"Is the glass half full or half empty?" Today, this expression pertains to the path one chooses to follow through life. To view the glass as half full is to see things optimistically or hopefully; to view it as half empty indicates one is pessimistic. Both describe habits of the mind--a disposition to take a positive or negative view of things--a Disposition containing an Intention to head in a direction compatible with ones views. Both optimism and pessimism operate in the realm of the Supernatural (what one makes up). In my life experiences it is better to be realistic or to straddle the Physical and Supernatural worlds by generating the expression of balance: "hoping for the best but preparing for the worst." However, Ancient Africans' Critical Thinking (CT) dealt only with the Metaphysical pertaining to African Cosmology. For example, they said the Law of Opposites and the Law of Complements exist before anything happens in the Objective Realm, including the Initiation and Manifestation of the Ether. In the Ancient African Bible, the Divine Light spoke a word that organized “Chaos” (the “material prima”--the forceful primordial state of undifferentiated universal existence) into a structured Cosmos. Thus, “Chaos” and “Order” are complimentary equals because each contains things involved in the other. Complementary Equals--mates independently doing different things--interdependently working better together to generate a dynamic balance inside a harmonious whole--and yet they contain the same "Genetics". Such is illustrated by the complementary female and male doing equally important things of different natures while going together in the same direction side-by-side, at the same pace, and at the same time to the same goal or destination.
So, all of this is occurring in the context of Mathematics--a science based on thinking in quantities. In Arithematic the quantities are displayed in Numbers--with every number being expressed from the smallest to the biggest by using ten figures or digits (named for those on a human's hand (1, 2, 3, 4, 5, 6, 7, 8, 9, 0). In Algebra the quantities are expressed in numbers and in symbols to serve as a short-cut to difficult problems in Arithmetic. Though any letter of the alphabet can be used as symbols, in Algebra "X" stands for an unknown quantity; addition is shown by + as in Arithmetic; and subtraction is shown by -. When two symbols are put together, as ab, this implies they are to be multiplied. To put a on top of b means to divide b into a. To symbolize “Chaos” and “Order” as complimentary equals--both possess a "Uniqueness" and "Sameness" in a manner that makes them compatible mates. Thus, Very Ancient Africans separated the two by an “equal sign.” This indicated that to discover the truth of one of the two opposites--i.e. in “Chaos” or in “Order”--is to discover "like-kind" principles in the other--both Qualities. Such was the basis of the Law of Correspondence--i.e. the harmonious fitting and agreement of the Spiritual Elements in every Cosmic off-spring--the "so above, so below" inference--the 'what is in' the microcosm is in the macrocosm, and vice versa. All of this occurs within the realm of Reality--a profound concept for CT.
Existing below the Subjective Realm are Complementary Opposites--positive and negative aspects of qualities--and both enhance each other when viewed one way; or they can cancel each other when viewed in reverse. One opposite is balanced by another through the ceaseless interplay and transmutation of existence--the alternation of creation and destruction. The universal value of pairs of opposites--e.g. high/low, dry/wet, clear/dark--is demonstrated in their continued use not only in physical and material ways but also in psychological, intellectual, and spiritual matters. The circular impulse in a binary symbol leading to inversion of the expected order imparts a sense of cyclic movement to the entity in question. This Inversion-Symbol is a basic strand for explaining alternations of life/death, light/darkness, and appearance/disappearance--all making possible the continued existence of phenomena. Other examples of alternating Dualism include fire, although clear and bright in the sky (or in air), it leaves black traces on earth (i.e. a charred object). Rain, although black in the sky (as rain-clouds) becomes clear on earth. This weaving and unraveling of the strands of all the pairs of opposites is the import of the Metaphysically positive/negative aspects of white/black working as a unity--white containing black; black containing white.
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