Tessellations for the End of History

I have long been fascinated by tessellations as metaphors for ways of knowing about and being in the world. A set of prototiles that can cover a world in an exhaustive and mutually exclusive way constitutes something like a theory of that world. The rules of the tiling are the rules of the world. The set of prototiles is the ontology underlying the theory. The size of that set is a measure of the efficiency of your understanding. Recognitions of repeating patterns in the emergent tiling are understandings of specific aspects of the phenomenology of the world. Actually creating a specific tiling by placing tiles on a smooth surface, to create navigable striations, is the praxis of the way of knowing.

To state it in terms of my new favorite frame, tessellations are something like metaphors for protocols of knowing and being. Given the right set of tiles, you can know the world and be in it, in a powerful way. Perhaps this is one way to understand the story of Robert Moses, architect of New York. He tessellated his world with tiles of his choosing.

Ideally, you want the richest, most complex tiling possible to cover a “blank” world, such as the 2d Euclidean plane, to maximally reveal the possibilities latent within it. Yes, you can cover the Euclidean plane with a boring regular grid of square tiles, but you can also cover it with strange aperiodic tilings, and in some ways, the latter constitute a truer “theory of the plane.” The intuitively appealing principle that you should look for the richest possible tessellation is a kind of dual to Occam’s razor. Instead of choosing the simplest explanation that covers a given world of facts, you choose the covering that produces the most complex world of facts. Ideally, the maximally complex set of facts. Instead of solving for explanatory parsimony, you solve for generative profligacy.

One proxy for such maximality is Turing-completeness, and at least some (all?) aperiodic tilings, like Wang tilings, are known to be Turing complete. Jed Yang published a PhD thesis in 2013 about the computational aspects of tessellations, and also connected tiling-based computation to Turing-complete cellular automata, such as Wolfram’s Rule 110. Googling around, I also found this fascinating presentation by Kathleen Lindsay about playing Conway’s Game of Life on an aperiodic tiling. It seems like tilings and cellular automata are equivalent ways of understanding universal computation, and at least to me, these spatial processes seem more intuitively appealing than infinite tape machines or the lambda calculus. And of the two, I think I prefer tessellations over automata, since the computational process is embedded in the texture of the space itself, as opposed to a 0/1 switching process playing out on it.

As you may have guessed, aperiodic tessellations have been on my mind lately because last week the first aperiodic monotile, the “hat” (an “Einstein” tile, named for the German ein stein, or one stone, rather than the physicist) was discovered. It is not quite a monotile since you have to use it along with its mirror image to aperiodically tile the plane (the blue vs. yellow instances in the picture below), but still, this is a fascinating leap. The last best attempt, the class of two-tile solutions known as Penrose tiles, seemed like the End of History of Tessellations to me, but apparently we had a chapter left. I suspect this is the end though. I somehow doubt we’ll get it down to a single kind of tile without the mirroring cheat (I wonder if anyone has proved that a single tile, without mirroring, cannot tile the plane aperiodically).

Aperiodic tiling with the hat, credit: Gringer, Wikimedia Commons CC-BY-SA 4.0

Recreational mathematicians are going a bit nuts with this discovery, and I’m 3d-printing a set to play with (I’m using this model) as we speak.

I’m especially intrigued by the idea of painted kites. The hat can be decomposed into 8 kite shapes that can be “decorated” in a way that the resulting hat tilings create strange aperiodic maps. These feel exciting in the same way the original pictures of the Mandelbrot set felt exciting in the 1980s. Unfortunately, my 3d printer is single-nozzle, so I can’t print these easily.

Credit: Galaxy Map account on Twitter.

While I’m nerdsniped by these tilings and painted tilings, I’m not enough of a mathematician to truly explore them in any technically deep way. But I suspect that after the late J. G. Ballard, whose complete short stories I just finished, I’m quite possibly the person who has spent the most time thinking about tessellations as world-narrative metaphors, so let me talk about that instead.

The goal: get to post-Ballardian ways of thinking about our End of History condition, via aperiodic tessellations (plus noise).

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Report Cards

As a kid, through most of middle and high school, I got good grades. I stayed comfortably near the top of the class without working too hard, and more importantly, without explicitly aiming to be there. I got good grades not because I “studied” conscientiously, but because I enjoyed most subjects enough that chaotic nerd energy was more than enough to coast near the top. That easy ride ended in college where that kind of marginal focus on grades was only enough to put me somewhere in the middle of the more gifted peer group. I didn’t work any harder, but I didn’t get as unreasonably rewarded for it.

