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Thread: Sacred geometry and number theory

  1. #1
    Fred Stakem Guest

    Default Sacred geometry and number theory

    In the west we tend to think of numbers as functional entities and geometry only as something we needed to know for the SAT. But it always hasn't been that way. I know the Pythagoreans in the west put special significance to numbers and geometry. Recently I have been looking into the significance of number thoery and geometry on the eastern martial arts. It may sound a bit strange, but some of the old fashion martial arts that have come from india and china place a great emphasis on the sacred geometry and number theory.
    Does anyone in the koryu know of similiar emphasis in the old japanese martial arts? If so, what significance does it play in the system and how well does the system follow the philosophy? What about the teacher...how much of it do they believe and how much do they pass on? Or is this sort of thing not taught to outsiders? I know some more modern martial arts talk about circles, squares, and triangles but these are after thoughts once the system has already been created. I am more interested in systems were the ideas were paramount.

    If anyone knows more than I do about this subject, I would be interested to colaborate to write up an article. I'm still in the process of trying to crack some codes.

    Fred Stakem

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    There is some material from the West during the late Renaissance and early modern era that also appears to use numerical symbolism; for starters, look at the 17th century Spanish schools of fence.

    For East Asia, the closest thing I've seen is John Lagerwey, _Taoist Ritual in Chinese Society and History_ (New York: Macmillan, 1987). Investigation into Asian finger-counting might be worthwhile. I don't mean one-two-three, but symbolic representations understood cross-culturally. For example, Roman numerals are all made by pointing fingers in appropriate ways, and the Arabs, Iranians, and Turks had similar systems that went everywhere they did. (Which is pretty near everywhere in Asia.) See, for example, Carl B. Boyer, _A History of Mathematics_, revised by Uta C. Merzbach (New York: John Wiley & Sons, 2nd edition, 1991) or George Ghevergese Joseph, _The Crest of the Peacock: Non-European Roots of Mathematics_ (London: I.B. Tauris, 1991).

    If you get enough for an article, EJMAS is definitely interested in publishing findings.

  3. #3
    Fred Stakem Guest

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    That is some interesting info. What got me on the idea was some of the sources you list. A friend found the text (The Crest of the Peacock: Non-European Roots of Mathematics_ ) but I haven't had a chance to look it through. He was interested in the magic squares of chinese mathmatics(also used in europe), and the relation to the 9 post exercise of bagau. I looked the idea up in Boyer, but wasn't able to get anything out of it beyond the mathmatical theory.
    Since I have a few months off I thought of doing a bit of research on the subject. I haven't seen much on the japanese martial arts and the subject and was wondering if there was any connection. My initial inclination is that these secrative ideas never made it across the sea of japan and any japanese method would be indigenous. What I have seen from okinawan karate is the lack of structure prevelent in orthodox chinese methods. Any ideas???

    Fred Stakem

  4. #4
    Dojorat Guest

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    Greetins,

    I don't know if this is off-thread but...

    I do know that the names of many of the original Okinawan Karate kata are based on certain numbers and their combinations. From pg 61 of P. McCarthy Sensei's "Classical Kata of Okinawan Karate"

    Kururumfa = Seventeen
    Neshishi = 24 steps
    Nipipo = 28 steps
    Pechurin (Suparinpi) = 108 Hands
    Pipuren = 8 Steps at a time
    Sanchin = Three battles
    Sanseryu = 36 hands
    Seipei = 18 hands
    Sesan = 13 hands
    Useishi (Gojushiho) = 54 steps

    The significance of these numbers beyond the readily apparent (and therefore very deceptive) number of steps, strikes, moves
    I leave for the Buddhist and other East Asian scholars.

    Cheers,

  5. #5
    Fred Stakem Guest

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    Patrick McCarthy has done a lot of research in the karate field so I take his inerpretations to be pretty good, but I was under the impression that the kata names were not completely understood. I could be wrong, but I think Morio Higionna wrote in his history of karate that the exact meaning of the names of many of the kata's were unknown. If those translations by Mr. McCarty were right, it would be interesting to know their logical progression in training.

