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See Inside Scientific American Volume 306, Issue 5

Math Rules

Some equations touch all our lives--whereas others, well, not so much



Illustration by Matt Collins

In his new book, In Pursuit of the Unknown: 17 Equations That Changed the World, Ian Stewart recounts one of the worst jokes in the history of science. You can develop your own setup from first principles once you know the punch line: “The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides.” Never mind how Native Americans were in possession of a hippopotamus—the important thing is that the Pythagorean theorem is so well known that comedy writers consider it fair game even if that game couldn’t possibly be found on the correct continent.

Stewart, who formerly wrote the Mathematical Recreations column for Scientific American, takes the reader on an engaging tour of vital math for a modern world. We go from Pythagoras’ right triangle (a2 + b2 = c2)—nice—to Newton’s law of gravity (F = G)—good—to Einstein’s special theory of relativity (E = mc2)—still with you—to the Navier-Stokes equation governing the movement of fluids——which pretty much convinced me to change my career trajectory from science to science journalism.

I highly recommend Stewart’s wonderfully accessible book and now share with you some additional equations not in its pages but of importance to me, personally.

HA > H at any time (t)
Technically an inequality, HA > H (t) means that at any time (t), the number of horses’ asses (HA) will exceed the number of horses (H). (Time should be understood to be limited to the period starting with the evolution of modern humans and ending with our eventual extinction.)

This concept is so obvious as to practically have the standing of axiomatic truth. The inequality clearly holds at racetracks and equestrian events, where HA may only slightly outnumber H. (Have you seen the hats some of those horsey folk wear?) Its true power to describe reality, however, is on display in situations where H may vanish to 0, such as professional wrestling or the vast majority of the programming on C-Span.

PSM (L) = 0
Someone’s winning the lottery, but not me.

MS1 + S2 + 3d = WTS
I discovered this equation only in the past few months, when I was traveling and working odd hours to the point of abandoning customary daily ablutions. The equation states that three days (3d) after your last shower (S1) and shave (S2), any man (M) will look exactly like William Tecumseh Sherman.

20x + 10y + 5z = 0C
This equation clearly states that when attempting to use a vending machine that takes singles, you will have in your possession some integer numbers of 20s, 10s and fives but no ones—and, therefore, no candy.

OPS =  [AB × (H + BB + HBP) + TB × (AB + BB + SF + HBP)] /
[AB × (AB + BB + SF + HBP)
]
When I was 10 years old, I started devoting ridiculous amounts of time to the analysis and generation of baseball statistics. Back then, it only got about as complicated as batting average equaling hits divided by at bats. Now, thanks to Bill James and other mathematically oriented fans, we have much more valuable stats, such as on base plus slugging (OPS), which also stands for the reaction of more casual fans to one’s spouting about it—namely, “Oh, please, shuddup.”

0.5x = 100
This equation had a major effect on a friend, which cascaded in my direction. The friend wanted to be an automotive engineer. But he had performed poorly in high school algebra and knew that there was more complex math to come on the way to any engineering career. So we worked for many hours on the algebraic basics. At the end of said hours, my friend was able to determine that 0.5 × 100 was equal to 50. But the leap to determining the X in 0.5X = 100 remained unleapt, which led to my advice that he consider a career as rewarding as automotive engineering that avoided complicated figuring. He went on to become an automobile insurance adjuster and is an invaluable resource to me whenever my car is struck by some HA.

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