In 1968, when computers were still seen as cold calculating machines, Jasia Reichardt curated an extraordinary exhibition in London called Cybernetic Serendipity. Artists, engineers, poets and scientists came together to explore the creative possibilities at the intersection of art and technology.The result was something remarkably ahead of its time. If you're curious about the early days of the relationship between computers and art, the catalogue is essential reading. The catalogue from Cybernetic Serendipity is filled with ideas, experiments and reflections that feel surprisingly relevant in our current AI era. You can read the full PDF for free here: [ X ]
Serene, stately, proud orchardsÂ
strolled about all by themselves in the eveningÂ
behind their fence rails. Once upon a time,Â
a handful of stars fell from their branchesÂ
into dark cisterns, where blind swansÂ
floated phantasmically.
A little lemon treeÂ
ran in its wedding dress, without anyone noticing,Â
and fell into the well. A faint white cloudÂ
rose among the trees. Someone, runningÂ
through the big outdoor iron gates,Â
shouted, âI saw it with my own eyes.â Ever since,Â
the keeper of the garden has been deaf and dumb.
Serene, stately, proud orchards strolled about all by themselves in the evening behind their fence rails. Once upon a time, a handful of stars fell from their branches into dark cisterns, where blind swans floated phantasmically. âYannis Ritsos (trans. Spring Ulmer), born #OTD in 1909
this film, a crucial prologue to Mamadou Diawara's problematization of display & appropriation; the re-sacralization in the 'temple' of the museum: âthe new ritual, that of being shown.â the spectacle of a thief's consciousness in curating African art
The Most Important Writer You Donât Want to Read // Youtube >>
Even if you don't know his name, you've felt his impact. William S. Burroughs wrote some of the most controversial and disturbing books in modern literature, and became a darling of artists and pop-culture icons alike. So what's so special about the way he writes and, more importantly, what does it say about our culture that he remains so relevant?
The Most Important Writer You Don't Want to Read
Even if you don't know his name, you've felt his impact. William S. Burroughs wrote some of the most controversial and disturbing books in modern literature, and became a darling of artists and pop-culture icons alike. So what's so special about the way he writes, and â more importantly â what does it say about our culture that he remains so relevant?
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Chapter 1: Diagnosing the Disgusting
"As you know, I'm not the kind of person that reads books â I've said this before many times, I'm not fond of reading. But I do, I have in the past made exceptions, and one of these exceptions was this part of the book that I'm sure you know, called Naked Lunch. Did I ever tell you about the man who taught his asshole to talk?"
That was Frank Zappa, cult musician and provocateur, reading at the inaugural Nova Convention, held in New York in 1978.
The book Naked Lunch was published in 1959 and met with outrage and bans across the globe for its allegedly obscene depictions of extreme hedonism. But by the late 1970s, having successfully shaken off multiple legal challenges, the novel and its author, William S. Burroughs, had emerged as heroes of an artistic revolution.
Once you get acquainted with Burroughs, he's hard to shake off. One moment he's talking with the likes of Francis Bacon; the next, rubbing elbows with Andy Warhol; and the next, meeting Debbie Harry of Blondie and Bob Dylan backstage. Punk poet Patti Smith said, "He's up there with the Pope â you can't revere him enough." Evidently, The Beatles thought the same.
Nowadays we call this kind of cultural phenomenon *going viral* â spreading through culture like a contagion. This epidemiological model for culture and the spread of ideas is so prevalent that, until viruses re-entered the public consciousness in recent years, you'd be excused for not remembering the original biological association, most concisely identified in Richard Dawkins' coining of the word meme as a derivation of gene.
But unlike an image or a song, you can't escape the legacy of William Burroughs. His viral quality is not only a matter of ubiquity in the culture. Given the controversial and often toxic nature of his work, you'd probably find him â like a virus â genuinely sickening. His writing focused on the taboos of his era: drug addiction, insanity, ultraviolence, death and sexuality, depicted in extreme, often gleeful detail. The stories and ideas behind it are a stomach-churning journey. Burroughs lived a life haunted by death, debauchery and despair. There is a bizarre, terrifying philosophy at work in his writing â a philosophy that lurks in the very DNA of the cultural experimentation of the late twentieth century.
In a world where art is increasingly judged alongside the life of the artist, what do we make of his all-consuming influence? What does it say about him that he's garnered such an artistic following? And more importantly, what does it say about our culture that we've taken to him so completely?
