#complex number system

[2-kamikou-1]

can someone give me one just ONE good reason why the complex number system needs to exist

[mandalicgeometry]

Can a number system be both the new kid on the block and older than written history?

The real number system as it exists today has been with us for a few centuries.  In foundation it is monovalent,  monophasic,  and sequential.

The probable number system dates to prehistory but was lost in the mists of time until recently rediscovered and resurrected.  In contrast to the real number system it is foundationally bivalent, biphasic, and cyclic.

The probable number system has considerably more structure than the real number system and is therefore more robust.  In this sense, it is similar to the complex number system.

In contrast to the complex number system,  the probable number system in its foundation presupposes that numbers can assume wavelike forms capable of  constructive and destructive interference  operationally through the compositing of higher to lower dimension.

By means of compositing of dimension probable numbers are able to  distribute  throughout the entire  mandalic unit vector cube  (which is structurally a  superposition  of  the 6-dimensional unit vector hypercube on the 3-dimensional unit vector cube) a function analogous in important ways  to that performed in the complex number system by the centralized imaginary unit i.

Another important way in which the probable number system differs from both the real number system and the complex number system is the absence of  nothingness  and the zero representing it.  In its place we find the concepts of  balance and equilibrium.  Nullification still exists in form of annihilation and its opposite in the form of creation.  But the Cartesian coordinate system  of ordered pairs and ordered triads  is transformed by this approach to handling number and dimension  from a ring into a field of hyperdimensional numbers over real numbers in three dimensions.

(to be continued)

© 2016 Martin Hauser

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-Page 315-

[powermodules]

Put n equally spaced marks around the circumference of a unit circle (radius of 1).  Then from any one of those marks, draw the chords that connect it to all the other (n-1) marks.  The lengths of these chords are then multiplied together, and amazingly, that product is always n.  So:  532 equally spaced marks, 531 chord lengths, and the product is incomprehensibly 532.  Here is the starting diagram for n=9: