Yuan Anxi Magical Square: An attempt at interpreting (original) (raw)

Sign up for access to the world's latest research

checkGet notified about relevant papers

checkSave papers to use in your research

checkJoin the discussion with peers

checkTrack your impact

Abstract

The tradition preserved in Arabic numerological lore professed that numbers were flesh, while the word-meaning, or root-meaning behind the numbers was the soul. Inasmuch as in neoplatonic arithmetic the type (soul) is eternal and the token (particular) is transient. Assuming that Arabs were artful at revealing and concealing, one might assume that various magical squares did not escape such patient treatment, that perhaps in a spontaneous manner, might reveal its hidden wisdom.

Figures (2)

The tradition preserved in Arabic numerological lore professed that numbers were flesh, while the word-meaning, or root-meaning behind the numbers was the soul. Inasmuch as in neoplatonic arithmetic the type (soul) is eternal and the token (particular) is transient. Assuming that Arabs were artful at revealing and concealing, one might assume that various magical squares did not escape such patient treatment, that perhaps in a spontaneous manner, might reveal its hidden wisdom.  Most probably, the Iron Square came into possession of Mongolians (who already conquered the Yuan part of China) after the conquest of Eastern Persia in the years 1218 — 1221. During the Northern Song Dynasty, Xi'an was known as Jingzhaofu. Its name was changed to Fengyuan in 1273 under the Yuan Dynasty. In 1275 Prince of Anxi (son of Khublai Khan) or Ananda , who was a Mongolian prince, built a palace city near Xi'an. It was called Dawang Dian in Chinese and Gan Erduo in Mongolian. Today, it is referred to as Anxi.  Mateusz Zalewski (2014)

The tradition preserved in Arabic numerological lore professed that numbers were flesh, while the word-meaning, or root-meaning behind the numbers was the soul. Inasmuch as in neoplatonic arithmetic the type (soul) is eternal and the token (particular) is transient. Assuming that Arabs were artful at revealing and concealing, one might assume that various magical squares did not escape such patient treatment, that perhaps in a spontaneous manner, might reveal its hidden wisdom. Most probably, the Iron Square came into possession of Mongolians (who already conquered the Yuan part of China) after the conquest of Eastern Persia in the years 1218 — 1221. During the Northern Song Dynasty, Xi'an was known as Jingzhaofu. Its name was changed to Fengyuan in 1273 under the Yuan Dynasty. In 1275 Prince of Anxi (son of Khublai Khan) or Ananda , who was a Mongolian prince, built a palace city near Xi'an. It was called Dawang Dian in Chinese and Gan Erduo in Mongolian. Today, it is referred to as Anxi. Mateusz Zalewski (2014)

The Base of Math in The Chinese Book of Changes - The Starting Point.

Here we are looking at an ordering of all numbers as they are placed into Images called Trigram's of Heaven and Earth. The Ho Tu's (Yellow River Map) directions starts North = 1 to 6, but the Binary Image's of Heaven and Earth give a base + 6s in their addition = 123 = 6 and 6, 12, 18 = 36, but they all = 7s in a multiplication or doubling = 124 = 7 to 6,12,24 = 42. These integer images of 6s and 7s are squared = 128 Trigrams = 8 x 8 = 64 Hexagrams in each of the 4 Directions or Elements. South = 2-7, East = 3-8, and West = 4-9 as all = + 5s to produce +10s. Value's 5 and 10 = the Central Magic Square of Earth or the 5th Element, which is created from the 4 Outer Directions as all squares are symmetrically constructed, in both integer, and binary image. In the pairing's of values attained = 1 + 9, 2 + 8, 3 + 7 and 4 + 6 all = 10s, and only then do value's of Precession = 25920 and 51840 appear in the Lo Shu. The average value of the integers = 5, which can only be added = 15 when the value's of 10s are attained. The Trigram Sequences in the Ho Tu gives reversals = 8-1 and 8-1, and all value's of 'The Well' = 9s produce 8 x 8 squares except +3s and +6s. This gives us an ordering of all numbers by placing them into binary images.

