D O M I N A N T S I N T H E D E V E L O P M E N T O F P H Y S I C A L K N O W L E D G E

D. G i n e v , A. P o l i k a r o v

Centre for Scientific Inform., Bu[#arian Academy of Sciences, 7 Noemvri, 1, 1040 Sofia, Bulga,ia The paper consists of three parts. The first one concerns a general treatment of the notion

of "dominant of scientific research". Four traits for identification of the dominant are considered there. The second part is devoted to formal analysis of scientific dominants by the fuzzy sers theory. And the third part illustrates dom�9 formation in mathematical biophysics.

1. By scientific dominant we understand a set of closely connected works on topical prob- lems, successful methods of their solution and decisive results which disclose the significance of the problems, the efficien™ of the methods and the importance of the very results [1].

Every scientific dominant exercises a growing impact within a certain (narrower or broader) domain. There are four traits by which the presence of a dominant as a topical and perspective trend of scientific research could be identified. These are the following ones:

A) Thematic coherence of the domain. It means that there exists a thematic centre which subordinates the research subjects of the domain. As a result, the scientific community possesses a "thematic map of the investigation process". The appearance of common values which char- acterize the style of scientific thinking is a consequence of the established thematic coherence The latter is ascertained by analysing the thematics of papers in scientific journals. A number of contemporary works are dedicated to such quantitative and comparative analyses [2--5].

B) Irradiation of publications. The shaping of a topical and promising research trend takes place on the basis of one or a few scientific papers. They fo rma network of united works which are characterized by different lines of propagation. This is a process of irradiation. The homogeneity of the network, expressed by the index of citations of the thematic centre's paper(s), depends on the intensity of the irradiation process. The future divergence of the lines of propagation provides a base for the framing of new scientific dominants.

(C) Correspondence between cognitive and social institutionalization [6]. From a sociological point of view a scient�9 dominant is associated with the activity of a certain scientific group or community which may have an informal ("invisible college") or formal status. The number of members of the community may vary in a wide range (from tens to thousands), but a necessary condition for the rise of a dominant is the presence of a sufficient "critical mass" of scientists in order to carry out the research process. The fise of a dominant becomes possible only if the acceptance degree of investigation standards, conceptual models, experimental and mathematical techniques and so on (the cognitive institutionalization of a dominant) corresponds to the effectiveness degree of those non-formal mechanisms which control the unity of scientific com- munity (the social institutionalization of a dominant).

(D) Historical stages. The scientific dominant could be identified not only in a synchronic but also in a diachronic aspect. From a historical-scientific viewpoint a dominant passes through three basic stages of development: rise, stationary or quasi-stationary state and decline.

2. The apparatus of fuzzy sets theory provides an interesting perspective for a formal analysis of scientific dominants. As it was already pointed out each dominant consists of thematic centre paper(s) (or paper(s) of first order) and papers (of second order) which are related to the former ones. In the process of irradiation the second order papers remove from the thematic centre. Hence, there are different degrees of remoteness from the thematic centre of "bel ts" of second order papers around it with different degrees of relevance to the dominant. These degrees could be estimated on the grounds of scientometrics data. (Formally there is analogy with the distribu- tion as it is determined by Bradford's law of scattering.) Moreover, there is a special kind of "diffusion" among the dominants, so that a certain paper may belong to various dominants with different degrees of relevance. As a result, one can distinguish clusters of interrelated dorn- inants by analogy to clusters of specialties in quite independent disciplines [7].

On the basis of these epistemological premises each scientific dominant may be represented

5 2 Czech. J. Phys. B 36 [1986]

D. Ginev, A. Polikarov.. Dominants in physical knowledge

as a fuzzy set, wherein first order paper(s) have a characteristic function of belonging (degree of relevance) with value 1 and second order papers have the saine functions with value less than 1. (A possible criterion for value estimation is the number of references to the first order paper.)

3. Let us illustrate the above text by an example showing how dominants of different order may be formed in the domain of mathematical biophysics. What we have in mind is the mathemat- Jcal modelling of distribution process in kinetic systems. This field of investigation consolidated itself as a rather interesting process in which research dominants were formed from historical roots entirely outside the biophysics and physical knowledge in general. In fact, mathematical models of distribution process in kinetic systems originated from two quite different non-physical domains: population genetics, and the cybernetic theory of induced fields.

While in the first domain mathematical models were created for the purpose of determining frequences of genes in polymorphous populations, in the second they had to face classical cybernet- ic problems. The chier works in the two domains are connected with the narnes of R. Fisher and A. Kolmogoroff [8, 9], and N. Winer and A. Rosenblute. They established a thematic centre for dominant research trends in mathematical biophysics. The process of irradiation correlates with an0ther process, namely "transportat ion" of ideas between different scientific domains. (However, this should hot be taken to mean that the works from the thematic centre are of no significance any longer for their initial domains, because their ideas being diffused œ into the field of mathematical biophysics. The fact is that the above-mentioned works create dominant research trends within their own domain as well. For example, the papers of Fisher and Kolmogoroff initiated important investigations into the mathematical theory of evolution.)

Let us point out the different lines of propagation, irradiating from the thernatic centre of mathematical modelling of distribution process in kinetic systcms.

(a) Investigating the spatial periodicity resulting from thermal diffusion [10]. (b) Investigafing dJssipative structures [ 11 ], further elaborated in the school of L Prigogine. (c) Investigating the kinetics of homogeneous auto-oscillatory reactions, B. Belousov. (d) Investigating on the basis of mathematical modelling of dot-reactions and distributed

auto-oscillatory homogeneous systems related to specific biophysical processes, e .g . , trans- mission of primary impulses in the nerves, muscular synchronization, etc. Initiated in the early 1960s, these investigations resulted from an interaction of the dominant being discussed with another one, auto-wave processes. These works stimulated further research trends within elec- trodynamics and hydrodynamics. This illustrates the "interference of dominants'L

To further elaborate the notion of scientific dominant one bas to address some methodological problems, such as determining what counts as a sufficient set of parameters for a classifcation of dominants; outlining a theory of how dominants interact; translating the scientometric param- eters of dominants into the language of fuzzy sets theory.

The solution of these problems may result in a specific model of sc�8 growth.

Received 13. 5. 1985.

References

[1] Polikarov A.: Methodological Problems of Science. Bulgarian Academy of Sci., Sofia, 1983. [2] Lewis G.: Soc. Stud. Sci. 10 (1980) 285--305. [3] Nadel E.: Soc. Stud. Sci. 10 (1980) 449--474. [4] Crane D.: Soc. Stud. Sci. 10 (1980) 23--54. [5] White D., Sullivan D.: Sci. Yugosl. 6 (1980) No. 1--4, 203--212. [6] Whitley R.: in Social Process of Scientific Development (ed. R. Whitley). London, 1974. [7] Vlach~ J.: Czech. J. Phys. B 3 2 (1982) 1311--1318. [8] Fisher R.: Ann. Eugen. 7 (1937) 355. [9] KolmogoroffA. : Math. Ann. 104 (1931) 415.

[10] Jost W.: Phys. Chemie 193 (1944) 322. [11] Turing A.: Philos. Trans. Roy. Soc. B 327 (1952) 37.

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