"The creative act is the discovery of new meaning in a new context" (Amit Goswami).
"Creativity is the marvelous ability to catch mutually distinct realities and gain a spark from their juxtaposition" (Max Ernst).
"Simplification facilitates discovery (Gödel).
Creativity
The concept of creativity
Intelligence, in general, is associated with the ability to relate ideas or concepts. Creativity goes beyond intelligence, since it is the capacity to generate unsuspected new relationships in a given situation or problem, which produce a new vision, perspective, awareness or superior understanding. These new relationships usually take place as a "crossover" or intersection of different ideas or concepts.
The opposite of creativity is the mechanical, the repetitive and lacking in novelty, which leads to consciousness trapped in the habitual, the limited and the restricted . "Creativity is the essence of everything that is not mechanical" [Hofstadter, 1987].
Consciousness and creativity
Consciousness and creativity are two things that are interrelated:
The greater the awareness, the greater the creativity. For greater awareness implies a greater capacity to relate and, therefore, greater creativity.
Creativity produces consciousness. The united ideas or concepts are contemplated from a higher level, so that consciousness expands, rises. Creativity are "sparks" of consciousness or openings of new doors of consciousness.
Creativity and the two modes of consciousness
There are, as we know, two modes of consciousness (associated with the cerebral hemispheres):
Left-sided mode.
These are the functions of analysis, sequential, step-by-step reasoning, of handling known elements (from the past) to elaborate new ones.
Right-side mode.
These are the functions of synthesis, of comprehension and global recognition, of visualization of objectives and goals that have a future dimension.
In creativity, the consciousness of the right side of the brain intervenes, since the capacity to relate, unite, synthesize, integrate, unify, abstract, generalize, etc., resides there.
The creative flash
Normally, the creative process usually happens "all at once". And it is that the association of previously unconnected elements occurs suddenly, like a flash.
The explanation lies in the nature of the creative act, which is one of synthesis, that is, of the mode of consciousness of the right side of the brain. In this mode all the elements present themselves simultaneously. The fact that they appear suddenly is due to the fact that the change from one mode of consciousness, with predominance of the left side, to another mode of consciousness, with predominance of the right side, occurs instantaneously. At that moment the person "sees", there is intuitive perception, there is no rational process and everything appears clearly in his consciousness. Later it is possible to reflect the new relationships in a rational way, thus connecting the deep (intuitive) with the superficial (rational).
Creative ideas occur to us suddenly. Creativity is a discontinuous process, occurring as a sudden inspiration, of creation of a new meaning that occurs all at once because the synthetic, intuitive mode of consciousness intervenes. The famous episode of Newton's apple is an example of sudden inspiration provoked by the fall of the apple, which triggered his intuition and he suddenly glimpsed universal gravitation.
Creativity is not the result of a rational process. It is a sudden leap of consciousness, a new conception, the opening of a new door previously closed, or the opening of a new channel previously blocked. Creativity is a discontinuous leap, a leap that we can call "quantum" because of its analogy with quantum physics, where non-local phenomena of an instantaneous type occur.
An example of a sudden change of mode of consciousness is what happens when one is drawing in the left-side mode and switches to the right-side mode [Edwards, 1994] [see Appendix - The Spiral Development].
The conditions of creativity
For creativity to occur, certain conditions must be met:
Nonconformism.
Nonconformism or dissatisfaction is the engine for exploring alternative ideas and contrasting them with old ones in order to bring a superior vision or understanding.
Intermediate knowledge.
An initial set of basic concepts is necessary to be able to produce new ideas. On the other hand, too much knowledge can restrict creativity, as it is not easy to break free from already known and experienced ideas. The ideal is an intermediate knowledge of the subject or problem under consideration, that is, a position equidistant between complete ignorance and maximum knowledge.
Flexibility.
It is the ability to modify certain characteristics of a problem or situation to obtain different versions or to see it from different perspectives. Creativity is only possible when there is capacity for maneuver, reorganization and restructuring. This implies that the system or situation must not be closed in order to be expanded or modified.
Creativity techniques
Abstraction.
Abstraction is a movement of consciousness that frees itself from the concrete aspects of things to look for common, generic or universal aspects. We say that something is an abstraction if it represents several objects or phenomena, but none in particular.
It is evident that a system, the more concrete, the more limited it is. And the more abstract, by referring to a wider field, the more general or universal it is.
