He investigates these occurrences in various facets of life on earth and seeks plausible explanations for some of them and hypothesizes about some others while widening your horizon.
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World of fiveThe universal number
By Louis Komzsik
Trafford PublishingCopyright © 2013 Louis Komzsik
All right reserved.
Chapter OneWorld of five
Have you ever wondered about the importance of the number five in your life beyond looking at your hands and seeing your five fingers? If you have not looked beyond this level, then you will now suddenly see a preponderance of fives in your life.
The popular American greeting of giving a "high five" demonstrates the everyday use of the number as well as anything else. Of course we know the most plausible reason for this phrase: the five fingers of our hands. But we will see many more deeply rooted appearances of the number.
Let us start with the silly superstitions related to the number. Some say that if a stem of an apple breaks after five twists, you will get married in that year. The apple itself will have another notable appearance later, and we will leave this a hope for those striving to find their life mate. Note the saying's gender independent nature.
Five pointed star shaped jewelry is supposed to turn away forces of evil. On the other hand five cookies fusing together when baking means the opposite and a likely ominous end. Then there are strong believers and lifetime seekers of five leafed clovers that are supposed to surpass the lucky qualities of the four leafed ones that are already hard to find.
There is only a short distance from superstition to politics and sure enough, the number five makes many appearances in political life as well. Many national flags depict a certain variation of a five-pointed star attesting to the religious foundations of those nations.
The United Nations Security Council has 5 permanent veto-carrying members. While we are at international politics, it is worthy of mention that the preferred system of economical planning in communist countries was comprised of five-year plans. In fact, the Chinese have just concluded the 12th five year plan since the installation of the communist system. Five in that might only be a convenient number to let certain programs develop and produce measurable results. This could also be a deliberate selection in a society with a 4 year election cycle to postpone measuring one's success past the re-election.
Then there is the Fifth Amendment of the US constitution, the right to avoid self- incrimination. This clearly is an accidental occurrence, the result of simply numbering the amendments, but noteworthy. The US Supreme court needs at least 5 votes to reach a decision. There are five branches of the US military, the Army, Navy, Air Force, Marines and the Coast Guard. We must then mention the center of all that military might, the Pentagon.
The building was designed practically overnight according to military records, due to wartime urgency. It had to satisfy specific footprint and height restrictions and was constructed in two years during the second World War. The building, shown on a satellite photo below, has a spectacular quinticity, to invent a word for our topic, meaning an unusual and frequent occurrence of five. Besides being of pentagonal shape, there are five pentagonal rings inside and five floors. It also has a five acre internal park. It is the world's largest office building housing tens of thousands of military personnel and billions of dollars in salaries.
While we are at the topic of architectures, it is worth mentioning the architects' love of buildings with five sides or a pentagonal footprint. The world's tallest five sided building is a 75 story 1002 feet tall skyscraper in Houston, Texas, a place of many big things. The tower was built about 30 years ago and then it was the tallest building west of the Mississippi and the 12th tallest building in the US. It was only, however, the 49th tallest building in the world at the time of its construction and now it is only about 62nd, a fact demonstrating humankind's thirst to reach the heavens by whatever mundane means possible.
Then we get to the everyday life occurrences. There are 5 players on a basketball team, one of the most popular sports in the US. Professional basketball has other rule components with the number 5, among these are the 5-second rules related to in-bounding the ball, close guarding or back to the basket dribbling.
There is also the popular indoor soccer or football game called five-a-side. This is played on a small field mainly during winter in those countries where outdoors is out of limits at that time of the year. The 5-count of professional wrestling to release a hold on a wrestler clinging to the safety ropes, or using an illegal hold, leads us to the truly coincidental.
Talking about sports, the five Olympic rings come to mind. They are clearly coincidental since they refer to the continents of which at the present time in our history we have five: Africa, Europe, Americas, Asia and Australia. As they were once connected in a primitive mainland called Pangaea, they may become one again in the future. There are incidentally also five bodies of waters deserving the ocean designation: the Atlantic, Pacific, Indian, Arctic and Antarctic. There are also large seas and since this categorization seems arbitrary, we'll leave it at that.
Is most European countries the school grading system is from 1 to 5. Despite that letter grades are awarded in US schools, the grade point average is often calculated on a scale up to 5. Five as a number means a good or perfect grade in anything from hotel stars to Michelin restaurant guide grades.
From school we can go to literature. There are many references and uses of the number, popular in titles like Slaughterhouse five, Kurt Vonnegut's American classic. It is frequent in alliterative expressions like fabulous five and so on. Well known is the pentameter poetry: using five separate metrical units per line, made fashionable by Shakespeare. Even the traditional Japanese poetry called Haiku is related as it contains three phrases, five, seven and five sound units.
In modern classifications there are five major literary classes: fiction, non-fiction, short story, novel, and drama. Theatrical dramas usually also contain five acts. Journalism schools teach the fundamental five w-s of a successful article: who, what, when, where and why? Surely an article presenting answers to all five questions stands on its own.
