Dec 3, 20213 min read

FIVE EQUATIONS THAT CHANGED THE WORLD

by Michael Guillen.

A book that expounds not only the power of mathematics but also the humanity of physics

Every student who has taken a course in physics probably was taught the five equations which are the subject of this book. While everyone remembers Newton’s law of gravity, Faraday’s law of electromagnetic induction, and Einstein’s special theory of relativity (at least the name if not the meaning), I doubt how many remember Bernoulli’s law of hydrodynamic pressure or Clausius discovery that the total entropy of the universe is always increasing. Part of the reason is that few textbooks, or for that matter, few physics teachers, would tell the students the background and events leading to the discovery, the human drama involved, and how these five equations changed the world. These missing links, which are what make physics so interesting and reveal the subject’s humanity, are described masterfully in this book.

Let me jot down a few things I learned which my education seemed to miss before I read this book.

It has become folklore that Newton discovered gravity when an apple fell on his head. Actually, the moon also played an essential role, and she was not given proper credit. Indeed, if the night when the apple fell on Newton’s head was a moonless night, humanity may have to wait a while, perhaps even a long time, before the law of gravity was discovered.

Although Johann Bernoulli, father of Daniel Bernoulli, taught his son mathematics, he became so jealous of Daniel that he conspired with Leonard Euler to try to deny Daniel the credit of being the first to discover the law of hydrodynamic pressure. Although Johann did not succeed in this duplicity, Daniel became so disgusted that he decided to quit mathematics. What a loss to humankind!

I wonder how many know of the name “Sandemanian Christian”, a Christian Sect which believed that only the poor could enter heaven. This Christian Sect no longer exists, but Faraday was a Sandemanian, which was why he declined when his bookbinder boss, who was childless and offered Faraday to inherit his fortune if he stayed to work in the shop, instead of taking the low-paying job as Sir Humphrey Davy’s assistant in the Royal Society. Faraday also declined to be buried in Westminister Abbey.

Rudolf Clasius combined energy and heat into a single entity he called “entropy”. He was a melancholy guy, who thought that the essence of both life and war were the epic and eternal struggles between right and wrong, life and death, victory and death. It was perhaps fitting that he was the scientist who discovered that entropy was always increasing, which led to the inevitable conclusion that eventually the Universe is running inexorably toward death and will be completely lifeless. (Ludwig Boltzmann later showed that entropy was a measure of a system's disorder.)

For Einstein’s special relativity, we always learn that the second postulate is “The speed of light in a vacuum is the same (300 million m/s) in all inertial reference frames regardless of the motion of the observer or source“. According to the author, this was inspired by the experiments of Armand Fizeau in 1851. However, I found no reference to this in physic textbooks, including the famous “Feynman’s lectures on physics.” If this is true, it seems so unfair to Fizeau.

It is amusing, but appropriate, that the following quote of Mark Twain appears in the chapter about entropy:

“Life would be infinitely happier, if we could only be born at the age of eighty and gradually approach eighteen.” (entropy decreasing?)

In conclusion, this is a book that expounds not only the power of mathematics but also the humanity of physics.