Static DIA Dynamic Math reflected through Prism of the Dialectic Interactive Approach
(Recti)linear Creative Framework for the Orientation in Time AND Space
In this creative article, it's going to be shown by this creator of knowledge that the developed concept of the simple(st) mind was DEEPLY IMPLANTED into the static (binary) math, that is, its origin is there. Or put it in another way, it might be argued, this kind of the math, interpreted in terms of its logics (logical mathematical operations), has its origin in this (basically) simplest (dynamical) concept FOR THE ORIENTATION and navigation in (recti)linear space and time. In short, it will be shown in a PICTORIAL way already perceived (self-)awareness by a number of scientists (philosophers, artists, and culturologists too) that the (modern) way of thinking is greatly influenced by various mathematical patterns of thought ("digitalisation"), that is, the math has been deeply imprinted into the (sub)consciousness of the people. This creator of knowledge has deeper reconsidered and elaborated this basic idea by going METHODOLOGICALLY BEHIND this observed challenge in the time DIA space.
Summarizing this introductory dialectical content under creative consideration, it will be shown that the genus Homo-Sapiens not only included various prehistoric Homo-species by interlacing genes but also assimilated their ways of thinking and cogitation not only about their view of the world around them but also to the inner worlds contained in this kind of universe in miniature, which modern scientists simple-reasonably identify with the constituent spheres of the human brain. In any case, the fact is that people orient themselves differently in time and space, as well as that they have different perceptions and experiences of time and space. In these creative articles, unlike the species of (wo)mankind, which in its biological "chip" already has a built-in tendency to group and mob as an inherited way of survival of their species, the focus of this creative research will be placed and emphasized individual properties and characteristics of the human and humane genus, whose members, when in danger of losing these typical individual characteristics and recognizable human features, that is, to be drawn and sucked into the vortex and hole of their inner darkness under the strong influence of the gravitational force of group and crowd thinking, always as great individuals they in right time become aware and realize who she, he really is, and find a way to rise above these low motives and passions of these species of (wo)mankind (dissociating from them). Of course, between these two poles there are many species of (wo)mankind that in this created bipolar world are inclined in the material, materialistic, and genetic sense, as well as in the rational and mental sense, and especially in the spiritual sense to one or the other pole of this imaginary bipolar line. For more information on this topic, read the creative article: The Concept of the Simple Mind dia Reason: Impact of these two different Creative Frameworks for Orientation in Time 'and VERSUS dia' Space on Happenings in the Dialectical Societal Universe
Mathematical Operations Multiplication and Addition
In short, by using the developed powerful "tools" of the dialectic interactive approach, understood in terms of the undertaking an appropriate creative traveling through time DIA space, there were deeply reconsidered the four basic operations of the dynamical mathematics (addition, multiplication, subtraction and division) from this DIALECTICAL methodological point of view. All these creative discoveries, respectively the previously mentioned mathematical (digitalised) patterns of thought, were graphically presented in the illustrations, shown in this paragraph. In other words, the developed concept of the simple(st) mind is not the bare invention (and fruit of the imagination) of this creator of knowledge, as some of you thought, but rather, by putting it before your eyes, it has become observable even with the five famous "scientific" senses. It follows from this that the developed concept of simple(st) mind has deep roots in the MATHEMATICAL WAY OF THINKING, understood in terms of the corresponding way of (creative) orientation in the (RECTI)LINEAR SPACE AND TIME.
Couple Dialect: Thesis DIA Antithesis
Dialectical Creative Framework for Orientation in the Eternity of Times DIA Infinity of Spaces
A Dialectical View on the Simple Mind, Seen from the Mathematical Perspective
As the first step, by reflecting it through the prism of the dialectical interactive approach, in this graphical illustration were displayed the differences (increments) of the interrelated mathematical operations of the multiplication and addition, by considering them AS A COUPLE DIALECT (thesis DIA antithesis). For example, in the row number one were displayed the increments of the mathematical operation of multiplication [shown in the row number two: 0*0=0, 1*1=1, 2*2=4, 3*3=9, etc.], as it follows: 1-0=1, 4-1=3, 9-4=5, 16-9=7, and so on. Note, if it were added (opposite operation) instead of being subtracted, the ordinal numbers of columns (cardinal numbers), which were shown in the row number zero, the result would be equal to the increments of the mathematical operation of multiplication: 0+1=1, 1+2=3, 2+3=5, 3+4 = 7, 4+5=9. After that by using this pattern of thought, in the row number four of this graphical illustration were displayed the increments of the mathematical operation of addition [see the row number three: 0+0=0, 1+1=2, 2+2=4, 3+3=6, etc.], as it follows: 2-0=2, 4-2=2, 6-4=2, 8-6=2, and so on. Finally, the increments of the mathematical operations of multiplication and addition were connected and dialectically synthesised as couple dialects into THE RIGHT-ANGLED TRIANGLES [see the row two and three]. Here it was demonstrated that the increments of each of two sides (angles) of a right-angled triangle, expressed by the related mathematical operation [successively by the subtracting (-) and addition (+)] makes the sum of the third angle. For example, the first triangle: 3-1=2, 2+1=3, 3-2=1 (thesis), the second triangle (antithesis) consists of the same factors: 3–1=2, 2+1=3, 3-2=1, making A PAIR OF THE RIGHT-ANGLED TRIANGLES [a renewed couple dialect: synthesis DIA the renewed thesis / (temporal) conclusion].
