Extracted from: Arie A Hanten. A suggested growth model of science and implications for information transfer. Journal of Research Communication. Studies, 1, 1978, pp. 83-98.

It has been suggested that science is a body of knowledge which grows on its epidermis (Price, 1969). This means that science mould grow along the research fronts, based on knowledge acquired by earlier research. In this respect there is a difference with the humanities, which also gram from within. However, it may be that the latter will change to some extent. I just refer to the social sciences which in recent decades have taken a strong intermediate position between natural science (and technology) and the humanities and which by applying more advanced methods also demonstrate increasing epidermal growth. But since I am a natural scientist, I prefer not to go too deeply into this and rather stick to my own domain.

An analogy: A very rough analogy that could be used is that of the growth of science to the growth of a crystal placed in a saturated solution: as the crystal increases in size, the new material is deposited on the surface, so that the rate of increase of the total weight of the crystal per unit time is proportional to the amount of surface area (Moravcsik, 1975). This analogy has in recent years been used in a number of analyses of science and appears to be useful in understanding interrelationships between major lines in the development of science.

The analogy is based on the assumption that new material is deposited on the surface of the body of knowledge at a constant rate per unit area. This rate of deposition may change, for instance, when the trend in the amounts of manpower or resources made available to be employed for scientific research alters. However, a small "speed-up" or "slow-down" factor would not greatly affect the quantitative conclusion: one keeps a growth curve which is very close to an exponential law. It requires a drastic "speed-up" or "slow-down" factor to change the quantitative conclusion. Up to the middle of the twentieth century, however, drastic alterations is controlling factors have not occurred, and hence the historical quasi-exponential behaviour of the growth of science emerges as a necessary consequence of the behaviour of a multidimensional system with a uniform surface deposition of new material (Moravcsik, 1975, p.83).

Spherical model of scientific knowledge: This analogy induced me to experiment with a growth model of scientific knowledge, in which the latter is represented by a roughly spherical body, expanding at its outside. A regular crystal of great size approximates this shape. The velocity of growth is determined by controlling factors as mentioned above.

Adoption of the model of a more or less spherically expanding body of scientific knowledge passes aver the rather subtle and complicated question of differentiating between scientific activity and scientific progress (Moravcsik, 1973, p.268), although it is in many ways relevant to the problem area. Strictly speaking, the exponential law has been established for the time variation of scientific activity, notably expressed in the volume of published work, while the epidermal growth model appears to pertain to the rate of scientific progress.

An important question is whether it is acceptable rationally to think of the body of scientific knowledge as a sphere. Should it not rather be described as a kind of thorn-apple or perhaps something looking like a raspberry, with growth in 'thorn points' or in up- doming areas being ahead of the overall advance of the in-between areas on the epidermis, or as some other three-dimensional body with a more irregular shape than that of a sphere ?

A non-spherical shape of the body of knowledge might occur if developments in some major scientific disciplines were systematically subordinated to those in other disciplines, for instance because some would only be of academic interest where-as others would provide many practical applications. However, this is not really the case. On an overal view, the physical, chemical, space, earth and life sciences are all characterised by an intricate intermingling of pure and applied research.

On the other hand, when looking at science in much closer detail, it is clear that more research effort is put into the examination of some subjects than in studying others. Similarly at the next higher level, more time and money is invested in certain subject fields than into others. However, this does not automatically imply that themes which receive less attention do proportionally lag behind (Fig.3). Neither does it mean that whole subject fields that are less blessed with funds and manpower do remain behind as indentations in the epidermis of the research front. In addition to advances made in the subject field itself, there are usually also emanation effects from surrounding areas which benefit the development of methodology and theory inthe poorer fields. For instance, much more research is currently done in palaeozoology than in palaeo- botany. Nevertheless it is not my" impression that in its essentials the latter field lags noticeably behind. The situation in palaeo- botany should rather be described as having a less dense tissue of knowledge in its epidermal zone underneath the outer research front. Furthermore, in the course of time growing points and growing areas may shift their positions. It is to this small scale of science growth in particular that Kuhn's theory about the existence of cycles of science development applies: lengthy periods of normal science, during which science progresses guietly, and relatively short outbreaks of scientific revolutions, during which methodological notions and fundamental knowledge change radically (Kuhn, 1970).

At a scale in between those of the shape of the total body of knowledge and the specialised scientific subject field, the development of heads on the research front is counteracted by the regular emergence of unifying concepts and the budding of interdisciplinary fields of research.

Examples of unifying theories which have greatly influenced research in a particular discipline include the concept of organic evolution, the theory of relativity, cybernetics. A more recent example of a unifying concept of wide relevance in an entire major discipline, that of the earth sciences, is plate tectonics. The latter is a hypothesis which provides a kinematic model of the outer part of the earth and links together a number of earlier concepts, such as the idea of a rheological stratification of the upper mantle and crust of the earth, the idea of continental drift and the idea of sea-floor spreading (cf. Le Pichon et al., 1973). Such wide concepts affect the position of the research front in the discipline concerned, in that they put a new and coherent plane skin over the projecting heads and also stimulate the filling-in of holes enclosed underneath this new skin, in between these heads, and the reexamination of large amounts of data already obtained.

It is to this large size of scale that Popper's paradox applies that the progress of knowledge can be described as a process of revolutionary change and not mere accumulation (Popper, 1962, 1963). I will return to this in a later section of this paper, when talking about developments within the body of knowledge.

Interdisciplinary fields of science fill up areas between advancing areas of research and integrate knowledge and experience from these different areas. Examples of interdisciplinary scientific fields are abundant: geophysics, biochemistry, geochemistry, physical chemistry, engineering geology, medical physics, etc. Also the recently blossoming environmental sciences should be mentioned in this connection. In particular their ecosystem approach is a clear case in that it integrates knowledge from botany, zoology, soil sciences, hydrology, chemistry, atmospheric science.

In conclusion, there is indeed a basis for stating that the total body of scientific knowledge can be described by the model of a growing sphere.

The SPINES Thesaurus Global Graph of Graphic Displays Reproduced from: SPINES Thesaurus; a controlled and structured vocabulary of science and technology for policy-making, management and development. Paris, Unesco, 1976, 3 vols.