||| ORCASIONAL MUSINGS BY STEVE HENIGSON |||
About 20 years ago, someone who lives near Orcas Village and the Ferry Landing made a serious error and released a domestic rabbit or two. Since then, the feral rabbit population has been growing, and they have marched mostly northward from the Ferry Landing’s greensward and forest, all the way past Eastsound, to the green grass of the homes along North Beach. Rabbits reproduce quickly, and the pressure of a growing population forces young bucks and does (or, more properly, jacks and jills) to look for greener, emptier pastures.
The speed of Leporidae reproduction has attracted the attention of farmers, hunters, and, believe it or not, mathematicians for centuries at least. Back in 1202, Leonardo of Pisa wrote a book about how to do mathematical calculations. In it he proposed that it was easier to use Hindu-Arabic numbers, rather than Roman letters, to do math and arithmetic. Nobody seems to have thought of that before, and the concept took Europe by storm. As one of his examples, Leonardo used the way that rabbits appear to, well, um, multiply.
Nowadays, we call Leonardo of Pisa by the name given him in 1838, by an Italian historian, which combines his family name with his place in its lineage. Leonardo was “filius Bonacci,” the son of the Bonacci family, so today we call him Fibonacci. Under the most ideal conditions, Fibonacci postulated, one rabbit is soon joined by another who wanders over to see whether or not the grass really is greener. That soon results in the production of another rabbit, and all of them, eventually and incestuously, produce a few more rabbits. And on it goes.
The sequence of Fibonacci’s set of multiplying-rabbits numbers is formed by finding the sum of the most recent integer plus the immediately previous one. We can start with zero, which is the modern method, or with one, as Fibonacci proposed. Either way, it comes out the same in the end. The series is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, … and so on.
Now, the truth is that Fibonacci was merely playing around with numbers, finding entertaining ways of getting people interested in using Hindu-Arabic notation. Rabbits don’t actually reproduce like that because they don’t live in an ideal world. Rabbits have predators, for instance minks and hawks. Rabbits associate closely, so they are prey to diseases which occasionally spread through, and decimate, their population. But, in truth, a band of rabbits does expand in a somewhat Fibbonaccian way, if you make allowances for predation, disease, and other negative factors.
Also, Fibonacci’s sequence of numbers actually does occur naturally, and in some surprising places. If you were to look separately at each circular segment of the spiral of the seeds in the head of a sunflower, you would frequently find that the number of seeds in each successive segment follows Fibonacci’s postulation. It also appears in the branching of trees, the arrangement of leaves on a stem, the number of hand-scratching points on the surface of a pineapple, and the location of pine nuts in a pine cone.
So when you see a feral rabbit making free with the carrots in your garden, you can freely curse the fool who let the first of them go, down at the Ferry Landing, while at the same time marveling at how we came to use Hindu-Arabic numbers, and the fascinating example that Leonardo of Pisa used to promote them.
Steve,
I love your columns: the connections between history and our current reality. Connections are what life is about. Just connect….
Tularemia might also be good to address? This is how bunnies’ epidemiology manages their overall mortality.
“filius Bonacci” I did not know that!
The Hindu-Arabic numeral system’s evolution, also fascinating because of the use of Zero, so it is interesting that “filius Bonacci” did not start his series with zero even though his cunicular problem was designed to illustrate the unique advantages of this numbering system. Even Leporidae calculus one would presume must include zero ..even as a wishful hypothetical. It is also astounding that 20 years ago we had not all learned the 200 year old lesson of Australia where a few bunnies took over that whole island. Interestingly the only hungry jumping gnawing multivorous multiplicitously fecund beasty to infest Orcas until then was sea-surfin WSF-synchronized Bambi 2.0.. Herself.