. Now that’s a model for sustainable technology.

— David Krakauer
President, Santa Fe Institute

From the Spring 2026 edition of the SFI Parallax newsletter. Subscribe for our monthly e-Parallax, or email “news at santafe.edu” to request quarterly home delivery in print.

“Chapman’s translation has often been praised as eminently Homeric. Keats’s fine sonnet in its honour everyone knows; but Keats could not read the original, and therefore could not really judge the translation. Coleridge, in praising Chapman’s version, says at the same time, ‘It will give you small idea of Homer’ . . . I confess that I can never read twenty lines of Chapman’s version . . .”

— Matthew Arnold
On Translating Homer (1861)

“Is it possible that the string-theory fashion is beginning to taper off? It is my own view that the representation of string theory has for many years been excessive . . . its stranglehold on developments in fundamental physics has been stultifying, and has in my view hindered the development of other areas that might have had more promise of ultimate success.”

— Roger Penrose
Fashion, Faith, and Fantasy (2016)

In an effort to make the progress of science smooth and cumulative, a number of physicists and philosophers in the first half of the 20th century endeavored to extend Niels Bohr’s “correspondence principle,” which originally connected quantum mechanics to classical mechanics by exploring infinitesimal or infinite limits. This was subsequently generalized into a system of correspondences aimed at establishing the unity of knowledge: searching for the simplest parameter space of a larger theory in which multiple different local theories apply. These generalized “correspondence principles” are, in effect, the desire for a “perfect” system of translation among theories in which, ceteris paribus, all local differences and histories are minimized and ignored, in order that epistemology might make neat slices through an omnivorous state space.

I call these local differences, histories, and latent variables the semantic dark matter of scholarship. Recall that dark matter is a rather mysterious and putative kind of matter, one that does not reflect light but has a gravitational effect. Semantic dark matter describes the invisible factors and processes that make models and theories work in a given context without threatening their basic assumptions. My purpose is not to dismiss dark matter, but to reveal the nature of its existence. And to encourage us to consider the possibility that, at some point, the causal efficacy of the invisible prompts us to consider new theories.

Darwin’s theory of evolution by natural selection plays the role of semantic dark matter in relation to the second law of thermodynamics, reconciling the local, and perhaps even transiently global, increase in functional order in the face of entropy increase. Game theory plays the role of semantic dark matter in the face of violations of Pareto efficiency (optimal solutions for all agents) in economic, ecological, and evolutionary processes.

In the philosophy of science, these “corrections” have been called auxiliary theories, but the implied second-class status hardly does them justice. One could transform the half-empty glass into a half-full one by reversing their prioritization: allow that some form of natural selection subsumes the second law (less likely) or that game theory subsumes optimization (more likely).

In her book-length essay on translation, This Little Art (2017), Kate Briggs describes with admiration the super-heroic efforts of a translator of Gustav Flaubert’s Bouvard et Pécuchet — for my money one of the three best treatises on stupidity in print — who replicated Flaubert’s research for the book by reading its 1,500 source texts. Briggs suggests it might have been even better to read them in the same sequence as Flaubert. Her point is that a great translation needs to wrestle with Flaubert’s semantic dark matter since these ideas are only implied by the written text but present to some degree in the minds of his contemporary readers.

In Fifty Sounds (2021), Polly Barton’s hilarious and exhausting autobiography of learning Japanese in her twenties, the author expresses bafflement at the violation of rules implied by translating “cheeseburger” as “cheese in Hamburg.” Barton explains this disregard for the semantic dark matter of the West as one requiring “considerable largeness of spirit to accept the way that these imported words were wielded with little consideration for their original usage and belonged to an utterly different web of associations to those they had in English.”

In his collection of profiles, Personal Impressions (1980), in a chapter on “Meeting with Russian Writers,” Isaiah Berlin describes the flowering of experimentalism in Russia in the late 19th century, including the futurism, supremacism, constructivism, Acmeism, and cubo-futurism movements, followed by its suppression under Marxist ideology as “unbridled individualistic literary license.” Subsequent to the German invasion, this censorship inverted: “An astonishing phenomenon took place: poets whose writing had been regarded with disfavor by the authorities and who had consequently been published rarely and in very limited editions, began to receive letters from soldiers at the fronts.” The semantic dark matter of war completely reversed the reception and meaning of artistic expression.

Scientific theories and the meaning of artistic work are always modulated through a complicated system of connections — what Gilles Deleuze and Félix Guattari described as a “rhizome.” This rhizome is not a “social construction” but a spanning feature of reality that is often too complex to subsume within a single framework. It becomes a constituent of the semantic dark matter of all ideas, and it makes translation challenging. Artificial intelligence, artificial general intelligence, artificial superintelligence, ad nauseam, are all slices through epistemic networks that are made sensible only by revealing their semantic dark matter. Various Turing tests and benchmarks are little context-probes designed to reveal the historical contingency of their behavior. When we say that a large language model is only as good as its training data, we are, in effect, trying to translate from the past into the present and urging caution for why this might fail. I note that this is an effort at translation that Thomas Kuhn described as finally incommensurable.

