Dear God,

There are so many things I can do…or not do. I can sit and do nothing or I can attempt to do many things. Please show me, Lord, what will you have me to do? I am open to your leading and willing for You to work through me to accomplish Your will. Whether my purpose is to accomplish something small or great, I know that it is important to the work of your kingdom and your plan for my life. Guide and direct me, please.

In the name of Jesus I pray, amen.

Dear Universe,

Show me the way!

Sincerely,

A lost one

Beyond Descartes - Part 10
Taoism Meets Boolean Logic: Introduction

Logic gate symbols

(continued from here)

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.

(continuedhere)

Notes

[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.

© 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. :)

-Page 293-

Beyond Descartes - Part 4
Directional Locatives

(continued from here)

Descartes derives his directional locatives from considerations of human anatomy, as does most of Western culture. The descriptive terms generally used for orientation purposes include left/right;up/down; and forward/backward.^[1] The first two sets have been extended also to refer to the cardinal directions, North/South and East/West.

To the degree that they conform to Cartesian coordinates, mandalic coordinates adhere to this schema as well.  However, mandalic geometry and the Taoist I Ching upon which it is largely based constitute a system of combinatorial relationships that is rooted mainly in  radial symmetry rather than bilateral symmetry. For mandalic coordinates, the principal directional locatives can be characterized as  divergentandconvergent, and the principal movements or changes in position, as centrifugalandcentripetal.^[2]

One of the important consequences of this alternative geometric perspective is that the frame of reference as well as the complex pattern produced are more integrative than in the method of Descartes. Looked at another way, Descartes is most enamored by specification of location of individual points whereas mandalic geometry is more concerned with relationships of parts - and the overall unification of the entire complex holistic system.^[3]

From this one seemingly small difference an enormous disparity grows in a manner reminiscent of chaos theory.^[4] Cartesian coordinates and mandalic coordinates can be made commensurate, but remain after all two exclusive systems of spatial awareness,  leading to very disparate results arising out of what seem small initial differences.^[5]

(continuedhere)

Image (bottom): Animation of a double compound pendulum showing chaotic behaviour. By Catslash (Own work). [Public domain], via Wikimedia Commons.^[6]

Notes

[1] Such terminology is of little use, despite its biological origins, to an amoeba or octopus,  not to mention those  extraterrestrials  who have been blessed with a second set of eyes at the back of their heads. (We wuz cheated.)

[2] To be more correct, the radial symmetry involved is of a special type. It is not simple planar radial symmetry, nor even the three-dimensional symmetry of a cube and its circumscribed and inscribed spheres. It is all of those but also the symmetry involved in all the different faces of a six-dimensional hypercube and the many relationships among them.

[3] To be fair, Descartes eventually gets around to relating his points in a systematic whole we now know as analytic geometry (1,2).  But as great an achievement though it might be,  Cartesian geometry  lacks the overarching cosmographical implications which characterize mandalic geometry and the I Ching. Descartes’ system is purposed differently, arising as it does out of a very different world view. To paraphrase George Orwell,

“All geometries are sacred, but some geometries are more sacred than others.”

[4] Chaos theory was summarizedbyEdward Lorenzas:

“When the present determines the future, but the approximate present does not approximately determine the future.”

[5] An example of one unique result of mandalic coordination of space is the generation of a geometric/logical probability wave of all combinatorial elements that occur in the 6D/3D hybrid composite dimension specification of the system. I envision this as offering a possible model at least,  if not an actual explanation, of the  probabilistic nature  of quantum mechanics.  Extrapolating this thought to its uttermost conclusion, it is not entirely inconceivable, to my mind at least, that probability itself might be the result of composite dimensioning. (And for such a brash remark I would almost surely be excommunicated from the fold were I but a member.)

[6] Starting the pendulum from a slightly different initial condition would result in a completely different trajectory.  The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. [Wikipedia]

© 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. :)

-Page 280-

Freshness

Then Moses said to them, “No one is to keep any of [the manna] until morning.” However, some of them…kept part of it until morning, but it was full of maggots and began to smell.

Exodus 16:19–20, NIV

—

When the Israelites were in the desert headed toward the Promised Land, God gave them a fresh supply of manna every morning. It only lasted for one day, but some didn’t listen and tried to hold on to the old manna, and it spoiled.

When you hold on to old manna—what God used to do, friends who were right for a season, a job that you’re afraid to step away from—it spoils. It won’t feed you. You won’t grow. Maybe you’ve enjoyed a friendship for a time, but at some point, you realize you’ve outgrown the relationship. Or what used to challenge you about your career doesn’t challenge you anymore. You feel God telling you to stretch, to get out of your comfort zone, but you’re afraid. You wonder why you’re not passionate, why you’re not growing. It’s because that manna is old; it’s not feeding you. God has new beginnings. He’s a God of freshness. The manna was temporary provision. God has new provision coming. Don’t hang on to the old.

“Father, thank You for every good thing You provide for me every day. Thank You that when the time on one of these provisions has ended, You are stretching me and getting me out of my comfort zone to bring me into new beginnings. Help me to not hold on to the old, but just let it go. In Jesus’ Name, Amen.”

Barry Jenkins’ near perfect film Moonlight did not need anything but faces and lyrics to engulf its viewer into some jaw dropping and mind boggling scenes. It tells us a story of a young, black, gay, poor and lonely kid, Chiron, living in Miami. The film pans over three parts, with three actors playing Chiron in his different stages of life. It is a character study of a boy who is trying to find his place in a world which has been nothing but ignorant to him. The films’ complex themes of sexuality, family and masculinity are portrayed by the characters with such care and precision. It puts us into a very difficult world and tries to question our whole social structure. Jenkins use faces and water to talk with the viewers about the evolution of Chiron from a child to a man. Water acts as a symbol for transformation and freedom. Whereas moonlight is shown as something under which, one can discover their true identity. The concept of masculinity is vital to the film’s exploration of Chiron’s identity and the societal forces that shape it. Jenkins gives us the visual proof of ‘some things are better left unsaid’. He uses close ups in this movie to invite us into these characters’ world. Juan(a drug dealer) and Kevin(Chiron’s friend) both presents Chiron with examples of standing up for oneself. When faced with the prospect of answering who are we against the grim need for change, personal acceptance seems like the only solution.

I always love a piece of art that emphasizes our traditional and cultural beliefs and poses questions that we never even cared to consider.

It is a film that anyone can watch without any specificity and it will leave them touched.