Information-analytical three-dimensional System of Units
Information-analytical three-dimensional System of Units (SI)
Evgeniy Bessonov
Annotation. A new information-analytical System of Units (SI) is proposed, which makes it possible to considerably simplify the work of scientists and researchers in the search for scientific information. A three-dimensional design of a new SI system and a variant of its systematizing table are provided. There is author's research which led to the creation of a new SI system and the classification of physical quantities.
Key words. Information-analytical System of Units (SI); three-dimensional SI system; a systematic table of SI Units.
Introduction
The International System of Units (SI) has become firmly established in our scientific life. Due to the SI system Units the unity of methods and means of measuring various parameters of the material world is achieved and the required accuracy of such measurements is ensured. To display basic information, the system of Units of physical SI values is traditionally represented as a multiline table of SI coherent derived Unit, into which the names of derived quantity, names of their Units and symbols are entered and expressed in terms of SI base Units [1]. A number of national collections of normative and technical documents and handbooks in multiline tables also contain information on the definition of quantities, their Units and dimension [2].
The main drawback of the traditional representation of tables in the System of Units (SI) is their unsatisfactory systemicity, since they are all one-dimensional and do not reflect the logical distribution in the unit tables and do not exhibit a systemic arrangement in the system of quantities [1-4]. In addition, the existing System of Units (SI) is very inconvenient to use in electronic form, since it is not classified, not systematized and is not divided into system-forming blocks, so it is difficult to establish a logical electronic connection (for example, hyperlinks) between web pages and files or individual elements.
These weaknesses in the traditional representation of the International System of Units (SI) inhibit the development of fundamental metrology and do not allow it to go level with the high level of development of the world science, based on modern methods of systematization and information technology.
There exist well-known attempts by scientists and researchers, for example, the authors [5-9] and many others, to make the system of physical Units more perfect, more fundamental and user-friendly have not yet yielded the expected results. Since the systems they proposed, as a rule, were based not on the conventional Units of the SI system, but on reduced Units that lost some of their original system-forming functions, which required a radical revision of the existing SI system. For this reason, the proposed systems of units turned out to be too unusual and difficult for general understanding and perception.
The main problem of the susceptible mapping of tables in the existing System of Units (SI) was the relative multiplicity of the basic and additional derived units forming the system in it, which made it impossible to construct from them systematizing tables. Thus, in a standard two-dimensional table, two rows of system-forming quantities and their basic Units with nominal degrees (for example, a meter-L^n and a second-T^n) are freely placed horizontally (in the header) and vertically (in the outset). Of these, only a small number of known derived Units can be formed, for example, such as: m×s^-1 (speed); m×s^-2 (acceleration); m×s^-3 (jerk) and others. The same thing happens with the three-dimensional construction of the table, where only three series of system-forming quantities and their basic Units (one on each axis x, y, z) of the required nine (L^n, M^n, T^n, I^n, Ɵ^n, N^n, J^n, rad^n, sr^n, where n is the value of the degree of physical quantities - natural, integer or rational numbers).
Research methods
After a series of studies that included statistical methods for collecting and processing information and methods of geometric modeling, the author managed to find a solution to this complex spatial-analytic problem [11-14]. It consisted in the formation of a three-dimensional table of triads in specially tailored to each other forming a system of quantities containing the basic and additional Units and mapping their projections on separate cells of the table, where they are synthesized into derived Units, forming known physical quantities.
The diagram (Pic. 1) presents a three-dimensional design of the information-analytical System of Units (SI), on which the orthogonal directions (axes) x, y, z of the system with triads of the system of quantities J^nM^nL^n, S^nN^nƟ^n и R^nI^nT^n.
Pic. 1. Three-dimensional design of the information-analytical System of Units (SI)
In Picture 1 the dashed arrows show the directions of the projections of the main and additional Units located in the header, outset and prefix from their base levels I-IV and VI-XIII to individual cells of the basic level V. At this level, all known to modern scientific Units and educated , on their basis, physical quantities, so the V level is a systematizing table (hereinafter - the table) in the proposed information-analytical System of Units (SI).
The author's studies also proved that the greatest compactness of the table is achieved by distributing the dimensions of the system-forming quantities and their basic and additional Units in the x, y, z directions along the following triads: in the header, J (cd), M (kg) and L (m) ; in the outset - R * (rad), I (A) and T (s); in the prefix - S ** (sr), N (mol), Ɵ (K). Moreover, the Units that in practice contain the smallest variations of the numbers of degrees should be located at the periphery of the table (J^n, R^n, S^n), and with their largest variation (L^n, T^n, Ɵ^n) closer to its center.
*,**- the notation of dimensions for the flat angle - R (rad) and solid angle - S (sr), given by the author, due to the absence of such units in the system of SI Units.
