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Misyurov Dmitry Alexandrovich

Associate Professor, Department of Philosophy and Socio-economic Sciences

Moscow State University of Geodesy and Cartography (MIIGAiK)

 

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E-mail: dmisyurov@gmail.com

101.8



Dialectical formulas based on the binary notation as the development formulas

Summary: The article suggests dialectical formulas based on the binary notation as the development formulas: formula with dominant and the non-dominant elements; universal formula; formula with symbolic weight of elements; tautological formula. For example, it suggests an opportunity to use the dialectical formulas for modeling and artificial intelligence creation, etc.

Keywords: dialectical formulas, binary notation, development formulas, artificial intelligence, modeling, interpretation

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Dialectical formulas based on the binary notation as the development formulas

The present article develops the experience in dialectics (see the book in Russian: .. : , , . - : ̻, 2012 - 288 .).

To begin with, we are going to demonstrate the dialectical nature of the rhyming binary notation, leveling the binary series (decimal equivalent for each composition is given in brackets):

00 (0) - 01 (1) - 10 (2) - 11 (3) -

100 (4) -101 (5) - 110 (6) - 111 (7) -

1000(8)-1001(9)-1010(10)-1011(11)- 1100(12)- 1101(13) - 1110(14) -1111(15)-

10000 (16) - etc.

The rhyming compositions in this arithmetical series, for example, in the end of each level - 11 (3), 111 (7), 1111(15), contain an internal contradiction, here between the ones, since according to their positions in the number they belong to different places. Resolution of mature contradictions is a revolutionary leap to a new level with the new ones and zeros appearing in the composition, when 11 (3) goes into 100 (4), or 111 (7) revolutionary (trough overturn) transforms into 1000(8), or the composition 1111(15) jumps in development to 10000 (16) etc., to further naturally follow the range of combinations of ones and zeros as simple evolutionary symbolic dialectical syntheses, to a new mature contradiction and its resolution, etc.

1) We are going to suggest the formula based on the binary notation with dominant (denoted with a capital letter, correspond to 1) and non-dominant elements (lowercase letter, correspond to 0). Let us denote the elements of the first level of the development: x, y, X, Y, the elements of the second level of the development: x, y, X, Y, etc., then the dialectical formula appears as:

yx (00) - yX (01) - Yx (10) - YX (11) -

Xyx (100) - XyX (101) - XYx(110) - XYX (111) -

Yxyx (1000) - YxyX (1001) - YxYx (1010) - YxYX (1011) -

YXyx (1100) - YXyX (1101) - YXYx (1110) - YXYX (1111) -

Xyxyx (10000) - etc.

In the example of a dialog as the basis of the development, the questions (q) and answers (a) dialectically develop through the logical transgression from one composition to the other, from one level to the other:

aq (00) - aQ (01) - Aq (10) - AQ (11) -

Qaq (100) - QaQ (101) - QAq (110) - QAQ (111) -

Aqaq (1000) - AqaQ (1001) - AqAq (1010) - AqAQ (1011) -

AQaq (1100) - AQaQ (1101) - AQAq (1110) - AQAQ (1111) -

Qaqaq (10000) - etc.

In more detail:

aq (00) initial state undeveloped question and answer. aQ (01) question dominant. Aq (10) answer dominant. AQ (11) stage of evaluation of the question-answer contradiction.

Resolution of the contradiction with a new question appearing:

Qaq (100) - question dominant; QaQ (101) correlation of the new question with the previous one; QAq (110) - correlation of the new question and the previous answer; QAQ (111) - correlation of the new question with the previous question and answer.

Resolution of the arising mature contradiction with a new question level appearing:

Aqaq (1000) - AqaQ (1001) - correlation of the new answer with the previous question; AqAq (1010) - correlation of the new answer with the previous answer; AqAQ (1011) - correlation of the new answer with the previous question and answer; AQaq (1100) - correlation of the new answer with the new question; AQaQ (1101) - correlation of the new answer with the new and previous questions; AQAq (1110) - correlation of the new answer with the new question and previous answer; AQAQ (1111) - correlation of the new question and answer with the previous question and answer as a composition of the mature composition.

Resolution of the contradiction new question:

Qaqaq (10000) - etc.

Formulas may be used for the algorithmization of the development, artificial intelligence creation. Particularly noteworthy are dialogical, dialectical nature of any development, not just the revolutionary leaps to a new level, but also the repetition, counterrevolution of the previous on new levels as the essential components of the development. If the new cannot solve the contradiction with the past, the development stops (suspends), in the same time on the dialectical development tree there may appear the new spirals with the new elements etc. Dialectical formulas may be used in describing the universe of the infinite set of crossing in the contradictory development dialectical universe spirals. Here the dialectical interrelation in the development of all the elements, unity and struggle of opposites, leaps between levels, negation of the negation, transformation from quantitative changes to qualitative, and vice versa.

