No. 2372:
Hobbes and Wallis

Guest post by Andrew Boyd

Today, a rancorous feud. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. 

He was the Apostle of Infidelity; the Monster of Malmsbury; the Insipid Venerator of a Material God. His name was Thomas Hobbes. Today he's considered one of the greatest political philosophers in history.

Thomas HobbesHobbes earned his reputation by offending pretty much everyone. He wasn't a bad person. But he disdained religious institutions. And he didn't believe in leadership by birthright. That put him at odds with both the Church and Kings. He described the human condition as "solitary, poore, nasty, brutish, and short"–not exactly a message of hope for the masses.

Respected mathematician John Wallis was among those who didn't like Hobbes or his ideas. Wallis might have kept his contempt to himself. But then Hobbes dabbled in Wallis' domain–mathematics. Euclid's Elements– a marvelous work of pure deductive reasoning– captivated Hobbes. So much so, it even influenced his political philosophy. Hobbes wanted to reason his way to truth- just like mathematicians a lofty goal, even if he couldn't possibly achieve it.

John WallisBut where Hobbes got into trouble was trying to solve real, bona fide mathematical problems. Hobbes claimed he could "square a circle": using only a compass and straight edge, construct a square and a circle with the same area. The problem was first posed by Euclid, but he couldn't solve it. Many people played with it over the centuries. Many people offered false proofs. Turns out it's not possible to square a circle. Mathematicians proved this in the late nineteenth century.

So Hobbes was wrong. And the mathematician Wallis tore into him – not just Hobbes' math, but the "poisonous filth" he "vomited." Wallis dissected Hobbes' arguments, viciously ridiculing them one by one. He savored showing the world "how little [Hobbes] understands the mathematics from which he takes his courage."

Hobbes returned the favor, attempting to refute Wallis' claims and referring to Wallis' writings as "mere ignorance and gibberish." Thus began one of the great feuds in the history of science. Name calling, slander. The bickering continued off and on until Hobbes' death almost a quarter century later.

Disputes are nothing new. They're common between public figures. A political candidate takes the stage and proclaims we should raise taxes. Another takes the stage and says we should lower them. Both claim to be right. Both provide rhetoric to support their position. But neither can prove– in a mathematical sense – who's right and who's wrong.

But the feud between Hobbes and Wallis was different. Hobbes was wrong. It's as if he'd claimed one equals two. Through arrogance and ignorance he clung to his position, even as he lambasted arrogance and ignorance. In his greatest work, Leviathan, Hobbes writes:

For who is so stupid as both to [make a] mistake in Geometry and also persist in it, [even] when another detects his error…?

Apparently, Hobbes was. 

I'm Andy Boyd at the University of Houston, where we're interested in the way inventive minds work.

(Theme music) 

Much of the factual material for this essay was taken from H. Hellman, Great Feuds in Science. (New York: Wiley and Sons, 1998).

See also: Douglas Jesseph, Squaring the Circle: The War Between Hobbes and Wallis. (Chicago: University of Chicago Press, 2000). 

Pictures courtesy of Google public domain pictures.