By the time Naked Lunch â his third and most infamous book â was published in full by the Olympia Press in 1959, William Burroughs was already steeped in controversy. His first two novels, Junky and Queer, had placed him outside the social and literary norms of modern America, detailing his experiences with drug addiction and his homosexuality respectively, in semi-autobiographical narratives following his pseudonymous protagonist Bill Lee. Because of its unflinching depiction of the use and abuse of drugs, Junky had been heavily censored in its first edition â but its extremity pales in comparison to what came next.
It's not really that helpful, or monetizable, to describe what Naked Lunch is actually about. A psychotic blend of noir fiction, social satire, pornography and body horror, it was initially released in snippets â known as routines â through small literary magazines, which Burroughs said could be read in any order. As such, attempting to summarize a plot doesn't really capture its bizarre, nonlinear, dream â or rather, nightmare â logic. At the very least, it features Burroughs' alter ego Bill Lee, who enters a strange land known as the Interzone: a dystopia filled with crime, corruption and conspiracy, which may well be the product of his drug-addled imagination.
But the most significant thing about Naked Lunch is the effect â or effects â it produces. Straightaway, disgust comes to mind, tied up in claims of obscenity. Disgust, at a basic level, serves to protect us from things which appear alien to us and may pose a threat to our survival, cause us harm. Bodily fluids repulse us because, through thousands of years of evolution, we've come to associate them with the spread of illness. Our disgust can keep us safe, and as one of our most powerful emotional responses, we tend to codify it in rationalized arguments. Looking at the horrified response of those seeking to censor Naked Lunch, we can see how moral judgments of the book were formed from such gut responses. Chief Justice Hudson, in the Boston obscenity trial, called it "a revolting miasma of unrelieved perversion and disease," particularly owing to its depiction of so-called deviant forms of sexual activity, ranging from extreme sadism to simple homosexual affection. Disease, in this case, represents what he saw as the contamination of public discourse with ideas and subjects outside contemporary community standards.
But disease also figures in the counterarguments defending Naked Lunch. Burroughs himself claimed that his novel treats the health problem of drug addiction, which was, in his view, the true root of the sickness portrayed in the book, its presentation necessarily brutal, obscene and disgusting â while at the same time critiquing a culture that often diagnosed homosexuality as something to be cured, through nightmarish medical scenes involving "cured" homosexuals.
Giving in to disgust isn't always the best course of action. When what repulses us is already within us, it needs to be confronted and treated, not ignored and suppressed. It's from this idea that Naked Lunch gets its title: the frozen moment when everyone sees what's on the end of every fork.
One of the reasons Naked Lunch was such a watershed moment in the culture is that it asked us to tackle and digest taboo but unavoidable subjects. When it was cleared of the obscenity charge â around the same time as Henry Miller's similarly explicit autobiographical novel Tropic of Cancer â it heralded the normalization of such controversial themes as acceptable subjects for art. America was developing a certain immunity to things previously seen as harmful and infectious.
This effective endorsement of the crass and explicit as an acceptable feature of art certainly explains Burroughs' appeal to Frank Zappa, whose lyrics often sound like something straight out of Naked Lunch, for all their gleefully transgressive detail:
"I am aâ dream, but now I feel likeâ and I'm a miserable son of a bitch. Am I a boy or a lady? I don't know."
Yacht rock pioneers Donald Fagen and Walter Becker also found something to like in Naked Lunch, naming their band Steely Dan after a mechanical, steam-powered instrument from the novel.
This might have been the biggest short-term effect of Burroughs' work, but there's more to it than just shock value. When Judge Hudson compared Naked Lunch to a miasma of literary sewage, he tapped into something Burroughs himself was trying to get across. It's a strange comparison, but like sewage, Naked Lunch is something of a waste product. In one sense it represented the digested, fermenting thoughts and experiences of social underworlds that Burroughs had traversed â from New York to Vienna to Tangier â a collection of notes on drug use which spill off the page in all directions:
"Kaleidoscope of voices, medley of tunes and street noises, farts and riot yips..."
The dulcet tones of William Burroughs. But in a more literal sense, it was constructed from literary waste. The rearrangeable routines that constitute the book were taken from a vast word-horde written between 1954 and 1958 â more than a thousand pages of typewritten content â from which Burroughs' friends and fellow writers Allen Ginsberg and Jack Kerouac helped to build the text. It was never conceived of as a homogeneous novel. As a result, beyond just how uncomfortable the ideas and descriptions contained in the book are, its very construction â as a nonlinear series of incoherent episodes â challenges the reader in the same way as a code or scrambled transmission. And this is kind of the point.