The author's introduction to the System of Units (SI), as a supplement to the basic Units, Units of radians – rad^n (R^n) and steradian – sr^n (S^n) is dictated by the need to make the system more complete. Therefore, in the author's edition the System of Units (SI) takes into account not only the physical state of the process, denoted by the derived physical Units, but also shows the influence (or its absence) on the spatial flow of the process (directionality, two- or three-dimensionality), which is characterized by the functions of flat (R^-1; 0; 1) or solid (S^-1, 0; 1) angles.
The systematizing table of the information-analytical three-dimensional System of Units (SI) compiled according to the method shown above is shown in Pic. 2.
The presented form of the systematizing table of the information-analytical System of Units (SI) shows the logical distribution in it of known physical quantities, their dimensions and derived Units (in a separate application), formed according to the principle of coherence.
For the purpose of disclosing the interconnection, all the physical quantities in the presented SI system were classified by the author according to "related" characteristics and broken down into groups, subgroups and species [16], and the indicators of the degree of the basic and additional units were placed in the ordering table in numerical order as with their increase, and with decreasing.
Group I includes mechanical and spatio-temporal physical quantities (mechanical, geometric, flow, flow and volume of substances, pressure, time and frequency); group II physicochemical, thermophysical and temperature values; in group III light (optical-physical), acoustic, ionizing and atomic quantities; in group IV electric and magnetic quantities (electrical, electrochemical, magnetic, radio engineering and radio electronic). In the subgroup a (M1^n), massive values were included, in their dimensions containing the mass (kilogram) and having positive values of the exponents; in the subgroup b (M2^n), are non-massive (inverted), including all quantities (except optical-physical ones) that do not contain mass in their dimensions; in subgroup c (M3^n), - inverted-massive, quantities included in dimensions containing mass (kilogram) and having negative values of exponents; in subgroup d (M4^n), are subtile ***, optical-physical quantities are included, which in their dimensions do not contain mass (Pic. 2). Similarly, all physical quantities were also divided into other subgroups containing dimensions: L^n; T^n; I^n; Ɵ^n; N^n; J^n; R^n; S^n.
All physical quantities in the information-analytical System of Units (SI), according to the author's classifications [16], were divided into 4 groups, 9 subgroups and 88 species that combined values according to "related" features: inertia, dynamism, activity, etc., which characterized by the physical state of the process, denoted by a particular physical quantity.
Pic. 2. Systematizing table of information-analytical three-dimensional System of Units (SI) (cut version)
It can be seen from picture 2 that the SI systematization table (hereinafter - the table) contains a significant number of empty cells, which, in time, can be occupied by new quantities that are not yet discovered by modern science.
***- subtlety - subtlety, fragility - the property of light (electromagnetic radiation).
Results
Usage of these methods allowed the author to develop several variants of systematizing tables for different categories of users.
Compact variant (pic. 2, appl. [15]). The table shows the physical quantities that are widely used in the curricula of schools and colleges. Therefore, it is advisable to use it for secondary education.
Extended version. The table is recommended for usage both students and teachers of technical universities. It’s stored in the Internet [17], and the application to it in the storage [18].
Specialized table of information-analytical System of Units (SI) (it is executed without application). It contains more than 1,400 known physical quantities and their Units, collected from a number of reliable sources of scientific information [10, 19, 20]. It is proposed to be used by scientists and researchers in scientific centers as a database, information-analytical and reference material on physics. The table is located in the Internet repository [21]. A fragment of the specialized table is shown in Pic. 3 (subgroups M1-4 of the table in Pic. 3 correspond to the subgroups a, b, c, d in the table in Pic.2).
The classification of physical quantities [16, 21 (Note 4)].
Conclusions/Outlook
Transferring System of Units (SI) from multi-line tables to systematizing tables can make it more productive, thereby facilitating the work of scientists and researchers in finding the necessary scientific information and in discovering new laws of physics that will make a significant contribution to the development of modern science.
There are several advantages of information-analytical three-dimensional System of Units (SI):
contains in one space all known sciences physical quantities and their Units, includes their full dimension, indicates their location in the table;
has a high analytical significance and displays a systematic distribution of physical quantities and their units in the table for "related" groups, subgroups and species;
it is universal - contains known quantities and their Units in all branches of physics, includes units with fractional powers and dimensionless quantities;
highly adapted to the use in electronic form;
can expand under new quantities and their units are entered into it, or narrow down when they are removed, without changing the integrity of their structure.
Pic. 3. The extract of the specialized table of the information-analytical three-dimensional System of Units (SI) [21]
Acknowledgments
The author expresses sincere gratitude to PhD in Physico-mathematical sciences: Anatoly Chuev (MSTU im. N. Uh. Bauman), Mirmovich Edward G. (GOU SPO MO "Khimki College"), Ivlev Viktor Ivanovich (N. P. Ogareva Mordovia State University), etc. for useful advice and positive feedback on the results of the research.
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