Mathematics, Geomancy, Arabic, Ilm Al Raml, Musa al-Khwarizmi, Sylvester James Gates, Thomas Fuller

Mathematics, Geomancy, Arabic,  Ilm Al Raml, Musa al-Khwarizmi, Sylvester James Gates, Thomas Fuller, Final Part

Arabic Geomancy

Ilm Al Raml (the science of the sands)

Ilm al-ghayb (the occult sciences)

Ilm al-Ḥurūf (the science of letters)

It is essential to situate mathematical concepts within atypical cultural and historical contexts that essentialize mathematical thought as embodied expressions of human endeavours. There is an ongoing investigation into the mathematical structures underlying an ancient historical and cultural divination practice known as ilm al-raml (Arabic translation of sand science). Principled by sociohistorical and sociocultural lenses, the study employs an ethnomathematical methodology. 

Ilm Al Raml (the science of the sands)

Geomancy is a method of divination that interprets markings on the ground or the patterns formed by tossed handfuls of soil, rocks, or sand. The most prevalent form of divinatory geomancy involves interpretation. Interpretation commences with a series of 16 figures formed by a randomized process including recursion, followed by analyzing them, often augmented with astrological interpretations. King Richard II thought geomancy was a greater discipline that included philosophy, science, and alchemic elements.

Richard II, also known as Richard of Bordeaux, was King of England from 1377 until 1399. He was the son of Edward the Black Prince, Prince of Wales, and Joan, Countess of Kent. Wikipedia

Born: 6 January 1367, Bordeaux, France 

Ilm Al Raml (The Science of the Sands) Binary codes and Elements

Died: 14 February 1400, Pontefract Castle, Pontefract

Siblings: Edward of Angoulême, John Holland, 1st Duke of Exeter, MORE

Spouse: Isabella of Valois (m. 1396–1400), Anne of Bohemia (m. 1382–1394)

Parents: Edward the Black Prince, Joan of Kent

Deposed dates: 1377, 29 September 1399

Many people from different social classes practised geomancy in the Middle Ages. Geomancy was a popular form of divination in Europe, particularly during the Middle Ages, except in Africa and Asia. Renaissance, although in Renaissance magic, geomancy was classified as one of the seven "forbidden arts", along with necromancy, hydromancy, aeromancy, pyromancy, chiromancy (palmistry), and scapulimancy. 

Ilm Al Raml (the science of the sands) Elements

The word geomancy from Late Greek *γεωμαντεία *geōmanteía translates literally to (earth divination); it is a calque translation of the Arabic term ilm al-raml or the "science of the sand". Earlier Greek renditions of this word borrowed the Arabic word raml ("sand"), rendering it as rhamplion or rabolion. Other Arabic names for geomancy include khatt al-raml and darb al-raml. 

The reference in Hermetic texts to the mythical Ṭumṭum al-Hindi potentially points to an Indian origin, although Stephen Skinner  thinks this unlikely. Having an Arabic origin is most likely because the expansive trade routes of Arabian merchants[when?] would facilitate the exchange of culture and knowledge.

One of the Symbol of the Hermetic Order of the Golden Dawn

European scholars and universities started translating Arabic texts and Treatises in the early Middle Ages, including those on geomancy. Isidore of Seville (560 – 636 AD) lists geomancy with other methods of divination – including pyromancy, hydromancy, aeromancy, and necromancy – without describing its application or methods. The poem Experimentarius, attributed to Bernardus Silvestris, who wrote in the middle of the 12th century, was a verse translation of a work on astrological geomancy. 

One of the first discourses on geomancy translated into Latin was the Ars Geomantiae of Hugh of Santalla (fl. early 12th century). By this point, geomancy must have been an established divination system in Arabic-speaking areas of Africa and the Middle East. However, archaeological, oral and symbolic evidence counter the Arab originator assertion. 

Sikidy Board Hierarchy

Other translators, such as Gerard of Cremona, also produced new translations of geomancy that incorporated astrological elements and techniques ignored by many.  

More European scholars studied and applied geomancy, writing substantial Treatises. Henry Cornelius Agrippa (1486–1535 AD), Christopher Cattan (La Géomancie du Seigneur Christofe de Cattan (1558 AD), and John Heydon (1629 – 1667 AD) produced oft-cited and well-studied Treatises on geomancy, along with other philosophers, occultists, and theologians until the 17th century, when interest in occultism and divination began to dwindle due to the rise of the Scientific Revolution and the Age of Reason.

