Drakon Book : Chaper 17 [English Translation]

Chapter 17

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CALCULATION OF ICONS and attempts to predict the future

Visualizations – the flesh and blood of thinking.

Rudolf Arnheim

VISUAL logical calculus

Include another “side of the spotlight” and try to look at the visual syntax of a dragon with the positions of mathematical logic. Our eyes will open an unusual picture. It turns out that any abstract dragon scheme is a theorem that is strictly deduced (proved) of the two axioms, which are the primitive and the blank-blank-silhouette.

- What is this axiom? - Has the right to surprise the reader. - It’s just a picture-mole rats! A dragon-circuit does not look like a theorem! Who and what they have to prove? Perhaps it was a joke or a metaphor.

- Not at all, not a metaphor. It will be shown that the visual syntax DRAGON built as a logical calculus (called the “calculus of icons”). This calculus can be seen as part of visual mathematical logic. The latter concept is not traditional. Mathematical logic and its basic concepts (calculus, a logical conclusion, and so on. D.) Formed within the text paradigm. In this chapter, apparently for the first time entered the visual analogues of these concepts and their basis of calculation of construction icons.

KNOWN ABOUT mathematical logic

The principal achievement of mathematical logic is the development of modern axiomatic method, which is characterized by three features:

  • explicit formulation of assumptions (axioms) to develop the theory of (formal system);
  • explicit wording of the rules of inference by which derived from axioms theorem theory;
  • the use of formal languages ​​for presentation of the theory of the theory.

The main object of study in mathematical logic are logical calculus. The concept includes the calculation of basic components, such as:

  1. formal language, which is given by the alphabet and syntax,
  2. axioms,
  3. rules of inference.

Thus, the calculation allows knowing the axioms and rules of inference, we obtain (t. E. Deduce prove) all theorems of the theory, the theorem as an axiom, recorded only in a formal language.

Recall that in the framework of mathematical logic three terms logical calculus, a formal system and the theory can be regarded as synonyms. Consequently, Theorem calculus theorems of the formal system and theorems of the theory – it is one and the same.

ON A common misconception

There are two approaches to the formalization of human knowledge: visual (graphic, pictorial), and text. This problem is related to a curious contradiction. On the one hand, the advantage of the graphics to the human-readable text is generally accepted as the human brain it is mainly focused on visual perception, and people get information when reviewing graphic images faster than reading text. I. Velbits cue rightly points out: “The text – the most common and least informative in the sense of clarity and speed perception of the presentation of information”, and drawing – “the most advanced integrated form of knowledge representation.”

On the other hand, the theoretical development of the principles of visual formalization of knowledge is still not adequately deployed. The reason for the backlog to be found in the history of science, in particular the peculiarities of the development of mathematics and logic.

In these disciplines for a long time (sometimes explicitly, often implicitly) assumed that the results of mathematical and logical formalization of knowledge in most cases should be in the form of text (but not images). For example, Stephen Kleene wrote: “As a formal theory of the structure is no longer a system of meaningful sentences and phrases, the system considered as a sequence of words, which, in turn, are sequences of letters … The symbolic language characters will usually correspond to a whole words, not letters, but a sequence of characters corresponding to the phrases, will be called “formula” … theory of evidence … suggests … the construction of arbitrarily long sequences of characters. “

From these considerations it is evident that the wedge (as well as many other authors) puts in the Research Center of textformalization and completely loses sight of the totality of the problems associated with visual formalization.

Analysis of the literature on this topic shows that the majority of scientists based on the implicit assumption that scientific knowledge-ing – is primarily a “text” knowledge that the most adequate (or even the only possible) form for the presentation of the results of scientific research is consistency and formalized formalized phrases, t. e. the text (rather than visual images). The basis for this assumption is erroneous view, which can be characterized as “absolute principle of the text.”

The principle of absolute text

The essence of it can be expressed, for example, in the form of the following considerations.