Pay attention to the use of twice the mathematical operation of subtraction (-), whereas only once was used the mathematical operation of addition (+). You can check other triangles yourself. Note, the numbers 2 (two), in the row number four, which present a STATIC (CONSTANT) INCREMENT of the mathematical operation of addition. Pay also your attention to the coming constant (static) increment - value two (2) in the row number 1, as a prior result of the mathematical operation of multiplication, that is, 3-1=2, 5-3=2, 7-5=2, etc. In other words, THE INCREMENT OF INCREMENT of the mathematical operation of multiplication is also static (constant), that is, it is equal to the 2. Or more simply said, the mathematical operation of multiplication, after the implementation of process of the incrementing only the one step extra, was made static ("inhibited"), that is, it was deduced on the mathematical operation of addition. By the way, if there were TRIANGULARLY connected points of these increments (for example, the increment 1 and 3) with the coming constant (static) increment of the mathematical operation of multiplication (the value 2), it would be formed an angular hollow, that is, it was revealed a hidden (lacking) triangle. In this way, one degenerate "three-pointed" star was completed (came to light): see also the graphical illustration in the case 3.4. I hope, you were able to recognise the multitude of images (sequences) of this rectilinear (creative) framework for the orientation in time and space, by representing and transforming these dialectical contents into their triangular manifestations (pairs of right triangles), on this imaginable "highway", formed by merging columns 2 and 3.
Bipolar DIA Binary Way of Thinking
A Dialectical View on the Simple Mind, Seen from the Mathematical Perspective
Dialectical Creative Framework for Orientation in the Eternity of Times DIA Infinity of Spaces
Either way, such an image (couple of the right-angled triangles), that is, the sequence between any two numbers was used as a framework for the presentation and interpretation of the developed concept of simple(st) mind, for example, during the process of creating knowledge. Note also that this (creative) framework presented with appropriate graphic illustrations (right triangles) is in fact a “degenerative” manifestation of the dialectical creative framework for orientation IN TIME DIA SPACE. This dialectical creative framework was developed and presented two years earlier (1999), that is, independently of this rectilinear story, by using other sources for the inspiration, to undertake an appropriate creative journey through this dialectical understanding of time and space. By comparing these two creative frameworks, it is noticeable that within the rectilinear creative framework for orientation in time and space (rectilinear spatial dimension) the central triangle (empty triangular hole) is missing. In other words, these two (creative) frameworks clearly and pictorially show the difference between a DIALECTICAL TRIANGULAR APPROACH for the orientation in time DIA space versus a DYNAMICAL RIGHT-ANGLED TRIANGULAR ONE for the orientation in time and space (the rectilinear approach).
Recall, in full agreement with the dialectic interactive approach, because in its focus are the dia-processes of transition, transformation, metamorphosis and transfiguration from a state in time DIA space into another one, everything is presented by the (various kinds of) TRIANGLES, whereas the lines were only used as some kind of the imaginative delimiters (separators) within the initiated dia-processes. To make the consideration of dynamic content (issues) within the developed dialectical interactive approach feasible, there were used the right-angled triangles, as a kind of SUBSTITUTE FOR THE LINES. On the other hand, the rectilinear methodological approach, because of being based on the dual (bipolar) way of thinking, all essential processes within this imaginary line were concentrated on its two poles (0-1): The everything else between them was simply attracted by the strong "gravitational" forces of these poles, understood in terms of the mutual approaching these two different points (of views, for example) by pressing all between them (compression). In other words, all that was not included with these two (OR-OR) poles (DIA one) was scattered or eroded, swallowed, neglected, neutralized.
This additionally demonstrates that the rectilinear methodological approach has truly its source of (creative) inspiration in the math (geometry): Between the two points can be drawn only one line. In short, by this imaginative line DIA its two poles, a typical natiocratic free(dom of) choice and appropriate freedom of will were presented, seen from this rectilinear methodological perspective. But this is not, in any case, the end of this endless rectilinear methodological story. In other words, this imaginative natiocratic line can be further thickened by the inclusion of an appropriate natiocratic concept of distinguishing evil from good, and so on (that is, growing even more thicker DIA fatter), followed each TIME IN this rectilinear SPACE with suitable regrouping the (imaginary) dots within this line, understood in terms of the previously elaborated effect of the "gravitational" forces of its two (dominated) poles (of the thinking).
