I never really got a chance to study abroad.
Living in a different country, traveling somewhere new 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
as 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 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 that way.
If the chair *can* move & rotate in every direction, engineers say 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 arm’s 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 tried to sit down in it.
By placing the chair on a floor, with gravity pulling it down and the floor pushing it up,
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
force that tries to tip it over, and it will successfully harness its new restrictions
to resist that force & remain standing.
The trouble only really starts when the methods we use to restrict degrees of freedom start
crashing into each other.
Say, in your enthusiasm to lock down your 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 an 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 “overconstrained” - 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, once you start looking for it.
A classic example is the number of legs on a 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, & 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 is a little uneven, now the stool will rock
back and forth, or straaain 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, the stool’s motion isn't super-extra-plus-alpha-turbo constrained, it's unpredictable.
Drawers are another great example - if you were a novice furniture maker, you might imagine
that a really top-quality drawer would have *as many guide tracks as possible* to make
*absolutely sure* it slides straight in & 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 misalignments between any 2 tracks will cause the drawer to jam.
Rather than spending a bunch of time and effort trying to massage every single track to be
perfectly aligned with its neighbors, it’s both easier & more reliable to eliminate all
but one of the guide tracks, to have a single authority determining the drawer’s motion
in that direction.
It's easy to imagine everything being perfectly parallel in theory, but this isn't theory,
it's woodworking.
Minimum constraint design can drastically improve the performance & 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 and really let
it sing.
But it also highlights an important distinction that many engineers struggle with, the subtle
difference between “extra” and “excess.”
Consider 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, the
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 & lightweight,
it cleanly 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
‘nother 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 and places
gain 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, thoughtlessly piling rigid constraint atop 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
one’s desired ends, *you* are also freed to pile on as much “oomph” as you need
- huge safety factors, insane rigidity, big beefy beans, if nothing is working at cross-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 THUNK.
Thank you very much for watching.
Extra-special turbo alpha thank yous to my friends and colleagues Ryan and Bennet 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 blah blah subscribe blah share, and don't stop thinking