The Arbitrary Five - 0
Essay Posted July 29, 2008 by James E. Nelson
On various occasions in these essays I have promoted my rather quixotic position that equinoxes and solstices don’t mark the beginnings and ends of seasons but rather the middle of seasons. In that instance Shakespeare got it right and the scientists got it wrong. The earlier English sensibility is that the solstices marked Midsummer and Midwinter. The centers of the seasons were clear while the moment of change—the edges of the season—were indistinct and difficult to define.
I have another quixotic notion that I have had for a number of years that I would now like to promote on this web site. This one has to do with age. This weekend I turned 50. But that is only an arbitrary milestone—much like solstices and equinoxes—that has far more to do with mathematical accidents than it does with any actual marker.
Decades are only remarkable because our decimal number system has ten digits. What if we didn’t use the base-10 (or decimal) numbering system? Computers use binary in their internal calculations. (That is a base-2 system, with only two digits, 0 - 1.) In binary I would be 110,010—hardly a remarkable birthday. But my 32nd birthday, in binary, would have been the big 100,000, and my 64th birthday will bee the big 1,000,000. (And everyone looks forward to their millionth birthday.)
When programers interact with computers they typically use hexadecimal (that is, base-16). Since we don’t have sixteen digits, the letters “a” through “f” are added, creating a number system with the following digits: 0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - a - b - c - d - e - f. (You’ve probably seen the hexadecimal numbers for screen colors if you’ve changed colors on your computer. The hex number 00FFCC, for instance, is a sea green sort of color. And my magical 50th birthday would be my 32nd in hexadecimal.
Base-7, while a bit unwieldy, is a bit more interesting because it is biblical. Periods of seven years and 49 years (seven years times seven) are common in prophecy, and seven years times seven plus one, or the fiftieth year, is a jubilee year when all debts are forgiven and the land lies fallow. But other than this biblical reference, fifty in decimal numbering is an arbitrary number. It’s only interesting because it ends in a zero.
But there’s another way of looking at numbers that’s both far more interesting and more deeply rooted in nature. This is the Fibonacci number sequence. The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself. Thus the first several numbers of the sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, etc.
While the sequence appears arbitrary, it shows up in nature repeatedly. Nature grows in a Fibonacci manner. Whether it’s leaf patterns, conch shell design, or the relative size of body parts to the whole, the Fibonacci sequence is at the root of growth and change. I first ran into the profound significance of Fibonacci numbers and the golden ratio when working with commodities markets. Markets move up and retrace according to Fibonacci patterns so frequently that it is clearly more than just a coincidence.
One of the fascinating things about the above Fibonacci sequence is that as the numbers get larger, the relationship between the numbers can be expressed as a consistent ratio. Each number is 1.618033987... times larger than the previous number in the sequence. It turns out this is how nature grows.
Consider an embryo. We were all taught in school that an embryo starts as a single cell and then splits into two, the two split into four, etc., so that soon there are, 8, 16 32, 64 ... cells. While that’s true in general, it’s not quite accurate. After a few cycles of cells splitting, some cells end up splitting slower than other cells, and some cells don’t split at all. So the actual growth rate is actually less than double. In fact embryos multiply from a single cell to a multiple cell organize at about the rate of 1.618 (rather than 2). They grow at the rate indicated by the Golden Ratio and the Fibonacci sequence.
In order to illustrate this, consider a square. Now double that square by putting a second square beside it. Now add a third square to the side of the first two, etc. Eventually we get a pattern that looks like this:
Note: All images from Wikimedia and are covered under a Creative Commons license.
Let’s assume that square #1 is one square inch. Square #2 is then four inches square and therefore has twice the area as the first two #1 squares combined. Square #3 is nine square inches (3x3) and is 1.5 times larger than the other squares. Square 5 (notice the numbers being used follow the Fibonacci sequence) is 25 square inches (5x5) and is 1.666 times the size of the previous squares combined. Square 8 is 64 square inches (8x8) and is 1.6 times larger.
What is occurring is that the ratio is bouncing back and forth on either side of the Golden Ratio (1.618...) while getting steadily closer to it with each ratio. By the time we get to the eleventh box, the ratio is 1.61818. By the seventeenth box we reach a ratio of 1.618034, and after that the ratio changes only minutely.
Now, let’s take those same boxes, but arrange them in a slightly different manner and draw a spiral through them. (It’s called the Fibonacci Spiral.) It looks like this:
Notice the similarity between this spiral and a nautilus. This is but one of many ways that the Fibonacci sequence shows up in nature.
It is my contention that human development follows a similar pattern. There is nothing particularly interesting about the 10th, 20th, or 30th birthday. They are marked as significant milestones only because in our world that uses the decimal numbering system, those years end in zero. On the other hand the first, second, and third birthdays mark significant developmental changes in babies—consider the “terrible twos as an illustration—but then the development begins to slow. If we jump ahead a few years, the 13th birthday is close to the time that a person moves from childhood into adolescence. The 21st birthday is around the time a person becomes a young adult.
Young adulthood—we could call these the virile years—are marked, not so much by physical growth but rather by development of endurance and strength. These are typically years of excess living. But by the mid-30s, people settle down and enter into their full adulthood.
People roughly between 21 and 34 are typically in their prime for especially physical athletic activities. Because the Tour de France ended last Sunday (July 27), my mind immediately turns to cycling. In this year’s tour the youngest rider is 21 and the oldest is 38. There is no minimum nor maximum age limit in professional cycling, but this is a typical age spread for professional cyclists (as it is for basketball and football players). Athletes who are in their very early 20s or younger have not yet developed the stamina necessary to be particularly successful as professionals. Young cyclists and young basketball players typically have to bide their time until their bodies are fully mature and ready to compete at the professional level.
Similarly, after the mid-30s, the body begins to decline. A 36 year old sprinter typically has lost a great deal of speed compared to when they were 34. Quarterbacks begin to fade (or at least in the case of the Green Bay Packers and Brett Farve, the management wishes he would just fade away).
And then, after that period of virility and development which typically occurs between the years of 21 to 34, a period of stability, strength, and stamina set in. If we continue to follow the Fibonacci sequence, this period would be roughly from 34 to 55. These are often the most productive years. There may be aches and pains, but they’re manageable. Only in cases of significant medical problems do those aches and pains become debilitating. But that begins to change into the 50s and 60s. This is typically when the diseases that accompany aging begin to leave their mark.
After one is 55 years old, the body may begin to fail, but one’s life experience begins to become increasingly valuable. If the younger ages were marked by physical stamina, then these older years are marked by wisdom and experience. One’s value is marked, not so much in what they can do, but in what they know and how they get things done.
Of course none of this is set in stone. Different people develop at different rates. Similarly, different bodies fail at different rates. But in spite of the vast array of differences, I believe there is strong correlation between the Fibonacci sequence and the significant periods in a persons life: Birth, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...
I have a brother who turned 55 just a couple of weeks ago. If we can look past the simplistic and arbitrary markers that we have created and consider life in a more fundamental and natural way, I suspect that his 55th birthday is a far bigger milestone and turning point than my 50th. Don’t get me wrong; I like black balloons and funeral dirges as well as the next guy. But during the next big 50th birthday bash, you and I can wink at each other knowingly. This celebration is for the sake of the ignorant masses. Those of us who know better are looking forward to the big Five Five. That’s when the Gold Ratio tells me I will actually enter the Golden Years.
Copyright © 2008 James E. Nelson (Just Another Jim). All Rights Reserved.
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