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I have written this document on ideometry from the works of the research group, “General Evolution Research Group” (GERG). The very first publications on ideometry date back to 1997-1998. In my opinion it is a new research field that is still very little known to researchers and the general public. Some of the more recent developments in ideometry are presented here. They are surprisingly original and relatively easy to read. One of the aims of ideometric research is to make science as a whole accessible to all, in a comprehensive, in-depth way, whilst dealing with scientific ideas in general.


We know that several technologies are currently experiencing extraordinary growth which brings about tremendous human development. What does science tell us about this phenomenon?

Firstly, according to science, this human development was preceded by three major evolutions, in the broadest sense of changes producing new entities over their duration:

The three great ideas of productive evolutions 

Evolution of the Physical Universe (EU) =>> Evolution of the Living world (EL) =>> History of the World (HW)

Each of these evolutions is composed of units, the combinations of which make up the evolutionary base:

The ideas of constituent units (complete structures)

Atom =>> Cell =>> Human being

The symbol “=>>”, made up of a line which stretches out into an arrow, represents an increase without quantitative measurement of complexity and organization. It expresses the fact that, for example, the cell is a system made up of a very large number of atoms with multiple functions. This is why it is known as a “complexification” symbol.

On occasion, chevron marking will be used to explicitly separate the idea from the assumed reality to which it refers, e.g. the idea of the atom may be marked <atom>. In some cases, the idea set in chevrons will act as the meaning for a sequence of ideas. The point here is to mathematize such sequences of ideas so as to better understand their meaning.


A general category theory

We use the function F(x) to represent the passage from one category of scientific ideas (in the sense of the category theory in mathematics; see Appendix) to another. It can be marked using the complexification symbol, such that

the relation A  =>> B equals the equation F(A)  =  B.

The expression F(f) represents an ideometric correspondence from two associated scientific ideas within the same category to the same type of association in a second category. In ideometry, this type of binary correspondence serves as a functor for a general category theory.

So using the symbols and correspondences from the first table:

EU  =>>  EL  =>>  HW

The algebraic formula gives the following:

F(EU) = EL   and    F(EL) = HW

The category theory generalized in this way, makes it possible to highlight a structure of ideas, in this case an evolution from constituent complete structures, i.e. the <atom>, the <cell (biological)> and the <human being>. We can therefore see that an invariant ideational structure is found in physics, biology and the social sciences. As will be seen later, there are many other ideometric structures, which are very discreet, or even hidden. Together they may form a surprising image.


Ideometry as a new type of language

As we have seen, ideometry initially presents itself as a new type of mathematics. It is also a new type of language in the strongest sense of the word, in particular as a vehicle for information and for shaping thought.

To demonstrate this, let’s look at the sequence of distinctive units below. These units do not only appear as the bases of a type of evolution, but also as the elements of languages that are very different from each other. This is obvious in the case of phonemes, which are the most simple elements of human languages. It is the same as far as biology is concerned, where nucleotides are the molecular elements making up DNA. As for elementary particles, they can also be considered as elements, the structures of which carry a wealth of information, so as a sort of language of purely physical complexity. Let us consider the extensions to this as follows:<

Three types of distinctive units… plus a fourth:

Elementary particles (quarks, leptons, bosons, etc.)  =>> Nucleotides (or nucleobases: adenosine, cytosine, etc.)  =>>  Phonemes (vowels, consonants, etc.; /a/, /ə/…; /p/, /m/, …)  =>> Scientific concepts (<atom>, <vertebra>, <missing mass problem>, etc.)

(chevrons implied)

This sequence represents a gradation of complexity. Nucleotides are large molecules, much more complex than elementary particles. At the next level phonemes presuppose biological organs, often much more complex than the cells which make them up. Then from physical bodies to biological beings, logically one moves to the next level of complexity, to the simplest human productions like scientific ideas. These presuppose a very complex infrastructure that is appropriate for research in human societies.

Ideometry, in which the objects of study are scientific ideas themselves, therefore appears as a type of language with a higher order of complexity. This makes it possible to describe the fourth term of the sequence of complete structures, which is (global) humanity, as the object of this new type of language. Moreover this language has been given the evocative name of “language of the Gods”. Of course, this name raises all sorts of problems. For the moment, let us stick to this construction and its coherence.

Comment: The fourth column displays chevrons so that the concepts within appear as objects in this category whereas, in the previous columns, the concepts shown are components of the theories in question.

All three sequences mentioned above make up a structure in an ideometric table.