Geomancy underwent a revival in the 19th century when renewed interest in the occult arose due to the works of Robert Thomas Cross (1850–1923 AD) and Edward Bulwer-Lytton (1803–1873 AD). Franz Hartmann published his text, The Principles of Astrological Geomancy (English translation: 1889) spurred new interest in the divination system. 

Based on this and a few older texts, the Hermetic Order of the Golden Dawn (founded in 1887 AD) began the task of recollecting knowledge on geomancy along with other occult subjects, like Aleister Crowley (1875–1947 AD) published his works that integrated various occultistic systems of knowledge. However, due to the short time, the members of the Golden Dawn desired to learn, practice, and teach the old occult arts, many elaborate systems of divination and ritual had to be compressed, losing much in the process. In effect, they had reduced geomancy from a complex art of interpretation and skill in recognizing patterns to looking up predefined answers based on pairs of figures.

Generating Geomantic Charts

Geomancy requires the geomancer to create sixteen lines of points or marks without counting, creating sixteen random numbers. Without taking note of the number of points made, the geomancer provides the seemingly random mechanism needed for most forms of divination. Once produced, the geomancer marks off two by two until either one or two points remain in the line. Mathematically, this is the same as drawing two dots if the number is even or one if the number is odd. 

Taking these leftover points in groups of four, they form the first four geomantic figures and form the basis for the regeneration of the remaining figures. Once finished, the "inspired" portion of the geomantic reading expires; what remains is algorithmic calculation.

Traditionally, geomancy requires a surface of sand and the hands or a stick, but also equally well with a wax tablet and stylus or a pen and paper. In divination, ritualistic objects may or may not apply. When drawing marks or figures, geomancers proceed from right to left as a tradition from geomancy's origins, and it is not mandatory. Modern methods of geomancy include, in addition to the traditional ways: 

Random number generators or thrown objects; others include counting the eyes on potatoes. Some practitioners use specific cards,  each representing a single geomantic figure; in this case, only four cards are drawn after shuffling. Specified machines are needed to generate completed geomantic charts.

The figures are recorded into a specialized table, known as the shield chart, which illustrates the recursive processes reminiscent of the Cantor set that forms the figures. The first four figures are the matres or Mothers and form the basis for the rest of the figures in the chart; they occupy the first four houses in the upper right-hand corner such that the first Mother is to the far right, the second Mother is to her left, and so on (continuing the right-to-left tradition).

The following four figures, the filiae, or Daughters, are formed by rearranging the lines used in the Mothers: the first Daughter is formed by taking the first line from the first, second, third, and fourth Mothers in order and rearranging them to be the first Daughter's first, second, third, and fourth lines, respectively. The process is done similarly for the second Daughter using the second line from the Mother, and so on. The Daughters are placed in the next four houses in order on the same row as the Mothers.

After the formation of eight matres and filiae, the generation of four nepotes (or Nieces) is by adding those pairs of figures that rest above the houses of the respective Niece. Including the first and second Mothers added to form the first Niece, the third and fourth Mothers added to become the second Niece, and so on. 

Here, addition involves summing the points in the respective lines of the parents. If the sum is an even number, the resulting figure's line will have two points; if the sum is odd, it is one point. Conceptually, this is the same procedure in mathematical logic as the exclusive or, where a line with two points is used instead of "false" and with one point instead of "true".

The calculation of the binary numbers of the four nepotes, the two testes (or Witnesses) is the same as the nepotes: the first and second Nieces form the Right Witness, and the third and fourth Nieces form the Left Witness. Creating the index or judge technique is the same as the Witnesses. A sixteenth figure, the Reconciler or superiudex, is also generated by adding the Judge and the First Mother. Nowadays, it is seen as extraneous and a "backup figure" in recent times.

Muhammad ibn Musa al-Khwarizmi

D’Ambrosio (1985, 1999 ) and Knijnik’s (2000) 

Muhammad ibn Musa al-Khwarizmi

Muḥammad ibn Mūsā al-Khwārizmī, or al-Khwarizmi, was a Persian polymath from Khwarazm who produced vastly influential works in mathematics, astronomy, and geography. 

He was appointed around 820 AD as the astronomer and head of the library of the House of Wisdom in Baghdad. 

Born: Khwarazm

Died: Baghdad, Iraq

Full name: Muḥammad ibn Mūsā al-Khwārizmī

Era: Islamic Golden Age (Abbasid era)

Influenced: Abu Kamil

Main interests: Mathematics, astronomy, geography

Fractals

Fractals are the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology. It is in many of the swirling patterns produced by computer graphics.