But my lazy, easy ride through grade school had already made me relatively immune to validation from grades. I had become incapable of working with any sort of discipline towards good grades. I had neither contempt nor respect for good grades. I was just indifferent to them, and addicted to the less legible fruits of nerding out. I was only motivated to do well enough that grades would never get in the way of things I wanted to do (now you know where my philosophy of mediocrity comes from). I neither tried to get straight-As, nor chafed against expectations of getting good grades. I neither disappointed my parents, nor made them exceptionally proud. Possibly because I was neither the sort of straight-A’s talent who is actually in the running for racks of prizes, nor the sort of maverick intelligence that schools are particularly good at detecting and destroying with extreme prejudice. I was the sort of kid who is not just indifferent to schooling, but the sort of kid schools are indifferent to. We’re neither good enough, nor bad enough, to be worth exceptional attention. I passed through the educational system like an unexceptional neutrino, all the way through to a respectable PhD.

Which isn’t to say I didn’t work hard at my learning at all. I just worked hard in the sense of nerding out over topics that I actually enjoyed, mostly by reading far beyond and outside of the syllabus on topics I got nerdsniped by, so that I learned what was in the syllabus almost in passing. I almost never encountered a subject I couldn’t get nerdsniped by. In college and grad school, this pattern mostly continued, though I of course discovered more subjects I had very little aptitude for and didn’t get nerdsniped by. I eventually got promoted to the level of my academic mediocrity, never having learned to work hard for grades along the way. This feels a bit tragic to me now.

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Summer of Protocols

A quick post about a thing I’m up to. This summer, I’ll be running a program called the Summer of Protocols (SoP) that will fund a bunch of full-time and part-time researchers to think broadly about, tinker with, and write about protocols. The scope is broad. Everything from climate and cultural protocols to TCP/IP and blockchains is in scope, and we’ll be focusing on both technology and science/humanities aspects of protocols. If you think you might be a fit for the program, consider applying. Here is a twitter thread with more details. We’re holding a Zoom town hall where you can learn more and ask questions on Friday, March 10th, 1530 UTC.

The program is funded by the Ethereum Foundation, and the goal is to connect the conversations around protocols that happen in the crypto world to similar conversations in other places.

The program grew out of a pilot project I led over the last 3 months, on the foundations of protocols. My collaborators and I just released a draft of the pilot study, The Unreasonable Sufficiency of Protocols, meant to prime the pump for the SoP. So if you’re interested, I recommend reading that. I also just went on a podcast to talk about the SoP that you may like.


I can’t remember where I read the theory, but apparently the salinity of our bodies matches that of primordial seas, so in a sense we never really left the oceans. Our micro-organic aquatic ancestors simply constructed meatbag spaceships with artificial life-support aquatic environments inside to explore beyond their oceanic home world. Much as we might construct generation starships in the future to travel to Alpha Centauri. Air-breathing multi-cellular life forms constitute the space program of primordial single-celled life. They get the missing resources of their primordial environment through clever artificial means, just as we might eventually mine our essential minerals from asteroids or gas clouds we fly by in outer space.

One of the effects of this evolutionary history is that all air-breathing life has to seek out perhaps the most important chemical that’s ubiquitous in the oceans but not trivial to find on land: salt. Salt-seeking is one of the most fundamental behaviors of terrestrial life. Animals in the wild seek out salt licks even at great risk of predation. Humans with salt deficiencies have serious problems, and beyond a point of salt deprivation, you die.

Giraffe and wildebeest at an artificial salt lick in the Pilanesberg Game Reserve, South Africa
(NJR ZA, Wikimedia Commons, CC-BY-SA 3.0)

This evolutionary history struck me as an interesting metaphor, and a superior alternative to the more familiar metaphor of “coming up for air.”

Oxygen, whether extracted from the air or water, is critical on very short time-scales, even by the standards of the lifespans of micro-organisms. You die in minutes without it. So the idea that you might be so swamped by work that you need to “come up for air” is evocative but not quite coherent. I can think of coming up for other kinds of macro-nutrients like water and food at the time scales of uninterrupted work (hours/days) but not air. If you’ve ever actually had to “come up for air” (I did a couple of times as a kid while learning to swim) you know it’s not some sort of restorative break. It’s a panic-inducing emergency of a sort that is not metaphorically like anything else.