There is a strong appearance of five in the culinary arts. There are five major food groups: proteins, dairy products, fruits, vegetables and grains. We all know that they should be balanced in our diet, but most of us prefer the first two over the other three.
Traditional Japanese dietary rules dictate having five colors to provide a fully nutritional meal besides pleasing the eyes. The colors are black, white, red, green and yellow. Some of those colors could be of course white rice, green beans and black sesame sauce. You may have a slice of yellow fish and the red could be a fruit, but let us move on before you dear reader put down this book and head for the kitchen.
From traditional we go to modern. We are now inundated by TV commercials about various 5-hour energy drinks. The use of the number is likely a marketing ploy on our affinity to the number and nothing seriously scientific is behind it.
Then comes humankind's favorite pastime: gambling. The concept of lottery was invented in China more than two thousand years ago. The game progressed through continents and millennia, and its appearance today in America is in the popular pick 5 games of some states. In this scenario the player must correctly select 5 numbers out of 39 to 49 numbers. The odds of winning a game of 5 out of 39 is 1 in 575,757; in itself an interesting number with its triple occurrences of five.
The value is arrived at by computing the product 39/5 · 38/4 · 37/3 · 36/2 · 35/1. This is a mathematical function called the combination that selects a group of (here 5) numbers from a set of (here 39) numbers. This was rather good odds for the players, so most states now opted to the 6 from 49 games.
You may use the above formula with logical extension to start from 49/6 and end with 44/1 with similar terms inside to figure out that the odds of winning decreased to 1 in 13,983,816 in this case. This is obviously a less appealing number in appearance (not even a single 5 in it) as well as in its odds value which makes it more advantageous to the states.
Five is also preferred in many organized lectures, health and self-improvement programs. They are probably five because three is too small a selection, 4 and 6 are just not as sexy numbers, and ten is too far away to remember. For example a self-improvement class on the internet recommends to follow five essential recommendations: do the important and not just the urgent, choose the best not the ordinary, schedule for big events and not the mundane, use technology but don't let it rule you, and be fiery but don't burn out too easily. Seems like these are sound advises, independently of five or not.
We cannot avoid mentioning the topic of numerology, assigning certain characteristics and beliefs to numbers. The positive characteristics of five or persons whose personal number is five are: imaginative, quick thinking, versatile, active and constructive. The negative aspects of such personality are restlessness, temperament, hastiness, impatience and discontentment. Five pros and five cons, the balance of the left and right hand. Whether one believes in such designations is a personal preference as the scientific foundation of it is certainly questionable.
On a more serious cognitive level, philosophy has five branches. They are the studies of existence, knowledge, action, art and force. Their respective names are metaphysics, epistemology, ethics, esthetics and politics.
Delving into politics is not our intention, but as a mild illustration of it we ought to mention the five most dominant empires in history. An empire is a political entity that has a sovereign territory surpassing its own and asserts a rule over other peoples. The five most dominant empires were the Roman, the Mongol and the Holy Roman empires in the historic past, as well as the Russian and British empires in the modern age.
The extent of the Roman Empire is well known; it stretched from the Middle East to the British Isles. The Mongols (the noted and much feared Genghis Khan) reached into the heart of Europe all the way to Hungary from the vast steppes of middle Asia. The Holy Roman Empire essentially covered most of Medieval Europe.
The Russian empire (the Tsarist) lasted for about 200 years and was the largest contiguous territorial claim ever by a nation (and was ended by the communists). Finally the British empire was famous for its multi-continental territory "over which the Sun never sets", as was proudly stated. Most of those empires now reside in history's graveyard and the two whose remnants still exist (Russian and British) are sad shadows of their former selves.
It is a natural logical path from empires to government and we must follow it since coincidentally five main types of government evolved in history. Their categorization was first proposed by Plato, who named them timocracy, aristocracy, oligarchy, democracy and tyranny. The modern classification is monarchy, aristocracy, republic, democracy and dictatorship. Oligarchy and republic, tyranny and dictatorship match despite the different names. The two names identical in both categorizations, aristocracy and democracy, carry similar meanings. Timocracy is hard to define in modern terms and describes a system where only the ruling class has possession of property. This is loosely comparable to monarchy that is ruled by a king or queen, or an emperor, who pretty much owned everything. While there are numerous countries were royalty remains (like the United Kingdom), those countries are not monarchies anymore.
Aristocracy is a rule by a privileged few, and that type of government is also defunct. A republic is where a limited number of elected people govern and democracy is a system governed by all the people. Dictatorship is usually a democracy gone bad, think of our neighbor Cuba or South Korea. There is also a hybrid system called democratic republic that is supposed to be governed by both the people and the electorate, but really that system is usually a communist dictatorship.
Finally we must also discuss the appearance of five in our life, literally. Human life is often categorized into five stages. They are the gestation period, infancy, childhood, adolescence and adulthood. Their lengths are 9 months (in normal circumstances), one year, nine years and eight years, respectively. Adulthood has the longest but unspecifiable duration from 18 to death.
