Contraption Theory

A meditation on things that from a distance look like helicopters

I have something of a helicopter fetish. My profile picture has been a helicopter (early Dalle-generated) for 4 years. When I was a kid, my landscape drawings would usually have helicopters in them. I just built this cool knockoff-Lego Technic helicopter, out of a cheap kit of assorted parts from Temu. I have a Meccano helicopter build coming up next weekend. And a cheap quadrotor drone sitting around I need to learn to fly.

Helicopters are proper contraptions, which I define as devices with a high system complexity to design integrity ratio. You can define the contraption factor (CF) like so:

But perhaps it is more useful to say that contraptions are helicopter-like technologies. Things that from a distance look like helicopters if you squint. At any rate, helicopters are going to be my running example for developing contraption theory. They are the E. coli of contraptions. The theory itself is of course a contraption, like all my theories.

Helicopters are enormously complex (or in more nuanced Cynefin terms, complicated). I recently bought my 7-year-old nephew a Lego helicopter, and after he built it with much excitement, I asked him if he knew why a helicopter has a tail rotor. He didn’t know, and perhaps more importantly, didn’t seem to care. I think that has more to do with helicopters having a high contraption factor than his curiosity. You tend to accept contraptions at face value, for what they are, rather than inquiring into their underlying generalities. Because you suspect there are no first principles to be found. No general theory to be grokked. It’s not that you won’t figure it out or learn things. You just suspect it will just be a highly specific n=1 thing. Not a design pattern that applies all over the place.

Contraptions tend to have lots of visible complexity that smells somewhat arbitrary, pre-empting foundational curiosities but triggering inventive urges. Though everything in a contraption is there for a reason and is necessary (ie the arbitrary-seeming bits aren’t greebles or feature-creep), it is rarely the elegant entailment of a bigger idea. And the reasons for things being the way they are, while valid, are often unsatisfyingly complicated. The reasons, you suspect even before you probe, aren’t going to be deep reasons that teach you things about the nature of the universe.

In those with no tinkering impulse, contraptions inspire annoyance rather than inventiveness. You tend to assume (incorrectly, as we’ll see) that the arbitrariness is the result of the opinions of some random human involved in the design, like font choices.

Contraption Complexity

In helicopters, the tail rotor is there to balance out the unbalanced angular momentum from the main rotor around the yaw axis. Without it, the body would spin in the opposite direction to the main rotor. And since the thrust the tail rotor creates is on a long lever arm relative to the center of moment, it can be smaller. But then it creates its own unbalanced angular momentum around the pitch axis, but that’s handled by the interaction of gravity and lift creating an appropriate opposed pitching moment — so long as the rotor is spinning.

But wait, there’s more! This is not obvious from pictures or simple models like the one above, but because the main rotor blades are moving faster relative to the air on one side, and slower on the other side, there is also laterally unbalanced lift around the third, or roll axis. This is handled by a very clever articulation mechanism that allows the pitch of each blade to change as it moves through its circle. In fact, each of the blades can move independently of the others. And the whole thing can tilt, allowing the helicopter to move omnidirectionally instead of hover. The mechanism design is like something out of a mad-scientist lab. Helicopter rotors are possibly the pinnacle of mechanical engineering. The thing fundamentally wants to spin out of control every which way, and you have to do clever but not deep contraptioneering to arrange all those tendencies so they cancel out.

The whole contraption is driven, in modern helicopters, by gas turbine engines via a complicated gear train. In fixed-wing aircraft, the shift from piston to jet engines led to a net reduction in noise and mechanical complexity that made things safer and quieter. In helicopters, you have the worst of both worlds: all the problems of jet engines and the mechanical complexity due to piston-engine style complex drivetrains.

That’s often a characteristic of contraptions — they synthesize the worst of many engineering worlds in a not-quite-harmonious juxtaposition. You don’t get a sense of cosmic inevitability from contemplating the design of a contraption. Helicopters are the opposite of iPhones that way.

Yet, the complexity of a contraption is not the superfluous complexity of Rube Goldberg machines or the ironic-artistic complexity of chindogu. It is a necessary kind of hard-gained synthesis that gets you to unique abilities.