But salt-seeking… now that’s an interesting metaphor that operates on a whole different time-scale. If you don’t lose any salt to perspiration, you can go without salt intake for days to weeks (it’s not so much a consumable nutrient as a sort of electrolyte concentration thing I guess).

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Bracketverse — I

The planet Kinsoro, in a star system on the edge of the Bracket nebula, had a strange climate marked by long alternating periods of wonderful and terrible climates. Each phase of the climatic cycle (whose origins were mysterious) lasted approximately 120 Earth years. The strange climate had given rise to an equally strange ecology early in the planet’s history: The more complex species were all polymorphic, typically existing in two forms adapted to the two regimes (and occasionally as many as six, adapted to minor climate epicycles). The dominant species, the Kinsorans, existed in two adult forms, which Kinsoran biologists called the S-type and the I-type. The two types had clear but minor physical differences, but more importantly, dramatically different behavioral and cognitive dispositions. While both types could survive both climates, the S-type flourished in the wonderful half-cycles, while the I-types flourished during the terrible half-cycles.

Kinsoran biologists calculated that the environmental variation ought to lead to a slow 240-year limit cycle in the S/I ratio between 80:20 and 20:80, but in practice the ratio showed much more extreme variation: swinging between 99:1 to 1:99. The reason was not hard to discover; during each half-cycle, the dominant type would violent repress and slaughter the subordinate type to near-extinction.

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2022 Ribbonfarm Extended Universe Roundup

This entry is part 16 of 17 in the series Annual Roundups

Somehow, I feel lowkey cheerful looking back at 2022. It feels like I hit an inflection point in the 15-year history of this blog, after 2-3 years of steadily letting go old ways and wandering in the desert. It feels like I am finally developing some interesting momentum in a new Act 2 direction that is a definite break from the past without being a rejection of it. I’m still muddling through, but now it is decisive muddling through. I think I let the somewhat frenzied experimentation of the peak pandemic years (2020-21) quiet down, and got some thorough reflecting, consolidating, and stock-taking done. Introspection that I hope will pay off in the next decade.

On to the extended universe roundup, featuring blog, newsletter, books, and a few more odds and ends. But first, a reintroduction.

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This entry is part 15 of 15 in the series Psychohistory

A counter-intuitive feature of wind power is that it is usable regardless of the direction the wind is blowing, so long as it is sufficiently steady and you have the right technology. A windmill that can pivot, or a sailboat, can make use of any kind of steady wind. A sailboat can sail in any direction relative to the wind, though it may have to to tack or jibe to do so. But if there’s no wind, the sails are useless. You have to row or burn fuel.

The metaphor of a steady wind is more expressive than that of a rising tide. A rising tide floats all boats, but all go in only one direction: up. By contrast, a steady wind eases all journeys, regardless of direction. Imagine a cluster of sailboats huddled together in a windless doldrums. Once a wind starts blowing, all can start moving. And if they’re all headed to different places, they will start moving apart. The little boat cluster will experience expansion.

Imagine a steady wind blowing across an infinite two-dimensional ocean, a worldwind. The little boat universe on it will experience expansion.

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The Art of Gig Books

My 2-volume collection of essays about independent consulting and life in the gig economy, The Art of Gig, is finally out. It is available in paperback and Kindle ebook form on Amazon.

For those of you who have no idea what this is about, between 2019-21 I wrote a limited-run Substack newsletter on the indie consulting life and the gig economy. About 2/3 of the newsletter issues were non-fiction essays. These are compiled into the two volumes above. All the essays have been carefully edited, updated, grouped into hopefully useful sections, and sequenced. The material flows surprisingly smoothly, if I do say so myself. The images and diagrams have been up-res’d, updated, and in some cases, entirely redrawn for the books.

As the subtitles suggest, Volume 1 establishes some foundational ideas, and Volume 2 builds on those foundations. Both volumes are at a roughly intermediate level of sophistication, and should be accessible to anyone with at least a year or two of work experience. If you’re in the gig economy, are considering diving into it, or have been unceremoniously tossed into it by layoffs and such, I suspect these volumes might be useful to you. They should also be valuable to recent graduates thinking about alternatives to traditional career paths, though I suspect the material will be harder to grok without at least a little work experience under your belt.