The widely varying durations cover drastically different developmental changes. The shorter the stage the larger the change, at least in a biophysical sense. Our adulthood, while lasts the longest, contains the least biophysical changes apart from the gradual aging of our bodies. This is compensated by our increased knowledge and wisdom.
While contemplating the five stages of our life, it is proper to mention that the object supporting our life, Sun, also has five major life stages. In its first stage it is called a nebula, a very large cloud of gas particles dominated by hydrogen. When gravitational forces take hold between the particles, the cloud condenses into the stage of a proto-star. This proto-star gradually heats up to the level that nuclear reactions start to convert its hydrogen into helium. These two stages last millions of years and culminate in the main sequence stage of the Sun.
This is where we are now with our approximately five billion years old Sun and we can hope for another five billion years before it will burn off all of its hydrogen. In fact, the surface temperature of Sun is approximately 5500 degrees Celsius, another appearance of five, albeit an accident of the chosen unit. The next stage is called the red giant stage when the nuclear activity continues and helium is fused into carbon. In the fifth stage of its life, our Sun will become a white and after completely cooling off, a black dwarf.
These lifecycle related occurrences demonstrate that we truly live in a world of five. They probably caused the strong human preference for five and its geometric manifestation throughout history.
Chapter TwoHistorical pentagrams
Humankind's recognition of the special nature of five as a number, the pentagon as its planar manifestation, and the related dodecahedron as its spatial incarnation dates back several thousand years. In fact, the geometrical representation in the form of pentagrams shown on the following figure appeared already in the Sumerian culture about five thousand years ago.
The pentagram is an image obtained by connecting the corners of a regular pentagon that has equal sides. In the earliest appearances the five corners likely had the directional meaning of east, west, north, south and upward. They may also have represented the then known five celestial objects: Venus, Mars, Sun, Moon and Jupiter.
Of course Earth was another celestial object but since we lived on it, its interpretation was somewhat distorted. We could view the others, but could not really see the Earth from the outside or above. The ancient Sumerians apparently had the figure related to the calendar year, the four corners standing for the two pairs of solstices and equinoxes. The top corner stood for the Sun as the, then not fully understood, maker of all those events.
Egyptians used the five pointed star to represent the womb from which all living things were born. Many images of Buddha show a five petaled lotus flower as the image of enlightenment. Shiva is also sometimes called five faced and the pentagram was used to represent it.
Ancient Chinese considered the symbol connecting their five elements, wood, fire, wind, water and metal. They sort of match with the 4th century BC Greek philosopher Aristotle's five elements of nature: water, air, earth, fire and ether. The perceived importance of the fifth element, or essence, resulted in the modern word of quintessential.
His countryman, Plato, was looking beyond the number and its planar appearance in the pentagram. He studied the dodecahedron, the spatial object with regular pentagon sides, and recognized that it was a member of an elite class of only five bodies. These are now named after him Platonic solids.
In Greek philosophical beliefs the five was also used to categorize the main human components. They were the body, soul, psyche, intelligence and spirit; a very intriguing categorization. We can detect the body, sense the psyche and even measure intelligence, but we are unable to pinpoint the location and mechanism of human soul and spirit. It is an enduring mystery of our lives.
The Mayans also attributed specific meaning to the number five. They believed that they were living in their fifth world that was to reach an apocalyptic end at the end of their calendar. Their special consideration of the number was very likely celestial in origin: they were astute observers of Venus and knew that in 13 revolutions around the Sun Venus passes Earth five times. This grand cycle of Venus will be discussed in more detail later.
Since we boasted in the preface about surviving the end of the Mayan calendar, we need to explain it in some detail. The calendar system contained five major measuring units: one day, 20 days, 360 days, 7200 days and 144,000 days. From these numbers a mainly base 20 system emerges, apart from the second step of 18. It appears that they may have tried to reconcile their bodily awareness to the 20 digits on their feet and hands, with their solar observations of the year's approximate length.
They called those units Kin, Winal, Tun, Katun and Baktun, respectively. The confusion and apocalyptic predictions are around the 13th completion of the fifth unit. It is assumed that their current calendar started on August 11, 3114 BC as Mayan date 0.0.0.0.0 referring to the five units. The date 18.104.22.168.0 or one Baktun would correspond to 12/06/2720 BC, 144,000 days after the start. The date 12/21/2012 corresponds to the 13th Baktun turn (let's call it Mayan millennium) of 22.214.171.124.0.
Excerpted from World of five by Louis Komzsik Copyright © 2013 by Louis Komzsik. Excerpted by permission of Trafford Publishing. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents
1 World of five....................5
2 Historical pentagrams....................15
3 Five fingers....................25
4 Pentameric plants....................35
5 Fivefold symmetries....................43
6 Golden pentagon....................51
7 Celestial quinticity....................61
8 Dodecahedral universe....................71
9 Quintic boundary....................81
10 The universal number....................93