A Thought Experiment - VII:

A 1:1 translation for a space of 2 dimensions

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This is much easier than translating from VII to 7. The notation for Cartesian ordered pairs is (x,y). By convention the numerical value on the x-axis (horizontal axis; first dimension) precedes the numerical value on the y-axis (vertical axis; second dimension). The corresponding Taoist notation shows the value on the x-axis in the first (lower) line and the value on the y-axis in the second (upper) line.

As the infolding, self-reflexive structure of mandalic geometry allows only* the values +1 (solid yang line) and -1 (broken yin line) any line of whatever dimension in the notational figures of this geometry will appear as 

Using the conventions described above it is a simple matter then to translate the Cartesian ordered pairs of the vertices of the unit square into the bigrams of Taoist notation.*** The equivalences arrived at are:

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*Logical extensions of the method of mandalic geometry can and do permit other values but that is a subject for future consideration. For our present concerns and for the foreseeable future the rule above applies and is correct within the stated context.

**In point of fact, Leibniz (1646 -1716), who first introduced the binary number system to mathematics was familiar with the Taoist notation and the I Ching. It would seem possible that his binary number system owes a debt to the Taoist notation system used in Ancient China centuries earlier.

***Note that the coordinates of these four points also define the sign signature of the respective quadrant in which each of the points resides.

© 2014 Martin Hauser