A Dialectical View on the Incommensurable Abyss between any Two Numbers, Seen from the Perspective of Time (X1) DIA Space (X1')
THAT WILL BE MADE STATIC
EITHER in terms of the Rectilinear Time OR in terms of the Rectilinear Space
As an example, note also, although the concept of natural numbers, or real numbers, if you so will, can be presented and interpreted in the mathematical ("static") sense as a RECTILINEAR array, that is, either as a right-angled triangular "road" of numbers (dialectic interactive approach), or as a continuous line (rectilinear approach), the dialectic interactive approach, reflecting this dialectical content through the core of its prism, has also BROUGHT TO LIGHT (OF THE DAY) a triangular hollow (cavity - the lacking triangle): The abyss between any two numbers of this mathematically made, rectilinearly dashed (dotted) line, that is, these rectilinear time intervals DIA the related distances of space between the DOTS (numbers) were transformed in triangular (incommensurable) forms (triangles). In other words, this imaginative line (array) of numbers was artificially made by connecting (compressing) all dots on it, accordingly expressed in the mathematical sense by rounding [that is, by transforming dots of this imaginary line in the small "circles": The building blocks of the emerging pores-spores] of these conceivable distances of space (and time intervals) between them, which in fact separates any two number's values.
This shows, seen from the perspective of the eternity of times DIA infinity of spaces, that not only the circular creations (pi - value) are irrational (incommensurable) but the same (could be argued) is also valid for any (recti)linear form. Or more simply said, although it is theoretically feasible to make static a dynamical process, understood in terms of THE TIME AND SPACE, for example in the mathematical sense, in the living reality (practice), the time DIA space cannot be ULTIMATELY stopped because of its previously mentioned DIALECTICAL FEATURES and processes (a continuous dia-process of change). On the other hand, it could be disputed by those who see it differently that despite these rectilinear mathematical efforts and endeavoring to stop the flow of time and space, the "kingdom of numbers" also continues to mimic and reflect the expansion of time and space (universe).
Mathematical Operations Subtraction and Division
The mathematical operations subtraction and division, expressed in terms of increments (the rows number 6 and 9), are very STATIC (0), that is, do not react on the change in this static time and space. As a consequence of it, it could be argued that mathematical operations addition and especially, the multiplication initiate and drive the process of dynamisation in terms of the notion infinity (∞), whereas the task of mathematical operations division and subtraction is to stabilise these dia-processes in terms of zero (0), accordingly to do deducing them DIA the control of their "escape" velocity in the realm of "mind" (possible). By this reinterpretation of four (4) basic mathematical operations, a triangular version (story) of the everyday (static) math was in fact presented, which is based on this linear way of thinking and interpretation of their rectilinear pathway from zero to plus infinity (0 → + 1, 2, 3, 4, .... ), forming in this way a road of triangles. Note, that this "triangular line" or more properly said the displayed endless "road" of triangles (surface) was imaginarily drawn by the rows number two and three (multiplication and addition), and, by the rows number seven and eight (subtraction and division) of this table. In other words, if I - thou - we express the deeply impressed and imprinted linear DIA dual way of thinking in my - thy -our (sub)conscious, interpreted and presented by the everyday language from zero to plus infinity (0 → +∞), understood in terms of imaginative point-punctures between (among) numbers, I - thou - we uttered the so-called natural numbers in terms of the road of (the right-angled) triangles. Hope, it is not difficult for thee to simulate (emulate) its inverse content, that is, the story from the zero to the minus infinity (0 → -∞) in order to be completed this story about the real numbers, respectively, to reinterpret it in a familiar way of thinking to me - thee - us. Or put it in another way, this TRIANGULAR story about the everyday math was re-straightened in terms of the road of triangles which passes through zero (0), from minus infinity in direction to the plus infinity (-∞ → 0 → +∞), understood in terms of the myriads of imaginative point-punctures (pores-spores).
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)
As a pattern of thought during your orientation in time and space, concentrate attention to the lesser value of the increment on this imaginative road [for example, to the increment 1, comparing it to the increment 3]. In this way, a triangular story of this "line" (road) of triangles from zero to minus infinity (0 → -∞) will be interpreted and presented; for the mathematical operation of multiplication, as it follows: (0*0=0, -1*-1=1, -2*-2=4, etc.) and addition (0+0=0, -1+(-1)=-2, -2+(-2)=-4, etc.): the first triangle: 1-3=-2, +1- (-2)=3, -2+3=1, the second one, a complementary triangle, consists of the same factors: 1-3=-2, +1- (-2)=3, -2+3=1. Mathematical operations of subtraction and division, expressed in terms of increments ranging from zero to minus infinity (0 → -∞), are also very static, that is, they do not reflect any change in this very static space and time too. Note, the mathematical operation of multiplication also does not reflect any change within its (negative) range, that is, its factors and increments keep positive value (negation of negation). From the all previously said, it follows that the RECTILINEAR story in the range from zero to minus infinity (0 → -∞) was conveyed and preserved within this triangular story, that is, within this endless "line" (road) of the triangles, which starts from zero to plus infinity (0 → +∞).