"To reach the truth it is necessary, once in a lifetime, to detach ourselves from all received ideas and rebuild anew, and from the foundations, our whole system of knowledge" (Descartes).
"Manage problems; accept nothing as an article of faith, look for clear and distinct ideas,
trust in yourself" (Descartes).
Origin
This work is a divulgation, extension and generalization of the Doctoral Thesis "MENTAL, un Lenguaje Generico de Especificacion de Paradigma Semantico" ("MENTAL, a Generic Semantic Paradigm Specification Language"), presented on May 8, 2003 at the Facultad de Informática of the Universidad Politécnica de Madrid.
But the story begins much earlier and had several phases:
When I started my thesis, the topic I chose was Object Oriented Programming (OOP), a topic that was (and still is) very much in vogue at the time. The object paradigm apparently promised to be the "definitive" programming paradigm.
After a relatively short period of time, I realized that the OOP paradigm was not universal, that it was just another programming paradigm (like the imperative, functional, logical and relational paradigms). It was then that I decided to design a universal programming language that could express all possible programming paradigms: the classic ones and others of more recent appearance such as aspect-oriented programming, event-driven programming, agent-driven programming, constraint-driven programming, etc. During my professional life I have had to learn a multitude of different computer languages. The idea of a universal programming language was a project that, if fulfilled, would be of enormous importance because it would affect the foundations of computer science.
I then began a period of reflection in search of a minimum set of concepts that would form the basis of computer programming. These concepts should be simple, not decomposable into other concepts and generic or universal. They should also possess the maximum combinatorial flexibility to express new concepts, as well as facilitate creativity.
The result of this search crystallized in a language that I called "MENTAL", because it was essentially a language of the mind and consciousness based on a set of orthogonal universal semantic primitives (independent of each other) that could be considered as "semantic dimensions". This language represented a universal programming paradigm, capable of expressing all particular programming paradigms.
As these primitives were of a supreme level of conceptual abstraction, I discovered that they were also applicable to mathematics. That they were, in addition to a computer language, a mathematical language and that they constituted a new common foundation for mathematics and computer science. In short, the boundary between these two sciences was blurring.
Mathematics has lacked solid foundations since 1931, when Gödel's incompleteness theorem appeared. And computer science has always relied on mathematics.
Later I intuited that the primitive universal semantics could be considered primary archetypes (or archetypes of consciousness) by uniting opposite or dual aspects: semantics and syntax, quality and quantity, simplicity and complexity, theory and practice, language and metalanguage, the descriptive and the operative, the generic and the specific, the real and the imaginary, the finite and the infinite, the continuous and the discontinuous, the objective and the subjective (internal world and external world), etc. In this way, language acquired a transcendental dimension: as the language of consciousness.
I also discovered that the primitive universal semantics were philosophical categories, and that they had certain analogies mainly with those proposed by Aristotle and Kant. But, unlike the traditional philosophical categories, the philosophical categories of MENTAL constitute a language, since they can be combined with each other without restrictions.
I also realized that MENTAL constituted a universal foundation of the formal sciences (sciences of a rational, systematic and coherent type) such as mathematics, logic, computer science, artificial intelligence, systemics, etc. A science cannot be founded on itself; its foundations must be sought at a higher (meta) level.
I also discovered that MENTAL, besides being a universal language, was the universal grammar sought by Chomsky, an innate grammar present in all human beings. And that it was also a model of the mind, or rather a metamodel of the mind because it is not a concrete model.
Later I became aware that MENTAL, because of its profound character, offered a privileged point of view that allowed to solve, simplify or clarify many problems of the formal sciences, and even of philosophy and psychology.
Finally, I discovered that MENTAL was a universal model and that it represented "the Magna Carta of possible worlds", that is, a unified, privileged and transcendental way of seeing everything, including the real world as a particular case. In short, that MENTAL represents the concepts of the highest level of abstraction necessarily present in all possible worlds.
In short, MENTAL is the result of an evolution, based initially on some very simple concepts that have led me, like Ariadne's thread, to a transcendental discovery, to the Minotaur, to the power that resides in the depths.
MENTAL is, indeed, a language. But it is not just another language. It is a mother language, a universal language that has no formal or syntactic (superficial) grammar, since its grammar is semantic (deep) and, therefore, inexpressible. From this language all possible particular languages arise.
The original thesis has been improved, while maintaining its spirit and philosophy, in several aspects:
The MENTAL language has been refined, eliminating unnecessary complexities, always seeking the maximum possible simplicity.
New applications have been added, both in mathematics (category theory, geometric algebra, vector algebra, etc.) and in computer science (new programming paradigms, operating systems, semantic web, etc.). In fact, this work can be considered as a rewriting, from new foundations, of mathematics and computer science.
New fields of application such as artificial intelligence, systemic, cybernetics, robotics, etc. have also been included.
The universalistic properties of MENTAL have been included, such as: ideal language, fractal, bootstrap, symbolic, local, multidimensional, transdisciplinary, etc.
Finally, comparisons with other universalist systems that have appeared throughout history have been included.
Motivation
Several factors have been involved in the conception of MENTAL:
First of all, my training as a theoretical physicist. Physics seeks conceptual unification through a minimum set of laws to explain the diversity of natural phenomena. In this sense, physics is the most universal of the natural sciences. I have been particularly inspired by the so-called "new physics", i.e. the conceptual challenges of quantum mechanics and relativity theory. A key aspect is that of dimension present in the string theory of quantum physics and in the theory of relativity, for when dimensions are considered, physical laws are simplified. Similarly, the "dimensions" of MENTAL make mental laws simple.
MENTAL has been conceived in the search for the maximum possible conceptual simplicity. I am convinced that "what is not simple is ill-conceived" and that behind the apparently complex lies an essence that is necessarily simple. I fully identify with Gregory Chaitin when he states: "I am not interested in complicated ideas. I am only interested in fundamental ideas". And I add: these fundamental ideas must necessarily be simple.
Secondly, my professional experience as a computer scientist. For many years I have suffered the drawbacks and limitations of programming languages: their diversity, their complexity and their semantic gap, that is, the existing gap between the human way of thinking and the language of machines. This has motivated me in the search for a simple, humanistic and universal language.
Thirdly, my interest in the subject of consciousness, especially the role played by the two cerebral hemispheres, in order to achieve a unified consciousness, where the particular (left hemisphere) is based on the general or universal (right hemisphere). In this sense, it is linked to universalist paradigms such as the holographic and fractal paradigms, considered the paradigms of the "new era". And this new era needs a universal language and a universal paradigm.
Structure of the work
The work emulates all theses, which begin with an abstract. In this case, there are two distinct abstracts: a "General Summary of the Work" and a "Summary of the Language". The reader should start with these two chapters, which will give an overview, before addressing the content of the work.
The section "Problematics" describes the main problems related to mathematics, logic, computer science, linguistics, physics and life, as well as the problem of consciousness.
The section "Fundamentals" describes the universal principles that underlie reality: the principle of descending causality, the principle of duality, the dialogical principle and the principle of economy, as well as consciousness as a universal foundation and as a new paradigm of science. It also includes three universalistic systems: the model of universal semantic primitives, the primary archetypes and the philosophical categories.
The section "MENTAL Language" exposes this language as a solution to the above-mentioned problem. It includes a description of the primitives, derivatives, as well as the different expressions and techniques.
The "Applications" section is related to applications in different domains: mathematics, logic, computer science, artificial intelligence, cybernetics, systemics, etc. The most representative ones are included. In fact, all formal sciences should be rewritten from the semantic-linguistic point of view provided by MENTAL.
The "Properties" section describes the different properties or universalistic aspects of MENTAL.
The "Union of Opposites" section describes the pairs of opposite or dual features of the language.
The "Comparisons" section compares MENTAL with different universalist system proposals presented throughout history.
Each chapter may include:
Addendum.
These are additional, secondary or complementary contents.
Bibliography.
Given the diversity of topics covered, a bibliography is included in each chapter, which consists of bibliographical references associated with the text (specified in square brackets) and recommended bibliography. Square brackets are also used to refer to other parts of the text. Thus, square brackets indicate references, both internal and external. The Internet bibliography ("webgraphy") does not normally include the addresses of web documents (unless it is the home page of a website), because they often change, so it is preferable to locate them from the title and/or author by means of a search engine.
This work has a didactic character. The first to learn was the author himself. In writing there is an extraordinary feedback process that clarifies knowledge and produces an elevation of consciousness. Some quotations:
"There is no better way to learn about anything than to write a book about it" (Martin Gardner).
"When I am interested in knowing something I don't know, I decide to write a book about it" (José Antonio Marina).
"Writing is the deepest way to know life" (Francisco Umbral).
From the didactic point of view, the work has a modular and highly structured content, including this Prologue. In addition to the usual hierarchical structure for the different sections, the contents of the sections frequently make use of lists (numbered or not, depending on the case) to indicate properties, attributes, aspects or characteristics. All this is done in order to present the concepts as simply and clearly as possible, and to facilitate their reading and understanding.
Compared to the literary or linear style, the structured style has great advantages:
It allows isolating or differentiating concepts or ideas, exposing them, bringing them to light. Literary style obscures them, buries them, hides them within a continuous text.
It is more didactic, more visual, easier to grasp and digest as it is offered in "pills".
It is easier for the author to write. And for the reader it is easier to read.
It allows to locate the contents more easily.