Since we’re just heading into the holiday season, you might want to consider gifting these books to any friends and family members who need a bit of a kick in the pants to think more creatively about their careers.

This is my first foray into print since Tempo 11 years ago, and it took quite a bit of effort to get the paperbacks done (it’s like 3x more work than ebooks alone). So everybody who’s been bugging me to do print editions of my books had better buy them. If this works out well, I might consider going back and doing print editions of my older ebook-only volumes.

Thanks to my collaborator, publishing veteran Jenna Dixon, I think both the ebook and print volumes turned out beautifully. Grace Witherell, my long-time artist collaborator, made the covers. I think she nailed the Sun Tzu Art of War homage I was going for perfectly. And huge thanks to the ~4k readers of the original newsletter. I’m not great at just going off by myself to write book-length things. I need weekly doses of validation to write, and the newsletter subscribers provided that in spades. The concluding section of Volume 2 has 3 chapters worth of Q&A, and I’ll be sending out complimentary copies of the books to people whose questions are featured.

Here’s the link to the page with both formats of both volumes again: The Art of Gig. The Kindle editions are $9.99 and the paperbacks are $18.95 each.

I’ll get around to making these available via more distribution channels eventually (non-Amazon paperback distribution, other e-readers). The Kindle versions should be available worldwide, but the paperbacks will currently only be available in markets where Amazon has print-on-demand fulfillment going.

Boosting, reviews, sharing on email lists etc. would be much appreciated. If you host a podcast on themes related to the books (gig economy, free agency, consulting, creator economy etc. etc.) I am happy to come on to shamelessly shill them, and talk shop. At least until I run out of social energy. Depending on timing/location, I may also be able to take on speaking gigs based on the books.

Many people have asked, but I currently have no plans to convert the material into an online course. But I might make a video or something. Or at least a nice slide deck (the books have a lot of diagrams in them, which I kinda want to do more with). If you run a course for which this material is relevant, I’m open to dropping by to do a guest session or Q&A. I’m not entirely sure this stuff lends itself to live delivery formats, but I’ll try at least a few experiments.

But Wait, There’s More!

The newsletter also featured an absurdist sci-fi/fantasy consulting fiction series (I think I invented this genre) set in a universe I call the Yakverse. This material is not included in the two volumes above.

I have different, more experimental plans for getting that material out next year. I know many of you were looking forward to that material in particular, but I suspect you’ll enjoy whatever I come up with better than if I’d just turned them into a third volume.

As you may know if you’ve been reading me for a while, this whole newsletter project was inspired by my 2015 short story, The Art of Gig, which was later retconned into the fiction series as a prelude. So you can read that online now for a taste of the Yakverse stuff to come.

I also have other random collateral stuff sitting around from the newsletter project, like a card game, a set of 100 consulting tips (included in Volume 2 as an epilogue) that I made into a learning deck, and silly Yakverse artifacts like coins. I’m still mulling what to do with all that. Suggestions welcome.

I have a rudimentary Book/Project Website at artofgig.com. Right now it just has the basic stuff about the books, but any future developments will unfold there.

One of the most rewarding things to come out of this whole project so far was the Yak Collective, our 3-year-old band of indies doing random creative projects together. If you’re looking for somewhere to go to chat about the themes and ideas of the books, there’s no better place. We have study groups going on interesting topics, a rover-building project, and more.

Anyway, thanks again to everybody who made these books possible. Now go buy them.

Storytelling — End-Times Tales

This entry is part 9 of 12 in the series Narrativium

It is perhaps a bit of a conceit, but I don’t like posting anything on this blog that doesn’t feel timeless. This does not mean ahistorical. In fact, timeless to me means acutely historical. The epics for example, are stories about very specific historical periods and events. They are timeless because of their immortal relevance, not because they are exercises in abstract thought ungrounded in time. Mathematics is timeless because we keep finding currently relevant properties of numbers in every era. Purely abstract ideas divorced from time are often the most transient and empty ideas of all.

History is, in a way, a test of the timelessness of the DNA of current events. To generalize Benjamin Graham’s idea about markets, in the short run, history is a voting machine, in the long run, it’s a weighing machine. And almost everything I think about these days feels very much situated in time in a… very lightweight way. Lots of votes for everything, but very little weight to anything.

