Magnificent Seven: The Happy Number

Magnificent Seven: The Happy Number

by Louis Komzsik

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Overview

In this easily readable volume, the author explains some of the reasons for our preference toward the number seven. He reviews its occurrences in our cultural, biological, chemical, physical, algebraic and geometrical world in an attempt to find the reasons behind them.

Product Details

ISBN-13: 9781490714011
Publisher: Trafford Publishing
Publication date: 09/19/2013
Pages: 118
Product dimensions: 5.50(w) x 8.50(h) x 0.28(d)

Read an Excerpt

Magnificent seven

The happy number


By Louis Komzsik

Trafford Publishing

Copyright © 2013 Louis Komzsik
All rights reserved.
ISBN: 978-1-4907-1401-1



CHAPTER 1

Heavenly sevens


One origin of humankind's affinity toward the number seven is truly in the heavens. The planets that were visible with the naked eye at the early ages numbered seven. Looking up into the skies from Earth were Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. The modern name of the five following Sun and Moon were given after Roman Gods, but they were recognized and named much earlier than that.

The Babylonians 6 thousand years ago already recognized the seven heavenly bodies, however, they arrived at the number seven from a more intrinsic phenomenon in nature. They observed the periodicity of Moon's behavior and created a calendar based on a lunar month. They divided the lunar month into four seven day periods, the predecessor of our week.

The month started with the first visible crescent of the Moon and the first period ended at the growing half Moon on the seventh day. The 14th day was at the end of the second period marked by the full Moon. The 21st day and the end of the third period was the waning half Moon, and the last period lasted until the 28th day which was the last visible crescent of the Moon. The 2-3 days during the time of the invisible Moon were smartly adjusted by the Babylonians to reconcile their lunar calendar with the solar year.

Then came the ancient Greeks with their Pantheon of gods. They associated their gods with the five planets of the seven celestial bodies they saw. They had Hermes, the god of travel and thievery, and Aphrodite, the god of love and beauty. Their god of war was Ares and Zeus was the head god. Finally Cronus was the father of Zeus.

The Romans had a Pantheon on their own with similar gods as the Greeks but with Roman names. Ares was Mars for the Romans, Hermes was Mercury, and Zeus was Jupiter. Aphrodite was of course Venus, and Cronus was equivalent to Saturn. Their godly personalities were similar in both mythologies, apart from the difference of interpretation between Cronus and Saturn. For the Greeks he was the supreme ruler of the universe until his son Zeus overtook his realm. For the Romans Saturn is associated with agriculture and happy life. Clearly the modern day names of the planets we inherited from the Roman side.

The Greeks also associated the visible celestial bodies with certain days of the week. The first day was the day of Sun and it is now our Sunday, the second was the day of Moon that is now our Monday, these are easy to recognize. The third became the day of Ares, the fourth the day of Hermes, the fifth day belonged to Zeus. The sixth and seventh days were dedicated to Aphrodite and Cronus.

These five days are less recognizable, hence the question: How did we get to the current names of the days of the week? Well, Saturday is also recognizable if we consider that Cronus' Roman equivalent was Saturn, hence Satur(n)day. The other days' names come to us from the English, Nordic and Germanic substitutions of the Greek and Roman gods.

One such substitution in the old English vernacular was Tiu for Mars resulting in our Tuesday. Wednesday is also of old English origin coming from Wooden's day. Wooden was an Anglo-Saxon god of similar dubious reputation as Hermes and Mercury. Thor was the head god of Nordic mythology and as such the replacement for Jupiter or Zeus. The fifth day of the week hence is Thor's day or Thursday for us now. Finally, Freya, the Nordic and Germanic goddess of love and beauty was a perfect match for Venus and Aphrodite, giving us Friday as Freya's day.

Let us now look deeper in the heavens for other notable occurrences of the number. The constellations Ursa Major and Ursa Minor (Big bear and little bear) both contain a cluster of seven stars that we were shown in childhood, called the Big Dipper and the Little Dipper in North America. Considering the bear picture, the handle of the Big Dipper forms the tail of the big bear. It is commemorated on the Alaskan flag and a portion of the flag is embedded into the front cover image.

The American colloquial names are due to the shape of the clusters resembling the utensil. The dippers are both comprised of a rectangle with four stars and a "handle" with three. The clusters were recognized by many cultures and the name given to them varied. In the British Isles the Big Dipper is known by the name of the Plough, again from a visual interpretation of the pattern. On the European continent the shape reminded people of a wagon or a cart. Germans call it the Grosser Wagen or great cart. Hungarians call it Göncölszekér, a heavenly chariot pulled by a magical invisible horse carrying medicines to cure ailments of humankind.

Some native American Indians saw the image above and described the cluster as three bear cubs following their mother in search of food. Some imagined three heavenly hunters chasing a bear. The common component was the bear, that is the parent constellation's usual visualization.

There are other clusters composed of seven stars. The most notable, known to humankind since antiquities is the Seven Sisters, or Pleiades. The cluster is located in the Taurus (Bull) constellation on the bull's shoulder. According to Hubble space telescope's measurements, the cluster is about 440 light years away from Earth and is considered to be about 100 million years old, almost 50 times younger than our star, the Sun. It is still old enough to predate humankind's celestial observations.