Dialectics of unity (u) and struggle(s)

su (00) - sU (01) - Su (10) - SU (11) -

Usu (100) - UsU (101) - USu(110) - USU (111) -

Susu (1000) - SusU (1001) - SuSu (1010) - SuSU (1011) -

SUsu (1100) - SUsU (1101) - SUSu (1110) - SUSU (1111) -

Ususu (10000) - etc.

Dialectics of matter (m) and motion (o) (the composition of the revolutionary dialectical synthesis are marked, the rest is evolutionary development):

om (00) - oM (01) - Om (10) - OM (11) -

Mom (100) - MoM (101) - MOm(110) - MOM (111) -

Omom (1000) - OmoM (1001) - OmOm (1010) - OmOM (1011) -

OMom (1100) - OMoM (1101) - OMOm (1110) - OMOM (1111) -

Momom (10000) - etc.

In this key development formula matter and motion exist not only in unity but also struggle on different levels, that is why, for example, occur physical matter and motion, chemical matter and motion, etc., including appearing of human being with his unique capacity to cognitively reflect and transform.

Dialectical formula of matter (m) and consciousness ():

cm (00) - cM (01) - Cm (10) - CM (11) -

Mcm (100) - McM (101) - MCm(110) - MCM (111) -

Cmcm (1000) - CmcM (1001) - CmCm (1010) - CmCM (1011) -

CMcm (1100) - CMcM (1101) - CMCm (1110) - CMCM (1111) -

Mcmcm (10000) - etc.

Dialectics of body (b) and soul (s) development:

Ripening of the body-soul contradiction:

sb (00) - sB (01) - Sb (10) - SB (11) -

Resolution of the contradiction through the new level of the body development:

Bsb (100) - BsB (101) - BSb(110) - BSB (111) -

New level of the soul development:

Sbsb (1000) - SbsB (1001) - SbSb (1010) - SbSB (1011) -

SBsb (1100) - SBsB (1101) - SBSb (1110) - SBSB (1111) -

New level of the body development:

Bsbsb (10000) - etc.

Development of society (s) and personality (p) is also dialectic:

ps (00) - pS (01) - Ps (10) - PS (11) -

Sps (100) - SpS (101) - SPs(110) - SPS (111) -

Psps (1000) - PspS (1001) - PsPs (1010) - PsPS (1011) -

PSps (1100) - PSpS (1101) - PSPs (1110) - PSPS (1111) -

Spsps (10000) - etc.

Importantly, in some compositions we can observe the dialectic unity and struggle of different development levels of just personality PsPs (1010), or just society SpS (101). The new personality and the new society are shaped dialectically.

2) Dialectical formula with symbolic weight (weight is connected with conversion to decimal notation):

y0x0(0) - y0X1(1) - Y2x0(2) - Y2X1(3) -

X4y0x0(4) - X4y0X1(5) - X4Y2x0(6) - X4Y2X1(7) -

Y8x0y0x0 (8) - Y8x0y0X1(9) - Y8x0Y2x0 (10) - Y8x0Y2X1 (11) -

Y8X4y0x0 (12) - Y8X4y0X1 (13) - Y8X4Y2x0 (14) - Y8X4Y2X1(15) -

X16y0x0y0x0(16)-X16y0x0y0X1(17)-X16y0x0Y2x0(18)-X16y0x0Y2X1(19)- etc.

The formula, in particular, shows the constant growth of the compositions weight, and also the increasing number of the compositions on each new development level, the dialectical spiral with each turn gets broader and heavier. Probably, formation of the operations with compositions, for example: y0X1(1) + Y2x0(2) = Y2X1(3), or X4y0X1(5) + Y8x0y0X1(9) = Y8X4Y2x0 (14). The result defines as well by the addition of the weights of the compositions in brackets.

Dialectics of question (q) and answer (a):

a0q0(0) - a0Q1(1) - A2q0(2) - A2Q1(3) -

Q4a0q0(4) - Q4a0Q1(5) - Q4A2q0(6) - Q4A2Q1(7) -

A8q0a0q0 (8) - A8q0a0Q1(9) - A8q0A2q0 (10) - A8q0A2Q1 (11) -

A8Q4a0q0 (12) - A8Q4a0Q1 (13) - A8Q4A2q0 (14) - A8Q4A2Q1(15) -

Q16a0q0a0q0(16)-Q16a0q0a0Q1(17)-Q16a0q0A2q0(18)-Q16a0q0A2Q1(19)- etc.

