In 1988, when I first encountered mathematician John Paulos’ national bestseller, “Innumeracy: Mathematical Illiteracy and Its Consequences,” I was heartened that he was highlighting what I had long known was a serious weakness in the general mathematical knowledge of “the common person in the street” (T.C.PITS)*. 

Sadly, however, it seemed to me that at the time that much of the national media reaction to Professor Paulos’ revelatory focus on disheartening “innumeracy” was both reactionary and accusatory. People were ignorant (so, blame the victim) and our educational system was a miserable failure (isn’t it always?). 

These all-purpose “spanking switches” with which to paddle the public are always transparent excuses and diversions signaling an aversion to any real willingness to engage with a social problem—in this case, the serious deficiency in the quantitative understanding of T.C.PITS. 

Unlike Sputnik, which 10-fold empowered our space efforts, no national projects were launched by the Paulos’ revelations. They became another collection of insights resting on a shelf.

A billion, not a million, and certainly not a trillion

Increasingly, in more current times, a billion (as in a billion dollars) and a trillion dollars (as in deficits) are both part of our everyday conversation. But how “big” are those numbers? (More properly, what are their magnitudes?).

As a child, I watched the McDonald’s “burgers served” sign over months and years go from enumerating 5,10, 50,100 billion, etc., eventually simply dropping the numerical count and writing an all-purpose and timeless “billions served.” 

A billion

By way of example, like another famous person, suppose you were born 2,000 years ago and had a billion dollars to spend (this will not ring plausibly true to historians, but they are not here). Being a modest billionaire, let us say you spent just $1,000 each day. In these 2,025 years that you have lived(!), have you yet spent your billion-dollar fortune?  Emphatically not!

For one year, $1,000/day x 365 days/year = $365,000 each year

For 2,025 years, 2,025 years x $365,000/year = $739,125,000

Since $1,000,000,000 - $739,125,000 = $260,875,000, that means you have more than $ 0.25 billion remaining. 

In today’s world, do you think you could “make it” on a mere $1,000 a day? Could Elon M.?

That still raises two questions, both up for next time: How high is a tower stack of 50 billion McDonalds hamburgers? Also, if you could string 50 billion burgers in a horizontal straight line, how far would that line stretch? For instance, could you go from Honesdale, PA to Miami, FL (like some snowbirds), and then, while still stringing burgers in a line on the road, perhaps doggedly return?

If you figure out some answers, send them to me via copyeditor@riverreporter.com. As with all math problems, if you solve these, the reward I offer is more, and probably harder questions. It’s all in fun—but not only.

*A modern and transparent play on a once popular mathematics book titled “The Education of T. C. MITS (The Celebrated Man In The Street): What Modern Mathematics Means to You” by Lillian R. Lieber. (1942)

John Pace is a retired mathematics professor. He lives in Honesdale, PA.