(translated by J. Harbeck and M. Hess)

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1. Intelligence exists. (in Plato’s sense)

1.01 For the theory of intelligence quotient, intelligence is an observable. (in Heisenberg’s sense)

1.1 Intelligence quotient measures intelligence in the following fields : mathematics, sciences, philosophy and literature.

1.2 The term intelligence in (1) is identified with these in (1.1) via the method of isomorphism. (in Sidis’sense)

1.3 There exists a normed classification of intelligence ; it corresponds to the scale of intelligence quotient.

1.31 This normed classification measures not only quick-wittedness but also reasoning power.

1.4 In the scale of intelligence quotient, there exist critical phase changes which correspond to qualitative aspects.

2. The fundamental values of critical phase changes are equal to : 1/1000, 1/1000000, 1/1000000000 (in sense of rarety) i.e. 150, 176, 196 in sense of intelligence quotient.

2.01 The qualitative aspects of this fundamental values respectively correspond, in a sufficient but not necessary manner, to the notions of : gifted, genius and universal genius.

2.1 The gifted is a singularity in the cognitive map of humanity.

2.2 The genius is a generic singularity in the cognitive map of humanity.

2.21 The genius is a creative gifted.

2.211 The creative act, via the thought, is the sine qua non condition of his existence.

2.22 For the cognitive dynamic, the genius is an attractive point.

2.3 The universal genius is an essential singularity in the cognitive map of humanity.

2.31 The universal genius is a genius whose existence, via his work, transforms humanity.

2.32 For the cognitive dynamic, universal genius is a superattractive point.

2.33 The universal genius is necessarily altruist.

3. Archetypes of gifted, genius and universal genius: Achilles, Ulysses and Prometheus.

3.1 Paradigms of genius: Champollion, Chomsky, Descartes, Feynman, Hawking, Newton, Nietzsche, Ramanujan, Voltaire and Wittgenstein.

3.2 Paradigms of universal genius : Archimedes, Aristotle, Dostoievsky, Einstein, Galileo, Goethe, Leibniz, Pascal, Socrate and Vinci.

4. There are correlations between the concept of intelligence and those of culture, thought and discovery when those are extreme.

4.1 If the intelligence quotient is higher than 150, we note a correlation between intelligence and culture. As if starting from this value the individual were to use an enriched intellectual substrate.

4.1.1 The verbal tests, not limited in time, are effective to measure this correlation.

4.1.2 These tests giving access to encyclopaedic knowledge, their cultural aspects or the mental projections of their creators cannot in any case be negative. In the same manner, the apparent cultural difficulty is transformed into a heuristic difficulty.

4.2 If the intelligence quotient is higher than 160, we note a correlation between intelligence and thought. As if starting from this value the individual could carry out face : speed of the intelligence and power of the thought.

4.2.1 The space and numerical tests, not limited in time, are effective to measure this correlation.

4.2.2 Intelligence and thought are different: one is innate and fluid, the other is acquired and crystallized.

4.2.3 We can learn how to think, not to be intelligent.

4.2.4 The fast tests measure the simple intelligence and the tests not limited in time measure the complex thought.

4.2.5 The intelligence is a raw material that the thought structures.

4.2.6 The thought is the language of the intelligence.

4.3 If the intelligence quotient is higher than 176, we note a correlation between intelligence and discovery. As if starting from this value the individual tested the need for using his intelligence to discover.

4.3.1 Only the extreme tests have the capacity to measure this correlation.

4.3.2 The spirit of synthesis generates the need for creation.

4.3.3 The discovery is the finality of the intelligence.

5. The group is superior to the sum of its parts.

5.1 Awareness of the scarcity of the cognitive singularity implies the necessity of a structure.

5.1.1 A group structure emerges from the the sum the elements of the group. (in the sense of Galois)

5.2 The topology of the group is neuronal or interconnected.(in the sense of Changeux)

5.3 Following the example of the theory of beams, for the group, each element illuminates the others. (in the sense of Grothendieck)

5.3.1 The combination of algorithmic abstractions are transformed in the group into a global abstraction.

5.3.2 Group synergy engenders a global, unified influence. (for the group)

5.3.3 This influence, by way of a gnoseologic infringement, generates a heuristic.

5.3.4 This heuristic is a paradigm of non-uniform (creative) reasoning (in the sense of Hofstadter.)

5.4 The group is saturated with “g”. ( in the sense of Spearman)

5.5 The group is a place of brainstorming.

5.6 If the group reaches critical mass, then it becomes a place of creativity and discovery.

5.7 From an ontological viewpoint, the memory of the group is self-similar. (in the sense of Mandelbrot)

5.8 If the group is Promethean, then it becomes a model of humanity.

5.9 The idea of the group is identified with that of society.

6 . Society is a mental system.

6.1 Society is an open structure. (in the sense of Eco)

6.2 Society is multidisciplined in accord with 1.1.

6.3 Society follows the teleological principal.

6.4 Society is conceived of as a center of inquiry whose principal goals are:

6.4.1 The study of intelligence. (in the sense of Jensen)

6.4.2 The study of complexity.

6.4.3 The study of the foundations of knowledge.

6.4.4 The study of irreversible processes. (in the sense of Prigogine)

6.4.5 The recognition of patterns by way of a global perception.

6.4.6 The inquiry into the isomorphism of concepts, laws and emergent properties. (in the sense of Bertalanffy)

6.4.7 The inquiry into invariant concepts.

6.4.8 The creation of generic cognitive models by mathematics.

6.4.9 The creation of paradigms by linguistic formalizations. (in the sense of Kuhn)

6.5 The society follows the principals of globalism.

6.5.1 Its approach is holistic.

6.6 The society is an existential meta-proof of the existence of the g-factor.

6.7 The Work creates Being.