The Fibonacci sequence, plant growth, and Vi Hart

(Cross-posted at NewAPPS)

The Fibonacci numbers are those in the following sequence of integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 etc. By definition, the first two numbers are 0 and 1, and each subsequent number is the sum of the previous two. The sequence is named after Fibonacci, aka Leonardo of Pisa, who introduced the sequence (known already in Indian mathematics) to Western audiences in his famous book Liber Abaci (1202) – which, by the way, is also one of the main sources for the dissemination of Hindu-Arabic numerals in Europe, no less. (Fibonacci had learned ‘Eastern’ mathematics while studying to become a merchant in North Africa -- see an earlier post on the importation of Indian and Arabic mathematics into Europe through a sub-scientific, merchant tradition.)

It has been known for a long time that the ratio between a number in the sequence and its immediate predecessor converges towards what is referred to as the golden ratio or ‘phi’: 1.618… It has also been known that the Fibonacci sequence and the golden ratio permeate a great amount of natural phenomena, in particular plant growth. This observation has given rise to all kinds of mystical, Pythagorean hypotheses on how numbers really are the building blocks of reality.

Enters Vi Hart. She is a video artist whose creations explain complex mathematical concepts in a fun, accessible way, mostly through “doodling in math class”. These videos can be seen as a manifesto against traditional math education and a plea for approaches which preserve the beauty and exhilaration that can be experienced through mathematics. She has a new sequence of videos in which she explains why the Fibonacci sequence is such a pervasive pattern in plant growth: the naturalist explanation (which has been known by botanists for a while) is that following a Fibonacci pattern allows plants to maximize sun exposure. No need to call upon Pythagorean hypotheses! Here is Part 1 of the series; for Parts 2 and 3, click here and here (H/T John Baez).

The applicability of mathematics to the study of natural phenomena is an old but still widely discussed philosophical question: is math (numbers in particular) really in the world, or are we just imposing an approximated, artificial order upon unruly natural phenomena? If numbers are not in the world, how come mathematics is such a powerful tool to describe these phenomena? But if numbers are in fact in the world, who put them there in the first place? Vi Hart’s Fibonacci videos suggest that what may appear to be almost eerie can also have a perfectly reasonable, down-to-earth explanation; the only premise to be accepted is the idea that, given time, the evolutionary development of living beings will tend towards maximization of use of resources that are important for survival (in this case, sun light exposure).

But anyway, eerie or not, one thing is clear: math is a many splendored thing. (And so is nature.)