Time on Enneagram

[gotogo]

Neither can the 5-7-8-4-2-1 for the powers of 5 or the 741741 for the powers of 7. And factors of 9 would be your zero point so the theosophical addition is just the offset from the factors of 9.

Exactly! I was (still ) thinking to 'generalize' my logic to powers of n (n is a number not divisible by 3 (or 'prime number' after 3 can be a better concept to fit 'repeating' - still 'intuitive' though)) also. ;)

 

[gotogo]

same goes for 1/3 + 2/3 .333333... + .66666666.... is .9999999999......

not quite unity in either case.

That is mentioned in InSearch, I believe, but I can't quote it right now, as it is on loan to a friend.

In math .9999... is actually considered to be one, the actual phrasing being something like as you take the limit of all those 9s you get one.

http://en.wikipedia.org/wiki/Limit_(mathematics)

Obviously 1/3+2/3=1 thus one would expect .33333... plus .66666 to be one also since .3333... =1/3 and .6666... =2/3. It's the ... (infinite amount) that makes it one. You might think you can't actually get to infinity but math doesn't think that way!

This is metaphysical math though.
That infinite progression not quite getting back to unity is significant.

Kris

RflctnOfU, I think it is an 'illusion' exists on how to 'express' a mathematical concept.
For example, if you use base-3 (ternary) notation the same number .33333... will be 'expressed' 0.1 and .6666... = 0.2 !
And 0.1 + 0.2 = 1 (base-3) = 1 (base-10).

 

[RflctnOfU]

same goes for 1/3 + 2/3 .333333... + .66666666.... is .9999999999......

not quite unity in either case.

That is mentioned in InSearch, I believe, but I can't quote it right now, as it is on loan to a friend.

In math .9999... is actually considered to be one, the actual phrasing being something like as you take the limit of all those 9s you get one.

http://en.wikipedia.org/wiki/Limit_(mathematics)

Obviously 1/3+2/3=1 thus one would expect .33333... plus .66666 to be one also since .3333... =1/3 and .6666... =2/3. It's the ... (infinite amount) that makes it one. You might think you can't actually get to infinity but math doesn't think that way!

This is metaphysical math though.
That infinite progression not quite getting back to unity is significant.

Kris

RflctnOfU, I think it is an 'illusion' exists on how to 'express' a mathematical concept.
For example, if you use base-3 (ternary) notation the same number .33333... will be 'expressed' 0.1 and .6666... = 0.2 !
And 0.1 + 0.2 = 1 (base-3) = 1 (base-10).

I agree with you that, ultimately, mathematical expression IS arbitrary. We are steeped in a base 10 world, however. (fingers/toes one example). And, as this is a discussion on the enneagram/time relationship, which represents base 10 (nine unique 'placeholders'/digits plus '0'), it is in this context that it is important. 9 is the number of the 'serpent' or 'fence' or 'binder'... JG Bennett's research into systematics (_www.systematics.org) describes 9-termed systems as 'Pattern'.

I've wondered how different our psychological processes would be if we operated in a different base-system eg base 8 or base 12. Computers have no problem with this of course, but, and I may be assuming quite a bit here, everyone has the instinctual<?> understanding of base 10. At least in the west. And trying to think in another base system just 'doesn't fit' - I can't speak for everyone on this (I tried thinking in base 12 before and it wasn't very, ah, successful) There are some neat patterns in base 12 though - for instance, pascals triangle with numerological reductions.

Anywho, I suppose the point of the .9999999 business is that one needs to include unity to reach unity again.

:)

Kris

 

[shijing]

GotoGo --

Just wanted to let you know I followed some of the Wikipedia links from my earlier post, and thought the following site was the most helpful:

_http://cjvlang.com/Dow/dowjpn.html_

The part that is germane to the earlier question about correlations between Western and Eastern names for days of the week is below:

The obvious question is: could there be a historical link between the 'seven luminaries' and the 'seven planets' of Western and Middle Eastern antiquity?

The answer is, yes. The most commonly accepted theory is that the use of the seven planets originated in ancient Mesopotamia and Egypt, was adopted by the Greeks and Romans, and then found its way to China. However, the specific route and timing is not clear. The Cihai (辞海), a Chinese encyclopaedia, carries the following entry for 七曜历 (七曜歴) qī yào lì, or 'seven luminaries calendar':

七曜历 qī yào lì, i.e., method of recording days according to the 七曜 qī yào. China normally observes the following order: sun, moon, Mars, Mercury, Jupiter, Venus, and Saturn. Seven days make one week, which is repeated in a cycle. Originated in ancient Babylon (or ancient Egypt according to one theory). Used by the Romans at the time of the 1st century AD, later transmitted to other countries. This method existed in China in the 4th century. It was also transmitted to China by Manichaeans in the 8th century from the country of Kang (康) in Central Asia (Note 3: The country of Kang).

