Ut tensio sic vis

And if two men ride of a horse, one must ride behind.

Shakespeare, Much Ado About Nothing

Sir Isaac Newton stands in popular estimation as the foremost intellect of his age; or perhaps, of any age. If a person is never truly dead while their name is spoken, then Sir Isaac stands with us still: partially overshadowed by Einstein at the dawn of the twentieth century, maybe, but never totally eclipsed.

But in the roiling intellectual cauldron of the Age of Enlightenment, even such a venerable polymath as Newton had some serious competition. As Newton himself modestly observed in a letter to a contemporary in 1676: “If I have seen a little further it is by standing on the shoulders of Giants.”

Except that one interpretation has it that the letter was not intended to be modest, but was rather a combative dig at the man to whom it was addressed: Robert Hooke, a man of but “middling” stature and, as a result of a childhood illness, also a hunchback. Not one of the “Giants” with broad philosophic shoulders to whom Newton felt indebted to, then.

Robert Hooke, as painted by Rita Greer in 2007. The painting is based on contemporary descriptions of Robert Hooke. No undisputed contemporary paintings or likenesses of Hooke have survived, possibly because of malicious intent on the part of Newton.

In popular estimation, therefore, it would appear that Hooke is fated always to sit behind Newton. At GCSE and A-level, students learn of Newton’s Laws of Motion, the eponymous unit of force, and his Law of Universal Gravitation.

And what do they learn of Hooke? They learn of his work on springs. They learn of “Hooke’s Law”: that is, the force exerted by a spring is directly proportional to its extension.

Ut tensio, sic vis.

[As extension, so is the force.]

— Robert Hooke, Lectures de Potentia Restituvia [1678]

Newton has all the laws of motion on Earth and in Heaven in the palm of his hand, and Hooke has springs. Perhaps, then, Hooke deserves to be forever second on the horse of eternal fame?

But look closer. To what objects or classes of object can we apply Hooke’s Law? The answer is: all of them.

Hooke’s Law applies to everything solid: muscle, bone, sinew, concrete, wood, ice, crystal and stone. Stretch them or squash them, and they will deform in exact proportion to the size of the force applied to them.

That is, if one power stretch or bend it one space, two will bend it two, and three will bend it three, and so forward.

The major point being that Hooke’s Law is as universal as gravity: it is baked into the very fabric of the universe: it is a direct consequence of the interactions between atoms.

Graph of interatomic force against distance between two atoms. Hooke’s Law applies in the red circle.

Now before I wax too lyrical, it must be pointed out that Hooke’s Law is a first-order linear approximation: it fails when the deforming force increases beyond a certain limit, and that limit is unique to each material. But within the limits of its domain indicated by the red circle above, it reigns supreme.

How do you calculate how much a steel beam will bow when a kitten walks across it? Hooke’s Law. How could we model the stresses on the bones of a galloping dinosaur? Hooke’s Law. How can we calculate how much Mount Everest bends when it is buffeted by wind? Hooke’s Law.

Time to re-evaluate the seating order on Shakespeare’s horse, mayhap?

1 Comment

Filed under Philosophy

One response to “Ut tensio sic vis

  1. Yet having read Lisa Jardine’s auto-bio and more recently other’s on various Unit namesakes I am drifting away from my previous earnest view that such “giants” matter greatly in the teaching of the subject. Like History there is maybe too much to cover to do justice to individual stars especially if, as with Einstein, you have to really cover the mistakes as well. I think that the problem in Eng Lit with Shakespeare is related too; he wrote some hard to understand stuff in funny lingo (cf Maxwell’s original equation format). Then there’s the geography angle I enjoy discovering that its not just UK scientists that we should be appreciating – there’s Langmuir’s American lady assistant for one who invented anti-reflective coatings etc.

    And finally (to cover Engineering & Design Tech) I remember from when I was much younger, a questioner at the conclusion of the latest Japanese manufacturing wizzo math/stat presentation had it pointed out that all this only applied in the linear case.

    O bene talis est vita

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