The progress of science ensures the success of logical-mathematical formalization and development of new scientific concepts and principles, rather than improving the picture. Formulas and words express the essence of scientific thought patterns – it’s just to illustrate the scientific text, they facilitate the understanding of the already finished formed scientific thought, but are not involved in its formation. In short, the language of science – a formula and proposals, but not images. The science is the essence, the core, on which depends the success of the scientific creativity and obtaining new scientific results (it is expressed in logical-mathematical formalism, scientific concepts and opinions expressed in words).And there are auxiliary tasks (training beginners, the exchange of information between scientists) – here’s the pictures and help facilitating mutual understanding. In addition, the drawings are optional, free and non-strict form, it is impossible to formalize. Therefore, the formalization of scientific knowledge is incompatible with the use of drawings.Thus, the drawings have something external to science. Improving the language of drawings and scientific progress – two different things, they are not related.

There are a number of works, indirectly prove that the principle of absolute text is wrong and harmful. Today more and more scientists have come to the conclusion that visual formalization of knowledge can not be regarded as something secondary for scientific knowledge, because it is part of the very fabric of the mental process of learning and “may mediate the deepest and creative steps of scientific knowledge.”

However, in mathematical logic visual methods, to our knowledge, has not yet been widely used. In other words, mathematical logic to this day remains a stronghold of the text of thinking and methods of text formalization of knowledge. This fact plays a negative role, interfering to put the last point in the dock-gations fallacy of “absolute principle of the text.”

Next we will try a particular example to demonstrate the principle of calculation icons to visualize at least some sections, or, more accurately say, questions of mathematical logic.

IMAGING CONCEPTS mathematical logic

We need a definition of two concepts: visual logic output (video output) and visual logical calculus (videoischislenie). To facilitate the study of the material already familiar to the reader to use the method of confrontation, by placing in the left column of Table. 6 well-known “text” concept, and the right – a new definition of “visual” concept.

The definition of “inference” The definition of “video output” (visual inference)
Deduction in V is a sequence of C 1, …, C n formulas such that for any i the formula C i is either an axiom of the calculus of V, or a direct consequence of the above formulas by one of the rules of inference. Formula C n is called a theorem of V, if there is a derivation in V, which is the latest formula C n Video output in videoischislenii V is a sequence of C 1,Cn videoformul, such that for any i videoformula C 1 is either videoaksioma videoischisleniya of V, or a direct consequence of the previous videoformul one of the rules of the video output. Videoformula C n is called videoteoremoy videoischisleniya V, if there is a video output in V, which is the last videoformuloy C n

It is easy to observe that the new definition (right) almost exactly coincides with the classical (left); The only difference is the addition of the prefix “video.”

The definition of “logical calculus” The definition of “videoischislenie” (visual logical calculus)
The logical calculus can be represented as a formal system of four

V = <u, S 0, A, F>

And where – set of basic elements (letters of the alphabet);

0 S – set of syntax rules, on which the letters are constructed well-formed formulas;

A – the set of well-formed formulas, elements of which are called axioms;

F – inference rules that allow the set A to receive new well-formed formulas – Theorem

Videoischislenie can be presented as a formal system in the form of four

V = <u, S 0, A, F>

And where – many icons (visual alphabet letters);

S 0 – a set of rules of visual syntax, based on which of the icons are built properly constructed videoformuly;

A – the set of well-formed videoformul, whose elements are called videoaksiomami;

F – the rules of the video output that the set A let you receive the new well-formed videoformuly – videoteoremy.(Many theories denote T.)

Building on this approach, and relying on the “text” determination log-cal calculation, by analogy to introduce the concept of “videoischislenie” (tab. 7).

CALCULATION OF ICONS

So, we have identified the desired visual concepts of mathematical logic. With their help, we can construct a calculus icons.

