# The Space of All Possible Bridge Shapes

August 3, 2007 — Stephen Wolfram

When I hear about something like Wednesday’s bridge collapse, I immediately wonder whether any of the science I’ve worked on can be of any help.

Bridge design is one of the classic—almost iconic—successes of traditional mathematical science.

And when I first talked about A New Kind of Science, a not uncommon reaction was precisely, “But can it help build better bridges?”

Well, as a matter of fact, I rather suspect it can.

Bridges have a long history. Early on, only a few types seem to have been used. But with the arrival of iron structures in the 1800s there was a kind of “Cambrian explosion” of different types of truss bridges:

But what is the very best bridge structure, say from the point of view of robustness? There’s a huge universe of possibilities. But so far, only a tiny corner has been explored–and that mostly in the 1800s.

It’s very much the same as in other areas of engineering. People have come up with particular structures to consider. Most often they’re just based on a sequence of identical repeating elements, or sometimes of nested elements.

But what about all the other possible structures? Maybe the best structures aren’t so simple-looking.

Well, I now know lots of examples where they’re not.

Here’s one example—from “Sorting Networks” in The Wolfram Demonstrations Project. Each of these pictures shows a network that will sort any set of 16 elements into order. The “classic” networks at the top have simple structures.

But it’s been known for a while that the best networks (shown at the bottom) don’t have that kind of simple structure. In fact, they almost seem in some ways quite random.

Well, what about bridges? I strongly suspect that there are much better truss structures for bridges than the classic ones from the 1800s—but they won’t look so simple.

I suspect one can do quite well by using simple rules to generate the structure. But as we know from NKS, just because the rules to generate something are simple, it doesn’t mean the thing itself will look simple at all.

Two students at our NKS Summer School (Rafal Kicinger and Tom Speller) have investigated creating practical truss structures this way–and the results seem very promising.

So what should the bridges of the future look like? Probably a lot less regular than today. Because I suspect the most robust structures will end up being ones with quite a lot of apparent randomness.

Those new kinds of bridges being built may be a bit shocking at first. After all, classic regular bridge structures—and things like the Eiffel Tower—are icons of our modern engineering-based civilization.

And in fact, even biology—with its iterative process of natural selection–probably can’t find structures as good—and irregular—as the ones I expect are out there.

So we’re going to end up being exposed to something really quite new. Something that exists in the abstract computational universe, but that we’re “mining” for the very first time to create structures we want.

We’re using these kinds of “mining” methods all the time now to find the best algorithms for Mathematica. I think bridge structures are a good example of where similar methods can be used for mechanical systems.

So if building better bridges is the test for what kind of science one should be using, I think it’s going to be a new kind of science that’s needed…

P.S. I haven’t done any serious analysis of these yet, but here are a few potential new bridge structures I just found in the computational universe…

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