Chapter 11

The IEML Semantic Machine

Having described the general properties of the IEML semantic sphere in Chapter 9 and the linguistic properties of IEML in Chapter 10, I will now describe the IEML semantic machine, which automatically constructs the mega-network of the semantic sphere and translates its nodes and links into natural languages. As shown in Figure 11.1, the semantic machine is the fundamental core of the IEML model of the mind. In order to clearly understand its role, it will be useful to review the different types of functions involved in modeling symbolic cognition.

11.1. Overview of the functions involved in symbolic cognition

11.1.1. Arithmetic and logical functions

According to the working hypothesis of the cognitive sciences, which I have fully made my own, it must be possible to model cognitive functions as arithmetic and logical functions. I will not insult readers by reminding them what arithmetic operations are. I will simply summarize the main operations of logical functions:

– Logical functions make it possible to manipulate sets of elements using union, intersection and symmetric difference operations. It is these set operations executed by logical automata that make it possible to automatically deduce, for example, that if all the elements of A possess property P and X is an element of A, therefore X possesses the property P.

– Logical functions also make it possible to correctly transfer truth between propositions. For example, if proposition X is true and proposition Z is false, then “X OR Z” is true, but “X AND Z” is false.

Since the mid-20th Century we have had programmable electronic automata capable of executing arithmetic and logical functions; for short, I will call them logical automata. They are increasingly miniaturized, distributed, interconnected and accessible in our everyday material environment.

The “great automaton” of the digital medium operates on a series of layers of encoding and protocols, the main ones of which are the following:

– digital encoding (0 and 1) allows logical automata to perform operations on numbers, characters, images, sounds and data in general;

– the operating systems of particular logical automata assign physical addresses to bits of information (0 and 1) in their local memory;

– the Internet protocol assigns universal physical addresses to logical automata, making it possible to operate networks or societies of automata practically independently of their geographic locations; and

– the Web protocol (HTTP, URLs, etc.) assigns universal physical addresses to data, which opens the way to the automatic, coordinated execution of arithmetic and logical functions on data distributed in the digital medium.

11.1.2. Hermeneutic functions

As we saw above, in the IEML model, ideas make up the contents of the mind, and hermeneutic functions (which categorize and evaluate percepts) are responsible for their assembly. The categorization function links a concept (formalized as a USL) and a percept (formalized as a URL), while the evaluation function determines the affect of the idea (which is formalized as a semantic current).

Now what about the calculable formalization of hermeneutic functions, i.e. their execution by logical automata? Since the affective dimension of ideas is modeled as a semantic current, whose value at a given time is indicated by an intensity and a polarity, i.e. by numbers, then it is calculable without major problems. With respect to the categorization of data by concepts, there are already all kinds of algorithms for this purpose in use today, which could be used or perfected in the Hypercortex. Categorization is therefore calculable. As for the multimedia content of URLs, it is already provided by the activity of Internet users, or produced and transformed automatically through such activity, for example, in massively multiplayer online games.

The main obstacle to the calculable modeling of the mind today lies in the absence of interoperable functions for generating and transforming concepts. The problem thus consists of formalizing the natural semantic functions represented in Figure 11.2 in a calculable way (to be executed by logical automata).

11.1.3. Natural semantic functions

We know that logical functions infer the truth or falsehood of propositions from the truth or falsehood of other propositions. But what do semantic functions do? They produce, recognize and manipulate concepts. The following are examples of semantic operations: (i) distinguish between the subject and object of a sentence; (ii) transform a verb in the past into a verb in the future; (iii) identify differences and similarities between the meanings of two complex discourses. More generally, semantic functions process the content or meaning of propositions, while logical functions process their truth value. I will first briefly discuss (since we have already analyzed them in the previous chapter) the natural semantic functions that the IEML semantic machine formalizes. The rest of the chapter will then be devoted to the description of the IEML semantic machine itself.

First, concepts, considered as categories or signifieds, are represented by texts, which are sequences of symbols or signifiers. But concepts are not the texts that represent them. We have no direct access to concepts except through the symbols that stand for them. A text represents a concept – and thus can categorize a percept in an idea – only because it belongs to a symbolic system or language that makes it possible to go from the text to its meaning. A concept is something abstract (a system of relationships) that can only be manipulated through a symbolic system.