Sacred Cubes within Sacred Spheres: The numismatic symbolic system that traveled to the East

Meouak, Mohamed, and Puente, Cristina (eds.), Connected Stories: Contacts, traditions and transmissions in Premodern Mediterranean Islam, Berlin/Boston: De Gruyter, 2022 (ISBN: 978-3-11-077256-2), pp. 160-193., 2022

The Almohad design of coins, combining squares and circles, spread from the Western part of the Islamic realm into the Eastern one, where it lasted for centuries. But why did the Almohads strike square coins or coins with squares inscribed in circles? After a critical state of the question and an exam of the explanations provided so far, attention is paid to the idea that Almohad square coins could have been regarded as protective objects. The quest leads then to the consideration that the model of the Quran, whose copies were square-shaped in Almohad and post-Almohad period, might point to the cubical shape of the Kaʻba, providing us with an answer to the initial question consisting in the sacred value granted to a system of geometrical symbols. This model of coins, plenty of sacred references, allusions and implications, is to be understood in reference to their own historical circumstances, but, paradoxically, was adopted in different historical contexts since it was imitated by Eastern Islamic dynasties.

Jacques Sesiano, An Ancient Greek Treatise on Magic Squares

Aestimatio: Sources and Studies in the History of Science

The two earliest Arabic treatises explaining the construction of magic squares date from the 10th century ad. One is found in the Commentary on the Arithmetical [Introduction] (Kitāb tafsīr al-Arithmāṭīqī) by ʿAlī ibn Aḥmad al-Anṭākī (d. 376 H/ad 987). Only book 3 of the original three books is extant, and that in a single manuscript. This book is divided into three chapters: the first is a collection of arithmetical definitions, statements of propositions, and identities assembled from Greek and Arabic sources; the second is on magic squares; and the third deals with “hidden numbers”, in which a person thinks of a number and another discovers it after operations are performed on it. Curiously, none of these chapters have anything to do with Nicomachus’ Arithmetical Introduction, on which the book is supposed to be a commentary. Reviewed by: Jeffrey A. Oaks Published Online (2022-07-31)Copyright © 2022 by Jeffrey A. Oaks Article PDF Link: https://jps.library.utoronto.ca/index.php/ae...

Magick Squares as the Cornerstone of Pythagorean Tetractys Symbolism

This essay shows all the most important numbers associated with the 7 magick squares of Cornelius Agrippa, along with others, can be found on an extended ordinal counting sequence version of the Tetractys of Pythagoras. That is by counting out numbers in a triangular form the "triangular numbers" are highlighted in the pattern and this also shows the numbers of magick squares. A detailed look at this numerical Tetractys is given, with interpretations on what it could mean for Pythagoras, the Kabbalistic cube of space, along with cubic numbers and even the Sri Yantra and Chakra systems. (Showing Kabbalistic numbers in the Sri Yantra) Building upon the work of David Fideler and his book "Jesus Christ Sun of God" gematria is used to interpret the biblical parables of 153 fish and the feeding of 5000. All this shows how magick squares and their associated numerology is the basis for various traditions of number mysticism. While there is far more to explore in terms of interpreting texts, with the evidence provided, the main thesis shows how the magick squares undeniably fit with the Tetractys and that Polygonal numbers in general are also very important.

Entangled Representation of Heaven: A Chinese Divination Text from a Tenth-Century Dunhuang Fragment (P. 4071)

This article provides the transcription and translation of a tenth-century Chinese divination text from a Dunhuang fragment (P. 4071) with substantial commentary. Great importance has been so far attached to this astrological text as the most ancient source related to the eleven luminaries which consist of the seven planets including the Sun and Moon with the four pseudo-planets. This Chinese text deals with horoscopic astrology which was transmitted to China via multiple routes along the Silk Road. The text consists of various astral traditions in terms both of region and religion. The original Hellenistic elements are no more than some planetary calculations and astrological interpretations, while certain indigenous parts of astral sciences in East Eurasia are central to the astral divination in the text. Of the four pseudo-planets, Râhu 羅睺 and Ketu 計都 are undoubtedly derived from the Indic astral tradition, and a specific calculation method in the text follows that of the Jiuzhi li 九執曆, an Indic astronomical system. From the religious standpoint, that calculation method appears in the Xiuyao jing 宿曜經 originally composed by a Buddhist monk Bukong 不空. On the other hand, we find certain Daoist influences through the positions of the four pseudo-planets, and the Yusi jing 聿斯經, a text used for astrological interpretation, was probably brought by East-Syrian Christians. This fact confirms that Central Eurasia, where the text was recorded, encompassed various kinds of cultural elements. These multiple elements were not merged into a single system, but emerged as a heterogeneous whole reflecting the cultural mosaic in Central Eurasia.

Reflections of Number symbolism on Egyptian sacred architecture

Numbers have long been seen as expressions of cosmic order, possibly deriving from ancient Babylonian observation of regular cosmic events, such as night and day, the phases of the moon and cycles of the year. Belief architecture Filled with symbolism for the reason of its indirect impact on the spiritual atmosphere of this type of buildings. Symbolism can be found in which symbolic colors, symbolic shapes, number symbolism and other symbolic tools that emphasize on the spatial experience of these buildings. The research deals with number symbolism in religious buildings in Egypt and their meaning. This study extends along three periods of Egyptian architecture; that represent Ancient Egyptian Architecture, Coptic Architecture and Islamic Architecture in Egypt.

Math and Magic: A Block-Printed wafq Amulet from the Beinecke Library at Yale

The Beinecke Rare Books Reading Room at Yale University houses an important collection of Arabic papyri and paper documents. Among them are at least two printed texts: RCtYBR inv. 2016 and RCtYBR inv. 2367. The latter is a small fragment containing but a few words, and is therefore of little value, while the former is a large fragment of an amulet, and is of considerable interest because it contains two magic squares, that is, squares in which numbers are arranged in such a way as to produce a constant sum in all rows and columns (Ar. wafq, pi. awfaq). Although the use of magic squares in amulets is well attested through theoretical works such as al-Buni's Shams al-ma(arif al-kubra, and through manuscript specimens, only one other example of a block-printed square is known. What is more, the present piece contains a rare occurrence of a magic square of the order 13 - perhaps the only such occurrence in all amulets published to date.

A Chinese Mythos of Mantic Turtles, Yu the Great, Number, and Divination

Bulletin of the Museum of Far Eastern Antiquities, 2018

This essay is about the link between numerology and the exploits of Yu the Great.2 It is an attempt to tie together some loose threads in divination, number magic, and hero worship, strands that exercised a powerful hold on the imagination in early China. As an exper- imental foray into some obscure domains it makes no claim to comprehensiveness. But I argue that what surfaces here is a genetic link showing how a variety of cultural phenom- ena ultimately derive from a seminal paradigm dating to the formative era of Chinese civi- lization. Matters taken up include: Numinous Turtles, the myth of Yu the Great, the Nine Provinces, the “Pace of Yu”, the cosmological ya-shape 亞,the TLV pattern in esoteric de- sign, the Magic Square, and finally, the ancient board game Six Wands liubo 六博. Not sur- prisingly, it was the recent archaeological discovery of some ancient tomb texts that pro- vided crucial new support for propositions concerning numinous turtles (or tortoises) that have been on my mind for some time.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

The earliest Arabic magic squares

Suhayl

My aim here is to shed light on the origins of magic squares in the Islamic world. This question has often been tentatively addressed, but previous studies have considered only part of the evidence. The earliest Arabic texts presenting squares (al-Ṭabarī, Jābir ibn Ḥayyān, Ghāyat al-Ḥakīm, Brethren of Purity) are examined here together for the first time, as well as the Indian medical sources. The extraordinary coincidences in the use of the square of three in therapy for a good delivery in both the early Arabic texts and the Indian, as well as the close cultural, geographical, and chronological context, strongly suggests that such eutocic practice represents the origin of Islamic magic squares.

ENCYCLOPAEDIA OF ISLAM - THREE 2023 = article MAGIC SQUARES

Encyclopaedia of Islam, 2023

Magic squares A magic square is called in Arabic a wafq (harmony, agreement) or wafq al-add (harmonious disposition of numbers), and ilm al-awfq is the study of such squares; occasionally the more general term for any tabular presentation, jadwal, was used (Günther and Pielow; Hallum).

Between Numbers and Images: The Many Meanings of Trigram Gen 艮 in The Early Yijing

Asiatische Studien 72.4, 2018

This paper examines the images of trigram Gen 艮 in the Yijing易經, with a focus on images in the Shuogua 說卦 commentary. The Shuogua presents images either found in or to be extrapolated from the base text within a structured and highly interpretive system that forms "image programs" for each of the eight trigrams. I argue the Shuogua's image programs have a defined architecture, and its images are not random lists of words collected without an agenda and devoid of relationships and mutual interaction with others. My main thesis is a high percentage of images in the Changes developed through a simple and direct pictographic method, like the one used in a recently discovered Warring States period divination guidebook called Shifa 筮法 (Method of Milfoil Divination*), that was done by matching the graphic shapes of individual numbers and the overall shapes of numbers in three-line combination to shapes of real objects and logographs. If a diviner could see so many pictographic images in single numbers and sequences of numbers in combination, like what we now see in operation in the Shifa, then we ought to assume that a deeper repository of subjective and innovative images could be observed in number combinations at the multiline, trigram, and hexagram levels. Stated directly, trigram and hexa-gram diagrams were not pictorially meaningless; numbers produced images, and images produced the words and judgments that form early layers of text. Professional diviners had an expert knowledge of the tradition and Warring States use of the Changes continued to develop and explain image programs for the eight trigrams along these guidelines.

