There are some weird connections to Fibonacci numbers in nature:
For example, in the bee community, an egg laid by a unmated female will hatch a male (which in that case only has one parent, the mom bee) while an egg fertilized by a male bee will hatch female. (The female bees therefore always have two parents).
As the Fibonacci number sequence starts: 0 1 1 2 3 5 8 13, we can see that the bee community follows the same pattern:
One male bee (1 bee), he has 1 female parent (1 bee). This female had 2 parents, a male and a female (2 bees). The female had two parents, a male and a female, and the male had one female (3 bees). Those two females each had two parents, and the male had one (5 bees) and so on.
So the family tree is quite structured don't you think.
Apart from this I'm not quite sure what the Fibonacci numbers has to do with the Doctor in Fringe. He might be playing a mathematical game, to put himself to sleep, or in fact, he instead of counting sheep, as we mortals do, he counts the bees' family tree.
Or maybe he is counting, by habit, the number of eggs he would have to produce to ensure that the soldiers he was growing, that was in fact related to the natural pattern of Fibonacci, was of the standard he wanted.
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