The first historical mention of the cluster appears to have been more than four thousand years ago by the Chinese. They already described them as the Seven Sisters. The name may have spread though India and the Middle East, there are ancient Greek references to them also as Seven Sisters, and sometimes as the Seven Virgins. In fact the ancient Mayans have also known and observed the Seven Sisters.

There are several hypotheses for the origin of the Pleiades name. A plausible one is that it derives from the Greek word plein meaning sailing. A neighboring star is called Pleione, a sea nymph in the Greek mythology. Pleione means the "sailing one", and the seven stars are said to be the daughters of Pleione, hence becoming the Pleiades, and ultimately the Seven Sisters. The star closest to Pleione is named Atlas of holding the heavens on his shoulders' fame, and is considered to be the father of the sisters.

The sisters are the stars named Alcyone, Merope, Electra, Maia, Celeano, Taygeta and Asterope. In the Greek mythology these sisters are all connected to the gods. Maia was the most beautiful of the sisters and according to Greek mythology was seduced by Zeus himself and gave birth to Hermes. Electra and Taygeta were also both seduced by Zeus and gave birth to notables, the founders of Troy and Sparta, respectively. It certainly appears that Zeus, the head god, took his liberties with the women of the heavens. The figure below shows the Seven Sisters with their names and along with their parents, Atlas and Pleione on the left.

Alcyone and Celeano were both seduced, not by Zeus but by Poseidon, the god of the seas. Asterope was also seduced by Aries if we are going to stick to this milder form of the Greek gods' adventures regarding women, although in this case some stronger words were used in the mythology.

Finally, Merope is the sister who escaped the wraths of gods and married a mortal man, albeit of some inexhaustible energy, as he was named Sisyphus. She is also called the lost sister sometimes. Whether it is because she was the only one without a god lover or because that is the faintest one of the stars of the cluster, is not known.

While we are at Greek mythology, we must mention that Odysseus, the hero of the Trojan War was kept on the island of Ogygia by the nymph Calypso for seven (!) years. Ultimately she released him upon the request of the god Hermes, the great-grandfather of Odysseus. The heavenly gods and number seven together again, but back to the sisters.

Since the cluster is the nearest star cluster to Earth, it is visible with the naked eye in the night sky and during the proper time of the year. In the northern hemisphere the cluster is visible to the right of Orion and slightly higher, when one is facing South. It is visible during winter from September to January and its highest location in the sky is in November.

It is also well visible during the (northern) summer in the southern sky. Hence the Seven Sisters touched the people of the Southern hemisphere as well. An almost extinct Argentinean tribe called the Abipones considered them to be their ancestors. Solomon islanders look at them to mark the beginning of planting in the fall (their spring). The Australian Aboriginal tribes also know and celebrate the cluster as heavenly beings being benign toward them.

There is an intriguing artifact found in Germany and dated to about 1600 BC. The artifact, found near a village called Nebra and called the Nebra disk, was an astronomical device. It is adorned with symbols representing Sun and Moon, as well as a cluster of seven stars. It is conjectured to be the first recorded image of the Pleiades.

Whether having seven members in a star cluster has an astronomical reason or is an accident of nature, is still debatable. The amateur astronomer John Michell, who was by profession a member of the clergy, in the second half of the 18th century computed that the probability of those seven stars remaining in such a firm relationship is about one in half a million. By astronomical standards these are not insurmountable odds against it being an accident, but still rather small.

Hence it might be possible that there is some specific celestial circumstance making those stars appear to keep their relationship the same when viewed from Earth. Since there is a physically meaningful appearance of the number five in the heavens in the five Lagrange points, there could also well be something like that related to seven. It is conceivable that some forces in the Big Bear constellation give rise to seven stationary points, at least from our perspective on Earth.

Gravitational circumstances in some celestial neighborhoods certainly appear to result in the number seven raising its head unexpectedly even in our immediate neighborhood. We are all familiar with the phenomenon of an eclipse. We have seen probably at least one in our lifetime and will likely see more. They are rare but not infrequent in the time scale of human life.

There are lunar and solar eclipses, distinguished by the fact whether Moon's shadow is moving over Earth, or Earth casts a shadow over Moon. Lunar eclipses last about half an hour to an hour. They occur at full Moon, but not at every full Moon. Since Moon's orbit is at an angle to Earth's, the number of occurrences is limited. The orbits cross each other only twice in a calendar year and eclipses could happen only then. Since it takes some time for the two orbits to completely clear each other, during which Earth and Moon do multiple rotations, there could be several eclipses per each orbit crossing.

A total lunar eclipse is when Earth is perfectly on the line between the Moon and the Sun. In that situation the Sun's rays, reflecting from the Moon and creating the Moon light, are completely blocked by Earth, hence Moon becomes dark. Since this could only happen at night, certain lunar eclipses are only visible from one hemisphere and not from the other.

