"The computer has produced a paradigm shift. The computer is a stupendous new philosophical concept. We can only understand something if we can program it." (Gregory Chaitin)
"Computer science is more than the science of computers." (Edsger Dijkstra)
"Computers change everything" (John L. Casti)
The Search for a Universal Formal Language
Humanity has always sought the foundation of reality in the form of the primary or fundamental concepts from which all others are derived. These concepts were sought mainly in philosophy, mathematics, psychology and linguistics.
These primary concepts also called "universal semantic primitives" would be independent of each other, but should constitute a language through the combination of these concepts. This language would not be a particular language, but the "mother" language of all languages, a universal language in which the primitives would be degrees of freedom. Therefore, this language would not have a concrete grammar, but would have a semantic grammar, a grammar based on the combinatorics of the primitives and which would serve as the foundation of a hypothetical universal science or meta-science. And finding a universal language would imply finding a universal paradigm and a "theory of everything".
A universal formal language is needed, with precise semantics and syntax. In reality, this search is philosophical: the search for the principles or foundations of things, for primary categories or concepts, and how these concepts combine to describe all reality and possible worlds.
Throughout history there have been numerous attempts to extract the essence of reality in the form of a universal language, such as the Ars Magna (Raymond Lully), the Mathesis Universalis (Descartes) and the Characteristica Universalis (Leibniz), but they were only generic proposals, without becoming true formal languages. There have only been two formal languages that tried to reach the ideal of universality: the Conceptography (by Frege) and Principia Mathematica (by Russell and Whitehead). Both were attempts to ground the universal in logic, attempts that ended in failure.
In recent times, a large number of new ways of looking at the world have emerged, new scientific theories, which call into question orthodox scientific approaches: chaos theory, catastrophe theory, cognitive science, fractal geometry, fuzzy logic, holographic paradigm, morphic resonance, synergetics, complexity theory, etc. The hypothetical universal language must also be able to express these new paradigms.
Science has only dealt with the superficial, with the phenomenal, but it is necessary to transcend the superficial and go to the deep level to found the hypothetical universal science, the mother science, the meta-science, the science that serves as a foundation for all the others.
The progress of science is both centrifugal and centripetal. It is centrifugal because it develops new theories and applications in different disciplines and domains. It is centripetal because it is always searching for the principles that underlie everything. This second challenge is the biggest and the main one, because all new advances and developments must be connected and grounded through the deep. This tendency is most notorious in physics, with the search for a "theory of everything", a theory that unifies and explains the diversity of phenomena in the universe.
Philosophy
Already the ancient Greek philosophers searched for the supreme categories of things hidden behind the diversity of reality. This search basically began with Plato (5 categories) and Aristotle (10 categories), but has continued up to the present day. The last attempt to identify the categories of reality was made by Gödel.
According to the Platonic doctrine, there are abstract entities that have an independent existence in a superior world, the world of ideas. Physical objects are imperfect manifestations of these ideal entities. The abstract is the superior. The concrete is the lower. True reality is to be found in the higher world.
Philosophical categories are supposed to be independent of each other. The problem with philosophical categories is that they do not form a language. If they did, then this language, by relating the supreme categories of reality, would be the universal and ideal language.
On the other hand, analytic philosophy tries to find in natural language the reflection of the deep structure of reality. The philosophy of ideal language tries to find, discover or construct an ideal language that serves to solve or clarify philosophical problems. The problem of language (natural or ideal) is the most important philosophical problem. Language is the foundation of all philosophy. This language-centered conception of philosophy has been called the "linguistic turn" in philosophy.
Analytical psychology
Analytical psychology has also searched for the deep patterns that govern internal and external reality: the primary archetypes. Jung (psychoanalyst) and Pauli (physicist) set out to find a "neutral language" based on primary archetypes that would serve as a foundation for the physical and psychic worlds. They only succeeded in identifying "number" as one of the primary archetypes.
Mathematics
Mathematics, as it is conceived today, cannot be the universal formal language sought for several reasons:
Because it has been unfounded since the appearance of Gödel's incompleteness theorem in 1931.
Because it lacks a formal language, although many mathematical symbols (arithmetic, logical, set theory, etc.) have become de facto standards. Mathematics is an open language; anyone can use any notation they wish, as long as they explain its meaning.