Creativity occurs in an abstract environment, by relating to or encompassing a broader conceptual area, by bringing out the hidden or underlying relationships between different elements.
Abstraction implies going deep. And through the deep, relationships can be established. And ultimately, with top-level abstractions, it is possible to relate all things. These ultimate abstractions would constitute the root of everything.
Abstraction is a filter that we apply to reality, which is complex, to make it more comprehensible and simpler. In fact, abstraction is the basic mechanism of all knowledge.
Abstraction is one of the complexity reduction techniques, along with modularization (the process of dividing a whole into parts) and projection (a technique that allows us to view a system with respect to a subset of its properties).
Integration.
Integration is the creation of a new concept from particular concepts, which encompasses, generalizes and synthesizes them. It is the general movement of consciousness from the particular to the general. It is the tendency of the mind to generalize in order to achieve higher level abstractions. In integration the component concepts retain their identity, coexisting with the integrating concept.
When two concepts unite or merge they produce a new higher level concept that is something more than the mere sum of the components. The result of the merger is then said to be synergistic.
Integration produces understanding. Put another way, to understand is to integrate, that is, to fit things into a larger, more general framework.
An important integrative mechanism is analogy or metaphor, i.e., the recognition of common structural or functional elements among apparently unrelated concepts. "Metaphorical perception is fundamental to science and involves bringing together previously incompatible ideas in radically novel ways" [Bohm & Peat, 1988]. Analogical thinking reflects the abstract similarities of objects. In analogy, emphasis is placed on characteristics or attributes, as they constitute a form of abstraction that allows the essence of things to be reflected. Many things may seem different, but if described in terms of attributes they are essentially analogous.
Unification.
Unification is different from integration. Indeed, integration refers to the existence or discovery of a higher-ranking concept that encompasses several particular concepts. Unification, on the other hand, is to consider several concepts under the same approach, in such a way that the previous concepts would be particular cases of the higher concept, the particular concepts being diluted in the unifying concept (i.e., they lose their identity).
Just as in integration the movement of consciousness is of the "down-up" type, unification is a mechanism of the "up-down" type, i.e., the application of a series of principles or definitions established a priori. These principles are the final result of the abstraction or elevating movement of the consciousness and are subsequently applied as a unifying mechanism in a descending process, allowing the fitting together of the different concepts or phenomena.
Unification is related to simplicity, that is, the use of as few concepts as possible. These concepts could be of low or high level.
If they are low level, comprehension and readability are sacrificed.
If they are high level, it is assumed that everything can be conceived by means of a few generic mental patterns, which give meaning to everything else.
Combinatorics.
One of the most widely used methods for creativity is the combinatorial method, which is a mechanism for obtaining new relationships. The most common combinatorics is the crossing of different concepts, which produces a new concept:
The more distant or different the concepts to be combined, the greater the creativity.
The more profound (abstract, generic or universal) the concepts combined, the greater the creativity. General principles help or encourage creativity.
The more concepts intersect or combine, the greater the creativity.
In the case that the concepts are opposite or complementary (those corresponding to opposite modes of consciousness), then the creativity is maximal.
A language, natural or artificial, is necessarily linked with the combinatorics of concepts. Webster's dictionary defines a language as "The words, pronunciation and methods of combining them used and understood by a community". The creativity of language is manifested in its combinatorial possibilities to obtain new concepts.
Now, the combinatorial criterion can be systematic or heuristic. In the systematic one, all possible combinations are explored, evaluating and selecting those of interest. In the heuristic one, only the combinations that a priori are known to be of interest are explored. The heuristic combinatorics is obtained from generic combinatorial patterns.
Exploration of limit concepts.
One way of looking at a problem or situation, during the exploratory process of possibilities or alternatives, is by generating limit states. This allows us to visualize the situation from extreme or borderline points of view, a process that broadens the vision of the problem or situation, while at the same time delimiting it.
Exploration of opposing concepts.
One way to explore boundary states is to consider contrary, opposite, complementary, or dual concepts, which provide a complete view from the two poles of consciousness.
Conceptual reflection.
Conceptual reflection is the application of a concept to one's own concept in order to obtain higher order concepts. In an ideal language, all its concepts must admit conceptual reflection.
Effects or consequences of creativity
Consciousness.
As the barriers that delimited isolated fields or concepts are broken down, there is a greater understanding, a new consciousness, a new meaning, a greater breadth and depth of vision and knowledge. Hence the exclamation "Eureka!" −which in Greek means "I have found it!"− of Archimedes.
