Inversion Transforms of the Cube - II

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Referring to the two simple rules of multiplication described in the preceding post,  we note that a transformative change occurs only if at least one yin (negative) line  is involved,  because yin is the inversion element throughout all dimensions.  It can appear as operator, operand or both, and in any or all dimensions. If yin does not occur in a line that corresponds  to a given dimension  in operator or operand trigrams,  no inversion occurs in that dimension. So the best strategy in following the transformative changes is to watch the yin lines closely, and let the yang lines fend for themselves, which they will.

The three daughter trigrams  (WIND, FIRE, LAKE)  all have only a single yin line. These three trigrams are able to produce change only in that one dimension with the yin line. WIND, with its negative line in the first dimension,  can engender change  only  in the horizontal dimension. Similarly, FIRE with its one yin line in the second dimension can induce change only in the vertical dimension,  and LAKE with its one yin line in the third dimension,  can produce change  only  in the forward/backward dimension.

The three son trigrams (THUNDER, WATER, MOUNTAIN) all have two yin lines.  They can therefore bring about change in those two dimensions with yin lines. THUNDER, with its yin lines in the second and third dimensions, produces change in those dimensions. WATER, with its yin lines in the first and third dimensions will produce changes in those dimensions.  MOUNTAIN, with yin lines  in  first and second dimensions will produce changes in those dimensions.

EARTH, the mother trigram, has yin lines in three dimensions and induces inversions in all three.  HEAVEN, the father trigram,  contains no yin lines and therefore produces no inversive changes at all, which is precisely what makes it the identity operator of multiplication.^[1]

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Notes

[1] Keep in mind that what the transformative changes described involve is essentially the multiplication of unit vectors  throughout the eight octants of three-dimensional Cartesian space. What one needs to grasp here is only use
of a different and unfamiliar notation system and dimensional multiplication which may seem  a strange operation to some at first,  but is just coordinated multiplication along multiple number lines in different dimensions.

© 2014 Martin Hauser

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