Ideometric table of the common structure of ideas for the three major types of evolution, and a fourth column to be confirmed

 <Language>   1) Particle physics   2) Genetic code    3) Human language  4) Ideometry 
Distinctive unit Elementary particles Nucleotides Phonemes Scientific ideas
Complete structure Atom Cell Human being Humanity
Evolutionary development   Evolution of the physical universe Evolution of the living world History of the world Global human development

(Chevrons implied)

As mathematical category theory already does for mathematics, ideometry could constitute a new language for science, as a more general, simpler and more powerful alternative to the languages that current scientific disciplines generally dispose of.


Ideometric calculations

Ideometry makes it possible to calculate ideas. It involves equations to find the value (meaning) of an unknown scientific idea using other known scientific ideas.

One of the general kinds of ideometric calculation is to proportion according to the rule of three: “A is to B what C is to D”, as in the very simple example: “x is to 10 what 10 is to 20”; what is the value of x?

This kind of calculation is the basis of ideometric calculation in general. It is formulated in at least four ways: A, B and C as three scientific ideas, in the form of exact analogies:

“A is to B what B is to C”, or

A / B  =  B / C, or, with an extra direction, in the form of an ideometric sequence:

A  =>>  B  =>>  C

or in an equivalent algebraic form such that

F(A) = B  and F(B) = C

Two types of exact analogy

Arithmetic analogy Analogy of ideas
 x is to 10 what 10 is to 20 x is to <cell> what <cell> is to <atome>
 x  =  (10 / 20) ∙10  = x = (<cell> / <atom>) ∙ cell =
 ½ ∙10 F(<cell>)
 x  =  5 x = <human being>

Let’s consider an exact analogy, which up to now has not been mathematizable but which can be with ideometry, i.e. that of the effective (E), the effectively possible (EP) and the really possible (RP)For example, for a young child, say about two years old, it is really possible to learn to read but it is not yet effectively possible for him. Normally it will become so when he is of school age. Then, one could observe that he has effectively learned to read.

Thus the relationship between what is really and effectively possible,

RP / EP,

conceptually equals the relationship between what is effectively possible and effective,

EP / E

and thus

RP / EP  =  EP / E

In words, this is formally translated as: the really possible is to the effectively possible what the effectively possible is to the effective, for example as far as learning is concerned for the child. It follows that the relationship between the effective and the potential is an invariant ideometric structure through some real-time moments .


Usefulness of ideometric calculations

Ideometric calculations may help research in several ways, including by:

  • Finding out new concepts in a disciplinary field based on other research fields
  • Playing a useful role in the teaching and popularization of sciences and philosophy
  • Serving scientific and technical predictions through the extension of ideometric sequences

These three types of use are outlined below.

Ideational numbers

After natural, rational, real, complex and other numbers come ideational numbers (French: idéels; German: ideell).

Ideational numbers logically complete the series of historical extensions to number categories: natural numbers N, integers Z, rational numbers Q, real numbers R and complex numbers C. Ideational numbers I would therefore come next. They come in the form of a “< [scientific idea] >” and they include, for example, the ideational numbers <electron>, <basalt> or <archeopteryx>, and also <unit of measurement>, <1>, <2>, <3>, etc., and all the numbers already recognized. Ideational numbers are both qualitative and calculable, therefore measurable and therefore … quantitative! Their meanings lie in the ideometric structures which are preserved by complexification functions such as F(x). The Universe of Complexity is one of the best examples of such a structure.


The Universe of Complexity

Current scientific ideas delineate a global reality which can be called the “Universe of Complexity”, so as not to confuse it with the “Physical Universe,” which is the object of study of physics alone (more particularly modern cosmology) because it is based on the mathematical models used in physics alone. A general cosmology which takes into account all the ideometric data, would suggest seeing our universe rather as a representation based on what we know about everything that is real.

pdnd image biosphère mtl


In general, a dynamic system changes its state over time, and an equation makes it possible to understand this in accurately from its initial state. This is also true even if the evolution is defined as discreet, therefore a sequence of distinct states, time itself taking the form of a dotted line. In this sense the Universe of complexity is a dynamic system in ideometric terms. Let us assume that P is the physical sciences category of ideas and represents the initial state of the idea of a discreet dynamic system (recurrence calculations), which is a general mathematical research object, B is the biological sciences category of ideas and H is the social and human sciences category of ideas. So we have

B = F(P) and H = F(B)

H = F2(P);

These three equations represent both the complexification process and the evolution duration ideas. F(x) describes an ideational process of representing what we believe we know about the real world, with the Universe of complexity being seen as a dynamic system which evolves from an initial state. The ideometry of this dynamic system allows the most exact actual representation possible, while serving as a base for the study of structures preserved by appropriate functors or morphisms. These structures enable us to see that the basic units have common properties which we can retrace and explain in ideometric language.