It is hard to “simplify” contraptions without breaking them functionally. The minimum-viable helicopter is fundamentally more complex than the minimum-viable fixed-wing airplane. That’s partly why it was invented much later.

But the unique abilities are what makes contraptions worth it, despite their complexity. In the case of helicopters, unmatched vertical and hovering flight capability and omni-directional maneuverability. Not just unique, but weird. Good contraptions have a One Weird Trick quality to them, achieved via an improbable and complex design with an unintuitive configuration of elements.

Bad contraptions — which is most of them — don’t work at all, while still being weird.

As you might expect, the complexity leads to helicopter controls being very weird and unintuitive. While you can trace a satisfying narrative line of descent from (say) horse reins to steering wheels to fixed-wing airplane controls, the controls of helicopters are a tightly constrained function of the weird physics that allows them to fly. The three main ones are called the cylic, the collective, and yaw pedals. Intuitive, huh?

This too is a feature of contraptions. You can’t just look at it and guess how the thing is supposed to work, and fuck around and find out. It works in weird ways that you’d better figure out before you kill yourself. Contraptions require some counter-intuitive pre-adaptation and foresight to use. They are not very FAFO-friendly.

Reasonable machines adapt to human sensorimotor capabilities. Unreasonable ones force humans to adapt to them, with contortions of bodies and minds. All progress depends on unreasonable machines.

This seems to be a general thing with helicopter engineering culture. For some unclear reason I haven’t delved into, Apache pilots must wear a helmet that has a monocular head-up display over one eye, and as they train, their eyes adapt so that the two eyes are literally moving independently and doing unrelated things. I recall reading some research that Apache pilots’ brains change as a result of this. They turn into aliens. It is not clear to me why they must do this but other sorts of pilots don’t.

And despite all the contortionist human effort that goes into using them, helicopters remain noisy, inefficient, high-maintenance, and temperamental machines.

This too is a feature of contraptions. By most engineering criteria, they are not worth the trouble. But because they can do One Weird Trick, they are worth it.

In the case of helicopters, they can even do their One Weird Trick on Mars, where no fixed-wing airplane has yet dared to go.

This is perhaps the most interesting feature of contraptions. All engineering is about managing tradeoffs, but generally the tradeoffs are of a symmetric sort. Two well-behaved qualities that constrain each other. Like weight vs. protection in armor-plating.

A contraption on the other hand, has a lot of well-behaved things on one side of the tradeoff, and One Weird Trick on the other side that never quite gets well-behaved. It remains a wild bit of engineering phenomenology. It’s like harnessing a cart to a team of honey badgers say, rather than oxen. The honey badgers aren’t going to like it, and are going to act wild and unruly and make you work really hard to get any work out of them.

Contraption Integrity

Let’s turn our attention to the denominator of my equation. What does it mean for a design to have integrity?

The terms vertical integration and horizontal integration provide some clues. Integration is a kind of tightening and monolithicization of a design along some vector. I am tempted to call it compression in an algorithmic information theory sense, but it’s not quite that. Integration is as much an aesthetic impulse as an engineering one. Compression is part of the game, but not all of it. There is also art and arbitrariness to it. One way to think of it is like so:

Design integration = compression + contingency + choices

Call it the 3Cs of design integration. Theoretical underpinnings and iterative refinement bring you the compression. Human tastes bring you the choices. But it is the contraption factor that bring in the element of contingency and limits how far you can go.

When you integrate the discrete elements of an engineered artifact, they become more shaped by each other, shedding complexity in one direction, and gaining it in other directions. They acquire path-dependency by working around inflexible constraints, and come to reflect human choices made along the way.

Integration typically makes things more well-behaved, reliable, efficient, and so on — along a chosen, preferred direction. You typically aim to simplify things net, by some scheme of values, in regimes you care about. You eliminate parts, remove optionality, and so on.

One particularly interesting sign of improving integration is increasing amounts of visible symmetry in the design. Symmetries typically represent surplus in a design space, which can be used for things beyond the main design problem, such as integration by some larger logic.

