Adam Smith in The Wealth of Nations compared an expert to an expensive machine, whose work “over and above the usual wages of common labour, will replace to him the whole expense of his education, with at least the ordinary profits of an equally valuable capital.” Training skilled workers is a capital outlay amortized through their working life.

Smith observed that every artifact involves two debts. The first is a debt of construction, and the second the debt of its operation. The ratio between these two debts, between the cost of making something and the cost of running and maintaining it, turns out to be a variable quantity describing all machines, in both the non-living and the living worlds.

Organisms grow by synthesizing new tissue and are maintained at considerable energetic cost, through an ongoing expenditure of metabolic energy working against the second law of thermodynamics. In his monograph What is Life?, Erwin Schrödinger described an organism as “feeding upon negative entropy,” noting that “the device by which an organism maintains itself stationary at a fairly high level of orderliness really consists in continually sucking orderliness from its environment.”

My colleagues Geoffrey West, Jim Brown, and Brian Enquist have described this negative entropy process as a partition of a fundamental equation that splits a lifetime metabolic budget between the production of new mass and the maintenance of mass. It is the maintenance term that eventually halts growth because as a body grows, the cost of maintenance rises until it consumes the whole metabolic budget. From a sparrow to a whale, across several orders of magnitude in mass, the fraction of lifetime energy devoted to growth barely rises above a few percentage points. Every animal, regardless of size, is overwhelmingly working as a maintenance machine. As Giuseppe Tomasi di Lampedusa wrote in his novel The Leopard: “If we want things to stay as they are, things will have to change.”

A data center through this metabolic framing functions like a vast biological machine. For all of its technological scale, its construction cost is modest when weighed against projected operation costs measured in megawatts over decades. Whereas a laptop, which is at least zoomorphic in its appearance, is not at all like an animal. The energy required for its fabrication, including its silicon, exceeds the modest amount of energy it expends over its life. Roughly seven-tenths of a MacBook’s lifetime energy is spent before it is switched on.

Increasing efficiency drives technological artifacts away from the patterns of energy expenditure in the biosphere. This is because with every generation, operation becomes more efficient, whereas fabrication stays at an approximately fixed cost. This means that the more power-efficient a technology, the more its energy migrates into its construction costs. The efficiency that our society commends on energy labels turns out to be a cipher-text whose plain-text message describes the relocation of energy costs into the supply chain. Big inefficient fab labs make fabulously small and efficient gadgets.

The memory shortage of 2026 is often described in terms of hyperscalers buying up the world’s wafers to put into high-bandwidth memory and about dynamic random-access memory (DRAM) prices rising faster than gamers can keep up. But a deeper reading is allometric, a scaling relation, capturing the ontogenetic tradeoff between the two Smithian processes of growth-construction and repair-running. The great ignominious maintenance-dominated machines of our era, data centers, are competing for the same silicon materials as construction-dominated laptops. Since high-bandwidth memory for data centers consumes three wafers for every one in a consumer product, the trophic logic of the data center is to emulate the supersized biological organisms that they resemble and eat the bodies of laptops and just about every other consumer-grade technology.

The current crisis is what happens when a huge maintenance-dominated machine and a small making-dominated machine consume the same finite supply of matter. And there are few biological precedents for this, because life has not been so overwhelmingly dominated by the cost of growth the way that technology has been. The pathology of the DRAM crisis is that the broken symmetry between the cost of making technological things (high) and the cost of running them (low) has started to symmetrize. The only thing that could possibly prevent the extinction of this unprecedented reallocation of energy budgets is to amortize the working life of a gadget or service. And this is not an easy feat when the gap between investment and revenue in new technology rivals the GDP of a mid-size nation, and new species of energy-efficient, open-source models are invading all of their niches.