Fractals

Sylvester James Gates

When physicist James Gates discovered recurring codes that dictate the behaviour of every sub-atomic element in the universe, he named it Adinkra. 

Sylvester James Gates Jr. (born on 15/12/1950), known as S. James Gates Jr. or Jim Gates, is an American theoretical physicist who works on supersymmetry, supergravity, and superstring theory. 

Sylvester James Gates

Jim Gates holds the Clark Leadership Chair in Science with the physics department at the University of Maryland College of Computer, Mathematical, and Natural Sciences. 

Gates is an affiliate with the University of Maryland School of Public Policy. 

He served under former President Barack Obama. 

He was a member of the Council of Advisors on Science and Technology.

Thomas Fuller

Thomas Fuller (1710 – December 1790), also known as Negro Demus and the Virginia Calculator, was an enslaved African renowned for his mathematical abilities. Born in Africa, likely between present-day Liberia and Benin, Fuller was enslaved and shipped to America in 1724 AD at age 14. He became the legal property of Elizabeth Cox of Alexandria, Virginia. 

Thomas Fuller

Despite his mathematical skills, Fuller needed to be more literate. Ethnomathematics researcher Ron Eglash theorizes that Fuller could have been Bassari, comparing his abilities to their mathematical traditions. Before colonialism, the Bassari used to have specialists trained in the memorization of sums.

Bassari People 

A Bassari Woman

The Bassari people are African people living in Senegal, Ghana, Gambia, Guinea and Guinea-Bissau. The total population is between 10,000 and 30,000. The Bassari mainly resided on either side of the Senegal-Guinea border southwest of Kedougou, Kédougou Region. 

These areas are referred to in French as Pays-Bassari, or liyan in the Bassari language. The Bassari speak a Tenda language, o-niyan, and call themselves a-liyan, pl. bi-liyan. Most of the group are animists, with a significant minority of Christians (both Catholic and Protestant). 

The Bassari have close relations with the Fula people centred locally in the nearby hills of the Fouta Djallon.

The end of the final part. Other Publications: Ancient Mathematics, Occultism and Astrology Part 1 King Solomon of Israel, Vs, Pharaoh, Amenemope The Immaculate Conception, an amazing deception Ifa, Sacred Geometry, Tetrahedron, Odu, Portals, Points The Baptismal Ceremony of The Gospel Of The Egyptians To learn more: A Study Finds that Yorubas Are Genetically 99.9% Igbo. There is a true story behind the Zombie legends. Ogham line alphabets, African Origin. This video presentation concentrated on prehistoric and ancient cultures in Africa and elsewhere. Namely, Gabon, Zambia, Nigeria, Mali, Chad, Congo, Khem, South Africa and Ethiopia. Gnostic Bible, The 34 Hidden Letters and Messages in Bismillah Al-Rahman Al-Rahim, Islamic Mystical Literature: Initiation and Prophecies of Djehuiti, Thoth, or Hermes and Atum

Ancient Mathematics, Ifa, Chinese, Sikidy and Geomancy Divination Systems, Part 2

Ancient Mathematics, Ifa, Chinese, Sikidy and Geomancy Divination Systems Part 2

Sacred Geometry is a complex and sophisticated science that requires objective study and subjective meditation. The most crucial shape in understanding possession by Ela is the tetrahedron. If you turn a sphere into a three-sided pyramid with the base at 19.5 degrees below the equator and the apex at the North Pole, the result should be a tetrahedron.

Illustration of Odu Portal Points

To complete Odu patterns, a Babalawo needed two tetrahedrons, with the apex of the top one on the North Pole and the bottom one on the South Pole, generating eight portal points. The Babalawos will then employ the pure philosophy of Ifa to decipher the portal points meaning.

To open portals, place the second three-sided pyramid inside a sphere with the base at 19.5 degrees above the equator and the apex at the South Pole. In Ifa, these portals or Odu means womb. Each point where the pyramid makes contact with the circumference of the sphere is a portal for Odu, which is the point of entry for light from the Invisible realm into the Visible Realm (Orun and Aye, heaven and earth). 

Illustration of Yoruba Multiplication Technique

The top tetrahedron and bottom pyramid counter-rotate in 255 of the basis of energy patterns rotate in opposite directions to create gravity. The blueprint called Eji Ogbe is anti-gravitational because both pyramids rotate in the same direction, eliminating polar tension. This pattern is one of the top secrets of alchemy. The remaining 240 Odus out of 256 are minor odus called Amulus (Admixtures). 