  • ? Many icons and (visual alphabet letters) given thesis 1 (see. Ch. 15) and shown in Fig. 1.
  • Many S o visual syntax rules described in Sec. 15 theses 2-37.
  • A set of visual axioms includes only two elements: the primitive and the blank-blank-silhouette (Fig. 115). Further, we call them primitive and axiom-the axiom silhouette.
  • The set T covering all videoteoremy calculus V, is nothing more than a set of abstract dragon schemes. Note that the set T does not include the axiom, since the latter contain blank critical points and, therefore, equivalent to let the operator. The set T is divided into two parts: a set of primitives of T 1 and T 2 set of silhouettes.
  • Many of the rules F the video output is also divided into two parts F 1 and F 2. Lots F 1 allows you to display all the theorems primitives belonging to the set T 1 of a single axiom-primi¬tiva. It contains five rules of inference: Enter atom, adding options, transplant vines, lateral connection, removing kon¬tsa primitive. These rules are described in the listing 10, 21, 28, 30, 31, 34, Ch. 15.
  • Many F 2 gives the possibility to display all the theorems of T-2 silhouettes of a single axiom-silhouette. It contains eight inference rules: entering the atom, adding options, adding branches, grafting vines, creepers ground, lateral connection, removing the last branch, an auxiliary input. Inference rules for the silhouette described in theses 10, 21, 28-33, 35 Ch. 15.

This construction calculation finishes icons.

It is known that the study of calculus syntax of the mathematical logic. In addition, the latter is engaged in semantic study of formal languages, the basic concept of semantics is the concept of truth.

In calculating icons trivial semantics. Various videoformuly (block diagram) can be true or false. Videoformula called true if it – or axiom, or deduced from the axioms using the rules of inference (ie. E. Is a theorem), and false otherwise. Thus, all well-formed abstract dragon design (theorems) are true. Conversely, properly constructed schemes that do not meet the rules of visual language DRAGON, are false. Examples of false schemes are shown in Fig. 131 and 132 in the left column.

ONCE AGAIN ABOUT skewer method

Earlier we defined a skewer method as a theory of visual structured programming. In this chapter, an opportunity to greatly enrich this concept and consider it as a calculus of icons, including the interpretation of the latter.

To emphasize the theoretical nature of the skewer method, it is advisable to slightly change the terminology. In particular, the use of the name DRAGON related to the practical development of specific programming languages, for theoretical purposes would be inappropriate. Therefore, we make the change of terms.

Skewer diagram – abstract dragon diagram. We emphasize that the skewer diagram is by definition abstract, t. E. Completely devoid of text.

Skewer-language – the language of the skewer-circuits. To skewer-language set only visual syntax, word syntax is not defined.

CHART skewers as an abstract model of the program

It has been said that videoprogrammirovaniya characterized by “splitting syntax.” Syntax S splits into a visual syntax S 0,which determines the rules for constructing a skewer diagrams and text syntax S 1, which defines the rules of the alphabet tekstoelementov and recording statements within the text icons. From this, it can be said that the skewer The programconsists of two parts: B 0 and B 1, where B 0 – skewer diagram syntax S 0; IN 1 – text portion of the program, ie. E. The total text kept all the icons of the program, defines the syntax S 1.

One is struck by the similarity between the undoubted skewer charts and diagrams programs. Noticing this analogy and repeating – with some almost obvious changes – the general outline of reasoning adopted in schematology, we can conclude that the skewer in the diagram 0 describes is not a single program, but a whole class of programs, ie. E. A poliprogrammoy and skewer-language serves multiyazykom – poliprogrammirovaniya language.

Class diagrams skewer is a subclass of large-block schemes, the degree of abstraction which occupies an intermediate position somewhere between Martyniuk schemes and standard circuits. Relationship between skewer charts and diagrams of programs is fundamental, and raises a number of interesting problems, in particular, to the fact that “the task effectivization broadcast programs grows into the problem of automation of designing quality programs.”