Second, we cannot think about or know the identity (the meaning, the category) of a concept independently of the relationships of this concept with other concepts. There are no isolated concepts, no concepts that have no relationships of inclusion, intersection, participation, complementarity, opposition, derivation, etc., with other concepts. Thus concepts are by definition nodes or junctions in networks of concepts. In short, a concept is a semantic circuit.

In order to manipulate concepts or semantic networks (which is the role of the conceptual function as such), we must therefore be able to manipulate the texts that represent the concepts (which is the role of the textual function) and translate these texts into semantic networks (which is the role of the linguistic function). In short, there are three distinct but interdependent semantic functions: the textual function, the linguistic function and the conceptual function. Let us examine these functions one by one with the help of the diagram in Figure 11.2.

11.1.3.1. The textual function

The textual function (S) produces and transforms texts according to syntactically ordered arrangements, so that the texts that result from its operations can be decoded according to the norms of a language. This corresponds to Chomsky’s universal grammar, the theory that human beings have an innate capacity to manipulate symbols according to complex syntactic rules.

11.1.3.2. The linguistic function

To “understand” a text, i.e. to infer a network of concepts from it, the mind must possess (consciously or unconsciously) the grammatical rules and lexicon (dictionary) of the language in which the text is formulated:

– The dictionary makes it possible to identify the lexical units and situate them in a network of semantic relationships with lexical units that do not belong to the text (but that belong to the dictionary). It is only in this way that the lexical units can “acquire meaning”. The semantic network that situates the text units in a linguistic circuit external to the text is the paradigmatic network.

– The grammatical rules make it possible to link the lexical units internal to the text according to relationships such as verb–subject, noun–modifier, etc. Thus from the linearity of the text the mind constructs a network of grammatical relationships among lexical units that form sentences, and a network of relationships among sentences that form more complex propositions, and so on to the level of the text. This semantic network internal to the text is the syntagmatic network.

Typically, the linguistic function (B) starts with a text – a sequence of symbols – and arrives at a complex semantic circuit – a network of concepts – in which a paradigmatic circuit and a syntagmatic circuit are intertwined.

11.1.3.3. The conceptual function

The mind can in principle manipulate signifieds or categories – i.e. networks of concepts – abstractly, and thus relatively independently of the symbols through which the concepts are expressed. The fact that we are capable of recognizing that two different expressions designate the same concept is proof of this. The capacity to manipulate abstract categories, the conceptual function as such (T), corresponds broadly to the symbolic faculty at its least figurative: the capacity to reason, whether deductively, inductively, abductively, analogically, metaphorically, analytically, synthetically, etc.

11.1.3.4. The interdependence of semantic functions

Since the mind is capable of semantic computation, we can assume that it incorporates a natural semantic machine combining three sub-mechanisms:

– a textual machine that manipulates sequences of signifying symbols;

– a linguistic engine that transforms texts into semantic networks and vice versa;

– a conceptual machine that manipulates networks of signifieds or semantic circuits.

The distinction between the three types of mechanisms (textual machine, linguistic engine and conceptual machine) is itself a conceptual distinction: in the reality of human cognitive activity, the semantic machine gives rise simultaneously to the semantic functions, which can only function together¹. One of the main conclusions that come out of this discussion is that it is impossible to formally represent the manipulation of concepts without at the same time formally representing the semantic machine (which combines the textual, linguistic and conceptual functions) in its entirety.

I wanted to describe the mind scientifically, so I had to construct a calculable formal model of natural semantic computation, the structure of which I have just outlined. In the reality of the nature of the mind, as evidenced by human history, the semantic machine is sufficiently general and universal to be adapted to a wide variety of different languages and symbolic systems. To model this machine, I had to choose one particular symbolic system. As I stated above, most “natural” symbolic systems have emerged in the course of cultural evolution and do not lend themselves to automatic semantic calculation. History has seen the invention of a numerical notation system that can easily be used for automatic calculation (the positional notation system with zero, of which binary notation is only one specific instance) and notation systems that permit the automation of logical reasoning (starting with Boolean algebra). In the same vein, I was obliged to invent a notation system for concepts – i.e. a symbolic system – that would make it possible to automate the operations of natural semantic computation. This was the origin of the invention of IEML.

11.2. Requirements for the construction of the IEML semantic machine

The encoding and manipulation of concepts in the IEML model of the mind meets four main requirements.

11.2.1. Concepts must be encoded in IEML as semantic networks

First, the nature of concepts is such that they cannot be encoded adequately as numbers or points in ordinary geometric space. It is agreed that everything that is processed by means of automatic calculations in the digital medium must somehow be represented by binary numbers. Furthermore, it is always possible to design interfaces representing the universe of concepts in two- or three-dimensional space. I only want to point out here that concepts expressed by languages do not have the same structure as numbers or points in geometric space. That is why the IEML model represents concepts using paradigmatic and syntagmatic networks, i.e. as semantic circuits.

11.2.2. The conceptual, textual and linguistic functions of the IEML semantic machine must be inseparable

Second, as I pointed out above, since concepts are necessarily represented by signifiers belonging to a symbolic system, they cannot be formalized without formalizing the symbolic system they belong to and the semantic functions that manipulate all aspects of that symbolic system. In other words, in order to automatically manipulate the semantic circuits representing concepts, a semantic machine must be designed that also automatically manipulates texts and reciprocally converts texts and semantic circuits.

11.2.3. Concepts encoded in IEML must be variables of a transformation group

Third, one of my main goals is to describe the modifications of concepts and their relationships using coherent calculable functions, and to thus be able to identify symmetries and invariances. This is why the semantic circuits that represent concepts have to be variables of a transformation group². Only a transformation group on encoded concepts permits us to attain a semantic interoperability worthy of the name. It is clear that there are already a great many algorithms that perform semantic functions, but they do it today according to ad hoc methods that differ depending on the language, the area of application, etc. The issue in the current discussion is the automation of semantic functions by means of a general method, using interoperable algorithms and working with a universal semantic code. Hypothetically, these interoperable semantic algorithms belong to the class of logical automata, i.e. they can be effectively implemented in the digital medium.

11.2.4. Concepts encoded in IEML must be automatically translated into natural languages

The fourth and last condition, which arises from a practical requirement that needs no comment, is that the addresses of the system of semantic coordinates – that identify and represent concepts – must automatically be translated into natural languages.

I constructed the IEML semantic machine, a diagram of which is shown in Figure 11.3, in order to have a calculable mathematical model of the natural semantic machine (see Figures 10.2 and 11.2) that would meet the four requirements stated above. We will see that this abstract machine is also consistent with the properties of the semantic sphere described in Chapter 9 and the metalinguistic properties described in Chapter 10.

The goal of my undertaking was the semantic sphere, i.e. a scientific system of coordinates of the mind. I pursued this goal over many years, patiently manipulating ideograms and formalizing these manipulations mathematically or algorithmically, constantly going back and forth between empirical bricolage and theoretical formalization. I only “found” this semantic sphere by creating it, following a perilous path of constructions and deconstructions that led me to increasingly simple and powerful, and yet more complex, structures. I finally reached my goal only by modeling an abstract machine capable of automatically generating and manipulating the semantic sphere. This semantic machine can be broken down into three submachines: (i) the textual machine, (ii) the STAR linguistic engine and (iii) the conceptual machine that manipulates the semantic sphere.

As shown in Figure 11.3, the semantic machine is made up of three types of mechanisms (inside the rectangle at the bottom):

– the textual machine includes finite automata that manipulate USLs. These textual automata correspond to the traditional operators of regular languages;

– the STAR linguistic engine includes a set of finite automata that symmetrically transform USLs into semantic circuits translated into natural languages;

– the nodes and links of the semantic sphere are labeled with USLs. The conceptual machine includes finite automata that perform transformations, trace paths, measure distances and calculate similarities on the circuits of the semantic sphere.

In terms of mathematical structure:

– the set of USLs is a transformation group on which all operations on regular languages can be carried out;

– the set of circuits of the semantic sphere belongs to a transformation group on which all operations on graphs can be carried out; and

– the STAR linguistic engine is a morphism – a function – that goes symmetrically between the group of USLs and the group of circuits (there is one, and only one, semantic circuit corresponding to each USL).

11.3. The IEML textual machine (S)

11.3.1. Introduction to the textual machine

Let us first look at the textual machine (on the left in Figure 11.3). The textual function acts as the interface between the logical and the semantic functions. It ensures that the signifying texts that are used by the IEML semantic machine as the medium for signified concepts can be transformed by logical automata.