The earliest use of the 'seven luminaries' (七曜 qī yào) is attributed by Cihai to Fan Ning (範寧 / 范宁), a scholar who lived from AD 339-401. Tellingly, the Chinese 'seven luminaries' were arranged in the same order as the Middle Eastern planetary names for days of the week, and not in the classic order of the Chinese five elements, which put water before fire.

Besides the Manichaean route noted by the Cihai, there was also an Indian route of transmission in the 8th century. The Chinese Buddhist monk Yi Jing (義凈 / 义净) and the Ceylonese or Central Asian Buddhist monk Bu Kong (不空, Amoghavajra) are both credited with referring to the seven-day cycle of planetary names in their writings, drawing on Indian sources. The Indians, in turn, appear to have taken this from the West.

Although there were several routes of transmission into China, it appears that the Indian route was the direct source of the Japanese names for days of the week. In 806, the famous Japanese monk, Kobo Daishi (弘法大師) brought Bu Kong's writings back to Japan along with a huge quantity of other Buddhist scriptures. Great interest was taken in Bu Kong's astrological work by Japanese astronomers, with the result that the planetary names found their way into Japanese calendars of the time. One such calendar was used by the Japanese statesman Fujiwara no Michinaga (藤原道長) for writing his diary in 1007, in which the present-day Japanese names for the days of the week can be found.

Although not in widespread use except for astrological purposes, this system of names was nevertheless maintained by the Japanese right through to the modern era. At one stage the days got out of kilter in eastern Japan and had to be rectified by a calendar reform in 1685. When they came under pressure to harmonise their working calendar with the West in the latter half of the 19th century, the Japanese turned to this old system to name the days of the week, officially adopting them in 1876. After this the names gradually came into general use in Japan.

In China, on the other hand, the planetary names largely died out. When the seven-day week was adopted under Western influence in the modern era, the Chinese turned to a completely different system to name the days of the week.

So according to this site, the similarities in planet associations and orders are a case of cultural transfer in the first century AD. More pertinent to your original question, the author says that the original system was Babylonian and astrological in nature (although an alternative theory is that it was Egyptian). It still doesn't answer why the celestial bodies fall in the specific order they do, but at least it narrows the search.

 

[gotogo]

Thank you, shijing. I read the linked page. Quite interesting!

He wrote:

So the Japanese days of the week are not a system of 'primitive elements' after all! In fact, they run in parallel with days of the week of the Ancient Greeks and Romans -- more closely in parallel, indeed, than modern English:

(After this is stated, he goes to what shijing quoted, which made "correlations between Western and Eastern names for days of the week" point clear!)
But I would like investigate more. Because "Chinese theory of the 'Five Elements' 五行 (wǔ-xíng)" on Enneagram also seems a quite important point of view.

Here is "Chinese theory of the 'Five Elements' 五行 (wǔ-xíng)" (from the same link):

Fire (火 huǒ) was equated to south, red, summer, midday, the planet Mars, and note 5 in numbered musical notation.
Water(水 shuǐ) was equated to north, black, winter, midnight, the planet Mercury, and note 6 in numbered musical notation.
Wood (木 mù) was equated to east, green, spring, dawn, the planet Jupiter, and note 3 in numbered musical notation.
Gold or Metal (金 jīn) was equated to west, white, autumn, dusk, the planet Venus, and note 2 in numbered musical notation.
Earth (土 tǔ), was equated to the centre, yellow, 18 days at the end of each season, the planet Saturn, and note 1 in numbered musical notation.

(Note: 'numbered musical notation' also described here but that does not seem to matching any orders we thought about before )

Actually I would like to ask for other people in other cultures how it sounds. Does it make sense to you also?

For me this mapping is so familiar that it is hard to separate (a 'hard wiring' in my brain through the language of mother tongue ).


Edit: grammar

 

[John G]

Here is "Chinese theory of the 'Five Elements' 五行 (wǔ-xíng)" (from the same link):

Fire (火 huǒ) was equated to south, red, summer, midday, the planet Mars, and note 5 in numbered musical notation.
Water(水 shuǐ) was equated to north, black, winter, midnight, the planet Mercury, and note 6 in numbered musical notation.
Wood (木 mù) was equated to east, green, spring, dawn, the planet Jupiter, and note 3 in numbered musical notation.
Gold or Metal (金 jīn) was equated to west, white, autumn, dusk, the planet Venus, and note 2 in numbered musical notation.
Earth (土 tǔ), was equated to the centre, yellow, 18 days at the end of each season, the planet Saturn, and note 1 in numbered musical notation.

(Note: 'numbered musical notation' also described here but that does not seem to matching any orders we thought about before )

Actually I would like to ask for other people in other cultures how it sounds. Does it make sense to you also?