Surprise.
A creative act initially produces surprise, and time seems to stop suddenly. This impression lasts for a certain time and then disappears, as the new situation is progressively assimilated.
Harmony and order.
Creative production is essentially the birth of a new order, of the generation of a new configuration and structure of a higher type. It is the consequence of going deep, for the deeper we go, the more order we find.
Simplification or reduction of complexity.
Creativity is not a more or less interesting facet to consider in problem solving. It is a real necessity, as it is the way to overcome the increasing complexity in many areas.
Creativity produces simplification or at least reduces complexity, bringing clarifying solutions to many problems, as a consequence of increased understanding and awareness. Consciousness and creativity always move towards simplicity.
Greater freedom.
The delimitation of concepts always involves a certain tension. When the boundaries between concepts fall down or when they fit into broader generic and simple concepts, there is a feeling of distension, of liberation, of greater freedom.
Greater effectiveness.
In a creative act, greater effectiveness is produced by expanding the framework of understanding and solution with divergent thinking. On the other hand, efficiency is produced within a delimited space and with convergent thinking.
Brain changes.
Knowledge, or learning in general, triggers new connections in the brain. But in moments of great inspiration and creativity the brain undergoes a sudden structural change, creating atypical, strong connections of a higher level than those produced by "normal" knowledge. This change produces the sensation of a new order, a new way of seeing reality, a new structuring of consciousness.
The creative flash has, therefore, its reflection at the cerebral level, since the neuronal network and the scheme of electric waves are altered [Hutchinson, 1990].
There is also a synchronization of the two cerebral hemispheres, as when an elevation of consciousness occurs when the two opposite modes of consciousness (the deep and the superficial) are united. This seems to be deduced from Jean Milley's experiences with biofeedback equipment [Brain/Mind, 1981]. This hemispheric synchronization is empirically correlated with a merging with the experience, an "entering into it." Instead of feeling separate and with limited awareness, one feels a merging with experience, with a sensory integration of the whole brain.
Methods of Creativity
There are many methods for idea generation and creativity. We highlight the following.
Lateral thinking
Lateral thinking is a technique created by Edward De Bono [2011] to stimulate creativity in problem solving. It consists of consciously creating provocative and absurd connections to stimulate the unconscious and contemplate or perceive the problem from new perspectives or different, unorthodox points of view. It is actually about breaking the rigid patterns of our concepts and traditional logical reasoning that limit our thinking, and introducing flexibility to look for new alternatives and possibilities.
De Bono uses the term "Po" (from "Provocative Operation") to refer to something beyond the "Yes" and "No" of traditional, conventional logic. With a Po we tried to relate concepts that were not consciously related. The Po's are all the more effective and powerful the simpler they are.
With a Po, with a provocative operation, we are bombarding (from one's own conscious) one's own conscious with its superficial ideas with resources from the unconscious, where all things are connected, to stimulate intuitive and deep thinking. A Po awakens and activates relationships, which in turn, in a process of resonance, activates other relationships, etc. In fact, many new ideas have arisen by mistake, chance, accident, or folly.
For De Bono there are two phases in thinking: 1) Perception, which is associated with a way of seeing the world; 2) Processing, which is the processing of that perception. Of the two phases, the most important is perception. With lateral thinking we expand our way of seeing the world. "Any one way of seeing the world is only one among many."
Both types of thinking (lateral and logical) are necessary. Lateral thinking tries to find new and original solutions. Logical thinking selects, orders and develops the new ideas obtained.
Synectics
Synectics is a discipline created by the inventor and psychologist William J.J. Gordon when he published in 1961 his book "Synetics" [Gordon, 1963]. The term "Synectics" comes from the Greek "synectikos", meaning "to join different things into a unified connection". Synectical thinking is the
process of discovering connections that link seemingly disconnected elements together. It is a way of joining elements of any kind to create a new intellectual intuition or consciousness. Synectics is applicable to all kinds of problems. It is universal.
Synectics is a theory and a method:
As a theory it studies the psychological mechanisms involved in creative activity. The creative process is fully analyzable, it is intelligible, it can be discovered, made conscious, trained and taught. The psychological mechanisms involved in the creative process are the same, regardless of the subject matter.
As a method it is a structured approach based on a procedure capable of increasing the chances of arriving at creative solutions to problems.