— David Krakauer
President, Santa Fe Institute

From the Winter 2025–2026 edition of the SFI Parallax newsletter. Subscribe for our monthly e-Parallax, or email “news at santafe.edu” to request quarterly home delivery in print.

Glittering below her in the sunlight was what appeared to be an immense crystalline orchid carved from some quartzlike mineral. The entire structure of the flower had been reproduced and then embedded within the crystal base, almost as if a living specimen had been conjured into the center of a huge cut-glass pendant.

“The Crystal World” by J.G. Ballard

In Thomas Mann’s final novel, Doctor Faustus — the biography of a musical prodigy, Adrian Leverkühn — there is a formative scene in which Adrian’s father, Jonathan, becomes entranced by ice crystals on a windowpane:

“Were these phantasmagorias an imitation of plant life, or were they the pattern for it? — that was his question.”

Jonathan pursues this question through a series of experiments that cause Adrian to wonder at the boundary of the purely physical and living world:

“The crystallization vessel in which this transpired was filled to three-quarters with a slightly mucilaginous liquid, diluted sodium silicate to be precise, and from the sandy bottom up rose a grotesque miniature landscape of different colored growths — a muddle of vegetation, sprouting blue, green, and brown and reminiscent of algae, fungi, rooted polyps, of mosses, too, but also of mussels, fleshy flower spikes, tiny trees or twigs, and here and there even of human limbs.”

Doctor Faustus was published in 1947, a period when Mann was living in California’s Pacific Palisades, in exile from Nazi Germany. The novel is a long meditation on the pattern and structure of music, the sacrifice of a personal life to beauty, and the symbological relation of musical form to the vacuousness of a perfectly ordered society.

The experiment with the crystal ultimately refers back to the idea of crystalline beauty in the writings of the philosopher Georg Wilhelm Friedrich Hegel, but their use in Mann’s novel derives from their development as a typology in art history. In his book Historical Grammar of the Visual Arts, the Austrian art historian Alois Riegl suggests that the world divides into inorganic crystalline forms and amorphous organic forms. Riegl asserts that “[b]ecause the crystalline motif obeys natural laws most perfectly, it is the only intrinsically appropriate and justifiable motif for human artistic creation.” The composer Adrian Leverkühn sees in the crystalline form the ideal of order that he wishes to realize in his music and that the National Socialists sought in parallel to realize in society.

The work of Charles Darwin is firmly rooted in the description of amorphous organic forms. Darwin’s metaphor for life, the “entangled bank,” is about as far from the crystalline as matter could diverge, and his mechanism for order is not based on regularity but irregularity — the contingent fit of form to function. In a period described as the “eclipse of Darwinism,” around 1880 to 1920, a new desire for symmetry reasserted itself in the work of two Scottish naturalists, James Bell Pettigrew and D’Arcy Wentworth Thompson, both faculty members at the University of St. Andrews. Pettigrew and Thompson showed extraordinary promise in their early careers. As an undergraduate, Thompson translated Hermann Joseph Muller’s work on the fertilization of flowers, accompanied by an introduction by Darwin. Pettigrew’s undergraduate drawings of cardiac muscle were so precise that he became the youngest scientist to deliver the Royal Society’s Croonian Lectures.

In 1908, Pettigrew published his monumental monograph, Design in Nature: Illustrated by Spiral and Other Arrangements in the Inorganic and Organic Kingdoms as Exemplified in Matter, Force, Life, Growth, Rhythms, &c., Especially in Crystals, Plants, and Animals, etc. The book is in three volumes, accompanied by around 2000 figures. Throughout, what is clearly an analog of Riegl’s “crystalline form” is adduced as evidence of parsimonious design and geometric wisdom. The closing section of the work sealed Pettigrew’s fate in the tomb of obscurity:

“He [man] is the highest of all living forms. The world was made for him and he for it…Everything was made to fit and dovetail into every other thing. There was moreover no accident or chance. On the contrary, there was forethought, prescience, and design.”

Pettigrew’s colleague, Thompson (whom Pettigrew hired at St Andrews), wrote an only slightly briefer, yet equally monumental, treatise on the crystalline principles inherent in the natural world, On Growth and Form. And like Pettigrew, Thompson was dismissive of the ideas of Darwin, whose case studies abound in what Thompson describes as the unnecessary teleological hypothesis. Unlike Pettigrew, Thompson pursued the Leverkühn question (“Were these phantasmagorias an imitation of plant life, or were they the pattern for it?”) through physics, not theology. For Thompson, the world, like artwork, was founded on a principle of perfect order — in his case, the order of Aristotle, Isaac Newton, and Pierre Louis Maupertuis.

