Methodological Consequences of the Way of Thinking based on the Static DIA Dynamic Mathematics
Four Basic Mathematical Operations presented like a Road of Triangles
Gravitational Abysses ("0" - Black Holes) Bounded with the Numbers (Values) TWO (2) AND ZERO (0)
This has been all about mathematics for now. Let me express the methodological consequences of this mathematical way of thinking, built into the applied static and dynamic models of reality. It was actually the ultimate purpose of the graphically illustrated dialectical contents, which were elaborated in the previous part of this creative article. Firstly, it is noticeable that the everyday (dynamic) DIA static math, respectively the quantitative math, can also be reduced (deduced) to a triad of triangles (DIA one incomplete triangle), and then express this dialectical content in terms of PAIRS OF RIGHT-ANGLED triangles. I also hope that in the graphic illustrations, as one final result of this dialectical consideration and re-examination of the four basic mathematical operations, shown below this text, pictorial representations of the "(Recti)linear or Rectangular Creative Framework for Orientation in Time and Space" is not difficult to recognize.
Four Basic Mathematical Operations Triangularly presented Together
Dialectical Creative Framework for Orientation in the Eternity of Times DIA Infinity of Spaces
(Recti)linear Creative Framework for the Orientation in Time AND Space
By comparing this illustration of the concept of simple(st) mind to the "Dialectical (Creative) Framework for the Orientation in Time DIA Space, (Jovanović, 1999)", it is clearly noticeable that this graphical illustration lacks one triangle, or the two right-angled triangles, if you so will. As a consequence of this deficiency, seen from the dialectical perspective, there is only the possibility of settling (with)in the "RECTILINEAR (Creative) Framework for the Orientation in Time and Space", either the dialect - MIND OR dialect - SPIRIT [it lacks a triangle: abyss DIA a creatively blank hollow]. In order to solve this unsolvable task, the dialects - mind and spirit are fused by the reason, that is, in this simply-imagined sphere. One additional consequence of this 'OR - OR' created defect is the rectilinear (bi-polar) DIA binary way of thinking, recognisable in the everyday language, as the brain - body, mind - matter, spirit - matter, soul - body, respectively yes - no, true - false, 0 - 1, black - white, with us - against us, and the like. READ, "Concept of the Simple(st) Mind". Due to the close and intertwined relationship between mega-dialects, space and time, this lack (deficiency) within the (recti)linear space will be reflected within the time dimension, in one or another way. Seen from the dialectical methodological perspective, because the notion of time takes place and occurs within the medium of mind dia reason (spatial medium), it can be argued, that in the reality the dialects future and present (time) were also merged (linear -binary tube) in some form of converging the present and future, that is, the time dimension (mega-dialect) ALSO LACKS a triangle. In other words, the dialect - present (time) took over and continues further to subdue and smother the dialect - future! READ, "The (Recti)linear Comprehending Space and Time: The Concept of the Physical Universe."
In the methodological sense, the dialectical content elaborated in the previous part of this creative article, dedicated to the dynamic (everyday) DIA static math, could be seen as an objective (observable) "proof" for the origin (and the existence) of the concept of simple and simplest mind, as a framework for behaviour and way of thinking of each "simple-reasonable" person. To remind me ⇄ thee ⇄ us, the "simple" one is a person that is able to speak (preach) one thing publicly (“babbling”), to think a quite another, to do something third, etc., until was accomplished a 666 scenario in time DIA situation in space. The source, as well as the inspiration for this multiprocessing this "simple-minded" one finds (with)in the lacking triangle, respectively (with)in the "dark hole" (behind the hidden, dark sceneries). In the models of reality, based on this way of thinking, so peculiar for the simple(st) mind (converged mind), respectively for the merged (fused) mind-matter (or matter-mind), the dialect - mind tries to occupy or usurp this innate place reserved for the dialect - spirit by subordinating and suppressing it. Apart from it, it is possible also a reverse scenario and situation in SPACE AND TIME, where the dialect - spirit subdues the dialect - mind dia reason. By the way, precisely in this constellation of constituent dialects of space (and time), the biological "chip" of every species of (wo)mankind is hidden, which shows this ingrained tendency to group and crowd. It is no coincidence that the old wisdom says that without the spirit of freedom there is no freedom (of speech, creative action: the voice of freedom), nor the typical individuality and peculiarities of the human being.