— David Krakauer
President, Santa Fe Institute

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

All of science is in the business of exorcism. When philosopher Gilbert Ryle coined “the ghost in the machine” in The Concept of Mind (1949), he was identifying an unnecessary explanatory entity in Cartesian dualism and expelling it. Descartes had posited a res cogitans, a thinking substance categorically distinct from the mechanical body. Ryle diagnosed this as a “category mistake,” and explained it away in the manner an Oxford professor does any superstition: like being shown the colleges, library, and playing fields of the university, and still asking the benighted question, “But where is the University?”

What Ryle did for mind, other sciences have done for their own spectral inhabitants. But the ghosts differ in kind, and so do their rites of exorcism. Physics exorcises supernumerary particles — unnecessary free parameters in pursuit of universality. Biology exorcises redundant processes — divine or teleological agencies. And the sciences of intelligence exorcise imposed patterns — transcendent sources of cognition. Each tradition seeks minimality, yet each means something profoundly different by it.

The deepest ambition of physics has always been to reduce the number of independent facts the universe requires us to accept. Theoretical physicist Eugene Wigner observed that symmetry and invariance principles act as filters on possible theories, eliminating free parameters with a scandalous efficiency. And Einstein’s general relativity derived gravitation from the minimal geometric postulate that spacetime curvature is gravity, eliminating Newton’s action-at-a-distance.

Biology’s ghost was never a free parameter but an agent. Before Darwin, the complexity of organisms demanded an intelligent designer the way a watch implied a watchmaker. On the Origin of Species (1859) performed an exorcism on the demiurge itself and replaced a transcendent creative process with a mechanical one. The ghost to be exorcised is the unnecessary rule, an act of God or Lamarckian inheritance. What remains after exorcism is not the universal parameterization of physics, but a universal mechanism (selection) that operates locally and iteratively.

Alan Turing showed in 1936 that a device of absurd simplicity consisting of a tape, a head, and a finite set of states could compute anything computable. Warren McCulloch and Walter Pitts demonstrated in 1943 that networks of binary threshold neurons could instantiate logical operations. Both of these exorcisms expelled patterns of architectural extravagance that Descartes and his followers had imposed on the mind. David Marr, in his 1969 model of cerebellar cortex, proposed a single, repeating architecture consisting of Purkinje cells trained by climbing-fiber error signals, that could learn arbitrary input–output mappings. Computation of near arbitrary complication could be solved through scale.

Computer scientists build architectures that seek to be spirit-proof. When physicists criticize biology for having too many parameters, they are applying parametric parsimony where processual parsimony is the goal. And when biologists accuse neuroscience of ignoring evolutionary constraint, they are importing processual parsimony into a domain governed by architectural parsimony. Each field is haunted by a different ghost, exists in a different intellectual bardo, each governed by its own rituals.

The old disciplinary ghosts aspired to be ontological, frightening entities posited to occupy ordered states of reality, from which ensuing and more skeptical generations banished them. We now have epistemic ghosts, patterns in large datasets, manifesting as regularities, correlations, and structures, that no human theorist seems to have previously named or noticed. LLMs suggest that we have been haunted by vast domains of regularity, in language, protein folding, weather, and genomics, that are simply too high-dimensional for human intuition to observe but not too complex for a sufficiently scaled statistical model to discern.

The ghosts are multiplying, many of them hallucinations, and scientific exorcists must learn new rites.

— David Krakauer
President, Santa Fe Institute

From the Summer 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.

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 to 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-21^st 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 Winter 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.

Arthur I. Miller subtitled his parallel biography of Einstein and Picasso Space, Time, and the Beauty that Causes Havoc. The upheaval to which Miller alludes is nothing less than the assault on our intuitive beliefs about space (cubism) and time (relativity). Put differently, familiar representations used to encode regular patterns in the world are, in fact, conventions. At a certain point these are deemed insufficient, or rather boring, and replaced. It is like the experience of touring through the Metropolitan Museum in New York City by starting in Greece with a Balsamarium decorated in lion skin, ambling through the Pacific past an Asmat ancestor, hastening through the Middle Ages fleeing from its terrifying two-handed swords, and coming to a stop at the inevitable lion in a Rousseau painting. They are different means of seeing not progressively but of encountering alternative depictions of reality.