We look back on these arguments, with their binary oppositions, and see that they have in no way abated, either in science or in art. The history of complexity science was to a considerable degree founded on the crystalline concept of self-organization, despoiled by the organic concept of selection. Complex reality is that which fascinated Riegl — it is a Frankenstein of organic asymmetry animated by a spark of symmetry.

— David Krakauer
President, Santa Fe Institute

From the Autumn 2025 edition of the SFI Parallax newsletter. Subscribe for our monthly e-Parallax, or email “news at santafe.edu” to request quarterly home delivery in print.

Herman Melville’s 1849 novel Mardi has been described as a metaphysical sequel to Jonathan Swift’s Gulliver’s Travels and an inscrutable prequel to his own Moby-Dick. The first comparison suggests a derivative work, and the second a subordinate one. Moby-Dick is considered the “classic” work — a term that, according to Italo Calvino in his book Why Read the Classics, is “given to any book which comes to represent the whole universe, a book on a par with ancient talismans” and “the more we think we know them through hearsay, the more original, unexpected, and innovative we find them when we actually read them.” In his book Transcendental Style in Film, Paul Schrader, for whom classic films are “more edifying and more permanent,” made similar remarks.

Classics stand apart from and above their contemporaries, ancestors, and descendants. When it comes to pictorial art, music, nonfiction, and certainly science, we often speak of classic works, but we are less accustomed or inclined to speak of prequels and sequels. There is a world more attuned to historical currents where special relativity would be called a prequel to general relativity, Charles Darwin’s The Descent of Man would be called a sequel to his On the Origin of Species, gene editing with CRISPR a sequel to ideas in evolutionary genetics, and gene regulatory networks a sequel to cybernetics.

If a prequel simply refers to preceding work that finds itself realized in a classic work, this is surely a widespread feature — and even a requirement — of all domains of inquiry. And if a sequel is the continuation of an idea or narrative, then this might be expected to be even more common. When it comes to the reluctance to speak of prequels and sequels in scientific ideas, several skeptical possibilities suggest themselves:

1. There are so few classics in science that to speak of sequels and prequels would be a kind of hopeful thinking, like describing the plains as the foothills to the prairie.
2. Classics are sui generis and severed from both the past and future. It is better to describe previous work as “preparatory studies” and subsequent work as “inspired by.”
3. The progress of science is a collective wave, not a solitary particle, and to speak of prequels and sequels would lead to a collapse of the conceptual wave function and is therefore purely an artifact of observation.
4. There is an implicit immodesty in the idea of a prequel and a sequel that borrows gravitas both backward and forward from a focal work that does not deserve to be called a classic.
5. Every scientific work is so original that it lives in a space dense with singularities fragmenting all paths through time.

This list of extremes is rather obviously tongue-in-cheek. Considered more carefully, they can be transmuted into five more serious variations, some of which might seem to be contradictory, but which capture a few real, increasingly salient tendencies in contemporary society and in contemporary scientific institutions that reflect a shunning of history and contingency.

1. The argument in some quarters that science is, like all other pursuits, merely a matter of contemporary opinion — opinions that vary in amplitude and not in verisimilitude.
2. Research metrics, having been built around a winner-takes-all mechanism, foster the idea that only a small number of papers matter — a sort of preferential attachment version of the Carlyle theory of heroes — where the winner takes all.
3. How the justified concern with fairness and broader recognition of teamwork (a counter to point 2) can inadvertently generate group think, excluding the possibility that sometimes an idea needs solitude to be incubated before emerging into the light of day.
4. The desire to spot the patterns of influence can obscure the revolutionary nature of an idea by situating it in a period of normal science.
5. The obsession with prizes, which tend to reward those who have already been overcompensated, can narrow the mind to the synthetic reality of concepts.

Ideas are built on ideas that have been tested against reality, not against the “Like” button. Popularity is the flimsiest proxy for the truth, and long-term influence speaks a very different language than the language of influencers. Recognition of the importance of collective intelligence should not diminish the process of alchemy undertaken by single minds, whose greatest prize is to become a part of collective intelligence. Harold Bloom in his Anxiety of Influence described the complex relationship that all work has with the past and the future in terms of “revisionary ratios” or the balance of following and swerving, which recognizes how achievement is always part reaction and part revolution.

We should learn to be more comfortable with prequels and sequels, which are honestly what most of us produce most of the time. There is even the word “interquel,” which can describe the incremental fractions of progress that typify serious research work, and the optimistic idea of the “paraquel,” or magical moment, when many ideas spring into existence together.

— David Krakauer
President, Santa Fe Institute

From the Summer 2025 edition of the SFI Parallax newsletter. Subscribe for our monthly e-Parallax, or email “news at santafe.edu” to request quarterly home delivery in print.

