Before we can hope to comprehend Taoist arithmetic and geometry we need to take a short detour through Boolean logic. First and foremost, we need to see how Boolean logic[1] relates to Cartesian coordinates. That will provide what may be the best foundation available for understanding the Taoist approach to mapping of spacetime and the methodology which mandalic geometry derived from it.[2]
For Descartes, his coordinate system is one thing, his coordinate geometry another. For Taoism, the coordinate system is the geometry.[3] Boolean logic helps to explain how the two perspectives are similar, how different. Cartesian coordinates are static and passive. Taoist coordinates and the derivative mandalic coordinates are active and dynamic. In brief, the latter are changeable and self-changeable, a feat carried out by means of a brand of Boolean logic intrinsic to the system. Although it is true that Descartes’ coordinates do encode much the same information, that is not where their focus of interest lies. Accordingly they turn our own attention elsewhere and we overlook those inherent possibilities.[4]
Descartes’ geometric system is one based on vectors, that is, on both magnitude and direction. But in the scheme of things, the former has somehow eclipsed the preeminence of the latter in the Western hive mind. The opposite is true of Taoist thought and of mandalic geometry. Direction is uniformly revered as primary and prepotent. Magnitude, or scale, is viewed as secondary and subordinate. This mindset allows the Boolean nuances inherent in the system to come to the fore, where they are more easily recognized and deployed.
From such small and seemingly insignificant differences ensue entirely disparate worldviews.
[1] George Boole’s monumental contribution to symbolic logic was published in 1854 but was viewed as only an interesting academic novelty until the second decade of the twentieth century, when it was at last exhumed as a mathematical masterpiece by Whitehead and Russell in their Principia Mathematica.
[2] In Boolean logic (Boolean algebra) logical propositions are represented by algebraic equations in which multiplication and addition (and negation) are replaced with ‘and’ and 'or’ (and 'not’), and where the numbers '0’ and '1’ represent 'false’ and 'true’ respectively. Boolean logic has played a significant role in the development of computer programming and continues to do so.
[3] This is true also of mandalic geometry in its current formulation.
[4] This might be a proper place to proclaim that nature has little use for Descartes’ breed of coordinates, finding them far too stagnant and limiting for her purposes. Fortuitously, she devised her own choice coordinate stock long before Descartes thought to invent his.
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Below we have the second of three frontal sections through the 3-cube, labeled with the Cartesian coordinates of each point. This “slice” is through a plane that lies between an identity face, which contains the trigram HEAVEN, and an inversion face with the trigram EARTH. As such it does not belong fully to either the one or the other, but it shares some characteristics of both. It is a plane, then, of mediation. Again we see here nine Cartesian ordered triads. Due to an artifact of the “slicing” procedure, the four edge centers deceptively appear as though vertices, and the four face centers could be taken as edge centers. Make note that these appearances are illusory. At the center of this section we have the origin point of the cube, Cartesian (0,0,0).[1]
The key to labeling of points in this section[2] and all those to follow can be found here.
[1] It might be well to note here that the origin point of the coordinate system never appears in either an identity plane or an inversion plane of any of the three section types. All of the planes in which it appears are mediation planes of three dimensions in the case of the Cartesian 3-cube, or of six dimensions in the case of the hybrid mandalic 6D/3D hypercube. This is likely the rationale for why in the I Ching a change involving passage through this central point is referred to as "crossing the Great Water.“ There must be more than coincidence in the fact that Western thought refers to this point as the "origin” and Taoist thought views it as the source and beginning of all things. It’s not that something important was lost in translation. The two notions arose independently, from two very different worldviews. Somehow in the scheme of things, the West came to equate “origin” with "zero" whereas the East came to equate "origin" with “the beginning and end of all things.” Taoism, in particular, sees in this a focus of both creation and dissolution. As we shall soon enough discover, this alternative perspective leads to a different species of arithmetic, one of great antiquity though long lost in the sands of time. Mandalic geometry has unearthed it and will reveal it here, in this blog, for the first time in millennia. As a teaser, it involves a different treatment of what the West calls “zero”. It is an arithmetic more in line with Boolean logic.
[2] The 2-dimensional version of this section is obtained from the x and y coordinates, which by convention are the first and second, respectively, in the Cartesian ordered triads seen here. So the only difference between this section and the FHsectionpreviously viewed is the fact that the z-coordinates here are all zero (0) instead of +1. In our next section, FE, the x and y coordinates will again be as seen here but all z-coordinates will be -1. I believe I detect a trend developing here.
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. :)
Rereading the last post a moment ago I see I fell into the same old trap, namely describing a concept arising from an alternative worldview in terms of our Western worldview. It is so astonishingly easy to do this. So it is important always to be on guard against this error of mind.
In saying that the Taoist number line is the basis of its coordinate system I was phrasing the subject in Western terminology, which doesn’t just do an injustice to the truth of the matter, it does violence to it, in the process destroying the reality: that within Taoism, the coordinate system is primary. It precedes the line, which follows from it. What may be the most important difference between the Taoist apprehension of space and that of Descartes lies encoded within that single thought.
Descartes continues the fiction fomented in the Western mind by Euclid that the point and the line have independent reality. Taking that to be true, Descartes constructs his coordinate system using pointsandlines as the elemental building blocks. But to be true to the content and spirit of Taoism, this fabrication must be surrendered. For Taoism, the coordinate system, which models space, or spacetime rather, is primary. Therefore to understand the fictional Taoist line we must begin there, in the holism and the complexity of its coordinate system where dimension, whatever it may be, reigns supreme.[1]
And that means we can no longer disregard composite dimension, postponing discussion of it for a later time, because it is the logical basis on which the I Ching is predicated. It is related to what we today know as combinatorics,Boolean algebra, and probability, and is what gives rise to what I have called the plane of potentiality. It is the very pith of mandalic geometry, what makes it a representation of mandalic spacetime.[2]
[1] In my mind, dimension is a category of physical energetic description before it is a category of geometrical description. When particle physicists speak about “quantum numbers” I think they are actually, whether intended or not, referring to dimensions. If this is true, then our geometries should be constructed to reflect that primordial reality, not arbitrarily as we choose.
[2] In speaking of logic and the I Ching in the same breath I am using the term in its broadest sense as any formal system in which are defined axioms and rules of inference. In reference to the I Ching, the logic involved is far removed from the rationalism bequeathed to Descartes by his times. It is a pre-rationalist logic that prevailed in human history for a very long time before the eventual splitting off of the irrational from the rational. This means also that the I Ching is among other things a viable instrument to access strata of human minds long dormant in historical times, other than possibly, at times, in poetry and art and the work of those select scientists who make extensive use of intuition in the development of their theories.
Note to self: Two contrasting systems of thought based on very different worldviews can never be adequately explained in terms of one another. At times though, for lack of anything better, we necessarily fall back on just such a strategy, however limited, and make the best of it we can.
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. :)
I don’t really need to reblog the most obvious jacked up crap out there for i can point out what’s wrong with it; it’s the only reason i don’t reblog such stupidity, or dark garbage, however this is different..
The matter that over thousands of people strongly believe this, just proves the point that Republicans to Consveratives(note; real ones not the ones that put a sticker and state they are this but fail at what it truly is to be conservative and republican) are making out there on YouTube, yall seriously need some mental help, and god badly - this ain’t healthy mindset rather a very toxic one that leads you going mad.
Many examples how this toxic dangerous mindset leads you mad - people’s actions show it off way too much online, so there is no hiding it.. Anyway that’s all I wanted to point out here.