The overall effect is to wonder at the multiplicity of descriptions of very similar objects and events. In 1781 Immanuel Kant made the question of “representation” the foundation-stone of a theory of knowledge. Kant kicks us off with his section on “Metaphysical Exposition of this Conception” in the Critique of Pure Reason:

“What then are time and space? Are they real existences? Or, are they merely relations or determinations of things, such, however, as would equally belong to these things in themselves, though they should never become objects of intuition; or, are they such as belong only to the form of intuition, and consequently to the subjective constitution of the mind . . .”

When are we entitled to call a representation objective (O) and when subjective (S)? There is a reasonable, operational form of naive realism that makes S mind and O sensation. Start with S1,O1: Ptolemaic astronomy (S1) viewed through the naked eye (O1) and replace it with S2,O2: Newtonian mechanics (S2) constructed from telescopic observations (O2). In this way, the accumulation of exact knowledge is the sequence Si,Oi → Si+1,Oi+1. And there is of course an evolutionary counterpart to epistemology — the sequence of adaptive steps mapping successive traits onto environmental factors described through a lineage.

Let’s just say that reality lies somewhere between the relatively simple history of science and life and a complex day trip to the Metropolitan Museum. What is striking is that in both cases — Miller’s central point in his biography — is that we must think of life and cognition as systems of reflection. This fact is what establishes, or delimits, what we call complex reality. Physics and chemistry have no need of S,O pairs, but we cannot begin to talk about biology, culture, or technology without some version of this duality.

John Holland and Murray Gell-Mann made the S,O pair the centerpiece of their definitions of complex systems, both describing the mirroring mechanism in the S as a schema of the O. For Holland a schema is a binary string whose fixed elements (as opposed to wild cards) define an equivalence class of coordinates encoding optimal solutions in adaptive landscapes. Complex systems are, for Holland, agents in possession of map-like schemata. For Gell-Mann, schemata, which he also called the IGUS (Information Gathering Utilizing System), are compressed rule systems capable of receiving inputs from history and environment in order to predict and act on states of the world. These span genomes, nervous systems, and even material culture.

Returning to Miller’s interest in the revolutionary transformation in the representation of time and space, we find the late James Hartle formalizing the IGUS in order to explore the origin of what he described as the emergent concepts: present, past, and future. These are not, contrary to received opinion, physical properties but representational concepts. By placing an IGUS in Minkowski space, Hartle traced what he called their “subjective” world lines. And in this way connected complexity (life) to simplicity (physics). What Hartle, re-representing Gell-Mann, re-representing Kant, initiated is a new science that might make aesthetics a fundamental principle of complexity — a rigorous connection between life, mind, and matter.

— David Krakauer
President, Santa Fe Institute

From the Autumn 2023 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 employees of Bell Telephone Laboratories described the company as an “institute for creative technology.” According to Jon Gertner, the historian of Bell Labs, “This description aimed to inform the world that the line between the art and science of what Bell scientists did wasn’t always distinct.”

In one of several Bauhaus manifestos written by Walter Gropius in the
nineteen-teens, Gropius described the aim of the new school as bringing craftsmen and artists together to create “the building of the future.”

There is a charming correspondence between the idea of a Bauhaus “building” and a Bell Labs “technology”: they both encompass more or less everything. For Bell Labs, communication and the transistor provided unifying technologies around which to build new systems of telephony, computers, psychology departments, language processors, and music and art software. At the Bauhaus, architecture provided a focus for the creation of typography, sculpture, furniture, art, cutlery, and books.

A slightly closer analysis of the history of these two institutions reveals a few basic ingredients of culture that provide clues to the scope of their influence. First and foremost, a focus on rigorous capability and creative freedom in community, and secondly, a healthy disregard for boundaries and benchmarks of disciplinary performance. Speaking about Claude Shannon, Gertner writes, “When confronted with ordinary number problems — 18 × 27, for instance — Shannon would work them out not in his head but on a blackboard. He wasn’t much for details; sometimes he would solve problems in a way that showed surprising intuition but a mathematical approach that some colleagues found unsatisfactory or lacking in rigor. Above all, he almost seemed more interested in doing work with his hands than with his mind.”