    The problem I see with finding a structure in karate is the way in which is was taught. Different individuals learned different numbers of kata and trained with numerous teachers. So many of the karate ryu are a mix of different kata probably from different styles. And on top of that some schools have even created their own kata. And then of course it is hard to tell how much of the boxing system they even learned in china. The best link I can think of is the little known ryu of kojo-ryu mention in Bishop's book. Once again it has been a bit since I have read up on karate, but I beleive they have a set of kamae based on animals or the zodiac?? That would be similiar to the 12 animals of hsing-i and have a relation to chinese cosmology.

    Some of the links to cosmology and other fanciful things like chi may sound silly to us today, but in largly rural uneducated populations these ideas were taken seriously. I have even met educated people today who go to teachers of feng shu for advice.

    Fred Stakem

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    Hello,

    The sword style I study is of modern creation, but alot of what we do is borrowed from older styles.

    We use several geometric images to "map" out visually important principles and philosophies.

    One core to our system is based off the crest of our style, which is a series of connected circles that symbolize the solar system.

    Have a look at this brief discussion here for more information about this if you like:

    Kuyo mon thread

    And from our web page:

    Kuyo Junikun

    I've seen symbols and renderings (in addition to sanskrit and esoteric Buddhist symbols) in Japanese books that relate to specific koryu, but have not translated the text.

    HTH,
    Nathan Scott
    Nichigetsukai

    "Put strength into your practice, and avoid conceit. It is easy enough to understand a strategy and guard against it after the matter has already been settled, but the reason an opponent becomes defeated is because they didn't learn of it ahead of time. This is the nature of secret matters. That which is kept hidden is what we call the Flower."

    - Zeami Motokiyo, 1418 (Fūshikaden)

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    Again it's Chinese MA rather than Japanese, but also see Tyrey and Brinkman, "The Luo-Shu as Taiji Boxing’s Secret Inner-Sanctum Training Method," _Journal of Asian Martial Arts_, 5:2 (1996), 74-79. Back issues are generally available for about $10.

    I checked my notes, and Lagerwey is definitely a book you need to find. Regarding Joseph's book, my notes show that pages 149-179 and 209 provided good information on this topic.

    Presumably the bibliographies of those books could take you farther afield.

    In your research, pay attention to the lowly Zero. Ca. 788 CE, the Indian philosopher Shankara achieved enlightenment. This is important because Shankara's theory that one could escape fate by achieving a mind empty of illusions (sunya) subsequently contributed to the development of the Zen Buddhist concept of the Void and the Indo-Arabic numeral zero.

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    I flipped through some of my books and found some more info for you. Three of them had some references to "zuan-shu" (diagrams/renderings) as related to koryu:

    * Koryu Bujutsu Gairon - Jun Asano; pg. 58.

    This page is titled "Jujutsu Kuden no Zuan-shu", and shows several examples with their related ryu. These zuan are used to assist in transmitting aspects of the ryu's oral traditions.

    It would seem that Yagyu Shingan ryu uses a swastika-like symbol and a circle on top of a square. There is something that looks like the "Buddhist Wheel of Life" that was used by the Yagyu ryu. Yoshin ryu jujutsu has a ring with eight small circles along it's circumference, and kanji next to each circle.

    Asayama Ichiden ryu uses a couple of interesting zuan - one is a six pointed star with cryptic looking brush marks in each point, and the other is a triangle with similar marks and a charcter (possible "kokoro"?) inside.

    * Gokui Soden Dai Ichi Maki" - Hirakami Nobuyuki; pg.11.

    A copy of Yagyu Shingan ryu hidensho (secret writings), including two spiraling coils going opposite directions, an upsidedown pentagram inside a circle, "Kokoro" inside a circle.

    * Nippon no Kobudo - Nippon Budokan. pg.337.

    The first page of Muhi Muteki ryu jojutsu shows part of their hiden densho, showing "kokoro" in the center of eight other kanji that encircle it. there is also a horizontal and verical line that cross in the middle (somewhat similar visually to our Shinkendo kuyomon, minus the circles and different kanji...).

    I'm sure there are many more examples that can be sited - perhaps some with more of the numeric aspects you were asking about. But these are the ones that jumped out at me from the books I opened.

