#history of chinese philosophy
Beyond Taoism - Part 5
A Vector-based Probabilistic
Number System
Part II
(continued from here)
Taoism and the primordial I Chingare in agreement that temporal changes have two different aspects: sequent and cyclic. Western thought in general follows suit. The I Ching differs from the other two in asserting that the direction of change - for both sequent and cyclic change - is fully reversible, with the proviso that sufficiently small units of measurement are involved.[1] The probability that reversal can be achieved diminishes proportionately to the magnitude of change that has taken place.[2]
Taoist appropriation of bigrams and trigrams of the I Ching to model such phenomena as change of seasons and phases of the moon is plausible if not quite legitimate. The natural phenomena so modeled are macroscopic and vary continuouslyandinexorably throughout an ever-repeating cyclic spectrum. And there’s the rub.
As they occur and function in the I Ching bigrams and trigrams are dicontinuous discrete elements, formed by other similarly discontinuous discretized entities, and they follow evolutionary courses which are most often nonrepetitive. So the Taoist usage is misleading at best, annihilative at worst. Unfortunately, as the I Ching itself evolved through centuries of commentaries and reinterpretations, it became ever more contaminated and tainted by these Taoist corruptions of meaning, at the same time that it was being inundated by Confucian sociological and ethical reworkings. What we have today is an amalgam, the various parts of which do not sit well with one another.[3]
Though it may in part be hyperbole to prove a point, the stark difference between the two approaches, that of Taoism and that of the I Ching, is epitomized by comparison of the Taoist diagram of the cycle of seasons with diagrams at the top and bottom of the page, which are based on the number, logic, and coordinate systems of The Book of Changes.[4] The increased complexity of the latter diagrams should not prove a stumbling block, as they can be readily understood in time with focus and attention to detail. The important take-away for now is that in the I Ching bigrams exist within a larger dimensional context than the Taoist diagram avows, and this context makes all their interactions more variable, conditional, and complex. As well, the same can be said of trigrams and hexagrams.
One of the more important aspects of these differences has to do with the notion of equipotentiality. As bigrams and trigrams function within higher dimensional contexts in the I Ching, this introduces a possibility of multiple alternative paths of movement and directions of change. Put another way, primordial I Ching logic encompasses many more degrees of freedom than does the logic of Taoism.[5] There is no one direction or path invariably decreed or favored. An all-important element of conditionality prevails. And that might be the origin of what quantum mechanics has interpreted as indeterminism or chance.
Next up, a closer look at equipotentiality and its further implications.
Section FH(n)[6]
(continuedhere)
Notes
[1] There are exceptions. Taoist alchemy describes existence of certain changes that admit reversibility under special circumstances. Other than the Second Law of Thermodynamics (which is macroscopic in origin, not result of any internally irreversible microscopic properties of the bodies), the laws of physics neglect all distinction between forward-moving timeandbackward-moving time. Chemistry recognizes existence of certain states of equilibrium in which the rates of change in both directions are equal. Other exceptions likely occur as well.
[2] Since change is quantized in the I Ching, which is to say, it is divided into small discretized units, which Line changes model, the magnitude of change is determined by the number of Line changes that have occurred between Point A and Point B in spacetime. Reversal is far easier to achieve if only a single Line change has occurred than if three or four Lines have changed for example.
[3] Ironically, Taoism itself has pointed out the perils of popularity. Had the I Ching been less popular, less appealing to members of all strata of society, it would have traveled through time more intact. Unless, of course, it ended up buried or burned. What is fortunate here is that much of the primordial logic of the I Ching can be reconstructed by focusing our attention on the diagrammatic figures and ignoring most of the attached commentary.
[4] These diagrams do not occur explicitly in the I Ching. The logic they are based on, though, is fully present implicitly in the diagramatic structural forms of hexagrams, trigrams, and bigrams and the manner of their usage in I Ching divinatory practices.
[5] Or, for that matter, than does the logic of Cartesian coordinate space if we take into account the degrees of freedom of six dimensional hexagrams mapped by composite dimensional methodology to model mandalic space. (See Note [4] here for important related remarks.)