The focus on thinking with all of one’s sense and sensibility was a dominant feature of the Bauhaus, where according to the art historian Magdalena Droste, “[t]hanks to their basic training on the hand loom, however, students were equally capable of running small, artistic crafts workshops” and “A profession was thus created within the textile industry which had rarely been found before — designer.”

Between the engineering design of Bell Labs and the artistic design
community of the Bauhaus, I like to position the Santa Fe Institute. Complex systems are that special part of the universe “designed” by natural selection and self-organizing dynamics or by human collectives: organisms, ecosystems, markets, computers, and cities. And all organizations dedicated to understanding design in this larger, distributed sense have no choice but to accommodate very different styles of thought.

When Dieter Rams first presented his Ten Principles of Good Design in the so-called Tokyo Manifesto from the late 1970s, he included: innovative, useful, aesthetic, understandable, unobtrusive, honest, durable, environmental, and minimal. Many of these characteristics are the hallmarks of good theories and models. One might debate the general accessibility of understanding when it comes to mathematical theory, and yet understanding is the ultimate goal of all good theory, and not prediction, which is a truth litmus-test and closer to the domain of statistics.

By placing SFI between The Bauhaus and Bell Labs, I feel that our community of scientists, mathematicians, and artists comes into sharper focus. Our project is a radical one, which seeks to explore the frontiers of complex reality — the garden of machines, as it were — and emphasizes the precarious balance between individual iconoclasm, communitarian vision, and creative production. Let me leave the final expression of this notion to our friend and colleague Cormac McCarthy.

“The world you live in is shored up by a collective of agreements. Is that something you think about? The hope is that the truth of the world somehow lies in the common experience of it. Of course the history of science and mathematics and even philosophy is a good bit at odds with this notion. Innovation and discovery by definition war against the common understanding. One should be wary.” (Stella Maris, 2023)

— David Krakauer
President, Santa Fe Institute

From the Summer 2023 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.

At a recent meeting at SFI, my colleagues Kyle Harper (history of Rome and pandemics) and David Wolpert (physics of information and computation) encouraged a small group of historians and complexity scientists to reflect on recent developments in the thermodynamics of computation. The premise of the meeting was that a full account of history requires some means of connecting the energetics of the natural world with information required for human societies to access and utilize this free energy. In Harper’s account, history is a series of “algorithmic” inventions that more effectively couple the energy supply to societal growth, diversification, and maintenance.

The “special relationship” between history and complexity has its own curious history — starting in media res with Philip Anderson’s foundational paper, “More is Different” (1972), in which he pointed out the absolutely central role of broken symmetry in establishing the basis for all complexity. Broken symmetry describes the “historical” selection of one state from a set of states, all more or less equivalent, with respect to the underlying symmetrical laws of physics. The best-known example is the chirality of biological molecules: nearly all biological molecules are “left-handed” or levorotatory, whereas physical law tells us that left and right should be in equal proportion. All mesoscopic and macroscopic structures (molecules and up) are built on broken symmetries, including mechanisms of gene regulation and neural decision-making — the “algorithms” that have come to define the evolution of complex life.

In 1948 Claude Shannon introduced a mathematical theory of communication that sought to explain the absolute limits to reproducing at one point in space a message encoded at another point in space. The information is measured as the number of messages that can be reliably selected from a large set — “all choices being equally likely.” In other words, the Shannon information measures broken symmetry in a space of equally probable messages. Consider the game of 20 questions. One starts in a state of maximum uncertainty (symmetry — where all possibilities are exchangeable) and through a series of binary questions (animal or vegetable? etc.) symmetries are broken. If we slightly change Shannon’s framework, replacing space with time (transmitting messages forward in time rather than across space), then history describes those moments in time where accidents become frozen (the archduke was shot, the Bastille was stormed, or a plague rat boarded a trade ship).