Helicopters are visibly less symmetric than fixed-wing airplanes in their gross features. The main rotor rotates in one direction, giving the machine a “handedness” or chirality. There is only one tail rotor, on one side. The blades are pitched differently in rotation on one side compared to the other. American helicopters are typically counter-clockwise designs while European ones tend to be clockwise designs. In an alternate universe, that might be reversed. The lower symmetry lends a vibe of contingency to the design space of helicopters. As an aside, Da Vinci’s impractical helicopter design, based on a screw, is also chiral, like any screw must be. So he was kinda on the right track and deserves credit for “almost inventing” the helicopter.

Of course, there is a deeper symmetry to be found if you know enough physics and math to peer deeper, but that’s the point. It’s not visible symmetry. The surplus latent in the deeper symmetries is harder to tap into and use for other purposes. You have to frack surplus value out of the hidden symmetries of helicopter designs with more ingenuity. The energy in to energy out ratio is not good.

An integration “direction” typically represents a goal that’s outside of the engineering logic per se. Vertical and horizontal integration are about business models and goals, not engineering per se. Integration efforts aim to utilize some of the freedom left over from the core engineering design to solve for other things. In engineering-speak, integration options are created by the underconstrained nature of the design space.

That’s why there’s an element of aesthetics to design integration. When engineers themselves hog all the freedom, you get what we call an opinionated design. When they leave it for others to use, you get stuff like opinionated auteur products, opinionated business models, opinionated military or political strategies, and so on.

Here’s the thing about contraptions though: They live in engineering design spaces that resist and limit integration along most directions.

Or to put it another way, they are more constrained (less unconstrained) ideas on the physics canvas they inhabit. Or to put it yet another way, they operate in tight and convoluted corners of scientific possibility space. Or to put it a fourth way: They are designs heading down either sharply depth-limited evolutionary dead ends or in need of scientific breakthroughs to enable continued evolution.

Or to put it in a fifth way that is perhaps my favorite: Contraptions are intrinsically opinionated artifacts. Kinda like orange cats (which have a reputation for being weird and opinionated compared to non-orange cats, which my experience with them validates). They naturally hog a lot of the design freedom that typically accrues to engineers, designers, and their bosses.

Don’t get me wrong. There are beautiful, well-designed, and elegant helicopters out there. There are vertically integrated helicopters and horizontally integrated helicopters. There are opinionated helicopter designs and companies. The point is, whatever the direction of integration, and whatever the aesthetic sensibilities and opinions driving the design, the limits are much sharper. And any design integrity you squeeze out of a helicopter design is much costlier. If Steve Jobs and Jony Ive had tried to make a platonic, puck-shaped helicopter, they’d have failed.

That’s what makes helicopters contraptiony — the tighter limits on human design opinions and tastes and the less forgiving nature of the configuration space of elements.

A thing is a contraption when it is hard to increase design integrity without increasing the complexity faster. When you can’t integrate it into an atomic-looking thing. When you can’t force the user experience into human-intuitive modes. When you have to work to tap into the surpluses from the hidden order of illegible symmetries.

These are the characteristics of wild things. Contraptions are, in a sense, the wildlife of engineering. They cannot be domesticated. At best, they can be tamed. And they’re more discovered than invented.

Taming Contraptions

Zoologists seem to make a distinction between animals that can be domesticated, like normal cats, dogs, and cows, and ones that can at best be tamed, like orange cats, honey badgers, lions, tigers, and elephants.

I don’t know how solid the distinction is in zoology, but I think it applies to technologies. Helicopters, I think, have to be caught in the wildernesses of their design space and tamed. They are not domesticated artifacts that can be bred easily in captivity and rendered docile and friendly from infancy. They are harder to fly. Not so fun fact — the aerospace engineering department where I went to graduate school is named for a helicopter pilot who died on a mission. But equally revealing — I did not have to take a required class on rotorcraft. The standard curriculum was all about fixed wings.

People have tried to make helicopters more tame and well-behaved over the years with mixed results. For instance, there are coaxial rotor designs, with two counter-rotating rotors on the main hub. This is the design used in the Ingenuity helicopter on Mars, and in Russian Kamov helicopters. More compact (“atomic”) and pleasingly symmetric perhaps, but as you might imagine, getting two rotors to rotate in opposite directions on the same axis is mechanically very tricky, with, you guessed it, a complexity cost. Then there are tandem rotors and tilt rotors, about which we might make similar observations.

All these variations on the helicopter theme move you around a little bit in the tradeoff space of helicopter designs but never get you any big reductions in complexity or increases in design integrity. The contraption factor (CF) seems to remain high no matter what you do.