We know that symbolic cognition, by definition, involves the use of symbolic systems. Furthermore, a symbolic system is necessarily based on a signifying code. In order to be manipulated automatically, this signifying code has to work transparently with logical functions, which is why IEML is a regular language. It must also work with specifically semantic functions, which is why IEML is homologous to the structure of natural languages.

The textual machine, i.e. the syntax of IEML, can be compared to a system of phonology, writing or typography: it automatically produces and recognizes sets of sequences of six primitive symbols. These sequences are marked by recursive triplication: sequences of three symbols, sequences of three sequences of three symbols, sequences of three sequences of three sequences of three symbols, etc. The IEML texts (sets of sequences) are totally manipulable by finite automata because of their formal syntax, but they have no meaning prior to their linguistic interpretation.

11.3.2. The mathematical properties of IEML

Texts in IEML, i.e. syntactically valid expressions in IEML, are called USLs. IEML is a regular language³, which means it is optimally suited for all kinds of automatic manipulations. IEML texts (USLs) are sets of sequences of symbols. That is why the set operations symmetric difference and intersection define a transformation group on the USLs. The key point is that IEML encoding provides the interface between arithmetic and logical computation on binary data and semantic computation on concepts and ideas.

The fundamental structure of the IEML language can be described quite simply by the following five propositions:

– All valid IEML expressions are constructed from a basic alphabet of six primitives (T, B, S, A, U and E).

– A triplication operation (concatenation of three sequences) recursively constructs seven layers (from 0 to 6) of sequences of primitives. The sequences in layer 0 contain only one symbol.

For example, T belongs to layer 0, USE to layer 1, USEABEEEE to layer 2, etc.

– Categories are sets of sequences in the same layer (i.e. of the same length).

For example {USE, ABE, EEE, TTE} is a category in layer 1.

– Catsets are sets of categories in the same layer.

For example {{USE}, {ABE, EEE}, {TTE, TBE}} is a catset in layer 1.

– USLs combine from 1 to 7 catsets from different layers.

For example,

{

{{T,S},{E,A},{B}}

{{USE},{ABE,EEE},{TTE,TBE}}

{{USEABEEEE,ASEABEEEE},{TSEABEEEE}}

}

is a USL containing three catsets from layers 0, 1 and 2.

From this structure certain mathematical results follow that will be demonstrated in the chapter entitled “Semantic topology”, in Volume Two. The following six points summarize the main results, which guarantee that IEML can serve as the basis for the construction of a semantic machine:

– IEML is a finite regular language, which means – I repeat – that it is suitable for transparent automatic manipulation.

– A symmetric transformation group on the “textual variables” that are the IEML expressions can be defined. Operations of union, symmetric difference and intersection can be carried out on categories in the same layer and USLs in general.

– Semantic relationships between categories or between USLs can be represented by graphs called semantic circuits.

– Operations useful for the definition of semantic relationships – and therefore for the construction of semantic circuits – are automatable.

– The set of semantic circuits (the vertices and edges of which are identified by USLs) form a transformation group.

– There are formal calculable methods for measuring the distance between two vertices of a semantic circuit (including the distance weighted by the intensity of the semantic current) and for measuring similarities between circuits (using spectral graph theory).

What is the semantic relevance of the structure of IEML and the mathematical results that follow from it? It is clear, first of all, that it is possible to automate all kinds of algebraic functions in order to manipulate both USLs (texts) and semantic circuits (which explicate the meaning of texts). Beyond that, one of the main advantages of the IEML semantic machine is the possibility of automatically transforming USLs into circuits, i.e. automatically translating IEML texts into semantic graphs expressed in natural languages.

11.4. The STAR (Semantic Tool for Augmented Reasoning) linguistic engine (B)

11.4.1. Introduction to the linguistic function

Let us now look at the linguistic engine (in the center in Figure 11.3). The linguistic interpretation of IEML texts (USLs) is ensured by the grammatical rules and dictionary of the STAR linguistic engine. It has been demonstrated that this engine can be broken down into a finite set of finite automata. Providing a linguistic interpretation of any IEML text means transforming the IEML text (a punctuated sequence of signifiers) into a hypertext network – paradigmatic and syntagmatic – of signifieds that are readable in natural languages. The linguistic function automatically goes from a transformation group of texts (which are sets of sequences) to a transformation group of signified concepts (which are graphs of texts interpreted in natural languages). This is how the STAR engine automatically produces a semantic sphere common to users of the Hypercortex: the interoperable set of the hypertexts signified by the IEML texts.