Every conception of time includes both a theory of change and a theory of permanence. Whereas dynamics and disorder have dominated scientific theories of time, science has paid less attention to what is timeless. The arts and mythology often treat the timeless as more important than the “timeful.” Much as we seek to explain the origin and role of time, we would like to understand the origin and value of timelessness.

The year 1872, viewed through the lens of three pivotal publications, encapsulates a few of the inevitable tensions that exist between temporal change and temporal stasis.

The first is Ludwig Boltzmann’s “Further Studies on the Thermal Equilibrium of Gas Molecules,” in which Boltzmann presents an equation for the time evolution of an ideal gas and demonstrates that its equilibrium solution is described by the Maxwell distribution. Boltzmann showed using his H-theorem that, regardless of the initial state of a gas, the solution to the equation ultimately converges on the maximum entropy distribution. In this way, Boltzmann sought to explain the inescapable mechanistic basis of the second law of thermodynamics — that the future is a shuffled version of the past.

The second publication came from a young professor of classical philology at the University of Basel, Friedrich Nietzsche, in the form of his monograph The Birth of Tragedy. Nietzsche’s thesis is that Greek tragic drama was born when the timeless world of ideal forms or “dreams” combined with the reality of human existence. The hybridity of great tragedy is described through Apollonian representations tempered by a Dionysian chorus — the symbol of the collective and chaotic will of the people.

The third is Samuel Butler’s Erewhon, a dystopian satire on the projected implications of evolution, as described in The Origin of Species, on the formation of a society. Charles Darwin’s mechanical view of nature, with its claims to timeless laws, is satirized in the response of the Erewhonians to the discovery of a pocket watch:

“But by and by they came to my watch . . . They seemed concerned and uneasy as soon as they got hold of it. They then made me open it and show the works; and when I had done so they gave signs of very grave displeasure. . . . a look of horror and dismay upon the face of the magistrate, a look which conveyed to me the impression that he regarded my watch not as having been designed, but rather as the designer of himself and of the universe; or as at any rate one of the great first causes of all things.”

For Boltzmann, nothing could be timeless; for Nietzsche, everything excellent need be born of the atemporal confronting the temporal; and for Butler, mechanized time is an assault on timeless values. And these three synchronous contributions to the dialectic of permanence and change are part of a far larger debate weaving together mythology, history, and science.

In the Lotus Sutra, time measures the slow revelation of enlightenment and yet the Buddha declared that there is no time, only an “eternal now.” For Isaac Newton, time is absolute and used to measure motion — and yet within his theory the past, present, and future have no meaning. For Edward Gibbon, social change in civilization follows from the stubborn foibles of human character — Gibbonian psychology is timeless. Georg Hegel argued that time was a timeless form of pure intuition and yet supports an historical and dialectical process of inexorable improvement. For Charles Darwin, evolution describes the temporal acquisition of adaptive order within a selective framework that is timeless — uniformitarianism. Henri Bergson equated time with conscious “duration” — far removed from the scientific quantification of motion, to be captured by the subjective experience of mental movement assayed by a timeless intuition.

Through a series of meetings, the Santa Fe Institute plans to explore the dual nature of time as a means of capturing what changes and what does not. How theories of change make strong assumptions about properties that are static and to states approaching equilibrium. We are interested in how historical theories typically ignore time and replace it with events, sequences, and contingencies. And why humanity’s greatest achievements and insights are ennobled as timeless — free from decay, corruption, and perhaps even replacement.

— David Krakauer
President, Santa Fe Institute

From the Spring 2025 edition of the SFI Parallax newsletter. Subscribe for our monthly e-Parallax, or email “news at santafe.edu” to request quarterly home delivery in print.

In his Ethics, published in 1677, philosopher Benedictus de Spinoza introduces a distinction between Knowledge of the First Kind (KFK), consisting largely of fragments of direct experience presented to the senses, and Knowledge of the Second Kind (KSK), or reason associated with the application of rules widely shared by everyone. The ability to distinguish the true from the false requires KSK. Spinoza uses the example of a geometric series to illustrate his point: the choice of starting numbers, let’s say (0, 1), lies firmly within KFK, whereas the derivation of a series or sequence of numbers — for example, the Fibonacci sequence (0,1,1,2,3,5, etc.) — lies within KSK. We might say that KFK is an input and KSK a function or a rule.

Between 1930 and 1933, Ludwig Wittgenstein gave a series of lectures at Cambridge University audited by the philosopher G.E. Moore, who kept very literal transcripts of Wittgenstein’s remarks. The lectures are filled with an abiding fascination with games. There is a point late in the course where Wittgenstein describes a very clear example of a rule of a game as writing down the development of the irrational number pi. This is what Spinoza had described through the idea of KSK. Wittgenstein also states that “discovering a game is quite different from discovering a fact” and facts are Spinoza’s KFK. For Wittgenstein, “Calculus is a game.” Indeed, every reason is only a reason within a game.