A Dialectical View on the Simple Mind, Seen from the Mathematical Perspective
After the previously uttered, there is a hope that the proponents of this way of thinking will orient themselves easier in time and space, while developing theories and models of reality, based on the dynamic DIA static math, accordingly on the quantitative math. In particular, when these models of reality of theirs were implemented in the realm of social sciences. An important role of the creators of knowledge, is to open eyes and to expand mind (horizons) in this dialectical conception of time and space. As an orientation point, creators of knowledge, while acting and creating in this (recti)linear environment, try to avoid the traps of the "MISSING TRIANGLE" within the (recti)linear creative framework for the orientation in time AND space, that is, traps of the "black hole" (abandoned cavity). In other words, if thou art aware of the basic assumptions DIA ultimate presumptions on which a methodological approach was founded, this awareness can used for avoiding its traps. On the other hand, if you ignore (neglect) them, that is, stubbornly do not want to know, nor to hear it, there is a great probability (unconsciously) to present your knowledge from this (mathematically) undefined "hole" (hollow). READ, "Capabilities of the Modern Mind seen from the Perspective of Creating Knowledge"
Four Basic Mathematical Operations presented like a Road of Triangles
In the opinion of this creator of knowledge, it is enough said about the bipolar (and dual) way of thinking and the models of reality based and developed on the math. At the same time, it is very important to emphasise that the innocent mathematics has nothing to do with the previously said. In other words, every one is free to choose the ultimate methodological presumptions DIA basic assumptions about the reality, on which her / his models of reality will be developed, that is, to be self responsible for the presented (developed) theories. In the following graphical illustration were connected two sequences of the mathematical operation of multiplication and addition DIA subtraction and division, that was presented in the previous part of this creative article, as a road of triangles. And now you can understand much better these four mathematical operations. Seen from a methodological point of view, note that it is necessary to "move" very carefully (in the objectivistic sense) around these holes, in order to avoid (metaphysical) "intrusion" into them. I also hope that you can recognise the "last step (scene)" of these two triangles (parallelogram / rhomboid), which were interpreted and presented in more details in the section, devoted to the "Dialectical Reinterpretation of the Plato’s Story". Or more simply said, this model of the dynamic DIA static mathematics dances around these two triangles DIA the four right-angled triangles, the following kinds of dance, in this very simplified model of reality: multiplication, addition, subtraction and division.
Parallelogram: Potentially a Fruitful Dialectical Upshot
Perhaps a New Opportunity?
It follows from the aforementioned that this model of the everyday mathematics cannot express mathematicallly in the DYNAMIC DIA STATIC sense, the DIALECTICAL dance of these two DIA four centrally positioned triangles but rather, this state of locked (static) time and space tries to last forever, by putting ("freezing") them into shackles DIA rules of the considered mathematical operations. On the other hand, it seems, this gravitational abyss ("0") was used only for deposing of the remainders of rounding numbers BY THE POINT-PUNCTURE (pora dia spora) during the accomplishing of diverse mathematical operations (by "feeding" this "black" hole). No more any kind of dynamics, as well as the quantitative mathematics is not (cap)able to make a (objective) diagnosis (of this kind of metaphysics for her), nor to express this (lost) time DIA space. It simply ignores (neglects) it, understood in terms of the rounding DIA skipping these insuperable and unfillable time intervals DIA corresponding distances of space, jumping from one dot to another of this imaginary mathematical (dashed dotted) line.
Dialectical Worlds of the Qualitative Maths: A Runaway from the Bipolar dia Binary Way of Thinking
Gravitational Abyss ("0") Bounded with the Numbers (Values) TWO (2) AND ZERO (0)
From the previously stated dialectical interactive content, using the breaking apart (and crushing) of the encompassed time DIA space [spirit, mind dia reason, matter] in the dialectical sense into tiny crumbs (dialectuls), again and again, in order to be dialectically re-synthesised, it is obvious that the mathematical operations of addition and multiplication managed to achieve the velocity, which allows them separation from the (strong "gravitational" force of) "zero", after the boundary of the number two (2) was crossed over. In my opinion, it was not accidental, as it was shown in the previous part of this creative article that the constant (static) increment of the mathematical operation of addition, as well as the coming one for the mathematical operation of multiplication too, is the value (number) TWO (2), whereas for the mathematical operations of subtraction and division is the ZERO (0). Note also that the first computed irrational / incommensurable, number (ABYSS), known in the Pythagorean time, was the square root of 2. In other words, this is Pythagoras' theorem expressed in another way: The length of the hypotenuse of a right-angled triangle, in which the other two sides are one unit long, will be equal to the square root of 2. These aspects and manifestations of time, in time and space were presented in the previous graphical illustration, by bounding these "gravitational" "holes" (hollows) with the numbers (values) TWO (2) AND ZERO (0): A kind of the "gravitational" spiral, clustered around this abyss ("0"), accordingly a mathematical interpretation of the black hole. In the opinion of this creator of knowledge, it is not also a coincidence that the thematic of zero drew at all time the attention of people, as a root DIA source (factory and fabric) of ALL OTHER NUMBERS, and as a kind of the magical "black (unexplainable) box".
