31
Convergence
Stimpunks × More Realms · Zine No. 31

Five Times a Crab,
Seven Times Not

convergence, attractors, and the ones who crawled back out of the valley


L★S
Love You Down
To Your Star Stuff
· open edition ·
The pattern

Everything keeps
becoming a crab


Give the ocean enough time and it keeps arriving at the same animal.

A wide flattened shell, a tail tucked under, legs out to the sides. Crustaceans have found that body over and over, from ancestors that looked nothing like each other and were never trying to match. The zoologist L. A. Borradaile named it in 1916 — carcinization, which he called one of the many attempts of Nature to evolve a crab.

It happened at least five times: once or twice among the true crabs, and at least three times among the false ones — porcelain crabs, hairy stone crabs, king crabs. King crabs are not crabs. They came up out of hermit crabs and arrived at the shape anyway.

And it isn't only crabs. Camera eyes evolved separately in us and in octopuses. Echolocation in bats and in whales. Flight in insects, pterosaurs, birds, bats. Convergence is real. We're not here to debunk it — it's one of the most striking things biology has found.

We're here for what happens next, when a real pattern gets read as a verdict.

five separate arrivals, one silhouette spongecrabs eubrachy-urans porcelaincrabs hairy stonecrabs kingcrabs nobody was copying anybody

carcinization · borradaile 1916
at least five times over

The part nobody quotes

And lost
seven times


The crab body plan was gained at least five times. It was lost at least seven.

Biologists have a word for that too: decarcinization. Wolfe, Luque and Bracken-Grissom, reviewing the whole field in 2021, count the losses as well as the gains — and add that there were likely several other losses besides, among fossil and living lineages both.

Read the tally again, because the headline never does. Leaving the crab form is the more common event. Lineages roll down into that valley and then climb back out of it, over and over, across hundreds of millions of years.

Which settles something. If the crab were the answer — the optimum, the ultimate form, the place complexity is trying to get to — then nothing would ever leave. Things leave constantly.

≥ 5
times gained
carcinization
≥ 7
times lost
decarcinization
A basin is not a destiny. It is just the shape of the ground you happen to be standing on.
into the form, and back out of it 5 became 7 stopped leaving is the commoner event

wolfe, luque & bracken-grissom 2021
the losses outnumber the gains

Inside the basin

Convergence is
not sameness


Here is the thing the word "converge" hides. They did not end up alike.

Crab-shaped lineages live in nearly every habitat on Earth — bright coral reefs, sealed marine caves, abyssal plain, mountain streams, dry land. Their bodies run from millimetres to metres. Reviewing that range, Wolfe and colleagues reach for Darwin's last line in the Origin and call it endless forms most beautiful.

So five lineages converged on a description — wide, flat, tucked — and then diversified wildly inside it. The attractor isn't a point. It's a neighbourhood, roomy enough to hold a pea-sized cave dweller and a metre-wide giant and count both as the same solution.

We already know this shape of argument. Sharing a category never made anyone identical, and the spiky profile survives the merge. Two rivers meeting run braided for miles.

Arriving at the same name is not arriving at the same shape.
one basin · millimetres to metres marine cave coral reef abyssal plain same solution · endless forms

the attractor is a neighbourhood
not a point

The route

Same window,
different wiring


Our eye and the octopus's eye are the showpiece of convergence: lens, iris, retina, a chamber that throws an image. Built independently. Built backwards from each other.

In our retina the light-sensing cells face away from the light, and their nerve fibres run back across the retina's inner surface and bundle out through it — which punches a hole in our field of view. You have a blind spot because of how yours is wired.

The octopus's photoreceptors face the light, and the nerves leave from behind. No hole.

Same outcome. Opposite construction. The function converged; the machinery never did.

Now say it about people. A system that grades the route instead of the outcome will mark a different route wrong — and a body that got there another way looks like a malfunction rather than an eye.

two camera eyes, wired opposite vertebrate nerves cross the retina → a blind spot octopus nerves leave from behind → no blind spot the outcome matched the route never did grade the route and you'll fail an eye

convergent function, divergent build
ours is the one with the hole in it

The terrain

The valley,
not the virtue


Why does anything converge? Because the ground slopes.

The embryologist C. H. Waddington drew the picture in 1957: development as a ball rolling down a landscape of branching valleys, its path canalized — a word he'd coined in 1942 — by the shape of the terrain rather than aimed at a target. Deep valley, reliable outcome. Same ball, different landscape, different animal.

