## Wednesday, April 25, 2012

### Tesseract, Revisited

The four colored line segments span opposite corners of the cube and those of its bounding box.  The axes presume to represent the traditional three dimensions of space, plus a fourth -- time, or Change.  We envision our fourth dimension via notions of expansion or contraction.  In this case, the blue cube expands (in the time domain) to fully occupy the bounding frame.  In our simple example, the time axis is not discrete from three-dimension space, but supplements it.  As the blue cube expands along the colored lines, we measure the elapsed time by noting the positional change of the vertices along their respective axes as a function of elapsed time. Is it but coincidence that the two opposed square pyramids (their tips meeting at [0,0,0]) within the bounding box resemble an hourglass?

Deriving a means to integrate the ashtapada and the hypercube representations of the Book of Changes has remained a goal of the author.  A physical model was fashioned with this end in mind.  While the yellow and green axes represent Earth and Air respectively, the blue and red axes symbolize Fire and Water.  Earth and Fire stand for OLD YIN and YOUNG YIN; Air and Water stand for OLD YANG and YOUNG YANG.  These four symbols (xiang) are the stuff of existence.Our model begins with a depiction of the four symbols (xiang) presented in pairs and forming a 2x2x2 cube (the "bagua cube").  A second, exploded bagua cube extends in space beyond the corners of the first along the major diagonals.
In total, this produces the framework of 4x4x4 tesseract.  If the ashtapada is a representation of planar/areal dimension ("Heaven is Round, Earth is Square") , here, we have "folded" space into a cubical form.  Imagine the outer eight cubes as an expansion of the inner 2x2x2  along the diagonals, and you will have seen the author's vision of space-time.