11.4.2. Metalanguage

As we know, human cognition usually manipulates concepts using various symbolic systems, first and foremost natural languages. Due to their irregularities, however, natural languages cannot easily be processed automatically. It was to remedy this problem that IEML was designed as a regular language. In order to usefully play its role of semantic addressing, this regular language keeps the main structures that permit natural languages to represent concepts: layers of increasing complexity (morphemes, words, sentences, etc.), grammatical functions (subject, object, etc.) and grammatical classes (noun, verb, markers of case, gender, number, tense, etc.).

The linguistic engine of the IEML semantic machine can be broken down into two parts. It includes, first, a set of rules for automatically transforming IEML texts (USLs) into semantic circuits – paradigmatic and syntagmatic networks – translated into natural languages. Second, it includes a dictionary, i.e. a set of correspondences between IEML terms and concepts expressed in natural languages. The dictionary itself is a formal semantic circuit among terms.

The STAR linguistic engine may be compared to a theory, the axioms of which are contained in the dictionary and the inference rules of which make it possible – on the basis of the axioms – to interpret any IEML text as a semantic circuit translated into natural languages. I call the calculable linguistic function of going automatically from an IEML text to the semantic circuit that represents its meaning in natural languages semantic inference, and call the mechanism that performs this function linguistic engine. The automation of the linguistic function will be dealt with more extensively in Volume Two, but I will now present the general principles.

11.4.3. Rules for the construction of circuits

The rules of semantic inference can be divided into rules for the construction of syntagmatic circuits and rules for the construction of paradigmatic circuits.

The syntagmatic circuit corresponds to grammatical relationships internal to the USL. It will thus explicate, in the form of a graph, relationships among propositions (which correspond to the distinct categories⁴ of the USL), among the sentences of a proposition, among the words of a sentence and among the morphemes of a word.

The paradigmatic circuit corresponds to the interdefinitional semantic relationships that connect terms in a dictionary. In IEML, these can be stated as various kinds of relationships: etymological, taxonomic, symmetrical (relationships of possible substitution) and serial (graduation of words or expressions on linear semantic scales, such as concrete to abstract). The paradigmatic circuit of a USL will therefore connect the terms of the USL with the terms of the dictionary that define their meaning.

11.4.4. The dictionary

The rules for the construction of circuits can be compared to the rules of logical inference. As long as no proposition is declared true, it is impossible to deduce anything. That is why any logical theory is based not only on inference rules (how to go from one true proposition to another in general) but also on an initial series of true propositions (axioms), from which other true propositions (theorems) are inferred⁵. Similarly, in order for the IEML semantic engine to be able to infer the semantic circuit translated into natural language corresponding to a given USL, it is necessary to first define the meanings of certain terms and their networks of paradigmatic relationships. In order to start operating, a semantic inference engine thus needs to be provided with a dictionary that specifies the semantic relationships among its terms and their translations into natural language. The dictionary may be considered an “axiomatic” paradigmatic circuit.

11.4.5. The STAR dialect

The structure of IEML and its resulting mathematical properties make the construction of a large number of distinct linguistic engines possible. All these engines must meet the same requirement: that of automatically projecting a semantic sphere interpreted in natural language based on the regular IEML language. A specific linguistic engine may be considered a dialect of the IEML metalanguage, a dialect that necessarily incorporates choices with respect to the architecture of the semantic sphere. In reality, there is currently only one IEML dialect (in 2011), which is called STAR. From the point of view of its origin, IEML can be considered a generalization of STAR. As I had a practical objective, I first created a dictionary and rules for the construction of circuits. Only then did I define the abstract mathematical structure of the IEML syntax, which will eventually make it possible to construct other dialects. Neither the semantic inference rules of STAR nor the paradigmatic circuits predefined in its dictionary are absolute or objective: they are conventional principles for the interpretation of USLs. This convention aims to be universal, like many useful conventions⁶, but it is a strictly linguistic one that necessitates no particular interpretation of the data. To apply a metaphor I used in Chapter 7, the syntax of IEML may be seen as a machine and its semantics (STAR) as the linguistic operating system of this machine. In other words, the STAR linguistic engine establishes a particular interpretation in IEML, but it leaves users entirely free to categorize their data as they wish.

