0, 1, 1, 2, 3, 5, 8, 13, 21... Fibonacci Life

Numbers are concrete, factual and logical, right? One thing I always loved about math class was how clearly defined truth is. It would always frustrate me when I'd see my grading on an essay in English class and whether I received an A or F, seemed almost arbitrary. There was no "right answer." But that doesn't apply to numbers and you can't argue with an equation. The ultimate truth is in numbers but some would argue that they lack in qualities of life. In life there isn't necessarily a right or wrong answer, and many things are not quantifiable. What number is equal to love? Further, the world we live in has imperfections or at least strays from what our idealistic mathematical models might predict. I think that numbers also have a magical quality and in many cases life and numbers share common qualities. It seems to me that numerical models represent the ideal, what reality and life tends towards. Pythagoras once said that numbers were the "cause of gods and demons," but I would say that numbers are the language of gods. Math is how we define the divine.


You have probably heard of the Fibonacci series, but if not it is a simple concept to learn. If we start with 0 and 1 then add the previous two numbers in the series to get the next, so 0 + 1 = 1 then 1 + 1 = 2 and 1 + 2 = 3 , this process leads to the Fibonacci series seen in the title. Its a simple idea, just add up the previous two numbers to get the next, but it appears everywhere in the natural world.

The series is sometimes referred to as the "bee ancestry code" because it represents the ideal genealogical history of a male bee. It is derived from three simple facts about bees:

1. An unfertilized egg (laid by a female) always hatches male.
2. A fertilized (by a male) egg always hatches female.
3. A male bee must have one parent (a female) while a female must have two parents.
   

"If one traces the ancestry of this 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). If one continues this sequence, it gives a perfectly accurate depiction of the Fibonacci sequence.

However, this statement is mostly theoretical. In reality, some ancestors of a particular bee will always be sisters or brothers, thus breaking the lineage of distinct parents." From here.

Another way Fibonacci shows up in life revolves around natural geometry. If you take the ratio of any two adjacent numbers in the series, they approach a common value as the numbers get larger in the series. For example, 3/2 = 1.5, 5/3 = 1.67, 8/5 = 1.6 and 13/8 = 1.63 after rounding. The value that this ratio tends to can be defined precisely, but lets just round to the nearest 1000th to get 1.618. Interestingly, if you take the ratio's the other way, so 2/3 = .67, 3/5 = .60, 5/8 = .625 and so on, you get the same number minus 1 or .618. This property makes this irrational number uniquely special and it is therefore called the golden ratio.

The golden ratio shows up in all sorts of places that you would never expect. Leonardo da Vinci discovered that beauty in art is often associated with the golden ratio and he strived to incorporate it into his works. He found that many of the proportions in the human body are close to this ratio and he depicted this in his Vertruvian Man and the Mona Lisa seen above and below. In these images the ratio of the length to the width of any rectangle and also the division of any line occurs at this ratio.

Its not just in art though, the golden ratio also leads to a spiral if you connect the corners of any two adjacent squares in the map above to form what is called the golden spiral. This is the spiral that the some sea shells form but its noteworthy that the nautilus does not. It is the spiral that you see in the seeds of a sunflower and other blooms. Hurricanes have this form and it is even found in the shape of our home, the Milky Way, and other galaxies.

Its even in the stock market. Many technical traders (those who use stock charts to determine whether to buy or sell) swear by the Fibonacci ratio and use it in their everyday strategies. The ratio often appears in charts on all time scales, 15 min, 1 week, 3 year, you name it. There are various levels of sophistication that are employed in using the golden ratio to trade, some of which are here. A simple approach is to connect the highest price and the lowest price in a pattern to find prices where the equity may pivot or change direction. I just drew up the Fibonacci ratios for the most recent pattern in the dow jones industrials weekly chart. Notice how the price tended to pivot at the 32.8% and 61.2% levels of the total (100%) move that recently completed.


The Fibonacci ratio appears in the lives of insects and the flowers they pollinate, the shells of the oceans and the hurricanes they feed, and the charts of stocks and the bodies of the Milky Way humans that trade them. This magical sequence of numbers goes beyond number theory and steps into life. Or maybe its life that is striving to become something divine. Any way you slice it the Fibonacci series is something substantially more than just a sequence of numbers.

note: Title image taken from: http://www.flickr.com/photos/myreflex/180524429/