They bring us closer to consciousness, for consciousness is order.
Armonizes the two modes of consciousness: that of the left hemisphere (linear) and that of the right hemisphere (visual, global).
It favors creativity, which is a discontinuous process of "conceptual leaps" or leaps of consciousness.
Mandalas
Each chapter of the work includes a mandala in its header, which has a function that goes beyond mere aesthetics. Additionally, images have been included that evoke universality, totality and consciousness as a union of opposites or duals, especially fractals and symbols.
A mandala is a figure of circular symmetry that symbolizes or represents the universe, the totality and the internal and external unity, where the center stands out, symbolizing the source (unmanifest) of all that exists (manifest). Mandalas are a way to connect with the universal, with the totality and thus approach the consciousness of the essential unity of all things. Mandalas activate, when contemplated, the right side of the brain, elevate consciousness, connect us with the depths of our being, with the unity, the totality, the timeless, where there are no borders. Mandalas are really doors to higher states of consciousness.
The mandalas in the work are made using elementary and universal symbols (circle, square, star-shaped polygon, etc.). Many mandalas have a fractal structure. A fractal is a figure in which a graphic pattern is repeated recursively at each level. Symbolic and fractal mandalas have even more strength, as they connect with the inner and the outer, as mind and nature have fractal structure.
All the mandalas in the work are made with the same program, a program that is simple and parameterized, where each parameter represents a dimension or degree of freedom. Each mandala corresponds to specific values of the parameters. Given the infinity of shapes that can be generated, the program is a perfect metaphor for MENTAL, that is, the combination of a few simple basic patterns (geometric archetypes) produces a great diversity and complexity of shapes. Moreover, MENTAL is a fractal language.
The process of generating mandalas is the search for beauty, order, harmony, attunement to wholeness and unity. It is a search for consciousness through geometry, which is the science that unites mind and nature. The mandala generation program can be considered as an authentic tool of consciousness.
In addition, mandalas introduce a factor of balance between text (analytical) and image (synthetic), that is, the two modes of consciousness converge. And mandalas serve to permanently remind us that MENTAL is a universal language, of totality, of consciousness, of the profound.
Prerequisites
A general background in mathematics and a basic knowledge of the world of computers, especially what a programming language means, is sufficient to understand the content of the book.
Access to content
The work has perhaps turned out to be excessively extensive, almost an encyclopedia. It is paradoxical that a simple language such as MENTAL, which can be described in a few pages, needs such a large development. This is justified by the great diversity of applications included to verify the universality of the language, and its enormous philosophical and psychological repercussions. The work combines the characteristics of book and encyclopedia, textbook and essay, as well as technical and philosophical work.
The reading of the work need not necessarily be sequential or complete.
It is important to initially have an overview of the content, an objective that is achieved with the General Summary of the Work and the Summary of the Language.
The reader who, for practical purposes, wants to know only the language, can go directly to the "MENTAL Language" section and skip (or read lightly) the previous sections.
Regarding the "Applications" section, readers can focus on the ones that interest them the most, ignoring the rest. For example, a reader interested in computers will logically be interested in computer applications, and will skip the rest of the applications.
The sections "Properties", "Union of Opposites" and "Comparisons" allow readers to delve deeper into the language. Here readers can also focus on the chapters of greatest interest to them.
Acknowledgments
To my constellation of family and friends for their interest and moral support. I am especially grateful to my brother Pepe (now deceased) -a convinced Jungian and whom I consider my intellectual mentor- for his guidance and advice. Without his influence and his knowledge, especially the concept of archetype, which plays a key role in this work, this work would probably not have been written.
To the following people from the Faculty of Computer Science of the Universidad Politécnica de Madrid:
Professors Rafael Gonzalo Molina and Valentín Palencia Alejandro, for their unconditional support in bringing the thesis to fruition.
Darío Maravall, director of the Artificial Intelligence Department when the thesis was presented, also for his support and confidence.
Each of the members of the tribunal that judged the thesis, for their assessment. In particular to the president, Professor Luis Laita de la Rica.
To Pablo Rubio Pérez, engineer by profession and mathematician by vocation, for his comments and suggestions about MENTAL, as well as for passing on to me his discovery of the generalized Pythagorean theorem for multidimensional objects.
To José Ignacio Sánchez Andrés, professor of mathematics, for his mathematical and universalist comments and observations.
To my nephews David Rodríguez-Roselló Torres and Iván Rodríguez-Roselló Muñoz, for their advice on the structure of my web. David provided the hosting for my web.
My thanks to all the authors who have preceded me. I must especially highlight the influence of Plato, Kant, Frege, Wittgenstein, Russell, Turing, Gödel, Jung and Chomsky.
Finally, my thanks to a universalist technology, the Internet, without which this work would have been impossible to write.
