Magic square cosmos is a concept that combines the mathematical concept of magic squares with the idea of a cosmic or universal pattern. Magic squares are grids of numbers where the sum of the numbers in each row, column, and diagonal is the same. The concept of magic square cosmos suggests that these mathematical patterns reflect a fundamental order that can be found throughout the universe. It implies that the same principles that apply to magic squares at a microcosmic level also apply to the cosmos at a macrocosmic level. Magic squares have been studied for centuries and are found in various cultures and civilizations. Ancient Chinese, Indian, and Arabic cultures all had their own versions of magic squares.
Making a magic square before an audience, if done properly, can be an impressive demonstration of one’s apparent command of higher-level mathematics. I’ll show you how to do this, using a seemingly more difficult 4×4 grid.
The popular game of snakes and ladders is controlled by the throw of dice, and the ladders and snakes originally referring to good and bad fortune, now refer to good and bad luck in the progress of the game. This idea still prevails, and many people all over the world use lucky charms, engage in superstitious practices, use horoscopes, and still have some kind of belief that there are such ways of influencing their lives.
Ancient Chinese, Indian, and Arabic cultures all had their own versions of magic squares. These squares were often associated with mystical or spiritual meanings, as they were believed to possess special powers or inherent cosmic harmony. In modern times, researchers have attempted to find connections between magic squares and the laws of nature or the structure of the universe.
From A Random World to a Rational Universe
In the time before the mathematical idea of randomness was discovered, people thought that everything that happened was part of the will of supernatural beings, the gods, who looked down upon human affairs and decided to 'tip the balance' one way or another to influence events. Hence, sacrifices were made and rituals performed to discover the 'will of the gods' or to try to influence human affairs. This idea still prevails, and many people all over the world use lucky charms, engage in superstitious practices, use horoscopes, and still have some kind of belief that there are such ways of influencing their lives. The gods may be dead, but 'Lady Luck' still survives.
The astragalus is a small bone, about an inch cube, found in the heel of hoofed mammals. Astragali have six sides but are not symmetrical, so there is no way of knowing which way they will eventually come to rest. For many ancient civilizations, astragali were used by priests to discover the opinions of their gods. It was customary in divination rites to roll, or cast, five astragali. Typically, each possible configuration was associated with the name of a god and carried with it the sought-after advice.
Astragali from the heel of a sheep showing the four positions of rest.
The small one in the foreground is made from pottery
Showing the four positions of rest. The small one in the foreground is made from pottery. Astragali found in excavations typically have their sides numbered or engraved. They were also used in board games in the First Dynasty in Egypt, c 3500 BCE; archaeological evidence consists of boards, counters, and astragali for various games, including one similar to Snakes and Ladders, still popular today.
The game of Hounds and Jackals dating from 1800 BCE found in an Egyptian tomb
The astragali have been used from classical times for gambling, and similar stones are still in use today for games like 'fivestones' or 'jacks'.
Die A
Gradually, over thousands of years, astragali were replace by dice [see note 1 below], and pottery dice have been found in Egyptian tombs. The earliest die known was made from pottery and excavated in Northern Iraq dating from about 3,000 BCE. It has dots arranged as in (Die A).
Die B
Die (B), from about 1400 BCE found in a tomb in Egypt, shows consecutive numbers opposite each other.
Die C
Dice with other markings like the names or portraits of gods have been found, probably used for special games or rituals, and others where some numbers are repeated, or 'loaded', for special purposes or possibly for cheating (Die C).
Once the Greeks had worked out the geometry of the polyhedra, dice of other shapes began to be constructed. However, whether cube or polyhedral, the shapes were not entirely regular and were therefore biased.
Over time, gamblers would get used to using the same dice, and have an intuitive idea of how they would fall, but given another set of dice, the odds would be different. Later, as the manufacture of dice became more exact, some ideas of the possible combinations of number began to emerge.
The Earth and The Cosmos
There were many other forms of rituals hoping to overcome the randomness of nature and man's condition. A few of these which became of particular mathematical interest are geomancy, the nine square grid or magic square, and temple designs, the ancestors of board games.
Geomancy
Geomancy means divination of or by the earth , and is a system of 16 mathematically related arrangements of stones, beans or other available small objects used to make decisions, answer questions, or foretell the future. The stones are cast upon the ground and the pattern formed is interpreted. The symbols represent a series of binary 'opposites' like good and evil, male or female, sadness and happiness, etc. Combinations of these opposites can be used to represent odd and even numbers.
The sixteen figures of the Geomancy system of Divination. The headings of the columns are: "The greater fortune" and "The lesser fortune". From a Book of Occult Philosophy published 1655. Notice that each pair of shapes are associated with the traditional signs for the planets and that each configuration could be interpreted from the throws of two dice.
As in all methods of divination, each of these figures has a number of interpretations depending on its relation to other figures shown, and many other circumstances like the time of day, the weather, and the kind of person who is asking the question.
