Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication or thinking would be possible. Efficient implementability for creating and reading language expressions is discussed and illustrated with a quantum mechanical model. The reason for interest in language is that language expressions can have meaning, either as an informal language or as a formal language associated with a mathematical or physical theory. It is noted that any universally applicable physical theory, or coherent theory of physics and mathematics together, includes in its domain physical models of expressons for both the informal language used to discuss the theory and expressions of the theory itself. It follows that there must be formulas in the formal theory that express some of their own physical properties. Inclusion of intelligent system in the theory domain means that the theory, e.g., quantum mechanics, must describe in some sense its own validation. Maps of language expressions into physical states are discussed as are conditions under which such a map is a Godel map. The possibility that language is also mathematical is very briefly discussed.
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication or thinking would be possible. Efficient implementability for creating and reading language expressions is discussed and illustrated with a quantum mechanical model. The reason for interest in language is that language expressions can have meaning, either as an informal language or as a formal language associated with a mathematical or physical theory. It is noted that any universally applicable physical theory, or coherent theory of physics and mathematics together, includes in its domain physical models of expressons for both the informal language used to discuss the theory and expressions of the theory itself. It follows that there must be formulas in the formal theory that express some of their own physical properties. Inclusion of intelligent system in the theory domain means that the theory, e.g., quantum mechanics, must describe in some sense its own validation. Maps of language expressions into physical states are discussed as are conditions under which such a map is a Godel map. The possibility that language is also mathematical is very briefly discussed.
This paper examines language modeling based on the theory of quantum mechanics. It focuses on the introduction of quantum mechanics into the symbol-meaning pairs of language in order to build a representation model of natural language. At the same time, it is realized that word embedding, which is widely used as a basic technique for statistical language modeling, can be explained and improved by the mathematical framework of quantum mechanics. On this basis, this paper continues to try to use quantum statistics and other related theories to study the mathematical representation, natural evolution and statistical properties of natural language. It is also assumed that the source of such quantum properties is the physicality of information. The feasibility of using quantum theory to model natural language is pointed out through the construction of a experimental code. The paper discusses, in terms of applications, the possible help of the theory in constructing generative models that are popular nowadays. A preliminary discussion of future applications of the theory to quantum computers is also presented.
The need for a common language If we wish to compare the methods, content, claims and experimental predictions of two physical theories we have to find some common ground between them. What is needed ideally is a language which embraces the essential elements of each theory as parts of a broader structure which transcends them both. There are two components to such a language, which might be called the formal and the informal. Briefly, by ‘formal’ we mean a precisely defined set of concepts and their relationships from which one can deduce unambiguous conclusions by a series of logical steps (mathematics); by ‘informal’ we mean the intuitive concepts and pictures that a theory employs in order to render intelligible the ‘reality’ for which it seeks to account. These two aspects are naturally closely connected. The possibility of constructing a language of this type is not given a priori . It may turn out that it is possible to develop only one of the two components, and the theories we want to compare may or may not be commensurable, or only partly so. We shall examine this question in connection with the relation between two physical theories of matter: classical mechanics and quantum mechanics. This relation is subtle and operates on several levels and we shall return to it throughout the book. For the present we confine ourselves to some general remarks. Roughly speaking, we may say that classical mechanics as a distinct discipline constitutes a language possessing both formal and informal aspects.
A philosophy of physics called “linguistic empiricism” is presented and applied to the interpretation problem of quantum mechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language‐dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantum mechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.
ENGLISH ABSTRACT: What are the information processing capabilities of physical systems? As recently as the first half of the 20th century this question did not even have a definite meaning. What is information, and how would one process it? It took the development of theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate mathematically what it means to compute or communicate. Yet these theories were abstract, based on axiomatic mathematics: what did physical systems have to do with these axioms? Rolf Landauer had the essential insight - "Information is physical" - that information is always encoded in the state of a physical system, whose dynamics on a microscopic level are well-described by quantum physics. This means that we cannot discuss information without discussing how it is represented, and how nature dictates it should behave. Wigner considered the situation from another perspective when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences". Why are the computational techniques of mathematics so astonishingly useful in describing the physical world [1]? One might begin to suspect foul play in the universe's operating principles. Interesting insights into the physics of information accumulated through the 1970s and 1980s - most sensationally in the proposal for a "quantum computer". If we were to mark a particular year in which an explosion of interest took place in information physics, that year would have to be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be solved easily on a quantum computer. But the applications of information in physics - and vice versa - have been far more widespread than this popular discovery. These applications range from improved experimental technology, more sophisticated measurement techniques, methods for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight into quantum theory and nature. In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.
While it is widely acknowledged that quantum theory is strange, and that the world view it implies is elusive, there is considerably less consensus as to why this is the case. This article will explore the possibility that the theory may be opaque because the mathematical language it employs is inarticulate. To address this possibility, three interconnected mathematical theories will be developed, each specifically designed to handle aspects of quantum theory's subject matter. The first will describe dynamic systems in terms that are general enough to be applicable to any kind dynamics, including both classical and quantum. That description will then be used to construct a theory of experiments, with the aim of understanding what types of experiments scientific methodology allows. Finally, the theory of experiments will found a theory of experimental probabilities applicable to any collection of experiments, so long as their probabilities are internally consistent. The resulting over-arching mathematical language will then be applied to quantum theory. In the initial application, it will be used to explain the core nature and structure of quantum measurement and probability. Following that, it will be used to explore quantum theory's models. Like any theory written in a mathematical language, quantum theory derives its meaning from its class of models. To understand the class quantum models, two models of central importance will be described. The first will be a conceptually simple construction that follows almost immediately from the above theory of dynamics. It fully satisfies both quantum theory and the above mentioned theory of experimentation; additionally, its macroscopic objects obey classical mechanics. The second will utilize a minimal amount of mathematical structure to satisfy the same conditions.
Creation of intelligent systems in the paradigm of logical decision-making requires formalization of knowledge in the form of ontologies, production models, etc.However, a rigorous formalization of knowledge is far from always possible due to the incompleteness, inaccuracy, and inconsistency of the data.In this regard, recently, the attention of researchers has shifted to extracting knowledge from natural language texts.Particularly noteworthy is the recently developing approach based on the use of quantum formalism to the objects of the macrocosm, which allows one to consider the uncertainty and inaccuracy inherent in the natural language.Numerous experiments conducted over the past 30 years demonstrate that the mathematical apparatus developed for modeling elementary particles also satisfactorily describes the behavior of people, which cannot be described by the mathematical apparatus of classical logic and probability theory.A review of the methods of processing natural language texts by means of quantum mathematics is presented.The methods are designed to eliminate the shortcomings of existing methods and means of information retrieval.