The triple equation succinctly expresses the following points:

1) General mathematization of science is possible;

2) Ideometric calculations promote the progress of science as a whole;

3) There is an invariant structure L in F(x), x = P, B and H.

These points are developed or illustrated below.

pdnd image pondichéryMatrimandir

Structure L

There is an unprecedented structure of ideas L (L for language), which is common to all current science and which is invariant and clearly identifiable in the main disciplinary fields, as is shown in the three tables below.

The invariant structure L through the sciences (rows 1 to 8)

<Language>  1) Particle physics  2) Genetic code 3) Language  4) Ideometry 
1) Distinctive unit Elementary particles Nucleotides Phonemes Scientific ideas
2) Complete structure Atom Cell Human being Humanity
3) Double articulation of the basic units Elementary particles/atomic nuclei Nucleotides/amino-acids Phonemes / morphemes Ideas / sequences of ideas
4) Signifier / signified Particles/atoms and other material objects DNA/proteins, cells and other organisms Acoustic images/words, speech, person Set of ideas/GAP, humanity
5) Presupposed interactivity Four basic interactions Molecular interactivity Sensory-motor capacity Mathematical discoveries/mathematical applications
6) Evolutionary development Evolution of the physical universe Evolution of the living world History of the world Global development of human societies
 7) Expression of the possible Expression of effectiveness (e. g. in quantum mechanics) Effective potential  (case of genetics) Real potential  (case of realizable utopias) Real potential of mathematics
 8)  <Effective actions> of <language> Spontaneous reduction (effective decoherence) Effective appearance of forms of life Effective (human) action Effective mathematical application

Ideometric table of ideas on types of consciousness:

Physics  Biology  Human and social sciences  <Science> 
Form of consciousness  Quantum reduction of a state of matter Perceptual consciousness (case of animal consciousness) Linguistic consciousness (case of human consciousness) Scientific thought (current state of knowledge)

(Chevrons implied)

Structure L appears as the common abstract form in each of the columns. The first column entitled <Language> best expresses some of its components. There are others which do not appear here (see the ideometric model of the child) and certainly many others will be discovered. Be that as it may, structure L really seems to be closest to the truth concerning what we can know about ourselves, and ourselves in terms of humanity.

Columns 3 and 4 of the three tables are the starting point for the model of the child applied to global humanity. The task now is to supplement them with many details on the development of the child in interaction with his environment and surroundings, and, through ideometric correspondence, use this to understand current humanity and its probable development better. The model of the child appears as a complex, inexhaustible structure, the relevant elements of which appear in parallel with the progress of current studies on the young child, particularly infants from 18 to 24 months, who experience extraordinary development in their ability to acquire language.




Notes on structure L:

  • Generalization of the idea of double articulation: The double articulation of basic units (Row 3: phonemes/morphemes), which was first defined in linguistics by André Martinet, is generalized here and becomes the idea that there are two basic units for a given scientific field, i.e. the unit of meaningfor the objects of the discipline and the constituent distinctive unit from which the units of meaning are themselves determined. The relationships between these two types of unit are apparently determined arbitrarily. For example, in physics the units of meaning are atoms (or atomic nuclei, which comes to the same) as constituent units of all material physical and chemical objects, and the distinctive units are elementary particles. Calculations on the movements of atoms are carried out independently of the laws governing elementary particles. In the case of ideometry, the sequences of ideas carry a meaning and may form a thought concerning what is real that stands independently from existing scientific ideas. These ideas only act as signifiers.
  • GAP (Global Action for Pedagogy) (4throw, 4thcolumn) are actions (global projects, manifestos, etc.) that use the Internet to advance humanity from all scientific, ethical, ontological, and other points of view, the self-organization of ideas being the main source of information. Several examples of GAP are given on my website, Agorathèque ( .


The ideometric model of the child:

The idea of the child (of infans, a child who does not yet speak) was already included in evolutionary development and language learning ideas. This model consists of a structure of ideas including ideas linked to the development of a very young child of about 12 to 24 months, who represents current humanity ideometrically due to his specific relationship with language. From Row 1 of the table, structure L allows us to see ideometry as a new type of language which “Humanity” is learning.

