Beyond Taoism - Part 1
A Lost Logic of Chinese Antiquity

The 64 Hexagrams of the I Ching
(for interactive version click here)

(continued from here)

In speaking of “Taoist thought” I have often throughout this work used the term as a convenient shorthand for “primeval Chinese thought.” Strictly speaking, this usage is historically incorrect. Laozi is traditionally regarded as the founder of Taoism and is associated with “primordial” or “original” Taoism. Whether he actually existed is disputed.  According to tradition the classic text attributed to him, the Tao Te Ching, was written around the 6th century BCE. The oldest extant text, however, dates to the late 4th century BCE. The earliest strata of the I Ching predate both these historical periods by many centuries, if not millennia.  Taoism derived its cosmological notions from the philosophy of yin and yang,  and from that of the  Five Phases  or  Five Elements. Both these schools of thought were overwhelmingly  influenced and shaped  by exposure to the oldest known text of ancient Chinese classics, the I Ching.^[1]

The actual symbolic logic of Taoism,  although derived from the I Ching is extremely simplistic compared with that of the original upon which it is based. Whereas the philosophy of yinandyang as presented in the Tao Te Ching comprises little more than a two-dimensional cycle of two-valued elements,  in the I Ching these two represent vectors in a six-dimensional combinatorial manifold of 64 hexagrams (1,2). Clearly, it is a difference like that  between night and day.  It is,  in fact,  a literal comparing of 2² with 2⁶, the latter holding many more possibilities. The actual difference^[2]  in the  logic and geometry  emerging from the two is greater even than it appears at first. It eventuates not from just a simple geometric progression but from a mandalic intertwining and association of logical elements that give rise to different amplitudes of dimension as well as to a greater number of dimensions.  This mandalic interweaving leads also to a richer catalogue of relationship types.^[3]

Long viewed as mainly an ancient text of Chinese divination,theI Chingencompasses many more categories of thought - - - among them symbolic logic, geometry, and combinatorics.  As a treatise which deals with combinatorics alone, it soars without equal, the first known compendium of combinatorial elements and still one of the finest. The logic and geometry  that are embedded in the  hexagram system  of the I Ching are best understood in terms of dimensions and vectors akin to those in Cartesian systematics, and of logic gates analogous to the truth tables of Boolean algebra. And still the cognoscente will want to explore beyond the pertinency of these disciplines as also beyond Taoism to find the full meaning and intent of the I Ching.^[4]

Having existed for millenia,  and itself a treatise regarding change^[5] in its many aspects, it would be inconceivable that the I Ching as we have it today is as it was in its beginnings. Popular at all societal levels through its entire existence,  reinterpretations and reworkings  have been myriad. Confucianism in particular interlaced its own brand of philosophical and “ethical-sociopolitical teachings”  during and after  the fifth century BCE. Other schools of thought added their unique perspectives to what became essentially  a massive melting pot of schematization,  one not always self-consistent by any means.

When one attempts to uncover the original face of the I Ching the difficulties encountered soon appear insurmountable. If involved in such a venture,  it is imperative to bear in mind the bedrock strata of the work were in some ways more ingenuous, and in some more intricate, than the traditional version that has come down to us.  The earliest layers arose in context of a preliterate oral tradition with all the many unique aspects of being that entails. In some ways the golden age of the I Ching ended with coming of the written word and literacy. The multidimensional logic that was readily accommodated by an oral tradition foundered and eventually was all but lost in the unrelenting techno-sociological onslaught of script with its associated inevitable linearity. Anyone who hopes to excavate the buried multidimensional logic of the primordial I Ching can expect to do a good deal of laborious digging.

(continuedhere)

Image:Source. Originally from Richard Wilhelm’s and Cary F. Baynes translation “I Ching: Or, Book of Changes” [3rd. ed., Bollingen Series XIX, (Princeton NJ: Princeton University Press, 1967, 1st ed. 1950)]

Notes

[1] Two diagrams known as bagua (or pa kua) that figure prominently in the I Ching and its Commentaries predate their appearances in the I Ching. The Lo Shu Square is sometimes associated with the  Later Heaven arrangement  of the bagua or trigrams, and the  Yellow River Map  is sometimes associated with the Earlier Heaven arrangement of trigrams. Both are linked to astronomical events of the sixth millennium BCE. Although part of Chinese mythology, they played an important role in development of Chinese philosophy.  The Lo Shu Square is intimately connected with the legacy of the most ancient Chinese mathematical and divinatory traditions.  The Lo Shu is the  unique normal magic square (1,2) of order three (every normal magic square of order three is derived from Lo Shu by rotation or reflection). [Wikipedia]

[2] Taking into account both changing lines and unchanging lines of hexagrams there are four possible variants for each line:  unchanging yin,  unchanging yang, changing yin,  and changing yang.  This results in a total of  4⁶  or 4096  possible different line combinations for each six-line figure.  This allows for an enormous number of logical / geometric configurations,  all of which map to various points of the mandalic cube or, in terms of  Cartesian coordinates,  to discretized points of the three-dimensional cube bounded by  the eight Cartesian triads which have coordinates of  +1  and/or  -1  in all possible combinations (corresponding to the eight trigrams.)