Midway through the Second World War in 1943, Hermann Hesse completed his novel The Glass Bead Game. The novel describes a community of scholars all hard at work on a game developed in the mid-21st century and built on mnemonics and melodics. In the game, dueling composers challenge each other to complete musical themes according to the strict application of formal rules. In its developed form several centuries later, the game involves advanced systems of deduction able to relate musical themes to mathematical propositions and Laplacian configurations of the physical world. Hesse sought to develop the kind of person who “would at any time be able to exchange his discipline or art for any other.” Assuming, of course, that all phenomena participate in the same game as described by Spinoza’s KSK.

When Richard Feynman published his Lectures on Physics in 1963, he presented physical theory as the effort to understand physical reality. Feynman writes, “What do we mean by ‘understanding’ something? We can imagine that this complicated array of moving things which constitutes ‘the world’ is something like a great chess game being played by the gods, and we are observers of the game. We do not know what the rules of the game are; all we are allowed to do is to watch the playing. . . The rules of the game are what we mean by fundamental physics.”

In an effort to provide an intuition for how evolved structure funnels chance into adaptive work, Manfred Eigen and Ruthild Winkler wrote their book The Laws of the Game (1981). The book contains a number of grid-based games, rather like Go. Many are inspired by the universalist goals of Hesse, which they describe in terms of “The dice and the rules of the game — these are our symbols for chance and natural law.” Reviewing the book in the London Review of Books, the evolutionary game theorist John Maynard Smith describes The Laws of the Game as an effort to show how understanding comes down to intuition for how “systems with different structures and relationships are likely to behave.”

The historian of religion James P. Carse, Spinoza-inspired to his core, wrote Finite and Infinite Games in 1986. In many ways, Carse extends Hesse’s premise by tempering it with Wittgenstein’s rule systems to achieve the open-ended possibilities for physical reality intimated by Feynman — and thereby promoting the kind of understanding sought by Eigen and Winkler. Carse writes, “There are at least two kinds of games. One could be called finite; the other infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.”

I like to think of complexity science as the natural continuation of these wide-ranging inquiries into the rules of the infinite game of reality. We might think of this science as the pursuit of Knowledge of the Second Kind conditioned on the happenstance of history and the debilitating finitude of our imagination.

— David Krakauer
President, Santa Fe Institute

From the Winter 2024–2025 edition of the SFI Parallax newsletter. Subscribe for our monthly e-Parallax, or email “news at santafe.edu” to request quarterly home delivery in print.

When the Scholastic cosmologists evaluated the Copernican contender against the Ptolemaic incumbent, it was not only the beauty of the simplicity of Copernicus’ contribution to calculating celestial tables that recommended his thesis, but the interesting possibility that the “wandering stars,” or what we now call the planets, were like our own Earth and teeming with the industry of contingent life — a plurality of worlds.

My colleague and collaborator Anthony Eagan recently published his new book, Kierkegaard’s Concept of the Interesting. Some philosophical background will be helpful in understanding the development of Eagan’s argument. The German idealists make a distinction between the outer and the inner. Immanuel Kant describes these as the sensible and the super-sensible, where the first describes the beauty of the mechanisms of physical law, and the second interesting features of the freedom of thought. The Romantic philosopher Friedrich Schlegel described Greek poetry in terms of “beauty” (closer to universal forms) and modern poetry as merely “interesting,” and confounded by the subjective details of human action and its fascination with content. Whereas Homer’s Hector enshrines the essential symmetries of beauty, Shakespeare’s Hamlet is full of the broken symmetries of the interesting; and hence to Schlegel, is the lesser creation.

As Eagan demonstrates in his book, Kierkegaard significantly enriches this debate by making the interesting relational — one might say that the interesting is a mapping or morphism from the latent or hidden laws of nature onto lived reality. The interesting is not merely the incompressible property of any work or idea but the noisy image encoded in a finite being of a pre-image mapped from a purely mechanical process, or in the religious context, from ultimate reality. And Kierkegaard describes the inverse mapping as the aesthetic impulse — the doomed attempt to construct the logic or function of the original (the natural world) from the degenerated counterpart (the cognitive world). In his Critique of Judgement, Immanuel Kant describes this sensation as trying to discern rather hopelessly in some physical object “formal purposiveness by the feeling of pleasure or displeasure.” This all reminds me of something the painter Robert Rauschenberg wrote in his journals: “Painting relates to both art and life. Neither can be made. I try to act in that gap between the two.” Rauschenberg carefully avoids concluding which of these two is interesting or beautiful.