Because mathematical notation is two-dimensional. We need a linear language that can be processed by a computer.
The physical world is concrete and perceptible. The mathematical world is abstract, formed by concepts that can only be perceived through the mind. However, the numbers of arithmetic and the points of geometry are not present, objectively, in nature. But they have acquired through their use throughout history a degree of objectivity that allows us to consider them almost as concrete elements, even though they are abstract.
Mathematicians of all ages have tried to "extract" the essence of reality in the form of abstractions. Historically, the first mathematical abstraction was the concept of number. This concept was followed by others: sets, sequences, functions, categories, etc. Mathematics is intended to go beyond reality. Mathematics does not study what is, but what can be. Mathematics opens our minds to possible worlds. The physical world is only one among the infinite possible worlds.
There are an infinite number of mathematical theories, branches or sub-disciplines: arithmetic, algebra, Boolean algebra, set theory, propositional logic, predicate logic, modal logic, geometric algebra, universal algebra, category theory, model theory, etc. All these theories are particular, separate paradigms without a common root. There have been attempts to generalize, universalize or unify all these theories, but so far no unifying theory has emerged, no universal paradigm that serves to ground mathematics.
The latest attempt has been the theory of categories. It is based only on objects and morphisms (arrows) between these objects. A morphism is an entity (of a higher type than objects) that makes an object A correspond to another object B, but it does not specify the concrete meaning of "correspondence", the semantics is open: it can be a function, a process, a sequence, a link, a communication, a transformation, etc.
It may seem surprising, to the uninitiated or specialized, but mathematics currently lacks a solid theoretical foundation since the appearance of Gödel's incompleteness theorem in 1931. In essence, this theorem proved that mathematics cannot be grounded in itself and that it needs a higher level of abstraction.
In the face of the complexity that makes intricate mathematical theories, with an esoteric notation, inaccessible to the common people, a simple, intelligible and practical theory is necessary, with the minimum number of concepts of supreme simplicity and abstraction. These concepts must be the foundation of a universal language.
Linguistics
Noam Chomsky was the great driving force behind modern linguistics when he invented mathematical linguistics, the application of mathematical formalism to describe language grammars. The grammatical language is based on a few primitives that make it possible to express rules describing infinite possible sentences.
Chomsky also postulated the existence of an innate universal grammar, a common structure in the minds of all human beings. A deep grammar that manifests itself in the various surface languages.
Chomsky's last proposal is the Minimalist Principle (MP): universal grammar must be based on a minimum set of general or universal principles that can be parameterized to describe all particular languages. It is not a theory, but a research program or proposal to explain all linguistic phenomena. PM is the application of the principle of economy to linguistic phenomena.
Chomsky has not discovered what the principles of this hypothetical universal grammar are. Nor how these principles are particularized to create particular grammars that describe particular languages.
Every language has syntax (the formal or superficial aspect) and semantics (the conceptual or deep aspect). The syntax of a language is expressed through a grammar. The problem is that semantics is inexpressible with the language itself.
"No consistent language can contain the means necessary to define its own semantics." (Tarski).
"Language cannot represent what is reflected in it. What is expressed in language cannot be expressed by us through language." (Wittgenstein, Tractatus 4.121).
Semantics cannot be formalized because if it were to do so, it would cease to be semantics, since it would be to bring the profound to the surface, which is not possible. The deep manifests itself as superficial. But the superficial cannot access the deep because the deep is at a higher level of abstraction.
Computer Science
In computer science, all kinds of languages have appeared in an attempt to formalize information and information processes. The consequence has been a tower of Babel with an infinite number of languages specialized in different domains: programming, specification, database management, markup, ontologies, web, etc. In turn, different paradigms have been applied in these domains. For example, in programming: imperative, functional, object, logical, relational, event-driven, constraint-driven, aspect-driven, etc.
The Internet has become the universal medium for sharing information. It has invaded all fields of human activity. It is the digital revolution based on computers and communications. Unfortunately, this revolution has not been accompanied by a single language for content. There is a single communication protocol (IP, Internet Protocol) and a series of standards: a language for page presentation (HTML), a data structure language (XML), etc. But accompanying these standards are numerous non-standardized specialized languages: in programming, database management, markup, ontology definition, etc.
