Alec Nevala-Lee

Thoughts on art, creativity, and the writing life.

The cracking pattern

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In his beautiful book Form, Function, and Design, the French architect Paul Jacques Grillo devotes several pages to the phenomenon of cracking. He reproduces photos of the cracked surfaces of India ink on glass, a porcelain vase, and an ivory pendant, and he notes that the patterns created are an expression of potential energy—a diagram of the forces operating on the material. Then he makes a striking observation:

The cracking pattern is the expression of total structural stability. We may wonder why a pattern associated with the idea of destruction should serve as a model for stability: but a structure is actually a pattern designed to offer the maximum strength at the weakest points, and the cracking pattern, considered as a pattern of rupture, is the pattern of the weakest points of a material, or of a surface.

Its negative duplicate becomes the pattern of the strongest lines of forces of a structure. We can imagine that if we build a wire structure made exactly as a negative of the cracking pattern on the Chinese vase, we shall have the strongest possible skeleton for its surface. For this reason, the cracking pattern has been widely used, although unconsciously, in all forms of design, from Chinese characters and Egyptian hieroglyphs—to stained glass windows and paintings.

In other words, structure—whether physical or virtual—is the inverse of weakness, as manifested where the material starts to break down. Take a photograph of an object in which its weakest points are visible, and then flip it into its negative, and you get a potential blueprint for how to reinforce it. This squares nicely with what the materials scientist J.E. Gordon says in Structures:

The entire physical world is most properly regarded as a great energy system: an enormous marketplace in which one form of energy is forever being traded for another form according to set rules and values. That which is energetically advantageous is that which will sooner or later happen. In one sense a structure is a device which exists in order to delay some event which is energetically favored. It is energetically advantageous, for instance, for a weight to fall to the ground, for strain energy to be released—and so on. Sooner or later the weight will fall to the ground and the strain energy will be released; but it is the business of a structure to delay such events for a season, for a lifetime or for thousands of years. All structures will be broken or destroyed in the end—just as all people will die in the end. It is the purpose of medicine and engineering to postpone these occurrences for a decent interval.

And sometimes the most straightforward way of postponing this kind of destruction is to reinforce the design at its weakest points, as expressed in the Japanese art of kintsugi, in which ceramics are restored with golden lacquer that draws attention to the breakage.

But it isn’t always obvious where or how to make these reinforcements. Any discussion of structure as a negative image of damage automatically evokes the work of the mathematician Abraham Wald on bomber armor in World War II, which has become something of a cliché, but is still powerful. Here’s how Jordan Ellenberg tells it:

You don’t want your planes to get shot down by enemy fighters, so you armor them. But armor makes the plane heavier, and heavier planes are less maneuverable and use more fuel. Armoring the planes too much is a problem; armoring the planes too little is a problem. Somewhere in between there’s an optimum…When American planes came back from engagements over Europe, they were covered in bullet holes. But the damage wasn’t uniformly distributed across the aircraft. There were more bullet holes in the fuselage, not so many in the engines…But exactly how much more armor belonged on those parts of the plane? That was the answer they came to Wald for. It wasn’t the answer they got.

The armor, said Wald, doesn’t go where the bullet holes are. It goes where the bullet holes aren’t: on the engines…The reason planes were coming back with fewer hits to the engine is that planes that got hit in the engine weren’t coming back…When you go to the recovery room at the hospital, you’ll see a lot more people with bullet holes in their legs than people with bullet holes in their chests. But that’s not because people don’t get shot in the chest; it’s because the people who get shot in the chest don’t recover.

Wald’s insight—that the places where the surviving planes had visible damage were places of strength, not weakness—might seem opposed to Grillo’s, but they’re really variations of the same underlying principle. Both are about deriving information from the history of an object in the real world, which, depending on your point of view, either layers an extra level of data on top of the design or peels back the surface to reveal the deeper structure underneath. The tricky part is how to interpret it. (It’s also worth noting that some of the solutions that emerge from Grillo’s approach are analogous to Wald’s. When you put expansion joints in a sidewalk or bridge, instead of trying to reinforce the places where it tends to crack, you’re acknowledging that what looks like a weakness is really a strength. A vase that breaks in the wrong way doesn’t survive to be admired by us. It just shatters.) And these examples all draw upon evidence that can’t be obtained in advance. The places where a surface is worn away, like the natural paths that the footsteps of passersby leave in the snow, create a map of use that can only be generated over an extended period. We rarely have the luxury of waiting to see how things turn out, and much of the lore of engineering is intended to anticipate these stress factors at the planning stage. As Gordon says, you plug values into your formula, look at the result with “a nasty suspicious eye,” and then “worry about it like blazes.” As a guideline, we draw inspiration from other works that have endured and bear the visible traces of that experience. We don’t always get it right the first time. But we can take a crack at it.

Written by nevalalee

May 5, 2017 at 9:28 am

One Response

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  1. That’s a really detailed article! It is very informative. I think the concept of weakness and strength is even applicable in our personal lives as well and while we improve our strengths we should not forget to fortify our weaknesses.

    rockbottomofthings

    May 8, 2017 at 8:28 am


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