Synectics is based on the following principles:
Creativity increases when we know the psychological processes involved in creativity.
The emotional component is more important than the intellectual, and the irrational is more important than the rational. The emotional increases the chances of finding creative ideas.
We must make the known strange and the strange known.
Synectics uses several techniques:
Personal (or animistic) analysis. It is a fusion or identification with the subject to be treated in order to see it from the inside.
Direct analogy. It is about establishing relationships with subjects that have some degree of similarity. To make an airplane, study the flight of birds.
Symbolic analogy. It is to formulate synthetic statements of poetic or metaphorical type of the subject we are dealing with.
Fantastic analogy. It is about giving free rein to fantasy.
The morphological method
The morphological method (or analysis) is an analytical-combinatorial method created by the astronomer Fritz Zwicky. It is a general method aimed at solving problems and stimulating creativity. It is based on analyzing the essential elements that make up a problem and their combinatorial possibilities to generate new ideas. To do this, it is necessary to overcome prejudices, dogmas and any kind of limitation of thought and to evaluate the possible combinations.
A problem can be decomposed in many ways, depending on the aspects considered. Thus, the elements can be attributes, physical components, subproblems, parameters, structural dimensions, functions, procedures, etc. In general, the method refers to attributes.
The method consists of the following steps:
Define the problem in a clear and precise way.
Identify the most relevant attributes (variables) that compose it. They should be as independent as possible.
Identify the possible variants (values) of each of the attributes.
Create the morphological space using the possible combinations of the variants of each attribute. The morphological space is also called "morphological matrix" or "morphological box". The total number of combinations is called the "morphological product". For example, if we have the attributes A, B, C and the variants (A1, A2, A3), (B1, B2, B3), (C1, C2), the morphological product is 3×3×2 = 18.
Reduce the morphological space by eliminating partial combinations (of two or more variants) that are considered infeasible and also eliminating all combinations derived from them.
Analyze the remaining combinations and select those that seem best. The analysis can be performed randomly (choosing one variant for each attribute) or systematically, analyzing all combinations one at a time.
Once the best combinations have been selected, study their economic and technical feasibility.
Zwicky, a Swiss astronomer of Bulgarian origin, developed his method during World War II, while working on the design of an engine for jet aircraft. Zwicky made numerous contributions to astronomy. He was the first to postulate the existence of dark matter, coined the term "supernova," predicted neutron stars, the origin of cosmic rays, galaxies as gravitational lenses, and clusters of galaxies. His colleagues ignored his predictions, which were later verified.
Zwicky wrote several papers on the morphological method and a book in 1969 [Zwiky, 1969]. He claimed that many of his discoveries were made by the application of his method. "Morphological analysis is simply an orderly way of looking at things" [Zwicky, 1948].
The morphological method is a very powerful tool for generating a large number of ideas quickly and easily. It is a general method applicable to any problem and the one that generates the largest number of potential solutions than any other tool.
MENTAL and Creativity
MENTAL is designed with creative criteria, as it meets the conditions and criteria of creativity:
Abstraction.
Primitives are conceptual abstractions. They represent, by themselves, creative resources (generalization, particularization, grouping, substitution, representation, etc.).
Integration.
In MENTAL it is possible to integrate several concepts (the primitives) to create higher type concepts, such as functions, rules, objects, procedures, etc.
Unification.
MENTAL is a unifying language, with primitives established a priori, so it provides a universal paradigm, which blurs the boundaries between the different domains, which lose their individuality or identity. Ultimately everything is the same thing: the primary archetypes (residing in the deep) connect all things and manifest themselves as programming language, as mathematical language, as operating system, as web system, as metalanguage (to define new languages), as model of the mind, as philosophical language, etc.
To connect or relate different things it is necessary to go to a deeper level from which you see things as manifestations of that deeper level. Everything is connected at a deep level.
Combinatorial.
With MENTAL, creativity is maximal because it allows to combine and connect the universal semantic primitives without restrictions, being orthogonal (independent of each other) dimensions (or degrees of freedom). Therefore, creativity reaches with MENTAL its maximum expression, the maximum power, because the deeper the concepts are, the greater the creativity when combining them. Its combinatorial capacity is maximum. Each connection between instances of primitives is an element or factor of consciousness, which favors creativity.
Boundary concepts.
MENTAL contemplates limit concepts such as null expression, existential expression and universal expression.