In more detail:

a0q0(0) the undeveloped question and answer synthesis. a0Q1(1) question dominant. A2q0(2) answer dominant. A2Q1(3) mature question-answer contradiction, with answer weight predominance.

Contradiction resolution on the new question level:

Q4a0q0(4) new question dominant. Q4a0Q1(5) - dialectics, unity and struggle of the new and the old question. Q4A2q0(6) dialectics of the new question and the old answer. Q4A2Q1(7) mature dialectical contradiction of the new question and the previous answer and question, with the new question predominance.

Contradiction resolution on the level of the new answer:

A8q0a0q0 (8) - new answer dominant. A8q0a0Q1(9) dialectics of the new answer and old question dominants. A8q0A2q0 (10) dialectics of new and old answers. A8q0A2Q1 (11) dialectics of new answer and old question and answer. A8Q4a0q0 (12) dialectics of new answer and question. A8Q4a0Q1 (13) dialectics of new answer and question and old question. A8Q4A2q0 (14) dialectics of new answer and question and previous answer. A8Q4A2Q1(15) mature dialectic contradiction between new question and answer and old question and answer.

Resolution of the contradiction by the revolutionary leap to a new level new answer:

Q16a0q0a0q0(16)-Q16a0q0a0Q1(17)-Q16a0q0A2q0(18)-Q16a0q0A2Q1(19)- etc.

Such dialogue may be endless with various new participants joining it.

Quantity (q) and quality (u) also function in a dialectical dialogue:

Ripening of the quantity-quality contradiction:

u0q0(0) - u0Q1(1) - U2q0(2) - U2Q1(3) -

Resolution of the contradiction through getting on the new quantity level:

Q4u0q0(4) - Q4u0Q1(5) - Q4U2q0(6) - Q4U2Q1(7) -

New quality level:

U8q0u0q0 (8) - U8q0u0Q1(9) - U8q0U2q0 (10) - U8q0U2Q1 (11) -

U8Q4u0q0 (12) - U8Q4u0Q1 (13) - U8Q4U2q0 (14) - U8Q4U2Q1(15)-

New quantity level:

Q16u0q0u0q0(16)-Q16u0q0u0Q1(17)-Q16u0q0U2q0(18)-Q16u0q0U2Q1(19)-etc.

3) Universal dialectical formula:

ba (00) - bA (01) - Ba (10) - BA (11) -

Cba (100) - CbA (101) - CBa(110) - CBA (111) -

Dcba (1000) - DcbA (1001) - DcBa (1010) - DcBA (1011) -

DCba (1100) - DCbA (1101) - DCBa (1110) - DCBA (1111) -

Edcba (10000) - etc.

For example, dialectics of feeling (f), morality (m) and rationality (r):

mf (00) - mF (01) - Mf (10) - MF (11) -

Rmf (100) - RmF (101) - RMf(110) - RMF (111) -

Frmf (1000) - FrmF (1001) - FrMf (1010) - FrMF (1011) -

FRmf (1100) - FRmF (1101) - FRMf (1110) - FRMF (1111) -

Mfrmf (10000) - etc.

In more detail:

Ripening of the contradiction between feeling (f) and morality (m):

mf (00) - mF (01) - Mf (10) - MF (11) -

Resolution of the contradiction with passing to rationality level:

Rmf (100) - RmF (101) - RMf(110) - RMF (111) -

New level of the feeling:

Frmf (1000) - FrmF (1001) - FrMf (1010) - FrMF (1011) -

FRmf (1100) - FRmF (1101) - FRMf (1110) - FRMF (1111) -

New level of the morality:

Mfrmf (10000) - etc.

Sample of dialectics of esthetics (e), ethics (t) and logics (l):

Ripening of the contradiction between esthetics and ethics:

te (00) - tE (01) - Te (10) - TE (11) -

Resolution of the contradiction with passing to logics level:

Lte (100) - LtE (101) - LTe(110) - LTE (111) -

New level of the esthetics:

Elte (1000) - EltE (1001) - ElTe (1010) - ElTE (1011) -

ELte (1100) - ELtE (1101) - ELTe (1110) - ELTE (1111) -

New level of the ethics:

Telte (10000) - etc.

With the dialectical formulas we can model development, build the educational system, plan the scientific studies, develop the creative approach, etc.