"Attractor" is a real term, borrowed here. It comes from dynamical systems — Lorenz found his in 1963 — where it means a state a system settles toward. Applied to evolution or to culture it is a metaphor, a good one, doing analogical work. We should say that out loud, because the metaphor is what makes the overreach feel rigorous.

And the honest state of the flagship case: reviewing all of it, Wolfe and colleagues report that the reasons for the repeated evolution of the crab-like body plan remain a mystery. They add that nobody yet knows whether it's true convergence or a shared inheritance being switched back on.

So the crab is not a proven optimum. It's a place the ground happens to slope toward, for reasons still being worked out. Convergence is evidence about terrain — the constraints, the pressures, the materials at hand — and not about the merit of whatever lands in the bottom.

waddington's landscape the slope decides, not the destination

canalization · waddington 1942, 1957
a valley is not a verdict

Ripeness

Ideas ripen
too


Discovery converges the same way bodies do, and for the same reason.

Newton had calculus by about 1666; Leibniz built it independently in the 1670s, and they spent years fighting about it. That story gets told as an anomaly. It isn't one. In 1922 Ogburn and Thomas assembled a list of 148 inventions and discoveries made independently by two or more people — sunspots four times over in 1611, conservation of energy four times in 1847, the telescope claimed by nine. Reviewing the same phenomenon decades later, Robert K. Merton concluded that these "multiples" are the dominant pattern in science, and the lone singleton the exception.

It's faster now. In November 2022 Terence Tao logged what he called maths at internet speed: Justin Gilmer posted a breakthrough on the union-closed sets conjecture on the 16th, Gil Kalai blogged it the next day, and four days after that three independent groups had sharpened the same argument to the same constant.

Ripeness is not inevitability, though. In 2025 Hannah Cairo, then 17, disproved the Mizohata–Takeuchi conjecture — roughly four decades of people trying to prove it, undone by one person going a different way. The field was ready. It still took her.

There is a name for what ripens, and it isn't the individual. In the mid-1990s Brian Eno — fed up with the art-history idea of genius, where gifted individuals turn up out of nowhere to light the way for the rest of us — coined scenius. In his own words it "means ‘the intelligence and intuition of a whole cultural scene’. It is the communal form of the concept of genius." He set it against the "Big Man" theory of history, and preferred a world constantly remade by all its inhabitants — a cooperative enterprise. His own list of scenius moments runs through Dada, the American experimental music scene, and punk, 1975–8.

Eno then guards the flank we would guard. He says plainly that it would be foolish to pretend everyone's contribution is therefore equal, and he would never claim it. Scenius doesn't dissolve the person who did the work — it moves the unit, from the lone mind to the scene that made the answer findable. Which is why the credit lands on whoever published on Thursday, and why Thursday was never the interesting question.

parallel arrivals NewtonLeibniz Gilmer3 groups calculus 1660s–70s same bound 5 days 148 documented multiples · ogburn & thomas 1922 what makes a scene ripe mutual appreciation rapid exchange of tools & techniques network effects of success local tolerance for novelties kevin kelly, after eno · all four are environmental

multiples are the rule, not the anomaly
a scene, not a singleton

The turn

An attractor is
not a mandate


In the ocean, the crab basin permits everyone who never rolls into it.

Most decapods are not crab-shaped. Shrimp, prawns, lobsters, crayfish — millions of individuals living entire successful lives outside the famous attractor, and nothing in the water enforces anything. The slope is just a slope. Non-crabs are not failed crabs; the category doesn't exist.

Engineered systems are different, and this is where the metaphor stops being charming. In a designed system, somebody picks the slope.

Every platform converged on short vertical video. Not because that is the optimum of human expression — because engagement was chosen as the objective, and everything downhill of that objective rolled to the same place. The convergence is real, and it is also somebody's decision, and the two facts are usually presented as one.

School does it more bluntly: one route to the answer, one pace, one accepted way of showing your work. Then the other routes — the ones that arrive by a different wiring and get there fine — collect a diagnosis. That isn't the terrain sloping. That's a wall, and someone poured it.

This is the Cavendish banana: uniform, efficient, one blight from collapse. The answer is Cavendish Space — environments built for caves and campfires and watering holes, for dandelions and tulips and orchids. Deliberately re-graded ground.

In Stimpunks' ARLES terms, this zine lives at the top two rungs — Environment and Systems. Change the terrain and the attractors move. They always did.

