Tangle Logic

The word tangle is generally used pejoratively in the English language, as in Walter Scott’s line, Oh what a tangled web we weave, when first we practice to deceive. Or at least disapprovingly, as in tangled mess. Darwin’s usage, in the last passage of The Origin of the Species, is the only famous example I know of where the word is used in an approving way:

“It is interesting to contemplate a tangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent upon each other in so complex a manner, have all been produced by laws acting around us.”

The Darwinian notion of a tangle can be understood as a snapshot of a robust, open, evolutionary process, with all the optimality and efficiency properties that entails or doesn’t (I would summarize it as “a mediocre slouching towards continued existence”). Darwin goes on to link his evocative observation directly to his theory of natural selection, but I think the idea of a tangle is more general, and has roots in the fundamental mathematical structure of reality. Take for instance, this picture of various optimal packings from a great thread of many such examples by Daniel Piker (thanks to all who responded to my twitter prompt looking for this sort of thing):

These are very simple examples of a large class of things I define to be proper tangles: complex things that are efficient but not orderly. And you know what these pictures remind me of? Traffic in India.

There is no biological angle in this problem of squares packing squares, except that these configurations could potentially be found by an evolutionary algorithm. It just so happens that an optimal packing in these cases has no obviously pleasing symmetry or structure to it. Not only is there no obvious simple symmetry, there isn’t even the sort of greebled fractal symmetry that traditional architecture enthusiasts seem to fetishize. I suspect these are pictures neither Christopher Alexander, nor Le Corbusier could love. There are squares but they exhibit neither high-modernist ideals nor any sort of suitable-for-sacralizing pattern language. They are not so much un-aesthetic as pre-aesthetic. There is neither legibility, nor feng shui, nor vaastushastra to be found here. They are like those obscure Go strategies AI programs find. They win efficiently, but there’s no obvious story to why.

To the extent squares can make a tangle, these are tangles of squares. Their only redeeming quality is that they are efficient and computable.

Why does this feel so surprising? I think it’s because we extrapolate from situations with more degeneracy to ones with less degeneracy. If I try to tile a 4×4 square with a 1×1 square, it is obvious by inspection that the regular tiling by 16 1×1 tiles is obviously optimal since it uses 100% of the space with no gaps and no spill-outs. Not only is it clear you can’t do better, it is also kinda clear you can’t match this solution with an irregular-looking tiling, though I can’t see an obvious way to prove it.

But when the ratio of the sides of the two squares is not an integer >2, these intuitions clearly don’t apply. I am not sure what intuitions do apply, but expecting tractable symmetry and regularity, with or without fractals, is clearly a mistake. Integral divisibility is a kind of degeneracy. When you lose that, things get complicated.

The world is full of situations far more complex than this. Darwin’s tangled bank, for example, is a tiling of an uneven manifold in 3d by a bunch of static and moving/growing (at various rates) creatures of a variety of shapes, sizes, and fractal self-similarity tendencies. And there are non-obvious constraints at work like fighting for sunlight or water, or surface area. You should expect it to look like a tangled mess. Not like a legible garden or forest. Or for that matter like either a traditional or modern building.

We get this intuitively with nature, but not with another class of phenomena: the technological built environment. For some reason, we expect efficiency and optimality in technological systems to also present as obvious pleasing symmetries and orderly geometries (whether literal or abstract). Which is another way of saying we expect such systems to be degenerate spaces.

But technology, when allowed to flourish, is as liable to produce a “tangled bank” as nature. In my Breaking Smart essays, I explicitly used the image of a tangled mass of creepers enveloping the world to convey the idea of “software eating the world.” It’s revealing that I had to use an organic metaphor to convey the point. We only intuitively expect tangles in organic things. With artificial things, we read tangles as poor design.