11.4.6. From USL to semantic circuit

After this general explanation of the functioning of the linguistic engine, I will now describe how the IEML model links ideas and concepts. Each valid IEML text (a USL) is a set of sequences of signifying symbols. The USL is transformed into a concept determined by the STAR engine. This transformation can be broken down into two logical steps. First, the USL is transformed into a network of USLs in the semantic sphere: the graph of USLs shown in Figure 11.4. Second, this network of USLs is translated into natural languages. The result, a network of USLs translated into natural languages, is a semantic circuit. Technically, then, in the IEML model, a concept is one-to-one correspondence between a USL and a semantic circuit. The concepts of the semantic sphere projected by STAR can then play their role as semantic addresses of ideas.

I make no claim to having completed the mapping of meaning with the STAR dialect in its current form (in 2011). The task will likely never be completed, and progress in the research program based on IEML will require cross-disciplinary and cross-cultural collaboration by many teams. All I have done is verify that it is possible to construct a system of semantic coordinates that can unify the nature of the mind within the computational framework of a transformation group.

11.5. The conceptual machine (T)

Once the semantic sphere is produced by the STAR linguistic engine, there is a finite set of finite automata (the conceptual machine: on the right in Figure 11.3) that transform the semantic circuits and trace pathways in them. The semantic circuits will be able to be used by collective interpretation games to produce, recognize and compare ideas and networks of ideas and to channel the circulation of semantic current.

11.5.1. The transformation of semantic circuits

Starting from the USLs that are provided as input, the STAR linguistic engine produces a coherent set of semantic circuits. The nodes of these circuits are USLs translated into natural languages, and their connections are explicit semantic (syntagmatic and paradigmatic) relationships among the USLs. I want to stress the fact that the circuits of the semantic sphere – representing concepts – are constructed regularly and automatically by the STAR engine from the IEML codes, the USLs. As a result, any transformation of a USL is reflected in a regular way in a transformation of the semantic circuit corresponding to that USL. Since there is a parallelism between the transformation of the USLs and that of the corresponding semantic circuits, it becomes possible to automatically manipulate concepts through the manipulation of texts encoded in IEML. In addition, the semantic circuits are variables of a transformation group⁷. The semantic sphere is thus not only a topological structure – a mega-network of concepts – it is also an abstract machine whose operations generate, transform and measure all the aspects of this structure. Of course, it is only because they are encoded in IEML – and because a STAR linguistic engine also exists – that concepts and their semantic relationships can be formalized as a transformation group. In short, the IEML semantic sphere makes it possible to address concepts by meeting all the scientific requirements for a system of coordinates of the mind.

11.5.2. The openness and complexity of the circuits of the semantic sphere

The IEML semantic sphere permits an intellectual openness and an unrestricted freedom of inter-conceptual movement. This is because the topology of the huge system of coordinates of the mind meets three requirements for semantic circuits: the first concerns their number, the second, their variety, and the third, their complexity.

The circuits of the semantic sphere permit a practically unlimited number of paths between two USLs. This means that for symbolic cognition, there is in principle no insurmountable divide, boundary or separation between two signifieds taken at random. Two concepts, whatever they are, can always be connected by a number of continuous series of semantic transformations, with these transformations modeling intellectual operations on concepts. The topology of the semantic sphere forms a single whole, and it makes universal communication among concepts, without which there is no free thought, possible.

Links (i.e. transformations) among the USLs of the semantic sphere can be created through an infinitely open variety of different functions. In particular, all the circuits that can be traced automatically in the semantic sphere are not (or not only) simple hierarchies of classes and subclasses. The same USL can be either the operand or the result for several different functions. This means that, from the point of view of pathways in the semantic circuits, each USL functions as a junction from which it is possible to choose not only the next node – the next destination – but also the next type of semantic transformation. In Volume Two, I will go into detail on certain functions of the construction of circuits.