The Background Simulative Methodological Assumptions of the Dialectic Interactive Approach
Bipolar DIA Binary Way of Thinking
By dialectically synthesising the aforementioned, I hope, you easier can comprehend, why it is so difficult to convince, or to encourage, if you so will, the actors, who work and create within the essential areas of human acting, such as science, philosophy, art and culture, as well as their creative upshots (decision makers) in the area of business and politics, to be abandoned this bipolar DIA binary way of the thinking. In other words, to cross over the magical boundary of number two (2), during their (creative) orientation in the time and space: 0 - 1, 1 - 2, 0 - 2: The greatest span of time and their range of the space, understood in terms of creative abilities of the simple mind. Paradoxically enough, this dialectical content regarding the expanding of boundaries of time and space is not unknown, as it was demonstrated in the previous part of this creative article, by the actors of the basic mathematical operations (numbers): STATIC DIA DYNAMIC (QUANTITATIVE) MATH.
"Anyway, in such a (recti)linear scenario in time DIA appropriate situation in space, no matter how someone TRIED TO ARISE the simplest one (within them), by firmly standing in the (safe) realm of the NUMBER THREE (3) and pointing out in the direction of the numbers 4, 5, 6, ...., that is, to elaborate to them the source of their problem (trouble), by suggesting and appealing to them to get rid of their (methodological) shackles, and finally to get out from this bottomless hollow on the light (of day); they, probably frightened of the something or simply believe that others are jealous on their creative environment and the related (creative) achievements, continue to fortify even more intensively their 'black' box". And now try to imagine the reaction of them, after this static and quantitative argumentation, on an additional creative proposal of this creator of knowledge, understood in terms of the entering into the worlds of the dialectical (qualitative) mathematics (higher knowledge): The world of the creating knowledge DIA the (inborn) gift of God, known as the creativity.
Ultimate Upshot of the Traditional Dialectical Way of Thinking within the Rectilinear Space and Time
The Endless Dialectical Worlds of a Six-Pointed Star in Time DIA Space
Seen from the perspective of the dialectical (qualitative) math, due to its starting postulate, that the "sum" (more properly ACCUMULATION) of the tiny pores dia spores of time, in time DIA space makes zero [point - puncture + point - puncture = zero (0)], and from this reason, 0 + 0 > (=<) 0, 1+1 > (=<) 2, and so on, the previously uttered dialectical content is in full compliance with the dialectical way of thinking. To understand the dialectical content, which follows, READ, "Dialectic Interactive Approach: Three Basic Dialectical Principles, Aspects, Properties and Manifestations in the Time DIA Space". Although, seen from the standpoint of patterns of thinking, firmly impressed and imprinted by the everyday use of quantitative (AND - AND DIA OR - OR) mathematics, it can be reasoned (cogitated) that this way of accomplishing operations of the dialectical mathematics sounds a little bit strange, the same could be argued for the dual (bipolar: OR - OR) way of thinking as well, accordingly, for the binary (OR) way of comprehending math. In other words, although at the first sight acquired without a deeper insight into this dialectical content under consideration, it seems there are two choices (options), as a final result of the OR - OR way of thinking (yes-no, black - white, 0-1, ....), this dialectical content has to be deduced (reduced) or simplified at the very end of this bipolar rectilinear process, either in "yes" OR "no", 0 OR 1 .... all OR nothing, while the fifty-fifty scenario in time DIA appropriate situation in space in this bipolar (rectilinear) time and space is undetermined, and for this reason unacceptable within the binary way of thinking [world of the strong gravitational forces of numbers zero and one].
On the other hand, various quantitative and qualitative upshots of the dynamic (DIA static) and dialectical mathematics are also present in living reality. For example, seen from this dialectical perspective, each barren intercourse (synthesis) of two species (thesis - antithesis) is also a ("dynamical") example of the everyday mathematics (1 + 1 = 2), that is, such barren activities still remain within its boundaries [never reaching and traversing the boundary of realm of number three (3)]. By the way, this stage of development of the dialectical way of thinking (thesis - antithesis --> synthesis), which takes place within the rectilinear time AND space was well elaborated by the philosophers of the end of 18-th and 19-th century: Johan Gottlieb Fichte and other proponents of this dialectical way of thinking, who followed after him. In short, by this stage of the (philosophical) development of the dialectical thought, only the first dialectical principle, aspect, property and manifestation in time and space could be explained and explained mathematically. As an example of this, just reconsider from this (traditional) dialectical methodological perspective, how mathematicians (of the quantitative maths) expressed mathematically this first dialectical principle so deeply and in details, respectively "The Unity (STATICS) and Struggle (DYNAMICS) of the Dialectical Tensions in Time and Space", starting from the four basic mathematical operations to the very complex ones, using the appropriate procedures and techniques.