Even technologists reliably err on the side of fetishizing orderliness for its own sake, especially when they succumb to “humanist” tendencies (the accusation that engineers are producers of dehumanizing orderliness is almost entirely projection), with all the attendant political tendencies towards authoritarian order. Technologies that are tinkered and shimmied into existence by many minds tend to look like tangles. Technologies imagined into existence from whole cloth as orderly auteur visions in service of a political vision are rarely tangles, but are also rarely successful.

This isn’t to say there isn’t symmetry and order in either nature or technology. Nature features symmetric animal bodies, generally functionally linked to mobility or signaling, and vehicles generally have some symmetries for similar reasons. The innards of both are asymmetric. Hearts, livers, engines, and drivers are asymmetrically positioned.

The point is that tangles are the default, and platonic orderliness exceptional. In complex systems, both natural and artificial, you might have spots of order within, due to special circumstances where it order is actually functional, and local degeneracies. But in general living systems, both natural and artificial, are tangles by default, orderly by exception. If the situation looks reversed, there is invariably an authoritarian force at work.

Only at fairly low levels of non-living pure-regime physics do you get obvious order and symmetry. The sun and planets are roughly spherical for example. Crystals are regular. The fundamental laws of physics are pretty authoritarian as you get close to them in their purer forms.

In intentionally designed human systems, orderliness is overwhelmingly likely to be an aesthetic rather than the natural outcome of optimization by design or evolution. Functional design processes land on tangles 90% of the time, orderly solutions 10% of the time. Human aesthetes, especially political ones, tend to find orderly solutions 90% of the time, and grudgingly accept tangles 10% of the time.

Orderliness is often a clear sign of a resource surplus, with the order serving to both signal it, and employ it to lower the cognitive burdens of existing within it (which is also often the case in biology). A straight street signals “human civilization” and is easier to walk down inattentively. The thing is symmetric and low information because you’re not putting it to full use. It’s a sign of high inefficiency, not efficiency. And note that the mere local presence of a surplus to fuel an orderly situation does not mean there’s an actual surplus. A coercive entity is likely simply appropriating a lot of local resources and wasting them, starving entities outside its boundaries (which it must naturally construct and enforce to preserve the untangled situation). This is as true of traditional architecture as modernist. It’s just that with fewer design dimensions, the ones available get more fractally packed. Look outside the island of orderly (whether traditional-fractal or modern glass-and-chrome) and you’ll find the same patterns of extractive impoverishment as a local externality.

For example, consider the famous 11th century Chola temple at Thanjavur, rightly celebrated for the sorts of awe-inspiring greebled symmetries that trad architecture mavens love. I just spent an enjoyable couple of days touring the area and loved it. But right outside the temple is a disastrously extracted mess of a neglected medieval town. You’d think a major tourist spot and a UNESCO world heritage site would find a few extra bucks to make the town around the temple as nice as the temple itself, but that’s… not how these things work. And the problem is not unique to India. I see signs of it even in the better-resourced monument areas of Europe

I’m not trying to be cynical here, just pointing out both sides of untangled situations that might present a pleasing aspect you enjoy and an unpleasant one you might be strongly tempted to ignore.

A tangle, by contrast, really presents only one aspect: a tangled one. It has not been separated into beautiful vs. ugly; surplus island vs. extracted surroundings. Which is why from the point of view of the tangle-positive crowd, trad vs. modernist is almost a distinction without a difference. In that debate, I tend to lean high-modernist (which may surprise some of you, given my past writings), but overall, I’m mostly pro-tangle, and anti-orderliness (it’s a more nuanced version of being for chaos and against order — I don’t think tangles are chaotic, but that’s a story for another day).

Tangles are surprising answers to complex problems, but shouldn’t be. Complex (as in visibly disorderly) answers to complex problems are exactly what we should expect, for many reasons (for instance, Ashby’s law of requisite variety if you want to take a complex systems view).