Infans Infans

The development of the model of the child

The tables for structure L may serve to deepen our understanding concerning human development in general. Columns 3 and 4 of these tables (its nine rows) particularly, make it possible to start to develop the model of the child so that it can, by ideometric correspondence, allow us to begin to understand the development of the whole of humanity as it appears today, as it will develop in the near future, and then in the distant future if possible. This is a simple introduction to the simplest use of this model, which is extremely complex.

Condensed extract of the triple table of structure L

<Language> 3) Human language  4) Ideometry 
1) Distinctive unit  Phonemes Scientific ideas
2) Complete structure Human being Humanity
3) Double articulation of the basic units  Phonemes / morphemes  Ideas / sequences of ideas
 4) Signifier/signified Acoustic images/words, speech, person Set of ideas/GAP, humanity
 5) Presupposed interactivity Sensori-motor capacity Mathematical discoveries/mathematical applications
 6) Evolutionary development History of the world Global development of human societies
 7) Expression of the possible Real potential (case of realizable utopias) Real potential of mathematics
 8) Effective actions of language  Effective (human) action Effective mathematical application
 9) Form of consciousness Linguistic consciousness (case of human consciousness) Scientific thought (current state of knowledge)

(Chevrons implied)

Firstly the table shows that the phonemes that the child learns to recognize and pronounce correspond to scientific ideas as basic distinctive units of intellectual structures in the case of humanity. Humanity discovers ideometry and starts to use it scientifically. At this point in his development, the child also discovers the units of meaning that are morphemes (Row 3). They correspond to the ideometric sequences that humanity is now discovering through and from you, the reader (!), as indicated by <Effective (human) action> in Row 8. At the following level of complexity, the child discovers sentences and speech, i.e. the independent structured sets of meaning. The exchange of several phrases, or word phrases, heard or pronounced by a child of this age, corresponds to the discovery or application of ideometric tables. A suitable example is therefore this introduction to ideometry, as a set of meanings discovered or applied by researchers in general. Contrary to what one might think, the sensory-motor development of the child does not correspond to the exploration of planetary or extra-planetary space for current humanity, but rather to a sort of abstract space in which objects and mathematical theories act as modes of perception for the child. Thus physical space corresponds to what the child perceives from inside his body, and research and mathematical discoveries correspond to the child’s explorations in his surrounding environment.


Some comments on the method used

In the table of structure L, the rows correspond implicitly with a time scale, from the start of the physical universe to current humanity, via the emergence of life and Homo sapiens. From an ideometric point of view, however, the ideas in a single row have appeared in a more or less contemporary way. For example, let us take the distinctive units of physics – elementary particles – and those of biology – nucleotides. The two are scientific concepts of primary importance. The standard model of particles was developed after the middle of the 20th Century, and then formulated in a stable way during the 1970s. As for molecular biology, its development goes back to the 1930s and this theory reached maturity also in the 1970s. The elements of an ideometric sequence are not always so strikingly concurrent, but they should belong to the same global configuration of scientific ideas. They also have similarities in terms of their relevance and their degree of importance in the theories considered. When the presence of an “unknown” is observed in an ideometric structure, i.e. a place left vacant, it is often relevant to look for what is as fundamental and coincides as much over time, as what is before or after the unknown, or in the case of a table, above or below the unknown, whilst taking into account overall coherence.

However, if ideometry is used to extend a sequence towards the future, the vacant place should be found based on what the sequence “says”, i.e. based on coherence, and taking into account the marked differences between the ideas of one era and the previous one. These differences are distinguishing marks and the “meaning” itself, if there is one, can only be understood based on the most marked difference that can be imagined. Contemporary ideas are frequently understood in this way, in relation to what we understood in previous centuries.


How can other elements be found using an ideometric table?