Complexity science as articulated across the twentieth century has exactly this bijective character. When Warren Weaver described complexity as “organized complexity” as opposed to simplicity, he was describing the evolved world of the interesting emergent historically from a universe of the beautiful. The same point was made by Philip Anderson in his paper “More is Different,” where he writes, “Thus, with increasing complication at each stage, we go on up the hierarchy of the sciences. We expect to encounter fascinating and, I believe, very fundamental questions at each stage in fitting together less complicated pieces into the more complicated system.” Finding some principled measure of this more complicated system drove the mathematicians Andrey Kolmogorov, Gregory Chaitin, Charles Bennett, and Ray Solomonoff into the domain of Turing machines, those evolved mechanisms that lie at the heart of the modern relational account of complexity: mappings from physical micro-configurations into coarse-grained logical categories.

In his 1843 Either/Or, Kierkegaard presents several pseudonymous authors, foremost among them the Aesthete, “A.” “A” writes on music and on Mozart’s Don Giovanni, more specifically. Kierkegaard makes the point that “the medium through which an idea becomes visible could be made the object of consideration,” and that the medium of music is the most abstract and hence best suited to describe or encode the symmetries of ultimate reality. In this connection he foreshadows the debate on the power of mathematics to encode universal regularities. As the mathematician Morris Kline wrote in Mathematics and the Physical World (1959), “Insofar as it is a study of space and quantity, mathematics directly supplies information about these aspects of the physical world.” But insofar as we are studying a specific space and quantity, and complications at different stages, then we need another aesthetic, and a rather different kind of “A,” who focuses less on the simply beautiful and more on the complexly interesting.

— David Krakauer
President, Santa Fe Institute

From the Fall 2024 edition of the SFI Parallax newsletter. Subscribe here for the monthly email version, or email “news at santafe.edu” to request quarterly home delivery in print.

The brain is set firmly within the cranium, but the position of the mind is indefinite. Part individual, part collective, part made, part acquired, part deliberative, and part automatic. The mind’s patchwork complicates the effort to separate individual capability from collective and tacit capacity.

In 1998 Andy Clark and David Chalmers asked where the mind stops and the rest of the world begins. They posed three thought experiments to confront what might be called the hermetic-mind hypothesis — that mind and brain are coextensive. Experiment one involved rotating shapes into a socket in one’s mind; experiment two rotating the same objects on a screen; and in the third, alternately using a neural prosthetic implant or one’s unassisted mind. Clark and Chalmers propose that the second and third share technology, whereas the first and third share cranium. Perhaps it would be more parsimonious to describe them all as cognitive.

The entwinement between thought and tool is illustrated by the instrument-augmented reasoning achieved by several technologies of intelligence: Galileo’s Sector, Napier’s Bones, Oughtred’s Slide Rule, and Newton’s Cursor. Each of them a mathematical device or part whose outputs are not material products but a dizzying variety of calculations. None of them is what might be described as “user friendly.” They are all expert-friendly and expert-enhancing. They are to the analyst what a tennis racket is to Roger Federer.

Galileo’s Le Operazioni del Compasso Geometrico et Militare was a proprietary operational manual for a range-finding and calculating compass. It introduced users to Galileo’s incredibly versatile, protractor-like device, capable of measuring heights, distances, depths, and weights, calculating roots and compound interest, and estimating volumes. It was made from two metal legs connected through an articulating disc with support for a plumb line. It is spanned by a quadrant with the faces of each part marked with polygonal, polygraphic, and stereometrical lines.

To the modern eye it is little more than a metal doodad, an alchemist’s gimcrack, or Renaissance savant’s idol. In practice, it is a case study in the minimal use of matter to amplify the power of mind. It barely has two moving parts and yet assists in calculations super-numerous.

As a mechanical device, it is very far in complication from the intricacies of the Pascaline (1644), the Stepped Reckoner (1673), the Arithmometer (1820), and the Difference Engine (1822). Each of these is a mechanical marvel. The Pascaline comprised eight axles and a perpendicular gear connected through numerous ratchets, gears, and drums. The Difference Engine required 25,000 separate parts, and for self-evident reasons, was never built.

The Pascaline and Difference Engine are the rightful progenitors of modern computers and algorithms, at least as defined in terms of mechanical or electronic degrees of freedom. This point was made by Turing in the 1950s. The sector and slide rule, along with their ilk, speak to a different history. The latter are on a cultural genealogy towards exbodiment, or minimally engineered artifacts that enhance the adaptive capabilities of their users. They are from a ratiocinating land that time forgot, or is perhaps trying to forget.

Anne Collins and Michael Frank* at Brown provide an insight into why studying these artifacts is substantive and not only nostalgic. Most non-trivial tasks or problems require the concatenation of several steps, each of which contributes a partial solution, evidence of “cascading hierarchical structures,” as Collins and Frank call them. These tasks are grounded in sensorimotor processing or “executive functions [that] cannot be modularized separately from perceptual and motor systems, and that … scaffold on top of motor action selection.” One implication of this work is that calculating instruments are like limbs and joints that move the mind through a sequence of calculations rather than a body through the space of behavior.