Every writer has their philosophy: an implicit or explicit set of ideas and values that color anything they write and inform thematic and aesthetic decisions. But with Burroughs, the lines between playful experimentation and sincere commentary are uncomfortably blurred. To try and fully explain just what Burroughs believed is far beyond the scope of a twenty-minute video essay, and even then it's hard to tell just where he stands. But it broadly boils down to this: while the majority of literature can be said to explore moral conflict, Burroughs rejected what he viewed as a dualistic perspective on the world, discarding the binary of good and evil in favor of a general antagonism towards control. Control could mean any number of things for Burroughs â religion, government, codes of ethics, rules, regulations, censorship â all things parodied in Naked Lunch. But most peculiarly of all, Burroughs believed that the ultimate form of control was language itself, and frequently compared it to a virus.
The virus as an image appears frequently in Naked Lunch before spreading across his other novels, and notably in his non-fiction writing. In his formulation, viral language â and indeed any form of communication â is designed to replicate itself from speaker to listener and so on, with language users becoming hosts to its codes, its DNA, like animal cells exposed to pathogens. Because everyone uses the same common words to refer to themselves, language makes us, Burroughs argues, functionally the same, mutating us into creatures exhibiting the same symptoms. And this is what makes it one of the most powerful instruments of control: supplanting our individuality with a one-size-fits-all pattern.
It's difficult to know just how far Burroughs actually took this theory. In some places it seems like more than a metaphor to him, with one essay theorizing that language resulted from a mutation caused by a virus in apes â an idea he attributes to a fictional doctor, Kurt Unruh.
We'll get a little more into his strange ideas later, but this idea of language as a kind of genetic aberration takes us back to that strange but iconic moment from Naked Lunch: the talking asshole monologue. A man developed speech in a part of himself that shouldn't talk. After a while, the asshole started talking on its own, eventually leading to the violent disintegration of his whole body.
"Then the asshole said to him: 'It's you who will shut up in the end, not me â because we don't need you around here anymore.' So finally his mouth sealed over. For a while you could see the silent, helpless suffering of the brain behind the eyes. Then finally the brain must have died, because the eyes went out."
It's funny, sure, and it does work well as a stand-up comedy routine. But it's also undeniably horrific â a vivid moment of body horror rooted in the acquisition of language. To combat what he saw as this tyrannical capability of language, which largely operates in the linear syntax of sentences formed by the grammar virus, Burroughs sought to scramble its messages of control. Hence, in Naked Lunch, the randomly ordered routines â with the reader's confusion at the nonlinear narrative acting as a circuit-breaker from the barrage of conventional media. Burroughs' book is simply a way of fighting fire with fire, a how-to book, as he calls it, for an up-and-coming counterculture resisting the mainstream's attempts to control it.
But this was just the beginning of his program of detox â a first step into a radical new aesthetic that would take the twentieth century by storm.
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Chapter 2: Cut-Ups and Control
In 1958, Burroughs' friend, the artist Brion Gysin, was in the process of making a table mat out of newspaper for his studio. Having cut the sheet into segments, he noticed that from the fragments of text he had created, by changing their order he could also change their meaning. This innovative form of collage, known as the cut-up method, had first been used by artists of the Dada movement in the 1920s before quickly falling out of fashion. But in the arsenal of Gysin and Burroughs it found a new, energized life across various media.
Notably, it became Burroughs' modus operandi for a significant period in his career. For Burroughs it was the perfect way of disrupting the coherence of control transmissions. But cut-up was also seen as a conduit to some great unconscious power that could dictate the shape and meaning of a work â even tell the future â lessening the creator's own control over his creation in favor of bowing to a grand metaphysical energy known as chance.
Burroughs' subsequent Nova Trilogy was written almost entirely using cut-ups â books that make Naked Lunch seem coherent and lucid by comparison. But while it makes for an even more impenetrable narrative experience, its possibilities for art in general were quickly exploited.