Quadrotors, of course, are at the center of the drone revolution. They are perhaps the simplest sort of helicopter, with the lowest contraption factor, since four rotors gives you a lot of design room (elegantly symmetric design room at that) to manage angular momentum neatly, get some natural stability, and eliminate some of the more annoying complications of single-rotor designs, like variable-pitch rotor blades.

But there’s not much headroom for improvement there. You can go to 6 or 8 rotors, but the complexity increases faster than the design integrity. And having one motor per rotor, plus a heavy battery, gives you very tight limits on payload capacity. I haven’t done the analysis myself, but I am told by people who have that we’re not going to see huge quadrotors beyond the largish ones being trialled for drone-delivery of light packages. The huge aircraft carrier sized thing in MCU movies is not physically plausible (I wish it were). My friend Star Simpson is betting that this limit has created an opportunity for other drone designs (her startup, Therecraft, is based on a lifting-body design)

Here is another way to understand the contraptiony nature of helicopters: They have no narratively compelling line of descent from nature.

I mean yes, there are tree seeds that fall slowly and drift by spinning like rotors — this is the passive effect underlying autogyros, an ancestor of helicopters — but it isn’t much. It’s a weird cousin of gliding in fixed wing airplanes. Autogyro effects are how you can try to recover a modicum of control over a crashing helicopter. But as you might expect, it’s not a very powerful life insurance policy. Random aside: spinning seeds are probably the closest things to evolved wheels in nature at the macro-scale, not counting things like molecular motors.

If you squint, you can see other partial lines of descent. In some features, especially the varying pitch of the blades as they rotate, helicopter flight is closer to some regimes of flapping bird flight, than fixed-wing flight. Especially if you compare the mechanics to birds that can hover, like hummingbirds. You could say hummingbirds are “reciprocating helicopters” whose rotor blades move back and forth in roughly elliptical paths while twisting. Hummingbirds don’t have a natural clockwise/counter-clockwise chiral nature to their flight though, so I don’t consider them natural helicopters.

But overall, the line of descent from birds and even insects to fixed-wing aircraft is clearer than to helicopters. While rotor blades are aerofoils that generate lift in the same way as fixed wings, they are not quite “wings” of either fixed or flapping varieties. They are something of a cross among wings, wheels, and screws.

Contraptions as Portals

There is something rather steampunk about helicopters. They seem to belong in some parallel universe where technology never evolved past early electric power, and therefore mechanical engineering had to keep getting more complex — and contraptiony — to add more technological capabilities to society.

In our own universe, the history of technology has a clear trend of complexity moving to the newest layer. Mechanical engineering got more complex — up to a point. Then it hit an uncompetitive limit, and electricity took over. Then electronics. Then computers. If you trace the evolution of a typical artifact, you can see the progression and migration of complexity in many machines, as it gets “eaten” by successive waves of technology.

For example, mechanical clocks gave way to grid-AC (60 Hz) electric clocks, which gave way to quartz-driven electronic clocks, which gave way to computer-based network time, synchronized via GPS-based atomic clocks. This evolution has happened in other surprising areas of mechanical engineering too. There are magnetic gearboxes. There are gyroscopes based on lasers (ring-laser gyros) and MEMS. Future generations of mechanical engineers may not learn about automotive differentials except as historical curiosities, because EVs mostly don’t need them.

But helicopters — they haven’t really been “eaten” much by successive waves of technology, and I doubt they will be.

Getting eaten by new waves of technology is what domesticated technologies do. They offer enough conceptual breadth and underconstrained design room to evolve along with the general trends of technology. They are defined primarily by their function rather than the specifics of their configuration of elements.

The idea of a “clock” for example, has enough conceptual breadth and breathing room to have jumped from paradigm to paradigm for millennia, getting transformed unrecognizably along the way. The same cannot be said for “hovering flight.”

Yes, MEMS accelerometers and powerful microcontrollers have made small quadrotors possible. V/STOL aircraft integrate some helicopter-y contraption elements. But helicopters fundamentally haven’t been “eaten” by each successive wave of technology. Or at least not to the same degree.

