Recently, we discussed about scientific breakthroughs in Tiedepiiri[1] (“The Circle of Science”). While this phenomenon is a close relative of scientific discovery, scientific innovation, and scientific revolution, the language of scientific breakthroughs has no established meanings in academic research concerning science.

The concepts of discovery, revolution, innovation, and breakthrough all have different connotations. Roughly: Discovery refers to a process where some phenomena or entity becomes known or explained. Innovation refers to a process where some new theory, concept, model, method, technique, or organization is established. The distinction between a discovery and an innovation is roughly between the objects of scientific research and the research itself (and we can of course debate the ontological significance of that distinction, i.e. to what extent the objects of scientific research are constructed). Scientific revolution refers to a process that leads to a fundamentally different understanding of the world and way of conducting research. Scientific revolution can have either a positive or a negative connotation. It can be viewed either as a process that leads to great improvement in our ability to understand the world; or it can be viewed as a process that disconnects old and new science and makes the older science incomprehensible from the perspective of the novel science (as is suggested by the Kuhnian picture of science).

Breakthrough, on the other hand, suggests either (i) that science has come to a point where a fundamental discovery or innovation is made or (ii) that science is finally able to fulfill its promises (concerning technological applications for example). These two meanings of breakthroughs have important differences. For example, scientific breakthroughs in the sense (i) are difficult to predict while breakthroughs in the sense (ii) are explicit promises of what the future of science can achieve. When a funding agency, for example, seeks scientific breakthroughs, these two senses should be distinguished. If one focuses only on the probability of technological or other applications of scientific projects, then scientific breakthroughs in the sense (i) are easily missed. Given the trend that scientific potential of a project is measured using citations in databases, this problem of missed opportunities becomes even more acute. If some scientific innovation or discovery is already applied in other research projects, a breakthrough in the sense (ii) is already made. Surely, funding agencies attempt to avoid this problem and it is often asked what the “potential for scientific breakthroughs” of a project is, but this question is rather impossible to answer. Given that we are searching for a breakthrough in the sense (i) and given that the potential for scientific breakthroughs in the sense (ii) depends on the contents of the breakthrough (i), the estimate for the “potential” for scientific breakthrough (ii) cannot be meaningfully established. Often, the distance between (i) and (ii) is greater than was expected.

Consider a historical case. During the Scientific Revolution, highly abstract mathematics was applied to physical reality. Floris Cohen calls this “realist-mathematical science” (2010). This surely was a breakthrough – perhaps the most important one – but what was its relation to practical applications? Cohen notes that

“What a few samples of practical mathematics had been able to accomplish so far was as nothing compared to what realist-mathematical science now pronounced itself capable of achieving. Galileo and his early pupils and disciples confidently peddled their ability to tame water currents, to determine geographical longitude, or to improve the accuracy of gunshot. Such promises did not fail to evoke the interest of princes and other secular authorities throughout Europe. They also had vast consequences.” (2010, 309.)

Cohen investigates the role of new mathematical science in practical applications and concludes:

“The net outcome of the investigation, then, is that by 1700, when the Scientific Revolution came to some provisional completion the usual gap between craft practice and mathematical science yawned almost as widely as it had at the onset of the Revolution, about a century earlier.” (2010, 323.)

He finds the following reasons for this:

“(a) The weightiest impediment was a serious underestimation of the real world’s messiness. For craft after craft it turned out that, besides determinants that were indeed taken into account in the mathematical model, there were others of at least equal significance, and also many second-order effects, which somehow had to be brought under mathematical rule as well.

(b) The mathematization of second-order effects required the ability to handle nonuniformly varying magnitudes, which the Euclidean doctrine of ratios was inherently incapable of. [–]

(c) Even if confined to Euclidean means only, craftsmen’s ability and/or readiness to grasp the esoteric language of mathematics were very limited. [–]

(d) Such communication was further impeded by social distance. Many a mathematical scientist stemmed from the lower or higher nobility or, if not, at least had to adopt its standards and thus tended to regard the equal footing required for fruitful exchange as beneath his dignity.” (2010, 325.)

This historical case suggests that we should take seriously the distinction between (i) scientific breakthrough as a fundamental discovery/invention and (ii) scientific breakthrough as a fulfillment of promises concerning applications. The search for (i) cannot be decided on the basis of (ii). The distance between (i) and (ii) is often too great. Following Cohen’s case, we can expect that the process from (i) to (ii) is a difficult one. This is due to (i) the complexity of the world, (ii) the fact that scientific innovation/discoveries rise new scientific problems that need to be solved in order to made the original innovation/discovery useful, and (iii) the social organization of science and its relation to relevant social and technological agencies.

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Cohen, H. Floris (2010). How Modern Science Came into the World: Four Civilizations, One 17th-Century Breakthrough. Amsterdam University Press.

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[1] A research seminar in history of science and knowledge, University of Turku.