“Ut Tensio Sic Vis”: Introducing the Hooke Graph

Or, The Return of Spring

By John Ladd

A 2004 portrait of Robert Hooke by Rita Greer, via Wikimedia Commons. Note the spring by his left elbow.

In A Description of Helioscopes and some other Instruments (1676), the natural philosopher Robert Hooke promised to publish a theory of elasticity sometime in the future and teased his readers with a frustrating (if pleasingly alphabetical) anagram: ceiiinosssttuu.

Thankfully, nothing in the current Six Degrees interface is quite so obscurantist, but there are parts of the site that have somewhat puzzling names. Right now in our visualization view, you can search for a “network,” and the result is a very specific kind of graph: a force-directed network visualization. These force-directed graphs are the dominant mode of visualized networks, the collection of nodes and links that you’re used to seeing everywhere. Here’s our friend Robert Hooke’s graph as an example:

(Go to the live version of this graph on Six Degrees)

This familiar arrangement is not the only way to display a network. Networks, after all, are made of data—edge tables or adjacency matrices that can be visualized in any number of ways (see below). And we have more visualizations in store for our redesign: circular layouts, timelines, and other schemes are in the works.

Examples from the web of other visualization layouts, from left to right: arc diagram, chord diagram, adjacency matrix, and hierarchical graph drawing¹

But we quickly ran into a problem. Since we plan to present more than one type of visualization to the user, it’s no longer suitable to refer to these original graphs simply as “networks.” Internally, we started calling them force-directed graphs to differentiate, but this name didn’t seem right for our site—it’s a bit vague and potentially confusing to the newly-initiated. In a force-directed graph, what kind of force is doing the direction?

This brings us back to Hooke and his mysterious anagram. Two years after A Description of Helioscopes, Hooke published the answer to his puzzle in Lectures de potentia restitutiva, or of spring. The anagram stood for “Ut tensio sic vis,” a principle that describes the behavior of springs. Basically it states that “a spring’s extension or displacement from its neutral position is directly proportional to the force applied.”² This principle became known as Hooke’s Law, and can be used in conjunction with other forces to produce network graphs in which there are “as few edge crossings as possible.”³ That is to say, Hooke’s Law helps create visualization algorithms that make network graphs readable. This is why force-directed visualization algorithms are often referred to as “spring layouts.”

We found the combination of a seventeenth-century scientific principle and modern network visualization impossible to resist, so we’ve rechristened our force-directed graphs “Hooke graphs,” in honor of the man himself. Look for the newly-redesigned Hooke graphs when the new site is released, and happy (belated) first day of Spring.