The Unity and Exerting of Dialectical Tensions in Time DIA Space
The Four Primary DIA Proto Paradigmatic Presumptions of the Dialectic Interactive Approach
Unfruit - Bringing DIA Stunted Eight - Pointed Star
Germinating DIA Potentially Fruit- Bearing Eight-Pointed Star
A Blossomed, Potentially Ripe Fruit - Bearing Twelve - Pointed Star
Fruitful DIA Potentially Germinating Four-Pointed Star
THE CREATIVE EXPANSES OF A FOUR - TRIANGULAR STAR
This creator of knowledge, apart from the redefinition of time and space, also extended the key-notion "synthesis" by introduction of the notions "DIA RENEWED thesis, renewed antithesis .... at a higher and higher level time DIA space.... until a temporal conclusion was reached". These very complex dia-processes were graphically illustrated in a picturesque way by using various forms of stars DIA their qualitative properties: A part of the hidden (lost) pre-ancient knowledge. In this way, a feasibility was also opened for the mathematical presentation of other two dialectical principles, aspects, properties and manifestations in the time DIA space, as well as showed, how they proceed from each other, and continue at each higher level (with)in eternity of times DIA infinity of spaces of the worlds of dialectics. For example, a fruitful (sexual) intercourse [synthesis DIA the RENEWED THESIS (a born child)] of a female and male being (thesis - antithesis) is a good example of the dialectical mathematics (1 + 1 = 3). This also clearly demonstrates, that first by appearance of a third category (option) was truly opened a way for the (co)existence of the "number" two (2), that is, crossing DIA extension of boundaries of the binary (0-1) math, respectively, overcoming gravitational force of the number zero OR one. For instance, first by the appearance of a third political party in a parlament, there is possibility of building political coalition of two parties (coexistence).
By the mathematical expression 3 + 3 = 7 (symbolically presented by a six - pointed star), were expressed various scenarios in time DIA appropriate situations in space, characterised by attempts of getting rid of the still PREVAILING QUANTITATIVE accumulations within this span of time DIA space until the desired quality of the number 7 was achieved. For example, for a traditional royal family coming on the world of a baby - girl (princess) was not the desired upshot of this dialectical synthesis (quality) of THESIS and antithesis, because a son was needed for continuation of the established dynasty. As a result of this qualitative failure, with the initiation of new dia-processes has to be continued, that is, by having a fourth, fifth, sixth child. In the dialectical sense, similarly as between every two numbers of the quantitative mathematics, there is a multitude of decimal numbers (the realm of a number), in the qualitative (dialectical) mathematics these dialectical contents [intervals of time DIA widereach of space of a star], including the issues of the "rounding", were symbolically presented by various forms of stars and triangles. Since here the word goes about DIALECTICS, each of the included stars and triangles within a dia-process follows its own [(pre)determined] life-cycles (stages of dialectical developments).
In the case that the desired result has not been still achieved, symbolically presented by an "None Fruits Bringing DIA Stunted Eight-Pointed Star", as a counterpart of the "Germinating DIA Potentially Fruit - Bearing Eight - Pointed Star", there is still a probability for the return from this higher dialectical span of time DIA space BACK into the abandoned world of the binary mathematics (span 0 - 1). For example, through divorce or through the death of woman, of the Quinn in this particular case. By the way, this scenario in time DIA appropriate situation in space is not unknown to the many fruitless couples (without own children dia birth of at least a son), living in traditional societies. Pay also attention that the MEANING of notion - quality is relative in (the natiocratic) time -DIA- space; respectively it is a final result of the established way (quality) of the distinguishing good (right) from evil (wrong) in a concrete span of time DIA space. In the sense of introduced dialectical interactive approach, this dialectical content can be reflected and, for this reason, be modelled by reconsidering (SIMULATING) it through the prism of great pyramid of culture, philosophy, art and science. Actually, in the core of each of them is methodologically stored the distinguishing good from evil, in one or another way, AT THE FIRST PLACE, within the dialect - culture (DIA religion).
