The Parable of the Mathematically Inclined Rancher

One day while teaching, Josh was asked, ”Teacher, since all other formulas seem to have failed, why don’t we just base immigration on the Fibonacci Sequence?”

Josh spoke thus:

A rancher was counting cows as they came into a holding pen.

One cow passed through the gate.

Soon after, a pair of cows passed through the gate together.

A few moments later, three cows passed through the gate.

A group of five cows came next.

The group of five cows was followed by eight cows in a bunch.

The rancher watched as thirteen cows followed the eight cows into the pen.  The rancher saw nothing notable in this.

The grouping of twenty-one cows that next came into the pen was indistinguishable from the grouping that preceded it.  The rancher did note that the cows were now entering more quickly.

There was a small gap before the next group of cows approached.  The rancher counted and duly recorded thirty-four cows.  One of the cows, the rancher noted, had a white patch above its eyes that made it look as though it was knitting its eyebrows in mathematical contemplation.  The rancher did not linger on this thought because a larger group of cows was following on.

The rancher had to count more quickly now, as this group was comprised of fifty-five cows.  Two cows jostled each other in the gate, and the rancher needed to be careful not to miss one or to double-count them.  The rancher very nearly lost count at forty-three, but did not falter.  The rancher decided that with the next group of cows, it would be best to make a tick mark on the rancher’s pad as each cow passed.  The rancher had a good memory and a good head for numbers, but the cows were coming in larger and larger groups, and larger groups meant less-predictable movement patterns.

When the next group of cows had passed there were eighty-nine new tick marks on the rancher's paper.  The rancher had a hunch this was one short, so double checked the figure to be sure.  Yes, eighty-nine was correct.

There was one more group to be counted, the last group being the largest.  The rancher counted out loud while simultaneously making the requisite tick marks.  As the last cows came in, the rancher counted, “one-forty-one, one-forty-two, one-forty-three.”

The herd were all gathered.

The rancher turned to a neighbor who was watching.

“I think I need another cow,” the rancher said.