It is revealingly hard to imagine distant science-fictional successors to helicopters. Retro-jets work but are mostly worse solutions, not better. So you either have idiotic design fictions like the ornithopters of Dune, or you have to make up completely mysterious deus-ex-machina hover technologies (why is it always glowing blue rings?). It is actually interesting how much science fiction worlds seem to need hover technologies to be compelling. It’s not as in-your-face dramatic as hyperspace travel, time travel, force fields, or even its big brother, anti-gravity. But you apparently need a proper hover technology that is not helicopters to make a cool universe. We yearn more to hover than to fly it seems.

Even the closest cousin of helicopters, fixed-wing airplanes, have evolved more willingly and significantly. There are now fairly large solar-powered airplanes entering commercial use. Again, I haven’t done the math, but I don’t think the power-to-weight equations will allow for solar-powered helicopters much larger than Ingenuity. You could use balloons I suppose.

One way to think about this is to think of helicopters — and contraptions in general — as alien artifacts from parallel universes that run on alternative techno-evolutionary logics that don’t quite apply in ours. In the case of helicopters, they are from some sort of steampunk universe where mechanical engineering has gone a lot further, and does a lot more than in ours. We’ve added bits and pieces from our universe to them, but they fundamentally aren’t from around here. They have alien DNA (notice how current UFO discourse focuses on the mysterious hovering-like capabilities of the supposed alien objects?).

Relative to the evolution of our own universe, steampunk is a fundamentally depressing kind of speculative fiction. It imagines a cul de sac of technological stagnation, but with a narrow sort of human flourishing that has a certain amount of romantic appeal. The appeal of steampunk is the appeal of reactionary nostalgia. It is more fantasy than science fiction, by Ted Chiang’s criterion of whether a speculative world is built around strange laws of nature or special people (genius-eccentric contraption inventors sporting Victorian-gentleman superhero personas?).

Fun aside there — the invention of the helicopter is a rare case, possibly the only major one, that relied on a successful artist (Rachmaninoff) giving an engineer (Sikorsky) money to work on his idea. Even the origin myth of helicopters seems to belong in an alternative universe where artists are more economically successful than technologists.

Yes, it’s kinda cool and fun to imagine a world that got wildly more contraptiony than ours did, where Victorian eccentrics tinker in labs funded by musicians. But it also means that world was stagnating because it was not finding new technological fires to harness, and archetypes beyond crackpot contraptioneers to drive evolution. I find this a bit depressing. High contraption-factor universes are technological dead-ends.

But the presence of an alien artifact from this depressing parallel universe is not depressing in our world. To overload the idea of contraption factor from before, the ideal contraption factor of a technological history is not 100% (in some suitably normalized sense), but it is not 0% either. A technology history with zero contraption factor would be depressingly determinate, non-path-dependent, and lifelessly bureaucratic. Contraptions are the spice of technological life. They provide the twists and turns that keep technology history interesting and weird. You probably need at least 5-15% CF to do that.

In its home universe, the helicopter perhaps embodies a larger paradigm exhausting itself, leading to a general evolutionary exhaustion down a cul de sac. But in our universe, it represents a bit of magic from a road not taken at all, governed by an alien logic. It lends a bit of sprezzatura to our universe, and adds a contraptiony aesthetic note to the human condition.

And it adds some superpowers that the regular technological logic of our universe cannot provide at all. It is notable that there are no good hover technologies other than helicopters. This makes technological history interesting. We need to inject a bit of alien logic to make it work at all, without stalling.

And just because the alien artifact resists systematization and domestication within the larger logics of our universe does not mean it is marginal. The helicopter is something of an exception to our theories of technology, but it is a high-value and load-bearing one. ChatGPT tells me there are around 60,000 helicopters in the world, and 100,000 fixed wings (seems low??). But if you start counting the exploding population of working (as opposed to toy) quadrotors, I think helicopters will start to dominate on raw numbers.

In terms of industry size and value though, the difference is stark — helicopters are a 50-60B industry, while fixed-wing craft are 800B-1T (again according to ChatGPT). But if you look at the uses they are put to, much of fixed-wing aircraft use is somewhat commodity.

Helicopters on the other hand, provision a lot of the One Weird Trick flight capabilities our world needs. Including highly critical ones, like flying patients to hospitals, running supplies to mountainous regions or oil rigs, helping supervillains escape from rooftops, and so on.