Around the time that Burroughs was working on finishing the trilogy, he was invited to give a reading at the Indica bookshop in London, and soon got talking with its patron, Paul McCartney. McCartney was in the process of recording The Beatles' seventh album, Revolver, and invited Burroughs to sit in on some of the studio work â discussing the power of using tape machines to cut and splice pre-recorded sounds, which feature heavily on several tracks. The sound collage on the album's closing track, "Tomorrow Never Knows," has a distinctly Burroughs quality, with its title evoking something of the cut-up's mystical powers:
"When you cut into the present, the future leaks out."
Perhaps more famously, David Bowie explicitly employed literary cut-ups in his lyrics, following an interview with Burroughs for Rolling Stone in 1973.
"This is the way I do cut-ups. I don't know if it's like the way Brion Gysin does his, or Burroughs does his â I don't know â but this is the way I do it."
Bowie had previously drawn from Burroughs in creating the Spiders from Mars, modeled on characters from Burroughs' novel The Wild Boys, but adopted his experimental method on the album Diamond Dogs.
There's something particularly viral about cut-ups â and not just because of how their influence has spread. Viruses, unlike bacteria, can't really be thought of as living organisms. Bacteria can survive on their own, replicating through simple cell division. But viruses depend on other cells to reproduce and spread. They contain the potential for life, but only in the form of isolated strands of DNA, ready to be grafted onto a host â like bits of cut-up material, reordered and inserted into other works.
What better analogy for Burroughs' form of writing, really. But there's also something pretty disingenuous â even sinister â about this comparison.Â
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Chapter 3: We Need to Talk About Bill
You see, Burroughs' theory of literature tends towards an assumption that works are independent of their creators. When a pandemic rips through a population, where it came from is usually of less concern than what illness it causes and how it can be treated. As the last fifteen minutes have demonstrated, there is plenty to talk about in the effects and transmission of Burroughs' viral works when we put them under a microscope. But in this neat extended metaphor, the man himself â as patient zero â is unsettlingly absent.
"Mr. Burroughs, do you regret anything in your life?"
*"I am very lucky if I get through a day without something I did wrong, something I said wrong, gestured wrong. And you talk of a lifetime? Good God. Practically everything."
This has been a difficult video to write. Because as impenetrable as this stuff can be, Burroughs is a visionary and undeniably unique writer with a cultural impact so far-reaching it's almost hard to encapsulate. But he was also a deeply troubled and troubling person. The whole separating-the-art-from-the-artist debate is a divisive one, but when it comes to Burroughs, because of how much of his own life he includes in his writing, it's pretty much impossible to keep the two apart.
The founding member of the Beat movement â along with the poet Allen Ginsberg and novelist Jack Kerouac â Burroughs' immersion in fifties counterculture also involved a fair few brushes with the law. He had become heavily addicted to morphine and then heroin while living in New York on a generous allowance from his parents. Having been rejected from service in the Navy, to get his fix Burroughs took to dealing and even forged prescriptions, leading to his second arrest â the first being for his implication in the murder of David Kammerer at the hands of his mutual friend Lucien Carr, whom both he and Kerouac assisted in the hours after the killing.
But the crucial moment in Burroughs' life â the black coal that consumes almost everything he does afterwards â came in 1951. On the 6th of September, Burroughs and his partner Joan Vollmer were at a party hosted at a friend's apartment in Mexico City. The couple had fled there following a string of drug-related charges, and with limited access to heroin, Burroughs turned to drink, having multiple gay relationships while they contemplated divorce. That evening, Burroughs shot Vollmer in the head. Their four-year-old son was present. Though he offered multiple stories as to how the killing occurred, the most famous and most reliable â corroborated by multiple witnesses â was that the couple had been drunkenly attempting to recreate the William Tell stunt, with Vollmer balancing a glass on her head. Burroughs missed.
Burroughs then fled back to the States and received a conviction for manslaughter and a two-year suspended sentence. The exact nature of just what happened is contested. But it's the way Burroughs processes this event that leaves a nasty taste in the mouth.
In the preface to Queer, written just under two years later, Burroughs writes that he has come to "the appalling conclusion that I would never have become a writer but for Joan's death." It's an admission of guilt that also frames his frenzy of writing â the creation of the word-horde that spawned Naked Lunch and much after it â as a kind of penitent act, or conversely, a release of creative energy. Though the guilt over this act would be understandably unbearable â particularly the idea that he had subconsciously wanted to kill her, as he often theorized â Burroughs didn't hesitate to weave the event into his pseudo-scientific philosophy, suggesting that the brain drew the bullet toward it, or that he had been possessed, infected by an ugly spirit: "monopolistic, acquisitive, evil." He then went on to question the certainty of conscious intent: "If everyone is to be made responsible for everything they do, you must extend responsibility beyond the level of conscious intention."