The Grid of Nine Squares
The Nine square grid is said to come from an ancient system for the division of land, probably from feudal India. In China the nine-square configuration was supposed to be an ideal arrangement, with eight farmers' fields surrounding a central well. The grid of nine squares, or a circle divided into nine sections by straight lines often appears as a central form in Tibetan sacred diagrams. In Scotland, the pattern was used at Beltane (the eve of May) where eight squares were cut out from the turf, and a bonfire lit on the central square.
In this way, from practical beginnings in different cultures, the nine-square grid acquired mystic importance and symbolised divine order, and the representation of control by the gods.
Magic Squares are directly related to the Sacred Grid, supposedly being the numerical mystery which underlies their physical form. The simplest magic square is the square of nine, ascribed to Saturn, where each row and column adds up to 15; the total of the rows and the columns is 45, and the diagonals 30. The 4x4 square with row and column numbers 34 is assigned to Jupiter, the 5x5 with row or column numbers 65 to Mars, and so on for the Sun, Venus, Mercury and the 9x9 square with row or column numbers 369, to the Moon [an NRICH article on Magic Squares can be found here at nrich.maths.org/1337].
As with other devices, these magic squares are all said to have correspondences to different numbers, various deities, days of the week, natural objects, different qualities, and so on. In the Hindu Temple Yantra [see note 2 below] you can see the nine squares, the 'sacred space', or source of energy, in the centre.
This is a Yantra from a Hindu Temple. Yantras (or Mandalas) are used as a focus for mystical contemplation and often for the basis of design for a temple. This one is based on a 5 x 5 square, with the 'sacred space' of the 3 x 3 square in the centre.
Board Games are clearly linked with divination, astrology and sacred geometry, and the designs of the boards can show their sacred or occult origins. The popular game of 'snakes and ladders' is controlled by the throw of dice, and the ladders and snakes originally referring to good and bad fortune, now refer to good and bad 'luck' in the progress of the game. In some cases the designs of the boards are the same as the plans of temples and holy cities with a 'sacred space' in the centre.
In the 16 th century the Catholic physician, astrologer, and theologian Cornelius Agrippa (1486–1535) constructed squares of orders from 3, 4, 5, 6, 7, 8, and 9 which he associated with the seven known astrological planets: Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon (the Sun and Moon were considered to be planets at that time.) Agrippa had a colorful life that included various dangerous run-ins with the Church and jobs as an occult scholar, lawyer, and military strategist. Agrippa’s De Occulta Philosophia stimulated Renaissance study of magic and got his name into early Faust legends. Agrippa believed that a magic square containing the digit 1—which exhibits the magic constant of 1 in all directions—represented God’s eternal perfection.
Some have suggested that the symmetry and patterns found in magic squares may be indicative of underlying principles of reality. They argue that the universal laws that govern the behavior of matter and energy may be similar to the rules that govern the arrangement of numbers in a magic square. Others have explored the relationship between magic squares and other branches of science, such as quantum mechanics. They propose that the mathematical properties of magic squares may have implications for understanding the nature of reality at the quantum level. However, it is important to note that the concept of magic square cosmos is highly speculative and is not currently supported by empirical evidence or widely accepted in the scientific community. While there may be intriguing connections and patterns to explore, further research is needed to establish any concrete links between magic squares and the fundamental laws of the universe. In conclusion, magic square cosmos is a concept that explores the potential connections between magic squares and the cosmos. It suggests that the fundamental patterns and symmetries found in magic squares may reflect a larger universal order. While this concept is interesting, it remains a topic of speculation and is not yet widely accepted in scientific circles..
Reviews for "The cosmic origins of Magic Squares"
1. John - 2 stars - I was really disappointed with "Magic Square Cosmos". The plot was confusing and difficult to follow. The characters lacked depth and were uninteresting. The writing style was bland and uninspiring. Overall, I found it hard to engage with this book and I wouldn't recommend it to others.
2. Sarah - 1 star - "Magic Square Cosmos" was a complete letdown for me. The story was slow-paced and lacked any sense of excitement or intrigue. The dialogue between characters felt forced and unnatural. The author's attempt at world-building fell flat, leaving me feeling confused and disconnected from the narrative. I struggled to finish this book and was left feeling unsatisfied.
3. Mark - 2 stars - I had high hopes for "Magic Square Cosmos" based on the positive reviews I had read, but unfortunately, it didn't live up to the hype. The writing was convoluted and overly descriptive, making it hard to follow the story. The characters lacked depth and their actions often seemed arbitrary. I was left feeling unsatisfied and underwhelmed by this book.
4. Emily - 3 stars - While "Magic Square Cosmos" had an interesting premise, I found the execution to be lacking. The pacing was inconsistent, with long stretches of slow development followed by rushed and confusing plot twists. The characters felt one-dimensional and their motivations were unclear. Overall, I think this book had potential, but it fell short of my expectations.
5. Michael - 2 stars - I struggled to connect with the characters in "Magic Square Cosmos". They felt flat and unrelatable, making it hard for me to invest in their journey. The storytelling itself was also lacking, with choppy transitions and a lack of cohesion. While there were some intriguing concepts introduced, they were never fully explored or developed. I wouldn't recommend this book to others looking for a satisfying read.