The Hewlett-Packard 35, HP35, is often described as the first “pocket calculator.” Pocket as defined by the sartorial specification of the engineer, the shirt pocket, or habitual receptacle of a slide rule. The slide rule is a transcendental marvel. Inspired by Galileo’s sector, extending Napier’s Lattice, and then hybridizing these with the carpenter’s rule to enlarge the class of possible calculations from multiplication and root-finding to exponential and logarithms. In 1972, the projected market of the HP35 was 50,000 total units. Within a couple months of production General Electric alone had ordered 20,000 units. Within a few years slide rule production ceased and HP’s revenue increased by a half an order of magnitude. The last slide rule, the endling of the line of Oughtred, was produced in 1976 and donated to The Smithsonian Museum where it remains a relic of reason.

The slide rule is nearly synonymous with ready analytical ingenuity. Any self-respecting employee of NASA from the age of Apollo would be naked without one. Buzz Aldrin was pictured with a slide rule in free-fall on board Gemini 12 in 1966. Spock saves the Starship Enterprise with a slide rule in the third millennium. Calculators like the HP35 would be laughable on the super-futuristic Enterprise. The slide rule projects a timeless cognitive semiotics of resourcefulness.

Spock is from a wiser future that understands what contemporary society is already forgetting in its infatuation with all things AI. That there are two technologies of intelligence, one complementary and the other competitive, the first the expert’s amanuensis and the other an extraordinary labor-saving device. Neither model conforms readily to what the philosopher Jerry Fodor called the language of mind, wherein all true cognition requires internal–intracranial representation. Both extend the mind in ways conceived by Clark and Chalmers, but only one of them threatens mindlessness.

— David Krakauer
President, Santa Fe Institute

* Collins AGE, Frank MJ (2016) Motor Demands Constrain Cognitive Rule Structures. PLoS Comput Biol 12(3): e1004785. doi:10.1371/journal. pcbi.1004785

From the Summer 2024 edition of the SFI Parallax newsletter. Subscribe here for the monthly email version, or email “news at santafe.edu” to request quarterly home delivery in print.

Charles Babbage — Lucasian Professor of Mathematics at Cambridge (follower of Newton), co-founder of the Analytical Society (turncoat champion of Leibniz), life-long advocate of super-natural causes, and designer of unbuilt calculators — made his name in 1832 with the publication of On the Economy of Machinery and Manufactures.

Babbage’s book was received as the definitive survey on the efficiency and production of machinery designed to supplement or supplant human work. Babbage described the project in his introduction as a review of:

“the effects and the advantages which arise from the use of tools and machines; — to endeavour to classify their modes of action; — and to trace both the causes and the consequences of applying machinery to supersede the skill and power of the human arm.”

Karl Marx in the much-discussed, unpublished seven-volume Grundrisse, or Foundations of a Critique of Political Economy, included extensive reflections on automation inspired by Babbage’s researches:

“But, once adopted into the production process of capital, the means of labour passes through different metamorphoses, whose culmination is the machine… a moving power that moves itself; this automaton consisting of numerous mechanical and intellectual organs, so that the workers themselves are cast merely as its conscious linkages.”

Babbage conceived of his book as “one of the consequences that have resulted from the Calculating-Engine, the construction of which I have been so long superintending.” It was not Babbage’s intention to inspire a radical political economy, but to assay the most efficient means of manufacturing calculating engines:

“This much-abused Difference Engine is, however, like its prouder relative the Analytical, a being of sensibility, of impulse, and of power.”

The insights of Babbage and Marx sound as if they were written in the last several months in response to AI.

The life and society of Babbage is exemplary of the nineteenth century and its obsessions with machines, engines, designs, efficiency, scale, populations, evolution, and revolution. Babbage hosted super-sized parties at his home and laboratory at 1 Dorset Street in Marylebone, London. Charles Darwin, Michael Faraday, Lord Kelvin, Charles Lyell, Ada Lovelace, Henry Fox Talbot, and Alexis de Tocqueville all attended. It would not be a stretch to describe Babbage’s informal soirées as the founding meetings in the precognition of a possible complexity science.

What we now broadly think of as complexity, the domain of far-from-equilibrium, self-organizing, and selected mechanisms of adaptation, grew directly from the work of Babbage’s guests and contemporaries. The age of steam provided the phenomenological set of necessary elements for complexity: thermodynamics, uniformitarianism, evolution, and computation. Their union would be pursued in the twentieth century through the work of Alan Turing, R.A. Fisher, Norbert Weiner, John von Neumann, Claude Elwood Shannon, the Santa Fe Institute, and others.