If it's not working, it's not the person. It's the environment, the relationships, or the system. — Stimpunks · ARLES
a slope, and a wall found terrain the ones who never rolled in are fine poured terrain the ones who don't get a diagnosis nature permits · institutions require someone chose the second slope · it can be re-poured

arles · environment & systems
change the terrain, not the person

The live argument

Gould's tape,
Conway Morris's constraint


Biologists have not settled this, and we should not pretend otherwise.

Stephen Jay Gould, in Wonderful Life (1989), argued that history is contingent: rewind the tape of life, play it again, and you get something else. We are here by accident, not by arrival.

Simon Conway Morris, in Life's Solution (2003), argued the opposite from the same evidence: convergence is everywhere, the channels are narrow, and outcomes — up to and including intelligence — are close to inevitable.

It's a genuine disagreement between serious people, and this zine does not resolve it. Both readings are compatible with five crabs and seven un-crabbings.

What we refuse is the thing that gets smuggled in when the second is read loosely: that because a form recurs, it is the form things ought to take. Convergence is a description of what happened. It licenses nothing about who belongs.

replay the tape Gould 1989 different every time Conway Morris 2003 the same, near enough unresolved — and either way, recurrence is not permission

a rhyme, not a proof
we are not settling this here

Held with care

What we are
not saying


Convergence is a beautiful finding sitting one inch from an ugly argument. Here is the inch.

Notconverge or lose. Most decapods aren't crabs and are doing fine. A shape that recurs is not a shape that's required.
Notoptimality. The reasons for the crab's recurrence remain a mystery in the literature, and it's been abandoned more often than adopted. "Recurring" and "best" are different words.
Notone right shape. The basin holds millimetres to metres, reef to abyss. Convergence never produced sameness, and belonging doesn't either.
Notbiology proving a politics. A rhyme, not a proof. That a pattern recurs in nature says nothing about what we owe each other — deriving an ought from an is is a fallacy we'd rather name than commit.
Not"you're a crab too." Belonging that requires you to have arrived at the same form isn't belonging. It's a membership test with better manners.
Nota counsel of despair about design. Attractors move when terrain changes. That's the whole reason to bother building anything.
the same forms, arranged two ways not a ladder one level different sizes, same standing no ticks · no crosses · no rungs variation is a spread, not an order

a spread, not an order
the universe doesn't pathologize its own variation

Closer to home

Ours was a
multiple too


The word you are reading this collection through is itself a case of ripeness.

"Neurodiversity" is not one person's coinage. Following Botha, Chapman, Giwa Onaiwu, Kapp, Stannard Ashley and Walker (Autism, 2024), "neurological diversity" and "neurodiversity" reached print in 1997 and 1998 through the journalist Harvey Blume — who attributed them to the online Autistic community — and the concept and its theory were developed collectively by neurodivergent people.

The terrain was ready. Jim Sinclair's "Don't Mourn For Us" (1993) and Autism Network International had done the ground work. Martijn Dekker's InLv list opened in 1996 and gave a scattered community one room. Kassiane Asasumasu coined neurodivergent in 2000. Nick Walker named the paradigm and the pathology paradigm it replaces.

Several people, arriving at the same words at nearly the same time, under a shared pressure none of them chose — and the pressure was the thing worth naming. That is a multiple, in our own history, about our own lives.

So both facts sit together, and neither cancels the other. Convergence happens. And nobody has to be a crab.

Five times into the valley. Seven times back out. The ground is ours to re-grade, and it always was.
a word arriving collectively neurodiversity inlv 1996 · print 1997–98 · developed collectively no single author · botha et al. 2024

ripeness, in our own history
a community is a terrain too

L★S Five times into the valley. Seven times back out. Nobody has to be a crab.
No. 8 The Universe Runs on Difference — monoculture, Cavendish Space & ethodiversity
No. 9 The Lines We Drew — the invention of "normal" & the constructed line
No. 27 Every Nervous System — more-than-human neurodiversity & reclaiming animality
No. 29 Only in Relation — relational quantum physics, double empathy & ARLES
No. 30 Always Migrating — migration, monotropism & the galaxy you're made of
No. 31 Five Times a Crab, Seven Times Not — convergence, attractors & terrain ← you are here
A thread to follow

Where has someone graded your route instead of your outcome?

Which slope in your day was found, and which one was poured — and by whom?

If you could re-grade one piece of ground so the shapes it produces change, which piece?