Socratic problem of the dialectics of knowledge (k) and non-knowledge (n) also may be denoted with the endless cognition spiral:

Ripening of the knowledge-non-knowledge contradiction:

k0n0(0) - k0N1(1) - K2n0(2) - K2N1(3) -

Resolution of the contradiction with the new level of non-knowledge:

N4k0n0(4) - N4k0N1(5) - N4K2n0(6) - N4K2N1(7) -

New knowledge level:

K8n0k0n0 (8) - K8n0k0N1(9) - K8n0K2n0 (10) - K8n0K2N1 (11) -

K8N4k0n0 (12) - K8N4k0N1 (13) - K8N4K2n0 (14) - K8N4K2N1(15)-

New non-knowledge level:

N16k0n0k0n0(16)-N16k0n0k0N1(17)-N16k0n0K2n0(18)-N16k0n0K2N1(19)- etc.

Dialectical formulas allow to study the problems in the development and interconnection, for example considering the social (s), economical (e), political (p) and cultural (c) development:

es (00) - eS (01) - Es (10) - ES (11) -

Pes (100) - PeS (101) - PEs(110) - PES (111) -

Cpes (1000) - CpeS (1001) - CpEs (1010) - CpES (1011) -

CPes (1100) - CPeS (1101) - CPEs (1110) - CPES (1111) -

Scpes (10000) - - SCPES (11111) -

Escpes (100000) - - ESCPES (111111) -

Pescpes (1000000) - - PESCPES (1111111) - ..

Following this logics, the resolution of the social-economical contradictions ES (11) goes through appealing to politics Pes (100), next are examining the social-political PeS (101), politically-economical PEs(110) and socio-economically-political contradictions PES (111). Then we move on to the culture level Cpes (1000), with the socio-cultural approach CpeS(1001), through studying the economics-culture dialectics CpEs (1010), dialectics of the social-economical and cultural spheres CpES (1011), interaction of politics and culture CPes (1100). Next in this development goes studying the bond of the social and political problems on the basis of culture - CPeS (1101). It is essential to take into account economical-political-cultural unity and struggle of the elements - CPEs (1110), and finally, the socio-economical-political-cultural model CPES (1111), after which in the formula there is the transition to a new level of the social approach, considering the previous development stages Scpes (10000) - - SCPES (11111) - etc. Applying the dialectical formula presupposes returning on a new level to solving the problem. Such method is in some degree close to the system-based problem analyzing or to solving problems with the method of full enumeration. However, system or comprehensive set of measures do not always imply development, while dialectics is first and foremost evolutionary and revolutionary development, with a system relation.

The Marxist idea of the social development in the dialectics of the economical basis (b) and political, legal, ideological superstructure (s) may also be reflected in the formula:

s0b0 (0) - s0B1(1) - S2b0(2) - S2B1(3) -

B4s0b0 (4) - B4s0B1(5) - B4S2b0(6) - B4S2B1(7) -

S8b0s0b0 (8) - S8b0s0B1(9) - S8b0S2b0 (10) - S8b0S2B1 (11) -

S8B4s0b0 (12) - S8B4s0B1 (13) - S8B4S2b0 (14) - S8B4S2B1(15) -

B16s0b0s0b0(16)-B16s0b0s0B1(17)-B16s0b0S2b0(18)-B16s0b0S2B1(19) - etc.

As we can observe, revolutionary transitions may happen both from basis to superstructure and from superstructure to basis. For example, the French revolution of 1789 is a leap from basis to a new superstructure, and the Russian revolutions of 1917 leap from the superstructure to building the new basis. The Soviet perestroika - revolutionary move to the new superstructure, etc.

Dialectics of structure (s) and function (f) development:

f0s0(0) - f0S1(1) - F2s0(2) - F2S1(3) -

S4f0s0(4) - S4f0S1(5) - S4F2s0(6) - S4F2S1(7) -

F8s0f0s0 (8) - F8s0f0S1(9) - F8s0F2s0 (10) - F8s0F2S1 (11) -

F8S4f0s0 (12) - F8S4f0S1 (13) - F8S4F2s0 (14) - F8S4F2S1(15)-

S16f0s0f0s0(16)-S16f0s0f0S1(17)-S16f0s0F2s0(18)-S16f0s0F2S1(19) - etc.

Thus, dialectical model can be used for formulating the development in structural-functional method.

Dialectical logics is connected with the historical dialectics. For example, in association with the development of agriculture (a), industry (i), and contemporary information society (f):

Ancient period: ia (00) undeveloped level of agriculture and industry (initially - craft), we will symbolically denote with the non-dominant hammer-sickle.

Feudal period: iA (01) primary development of agriculture, symbolically hammer - SICKLE.

