5. Description of physical equations
Physics formulates the universal laws of the real world by means of physical equations. In this section, we are focused to finding a way to describe physical equations, which describe the laws of the real world. Physics describes not reality itself, whatever it is, but its quantitative aspect; that’s why for describing it physicists use mathematics as description language in physical equations. So physical equations describe quantitative reality. In our approach, we describe information units, denoting our experience of external reality, by finding the relationship of operational structures to the semantic information. It would be appropriate to verify our hypothesis about the existence of a nonsemantic level in speech in describing physical equations too. We will take just a few simple equations with variables connected by arithmetic operations. These equations will give a general answer to the question whether operational structures are used in conveyed information and hence will help to confirm or refute the existence of the nonsemantic level.
We have seen that operational information serves as a general characteristic of word classes and word forms information and so can be considered as its basis. We have also seen that being formed as a relationship between the operational structure and the state of a single operation, it creates a new unit based on the substitution (negation) or inclusion (hyponymization) of states. We will show now that operational information represented by a single (not coupled) state points to the initial quantity of the feature forming an ordinal scale or to the starting point in the sequence formed by substituted moments of time. In this case, the pointing carried out by the single state is included in the word’s meaning, whereas the feature’s scale and the time sequence which allow the pointing to be implemented occur when the meaning becomes an information unit in speech.
A single quantitative state is incorporated into the meanings of parametric, or gradable, adjectives and nouns. Parametric adjectives are, for instance, ripe, tasty, expansive, good, strong, massive, energetic and parametric nouns are force, mass, energy , etc. They denote any qualities detected in an object or attributed to it, which are much more numerous than those perceived by our senses. Parameters used in physical equations (time, velocity, mass, energy, etc.) are, on the contrary, less numerous and are selected among quantitative parameters denoted by NoI.
Let us call nouns and adjectives that contain a single quantitative state dimensional. Dimensional nouns nqquantity, degree, height, width, thickness, volume, weight, temperature, speed, kindness , etc., are part of parametric nouns. Dimensional nouns nq differ from the other parametric nouns: The parameter they recognize is recognized not only by the corresponding dimensional adjective Δnq but also by its negation Δnq . Let us compare the dimensional noun height and the parametric but not dimensional noun kindness . Height : not only highbut also not high means ʻhaving some heightʼ. Kindness :not kind doesn’t mean ʻhaving kindnessʼ.
The dimensional adjectives large, high, frequent, strong, deep , etc. differ from the other parametric adjectives which recognize object parameters by recognizing not an arbitrary value of the quantitative parameter but a value that is implemented on only one of the opposite parts of the parameter values’ range. So, high means not merely ʻhaving heightʼ but ʻhaving a great heightʼ; smart , not just ʻhaving mindʼ but ʻhaving a great degree of mindʼ; low , ʻhaving a small heightʼ. One can explain this characteristic of the dimensional adjectives by the assertion that a dimensional adjective meaning comprises a single quantitative state Q which forms quantitative information in the basis of its semantic information. If dimensional nouns are used with dimensional adjectives as words containing Q , they must have or be vested with q 0, which should be included in Q .
Single quantitative states in conjunction with single elective states participate also in forming numeral meanings, which become numeral information (NuI) when used with a noun in speech. Their formation is fulfilled in interconnected semantic relations of single states where one implies the other. The single states are interconnected as following: The elective state E recognizes the ordinal numberk -th expressed by an ordinal numeral ΔK forming the NoI’s increment if the quantitative state Q recognizes the numberk expressed by a cardinal numeral K forming the NoI’s alternative increment. Interconnecting the relations of these states is that the structure of any ordinal numeral ΔK can be represented through the relation with a preceding ordinal numeral as “after” and the one of the cardinal numeral K can be represented accordingly through the relation with a lesser cardinal numeral as “more than”. If a numerical value is assigned to a hyponymized singular noun denoting a separate entity, it is understood as a unity. The numeral denoting a unity is K 0 one . The corresponding ordinal numeral is ΔK 0 first .
Units of measurement are used in equalities and equations. A noun used as a unit of measurement, like foot , includes a dimensional noun as its hypernymic base (ʻdistanceʼ in case of foot ), which we will call dimensional base, and presumes the single state Q of the cardinal NuI K . So units of measurement are used mostly with a numeral and recognize the numerical value of the dimension recognized in turn by a dimensional base, for example, seven miles (indistance ), 5 feet (in height ).
Units of measurement can have the same dimensional base, for example: (ʻdistanceʼ) + (ʻdistanceʼ) = (ʻdistanceʼ); (ʻdistanceʼ) × 2 (a dimension base is absent: dimensionless coefficient) = (ʻdistanceʼ); 1,000 × (ʻweightʼ) = (ʻweightʼ). Or they can have different dimensional bases, like in the equality: (dimensional base ʻlengthʼ) × (ʻwidthʼ) = (ʻareaʼ) and the equations – geometric formulas and algebraic equations: V l (dependent variable) = a dm ×b dm × c dm , or (without units of measurement) V  = abc , where the variables a ,b , c are edges (ʻlengthʼ, ʻwidthʼ, ʻheightʼ), the variableV is the ʻvolumeʼ of a rectangular parallelepiped. Units of measurement have different dimensional bases in physical equations too:s  = vt , where s is the ʻwayʼ of a body moving with uniform velocity (e.g., s nautical miles), v , ʻvelocityʼ (e.g., v knots ), t , ʻtimeʼ (e.g., t hours);pV  = const, where p is ʻpressureʼ, V , the ʻvolumeʼ of an ideal gas.
The physical equations include a limited number of quantitative parameters and describe the relations between them. Thereby, the physical description with equations reduces a large number of objects to a lesser number of description units and so physics describes not just quantities of the parameters but the quantitative aspect of reality in its entirety.
The single elective state e can be part of VeI and of NoI operational structures. The single elective state of VeI operational structures points to the actual moment. Its role in the noun operational structure is more complicated. Let us quote Émile Benvéniste (1976) about subjectivity in language: “Je ne peut être défini qu’en termes de “locution”, non en termes d’objets, comme l’est un signe nominal. Je signifie “la personne qui énonce la présente instance de discours contenant je (252). [I cannot be defined except in terms of “locution”, and not in terms of objects, as is the case with the noun. I signifies the ʻperson enunciating the present instance of discourse containing I ʼ]. La «subjectivité» dont nous traitons ici est la capacité du locuteur à se poser comme «sujet». Or nous tenons que cette «subjectivité», qu’on la pose en phénoménologie ou en psychologie, comme on voudra, n’est que l’émergence dans l’être d’une propriété fondamentale du langage. Est «ego» qui dit «ego» (259-260). [The ”subjectivity” we are discussing here is the capacity of the speaker to posit him/herself as ”subject”. Now we hold that that ”subjectivity”, whether it is placed in phenomenology or in psychology, as one may wish, is only the emergence in the being of a fundamental property of language. ”Ego” is who says ”ego”.]”. Without contradicting this definition, we define the operational structure of the personal pronoun I , recognizing the speaker, as formed by the single elective state e which is introduced in the NoI structure within its increment formed by the hypernymic base of speech VeIvl >:nl (|e |), where l is the hypernymic base of speech VeIvl >, eimplements the relations e  ← e 0,e  → E with the sentence VeI elective states.