His use of cut-ups similarly wishes to do away with the idea of conscious intention, through the element of randomness involved. But these words come from somewhere. Words may be inherited, transmitted and passed on like germs, their effects to an extent determined by the host at the receiving end â but ideas and utterances are produced with a purpose. Burroughs' disdain for control gives him a vehicle to escape personal responsibility, while elsewhere he argued for strangely authoritarian ideals. He paradoxically espoused the benefits of a segregated society, applying his pseudo-biological lens to refer to women as "a basic mistake of evolution," with the family being "a ridiculous unit devised in order to control the individual" â a convenient concept for a man who spent his limited time as a parent exposing his young son, Billy Burroughs Jr., to drugs that he would become addicted to, and alleged molestation.
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Chapter 4: Infection or Inoculation?
Everyone is entitled to their own experience, but when I read Burroughs in light of all of this, I can't help but feel implicated in â or infected by â the nihilistic worldview he propagated. His influence may be contagious, but what about his guilt? The thing that spawned his writing in the first place.
For all his outrageous transgression and obscenity, Burroughs was an expert in hiding in plain sight. His style, ripped from Hollywood detective films, made him seem more like a figure from a bygone age â too quaint, too scholarly to be harmful. But he understood the power of aesthetic choices to hypnotize people. All the way back in high school he'd written an essay on personal magnetism. Ultimately, he was able to ensnare and infect a generation with his art.
And that's the thing about him. As much as I'm morally repulsed by him, disturbed by his imagery and ideas, there's something compelling about his confidence and the boldness of his writing. That's his trick â transforming moral stances into simple aesthetic features. The most unsettling example is his late-career foray into shotgun art, where cans of paint would be fired at canvases to create random patterns â literally making art with the tool that authored his wife's death. It's arguable that our cultural acceptance of his art, because of the nature of it, is also to an extent an acceptance of his morality.
Children who are believed to possess special traits or abilities
Indigo children, according to a pseudoscientific New Age concept, are children who are believed to possess special, unusual, and sometimes supernatural traits or abilities. The idea is based on concepts developed in the 1970s by Nancy Ann Tappe, who wrote that she had been noticing indigo children beginning in the late 1960s. Her ideas were further developed by Lee Carroll and Jan Tober.
One underlying ideology of democratic things is a strong version of egalitarianism: the idea that we are all equal, not just in some Christian metaphysical sense of having equal dignity under God, but in some more concrete sense of all having equally valuable things to say and deserving an equal voice in the world.
It is sometimes considered impolite to disagree with this directly. But at the same time, all major political tribes have their rhetoric for rejecting it. Some believe not in egalitarianism, but in meritocracy: inequality that comes from differences in performance, effort and skill is acceptable, inequality that comes from inherited title is not. Others believe in "expertise" and denounce "populism". Years ago, there was an abortive trend to re-embrace credentialism (eg. I remember the attempt to push people to call Jill Biden "Dr. Jill Biden"). And still others don't give a crap about even the pretense of egalitarianism, and seek to build 150-meter statues to ancient Roman and Greek gods and express pride in unbridled domineering masculinity.
I think it is true that some have more expertise than others, and this expertise should be listened to. And even the "second line of defense" comfortable fiction - that people who are higher on some skills and virtues might be lower on other more subtle and immeasurable ones - is on average false. But democratic things are very valuable despite this, for two reasons:
Egalitarianism as a floor, not as an absolute. If you take the above arguments too seriously, you run into the problem that you leave many people with no voice at all. This is a dangerous position: it means that there is no disincentive at all to impose ruinous outcomes on them. Chickens are far stupider than humans. But if I could give each chicken even 0.01 votes on agriculture law, in some way that effectively captures their preferences, would I? Hell yes.
Pluralism. Democratic things (as well as eg. ideas such as free speech) are not just about providing a floor at the bottom, they are also about diversifying the top. A goal is to create space for alternative groups of elites, that are able to challenge existing elites. This is where pluralistic voting models, that focus on finding "consensus across difference" are so valuable: they inherently empower diverse viewpoints, and prevent an intellectual or decision-making ecosystem from being overly dominated by monoculture.