[6] This is the closest frontal section to the viewer through the 3-dimensional cube using Taoist notation. See here for further explanation. Keep in mind this graph barely hints at the complexity of relationships found in the 6-dimensional hypercube which has in total 4096 distinct changing and unchanging hexagrams in contrast to the 16 changing and unchanging trigrams we see here. Though this model may be simple by comparison, it will nevertheless serve us well as a key to deciphering the number system on which I Ching logic is based as well as the structure and context of the geometric line that can be derived by application of reductionist thought to the associated mandalic coordinate system of the I Ching hexagrams. We will refer back to this figure for that purpose in the near future.
© 2016 Martin Hauser
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Earlier to Later Heaven: Fugue V Alchemy Is Not a Dirty Word
(continued from here)
As is the case with all great mysteries, many different explanations for the origins of both the EARLIER and LATER HEAVEN arrangements of the trigrams have been proposed. In seeking plausible explanations, it is well to keep in mind what the worldview contextual origin of these two different arrangements might have been. The dates of their origins seem to be separated by thousands of years.[1] They grew out of very different worldviews. Still there was a clear attempt to correlate LATER HEAVEN with EARLIER HEAVEN. At the time LATER HEAVEN appeared on the scene, there was a longstanding tradition in place which was not entirely discarded. A kind of conceptual amalgamation took place.[2] The mystery lies in how and why that was accomplished.
Alchemy in its most fundamental aspect has to do with all kinds of relationships and from such a perspective both Earlier Heaven and Later Heaven are alchemical in nature. But differently so. They are reflections of different ways of seeing reality. Both, however, are debilitated, in the sense that they are missing a third dimension. The trigram, having three Lines, is a combination form which maps three dimensions. It cannot be adequately represented by figures of one or two dimensions. Any attempt to do so inevitably provokes injustice to reality by misrepresenting all the combinatoric relationships possible among the eight trigrams.
Placing Earlier Heaven in context of three dimensions enables it to express the full range of relationships and changes that can occur among the eight trigrams, thereby creating a combinatoric system resembling a Boolean lattice. This is very likely the form in which Earlier Heaven was originally understood, whether explicitly or implicitly. At some stage of the development of Chinese philosophy, it lost its clear connection to the third dimension, possibly as a result of the new method of encoding and storing ideas in writing, which demanded linear text, displacing the older oral tradition. And that suggests a possible clue to the mystery of the two trigram arrangements.
(continuedhere)
Notes
[1] Both arrangements of the trigrams are of great antiquity, Earlier Heaven possibly dating to around 3000 BCE and Later Heaven to the 8th century BCE. The point here is that the two arose in widely different cultural contexts having differing worldviews with all that entails. Yet they were related one to the other in the Chinese mind. Imagine, if you will, say, the unlikely amalgamation of the phlogiston theory with the scientific oxygen theory of combustion or with modern thermodynamics in the West. How likely is it that such amalgamations could have occurred though the ideas involved were separated not by millennia but only a few centuries. Something very strange and unexplained happened in the history of Chinese thought when these two widely different arrangements of trigrams were entangled with one another. Things are not as they appear on the surface here. Something hermetic and profound is going on at a deeper level.
[2] Something similar did occur in the West when chemistry took over from alchemy. Though chemistry owes a debt to alchemy for its very existence it is somewhat in denial regarding its origins or at least about this particular aspect of its origins. Having alchemy in its family tree, however, is not something for chemistry to be ashamed about. Alchemy had been practiced in many parts of the world for several millennia before chemistry appeared and can boast many important accomplishments in the history of human cognition. It could be said chemistry threw out the baby with the bath water when it conclusively broke with alchemy, except that it never did do that, not completely. Alchemy in the broadest and best sense has to do with relationships of objects, one to another. Much the same can be said about chemistry.
Modern astronomy also pays homage to an earlier form of ideation when it invokes the notion of a constellation, a term first used in astrology which was considered a scholarly tradition throughout most of its history. Constellations in most cases are composed of stars which, though visible in the same general area, are often located at very different distances from Earth. Nonetheless the tradition of referring to constellations is still in use by astronomers today. Its expediency is considerable as any given point in a celestial coordinate system can easily and unambiguously be assigned to a constellation, 88 of which are officially recognized and used in modern astronomy. The past lives on, in the history of ideas, but changed.
© 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
n = x + 1 - p. :)
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