In computer science, there is a generic model for approaching problems or formalizing a domain: the model of semantic primitives, which are the concepts that underlie a domain. The problem in computer science is to find universal semantic primitives, i.e., a set of primary concepts that can be used to model all domains. Having universal semantic primitives would make it possible to develop applications with less effort because of the availability of powerful resources. Computer instructions are low-level and have combinatorial constraints. Universal semantic primitives have no such restrictions and can be freely combined.
The digital revolution and the "semantic ascent".
Until the middle of the 20th century, the dominant paradigm was energy. But then the computer was invented, ushering in a new era. We are living through a new revolution: the digital revolution − also called "the third industrial revolution"−, the implementation of digital information and communication technologies in all areas of society: science, education, culture, economy, administration, leisure, politics, etc. All analog technologies have been (or are being) converted to digital: telephone, radio, television, video, music, photography, books, newspapers, etc. Digitalization is also reaching money: we will pay with digital money, physical money will no longer be needed. With the "internet of things", everything will be connected and devices will communicate with each other and with humans. Everything will be part of a global digital communication network.
Our new understanding of the universe is no longer based on energy alone. It is based on a new dialectic between information and energy. Energy cannot be understood without information.
The main features of the digital realm are:
Higher dimension of freedom.
The digital is a higher dimension, a dimension of greater freedom in which physical limitations disappear. We can invent virtual worlds, with the laws we want. With virtual reality we can fly, move instantly from one place to another, see the virtual world from different points of view, interact with it, and so on. Thanks to virtual reality, the real world is relativized because it is seen as one of the infinite possible worlds.
In virtual space, distances disappear. Time also disappears because communications are practically instantaneous. Digital content transcends matter and can be "embodied" in multiple forms.
The digital universe frees us from having to travel physically to work, get training, shop, bank, etc. Everything is just a click away and in a very simple and intuitive way. When we move physically, it will be for pleasure, not out of obligation.
Globalization.
The Internet, the global network, is a huge repository of knowledge. We can access multiple types of content: documents, videos, e-books, podcasts, music, live broadcasts, etc. This network will be a global mind when the semantic web is implemented.
Democratization.
Digital technology makes it possible to do everything in a direct and simpler way, without intermediaries. Everything has been democratized. We can create and publish all kinds of digital content: books, videos, music, 3D objects, etc. One of the most promising technologies is 3D printing, which is making it possible to print all kinds of objects with the maker philosophy (do it yourself).
New consciousness.
The digital revolution is unstoppable because it is part of the evolution of the world towards a new era of knowledge, towards a higher consciousness through the integration of information and communication. The digital revolution is a new paradigm, a new and universalistic way of looking at reality.
The digital revolution has only just begun. There are still many challenges ahead, such as the development of human robotics, more realistic human-to-human interaction, augmented reality, and so on. Thanks to the sharing of information, this revolution is feeding back on itself, which is causing it to advance at an ever-increasing pace.
The problem of the digital revolution is that digital contents have no more structure than a sequence of zeros and ones. There is no more semantics than that, so digital contents need an external interpretation. We need a "semantic ascent" (a term used by Quine) to go beyond the digital to arrive at a universal language capable of expressing all types of content. This language must be based on semantic primitives to achieve a universal paradigm, a unified way of contemplating reality and possible worlds.
The New Computer Paradigm, a Universal Paradigm
The computer has produced a paradigm shift, a paradigm that we can qualify as universal because it has affected all fields of science and even philosophy. Perhaps the author who has best understood this has been Gregory Chaitin, mathematician and computer scientist:
"The computer has brought about a paradigm shift."
"The computer changes epistemology, it changes the meaning of understanding."
"Computers are not only an enormously useful technology, they also involve a revolutionary new kind of mathematics with profound philosophical consequences. They unveil a new world to us."
"We can only understand something if we can program it."
"The computer is a stupendous new philosophical and mathematical concept."
"The computer was invented to help clarify the philosophical question of the foundations of mathematics."
"The idea that the simplest theory is the best theory translates into saying that a concise computer program is the best theory."
"Now everything has been upset. It has been upset, not because of any philosophical argument, not because of Gödel's results or Turing's results or my own incompleteness results. It has been disrupted for one simple reason: the computer!
