The mandalic number line
As introduction it must be asserted that mandalic geometry views lines and points as convenient fictions. As a geometrical description of force fields at the Planck scale mandalic geometry involves forces interacting simultaneously throughout all dimensions existing at that scale. To speak or think in terms of lines and points is therefore a corrupt formulation of how reality expresses itself.
With that understanding as preface let’s view what a fictional formulation of a mandalic number line[1] might entail and compare it with the real number line considered in the previous post. Despite the superficial resemblance we will find a number of highly significant differences between the two.
Important points of distinction from the real number line:
- The line is finite with an extremely limited length extending from -1 to +1. This is due to the fact that it is embedded within a polydimensional self-reflexive context which bends back upon itself, bringing about confinement to the Planck scale.[2]
- The line deals with geometric vectors rather than scalar quantities. Accordingly -1 has a magnitude identical to +1, the difference between the two being a matter solely of direction of potency or force rather than size or amount.
- 0 is viewed as the locations on the line equidistant from -1 and +1. It possesses null magnitude but lacks a null content and may have a direction tending toward either -1 or +1. It is better viewed as the origin of a coordinate system (here a coordinate system, in the abstract, of one dimension) rather than as the conventional zero of Western mathematics.
- The zero point of the line corresponds to two or more different and distinct higher-dimensional numbers which are related to one another in a specific manner to be described later.
- Two or more higher-dimensional numbers can be mapped to and occupy the same point at certain locations on the line (in general those locations corresponding to 0.)
- The mandalic number line plays no role in either Euclidean geometry or Cartesian geometry.
In future posts we will examine how and why these differences come about.
Notes
[1] Addendum: A more recent revised version of the mandalic number line can be found here. The essential difference is that the newer version makes explicit the inverse relationship between yin and yang. In accordance with this relationship it labels the central point that corresponds to zero in the Western number line with yin = -½; yang = +½ rather than 0. As the sum of these two is still zero I think it better correlates the two number lines.
[2] Addendum (02 October, 2015): I should point out that the description here pertains to the mandalic number line as it occurs in context of the mandalic cube which is to say, as confined in the hybrid 6D/3D unit or mandalic building block of mandalic geometry which possesses tensional integrity and which is intended to represent Planck scale space. Beyond the confines of this “box”, though, the mandalic line and all the dimensions of the geometry can be extended to infinity in a manner similar to and yet unlike the geometry of Descartes. Rather than progressing in a scalar manner based on the Western number line it progresses by recursive inversions à la Lewis Carroll’s looking-glass house. Much more on this to come in future posts (but not the immediate future as this topic is far down on my list of priorities to cover.)
© 2013 Martin Hauser