Luo Shu Ancient Chinese Magic Square on Linear Alg

Feng Shui, still popularly practiced today, was closely related to philosophy, natural science, geography, environmental science, architecture, metaphysics, and astrology in ancient China. It is basically divided into the Form School and the Compass School. The latter deals with numerology, calculation, orientation, and time. Luo Shu [洛書], associated with the eight trigrams [八卦], being an ancient Chinese magic square, forms the foundation of the Compass School. The original Luo Shu, a 3 × 3 magic square, was not unique in ancient China but the extension of it to a total of 18 to 36 standard charts was unique, which are still used by all Compass School Feng Shui masters. In this article, modern linear algebra, developed only in the mid-19th century, is employed to prove that there is a strong coherence between the 36 charts if they are treated as 36 matrices and such correspondences conscientiously agree with ancient theories of Feng Shui. This article may help to form a scientific base for the systematic understanding, development, and further research of Luo Shu-related applications.

Mathematics in China

Encyclopaedia of the History of Science, Technology, and Medicine in Non Western Cultures, 2008

Archaeologic finds from the Shang dynasty (fourteenth to eleventh century BCE) show the earliest number symbols inscribed on bones and tortoise shells. By then, different decimal and sexagesimal systems were in use. The use of rod-numerals is also attested on coins as early as from the Wang Mang period (9-23 AD). These are related to the instruments in use. For calculations, numbers were represented on a calculation surface by counting rods. The representation follows a decimal positional notation, where nine different signs for the numbers from 1 to 10 consist of either vertical or horizontal bars used to mark units, hundreds, myriads, etc. or tens, thousands, and other odd powers of ten. Three hundred twenty-six for example was thus put down in the following way: III = T. For negative numbers, black instead of red counting rods were used. In printed records (from the eleventh century onwards) they were marked by an oblique bar (Fig. ). "Brush calculations" written on paper and the abacus were widely spread by the sixteenth century, but the latter may have existed one or two centuries earlier. Procedures linked to abacus calculation are mostly written in versified form for easy memorization, and historians have shown how these evolved out of earlier procedures for counting rods (Fig. ). The scope of research into the history of mathematics in China today is determined by the available source Mathematics in China. Fig. 1 Solving a cubic equation with counting rods as shown in Hua Hengfang, Xue suan bitan, 1885. Mathematics in China. Fig. 2 An abacus as represented in Cheng Dawei, Suanfa tongzong, 1592.

mathematics of ancient China

2007

Many pieces of evidence converge towards the conclusion that generality was the main theoretical value prized by the practitioners of mathematics in ancient China and that it was valued more than abstraction (Chemla 2003). More precisely, these scholars regularly aimed at the greatest generality possible, but did not always achieve or express it through abstract terms. This does not mean, however, that abstraction played no role for them and that they did not find it necessary in some cases to carry out operations of abstraction. In fact, the earliest Chinese mathematical sources handed down through the written tradition, The Gnomon of the Zho1 u (Zho1 ubı4 , probably 1 st century C. E., Cullen 1996), The Nine Chapters on Mathematical Procedures (Jiu3 zha1 ng sua4 nshu4 , below: The Nine Chapters; probably 1 st century C. E.), 1 as well as their commentaries, bear witness to several uses of abstraction. On the other hand, the relationship between generality and abstraction that they evince differs from what can be found in, say, Euclid's Elements. 2 In correlation with this, both the generality

An Analogy between Pictorial Representations of Numerology in the Ancient Egyptian Civilization and the Islamic Civilization.

This study explores the principles behind numbers from zero to nine, and the different art forms expressing them in both the Ancient Egyptian and in the Islamic traditions, as two major components of the Egyptian culture. Executing an analogy between pictorial representations of numerology in both civilizations through an analytical comparative study mainly sheds the light on the conceptual similarities of archetypal spiritual aspects in both systems of belief and their different pictorial representations in relation with numbers, in order to benefit from the old in finding new means of expression.