Contraptions for the End of History

I really liked Bryan Arthur’s Nature of Technology as a general theory of technological evolution, but it’s a bit too general for my tastes. It is a theory of technological evolution in all possible universes, not just our own. I don’t like theories that are totalizing in that way. I like my theories to be fundamentally contingent. I like them to have a non-zero contraption factor. I like technological history to be littered with contraptions that didn’t have to be. That were not inevitable, and not part of larger logics that came to “eat” all of technology.

History — all history, not just technological history — should be something of a contraption. That’s what saves it from being a historical determinism. And when the logic of a history gets too deterministic and totalizing, and winds its way to an “end” of sorts, what can restart history is a sufficiently powerful contraption stolen from a neighboring dead-end universe.

This idea is interestingly orthogonal to Clarke’s Law — that every sufficiently advanced technology is indistinguishable from magic. Helicopters (and contraptions in general) are not magical in that sense of being either inscrutable or obviously “advanced.” But they feel magical in a lateral way. Because their governing logic is alien, restricted to small pockets in our universe. Clarke-magical technology is described by the Promethean allegory of stealing fire from gods. Contraption-magical technology needs a different allegory, likely involving parallel universes. I can’t think of one, but am open to suggestions.

Are there are other contraptions in history, or around us? Important ones, not marginal curiosities like hovercraft?

I think so. Antibiotics come to mind. Probably Javascript. Blockchains perhaps. Maybe Ozempic/GLP-1 agonists. Kalman filters. Zero-knowledge proofs. Nuclear reactors.

A lot of emerging Chinese technology seems contraptiony to me in a good way. Temu is junky, yes, just as Amazon is beginning to be. But it is also contraptiony, in a way Amazon will likely never be. TikTok seems to be full of contraption videos. I think the Chinese intuitively get contraptioneer thinking in a way early modern Westerners perhaps did, but modern ones don’t. High-modernist engineering aesthetics and the lure of Progress™ have kinda killed the contraptioneer spirit to some degree.

Still, there are contraptions all around us, and this is a good thing. We are surrounded by technologies from invisible parallel universes, governed by logics our philosophies of technologies don’t comprehend well, or at all, but patching their deficiencies.

Contraptions mess up the narrative logic of authoritarian high-modernist Progress. They don’t provide meekly unopinionated fuel to drive evolution along planned tracks where Important Problems™ get solved, and the Standard of Living™ increases Sustainably™ at 3.5% per year as we continue on a death march towards utopias that inspire nobody. The inject a bit of wildness into our futures, and challenge the narrative of technology as a progressively domesticable force. They periodically rebase the thing itself whose growth causes so much angst.

Contraptions are what provide periodic sideways knocks that kick us out of our ruts and local equilibria. They are what provide us with wtf sideways technological leaps that get us thinking more laterally about our fates.

To snowclone Kant, out of the contraptiony timber of technology, no straight history was ever made. But that’s precisely why contraptions are central to how we might finesse ourselves out of the End of History. The way out of our cul de sac is to be found in parallel universe cul de sacs.

I think I like helicopters and all they represent because I’m fundamentally a contraptiony thinker myself. I can get from vague impulses to loosely coherent unoptimized things. I’m bad at taking a loosely coherent thing and then solemnly subjecting it to theoretically sound integration/optimization forces and aesthetics to produce beautiful, inevitable-seeming things, capable of driving inevitable-seeming futures.

I like things that resist cohesion and relentless optimization; that retain an ornery nature, yet are not mysterious. They merely operate by a frustrating-to-some wild and local logic that doesn’t generalize or scale very well. A punk logic. Helicopters are punk.

All my writing is contraptiony I think. My consulting involves contraptiony constructs like 2x2s and 2-of-3s. And in my brief career as a working engineer, I mostly produced contraptions. In my varied current workshop activities, I mostly get excited about building contraptions. Only once in my career did I produce a tightly integrated elegant thing whose inner logic flowed naturally and inevitably from a larger logic. Contraptioneering is a very different headspace from mainstream engineering headspace.

But while it is very limited and local in each individual case, in the long run, I suspect contraptions are what make technology an infinite rather than finite game.

In the long run, the helicopters will save us.