From the point of view of the theory videoprogrammirovaniya, graph-scheme used in the (text) theoretical programming, have the disadvantage – as conventional flowchart application programming, they are informal. Although the works of Ershov made a step toward formalizing the graph-schemes, but his solution is not satisfactory, because the syntax used Ershov visual graph-scheme does not yield an unambiguous strictly deterministic visual configuration (topology) graph-schemes and, consequently, It does not provide a unique solution of visual problems.

However, Yershov and did not set out such tasks. However, for our purposes is strictly formalizing syntax visual flowcharts (including flow-chart) plays a fundamental role.

CONVERSION skewer skewers schema in program

We emphasize once again that we have constructed language (skewer-language) – this is not a programming language and the language programs of large-block schemes, ie. E. Poliprogrammirovaniya language. However, it can be easily converted into a programming language, which can be done in many ways. To do this, you must also set a text syntax and semantics of S 1 Q 1 text operators placed in the icons skewer charts. For example, if you take the text syntax and semantics of the corresponding Pascal obtain visual programming language that can be called “spit-Pascal.” Similarly, you can build a language-BASIC skewer, skewer-si and so on. D.

Using the terminology schematology, we can say that the program has a skewer skewer interpreted diagram, however, the concept of interpretation in this case is markedly different from the classic. Detailed consideration is beyond the scope of this book, we restrict ourselves to a brief remark. To specify the interpretation of the skewer-circuit and turn it into a skewer program, it is necessary, first, to extend the definition skewer-language and turn it into a programming language that describes the syntax and semantics of S 1 Q 1 text operators. Secondly, the text should include specific statements recorded in accordance with the syntax of S 1 and placed in the icons skewer-circuit to 0. This will set the text of the skewerin one program in. Thus, the interpretation of the skewer-circuit is defined as a triple <S 1, Q 1, B 1>.

This implies the following obvious remark.As a skewer-language is an abstract model of any imperative programming language (Empire language) insofar Empire language is interpreted by a skewer-language. This interpretation of the skewer-language, transforming it into a specific language Empire, defined as a pair < S 1 , Q 1 >.

Skewers METHOD AND EVIDENCE right program

According to R. Anderson, “the goal of many studies in the field of proof-of-program … is the mechanization of such evidence.” D. Grice points out that “the evidence must stay ahead of the construction program” 11 . By combining both requirements, we find that the automatic proof-of-building program should be ahead. It is easy to verify that the skewer method provides partial fulfillment of this requirement. In fact, in the beginning of the chapter, it was shown that any well-formed skewer chart is strictly proven theorem. The algorithms DRAGON editor coded numbered icons, so any skewer diagram built with his help, the true, that is. E. A properly constructed. This means that the dragon-editor provides a 100% automatic proof-of-skewer schemes guaranteeing fundamental impossibility of visual syntax errors. As a skewer, skewer scheme is part-program, said equivalent proof of partial correctness skewer program.

At the beginning of the chapter, we asked a funny question: if the Dragon scheme – a theorem, who are supposed to prove? The answer is simple. They had not been required to prove, as they proved once and for all because the work Dragon editor is built as a realization of calculation icons.

Now, add a spoonful of tar in a barrel of honey. Unfortunately, this method enables us to prove the correctness of the skewer-circuit only. It is only a small part of the total work to be performed to prove the correctness of the program is 100%. However, there is a small consolation: a partial proof of the correctness of the program with the help of the Dragon Editor done without any human intervention, and achieved for free, as additional labor costs, time and resources are required. A gift horse in the teeth not look.

POSSIBLE THEORY visual programming?

