The Power of Math

By Richard Gosselin

There is no doubt that most intelligent people would recognize that a literate public is necessary for a prosperous and well-functioning society. But when it comes to the question of whether it is necessary that that same public be numerate my bet would be that there wouldn’t be as much agreement. How many of us of heard not only from our own children but even from grown men and women that they are just “not good at math?” There seems to be an obvious dichotomy here. It’s a public scourge to be known as illiterate, but it seems to be in fashion to claim that one is not good at math. A good case can be made that this notion is not only unfashionable, but it is also not conducive to a good life in a free society. Let me offer a few examples to illustrate the point.

In a two party system it appears to be a simple matter of what should be required for one candidate to win an election. Whoever has more than 50% of the vote is the winner. Right? That solution is uncontroversial. Now let’s introduce a third candidate. Is the obvious answer still the person who earns more than 50% of the vote? Well, it could be. But what happens if no one gets more than 50% of the vote? Is the simple answer that we merely declare the winner to be the candidate with the most votes? The election rules could certainly be written this way. In fact some states and municipalities have rules that follow just this simple formula. However, in a democratic society that values majority rule, one might be less inclined to support such a rule if the possibility leads to a candidate being declared the winner with only 35% of the vote! How could this be you say? Well, it is very possible that the votes could be 35% for candidate A, 33% for candidate B and 32% for candidate C. But that would mean that 65% of the public actually voted against the “winning” candidate. A small amount of numeracy goes a long way to help the informed citizen realize that even something as seemingly simple as voting requires some analytical reasoning.

Now let’s take a look at another example. Ben Franklin is famous for his witty sayings, not the least of which is “a penny saved, is a penny earned. ” Franklin actually practiced what he preached. Before he died, he bequeathed to the cities of Philadelphia and Boston the amount of 1000 pounds sterling each. The only condition was that each city must invest the money in such a way that it could earn 5% annually and that the earnings could not be touched for 100 years! After that time, each city could spend ¾th of the money and reinvest the remaining 25%. But there was one more catch. Both cities needed to wait another 100 years before it could spend the new sum of money that awaited them. Now if things had all worked out as planned both cities would have had about $650,000 waiting for them after the first 100 years and would have been able to spend ¾ of that and invested the remaining 25%, which would have been about $160,000. Taking this sum and investing it another 100 years could have potentially led to a sum that would have easily topped $21 million! All of this of course is possible with the power of compound interest. Now the truth is a little less dramatic but still very impressive. Because of economic hard times it wasn’t always possible to invest and earn a rate of return of 5%. Nonetheless, after the 200 years Boston sported a balance of over $5 million dollars while Philadelphia earned about half that amount. Now, if that isn’t an argument for the boys to learn their exponents and learn them, well then, I don’t know what is.

Lastly, I close with a simple, but gritty example. In fact it’s a personal example. In our home, which was built in the 1960s, the kitchen wasn’t big enough to have a pantry. Not to be deterred, I decided that we would buy a piece of furniture with drawers and cabinets from IKEA, which could serve as a suitable substitute. I dutifully took measurements of the width of the kitchen and the height as well. When I went to the store, I looked for the unit that had a height that was lower than the height of my ceiling. Not wanting to waste any space I decided to pick one that milked it for all it was worth and came within just a couple of inches of touching the ceiling. So far, all looks like it is going according to plan. However, I knew that I would have to assemble this furniture on the floor and then lift it upright when complete. This meant of course that since the unit had depth as well as height and width that the hypotenuse would be larger than the height of the unit and could potentially give rise to the possibility of hitting the ceiling as I raised the assembled piece of furniture against the wall. So I used the Pythagorean theorem to calculate the hypotenuse and discovered that I had one-half inch to spare. Feeling confident, I bought the furniture, made my way home and with great enthusiasm began to assemble what would become our new pantry. Now the moment of truth came. I enlisted one of my boys to help me raise it up and lo and behold it hit the ceiling! How could this be? Well, it turns out that after careful measurement of the ceiling once again I discovered that one side of the room measured slightly smaller than the other side of the room. So what happened? Well, the house is over 50 years old. There had been some settling, and I didn’t take this into account when I had only measured one side of the room. Moral of the story – measure twice, cut once. It did, however, have a happy ending. I removed the top of the unit and the front and simply installed it against the wall. I then used a ladder to put the top and the front on with the help of two of my sons. It turns out that knowing just a little bit of math can be exceedingly helpful.

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