The Transcendent Brain
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Highlights
- Each number of the sequence, after the zero, is the sum of the previous two numbers. As you can test for yourself, the ratio of a number in the sequence to the one before it approaches the golden ratio as we go to bigger and bigger numbers. For example, 21/13 = 1.615, 34/21 = 1.619, 55/34 = 1.6176. So this special series of numbers is closely related to the golden ratio. Even at this point, anyone with an appreciation for mathematics can see much beauty in the golden ratio and its relation to the Fibonacci series of numbers.
- Such behaviors are called “emergent phenomena.” An example would be the behavior of certain kinds of fireflies. When a group of these insects congregate in a field at night, at first they flash randomly, like the blinking lights of a Christmas tree. But after a few moments, the fireflies begin flashing in unison. Such behavior could not be predicted by the study of an individual firefly, but can be seen readily in groups. Another example is the large and complex mounds built by termites, called “termite cathedrals.” The cathedrals sometimes have elaborate galleries and chimneys to control airflow, temperature, and humidity. Building such a complex structure would seem to require some kind of master plan, executed by the hundreds of thousands of termites in the colony. But individual termites, which are blind, cannot perceive even the overall shape of a mound, much less direct its design. Somehow, the complex mound arises from the collective behavior of the full colony. Researchers believe that termites exchange chemical signals with one another and also respond to cues from airflow and temperature, which are affected by the shape of the mound.