Although videoprogrammirovanie – a relatively new trend in this field for a considerable number of interesting applications development. However, the theoretical visual programming is in its infancy. In the available literature, the author was able to find only a few lines, which can to some extent be interpreted as a program for future research in the field of theory videoprogrammirovaniya: “For visual programming is necessary to conduct rigorous scientific studies, mathematical definitions and models – the majority of developments in this area is yet empirical character. Perspective can be use in the graphical user interface technology of artificial intelligence, which is commonly used to describe the application area. The system of knowledge representation may include a set of visual primitives, their symbolic description and rules of inference conclusions. “

As probably the reader noticed, in this paper, addressing a similar problem (the problem of the withdrawal of formal conclusions by performing operations on visual features, which are mainly used icons skewer charts), we went to a somewhat different way. The difference is as follows. The authors cited the work speak of “symbolic descriptions” visual primitives, meaning text rules of inference conclusions adopted in the traditional text of mathematical logic. However, even in the construction of A. Ershov calculating equivalent transformation schemes Yanov first attempt to move away from “pure text” mathematical logic, using the formulas of inference rules is not only symbolic descriptions, and graphics.However, the method Ershov due to defects in the visual syntax not entirely formal.

In this book, the development of ideas Ershov went in two directions. Firstly, mentioned defects are eliminated, which made the formalization of an abstract syntax flowcharts comprehensive and rigorous. Second, it was launched and enforced the idea of ​​complete abandonment of the symbolic description of visual features (intraengine binary representation does not count).

We can assume that the above principles of visualization of mathematical logic, implemented using the concepts of visual calculation and visual inference can be useful for a more complete and rigorous formalization of not only the language of abstract block diagrams (skewer-language), but other visual languages knowledge representation and visual programming.

Assumptions about the future imperative programming languages

Summarizing the material, the author could not resist the temptation to look to the future and in order to express their preliminary discussion possibly erroneous assumptions about the development imperative languages, which are presented below in the form of eight theses.

  • Despite sharp criticism from John Backus and other researchers von Neumann (mandatory) language still are widely used and continue to hold strong, and in some areas – the dominant position. It is logical to assume that this or about this situation will continue in the future. A similar position is taken by other authors, according to which the mandatory languages ​​”in the foreseeable future will remain a dominant position in practical programming.”
  • In the coming century due to the further reduction of the unit cost of equipment, many personal computer screen, apparently to increase the size of the desk, which will facilitate the visualization of programming by allowing direct work with the drawings A1 or A0 PC screen on the principle of WYSIWYG – What You See Is What You Get (What you see is what you have). According to the hypothesis developed, this will allow better use of the solid angle and structure of the human field of vision, finally put an end to the systematic underutilization of the rich possibilities of the human eye, use the powerful reserves of simultaneous perception and thus significantly increase the speed and efficiency of the brain programmers and users. Given these considerations and the seriousness of the problem of productivity in programming, we assume that the expected increase in the size of screens will provide a powerful incentive for the large-scale replacement of the text in the visual imperative languages.
  • If we assume that the rendering imperative languages ​​is inevitable, it is advisable to carry out its not spontaneously, but according to a pre-planned and coordinated plan, one of the goals which should be considered as a partial unification of languages.
  • In this regard, the question arises: is it possible to unify the (at least partially) the imperative programming languages? Is there a possibility to allocate a certain invariant, which can be pre-entered in the composition of all or almost all of the visual imperative languages? From the perspective of the skewer method, any visual imperative language includes three languages: routing, command and declarative (see. Ch. 12).
  • The proposed unification of imperative languages ​​are not related to the current (text) and for the future (visual) language. The essence of the proposal is that all the visual imperative languages ​​should include in its membership the same trip language (skewer-language) and can be any differences in command and declarative languages.
  • Within the framework of the hypothesis developed skewer-language can be considered not only as an abstract model, but also as a logical invariant of any visual imperative language (including assembly language, but in the latter case, may require some modification of the skewer method).
  • Standardization dedicated invariant imperative languages ​​is carried out using standard skewer editors, the use of which shall be governed by the certification procedure agreed with the International Organization for Standardization ISO. Experience in the creation of national and international standards for flow charts and their widespread use gives hope for the success of the proposed venture.
  • Obviously, in principle, one can construct the compiler that converts the drawing skewer programs directly to the assembler and object code, without an intermediate conversion into the original text high-level language. It is possible that the predicted process visualization software and education on this basis a new generation of (visual) imperative languages ​​will create conditions under which such a direct compilation in many cases would be more preferable. In such situations, the concept of source code probably will completely disappear from the vocabulary of “imperative” programming, replaced the term source drawing program .