"Formal axiomatic systems are a failure. Algorithms for proving theorems do not work. Only trivial theorems can be proved. Formalisms for computing are a success."
"Turing's 1936 paper is a paper on epistemology."
"Maybe God is a computer programmer."
Computer Science
With computers, computer science was inaugurated. This discipline was basically born from two ideas of Alan Turing:
The definition of computation as a process on a theoretical machine (what today we call "Turing machine"), with very simple primitives.
The idea of making the machine universal by storing the program in memory, which made a structure that was inherently rigid - the hardware - more flexible. It was the invention of the universal Turing machine.
IT has evolved very rapidly and has been changing its own identity. It has gone through several phases. From data processing to information systems and knowledge management systems. From batch processing to interactive processing. From single-user to multi-user systems. From standalone to networked systems. But its final identity will be to become an artificial mind, emulating the human mind.
With the computer, artificial intelligence (AI) was soon born, a discipline that is part of Cognitive Science, the science that attempts to explain the workings of the human mind.
Computer science has provided many formal computer languages, but there is no standard, universal formal language.
Mathematics
Since the advent of the computer, we no longer look at mathematics in the same way. The new axioms are the instructions of the computer. The new theorems are combinations of axioms oriented to produce a result. This new mathematics is closer to the intuitionist or constructivist school, which only admits as mathematical truths those that can be constructed in a finite number of steps.
Psychology
The computer is a metaphor or model of the mind/brain, where the mind would be the software and the brain the hardware. It has even been suggested that the computer is also a metaphor for consciousness, since consciousness links the deep (the instructions of the computer) with its manifestations (the computer programs). And even more so if those instructions are of supreme simplicity, since consciousness is also associated with supreme simplicity, where everything is connected. The instructions would be the archetypes of the consciousness.
Philosophy
The instructions of a computer, if they are sufficiently generic, can be considered philosophical categories. And the machine would be a "philosophical computer".
Physics
Konrad Zuse hypothesized in 1967 that physical phenomena are computations and that the universe can be conceived as a digital computer (as a real physical device or mathematically isomorphic to such a device) that is computing at all times its evolution, its own future. He expounded this in his book "Rechnender Reum", translated into English as "Computing Cosmos / "Calculating Space". For Zuse, the computer that computes the universe could be a giant cellular automaton. Zuse built the first programmable computer and devised the first high-level programming language.
Years later, similar ideas about the computational universe were proposed by Edward Fredkin (in the 1980s), Jürgen Schmidhuber (in the 1990s) and more recently by Stephen Wolfram (2002). The latter author also proposed the idea of a computational universe, which could be a very simple Turing machine. Zuse and Schmidhuber claimed that there must exist a very short order program capable of systematically executing all possible universes optimally with computable physical laws.
Zuse inaugurated the field of "digital physics", although this term was first used by Edward Fredkin, who later replaced it with a more general term: "digital philosophy".
Some issues that arise with this model are:
Is the universe really computing its own future? Is the future of the universe deterministic?
Is the computation performed by the universe fixed, always the same, or does the universe change its own evolutionary program?
If the universe computes, this is a superficial aspect. But what is its deep aspect? The universe can only be understood from the deep level.
Conclusions
In short, the computer can be considered the most important invention in the entire history of mankind. It is a universal model and a universal paradigm of the inner (mental) world and the outer (physical) world, of the universe and of possible worlds.
If a universal language were to be created or discovered, learning it would be the most important thing in the world. This language must necessarily be incredibly simple and would help us to know the internal and external world as manifestations of the same resources: the primary archetypes or archetypes of the consciousness.
Currently the search for that hypothetical universal language and the foundation of everything is being sought in consciousness. This is paradoxical because we do not know exactly what consciousness is and, without knowing it, it is impossible to use it as a foundation.
The third industrial revolution has been a revolution that we can describe as superficial: of data processing, information, knowledge and intelligence. The fourth industrial revolution will be a deep revolution: of semantics, mind and consciousness. The evolutionary scale is:
Data ⇒ Information ⇒ Knowledge ⇒ Intelligence ⇒ Wisdom ⇒ Transcendence ⇒ Consciousness