, where I argue that the Gini is a bad inequality index because it ultimately conflates two very different problems (floor too low, top too concentrated), and actually we need to treat both separately.
Also, see also this piece from Ruxandra:
In a secular world, equality is a last attempt to offer some dignity to the weak
AI
The main challenge in building new institutions of any type, is that people are lazy to change their habits. Even existing nation-state voting only survives because (i) it's only one bit of info per four years, and (ii) it has hundreds of years of historical legitimacy.
This makes a lot of work more difficult. For example, an alternative approach to dealing with the chaotic era is to find "islands of stability", and build more holistic institutions at smaller scales, with the goal of copying or adapting them to larger contexts later. The problem is, even there, getting these institutions to succeed enough that others want to copy them takes too long, compared to a fast-moving world. So what do we do?
One benefit of AI is that it potentially allows us to make much higher-bandwidth provision of input literally zero-cost. LLM "shadows" of ourselves, fine-tuned on our corpus of both public and private actions, can make decisions on our behalf.
This opens the door not just to higher-bandwidth feedback with near-100% participation rates (if done as a software default), but also fundamentally new possibilities. For example, a weakness of distributed decision making is that it cannot take into account secret information. This is often a justification for centralizing key decisions. In a chaotic era, the set of such situations is magnified. But LLM shadows of ourselves could make votes based off of private information, thanks to the magic of cryptography.
Conclusions
Today's disillusionment with democratic things is real. But what is also becoming real very rapidly is disillusionment with the alternative, where various groups of elites visibly and openly don't care about the effects of their actions on regular people. Where "you can just do things" slides into "you can just bomb people", or "you can just openly talk proudly about how superintelligent AI you are building will bring unemployment to everyone", or...
And so we need to start the next round of this cycle sooner. It needs to start on realistic principles, learning from the failures of the previous era, but it does need to happen.
Life has one very fundamental property:Â it repeats.
The heart beats. Stops. Beats. Stops. You sleep. You wake. You sleep. You wake. Cells divide, grow, divide again. Neurons fire, rest, fire again.
These repeating, cyclical processes are called oscillations. A system that oscillates is called an oscillator.
The purest form of an oscillator is this: there is a state, the system moves away from that state, then returns, then moves away again. Continuous, regular, periodic. Think of a pendulum: it swings left, comes right, swings left again.
In living systems these kinds of oscillations are everywhere. And this is exactly what Winfree was interested in:Â the clocks inside living things.
2. What Is a Biological Clock?
When we say "clock" we are not talking about anything mechanical. A biological clock is the capacity of a cell or organism to measure time from within.
The classic example: circadian rhythm. "Circa dies" in Latin means "approximately one day." In all mammals, insects, plants â even single-celled organisms â there is an internal cycle of roughly 24 hours. Even without daylight, the body knows when to sleep and when to wake, because a clock is running inside it.
How does this clock work? At its core it is a chemical loop: certain proteins are produced, they accumulate, they suppress their own production, they decrease, they begin to be produced again. This accumulate-suppress-decrease cycle completes itself in roughly 24 hours.
But Winfree was less interested in how the clock works and more interested in this question: What happens when something happens to the clock?
3. Phase: The Clock's Current Position
A clock has an hour hand and a minute hand. You look at them at 3:00 PM and you say "it's 3 PM." But you can say something more fundamental:Â "This clock has completed this much of its cycle."
That ratio â the position within the cycle â is phase (Ï).
Phase is usually expressed between 0 and 1, or between 0° and 360°. Zero is the starting point, 1 or 360° is the end of a full cycle (which is also the beginning of the next one).
Example: In a circadian cycle, if you define sunrise as "phase 0," then sunset is roughly "phase 0.5." Midnight is around "phase 0.75."
Phase sounds abstract but it is actually describing something very concrete:Â "Where in its cycle is this system right now?"
4. Perturbation: What Happens When You Hit the Clock?
Now we reach the interesting part.
You do something to a biological clock from the outside â you give it light, a drug, a signal. This intervention is called a perturbation, roughly meaning a disturbance or a jolt.
What will the clock do after this jolt?
Two possibilities:
Possibility 1:Â The clock is unaffected and continues from where it was.
Possibility 2:Â The clock's phase shifts â its position within the cycle changes.