It certainly feels like there are typical kinds of historic things going on, but it is hard to talk about them in an appropriately timeless way. The upcoming US elections smell historically significant, as does Musk’s messy takeover of Twitter. But it’s not obvious what the underlying historic big story is. One I’m playing around with is that we are at the tail-end of an up-cycle in de facto monarchism that began with the charismatic presidency of Ronald Reagan, and the charismatic CEO-ship of Jack Welch. In this view, the timeless thing going on is Trump, Musk, Xi, and Putin bringing up the rear of a half-century flirtation with monarchist social orders built around political cults of personality and billionaires, and that we’re heading into an anti-monarchist half-cycle.

Or perhaps the monarchist cycle is beginning rather than ending. I could argue either case. That’s the problem. There is no compelling reason to buy any particular attempt to historicize current events into timelessness through appropriate kinds of frame stories. When every half-assed story sorta fits, none of them actually works.

It’s this very insubstantiality of historical speculation that makes me feel like we are living in a not-very-timeless time. Every just-so story like my two alternate monarchist-cycle theories feels sort of arbitrarily made up. And I could make up a dozen more invoking various obviously important things — climate, AI, crypto, the end of Moore’s Law, gender culture, and so on — that would pass a basic sniff test but wouldn’t be deeply compelling. We are in the sort of era that’s easy to forget in longue durée history writing. It’s an interregnum. A liminal passage full of sound and fury signifying nothing. And we’re all ghosts for the time being, looking for identity-anchoring structure in circumstances where there’s only the clutter of chaotic transition.

A darker thought I’ve had is that perhaps the sense of timelessness is harder to find because we are, in fact, running out of time, and that our mortal civilization is ending. Not just in a Fukuyama end-of-history way, but literally.

A funny related notion I’ve been toying with is that we are drowning in a sea of reboots, reruns, and recycled stories on television and movie screens for the same reason dying people supposedly see their lives flash before their eyes. The story is ending. Despite living through arguably the greatest era of storytelling technology in history, we have no new stories to tell ourselves.

Now this is not entirely true. I’ve found the occasional fresh new story. Station 11 is an example, a lovely recent TV show, but rather tellingly, set in a post-apocalyptic world where for some reason the survivors perform budget Shakespeare reboot productions in a slightly nicer Mad Max world (really? the world ended and Shakespeare is still the source of the most interesting stories you can tell yourself?). And there are formal innovations too. I suspect the metamodern turn I wrote about last time has at least a little substance (though the latest Taika Waititi Thor movie is a big disappointment). But it feels like too little, too late.

So overall, I can’t shake this sense that the difficulty we face telling fresh new stories, about both real and fictional events, is a sign of the End Times.

I’m fairly certain this sense is entirely wrong. There are big problems in the world, but not world-ending ones. Even in the worst-case climate futures, we are not talking about the world ending. We are talking about a very tight evolutionary bottleneck which might lead to severe depopulation and de-complexification (though not back to stone age primitivism). The fraught political events are well within the historical range.

But definitely, something is going on that has temporarily shut down our ability to access a sense of the timeless in order to construct stable notions of ourselves in relation to it. For the time being, we seem to be eternity blind, unable to see past the sound and fury of reboots and reruns of our collective memories.

Ark Head

This week is probably the closest we’ve ever gotten in my lifetime to the brink of nuclear-powered World War 3, yet people seem strangely indifferent to the developments. I share in this under-reaction. Shouldn’t we, I don’t know, have a stronger collective reaction?

There’s of course other stuff going on–a potentially extreme climate-change-amplified hurricane, the UK economy collapsing, and so on–but all that does seem to be categorically of a lower order. Visa shared this meme that gets at this feeling of curious under-reaction.

As Steve Walsh said in a reply, “I suspect this is actually how people in 2022 would receive UFO’s.” I agree with that assessment. Aliens landing would be at least a couple of levels of weird past nuclear World War 3, but I don’t think we have it in us anymore to generate reactions a couple of levels more intense. There is something exhausted about the collective human psyche right now. It’s been battered so relentlessly for so long with things calling for reactions (either practical, or in the form of futile derangement syndromes) that we’re at saturation. We can’t respond any more strongly. We can’t get any more deranged than we already are.

Hunter S. Thompson famously remarked that when the going gets weird, the weird turn pro. Well, we can’t turn any more pro at this point.

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