I never really got a chance to study abroad. Living in a different country, traveling to see somewhere new and exciting every weekend, it really sounds like a degree of freedom. Back in episode 136, we discussed an engineering principle called Tolerance. The practice of calculating, with great precision, how bad a part needs to be before it stops working is intended. If Tolerance is about finding the widest possible margins for error, its sister principle, minimum constraint design, is about vastly widening those margins by avoiding designs with internal conflicts, reducing or removing the need for Tolerance. Imagine a chair floating in the void of outer space. There are a few ways that you might move it around. If you pushed flat against one face, you could shove it away from you, or if you grabbed and twisted it, you could spin it. Actually, any motion of the chair can be described as a combination of six possible movements, moving in a straight line, up, down, left, right, forward, back, or spinning around those three axes. This way, this way, or this way. If the chair can move and rotate in every direction, engineers would say that it has six degrees of freedom. Of course, degrees of freedom don't just apply to space chairs. If you look at any object in arms reach, you can imagine it moving in exactly the same six ways, and you can imagine various methods you might use to keep it from moving in those ways. To restrict its degrees of freedom. That might sound authoritarian, but it's part of how we make objects useful. The space chair can't do much good floating around totally untethered, gently drifting away from your butt if you try to sit in it. By placing the chair on a floor with gravity pulling down on it, we restrict its motion in the up, down direction, as well as its ability to spin away from us, or flat to front, meaning we can apply a downward force on it, maybe even a slightly diagonal downward force that tries to tip it over, and it will successfully harness its new restrictions to resist that force and remain standing. The trouble only really starts when the methods we use to restrict degrees of freedom start crashing into each other. Let's say, in your enthusiasm to lock down the chair's degrees of freedom, you push it into a corner. It's a good plan, but unfortunately, this room isn't quite square, and the corner it settles into is in annoying 91 degrees. As you push on one side, the opposite edge rocks up and away from the wall. You shove the other direction, and the chair swings back. You push in both directions harder and harder, getting angrier and angrier, rocking it back and forth between these two positions, but you'll never manage to find a stable configuration where it's not on the cusp of rocking back the other way if it gets tapped a little too hard. The problem here is that the chair is being over constrained. There are multiple elements trying to restrict its motion, but because there's some overlap in which elements are assigned to which degrees of freedom, if every part of the system isn't made or aligned 100% perfectly, there are now competing ideas about where the chair is supposed to end up. It's an obvious thing when you start looking for it. A classic example is the number of legs on the stool. A stool with one leg can fall over in any direction. With two legs, it can tip in only one axis, and with three legs, it's stable. If you're a math nerd, you can reflect here on how it takes exactly three points to define a plane. Designing the stool around that minimum number of constraints allows it to sit stably on almost any surface, no matter how uneven, and no matter how mismatched the legs are when they're manufactured. Each leg could be a different length, and it would still work. But once you add a fourth leg, now you've got one more constraint than you need. If something's a little bit short, or the ground's a little uneven, now the stool will rock back and forth, or strain and distort itself to get all four legs to touch. It's just like the 91 degree corner, with overlapping restrictions on how it ought to move, or not move. The stool's motion isn't super extra plus alpha turbo constrained. It's unpredictable. Drawers are another great example. If you were an office furniture maker, you might imagine that a really top quality drawer would have as many guide tracks as possible to make absolutely sure its slides straight in and out. Unfortunately, every track you add beyond the first adds another opportunity for some minor disagreement between them about what straight in and out means. Even tiny misalignment between any two tracks will cause the drawer to jam. Rather than spending a much of time and effort trying to massage every single track to be perfectly aligned with its neighbors, it's both easier and more reliable to eliminate all but one of the guide tracks. A single authority determining the drawer's motion in that direction. Minimum constraint design can drastically improve the performance and manufacturability of manmade stuff. There's something almost magical about how seemingly minor changes that remove elements of a design can cut it free of internal conflicts, really love it, but it also highlights an important distinction that many engineers struggle with, the subtle difference between extra and excess. After a suspension bridge like the Golden Gate Bridge, as with the stool, we only need three points to fully define a plane, so if we wanted to fix the deck of the bridge in space, we should only support it with three cables, right? At first glance, that's way too many cables, but you might notice that the deck isn't attached directly to the big vertical support towers. There are these two big cables draped over the tops of the towers, and the vertical hanger cables that suspend the deck are hooked to them. The big cables flex and bend as the forces on the bridge shift. If one hanger cable is struggling under a large load, that draped cable will sag a little more in that spot, distributing the load evenly to its neighbors. This isn't just an ingenious way to make a bridge that's very strong and lightweight, it clearly satisfies the principle of minimum constraint design. There's no part of the bridge that's fighting any other part to decide where it ought to be in space. Everything is flexible enough to give a little where it needs to. And here's the kicker. Because of that design, a suspension bridge can have crazy redundancy. You could potentially double the number of hanger cables if you wanted to, add a whole another bridge to your bridge just in case, and it would keep working in more or less the same fashion. That's not true of everything. If you were to start adding random beams to a rigid structure like a truss bridge, an engineer might frown and ask if the new bits were adding new stresses, whether they might screw things up if the bridge were to expand slightly in warm weather. That sort of stuff. But because it satisfies minimum constraint design principles, you can feel good about adding as much redundancy to your suspension bridge as you can get away with. That's hinting at a bit of wisdom that I see echoes of in many things. Programmers talk about the magic of once and only once. Architecture theorist Christopher Alexander discusses the quality without a name, a vitality that people in place has gained from being free of internal inconsistencies. There's a sort of friction that's generated when we try to force a thing to obey too many masters. Foughtlessly piling rigid constraint, a top rigid constraint because we assume we know the exact shape of the world. Or maybe because we're willing to ignore any small deviations from what we imagine that shape ought to be. The power of minimum constraint design is that by freeing things to be however they really are, and constraining them only in the ways that are absolutely necessary to achieve once desired ends, you are also freed to pile on as much as you need. Huge safety factors, insane rigidity, big beefy beams. If nothing is working across purposes, that oomph isn't excessive, it's just extra. Can you think of any places where minimum constraint design seems like a useful mental framework? Did you know that thing about suspension bridges? Please leave a comment below and let me know what you think. Thank you very much for watching. Extra special turbo alpha thank you to my friends and colleagues Ryan and Bennett for their help with the script, and to Mike Rugnetta for the chair animations. If you'd like to check out Mike's stuff, which is one of the reasons I got into this hobby, I've linked it in the description. Don't forget to follow us on our channel and don't stop thinking.