It’s that time of year when we are staring at those columns of numbers on our balance sheets, trying to prepare for taxes. It is a challenge trying to keep up with the bookwork for our 18 separate farm enterprises that all operate within the same farm framework. Unfortunately, no one in our family has a delight for numbers and math. My brain isn’t exactly wired for numbers. I received good grades in school on arithmetic and algebra and such like, but that doesn’t mean I understand it! I’ve discovered that my off-the-wall reasoning and math don’t always mix.
I recall a lengthy discussion with my teacher about the concept of how two positive numbers can equal a negative number. I argued that this concept didn’t make sense, because on a thermometer there is no way that you can get two hot temperatures to equala cold one. She said I was way off in another field, but I still wanted to know why positives and negatives weren’t consistent across thefield. I gave up and just wrote the answers they wanted, even if I didn’t understand them.
Just the other evening Dad was trying to explain the concept of compounded interest to me. I was shocked to discover that, essentially,the interest rate doubles every year on what you have borrowed. Dad said I was doing the math wrong; that it wasn’t correct. After anhour of comparing numbers, we discovered that my method of computing still arrived at the same answer, just from a whole differentdirection. And herein lies my greatest struggle with math, because I solve my problems backwards from the conventional way.
You just can’t trust numbers. I know there are some folks who say that numbers never lie, and they may not, but the way they arecalculated can be deceiving enough that it is nearly a lie. I found a good illustration of this in an old Peanut comic strip. I typically fail tounderstand the Peanut comic strips, but on rare occasions I find them amusing or profound. In this case, Charlie Brown’s little sister is trying to practice her alphabet letters. “You just can’t trust numbers”, she sighs as she hold up her paper. “Now this is supposed to be aThree, but now (she tilts it forward) it looks like a mountain. And here it could be a bird (laying on its back) or it could even be an “E”!”She sighs heavily. “You just can’t trust numbers!”
I agree wholeheartedly with this discouraged elementary student. Numbers can be tricky and slippery. Just when you aresure the numbers are saying you have made a profit, they flip and you and show a loss. The best illustration of this concept is an old story:
Three young men were traveling and stopped to seek a room at a hotel. The clerk said that he had a room available for $15. The boyseach paid $5 and went up to the room. (Obviously, this story is a historical one and not modern day. You can’t even buy a pillow for $15!)But this clerk realized he had overcharged the boys. The room they took should have only cost $10. Being a man with a conscience, he instructed the bellboy to run the $5 reimbursement up to the boys. On the way up to the room, the bellboy considered the fact that theboys had all paid equally for the room. Having less of a conscience than the clerk, the bellboy decided that since $5 would not divide equally among three, he should solve the confusion and pocket two of the dollars. Each boy was delighted with his one dollar reimbursement, as that brought the cost of the roomdown to $4 for each of them. But, here is a problem: The three boys each paid $4 and the bellboy has $2, but that totalsonly $14! Now, where did the other dollar go?
Some folks will say, well you didn’t do the proper math steps in this story, which is why you have come up with a missing dollar.But I say, who says? This story illustrates a lot of things. Can’t you just
see some slick accountant saying to an IRS agent “No, no you didn’t do the proper math step!” I believe that a lot of people don’t actually cheat on their tax returns; they just know how to do the math so that the $15 looks like $14. Or the 15 million looks like 14 million. This doesn’t encourage me at all, when I know that the IRS may be doing the math differently than I do when they review my tax return…
But the bottom line is, numbers are nimble little guys, and you never know what form they are going to show up in. I haveconcluded that mathematics is a bit like art: some of it can be understood, and some of it never will.