Capitalist period: Ia (10) industry domination, symbolically HAMMER-sickle.

Socialist period: IA (11) industry and agriculture development with emphasis on industry, symbolically HAMMER-SICKLE, which are the main USSR symbols and can be also found on the flag of the Chinese Communist party and some other organizations.

Postindustrial period information level, develops in unity and struggle with industry and agriculture on a new level: FiA (101) - FIa(110) - FIA (111).

The next development level will probably be connected with the new level of the agricultural development - A, biotechnologies, genetic engineering etc.:

Afia (1000) - AfiA (1001) - AfIa (1010) - AfIA (1011) -

AFia (1100) - AFiA (1101) - AFIa (1110) - AFIA (1111) - .

After this level there may be the new level of the industrial development of the world, and then the new level of the information society, t.i. continuation of the dialectical spiral with partial repetitions of the past elements on the new levels.

Dialectics of elite (e) and mass (m) culture, with transition to a dialectical culture (d):

em (00) - eM (01) - Em (10) - EM (11) -

Dem (100) - DeM (101) - DEm(110) - DEM (111) -

Mdem (1000) - MdeM (1001) - MdEm (1010) - MdEM (1011) -

MDem (1100) - MDeM (1101) - MDEm (1110) - MDEM (1111) -

Emdem (10000) - - EMDEM (11111) -

Demdem (100000) - - DEMDEM (111111) - etc.

Dialectical culture gives impulse to developing on the new levels to both mass and elite cultures, which with growing recognition acquire dialectics for developing nature, society and thought.

Historical periods of dialectics (d) and metaphysics (m) domination in unity and struggle:

Ancient period: dm (00) - dM (01) Dm (10) - DM (11) -

Feudal period: metaphysics dominant: Mdm (100) - MdM (101) -

Capitalist period: MDm(110) - MDM (111) -

Socialist period, new level of dialectics dominant:

Dmdm (1000) - DmdM (1001) - DmDm (1010) - DmDM (1011) -

DMdm (1100) - DMdM (1101) - DMDm (1110) - DMDM (1111) -

Contemporary period of global capitalism, new level of metaphysics development:

Mdmdm (10000) - etc.

In future, period of any new -ism, dialectically negating global capitalism and all the previous periods new level of dialectics development.

4) Tautological formula example, for X and Y:

XX(00) - XY(01) -YX (10) - YY (11) -

YXX (100) -YXY (101) -YYX (110) -YYY (111)-

YXXX (1000) - YXXY (1001) - YXYX (1010) - YXYY (1011) -

YYXX (1100) - YYXY (1101) - YYYX (1110) - YYYY (1111)-

YXXXX (10000) - etc.

If we take commodity (c) and money (m), then the dialectical formula:

CC(00) - CM(01) -MC (10) - MM (11) -

MCC (100) -MCM (101) -MMC (110) -MMM (111)-

MCCC (1000) - etc.

Here the formulas from K. Marxs Capital commodity - commodity, commodity - money - commodity, money - commodity - money in development, are complimented by the other, not less important for development studying, commodity-money relations. With the help of the dialectical formula based on binary notation, combinations of the opposite mass and velocity V, we may demonstrate the historical dialectical consistency of formula of the impulse VM, and energy, including the famous A. Einsteins formula E=mc2= ccm deriving, as a special case of the dialectical combination VV, etc. in development.

Dialectical relation is also observed in the development of interpersonal (p), national (n) and world (w) communication:

np (00) - nP (01) - Np (10) - NP (11) -

Wnp (100) - WnP (101) - WNp(110) - WNP (111) -

Pwnp (1000) - PwnP (1001) - PwNp (1010) - PwNP (1011) -

PWnp (1100) - PWnP (1101) - PWNp (1110) - PWNP (1111) -

Npwnp (10000) - - NPWNP (11111) -

Wnpwnp (100000) - - WNPWNP (111111) -etc.

Dialectics of theory (t) and practice (p):

tp (00) - tP (01) - Tp (10) - TP (11) -

Ptp (100) - PtP (101) - PTp(110) - PTP (111) -

Tptp (1000) - TptP (1001) - TpTp (1010) - TpTP (1011) -

TPtp (1100) - TPtP (1101) - TPTp (1110) - TPTP (1111) -

Ptptp (10000) - etc.

The suggested dialectical formulas based on the binary notation reflect the development in the interconnection of various elements of the universe, in dialectical spirals. Formulas may help in resolving the accumulated contradictions, in patterning various processes, may be used in education and science, in creating the artificial intelligence and in creative development.


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