In 1961 a researcher at IBM, Rolf Landauer, attempted to connect Shannon’s message-bits to thermodynamics. Landauer realized that for every broken symmetry, energy would need to be expended. He proposed that in a given temperature environment, the least possible expenditure of energy would be greater than or equal to kTln2, where T is the temperature and k the Boltzmann constant. Hence information requires a source of energy and as this increases the noisier (higher temperature) the environment. Landauer unites elements of Anderson and Shannon with thermodynamics, and in effect tells us that the longer a history (the more frozen accidents the Shannon information counts), the more energy needs to be expended.

The problem with the Landauer bound is that while it places a lower bound on the cost of information, it tells us nothing about the cost of the decision the information encodes. By analogy, Landauer might say opening and closing a door requires more energy than flicking a switch, but ignores the fact that the door provides access to meager calories in a pantry, whereas the switch turns on a monstrous hydroelectric dam. As Shannon and Weaver wrote in 1964, “information must not be confused with meaning” such that for two equally informative messages, one is “heavily loaded with meaning and the other . . . is pure nonsense”. As David Wolpert puts it, we are less often worried about the cost of a bit and more interested in “the bang per bit.”

One of the keys to understanding the cost of the meaning of information is to explore more carefully how the information is used — how an algorithm or procedure takes an input and processes it into an output that we would describe as the “correct” solution to a local problem. This goes beyond moving a message around in space or time to consider how the message is transformed into something useful — how a message is computed. This is the problem that Charles Bennett tackled in his 1988 paper “Logical Depth and Physical Complexity.” Bennett showed that a principled measure of complexity can be calculated as the running time of the fastest computer making use of the shortest instruction set (the Kolmogorov complexity) to achieve a desired solution.

The Harper–Wolpert meeting sought to take these foundational insights and ponder how they might be extended by considering recent progress in the non-equilibrium thermodynamics of computation. This in brief builds on a profound connection between energy dissipation and non-reversible transitions between meta-stable states described by a Markov process. It is not clear how this will be done. What is clear is that measures of history bear a very close resemblance to measures of complexity. And that as Murray Gell-Mann and Seth Lloyd showed us in their work on “Effective Complexity,” anything complex must have a long history. History should not be confused with time but identified with the steps of social procedures. History does not flow like a river but clicks like a wheel, and whereas in some centuries it is cacophonous in others it is barely audible.

— David Krakauer
President, Santa Fe Institute

From the Spring 2023 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.

In his 1901 essay, “Mathematics and the Metaphysicians,” Bertrand Russell suggests that George Boole, the autodidactic son of a cobbler, was the discoverer of pure mathematics in his work, An Investigation of the Laws of Thought (1854). Russell argues that Boole was “mistaken in supposing he was dealing with the laws of thought” — that in fact the book is concerned with “formal logic, and this is the same thing as mathematics.” In case one supposes that it was Aristotle who invented logic, Russell dispatches such quaint historicism, observing that “in each decade since 1850 more has been done to advance the subject than in the whole period from Aristotle to Leibniz.”

What Russell’s essay is really about is infinity, and through the work of Georg Cantor and others, the anchoring of mathematics in logic and logic in infinity. Although Russell did not yet see it, whereas ironically Boole already had, infinity is ultimately the constructive principle supporting knowledge and thought. As Boole puts it in “Constitution of the Intellect,” the final chapter of An Investigation of the Laws of Thought: “When from a large number of observations on the planet Mars, Kepler inferred that it revolved in an ellipse, the conclusion was larger than his premises, or indeed than any premises which mere observation could give. What other element, then, is necessary to give even a prospective validity to such generalizations as this? It is the ability inherent in our nature to appreciate Order . . .”