    Regards,
    Nathan Scott
    Nichigetsukai

    "Put strength into your practice, and avoid conceit. It is easy enough to understand a strategy and guard against it after the matter has already been settled, but the reason an opponent becomes defeated is because they didn't learn of it ahead of time. This is the nature of secret matters. That which is kept hidden is what we call the Flower."

    - Zeami Motokiyo, 1418 (Fūshikaden)

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    Originally posted by Dojorat
    Kururumfa = Seventeen
    Neshishi = 24 steps
    Nipipo = 28 steps
    Pechurin (Suparinpi) = 108 Hands
    Pipuren = 8 Steps at a time
    Sanchin = Three battles
    Sanseryu = 36 hands
    Seipei = 18 hands
    Sesan = 13 hands
    Useishi (Gojushiho) = 54 steps
    I hope I am not repeating what someone has already pointed out but at least number nine has a special significance in Japan (anywhere else?). You notice that many of the kata names point to numbers that are divisible by nine. Are there other similar numbers that occur again and again?

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    I'm not very good on gematria, but three is the probable divisor. Trinities are important...

    Some background. If you know more or see errors, please let me know.

    About 500 BCE, the Hellenic philosopher Pythagoras died, reportedly during an arson fire set at the house of the wrestler Milo of Kroton. Pythagoras is remembered for various things today, including (reportedly) discovering that the square root of two is an irrational number, determining a method for measuring right angles, and creating a system of rhythmic exercises done to the accompaniment of musical instruments. There is no contemporary evidence to support any of these claims. It also has been claimed that Hellenistic philosophers such as Apollonius of Tyana spread these Pythagorean exercises into India during the fourth century BCE, and that in the fourth century CE Buddhist monks introduced similar exercises into China. This is also unproven.

    Now, on more solid historical ground, during the second century BCE a school of philosophers called Neopythagoreans invented gematria, which is the art of assigning numbers to letters and thus to words, which in turn was supposed to provide metaphysical guidance. The reason this worked was that until the fifteenth century CE, Europeans used letters to represent numerical values, and some including the Armenians, still do. (And even in English, numerals less than twenty are commonly written in books as words rather than numerals. The previous sentence contains an example.) So ancient numerology also included the ability to use numbers to create both magical and obscene words. The most famous example is of course the example in Revelations 13:18, in which the numerical value of a man’s name was said to be six hundred and sixty-six. Now, as most any name from the Roman emperor Nero to the televangelist Pat Robertson can be beasted, who precisely was meant is unknown. Nevertheless, when the Bishop Irenaus of Lyon first remarked the entry during the second century CE, the allusion was probably to a Roman emperor. (That said, the practice of assigning numerical values and vibrating tones to individual names only took root during the late nineteenth century. Pioneers of this practice included Mrs. Lorenzo D. (Josephine) Balliett of Atlantic City, New Jersey.)

    Anyway, over time gematria spread through Eurasia, and as a result the names of many modern martial art practice forms have numerological significance. Examples include the Okinawan karate kata suparinpei and sanchin. The former translates as "One hundred and eight meanings" and alludes to the place in the Buddhist hell where souls receive their final decisions on reincarnation while the latter translates as "Three straight" and alludes to the three bodies of the Buddha that can be understood only through direct intuition.

    Ain't math grand?

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    Originally posted by Joseph Svinth
    I'm not very good on gematria, but three is the probable divisor. Trinities are important...
    At least in Japan, nine was "the big deal". Nine times two, makes "the perfect eighteen", also the amount of warrior skills to study.
    Last edited by Jari Virta; 2nd October 2001 at 13:38.

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    To add to Joe’s letters into numbers and back. Arabic and Hebrew both have systems of encoding or deriving numbers from words and then connecting those numbers to new words in order to expand meaning. Added to the increased ability to use puns and homonyms this creates deep layers of meaning to texts. As Islamic civilization influenced Europe in the middle ages many of these concepts entered Europe along with the reintroduction of ‘lost’ classical knowlege. I would also suspect that similar processes were at work to the east as well through India into China and beyond. See The Sufis by Idres Shaw for a good discussion.
    Doug Walker
    Completely cut off both heads,
    Let a single sword stand against the cold sky!

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