I have indicated in the last few weeks the importance attached to technological innovation in economic growth. The ideas about how it occurs could also be used to describe the processes of academic research, so the theories should come quite naturally to a reflective analyst.
The most immediate theory about research views its characterising process as producing incrementally improved new products for the market which are subject to constant demand, while another theory emphasises the variety of capital goods produced by the market, while another related set of theories consider the characterising process to be the act of innovation as lowering the future cost of learning. The last two theories stress human knowledge as accumulative, in the same way as economic researchers attempt to learn from the work of other researchers or find short cuts in their past studies to speed up future production. The theories tend to recognise the abstract scientific elements of innovation, but stress more the applied elements where people have to invest a great deal of time in finding out how to work with the scientific processes.
The underlying nature of the science in scientific innovation is, I think, relatively downplayed. Science tends today to be intensive as much as extensive, trying to discover the underlying processes of known phenomena rather than looking for new ones. The result is that the number of possible scientific applications can be subject to exponential, or higher, increase. Consider, for example, if we know about the existence of the atom, and then are informed that atoms consist of protons, electrons, and neutrons. We had just one object for use before the information; now we have three. If the subatomic particles are themselves split up into three components, we now have 3 x 3 = 9 components. The number of combinations of inputs in the first instance is two, an atom or not; in the second instance, it is 2^3, electron or not, proton or not, neutron or not; in the third instance it is 2^(3^2). This greater-than-exponential growth occurs in chemistry and biology too, for example in the decomposition and rearrangement of DNA strands.