Category: Wonder

If you have a fox, a goose, and a bag of beans, what is the best way to cross a river?

In a year of desert driving, I played this question on loop. I wanted a mind for numbers, but seemed to retain only the set-up sequences of word problems.

With a tendency to wondering and feeling too much at once, and with enough sky to lose myself in, I thought mathematical thinking might ground me.

One recurring problem was this: by a fire, under stars, I would go dizzy looking for the farthest ones until my vision blurred.

By then, I did not remember most equations, only the premises for which they were needed. If two trains x miles apart are traveling in opposite directions at different speeds, how much time until they meet? If Jack has eleven pieces of fruit and five are bananas, how many apples for Jill?

The antidote to dizziness, I was trying to learn, had something to do with overriding my first response, which was to be knocked off my feet by the size of it. The sky, that is. And, when it came to math, it was that fact that someone thought like this, imagined a way to sort a world such that these considerations, one parcel at a time, were all. The brilliance.

If a pie and so many guests, cut pieces. Not everyone will want the pie. To calculate circumference, use the number pi. An irrational number to spin the head, but if you knew how to use it, it could help you figure some finite amount of pie, stones, or tire tread.

In the passenger’s seat, I looked through glass and could not take it in. The riddle at least was a smooth and solid thing I could turn in my pocket like a river stone. The river was part of the set up. Mr. Stone was my teacher.

If you have to get across a river by boat. . . the set up went. How do you do it so the fox does not eat the goose, and the goose does not eat the beans? 

What relief. To hold one thing at a time, solidly. I wanted a valve for my mind, some pacing for the flow. One challenge. Then another. A way to stop and then go. At that point, the flooding was out of control. My perception far exceeded my abilities to make any sense.  

The answer to the riddle was: start with the goose. Mr. Stone told us why. But I was back in the river by then. Where to now, goose?

Who do you think you are? This was a challenge that frightened me some, because it tended to come at critical moments with a tone of authority, as if the person voicing it knew exactly what time Train A would cross Train B, how many apples on each, and whether or not the geese should be eating the beans.  If I could focus on one thing at a time, perhaps I would start to see it coming? And have a few answers ready, just in case?

I thought string beans would create less disturbance in the goose. But my mind tended toward the pintos I would buy in five-pound bags from Wal-Mart, which I would scatter in batches over a plate every time I prepared to soak them, checking for rocks. To find one was good. Here was a solid thing I could remove.

Who do you think you are? When these demands came, I would experience the full force of new awareness of the errors of my ways, in dizzying magnification. I meant to apply this force to finding some solution, but I had none.  Which river? Which goose, fox, season? Is anyone else on the boat with me? Am I allowed to touch the goose? Are there eggs to come?

The image of trains hurtling in opposite directions calls to mind rail spine, the nervous condition that did not appear until the advent of railroad travel, caused by the feeling of hurtling through space at speeds disconcerting to a body familiar with horse and foot travel. Not to mention the related and perhaps equally anxiety-producing imposition of standard time.

I had once seen a fox while running on a horse trail in lower New York. Much of the trail ran adjacent to the Hutchinson River Parkway, but certain parts meandered into woods and along lakes such that the roar of cars was more muted, the way crashing surf may be if you are several blocks away.

Perhaps if I had gone beyond 12th grade calculus, I would have developed a more familiar and integrated symbolic language with which to explore the interference effect of a series of infinite variables on a given problem and been more erudite in my explanations about baseline insecurities. But I hadn’t at the time and was still young enough to believe that eventually I might, If I focused harder, see with greater clarity. 

The river, between then and now, has continued to flood me. But the goose is still on it, and the fox, and the bag of beans. They rest at the banks, where the goose and the fox appear to wear bemused expressions, waving. I don’t know why it is this way, or where the boat has gone, but here I am, waving back.

***

This riddle, which I encountered decades ago, is one of those earworms that shows up again and again. I love the setup, the characters, the play, and the mystery. If, in a given year, I scratch 1,000 pages across several notebooks, an estimated 9.5 of them will feature this goose. Who knows why?  Rarely do I publish these, but sometimes it happens. Prior to today, I think the most recent iteration of these creatures in a published work happened in The Closed Eye Open, Issue 10,  Fall 2023, under the title Mathematical Goose.