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

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.

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.

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.