This work cannot be described as physics, biology, or sociology, but a larger endeavor to make sense of the principles governing purposeful matter. We follow in the footsteps of the belligerent Babbage, with a troublemaker’s attitude to mechanisms, making a stand for steampunk:

“Chaos was my philosophy. Oh, yeah. Have no rules. If people start to build fences around you, break out and do something else.” — “Johnny Rotten” John Lydon, the Sex Pistols

— David Krakauer
President, Santa Fe Institute

From the Spring 2024 edition of the SFI Parallax newsletter. Subscribe here for the monthly email version, or email “news at santafe.edu” to request quarterly home delivery in print.

We might like to know what sets the speed of scientific discovery. And if we knew this, how to accelerate, cruise, break, and perhaps even stop. In the last couple of years, a great deal has been made of the high speed of progress in machine learning, many suggesting that we have achieved as a cultural mass, a dangerous momentum — Elon Musk, for example, warning that “If you’re not concerned about AI safety, you should be.” This is reminiscent of the fear of speed in the early ages of the automobile. In an article in the Detroit Free Press from 1914, there are dire warnings over the risks of driving at 40 miles an hour: “An automobile… rounded the corner from Labelle Avenue onto Woodward Sunday evening and turned turtle going at least 40 miles an hour.” Admittedly the driver was in all likelihood intoxicated. But perhaps the same could be said of the legions of large language model users and their ghost-in-the-machine-written spam epistles.

The metaphor of the automobile, or machine more generally, is fitting in more ways than one. The science of science has at various points emphasized the idea that fundamental science, unlike statistical science, is slowing down. It could have run out of fuel (new ideas), been hindered by too much friction (institutional inertia), excessive congestion on the roads (too many researchers on a project), a paucity of streets and highways (conservative ideas about where science should go), and bad driving (poor educational foundations). And there is ample empirical evidence for every one of these factors. In a recent meeting at SFI on “Accelerating Science,” many of these topics were discussed and everything from the conservative forces operating within large teams to the economics of risk-aversion were covered.

I would like to take a stab at relating these ideas to what the physicist David Deutsch has called Constructor Theory. According to Deutsch, the theory seeks to renovate physics, or what he has called the “prevailing conception,” and to provide a rigorous, consistent framework for talking about possible and impossible transformations. My sense is that the true value of Constructor Theory is the way it allows us to talk about possibility and less for what it has to say about physics. The theory builds on John von Neumann’s Universal Constructor argument for the origin of life, and adds details from what we know about enzyme kinetics (EK).

Von Neumann pointed out that a non-trivial life-form requires far more than replication; it requires programmable development. His argument was reminiscent of the current AI Paperclip Apocalypse, where an algorithm might determine that its objective function is to saturate the universe through the endless replication of a trivial function. A simple replicator likewise might fill the universe with a single bit of information. Von Neumann understood that complex organisms require a means of replicating information, which provides a blueprint for “constructing” a functional machine. As the evolutionary theorist George Williams wrote, all of biology operates through both codical (replicating) and material (phenotypically interacting) domains. It is not a stretch to extend this idea to scientific knowledge, where our educational systems, funding sources, and risk-averse norms, all emphasize replication of existing ideas over the possible construction of new ones.

Within the Constructor Theoretic framework, there are elementary inputs to a machine, the constructor, and outputs that are new configurations of matter. As von Neumann first noted, simple replication can dispense with the constructor, but the constructor is where almost all the interesting affordances and constraints live. In ontology, gene regulatory networks play the role of constructors, and through phylogeny, natural selection is a constructor.

The process of knowledge creation — that is, epistemic causality — resides in constructor mechanics. And of course the constructor is a machine that obeys the second law, and so its contribution to the generation of knowledge (under reasonable assumptions) implies an equal contribution to the production of waste, possibly even misinformation. Moreover, since the constructor is a kinematic machine, it obeys the combinatorial laws of chemical kinetics. And these imply that the speed of reactions is governed by the unique interactions of elements with constructors, the free energy available for transformation, the population size of the inputs, the time delay during the construction process, and so forth. All of the necessary ingredients for a scientific theory of knowledge production.

The historian Fernand Braudel, in the third volume of his Civilization and Capitalism: The Perspective of the World, writes of the “rhythms of conjuncture,” meaning the variable rates of synchronous events throughout history required to transform the cultural world, and that “human life was subject to fluctuations and swings of periodic movements, which carry on in endless succession.” And Jürgen Osterhammel, in his equally titanic The Transformation of the World, suggests that it was in the nineteenth century that what he calls “asymmetrical efficiency growth” accelerated, fueled by the increased mechanical productivity of labor, new sources of energy from new territories, and sequelae of conflict. The tempo of science is a microcosm of the rhythms of history, and as such, the outcome of intelligible construction processes realized at the global scale.

— David Krakauer
President, Santa Fe Institute

From the Winter 2023–2024 edition of the SFI Parallax newsletter. Subscribe here for the monthly email version, or email “news at santafe.edu” to request quarterly home delivery in print.