Methodological Consequences of the Way of Thinking based on the Static DIA Dynamic Mathematics
Four Basic Mathematical Operations presented like a Road of Triangles
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Gravitational Abysses ("0" - Black Holes) Bounded with the Numbers (Values) TWO (2) AND ZERO (0)
This was all about the math for now. Let me express DIA left impressions of this dialectical content in time DIA space, the methodological consequences of this way of thinking, which were implanted into the static mathematical models of reality, based on this way of thinking. 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, also might be deduced DIA expressed in terms of the COUPLES OF RIGHT-ANGLED triangles DIA triad of triangles. I hope too, in the below shown graphical illustrations, as a final result of dialectical reconsideration of the four basic mathematical operations, it is not difficult to be recognised the images of the "(Recti)linear Creative Framework for the Orientation in Time AND Space".
Four Basic Mathematical Operations Put Together |
Dialectical Creative Framework for Orientation in the Eternity of Times DIA Infinity of Spaces
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(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 place ("possibility") to be expressed DIA impressions, either the dialect - MIND OR the dialect - SPIRIT (with)in the "RECTILINEAR (Creative) Framework for the Orientation in Time and Space" [it lacks a triangle: abyss DIA a creatively blank hollow]. A 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 and the like. READ, "Concept of the Simple(st) Mind". Because of the close and intertwined relation among 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 conceiving of time occurs within the medium mind, it might be argued, that in the reality the dialects future and present time were also merged (linear -binary tube) in some form of the converging present time (and future), that is, the time dimension (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 methodological terms, the dialectical content elaborated in the previous part of this creative article, devoted to the dynamic (everyday) DIA static math, might 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 a "simple-resonable" person. To remind me, thou, 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). READ: "An Upshot of the Conflict within the Simple(st) Mind: The Concept of a Simple-Minded Person". 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 DIA usurp the inborn room determined for the dialect - spirit by subordinating and suffocating 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.
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 DIA 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 time DIA 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 hollow). In other words, if thou are aware of the basic assumptions DIA ultimate presumptions on which a methodological approach was founded, thou can use this awareness 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
To the opinion of this creator of knowledge, it is enough said about the bipolar (dual) way of thinking and the models of reality based DIA developed on the math. At the same time, it is very important to emphasise that the innocent math 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 will be developed her / his models of reality, 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. Pay your attention that seen from the methodological point of view, it is necessary to be "moved" very carefully (in objectivistic terms) around the holes, in order to be escaped a (metaphysical) "dropping" into them. I also hope that you were able to 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 math 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
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Perhaps a New Opportunity?
In other words, this model of the everyday math cannot express mathematicallly in DYNAMIC DIA STATIC terms, the DIALECTICAL dance of these two DIA four centrally positioned triangles but rather it is tried to be preserved this state of the suspended (static) time and space for ever, 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 math is not (cap)able to make a (objectivistic) 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 intervals of the time DIA corresponding distances of space, by jumping from a dot to the another dot of this maginary mathematical (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 uttered dialectical interactive content, by using the breaking apart of the encompassed time DIA space [spirit, mind, matter] in dialectical terms into small 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. To 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 too that the first computed irrational / incommensurable, number (ABYSS), known in the Pythagorean time, was the square root of 2. In other words, here it deals with the Pythagorean theorem uttered in an 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 in / of time and space were presented in the previous graphical illustration, by the 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. To 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 the 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 and understand, 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. bipolar DIA binary way of the thinking. In other words, to be crossed over the magical boundary of the 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 DIA 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 DIA situation in time DIA 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) math (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
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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 point-punctures (poras dia sporas) in / of 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. In order to be able 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, might be reasoned (cogitated) that this way of accomplishing operations of the dialectical math sounds a little bit strange, the same might 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, 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 DIA simplified at the very end of this bipolar rectilinear process, either in "yes" OR "no", 0 OR 1 .... all OR nothing, whereas the fifty-fifty scenario in time DIA situation in space, in this kind of the bipolar (rectilinear) time and space is undetermined, and from 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 math are also present in living reality. For example, seen from the dialectical perspective, any barren intercourse (synthesis) of two species (thesis - antithesis) is also an ("dynamical") example of the everyday math (1 + 1 = 2), that is, such barren activities still remain within its boundaries [never reaching and crossing over the boundary of the number (realm) three (3)]. By the way said, this stage of development of the dialectical way of thinking (thesis - antithesis --> synthesis), taking 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 said, by this stage of the (philosophical) development of the dialectical thought can be only mathematically explained and elaborated the first dialectical principle, aspect, property and manifestation of the dialectics in time and space. On the other hand, just reconsider from this (traditional) dialectical methodological perspective, how mathematicians (of the quantitative math) expressed mathematically, so deeply and in details, the first dialectical principle, 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 suitable procedures and techniques.