Millennia of human building have convinced us that orderliness (with or without greebles) is somehow efficient and tangles are “messy and inefficient.” And it’s not a modern or even medieval phenomenon. I recall my high-school history teacher instructing us that the streets of Indus Valley cities were “efficient” because they intersected at right angles and were “well-laid out” in an obviously planned way, compared to other Bronze Age peer civilizations. She taught us the usual textbook justification: that this somehow made them self-cleaning because the wind swept the streets naturally. More modern thought typically treats straight lines anywhere (roads from capitals to airports, and colonial-era boundaries being the classic examples) as a mark of an authoritarian presence. There may be some accidental benefits for narrow use cases, such as street-sweeping by prevailing winds, but that’s not the reason they exist. They exist because an authoritarian has carved out an island of surplus resources for himself and his buddies, and decided to lay it out as a neat, untangled zone.

I suspect a lot of people intuitively prefer tangled aesthetics because they sense all this subtext to orderliness. There is a sort of obvious anarchic egalitarianism of opportunity to a tangle. Not the illusion of it that “meritocracy” offers, but the real thing. A tangle looks like a “mess” because many agents are empowered to do whatever conflicting things they want in a confined space of possibility, and none of them is strong enough to dominate the rest. The result is a sort of moving negotiated equilibrium of efficient needs-fulfilment: a tangle. You just need to appreciate it the way Darwin did his tangled bank.

Let me cut to the example which inspired this essay, traffic.

Having been in India for the last couple of weeks, I’m struck by what I finally grok as the logic of Indian traffic: it is tangle logic. It was evident even back in the day when I lived and drove here (I no longer dare to), on both 2 and 4 wheels, but it is completely unmistakeable now, 25 years later, where the number of cars and two-wheelers on the roads has absolutely exploded, while the infrastructure has just barely kept up.

The result is what I think of as snarls that work, or what we might call traffic tangles. Except on the few modern multi-lane gated highways where a semblance of international-standard traffic discipline has been imposed, most city traffic, especially in the hearts of old cities like Coimbatore from where I’m writing this, is tangles.

A traffic tangle is when all entities in a volume of space-time — 2, 3, and 4-wheelers, and 2 and 4-legged creatures, some with wings — attempt to sort of phase through the tangle, Flash style. And they do so in highly mutually constrained ways. By which I mean if you’re in the volume of a tangle, you are either driving/walking extremely mindfully or you die. It’s race-car level mindfulness, except at relatively low velocities, and devoted to navigating maneuvering complexity rather than high speed.

Unlike the boundary of an island of orderliness, which is set by an authoritarian force, the boundary of a tangle emerges naturally where the problem of navigating it gets hard enough that you have to slow down and reorient into a sort of “tangle headspace” which involves getting into the headspace of everybody else in the tangle, and letting them into yours. It’s where mutualism necessarily begins.

In an Indian traffic tangle, the law is treated as a suggestion at best, and assumed to be a generally bad suggestion for the best way for everyone to get where they want to go. But the alternative is not a Hobbesian free-for-all. Instead it’s a live, surprisingly accommodating and understanding process of getting everybody’s needs met through a seemingly anarchic set of behaviors. A process that extracts about 10x the capacity out of a system relative to what the law thinks it is designed to handle. It’s just that it’s an ungoverned process.

So: Traffic comes down the wrong side, arbitrarily straddles lanes, cuts across randomly, weaves unexpectedly (especially two-wheelers) to avoid potholes, humans, dogs, or chickens (cows are actually not much of a problem since they’re usually stationary and too large to miss — it’s only an issue when they get on highways). The accident and fatality rates are higher than the West, but not by as much as you’d expect given just how far past the nominal and “rational” capacity the system operates. It seems to operate at about 10x what a Western planner would consider a reasonable “capacity” but with only perhaps 2-3x the risk.

In fact, I have a suspicion that the fatality rate is probably higher in the non-tangled parts where high speeds are even possible. The tangled parts lead to annoying scrapes and bumps and frayed tempers, but I have never seen an actual serious accident unfold on an Indian “tangle” street. But I’ve seen a few on the highways, and plenty in the US even off highways.