Far from being limited to linear sequences, the paths of semantic current can branch out into graphs of indeterminate complexity. At the smallest scale of cognitive activity, that of the oscillatory rhythms of the central nervous system, it is likely impossible to consider more than one “idea” at a time⁸. However, our everyday experience creates movements of thought and relationships of meaning that do not necessarily occur sequentially. At least subjectively, we are capable of following several discursive threads simultaneously and performing certain activities in “multitask mode”. This is even more obvious for the collective intelligence of a community as it may be manifested in the dynamics of the use and collaborative transformation of its computerized system of knowledge management. In this case, if there is a common conceptual network – in the form, for example, of a thesaurus or ontology⁹ structuring a database – it is clear that, starting from a given concept, many conceptual paths can be followed simultaneously by the collective intelligence of the community. In general, for a living intelligence, the actualization of relationships among concepts – modeled as current flows in the IEML semantic circuits – takes the form of complex branching, even fractal rhizomes¹⁰. Effective intellectual circulation among concepts probably resembles the pulsations of asymmetrical lightning illuminating thick clouds of phenomenal data more than well-behaved hierarchies on an administrative organizational chart. Still, it must be possible to inscribe even the meaningful tempests of a brainstorming session or a lovers’ quarrel in the functional topology of the semantic sphere.

In short, the coherent set of circuits of the semantic sphere opens up practically an infinity of intellectual paths among an open variety of distinct concepts, according to an unlimited diversity of transformations along indefinitely complex sequential or parallel paths¹¹. In the model of symbolic cognition based on the semantic sphere, the movements of the mind can go in an infinity of different intellectual directions from a given concept, represented by a USL. Against this backdrop of limitless virtualities, however, nothing prevents us from deliberately inscribing semantic paths of limited number, variety and complexity in order to model specific cultural structures or intellectual operations. Freedom of thought is thus ensured. In addition, each step along a path, each link, remains precisely identifiable by the semantic coordinates of its starting point, the semantic coordinates of its end point and the automatable transformation that leads from one to the other. The scientific requirement of calculability is thus respected.

11.6. Conclusion

11.6.1. The unit of semantic information

The IEML semantic machine can be seen as the “missing link” of cognitive modeling. The first consequence of the formal existence of the IEML semantic machine is that there is no longer any theoretical obstacle to the calculable modeling of the mind in the digital medium, and thus to its reflexive scientific observation. Indeed, this machine ensures the calculability and interoperability of the hermeneutic and semantic functions. Since the circuits of the semantic sphere are variables of a transformation group, we have a universal system of coordinates that can contain the world of ideas. In the model of the mind that uses the semantic sphere as its system of coordinates, an idea is represented by a unit of semantic information (see Figure 11.5). A concept is encoded as a USL, which is automatically converted into a circuit of the semantic sphere and translated into natural languages. An affect is encoded as a semantic current (polarity, intensity) flowing in this circuit. Finally, a percept – multimodal data – is addressed as a URL.

The adoption of the unit represented in Figure 11.5 as the standard for the semantic information economy would make the digital medium the supporting structure of a Hypercortex, i.e. a universal cognitive calculator or a mirror of collective intelligence. The Hypercortex would be fuelled by public data on the Web and would be “programmed” by creative conversations through a wide variety of collective interpretation games.

11.6.2. The two faces of the semantic sphere

The IEML semantic sphere can be seen as having two faces. The first one expresses all the relationships of meaning among the texts (the USLs) of a calculable metalanguage. These texts can be manipulated according to semantic criteria and translated automatically into the natural languages supported by its dictionary. On this metalinguistic face, IEML presents a system of semantic notation capable of precise correspondence with natural languages, and thus with data. This aspect was discussed in Chapter 10.

The semantic sphere also has another face: that of a monadology of concepts. The USLs are the encoded addresses of the nodes of a hypercomplex semantic topology. Although huge and fractally intricate, the hypertext network of concepts is nevertheless a symmetrical system of algebraic transformations that can be manipulated automatically. This aspect was studied in Chapter 9 in Part 2, with more detail here in Chapter 11. The IEML semantic machine really does meet the requirements for scientific knowledge of the mind. Indeed, the semantic sphere constructed and surveyed by this machine provides symbolic cognition with an addressing system that is unifying, symmetrical, coherent and meaningful, while allowing for inexhaustible complexity.