It is order that empowers the archiving mind in finite time to operate in an infinite universe. And this permits in the words of Boole, “The necessary sequence of states and conditions in the inorganic world, and the necessary connexion of premises and conclusion in the processes of exact demonstration thereto applied, seem to be co-ordinate.” Knowledge and reality converge through the right choice of system.

Perhaps too much has been written about Jorge Luis Borges’ story, “The Library of Babel.” But to my knowledge, much of this commentary has been aimed at scholarly futility and the impossibility of originality. The great power of infinity — as obtained through the ordering principles of Boole, Cantor, and Russell — is that like alchemy, it seems to transform discovery into creativity, or search into invention. When Borges writes that “The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries” and that within these hexagons are all the books that could ever be written, he is suggesting that if there is a catalog or index to the library (a source of order), then knowledge is identical to intellection — to know where something is equates to its discovery. To know it all is to appear genius.

This last year has been full of know-it-alls. The artists have names like NightCafe, DALL•E 2, and Stable Diffusion, and the writers, GPT-3 and Bloom. They are Babel Algorithms, accumulating limitless hexagons of online information, where every artist born and unborn is somewhere in the endless permutation of what came before. And the search index seems to provide the necessary order to turn mere facts into fancy. It is a challenge for a dawning science to think through the implications of solving problems by exploiting practically searchable “effective infinities.”

Boole had foreseen this utilitarian dilemma in a bygone configuration as well as its dire limits for the future: “In the extreme case it is not difficult to see that the continued operation of such motives, uncontrolled by any higher principles of action, uncorrected by the personal influence of superior minds, must tend to lower the standard of thought in reference to the objects of knowledge, and to render void and ineffectual whatsoever elements of a noble faith may still survive.”

— David Krakauer,
President, Santa Fe Institute

From the Winter 2022–2023 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.

Jean-Luc Godard 1930–2022
Javier Marías 1951–2022

In the opening scene of Jean-Luc Godard’s absurd and irresistible science-fiction film “Alphaville,” the computer Alpha-60, an omniscient and omnipotent artificially intelligent overlord, declares, “Sometimes reality can be too complex to be conveyed by the spoken word. Legend remolds it into a form that can be spread across the world.” This so-called reality is human existence and the legend is technique and efficiency. Alphaville’s maxim is “Silence, Logic, Safety, Prudence” and Alpha- 60 rules over it with intractable vacuum tubes.

“Alphaville” was made in 1965 in black and white. Travel between worlds is by dilapidated highway, if we are lucky, in a Citroën DS19. The most advanced prop in the film is a curvy jukebox. Everyone smokes. The hero, Lemmy Caution, is a squalid Philip Marlowe–type in a Peeping Tom trench coat. Caution is on a mission to abduct, or at least kill, Alpha-60’s architect, Professor von Braun — formerly known as Leonard Nosferatu. When Caution eventually meets Alpha-60, he is giving a lecture on what sounds like Gödel’s rotating universe: “Time is like a circle spinning innately.”

The Spanish writer Javier Marías was obsessed with espionage, spies, and secrecy. His characters are often misanthropic misfits, like Godard’s Lemmy Caution, who live vigorously in shadows. In a series of novels starting in 2002, Marías began a systematic analysis of those working within secret systems, those seeking assimilation, and the majority who are merely controlled. Marías’ father, the philosopher Julián Marías, sometimes described as the Spanish Bertrand Russell, was the author of numerous books, including the tantalizing “Metaphysical Anthropology: The Empirical Structure of Human Life.” In his book, Julián Marías described how a life is created in relation to networks of circumstances and experiences, a system of relations which through individuality achieves a “maximum condensation.” Javier Marías in his novels often seems to be exploring his father’s twin world, one where relationships are so concealed that individuals achieve a maximum of dispersal.

In one of Marías’ most recent books, “Berta Isla” (2017), a young spy in the making, Tomás Nevinson, is recruited by an inscrutable scholar, Sir Peter Wheeler. Wheeler describes spies as the ones who “are not exposed, who can’t be seen; unknown, opaque beings about whom almost no one knows anything . . . . Those who act swathed in mist . . . they are the ones who most disturb the universe.”

