 |
| Ábaco Mágico Solar from Magic Abacus exhibition.-march 2007. |
WHAT IS THE USE OF MAGIC SQUARES? ( Magic Abacus)..
What is the use of the magic abacus? We know they have been and are still used to anticipate and / or to diagnose events, as a model from which you can make works of music, of paint, of self-knowledge, technical matters, mathematical, architectural, and so on...
The only condition to use properly the magic abacus is to have full knowledge of them.
|
A magic square is obtained by dividing it into cells, also square, where the numbers are placed in a regular progression, arranged in such way that if you add them in a vertical, horizontal or diagonal form you obtain the same amount.
Making a magic square is an ancient entertainment and it is still used by amateurs and mathematicians.
They have been used -and this happens nowadays- in games of wit or random, as a source of inspiration for artistic compositions and to diagnose and anticipate events ...
The following is a magic square of 9 (nine) cells. It is the smallest one to be obtained :
4
|
9
|
2
|
3
|
5
|
7
|
8
|
1
|
6
|
It is composed by the first 9 integer digits of the natural numbers’s system and it is called of Saturn . Its constant - sum of each row, column and diagonal, is number 15.
What evokes us a square figure?
It takes us to the geometry world, the natural kingdom , the golden number and the tissue between science, myth, art and history from which we emerge.
It takes us to the geometry world, the natural kingdom , the golden number and the tissue between science, myth, art and history from which we emerge.
Why a square has been called Magic?
In first place, the word magic suggests us the concept Magister, which means Teacher and - if we take note of this sense - we should be aware of the teachings that we can obtain of the magic-square-teacher.
In this regard, remember that the tarot arcana number 15 is assigned, among other interpretations to: the scientist, the devil. And Saturn is called the old devil, and also the old teacher.
Heinrich Cornelius -“ Agrippa” - assigned the name by which this magic square is known: Magic Saturn Abacus.
Let us analyze the constant 15. The number 15 is equal to 3 times the central number of the abacus: 5 ...
Let us analyze the constant 15. The number 15 is equal to 3 times the central number of the abacus: 5 ...
We revive Russian fairy tales, in which the zarevitz should arrive to the country three times 9, beyond the country 3 times ...
The number 15 is also relevant in Astrology.
Not only because obviously the zodiacal signs are equal to 15
Not only because obviously the zodiacal signs are equal to 15
degrees x 2 (30 degrees), but because most of the aspects used are multiples of 15. To wit:
Semisextile
|
15
|
x
|
2
|
=
|
30
|
degrees
|
Semisquare
|
15
|
x
|
3
|
=
|
45
|
degrees
|
Sextile
|
15
|
x
|
4
|
=
|
60
|
degrees
|
Quadrature
|
15
|
x
|
6
|
=
|
90
|
degrees
|
Trine
|
15
|
x
|
8
|
=
|
120
|
degrees
|
Sesquiquadrate
|
15
|
x
|
9
|
=
|
135
|
degrees
|
Quincunx
|
15
|
x
|
10
|
=
|
150
|
degrees
|
Opposition
|
15
|
x
|
12
|
=
|
180
|
degrees
|
Conjunction
|
15
|
x
|
24
|
=
|
360
|
degrees
|
It remains to analyse, among others, numbers 18, 36, 72, and 144*, all divisible by 9 (nine), number of cells of this magic square. We´ll return over this topic.
And what may we add about the square ...? We thought it spinning in space, it shows the cube´s faces , the pyramid´s base, a king’s throne , a charming crystal emerging... It is impossible to delimit all the images ...
Let’s go back to the constant 15. Remember that 15 degrees are contained 24 times in the interior angles of a square, and we know that 24 x 9 - number of boxes of this magic abacus- is equal to 216 which happens to be the number of Heaven to the ancient Chinese.
From the historical point of view, the oldest magical abacus that has been reported is about the fourth century BC. It comes from China.
According to legend, it was carved on the caparison of a turtle -as a world model.
This turtle emerged from the Yellow River (Lo River) in the presence of the mythical hero YU, after he had reduced the waters to duty, having disciplined the rivers.
YU was founder and demiurge, master blacksmith, and an expert surveyor. He received a mandate from heaven by which he should order the world according to the image inscribed on the caparison of the turtle, so the Earth -square- could be cultivated. Thus, YU divided the world into nine square regions. Within each region he drew the headings of the Hong Fan (Big Model).
What may represent the above headings?
A group of symbols capable of impose categories that evoke the spirit of the universal order:
Around number 5 (as sovereign emblem of the space center) these items were simply the first numeric symbols.
With this beautiful myth we say goodbye ... The Magic Abacus spins this time in the space..
Arelisa Beatriz Romero
What may represent the above headings?
A group of symbols capable of impose categories that evoke the spirit of the universal order:
Around number 5 (as sovereign emblem of the space center) these items were simply the first numeric symbols.
With this beautiful myth we say goodbye ... The Magic Abacus spins this time in the space..
Arelisa Beatriz Romero
 |
| This turtle emerged from the Lo River . |
Notes:
* 144 was the number of the Earth to the ancient Chinese.
If you add to it number 216 (number of Sky to the ancient Chinese) we get 360. The circle!.
If you add to it number 216 (number of Sky to the ancient Chinese) we get 360. The circle!.
Bibliography:
Mouni Sadhu: “The Tarot”. Editorial Kier S.A. Bs.As. 1987
Liz Greene. “Saturn: A New Look at an Old Devil”. Samuel Weiser, Inc.(York Beach, ME, 1976).
Richard Wilhelm: "YI-KING." Editorial Sudamericana. Buenos Aires 1979.
Encyclopedia /Arte Rama. Editorial Codex. BA 1969.
Martin Gardner "The unexpected hanging and other Mathematical Diversions”. Simon and Schuster 1969.
Encyclopedia /Arte Rama. Editorial Codex. BA 1969.
Martin Gardner "The unexpected hanging and other Mathematical Diversions”. Simon and Schuster 1969.
Ibero-American Encyclopedia. Madrid 1900.
Johan Gunnar Andersson "An early Chinese culture." Pekin 1923.
Research by Arelisa Beatriz Romero and Alex Piler.
Published with the signatures of Alex Piler and Arelisa Suoboda in may 1998, in number 11th of Ciencias Milenarias, - Editorial EDISER : www.croattodesign.com.ar . Protected by copyright.
Note: The paintings "Abaco Mágico Solar " and "this turtle emerged from the Lo River" were not part of the original article. They are protected by copyright and they cannot be reproduced in whole or in part without the permission of the paintress.
