The Balanced Ternary as the Number Base of Complex MVL Systems

It is posited that the two balanced ternary systems, (-1, 0, 1) and (-i, 0, i), are positioned on the line of real numbers and on the axis of complex numbers, respectively. In the event that the system is reduced to a single entity, the digits of the resulting system will be as follows: { -1, -i, 0, i, 1} The set (-1, -i, 0, i, 1) is transformed into a base five system. In this article and the following ones, I will outline the aforementioned relationship and its considerable potential for implementation in the domains of computer technology and a novel programming language. In addition to laying the groundwork for the trivalent system, which was clearly and brilliantly developed by Jan Łukasiewicz, we can expand beyond the {third middle defined by Aristotle in Chapter 9 of his treatise “De Interpretatione”, which was written in opposition to the Stoics’ determinism. This perspective enables us to extend the law of middles to the fourth, fifth, sixth, and so on, while adhering to the principles of polyvalent systems. This generates a proliferating field of probabilities where we can establish a chain of closely related probabilities, link by link, where each one is equally likely to be true or false. This allows us to approach or separate from the local truth or lie. I understand that the concepts of truth and falsehood, as developed by mathematical logic in a bivalent system, refer to a particular truth or lie. Thus, absolute truth is universal and impossible to know. However, it is not necessary to know absolute truth because what affects us in our daily lives is local truth or local falsehood. Then, it is appropriate to discern between a local truth universally accepted and a falsehood that can also be accepted as true, as well as the distinction between a true truth and a falsehood that could also be a true lie. In this article, we will analyze up to the third dimension (3D) which is composed by the following structures: i. A polyvalent system of “fifth truth degree”, where the fifth middle is introduced. ii. A balanced system of base seven, in which seven coordinated points are introduced. iii. This balanced system operates within the Ternary Balanced system. iv. The Ternary base number defines the lowest and highest limits. v. Every volumetric body is founded on its complex plane, but empty space, between the volumetric bodies is a volume of its respective dimension. vi. Every mathematical operation can be developed directly as (ST110i0)(1T0S1) or (ST110i0)/(1T0S1) without requiring the complex polynomial form. A polyvalent system allows us to construct volumes of bodies, then surface of volumetric bodies, then volumes of volumetric bodies, then surface of volumes of volumetric bodies, and so forth. I briefly glance beyond the seventh base to the eleventh, thirteenth, and fifteenth bases.