Earth is not just a pinpoint in the sky, its finite and massive size makes its shadow on the lunar surface comprised of a dark central circle and a lighter outer circle. They are called the umbra and penumbra, respectively. Hence a lunar eclipse consists of three phases, two so-called penumbral and an umbral phase, latter being the total eclipse of the Moon.

A recent lunar eclipse occurred on May 25, 2013 and it was a penumbral event slightly visible in Western Europe, Africa and the Eastern side of the Americas. It was not be visible in Asia because it was daytime over there. There will be a total lunar eclipse over most of America (both North and South), Australia and the Pacific Islands on April 15, 2014. Hopefully the coincidence of that day being tax day in some countries will not result in doomsday predictions and actions. Lunar eclipses accompanied by certain colors created irrational fear in peoples who did not understand the phenomenon.

During total eclipses, for example, a phenomenon called red Moon occurs when the Moon is totally in the shadow of Earth. In this case, however, there is still some light that passes through the atmosphere and is bent toward the Moon. The red component of the light, a subject of further consideration in a later chapter, is the least sensitive to be scattered by the atmosphere and will arrive at the Moon, painting it red.

According to some historical records Columbus used this, then already known phenomenon, to his advantage. He had an eclipse calendar and knew of a coming eclipse in 1504 when he was grounded in Jamaica because his ships were damaged. Columbus threatened the natives by an angry god using his prior knowledge of the coming eclipse. Sure enough, the natives were scared and fed Columbus' crew for about half a year until help came and he was able to sail back to Spain.

A solar eclipse is when the Moon is between the Earth and the Sun. The fact that a solar eclipse can occur at all is due to the extremely fortuitous relationship between the size and the distance of the Moon and the Sun. If Moon would be smaller or farther away from us, it would never be able to fully block the view of the Sun, that is the total solar eclipse. It would only pass in front of the Sun, an event called a transit. Venus and Mercury are demonstrating such events.

There are also different kinds of solar eclipses. The total event mentioned above is rare and visible only from a narrow path on Earth. On other parts of Earth the viewers see a partial solar eclipse, when a section of Sun is covered. The third distinct kind is when the visual image of Moon is smaller than the Sun, but the alignment is perfect, hence positioning the Moon in the center of the Sun. This event is called a coronal solar eclipse, as a ring of Sun is visible outside of the lunar image.

The length of a solar eclipse is maximum 7 and a half minute dictated by Moon's speed moving across the image of Sun. Most of the time it is much shorter. They usually occur in every year and a half at some point on the Earth, but a repeat event at a particular point is extremely rare, and could happen only once in about 400 years.

A total solar eclipse occurred on November 3, 2013. The visibility ranged from the Atlantic Ocean through parts of the eastern side of South America, and throughout most of Africa. A coronal solar eclipse will occur in 2014 mainly in Australia, with partial visibility in Antarctica. For the next total eclipse we will have to wait until March 20th, 2015. The residents of Western Africa, Europe and Northern Asia will be the lucky observers.

The frequency of either solar or lunar eclipse happening clearly depends on the particular celestial positioning between the two. The number of the solar and lunar eclipses vary between years with a very notable limit: the maximum number of the sum of lunar and solar eclipses that can happen in a year is seven!

Such years when seven eclipses occur are, however, really rare. The last year with seven, four solar and three lunar, eclipses occurred in 1973. Prior to that in 1934 there were five solar and two lunar eclipses. A repeat of the 1973 event is scheduled to be in 2094, hence likely only the readers born in the year of the publication of this book would be able to view it.

Returning to the seven planets that started this all, we point out that in the ancient alchemists' books there were seven famous metals. They were also affiliated with the seven planets in the following pairing: Gold was linked to the Sun, naturally, and silver to the Moon. Mercury was the metal of Mercury the planet, copper was the metal of Venus and iron of Mars. Tin was associated with Jupiter and lead with Saturn.

The propagation of the number into our life continued. In medieval times arts (that included science) were also classified into seven subjects: grammar, logic, rhetoric, music, arithmetic, geometry and astronomy. We will follow some of these areas in the following chapters.

CHAPTER 2

Humanly virtues


We will start with another intriguing ancient reference, the so-called seven circle labyrinth, shown below, dating back to the 5th century BC.

The design found on Cretan coins, therefore known as the Cretan labyrinth, is associated with the myth of Theseus and the Minotaur. According to the myth, the labyrinth was built at the Knossos palace to contain the Minotaur, a half-man half-bull creature. The legend also says that the labyrinth was used to give sacrifices to the Minotaur. The sacrifices were: seven young men and seven virgins in every seventh year, a cornucopia of sevens.


(Continues...)

Excerpted from Magnificent seven by Louis Komzsik. Copyright © 2013 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

Contents

Acknowledgements, 1,
Preface, 3,
1 Heavenly sevens, 5,
2 Humanly virtues, 17,
3 Wonders of the world, 31,
4 Leafs of life, 45,
5 Colors of the rainbow, 57,
6 The happy number, 69,
7 Crossing bridges, 85,
Closing remarks, 103,
References, 105,

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