For me this mapping is so familiar that it is hard to separate (a 'hard wiring' in my brain through the language of mother tongue ).

GotoGo, the elements would be like axis endpoints and an origin on which the Enneagram is plotted. Chinese Asrology uses the elements that way too (the colors and directions shown here):

You can think of the axes as an octave too which is what the Ho T'u heavenly order of the I-Ching kind of does:

Like the music order for the elements does a center-west-east-south-north, the Ho T'u is crosslike, it keeps crossing over the center. The difference between the octave as element axes/origin and the octave as points on an Enneagram or Chinese Zodiac for me math-wise is like the difference between the Cartan Subalgebra origin and its associated Lie Algebra root vector polytope vertices.

As for why the planets were picked the way they were picked I have no idea. Mars as red, Saturn as yellow, and Venus as white almost seem color of the planet related but then you have Jupiter as green and Mercury as black which don't fit. Also maybe Mercury and Venus may seem directionally opposite Mars and Jupiter relative to the Earth. Maybe Saturn gets to be the origin cause it changes position in the sky the slowest (longest orbit)?

 

[gotogo]

Hello Bluelamp,
Thank you for your input. Ummm, interesting but I have again some difficulties to understand what you wrote. So please bear with me for asking more questions.

the elements would be like axis endpoints and an origin on which the Enneagram is plotted.

Is it what you think or you have some back up data to connect the elements (you are referring to "Chinese theory of the 'Five Elements' 五行 (wǔ-xíng)", right?) and the Enneagram in this way?

I am pretty sure there should be 'significant' ways to connect them IF what Gurdjieff said about the Enneagram in ISOTM such as the following is correct (that I did not completely 'verify' it yet but that is what I would like to challenge here through the 'Networking' though...):

Here is "Chinese theory of the 'Five Elements' 五行 (wǔ-xíng)" (from the same link):

Fire (火 huǒ) was equated to south, red, summer, midday, the planet Mars, and note 5 in numbered musical notation.
Water(水 shuǐ) was equated to north, black, winter, midnight, the planet Mercury, and note 6 in numbered musical notation.
Wood (木 mù) was equated to east, green, spring, dawn, the planet Jupiter, and note 3 in numbered musical notation.
Gold or Metal (金 jīn) was equated to west, white, autumn, dusk, the planet Venus, and note 2 in numbered musical notation.
Earth (土 tǔ), was equated to the centre, yellow, 18 days at the end of each season, the planet Saturn, and note 1 in numbered musical notation.

(Note: 'numbered musical notation' also described here but that does not seem to matching any orders we thought about before )

Actually I would like to ask for other people in other cultures how it sounds. Does it make sense to you also?

For me this mapping is so familiar that it is hard to separate (a 'hard wiring' in my brain through the language of mother tongue ).

'Networking' is really something! I can not extend to such wide range of thoughts by myself alone. So thank you! :)

 

[John G]

GotoGo, the yellow center of the Chinese Zodiac relates to your "Earth (土 tǔ), was equated to the centre, yellow", the black north on the zodiac relates to your "Water(水 shuǐ) was equated to north, black" and so on thus the elements are just mentioned on the Zodiac via color and position not directly by their name. Here's a link with a table that does match the element names to the Zodiac animals and notice it also matches with the colors of the dots next to each zodiac animal on the Zodiac you were looking at.

_http://www.chinesefortunecalendar.com/5Elist.htm

The five elements have also been related to the four sides and center of the Sri Yantra:

http://www.valdostamuseum.org/hamsmith/PDS3.html#sriyantra

A plot of Enneagram numbers on to Sri Yantra-like axes is the D4 plot here (the D3 plot is a Zodiac-like one):

http://docs.google.com/View?docid=dhspfskq_353tqfg5

So if you think of the Enneagram, Astrology (Eastern or Western), Sri Yantra etc. as a shape with vertices then you can think of the elements (Eastern or Western) as Axes. The idea of North-South would be one axis, East-West another. The idea of the Ho T'u cross movement is a Law of 3 thing; think of the 5 (center) - 6 (down) - 7 (up) as a law of 3 neutral - passive - active also the musical order 1 (Earth center) - 2 (Venus West) - 3 (Jupiter East); it's two opposites with a center, two axis endpoints with an origin. The Ho T'u is related to the Enneagram's law of 3 here:

http://tap3x.net/EMBTI/j4selfc.html

The Western astrology elements are earth-fire-water-air. They come with personality descriptions and the Chinese elements do too:

http://en.wikipedia.org/wiki/Wu_Xing

Thus the Wood-Metal's Sensitivity-Intuition sounds much like a Jungian Sensing-Intuition axis and Fire -Water's Creativity - Spontanaeity seems Jungian Thinking - Feeling. The D3 and D4 plots mentioned above use these Jungian traits as axis endpoints.