Godard and Marías were interested in systems and agents from both sides of the divide: citizen and instrument, and both sought to expose the risks of subjugating the individual will to the potentially obfuscating technologies of society. They were transmuting into art the concerns that Jacques Ellul surveyed in his 1954 book, “The Technological Society.” Ellul described technologies as all standardized means of obtaining results, or arriving at a perfect outcome, however questionable the result might be — in other words, our fascination with carelessly examined ends that bend values before efficiencies.

Ellul’s analysis of technology was building on Thorstein Veblen’s earlier interests in industry in his 1921 monograph, “The Engineers and the Price System.” Veblen foresaw an emerging mechanical world order with an inclusive organization of “interlocking processes and interchange of materials.” Veblen maintained that in such a world, entirely new forms of literacy would be required, “a joint stock of knowledge and experience held in common by the peoples.” Neither Veblen nor Ellul could have anticipated the degree of system opacity threatened by modern computer software and machine learning. Today these systems are diverging from Wheeler’s shrouded actors and threatening to converge on Godard’s algorithmic dictator.

Godard and Marías were two virtuosi who, in zany and subtle ways, increased awareness of the dangers of secrecy and the latent confidentialities of technologies — human and mechanical — and remind us of the role that art has always played in bringing complex, systemic ideas into aesthetic experience.

— David Krakauer
President, Santa Fe Institute

From the Fall 2022 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 do not have too much intellect
and too little soul, but too little
precision in matters of the soul.

— Robert Musil

The near-infinite question of how best to describe the world has yielded a relatively predictable taxonomy of answers. At least this is true if we judge this question in terms of the species of avocation/profession, categories of object or artifact, and scholarly departments.

We are told that there are (and worse still that we are) scientists, artists, humanists, or electrical engineers, plumbers, and gardeners. The list is long and also disappointing. So much seems to be lost, or perhaps contracted, by the labels.

An alternative and, I think, more liberating approach is to look at the organic shaping of ideas over the course of careers, and thereby trace biographical territories that are explored and the many borders that are crossed in the making of minds. When Robert Musil wrote of precision in his essay, “Helpless Europe,” in 1922, he was expressing an opinion that found its most complete expression in his encyclopedic novel, The Man Without Qualities:

“If there is a sense of reality, there must also be a sense of possibility. To pass freely through open doors, it is necessary to respect the fact that they have solid frames. This principle, by which the old professor had lived, is simply a requisite of the sense of reality. But if there is a sense of reality, and no one will doubt that it has its justifications for existing, then there must also be something we can call a sense of possibility. Whoever has it does not say, for instance: Here this or that has happened, will happen, must happen; but he invents: Here this or that might, could, or ought to happen. If he is told that something is the way it is, he will think: Well, it could probably just as well be otherwise. So the sense of possibility could be defined outright as the ability to conceive of everything there might be just as well, and to attach no more importance to what is than to what is not.”

In a profound sense, it is the business of science to express as rigorously as it can a sense of possibility. Quantum mechanics has a very nice phrase, “counterfactual definiteness.” It describes the perfectly reasonable meaning that can be attached to measurements that have not yet been performed. Einstein made a career out of proliferating thought experiments in a physical universe with very “solid frames” in order to reveal through a sense of possibility that it also has more doors than a Royal Palace.

In the spirit of expanding our sense of possibility, SFI and the SFI Press are starting a new magazine of interviews, featuring our Miller Scholars (artists, historians, and humanists) and Fractal Faculty (distinguished sabbatical researchers) in collaboration with our partners at Santa Fe Magazine. It will be called ExtraTerritorial. We are borrowing the title from George Steiner’s book of the same name in which he describes the paths of linguistic nomads defying the borders of cultural identity. Through interviews that connect the zigzag of a life to the accretion of ideas we hope to lend some precision to matters of the soul.

— David Krakauer
President, Santa Fe Institute

From the Summer 2022 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.