Opposite concepts.
MENTAL is the universal integration of opposites on two levels: 1) In the primitives themselves, which integrate reductionism and holism, simplicity and complexity, science and humanism, etc.; 2) In their expressions, such as: operative and descriptive, qualitative and quantitative, structural and functional, real and virtual, exact and diffuse, etc.
Conceptual reflection.
MENTAL primitives are reflexive. For example, sets of sets, sequences of sequences, substitutions of substitutions, numbers of numbers, etc., can be defined. And derived concepts such as rules of rules, functions of functions, generic expressions of generic expressions, etc., can be defined.
Regarding creativity methods:
Lateral thinking.
In MENTAL the technique of lateral thinking can be used, because it allows to build unorthodox expressions such as: sum of functions, rules of procedures, imaginary expressions, etc.
Morphological method.
The "attributes" that can be applied at any time are the primitives.
Synectics.
With MENTAL the creative mechanisms, which are the combinations of the primitives, are made explicit.
Specific contributions
The use of MENTAL facilitates and stimulates creativity. It is a language that serves to make us aware of the dimensions of consciousness or universal resources available to us, which manifest themselves as creative resources that lead us to the discovery of new concepts. Among the specific contributions are a series of new concepts, including the following:
Semantic axioms (the universal semantic primitives).
Generic expressions. They allow the specification of functions, rules, objects, universal quantifiers, etc. In short, it is the primitive that allows integrating the different paradigms. It also allows the specification of shared expressions: linked, interlaced, self-interlaced, virtual, fuzzy, etc.
Derived concepts such as function, category, vector, tensor, matrix, infinitesimal, infinite, etc. All these concepts can be defined and expressed through language, without the need to use natural language. MENTAL is self-sufficient.
The generalization of concepts and predicative, modal and fuzzy levels.
Abstract space and time, abstract graph, abstract life and abstract vibration.
Qualitative magnitude, of the form f*quality, e.g., 0.7*high. A case of qualitative magnitude is the logical magnitude of truth, of the form f*V or f*F, e.g., 0.4*V.
Attribute of an operator. For example, +/v (vector sum), +/m (matrix sum), and so on. And also attributes of the sets of integers and real numbers: Z/+ (positive integers), Z/− (negative integers), R/+ (positive real line) and R/− (negative real line).
The definition of infinitesimal, which opens the way to the automation of the calculus of derivatives and the definition of infinitesimals of higher order.
Imaginary expressions, which can be of two types: operative and declarative. Examples of operative imaginary expressions are the definitions of the imaginary unit and the infinitesimal. Examples of declarative imaginary expressions are:
{a b}∈{a}, A⊂A, 3>4, etc.
A simpler, more consistent and generic notation for the contravariant operations of the x⊥y operation, "⊥" being a dyadic operator, would be as follows:
x(⊥')y // contrary operator on the right side
x('⊥)y // left hand inverse operator
For example, the exponentiation operation x^y:
x(^')y indica y√x
x('^)y denotes logyx
When the operation is commutative, the left and right inverse operators are equal.
Addenda
Serendipia (Serendipity)
It is a word coined by the English politician and writer Horace Walpole (1717-1797) inspired by the Persian tale "The Three Princes of Serendip". Serendip corresponds today to Sri Lanka (the former Ceylon). In the fairy tale, the three princes always made fortunate discoveries.
A serendipity is a fortunate and unexpected discovery or find that occurs by chance, coincidence or accident, when you are looking for something else.
Serendipities are frequent in the history of science. Three examples:
Archimedes' principle states that any body immersed in a fluid experiences a vertical upward thrust equal to the weight of fluid dislodged. This principle was discovered by pure serendipity when Archimedes was taking a bath and thinking about an issue raised by Hieron, the king of Syracuse.
It is said that Newton conceived his law of universal gravitation while in the shade of an apple tree. While he was resting, the fall of an apple caused him to reflect on the cause of the fall. Eventually, he concluded that the cause was a force, the same force that kept us "stuck" to the Earth and that kept the Moon in orbit around the Earth.
Oersted discovered by chance the connection between electricity and magnetism while lecturing (in 1812) on the conversion of electricity into heat. Accidentally placing a compass near the electric wire, he observed that when he turned on the switch to circulate the electric current, the compass needle changed direction. Subsequent experiments proved that moving electric charges produce magnetic effects.
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