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Fibonacci’s 0 and 1’s
By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number
is the sum of the previous two.
The sequence Fn of Fibonacci numbers is defined by the recurrence relation:
Fn = Fn-1 + Fn-2
with seed values
F0 = 0, F1 = 1
Both the Fibonacci sequence and Wheeler’s foundational question rely upon 0 and 1. Despite Wheeler’s
0 and 1 being mainly symbolic, the basic idea of 0 and something as alternative answers to yes/no questions lends to information. Likewise, Fibonacci begins with something and nothing.
Fibonacci numbers occur in mathematics as the sums of shallow diagonals in Pascal’s triangle, they can
be found in different ways in the sequence of binary strings, and are related to the Golden ratio. Every
second Fibonacci number is the largest number in a Pythagorean triple. All positive integers can be
written as a sum of Fibonacci numbers. Fibonacci sequences appear in biological settings, in two consecutive Fibonacci numbers, such as branching in trees [1], arrangement of leaves on a stem, the fruitlets of
a pineapple [2], the flowering of artichoke, an uncurling fern and the arrangement of a pine cone [3]. The
Fibonacci numbers are also found in the family tree of honeybees [4].
Perhaps it isn’t too much of a leap of faith to include reality’s relationship with information, “It from Bit”,
as another of Fibonacci’s attributes.
ICY SCIENCE | QTR 1 2014