Mathematics Corner: Real-Life Math Joke Debunked

By: Jimmy Z., Grade 8

Mathematics Corner: Real-Life Math Joke Debunked

Hey guys, Jimmy here with my first blog post! If you don’t know who I am, I’m an eighth grader at Greene with a slight amount of nerdiness. Due to that aforementioned nerdiness, I enjoy browsing mathematical books during my free time (please don’t make fun of me). In one of the books, namely Professor Stewart’s Hoard of Mathematical Treasures (I advise you to check it out from the Palo Alto Library if you are also intrigued by math), I came across a quaint mathematical joke that goes something like this:

“Knowledge is power and time is money. But by definition, power = work/time. So, time = work/knowledge. So this implies that for any amount of work, the more you know, the less money you get.”

(By the way, for the curious reader, this was on page 239, under the label “Ah, That Explains It…”.)

At one glance, it is easy to tell the conclusion statement is inherently flawed. If in our society an abundance of knowledge leads to a lower salary, why would schools exist? Why would your parents (hopefully) strive for you to attend a prestigious college? Who would put in the time and effort to learn only to receive a fiscal disadvantage?

Let’s dive into the intrinsic mistakes present in these curious equations!

The errors in this system of equations lie not in the algebraic manipulations of statements (they’re entirely valid) but in the fallacious belief that the word “is” and the equal sign are equivalent.

First of all, the oft-repeated proverb “Knowledge is power”. In the equation, it is mathematically implied to be stated as “Knowledge equals power”. On account of the rules of mathematics, this can be manipulated as “Power equals knowledge”. However, knowledge is only a form of power, so not all power is derived from knowledge. As my Social Studies teacher would say, there are six types of power, as follows: Physical Force, Wealth, Ideas, State Action, Social Norms, and Numbers. However, one glance at the list will verify the fact that not all of the six items are knowledge-related. So, although the statement “Knowledge is power” may be true, the equation “Knowledge = power” may not necessarily hold for all definitions. For clarification, the proverb might be rewritten as “Knowledge is a form of power”, but one can agree that that is not as catchy as the original.

The same fate befalls the other proverb, “Time is money”. The bold assumption that the word “is” implies equality can again be refuted. One can have time without money, for example a broke middle school student with a plethora of free time. Vice versa, a counterexample can be found too, such as a millionaire who spends all their free time in the office. Therefore, the second proverb is also fallacious. It would be logically beneficial to transform it into “Time is precious like money”, but as my English teacher would point out, the phrase would also be a metaphor, and such a transformation would ruin the figurative language effect.

So what did we learn? We found out that well-known sayings such as proverbs cannot be simply interpreted. Mistakes are bound to occur, particularly in a study as rigorous as mathematics. But don’t disregard proverbs completely though either; you just have to discover the piece of wisdom in them that relates to your personal life.