Within the next span (stage) of the dialectical math, presented by mathematical expression 7 + 7 = 13 (symbolically presented by the twelve - pointed star), the qualitative aspects and properties had significantly prevailed. And from now, within the all coming dialectical spans of time DIA space (13 + 13 = 25 ....), these inherited qualitative aspects, properties and manifestations of THE DIALECTICS is much easier to maintain as well as to improve them over passage of this dialectical understanding of time and space: Continual qualitative repetitions DIA improvements of the afore mentioned dia-processes through multifaceted dialectical synthesis (stages of development of dialectics), which are symbolically presented by these stars, shown on thy left side, until a temporal conclusion was achieved, accordingly a great dialectical breakthrough. These very complex dialectical interactively - creative contents and corresponding initiated processes, were symbolically comprised and presented by a Four - Triangular Star, respectively, they take place within its enormous DIALECTICAL EXPANSES.
As a demonstration of the hidden VASTNESS in this simple graphical illustration, acquired at the first look without a deeper insight into its hidden dialectical expanses, just initiate dia-processes of this (ground) plan of PYRAMID, by dialectical connecting its sides ("triangles"), symbolically presented by the Four Primary DIA Proto Pre-Ancient Dialects (creative substances): fire, water, air, earth. By thy choice, at first create from couple-triangles two six-pointed stars, and then dialectically synthesize them into a twelve-pointed star, which will be transformed, after reaching the stage of development of the Fruitful DIA Potentially Germinating Four-Pointed Star, with the passage of this dialectical understanding of time and space into a Four - Triangular Star. Simultaneously, the Four Primary DIA Proto Pre-Ancient Dialects of the ground plan of this pyramid (fire', water', air', earth') at this (new) higher level of time DIA space, representing the first dialectical principle, aspect, property and manifestation in (of) time DIA space too, by growing (swelling) inside of its protective membrane (creative framework) will be transformed into the Germinating DIA Potentially Fruit - Bearing Eight - Pointed Star. After the passage through the stage of developing a Blossomed Potentially Ripe Fruit - Bearing Twelve - Pointed Star and the Fruitful DIA Potentially Germinating Four-Pointed Star ("seeds"), another Four - Triangular Star will be formed as well. I hope, it is not that difficult to conjure up that the continuation of these mutual creatively interactive dialectics of dialectics of time, in time DIA space, without NEGATIONS OF NEGATIONS in the form of some kind of annihilation and annulment of them, will sooner or later be filled up each kind of the universe (of universes), no matter, how it (this dialectical interactive content) eternal DIA infinite was. But not also the eternity DIA infinity of the worlds of dialectics, which were introduced in this dialectical (creatively) interactive methodological approach.
Four Basic Mathematical Operations presented like a Road of Triangles
Gravitational Abysses ("0" - Black Holes) Bounded with the Numbers (Values) TWO (2) AND ZERO (0)
By dialectically summarizing the all previously said, these dia-processes seem to be particularly strong in the range between the zeros (0) and the number (+ / -) two (2): The realm of the first dialectical principle, aspect, property and manifestation in the time DIA space [The Unity and Exerting of Dialectical Tensions (Contradictions) in / of Time DIA Space]. With careful re-reading, understood in terms of dialectical synthesis (qualitative summarization) of this dialectical content, it might be argued, that here are MATHEMATICAL roots DIA sources of any kind of the (creative) synergetic effect or of the synergetic defect, if you so will, that is, of other two dialectical principles, aspects, properties and manifestations of time, in time DIA space. In either case, four basic mathematical operations in the range from 0 to 2 due to strong binary gravitational forces 0 - 1 [conflict area: the Bipolar DIA Binary way of thinking], are very blurry DIA confused.
This is especially noticeable in mathematical operations of addition and multiplication. Note, that 0 + 0 = 0 * 0 and 2 + 2 = 2 * 2 (the balance), whereas 1+1 > 1 * 1, and after the magic boundary of the number two (2) was traversed and overcome, the mathematical operation of multiplication surpasses the mathematical operation of addition, that is, the 3 + 3 < 3 * 3, 4 + 4 < 4 * 4, and so on to the eternity DIA infinity. In the dialectical sense, the "strangest" (most interesting) is the mathematical operation of dividing by zero (0). It violates the basic mathematical rule that each number divided by the same value gives the result of one (1). In the mathematical sense, 0 : 0 = the infinity (∞) because mathematicians have noticed that each number divided by a decimal value approaching (dynamically near) zero, the result of this division also approaches infinity (∞: infinity concept). I think everyone is, at least for a period of her, his life, was puzzled by this mathematical rule. In the following case study, my troubles with this "strange" mathematical rule as well as with these very enigmatic concepts of infinity and zero will be presented.