What actually happens is always the second. And the amount of this phase shift depends on two things:
When the perturbation was applied (the clock's phase at that moment)
How strong the perturbation was (its magnitude)
A simple example: light exposure affects the human circadian clock. If you get light in the early morning, your clock advances (you want to sleep earlier). If you get light late at night, your clock delays (you want to sleep later). If you get light at noon, almost nothing changes. So the same intervention, at different times, produces different effects.
5. The Phase Response Curve: The First Map
Winfree and researchers before him did the following: they applied the same perturbation to a clock at different points in its cycle (at different phases) and measured the phase shift each time.
Then they drew this: horizontal axis â "at which phase was the perturbation applied," vertical axis â "by how much did the phase shift."
This graph is called a Phase Response Curve (PRC).
This curve is like a system's personality â how it reacts if you shout at it, how it reacts if you speak calmly. Different organisms, different clocks, have different phase response curves.
Up to here everything is relatively ordinary biology. Now let us come to Winfree's genuinely revolutionary contribution.
6. Thinking in Two Dimensions: The Surface
The phase response curve had only one variable: the timing of the perturbation. Winfree asked:Â "What if we also vary the strength of the perturbation?"
So now you have two parameters:
When the perturbation was applied (initial phase)
How strong the perturbation was (magnitude)
And for every combination you measured: what did the clock's phase become after the perturbation?
This is a three-dimensional table:
Axis 1: Timing of the perturbation
Axis 2: Magnitude of the perturbation
Axis 3 (result): The resulting phase
When you visualize this three-dimensional table, what emerges is a surface â a geometric object like a mountain range, high in some places, low in others, flat in others.
Winfree examined this surface and noticed something very strange inside it.
7. Phase Singularity: The Place Where the Clock Stops
At one specific point on that surface, something strange happens:Â phase becomes undefined.
What does that mean?
Under normal circumstances, the clock has a phase at every point â it is somewhere in its cycle. But at that special point, after a perturbation applied with a special magnitude at a special time, the clock is... nowhere. It cannot be assigned to any phase in its cycle. Mathematically, it has no phase value.
Winfree called this a phase singularity.
To understand it, think of it this way: a normal compass always points in some direction â north, south, east, west, or somewhere in between. But if you stand at the exact north pole, the compass cannot point in any direction. Every direction is simultaneously "north." Direction is undefined. A phase singularity is exactly this â the polar point of the clock in time-space.
What does this mean in practice? When you apply that specific perturbation, the clock resets. The cycle stops or restarts randomly. The biological rhythm collapses.
This is not merely a theoretical curiosity. Winfree proposed that this singularity is directly connected to cardiac arrhythmias. If the heart's electrical system receives a signal at the wrong time, at the wrong strength â landing exactly on the singularity point â the heart loses its normal rhythm. Fibrillation begins. This can be fatal.
8. Topology: Thinking Through Shape
Now let us understand why Winfree used topology.
Topology is a branch of geometry, but it is not concerned with exact measurements of shapes â it is concerned with their general structure. A sphere and a cube are topologically different in some respects, but more importantly: a sphere and a torus (a donut shape) are topologically different because the torus has a hole through its middle and the sphere does not.
The question in topology is: "Can this surface be transformed into that one without tearing or puncturing it?"
Because both the "initial phase" axis and the "resulting phase" axis are cyclical â when they reach 360° they loop back to the beginning, just like a clock going from 12 back to 1. A surface formed by two cyclical axes is mathematically a torus.
And what Winfree demonstrated is this: the phase singularity on this torus is necessary â it is a topological requirement. You cannot remove the singularity without tearing the surface. This is a truth that cannot be seen through differential equations alone, but only through topology.
9. The Experimental Object: Drosophila
Winfree tested all of this theoretical framework primarily on Drosophila melanogaster â the common fruit fly.
Why the fruit fly? Because:
It reproduces fast, with a very short generation time
Its genetics are well understood
Its circadian clock is strong and measurable: the transition from pupa to adult (eclosion) happens at specific hours, and this reveals the clock's phase
Winfree ran hundreds of experiments: he delivered light pulses at different moments, of different durations, and measured how much the fly's eclosion rhythm shifted. He converted this data into the three-dimensional surface. And he found the singularity.
10. Other Systems: A Universal Framework
Winfree's claim was not limited to fruit flies. He showed that the same mathematical framework applies to these systems too:
The Belousov-Zhabotinsky reaction:Â A chemical oscillator. When certain chemicals are mixed together, the solution begins to change color â blue, colorless, blue, colorless â at regular intervals. Not alive, but oscillating. Winfree found the phase singularity in this chemical clock as well.