In the process of divination, Ifa priests employ the use of a complex system of signs/codes. These codes are widely studied, and to foster in-depth understanding, researchers have considered them vis-a-vis their relationship with other fields of study, for instance, carried out code characteristics of Ifa signatures akin to binary operation in computer science. 

Amulu

The need for further study of these codes is supported by those who opined that despite several studies devoted to it in recent times, Ifa remains an intractable subject for many, a bewildering cellar of ancient wisdom, and this is not only due to the complex web of fetish associated with it but also to the paraphernalia and elaborate divination procedure incidental to life.

According to Ifa divination mythology, the generation of the signature codes occurs during divination. These codes, in conjunction with the entire Ifa divination system, possesses a large spectrum of properties that demands exploration still, only a few of these properties have, and it led to a lack of basic understanding of the working of the divination system and a high level of misconception about Ifa. Ifa thus becomes unattractive, considered obsolete and evil in some parts of African society and beyond. 

Chinese Divination System

In the middle of Figure 1 is the symbol of Tàijí, "the Extreme Ultimate". Tàijí is the unity from which everything originates: it splits into duality, the duality splits in four, and the four splits in eight. 

Figure 1

The Taoist universe consists of an infinity of binary data - yins and yangs constantly turning into each other. The only unchanging thing is the ultimate principle itself. 

Trigram symbols are everywhere. The flag of South Korea contains four symmetrical three-bit binary numbers. 

In the Feng Shui system (mega-fashionable in the West nowadays), you may even hang binary numbers on your walls because you believe in their magical power of modifying the energies inside the building.

Three bits is the smallest binary number that allows a "true RGB palette" (one bit for each red, green and blue component). 

Incidentally, the Chinese trigrams are also traditionally associated with colours. The image below Figure 2 presents the six-bit binary combinations in two different arrangements: an eight-by-eight matrix (in ascending binary order) and a "xiantian"-ordered circle. 

The figure was composed in the 11th century by Shào Yong, the famous philosopher and oracle who believed it was the original "xiantian" order in which the legendary emperor, Fú Xi, discovered the hexagrams millennia ago. Centuries later, the German philosopher G.W. Leibniz received a copy of this figure from Jesuit missionaries trying to convert Chinese people to Christianity.

Figure 2

Leibniz was so astonished by this figure that he wrote the first European text about binary mathematics (Explication de l'arithmetique binaire, 1705 AD). Leibniz later wrote some interesting stuff about the relationship of binary numbers to the very essence of the universe, but that's a different story. Yì Jing ("I Ching") is an ancient book with sixty-four hexagrams and associates them with names and mysterious verses. 

It is basically an oracular handbook ("Give me a random number, and I'll tell you what lies ahead"). However, due to its highly-honoured status in Chinese culture, its "message" has been thoroughly examined during the millennia. The properties of the six-bit binary numbers are examined as whole entities (symmetry, yin/yang constitution, visual shape) and in small pieces (the properties of every sub-trigram and the properties of each bit separately). 

In the Pythagorean numerology, natural numbers had mystical properties and even personalities, including similar numerology applied to binary combinations in ancient China. In the Yì Jing divination, each line of the result can be either static or changing (the resulting hexagram turning into some other hexagram). 

Figure 3

It gives 4096 possible readings. A man named Chiao Kan actually wrote 4096 rhymed verses to describe every possible transition. After this, philosophers started to speculate about interchanging evolutions. 

In the words of Shú Xi, if from the 12-line diagrams we continue generating undivided and divided lines, eventually we come to 24-line totalling 16,777,216 changes. 

Taking 4,096 and multiplying it by itself also gives this sum. Expanding, we do not know where it ultimately ends. 

Although we cannot see its usefulness, it is sufficient to show that the Way of Change is inexhaustible. No one was prolific in a lifetime enough to write out all the 16,777,216 second-order transitions. 

However, what makes the six-bit code especially divine even for modern people is its application in the genetic code that describes the hardware of every living organism on this planet. (In fact, a "genetic byte" consists of three symbols from an alphabet of four, but the amount of information is exactly the same).

Rhind Papyrus

The Rhind Mathematical Papyrus is one of the best-known examples of ancient Egyptian mathematics. Alexander Henry Rhind, a Scottish antiquarian, purchased the Papyrus in 1858 AD in Luxor, Egypt, and named it after him. The awareness of the whereabouts of the Rhind Papyrus became known during illegal excavations in or near the Ramesseum. 