DISPLAY OF LOGIC and intensify intellectual activity

Thus we have shown that the visual syntax skewer-language is a visual logical calculus – calculus icons. In this case it is useful to make a few comments.

  • The fact of formalizing the system of visual images in the form of a logical calculus icons can seem to be regarded as proof of the complete failure “of the principle of absolute text.” In other words, the formalization of human knowledge is not limited to text form, but also includes visual representations. It is important to emphasize that visual formalization of knowledge is not a “product of the second-class”, it meets the most stringent criteria of mathematical logic, and in this sense, is a legitimate and full intellectual product. The highest intellectual efficiency is achieved by using synthetic method combines the advantages of textual and visual formalization.
  • According to the traditional view, the verbal-logical (left hemisphere) thinking different precision and clarity, while the figurative (right hemisphere) thinking there is something vague, intuitive and almost imperceptible. The results suggest that at least part of the abstract visual images can be converted into a perfectly strict form, split into separate mikroobrazy (icons), turned into a computer equipped with a menu and strict rules, allows you to build large and complex visual images of atomic mikroobrazov.
  • It is known that “the rich formal language of mathematical logic and successful experience with them created one of the objective conditions for the creation … of computers, now enjoys a very diverse range of formal programming languages.” This statement until recently was limited to the scope of the text paradigm and against logic, with regard to programming. The emergence of visual estimates allows to expand the framework and to extend them to a visual event.
  • The need for this is long overdue, since the theory in this matter behind the practice. With the advent of integrated CASE-tech computer drawings (eg circuit “entity-relationship”, the decomposition scheme, the scheme of data flows, and so on. D.) We purchased a number of remarkable properties. They have turned to the formal visual language accuracy. The computer can understand the exact values ​​of these drawings, store them in a form suitable for deep-processing, convert drawings into each other, to identify the discrepancy between them, and their incompleteness to ensure the integrity of the picture. And, most importantly, extracting relevant information from the drawings, the computer using the “code generator” receives the executable code. Thus, we can hope that in the future the traditional friendship of mathematical logic and computer science will no longer be limited to textual paradigms decrepit fence and spread to a wider visual field problematic.
  • Cognitive formalization of knowledge – a synthesis of logic-mate¬maticheskoy formalization and cognitive approach. The purpose of the method – to improve the comprehensibility of formal descriptions and complex problems by taking into account the actual characteristics of the intelligent person on the basis of the achievements of ergonomics. Above the author tried to demonstrate the application of the method of cognitive formalizing a live example – the development of the language of dragons. In Sec.1-15 systematically emphasized that creating a language DRAGON ergonomic considerations are the main, fundamental; It described a large number of specific ergonomic techniques, figuratively speaking, ergonomic bricks that build finished ergonomic shape of the tongue.At the same time, however, he remained in the shadow of the question whether the constructed language (more precisely, its visual part) is strictly formal characteristics? In this chapter, based on the calculation of icons, we can give a reasonable answer is yes, has.

    Thus, cognitive formalization of knowledge – is not a utopia, not wishful thinking or a dream of pink and workable method that can bring the desired fruits of increased productivity and ensure the human brain.