Slime mold aggregation:Â A single-celled organism called Dictyostelium, during periods of starvation, begins to gather together. This gathering spreads in waves, and these waves point to an underlying oscillating system.
Cardiac arrhythmias:Â The heart is an oscillator with its own electrical cycle. Winfree proposed that the singularity concept could explain ventricular fibrillation â and in the following decades this prediction was largely confirmed.
11. The Time Crystal: The Most Abstract Concept
Now we come to the most poetic and abstract concept.
What is a spatial crystal? It is the arrangement of atoms or molecules in space in a periodic (regularly repeating) pattern. A salt crystal: sodium and chlorine atoms repeat at fixed intervals. This repetition takes place in space.
Winfree asked: instead of a structure that repeats in space, could there be a structure that repeats in time? The temporal equivalent of periodic spatial symmetry?
And his answer was: yes, and its name is a time crystal.
But note carefully: Winfree's time crystal is not a concrete physical object. It is the toroidal phase-response surface itself â a structure that is periodic in time, geometrically regular, existing not in space but along the dimension of time.
Frank Wilczek independently rediscovered this concept in 2012 (and received the Nobel Prize in 2022 for related work). Winfree had put forward the same idea decades earlier, in a different context, to far less notice.
12. About the Book Itself
The book was published in 1980. Computers were still very primitive then â some figures are hand-drawn, others are early computer printouts. This mixed appearance gives the book a strange but sincere character.
Winfree is unusually candid about uncertainty. He writes sentences like "this is still not understood" and "this is speculation rather than conclusion." Most science books try to project an air of certainty; this book does the opposite.
It needs to be read slowly because each chapter builds on the previous one and the concepts are cumulative.
Summary: How Everything Connects
Living systems contain cyclical processes â Every moment of these cycles is defined by a PHASE â External intervention (perturbation) shifts the phase â Mapping perturbations at different times and strengths produces a SURFACE â This surface has a TOROIDAL (donut-shaped) structure â On this surface, a PHASE SINGULARITY necessarily exists â At that point the clock resets â rhythm collapses â This entire structure, as an object periodic in time, is called a TIME CRYSTAL
In the next lesson we can go deeper into any point you like â topology, phase response curves, or the connection to cardiac arrhythmias.
Rainbow body
The rainbow body phenomenon is a third person perspective of someone else attaining complete knowledge⊠The attainment of the rainbow body is typically accompanied by the appearance of lights and rainbows around the body. < wiki >
(via @tinyrainboot)
Arthur T. Winfree â The Geometry of Biological Time (1980, Springer-Verlag)
Winfree was a theoretical biologist working at the intersection of mathematics and living systems. This book is his attempt to describe what he called biological clocks â the oscillating processes that govern circadian rhythms, heartbeats, cell division, and neural firing â not through differential equations alone, but through topology: the geometry of continuous mappings, phase spaces, and singularities.
The central concept is phase (Ï): the position of an oscillator within its cycle at any given moment. When you perturb a biological oscillator â hit it with a pulse of light, a drug, a stimulus â its phase shifts. Winfree's core insight is that if you map stimulus magnitude against timing across the full parameter space, you get a surface. And that surface, under certain conditions, contains a phase singularity: a point where phase becomes undefined, where the clock is effectively reset to nothing.
The fruitfly (Drosophila) circadian clock is his primary experimental object, but the framework reaches toward cardiac arrhythmias, slime mold aggregation, and chemical oscillators like the Belousov-Zhabotinsky reaction.
The term time crystal as it appears here â decades before Wilczek's 2012 paper â refers to a structure that is periodic in time the way a spatial crystal is periodic in space. Winfree's "time crystal" is the toroidal phase-response surface itself: a repeating geometric object defined by temporal, not spatial, symmetry.
The book is dense and idiosyncratic, written with unusual candor about uncertainty and with hand-drawn figures alongside early computer printouts. It rewards slow reading.
< https://www.scribd.com/document/437275853/Arthur-T-Winfree-The-Geometry-of-Biological-Time-pdf?doc_id=437275853&download=true&order=690071448 >
Louis de Broglie < https://en.wikipedia.org/wiki/Louis_de_Broglie#Conjecture_of_an_internal_clock_of_the_electron >
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