Five Times a Crab, Seven Times Not is Zine No. 31 in the Stimpunks Star Stuff series. It was written after Brett D. Wick's essay When Everything Becomes a Crab: The Strange Phenomenon of Convergent Evolution in Nature, Mathematics, and Human Systems (Washington University in St. Louis, 2026), which supplied the frame — convergence as attractors in possibility space, across biology, mathematics and technology — and the mathematical cases. Wick is not part of this collaboration and this reading is not his; the turn the zine makes, and the three findings it turns on, come from the primary crab literature rather than from the essay. A companion to The Universe Runs on Difference (8), The Lines We Drew (9), Every Nervous System (27) and Only in Relation (29).

Sources & notes. Wolfe, J. M., Luque, J. & Bracken-Grissom, H. D. (2021). How to become a crab: Phenotypic constraints on a recurring body plan. BioEssays, 43(5), 2100020 — read in the primary; source of the counts (carcinization "has evolved at least five times, and has been lost at least seven times," with likely further losses), of the statement that the reasons "remain a mystery," of the unresolved parallelism-versus-convergence question, and of the habitat and millimetre-to-metre range. "Endless forms most beautiful" is Darwin's closing line in On the Origin of Species (1859), which Wolfe and colleagues borrow. Borradaile, L. A. (1916) coined carcinization. Waddington, C. H. (1942). Canalization of development and the inheritance of acquired characters. Nature, 150, 563–565; and The Strategy of the Genes (1957), where the epigenetic landscape appears. Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130–141 — the attractor as a term of art. Ogburn, W. F. & Thomas, D. (1922). Are inventions inevitable? A note on social evolution. Political Science Quarterly, 37(1), 83–98 — the 148 multiples. Merton, R. K. (1961). Singletons and multiples in scientific discovery. Proceedings of the American Philosophical Society, 105(5), 470–486. Scenius is Brian Eno's, coined in the mid-1990s and set down in A Year with Swollen Appendices (Faber, 1996) in a letter to Dave Stewart among the appendices — quoted here from that primary, along with the “Big Man” theory of history, the cooperative-enterprise passage, his list of scenius moments (Russia 1905–15, Dada, the American experimental music scene, the Anglo-American psychedelic sixties, punk 1975–8), and his own caveat that it would be stupid to pretend everyone's contribution is therefore equal. A note on the wording: the version of the definition in wide circulation — “Scenius stands for the intelligence and the intuition of a whole cultural scene. It is the communal form of the concept of the genius” — is not what the book says. It entered circulation through Kevin Kelly's “Scenius, or Communal Genius” (The Technium, 10 June 2008), which presents it as Eno's exact words; Eno's actual text reads “it means ‘the intelligence and intuition of a whole cultural scene’. It is the communal form of the concept of genius.” We follow the book. Kelly's four conditions for a ripe scene — mutual appreciation, rapid exchange of tools and techniques, network effects of success, local tolerance for novelties — are Kelly's own, from the same post, and are the reason he is credited on the figure. Tao, T. — "Maths at internet speed," Mathstodon, 23 November 2022, on Gilmer's union-closed sets bound of 16 November and its sharpening by three independent groups within five days. Cairo, H. (2025). A counterexample to the Mizohata–Takeuchi conjecture. arXiv:2502.06137. Gould, S. J. (1989). Wonderful Life. Conway Morris, S. (2003). Life's Solution: Inevitable Humans in a Lonely Universe. On the eyes: cephalopod retinas are everted, with photoreceptors facing the light and axons exiting behind, so there is no blind spot; vertebrate retinas are inverted, which is why ours has one. Botha, M., Chapman, R., Giwa Onaiwu, M., Kapp, S. K., Stannard Ashley, A. & Walker, N. (2024). The neurodiversity concept was developed collectively: An overdue correction on the origins of neurodiversity theory. Autism, 28(6), 1591–1594. Sinclair, J. (1993). Don't Mourn For Us. InLv — Independent Living on the Autistic Spectrum, founded by Martijn Dekker, 1996. Neurodivergent is Kassiane Asasumasu's (2000). Cavendish Space and ARLES — Stimpunks glossary.

Held honestly. Carcinization and its losses are counted from the phylogenetic literature and are stated there as minima, on a working hypothesis the authors flag as one possible path of character evolution rather than the settled one. "Attractor" is borrowed from dynamical systems and used here analogically; Waddington's landscape is a picture, not a mechanism. Gould and Conway Morris disagree and we have not resolved them. Most importantly: none of this makes the ethics true. That variation recurs in nature is not why difference deserves welcome — difference would deserve welcome in a universe that made only one shape. As about.html puts it, we are noticing a rhyme, not collecting a proof.

The star stuff is Carl Sagan's, and the SN 1006 remnant on every Stimpunks page. The universe doesn't pathologize its own variation. It just keeps making shapes, and letting them go.