Engines of Our Ingenuity

No.760:
GALILEO, NEWTON, AND MATH

by John H. Lienhard

Click here for audio of Episode 760.

Today, we learn why we've let physics intimidate us. 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.

Joseph Schwartz tells an arresting tale of scientific compromise. It's a tale about Galileo and Newton.

Galileo died, and Newton was born, in 1642. That was a time of terrible religious persecution. During their lives, 50,000 women were accused of witchcraft and burned alive. Nineteen witch hangings in Salem were small potatoes beside that slaughter.

Meanwhile, Galileo's science drifted into conflict with the Church. For years he'd attacked the Church's Aristotelian science. He did all right until late in life. Only near the end did the sun-centered universe become too much for the Church.

And the real question isn't, "Why did Galileo get into trouble?" It is, "How did he stay out of trouble for so long?"

Early in the game, Galileo learned a secret. He knew his observations must not contradict Church doctrine. But math was different. It was tool of God. He could wield math with impunity.

In 1623 Galileo published his treatise, Il Saggitiore. He took pains to say people wouldn't be able to read it unless they mastered its mathematical language. He got away with that. He held the Church off for years by dressing physics in math.

Sixty years later, Newton published his Principia. It was a formidable exercise in math. He wrote it in the near wake of Cromwell's religious persecutions. English conservatives were still attacking the new empirical sciences when Newton said:

To avoid being baited by little smatterers in mathematics, I designedly made the Principia abstract; but yet as to be understood by able mathematicians ...

A friendly theologian wrote Newton for help in reading the Principia. Newton gave a disarming answer:

... it's enough if you understand the Propositions with [a few of the easier] demonstrations.
You can, in other words, understand what he has to say perfectly well without the math. He's replaced one witchcraft with another.

So, Schwartz argues, physics took its modern form. Of course what began as protective cover eventually came to serve us. But we still know too many scientists who can't say what they've done without using math. Now they protect themselves, not from religious persecution, but from intellectual bullies. You hardly dare speak without mathematical erudition.

Someone once said, "Math lets fools do what you must be wise to do without it." Math can be a servant instead of a tyrant. It can truly be means for clarifying instead of obfuscating.

That's why I remind myself daily that I use math just because I'm no Galileo or Newton. Used properly, math lets me deal with things my mind couldn't hold otherwise.

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

(Theme music)


Schwartz, J., The Creative Moment. New York: Harper/Collins, Publishers, 1992, Chapter 1, "Florence 1623/Cambridge 1687."


The Engines of Our Ingenuity is Copyright © 1988-1997 by John H. Lienhard.

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