Word Problems, Poverty, and Beauty

By Borden31 (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons

Consider this word problem posed by the mathematician Steven Strogatz:

Suppose three men can paint three fences in three hours. How long would it take one man to paint one fence? (Steven Strogatz, The Joy of x, p. 64)

Did you guess 1 hour? You're wrong. The correct answer is three hours. Strogatz explains:

If you visualize the problem--mentally picture three men painting three fences and all finishing after three hours . . . the right answer becomes clear. For all three fences to be done after three hours, each man must have spent three hours on his. (Strogatz, p. 64)

This problem illustrates the value of mathematics: math forces us to pause and think. It forces us to question our assumptions and pay careful attention to the problem at hand. It forces to ask these very important questions: What do I know, how do I know it, and what is the relationship among the things I know? Math is, Strogatz says, a "practice in being mindful."

Math can also be a spiritual practice. Here's why:

• Math teaches us to slow down. If you looked at the problem linguistically, you might see the pattern 3 men : 3 fences : 3 hours and rush to the conclusion that 1 man : 1 fence : 1 hour. But this incorrect. If you stop and visualize, you can see the reality of the problem. Once you see that, the solution is straight forward. It's the same in our spiritual life. If we rush to judgment about our feelings of consolation and desolation, we will not understand what God is trying to tell us. Instead, if we stop and attend to these feelings without judgment, the answers will become clear.
• Math teaches us how to use our imagination. When we visualized the problem--that is, when we used our imagination to see the problem in a new way--the answer became clear. Imagination is essential in the spiritual life. God speaks to us through our imagination. When we see a beautiful sunset, when our hearts are lifted by song, or we see the face of Jesus in the poor, the suffering, and the marginalized, our imagination speaks to us of God.
• Math teaches us the elegance and beauty of simplicity. The solution to the above word problem was simple, once you saw it in the right light. Of course, I could have solved it another way. I could have imagined that 3 men all worked on one fence together. If it took them three hours to paint three fences, then it would take all of them one hour to pain a single fence. Assuming they were working at equal rates, I can conclude that each man paints one third of a fence in that hour. Thus, if that man was to paint the entire fence, it would take him 3 hours (1 fence / (1/3 fence/hour) = 3 hours). But the first way was simple, elegant, and beautiful. There is beauty in simplicity. I understand this spiritual truth in a single word: poverty.
• Math teaches us humility. I must admit--I answered the problem incorrectly when I first read it. That really pissed me off. I have a B.S. in Math and spent a year in graduate school studying math. I've been a math editor for years. I should have gotten that problem right! But humility requires me to acknowledge when I am wrong and accept correction so that I can see the problem in a way that makes it easy to solve. It's hard to ask for help. Math teaches us to do exactly that.

Slow down, use your imagination, appreciate the beauty of simplicity, and practice humility--these are spiritual practices that math can help you develop. Here is another problem to ponder:

A bathtub has two faucets--a hot-water faucet and a cold water faucet. The cold-water faucet can fill the tub in a half-hour; the hot-water faucet can fill the tub in one hour. How long will it take to fill the tub when both faucets are running together? (Strogatz, p. 59)

I'll leave it to you to discover the answer.