To this point changing lines have not been discussed to avoid overcomplicating already complicated matters too soon.  Changing lines play an indispensable role in all changes of yin lines to yang lines and vice versa,  and therefore, in changes of one hexagram to another.  They are also essential elements in formation of the geometric line segment generated by the I Ching hexagrams which I have earlier referred to as the  "Taoist line“  and which we have yet to broach fully. Mandalic line segments uniformly comprise sixteen interrelated elements,  hexagrams with changing and/or unchanging lines.  Though various mandalic line segments have different compositions in terms of six-dimensional hexagrams,  these hexagrams can always be reduced in logical and geometrical terms to  sixteen bigram forms containing changing and/or unchanging lines. These bigram sets are all identical. No other variants are possible, since 4² equals 16. In this sense there is a single species of mandalic line segment but one which takes on different characteristics in different dimensional contexts.  Every hexagram has a commentary appended to each of its six lines,  which annotation is intended to be reflected upon only if the line is a changing one at time of consulting the oracle. Justly put, this system is brilliant beyond belief.

[3] Understand here that ‘relationship types’ may variously refer to human relationships in a society, to particle relationships in context of the atom, or to any other species of relationship one might imagine.

[4] For an exhaustive listing of linkstoI Ching related materials on the Web see here.

[5] Indeed, an alternative name of the I Ching in English is Book of Changes. The ensconced multidimensional logic encoded in the original work purports to be a microcosm describing all possible pathways of change, and their incessant changing relationships in the greater macrocosm of the universe.

© 2015 Martin Hauser

Please note:  The content and/or format of this post may not be in finalized form. Reblog as a TEXT post will contain this caveat alerting readers to refer to the current version in the source blog. A LINK post will itself do the same. :)

Scroll to bottom for links to Previous / Next pages (if existent).  This blog builds on what came before so the best way to follow it is chronologically. Tumblr doesn’t make that easy to do. Since the most recent page is reckoned as Page 1 the number of the actual Page 1 continually changes as new posts are added.  To determine the number currently needed to locate Page 1 go to the most recent post which is here. The current total number of pages in the blog will be found at the bottom. The true Page 1 can be reached by changing the web address mandalicgeometry.tumblr.com to mandalicgeometry.tumblr.com/page/x, exchanging my current page number for x and entering.  To find a different true page(p) subtract p from x+1 to get the number(n) to use. Place n in the URL instead of x (mandalicgeometry.tumblr.com/page/n) where
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-Page 295-

The sage’s way,
                            Tao
                                    is the way of water.

There must be water for life to be,
and it can flow wherever.

And water, being true to being water,
                             is true
                  to Tao.

Those on the Way of Tao, like water,
need to accept where they find themselves;
and that may often be where water goes
to the lowest places, and that is right.

Like a lake,
                               the heart must be calm and quiet
having great depth beneath it.

The sage rules with compassion,
and his word needs to be trusted.

The sage needs to know like water
how to flow around the blocks
and how to find the way through without violence.

Like water, the sage should wait
for the moment to ripen and be right:

water, you know, never fights;

it slows around
                                   without harm. 

— from The Illustrated Tao Te Ching(translated by Man-Ho Kwok, Martin Palmer, and Jay Ramsay)

Lost and Found

Deadheading between airports to pick up an airplane, I randomly thumbed through my copy of the Tao Te Ching, pondering the words I chanced upon…A priceless time of reflection in what would otherwise be a time of listless boredom. Guilty of a short attention span, I moved on to other things, stowing my books in the seat back, and began looking at weather and plans for my coming flight. Only after…

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Lao Tzu - Tao Te Ching

Went to Half Price Book Store- found a gorgeous hardcopy of the Autobiography of Benjamin Franklin. I read it last year and it was fabulous. I recommend. Still looking for the upcoming Aeschylus, Confucius, and Sophocles. Publishers need to make more good translations that are pretty classics too.

For anyone who wants to read with me the beginning of the Mother of All Book lists is as follows (looks crappy when you realize that I’m still on 3- but I have read a lot of these already, just not in context):

1. 1800 BC Anonymous. The Epic of Gilgamesh
2. 1000 BC Vyasa. The Mahabharata
3. 900 BC Sage Ved Vyasa. The Bhagavad Gita (Part of the Mahabharata) *date unknown
4. 855 BC Homer. The Odyssey.
5. 850 BC Homer. The Iliad
6. 512 BC Sun Tzu. The Art of War (Recorded in the Records of the Grand Historian)
7. 500 BC Lao Tsu. Tao te Ching
8. 500 BC Mencius. The Book of Mencius
9. 480 BC Aeschylus. Prometheus Bound.
10. 479 BC Confucius. The Sayings
11. 478 BC Confucius. The Analects
12. 472 BC Aeschylus. The Persians
13. 467 BC Aeschylus. Seven Against Thebes
14. 463 BC Aeschylus. Suppliant Maidens
15. 458 BC Aeschylus.  Agamemnon, Libation Bearers, Eumenides(The Oresteia Trilogy)
16. 450 BC Sophocles. Ajax
17. 450 BC Sophocles. Trichinae
18. 441 BC Sophocles. Antigone
19. 438 BC Euripides. Alcestis
20. 431 BC Thucydides. The History of the Peloponnesian War.

thecalminside:

“Can you step back from your own mind and thus understand all things?”

Lao Tzu

“The fool who persists in his folly will become wise.”

“A fool sees not the same tree a wise man sees.”

- William Blake