Suppose we want to exploit the ideometric structure L further by looking for new elements located at a certain place in its descriptive tables. For example, say we wish to find two new ideometric correspondences concerning the <presupposed interactivity> by the child-humanity in the exercise of speech. These would therefore appear in the last six cells of the following table:

Extract from the table of structure L

Structure L 3) Human language 4) Ideometry
1) Distinctive units Phonemes Scientific ideas
2) Complete structure Human being = Child (12-24 months) Current humanity
3) Double articulation of the basic units Phonemes/morphemes Ideas/sequences of ideas
4) Signifier/signified Acoustic images/words, speech, person Set of ideas/GAP, humanity
5) Presupposed interactivity

Sensory-motor capacity

Discoveries/mathematical applications


(Chevrons implied)

The six question marks correspond to missing elements which could serve as specific cases concerning <Interactivity>, <Sensory-motor capacity> and <Discoveries/mathematical applications>. The following is fairly representative of acceptable answers:

5,1) Phonemic interactivity Recognition and pronunciation of new phonemes Discovery and propagation of new scientific ideas
5,2) Comprehension and use of semantic elements of language Comprehension and use of new words Discovery and application of sequences of scientific ideas

Six new elements of the table are shown. Firstly,<phonemic interactivity>, which is the idea of <exchanging sounds with other people>. Then

the <Recognition and pronunciation of new phonemes> in correspondence with the <Discovery and propagation of new ideas>, etc. The six ideas are woven into the table in a coherent, original way. Taken as a whole, this may help researchers to understand ideometry and its subsequent developments.

When we grasp the meaning conveyed by this type of table, we can coherently find other corresponding elements, and a large number of researchers will be able to participate, whatever their chosen field(s).



The general category theory

The general category theory studies the structures of scientific ideas in general, in disciplines such as physics, biology and mathematics, but also, philosophy, and human and social sciences. Furthermore it applies to the ideas of all research disciplines in general, in a unifying manner.

The study of idea categories has been driven by the existence of conceptual or mathematical structures which cut across some aspects of all disciplines, even though they are unaware of each other. These structures often take the form of exact analogies, including several mathematical analogies in physics, and also some conceptual analogies between the physical sciences, the biological sciences and the human and social sciences.

The definition of the general category theory consists primarily of setting out categories of scientific ideas. For example, the ideas of physics form one category, that is one algebraic structure whose objects, known as ideas, are concepts, theories, hypotheses or problems, etc. from physics. It is assumed that this definition is clear and accurate enough to allow researchers in general to obtain interesting results.

The abstract definition of ideometry is primarily modeled on the definition of mathematical object categories. A category of scientific ideas is made up of the data from a class of such ideas and the correspondence between these ideas, known as ideomorphisms. Therefore let us set out a function F: C → D of a category C to a category D, which associates a scientific idea F(X) of D to any scientific idea X of C so that any ideomorphism f:  X → Y of C, is associated with an ideomorphism F(f): F(x) → F(y) of D, which preserves the structure of C, i.e. which includes a neutral element F(IdA)= Id(Fa) and which preserves the composition: for all objects X, Y and Z and morphisms f: X → Y and g: Y → Z of C, F(g • f) = F(g) • F(f).

In ideometry, C and D are defined as two fields of scientific ideas, for example physics and biology, X and Y as two scientific ideas from a single field of ideas, for example <elementary particles> and the <atom>, an ideomorphism (ideometric morphism) f or g as a formal association of scientific ideas.


Natural transformations

Another essential aspect of the general category theory is what is known as natural transformations. Undoubtedly their importance stems from their usefulness in studying the frequent, fairly obvious, but poorly understood character of certain fundamental relationships of mathematical objects with each other. For the general category theory, this basically involves the different ways in which the functions of scientific ideas interconnect.

So let us define natural transformations in such a way that they might be useful for the development of ideometry.

For two categories of scientific ideas and ideomorphisms C and D, we first define Ideas(C), all the ideas of C, and ideo (D), all the ideomorphisms in D. Then we define two functions F and G of C in D; we call natural transformation of F in G, and we note m: F → G, an application m of Ideas (C) in Ideo (D) verifying:

1)         for any object A of C

m(A): F(A) in G(A);

2)         for any ideomorphism f: A → B of C,

we have

m(B)F(f)  =  G(f)m(A)

Example: It is possible to check that the two functions corresponding to the properties of being one constituent unit of an order of reality and being a basis for productive evolution are linked to the function applying a type of evolution in a type of higher complexification of evolution, so as to make up a natural transformation.

 An implicit structure in physics, biology and social sciences
Natural transformation of correspondences between two orders of reality:

<constituent unit of an order of reality>
<evolution specific to an order of reality>

The ideomorphisms of ideas from physics and those of biological ideas are once again the ideas of other categories of ideomorphisms, which represent structures of ideas. Ideometric natural transformations highlight the structures they preserve, which can be presented in sequences or in tables of ideometric sequences. It appears that structure L represents a set of features from several natural transformations.

Posted online on January 29, 2016 (first version)