Rhind Papyrus

It dates to around 1550 BC.

Author: August Eisenlohr

Date: Second Intermediate Period of Egypt

Language(s): Egyptian (Hieratic)

Place of origin: Thebes

Moscow Mathematical Papyrus 

Moscow Mathematical Papyrus

The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra. 

Owner: Vladimir Golenishchev

Date: 13th dynasty, Second Intermediate Period of Egypt

Euclid

Euclid was an ancient Greek mathematician active as a geometer and logician. Credited with the accolade of the father of geometry, he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century.

Died: Alexandria, Egypt

Nationality: Greek

Influenced: Isaac Newton, Apollonius of Perga, and more

Inspired by Pythagoras, Thales of Miletus, Eudoxus of Cnidus, Hippocrates of Chios, and Theaetetus.

Sikidy Divination System of Madagascar

The study of divination and divination systems, particularly in so-called non-technological societies, presents unusual problems that challenge the core of rational and epistemic thought. Even so, the strenuous efforts in researching cultural genres, such as religion, magic, and myth, fall short of distinguishing constituent theoretical and ontological underpinnings of divinatory principles. 

Sikidy's Order

Ifa ((West Africa), Haiti, Cuba, Brazil, Caribbean, America)) the four-tablet system (South Africa) and Sikidy (Madagascar). 

The first step in Sikidy is to arbitrate four columns of four bits (a four-by-four matrix). 

The arbitration of one bit usually happens by grabbing a handful of seeds from a bag and removing two at a time until only one or two are left. 

The remaining seeds must be placed properly on the Sikidy board. 

Sikidy processing gives a new meaning to the concept of (random number seed). 

The random columns ( Mother-Sikidy) are in the upper right corner. 

The values of the columns from right to left, bottom to top, are 1010, 1001, 1011, and 0010. 

The next thing to do is to form the Daughter-Sikidy by rotating and flipping the matrix.

Mother Sikidy

The rightmost column of the Mother-Sikidy (bottom to top) becomes the top row (left to right) of the Daughter-Sikidy, and so forth. 

Our Daughter-Sikidy (placed to the left of the Mother-Sikidy) is 0110, 1101, 0000, and 0111. 

The rest is pure binary arithmetic. 

The columns below the Mother-Sikidy and Daughter-Sikidy are formed by eXclusive-ORing each pair of columns: (1010 XOR 1001 = 0011), (1011 XOR 0010 = 1001), (0110 XOR 1101 = 1011) and (0000 XOR 0111 = 0111). 

Daughter Sikidy

As for the witnesses, it is (0011 XOR 1001 = 1010) and (1011 XOR 0111 = 1100). The Xor operator might look complicated but it is simple, for example, if you add (1010 to 1100 = (2110) we have to change the two, which is even to zero (0110) the binary number of the judge).

The image above shows an example of a completed Sikidy board. 

This process is repeated to all the new lines until only one column is left (the bottom column, 0110 in the example). 

We now have a complete Sikidy tableau, right to left (1010, 1001, 1011, 0010, 0110, 1101, 0000, and 0111) Mother Sikidy, Daughter Sikidy (0011, 1001, 1011 and 0111), Witnesses (1010 and 1100) and the Judge (0110), what is left is the interpretation. 

Witnesses and the Judge

Each of the sixteen Sikidy binary values has meaning, and each memory slot has a designated definition. 

The Sikidy system was also adopted by Arabs (under the name of ilm Al-raml, the science of sand), and from Arabs, it even spread to Europe in the Middle Ages. 

The end of part 2 and the final part will follow soon. Other Publications: Ancient Mathematics, Occultism and Astrology Part 1 King Solomon of Israel, Vs, Pharaoh, Amenemope The Immaculate Conception, an amazing deception Ifa, Sacred Geometry, Tetrahedron, Odu, Portals, Points The Baptismal Ceremony of The Gospel Of The Egyptians To learn more: A Study Finds that Yorubas Are Genetically 99.9% Igbo. There is a true story behind the Zombie legends. Ogham line alphabets, African Origin. This video presentation concentrated on prehistoric and ancient cultures in Africa and elsewhere. Namely, Gabon, Zambia, Nigeria, Mali, Chad, Congo, Khem, South Africa and Ethiopia. Gnostic Bible, The 34 Hidden Letters and Messages in Bismillah Al-Rahman Al-Rahim, Islamic Mystical Literature: Initiation and Prophecies of Djehuiti, Thoth, or Hermes and Atum