As language and calculable topology, linguistic system for categorizing data and system of algebraic transformations, the IEML semantic sphere is the cornerstone of the Hypercortex: it makes it possible to go from logical calculation to semantic calculation and it opens the way to computational modeling of symbolic cognition. The semantic sphere emerges from the operations of a machine that formalizes human semantic functions and it organizes a perspectivist hermeneutic memory driven by an unlimited variety of collective interpretation games. Symbolic cognition then appears as an infinite but coherent nature, a cosmos that is indefinitely explorable by scientific means.

11.6.3. Directions of development

It is very difficult at this point to foresee all the applications of the Hypercortex based on the semantic machine. I can nevertheless indicate four probable directions of development.

First, we already have a common addressing system for data (URLs), but the organization of metadata is still opaque and fragmented. The Hypercortex will make it possible to augment all the processes of semantic collaboration. It will, first of all, enable us to overcome the compartmentalization that still exists in 2011, caused by natural languages, ontologies, social media platforms, search engines and in general by the big corporations of the Web that use cloud computing. Next, it will significantly augment the power and interoperability of calculations on metadata, since USLs and the semantic current are variables of transformation groups. The Hypercortex will therefore make it possible to more effectively practice: (i) collaborative semantic tagging; (ii) collaborative semantic filtering of data and individuals; and (iii) collaborative semantic search.

The second direction of development is semantic knowledge management, whether personal or collective. The Hypercortex based on IEML provides a perspectivist organization of accumulated knowledge that is suited to the multimedia digital memory and calculating power we now have available. We have to think simultaneously about hermeneutic freedom – the capacity to develop large numbers of functions for categorizing and evaluating data, functions that vary according to the traditions, interests and points of view of creative conversations – and about the capacity for interoperability, comparison and open exchange through a common system of semantic coordinates.

The third direction of development is simulation and modeling of individual and collective cognitive systems in the human sciences, of course, but also management, design, marketing, the design of collaborative games, networked art, digital storytelling, etc. Again, the key point is that cognitive models produced within the frame of reference of the Hypercortex, as varied as they may be, are generative, evolving and interoperable and can exchange units of information, data and functions.

Ultimately, we can imagine new types of interfaces, as yet unknown methods of navigation in data – and even in knowledge – that will likely take the form of massively multiplayer collective interpretation games and will be based on augmented reality technologies using pervasive computing and wireless devices.

In short, the Hypercortex will contain a new generation of socio-semantic automata that support the creation, exchange and appropriation of knowledge. The IEML semantic sphere will serve as technical support for a decentralization of computing, with each collective interpretation game using the common system of coordinates and the calculating power available in the “clouds” in its own way. Beyond technical advances, the Hypercortex will improve the productivity of a knowledge-based economy and will make it possible to refine collaborative strategies for human development adapted to a multitude of situations and contexts.

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1 The nature of the mind does not carry out computation that is purely syntactic, i.e. limited to the textual machine. The fact that natural cognition always encompasses conceptual (therefore semantic) computation is clearly shown by Brian Cantwell Smith in his Age of Significance [SMI 2010].

2 See the discussion of symmetry in section 9.4.

3 In Chomsky’s sense. See [CHO 1963].

4 The word category is used here in the technical sense it has in IEML: “set of sequences of the same length (or in the same layer)”; see section 11.3.

5 On this point, see Robert Blanché on axiomatics and the history of logic [BLA 1955, BLA 1970].

6 See the discussion of this point in section 5.3.3.

7 See the demonstration in Volume 2.

8 Discursive thought, like speech, is sequential. As Varela et al. point out, it is as if the structure of lived time is not continuous, but rather is a sequence of functional quanta. Francisco J. Varela, Eleanor Rosch and Evan Thompson, The Embodied Mind: Cognitive Science and Human Experience [VAR 1991].

9 The term ontology is used here as in computer science, meaning “a formalized network of concepts used as the basis of logical calculations by programs” and not in the metaphysical sense of the general study of being.

10 I recall here that the concept of rhizome was developed philosophically by Gilles Deleuze and Félix Guattari in the introduction to A Thousand Plateaus [DEL 1987b]. The rhizome provides an image of thought characterized by active a-centric multiplicities and reticular dynamics that cut across hierarchical organization and classificatory tree structures.

11 A glimpse of this model can be found at the beginning of Michel Serres, Hermès I, La Communication [SER 1969].