The Unity and Exerting of Dialectical Tensions in Time DIA Space
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The Four Primary DIA Proto Paradigmatic Presumptions of the Dialectic Interactive Approach
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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 DIA space, had 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 was reached a temporal conclusion". 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 was also opened a feasibility 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 a RENEWED THESIS (a born child)] of a female and male being (thesis - antithesis) is a good example of the dialectical math (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 over DIA expanding the boundaries of the binary (0-1) math, respectively, 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 situations in space, characterised by attempts of getting rid of the still PREVAILING QUANTITATIVE accumulations within this span of time DIA space until was achieved the desired quality of the number 7. For example, for a traditional royal family coming on the world of a baby - girl (princess) was not a desired upshot of this dialectical synthesis (quality) of THESIS and antithesis, because it was needed a son for continuation of the established dynasty. As a result of this qualitative failure, it has to be continued with the initiation of new dia-processes. For example, in the everyday language it is uttered by getting a fourth, fifth, sixth child... In dialectical terms, similarly as there are between any two numbers of the quantitative mathematics, a multitude of decimal numbers (the realm of a number), in the qualitative (dialectical) math these dialectical contents [intervals of time DIA widereach of space of a star], including the problematic of the "rounding", were symbolically presented by various forms of stars and triangles. Since here it deals with 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 said, this scenario in time DIA 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 terms of the 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 DIA 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 reached, accordingly a great dialectical breakthrough. These very complex dialectical interactively - creative contents DIA 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 VASTNESS of this, on the first look a simple graphical illustration, acquired 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, by passage of this dialectical understanding of time DIA 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"), it will be formed another Four - Triangular Star as well. Hope, it is not that difficult to be conjured up that the continuation of these mutual creatively interactive dialectics of dialectics of / 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 of God, which was introduced in this dialectical (creatively) interactive methodological approach.
Four Basic Mathematical Operations presented like a Road of Triangles
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Gravitational Abysses ("0" - Black Holes) Bounded with the Numbers (Values) TWO (2) AND ZERO (0)
By dialectically synthesising the all previously said, it seems that these dia-processes are particularly powerful within the range between the zero (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]. By mindfully re-reading this DIA the dialectical synthesising 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 in (of) the time DIA space. In either case, the four basic mathematical operations, in the range from the 0 to the 2 because of the binary gravitational forces of 0 - 1 [conflict area: the Bipolar DIA Binary way of thinking], are very blurry DIA confused.
In particular it is visible when accomplishing the 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 it was traversed and prevailed the magic boundary of the number two (2), the mathematical operation multiplication surpasses mathematical operation addition, that is, the 3 + 3 < 3 * 3, 4 + 4 < 4 * 4, and so on to the eternity DIA infinity. In dialectical terms, the most "strange" (interesting) is the mathematical operation of the dividing by the zero (0). It breaks the basic mathematical rule that each number divided by the same value makes result one (1). In mathematical terms, 0 : 0 = the infinity (∞) because it was observed by the mathematicians that each number divided by the almost (dynamic) zero, more and more was approached the infinity (∞). I think that every one, at least within certain period of her / his life, was puzzled by this mathematical rule. In the following case study, it will be presented my troubles with this "strange" mathematical rule.
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