Fibonacci Discovers a Pattern

While averages settle into a number that’s lower than the highest in the series and higher than the lowest, other sequences involving three numbers expand.  Threes can be represented by relationships of two things to a third in a sequence that’s additive and infinite.  The Fibonacci series, for example, is a sequence of sums.  Starting with 0, add 1 to equal one.  0 + 1 = 1.  Then add the two preceding numbers.  1 plus 1 equals 2.  Add 1 and 2 to equal 3.  Two plus three equals five, and so on.  The series rolls out like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, etc. 

Fibonacci numbers were named after Leonardo of Pisa (c. 1170-c. 1250) who was known as Fibonacci.  He published a book on mathematics in 1202 that described the series, although it had originated in India several centuries before.  Fibonacci found examples of the series in nature.  One of his first studies was the creation of the sequence of individuals from a single pair of adult, mating rabbits.  He concluded, given the parameters of his study, the rabbit pairs would multiply in accord with the numbers in the series identified with him.  Fibonacci numbers are used in financial markets today to make predictions about the movement of prices. 

From Threes, Chapter 2, “Threes in Math”  

Three Graces

Grace fascinates for its many dimensions. It goes well beyond the spiritual meanings. You can think of physical grace or gracefulness, which is an ability to move around effortlessly. You can think of social grace. In Greek mythology the Charites, known as The Three Graces, were the goddesses of joy, charm and beauty. They were named Aglaia (Splendor), Euphrosyne (Mirth), and Thalia (Good Cheer). The Graces presided over banquets, dances, and all other pleasurable social events, and brought joy and goodwill to both gods and mortals. In Roman mythology they were known as the Gratiae, which connotes gratitude.  With grace and gratitude derived from the Latin gratus, the meaning of grace can be extended to mean a sense of gratitude or gratefulness. “Gratitude unlocks the fullness of life. It turns what we have into enough, and more. It turns denial into acceptance, chaos into order, confusion into clarity. It turns problems into gifts, failures into success, the unexpected into perfect timing, and mistakes into important events. Gratitude makes sense of our past, brings peace for today and creates a vision for tomorrow,” writes Melodie Beattie.        

from Threes, Chapter 4, “Threes in Religion and Mythology”  

Three Reactions to Government Arrogance

A father writing to his hero son (Marine Corps officer) with three tours in Iraq expresses his anger when he says, “That a soldier who murdered 13 other soldiers on a Texas Army base, and who admitted he did it, is having a show trial (court martial).  I'm pretty sure UCMJ calls for his summary execution....That another soldier (Manning) who revealed sensitive, classified operational shit to the world won't be executed for treason, no matter how long he is in the slammer.  Better be Leavenworth. They make you break rocks with a sledge hammer, every day.  Till you die.  I can live with that....That a govt contractor who did the same is hiding in Russia.  Russia!”

These three strong, individual reactions from Hasan, Manning and Snowden remain in the news.  We could believe the reactions resulted from U.S. government responses to the September 11, 2001 attack that took the form of deception at the United Nations, an invasion of Iraq in 2003, and an explosion of government-directed intelligence-gathering capacity.  For many the news of these episodes of retribution or betrayal is disheartening and disgraceful.  For others, it represents examples of the moral courage it takes to oppose overwhelming institutional force. 

Conceivably, governments can be plotted along an imaginary line from benevolence on one end to malevolence on the other.  Most governments fall along that line with a majority, presumably, occupying a middle ground.  As governments creep away from benevolence they can begin to display arrogance, which falls far short of malevolence for sure but elicits nevertheless strong reaction from individuals such as Thomas Paine, Daniel Ellsburg, Nelson Mandela and right now, Hasan, Manning and Snowden.  Some we regard as patriots; some as traitors.  Wise leaders in governments pull back from arrogance.  

Threes of Modern Design

Ever wonder what constitutes successful modern design?  IDEO, a large, international firm, designed the Apple mouse way back when and the Palm hand-held organizer.  Recently, a wider lid for Samuel Adams beers.  It designs services as well.

“There are three main elements to IDEO’s ‘design thinking.’  The first is ‘lots of different eyes.’  It employs people from wildly different backgrounds—surgeons and anthropologists as well as engineers and designers—and lumps them into multidisciplinary teams.  The second is to look at problems from the consumer’s point of view: for example, conducting detailed interviews with patients about their daily pill-taking routines and how they feel about them.  IDEO likes to focus on the outliers rather than the typical customers—people who have demanding medical regimes or who constantly forget to take their tablets—on the assumption that this produces more useful results.

“The third element is making everything tangible.  The company produces mock-ups of its products and processes to see how people react to them ‘in the wild.’”

We need firms such as IDEO to help us re-think everything every so often.

from Schumpeter, “Back to the drawing-board,” The Economist, July 6, 2013.