Note that I’m not condoning the problems of tangles. It would be nice to have the (externality-free?) surpluses where everybody could go where they wanted without tangles, via orderly pathways. But given the resource constraints that are actually present, tangles are a good solution. Because the thing is, traffic tangles are messy, but they actually work for the situation that actually exists. By contrast many alternative proposals are for situations that would be nice to have, but don’t exist.

Thinking like a control engineer for a minute, clearly what’s happening is that everybody is sampling the situation at an incredibly high rate, and maintaining highly speculative, low-confidence predictive models of what everybody else might do. In the US you expect the car next to you to basically stay in its lane 90% of the time, and if it suddenly cuts across, it’s really dangerous because you’re neither expecting it, nor updating frequently enough to notice and adapt in the much shorter time entailed by higher speeds. But in India, the current position and velocity of every entity in your 360 degree visual field is only a weak indicator of where it might be the next instant. And since everybody is thinking the same way, extremely efficient packing solutions can be found in real time. It’s closer to streams of water flowing in weirdly mutually aware ways. So creaky old 2-lane infrastructure from bullock-cart eras sees a bumper-to-bumper continuous flow of everything from small scooters to medium trucks. Entities kinda just wiggle and twist on both 2 and 4 wheels (and 2 and 4 feet) and work it out like every intersection is a game of twister. Almost literally so. And two lanes seem to get overclocked into four.

In one outing last week, I had to help my Dad maneuver out of a really tight tangle where 3-4 cars were all trying to squeeze past each other with clearances between -0.1 to +5cm in a very narrow street, with dozens of two-wheelers and cars parked on both sides. Many helpful bystanders joined in, directing traffic inch-by-inch, occasionally even lifting locked two-wheelers out of the way. This is a common sight in India. Traffic would grind to a halt if impromptu volunteer traffic coordinators didn’t step in. The few traffic cops around are overwhelmed managing the larger intersections and construction zones.

This is why, if you can get over your instinctive fears, crossing Indian roads on foot at random points with no crosswalks, squeezing through or over dividers if any, is not quite as dangerous as it looks. They’re not actually trying to kill you. In fact they are much more actively engaged in trying not to, compared to drivers in the West. The entire traffic field is paying far more attention, and is far more willing and able to immediately adapt and flow around, than you think. The tangle is about 10x more responsive than a similar tangle in the US. A blind person stumbling into a traffic stream is less likely to get killed in India than in America, other things being equal. The math of it is of course, obvious. In America you can be a much lazier, more inattentive driver because there are more resources being used by fewer entities. You don’t have to continuously solve optimization problems whose solutions are tangles.

The most dangerous thing you can do in Indian traffic is looking like you are hyperaware and present but don’t know what you’re doing or where you’re going, because then nobody looking at you can guess what you’re doing (attributing full agency to you) and adapt. Which means they make different predictions and the problem snowballs. Developed-country foreigners in India — and I’m increasingly one of them — often have that tell: they turn working tangles into honking snarls because they look like they could, with equal probability, walk across, run across, stumble backwards, freeze in terror, punch somebody, or leap up and fly. Locals are often extra solicitous of foreigners primarily to make sure they don’t turn into problems. They are chaos actors in a system that wants to keep chaos at bay. Just not with order.

That’s actually a good functional definition of a tangle: a way to keep chaos at bay with something other than order.

Once you orient in a tangle-space, this kind of thinking comes naturally. I see it everywhere in India — bank bureaucracies, airports, shops. I call it tangle logic.

I even have a theory that the famous Indian head-wobble — neither a yes, nor a no — is a sort of entanglement acknowledgment of being present in a tangle logic. When you get that head wobble, it means you’re kinda in sync about the fact that you’re negotiating your respective paths through the present tangle with mutual awareness, even if the path through isn’t immediately clear. You commit to recognizing each other, and being mutually responsive for as long as your paths need to be in the same tangle.

The world will only get more tangled, as it gets more globally entangled in every way. As islands of resource surplus with coercive boundaries shrink, and the tangle zone expands. And soon everyone will be doing the head wobble, and you’ll all be Indian.