  • The logical formalization of knowledge, going back to Aristotle’s syllogism, which was first used to refer to the letter of concepts was a remarkable achievement of human genius. For two thousand years of existence, the logical science has achieved outstanding success. But here’s the paradox: calling himself a science of the laws and forms of human thought, the logic at the same time completely abstracted from the specific characteristics of the human mind and brain, studied psychology, neuroscience and ergonomics. In the early stages of human development, when intellectual tasks were relatively simple, and the number of knowledge workers is small, like ignoring it did not bring significant harm. However, today the situation has changed.
  • Avalanche complication of civilization processes led to the intellectual tasks previously unimaginable complexity that are at the limits of the human brain. The urgent need to intensify the intellectual property associated with this process requires the establishment of radically new forms and methods of intellectual work that could qualitatively enhance mental performance (brain) knowledge workers and students to improve the quality of intellectual interaction between people, to ensure the best possible protection from intellectual confusion, mistakes, confusion and misunderstanding, strengthen the effectiveness of individual and collective human intelligence. It seems that the formalization of the cognitive knowledge, combining the power of traditional mathematical and logical methods to develop the ergonomics (including psychology and neuroscience) accurate view of significant cognitive performance of the human brain and intelligence in a single integrated concept can to a large extent contribute to solving the identified problem.
  • The materials presented allow us to make educated guesses about the development of information technologies in the XXI century. With further improvement of productivity of computers lack the human brain will be a major deterrent to the growth of the efficiency of organizations and limiting the possibility of intelligent humanity.
  • It can be expected that the improvement of the mind, increase intellectual capacity of man will become a central issue of information technology. However, the existing theory and practice of information and computerization did not have an effective means to solve the problem. Hence the need for new theoretical approaches to use them to build a new kind of information technology – cognitive information technologies, a distinctive feature of which is that the increase in productivity of the brain is considered as the highest, the priority objective, which is subordinate to all other goals (taking into account the necessary compromises dictated by economic and other restrictions).
  • We believe that in the XXI century will return to the widespread use of information technology in cognitive science, engineering, education, medicine, defense, business, public service and other sectors that will significantly increase the intellectual potential and intellectual capacity of society and thus pave the surest way a new quality of intellectual life.

This is a huge, truly immense complexity of the problem, going far beyond the scope of this book. To solve necessary change in the consciousness: it is necessary to understand that the human brain has an enormous intellectual reserves that are currently not used, but which can and should involve using cognitive-ergonomic methods. Again, a reservation: the existing cognitive techniques are not sufficient for this, we need new approaches. Where to find them? According to the author, the materials in this book, though related to the particular case, however, are sufficiently common and can be the basis for the development – with the need to clarify – the new generation of formal cognitive-ergonomic methods.

CONCLUSIONS

  1. The contradiction between the modest intellectual abilities of an individual and an almost unlimited amount of knowledge, which he must acquire during their lifetime – one of the most dramatic contradictions of modern society based on knowledge. Today, science has no effective means to solve this problem.
  2. Out of the situation we see in total ergonomizatsii science and education, the purpose of which – to radically improve the visual forms of fixing knowledge, coordinating them with the subtle characteristics of the eye and the brain.
  3. Development of calculation icons speaks in favor of this hypothesis, and serves as an example that confirms the relevance of the new interdisciplinary direction – logic-ergonomic research.
  4. The spontaneous process of visualization of logic, which begins to unfold in recent years, should be based on sound ergonomic basis.
  5. A major obstacle to the realization of ideas ergonomizatsii knowledge is outdated notion that scientific knowledge in the visual-sensual images occupy a subordinate place and only serve to create a visual model of informal, drawings, blueprints.
  6. Proponents total ergonomizatsii science and education must fight on two fronts:
    • against the supporters of the principle of absolute text;
    • heralds against spontaneous visualization, who do not understand the difference between artisanal transformation of text into an image and scientific imaging techniques, based on a firm mathematical logic and ergonomic base.
  7. Ergonomizatsii important direction of science and education is the development of cognitive ideas formalization of knowledge and cognitive information technology, which, in our view, the future belongs.

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