Abstract
This paper models scientific productivity and reward, as well as the emergence and dynamics of new scientific fields. The crucial features are the individual reward that depends in addition on own abilities and the collective knowledge of a field. The overall knowledge about a field leads to increasing, at low levels (i.e., at the beginning) and at high level to decreasing. This set up renders individual as well as collective decisions, planned or as a market outcome, non-trivial. We suggest, formulate (and partly solve) problems about individual and collective behavior of scientists and study the conditions that a field emerges.
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Notes
- 1.
The field can correspond, for example, to the (first) letter in the JEL classifications in economics and similar in other sciences. A subfield is then identified by the following two numbers of the JEL-code. The only crucial point is that we assume that a subfield can be invented by a researcher (but rarely a larger area which we call field) and generate several publications by one or many persons.
- 2.
This is only used as a metaphor. Both, mining and research, are looking for useful elements that are mixed with things useless. The analogy is in growing skills to find a mine (or research subfield) and in lowering the probability to find something useful after some time of exploitation. Both processes can be described by similar mathematical models.
- 3.
He was treacherously committed to an asylum by his colleague where died 14 days later after being beaten by the guards.
- 4.
Scientists are among the most vain people as Carl Djerassi, the discoverer of the anti-baby pill observed. Richard Blair wrote under the pseudonym George Orwell, but the idea that Einstein had published his general theory of relativity under a pseudonym is absurd. Sir Isaac Newton is another example in his fight against Gotthold Ephraim Leibniz about priority over calculus.
- 5.
In physics, when we move to the height h above the sea level, the density of atmosphere declines exponentially. This is also an example of a deterministic outcome for the law of large numbers, due to very large number of particles. The similar deterministic equivalence of random outcome is assumed here in “research mining,” but it is less justifiable and is assumed for simplicity.
- 6.
Scientific reward is not directly linked to productivity due to the so-called Matthew effect (“For to everyone who has will more be given, and he will have abundance; but from him who has not, even what he has will be taken away,” Matthew 25:29). This point was first addressed by the sociologist Merton [19], in order to explain why eminent scientists get disproportionately credit for their contributions, while relatively unknowns get disproportionately little. Therefore, a person with many written, maybe partially unpublished, papers gets lower reward per written paper compared to a famous scientist, even after accounting for quality.
- 7.
G corresponds to both output and time. G can be calibrated as typical life cycle of a subfield, for example, 100 years. If the unit of time (t = 1) is, for example, 40 years then G = 2.5. If the maximal productivity in this subfield is G2/4, it can be measured by maximal intensity of total publications per unit of time (here 40 years). If G2/4 = 2.52/4 = 3.125 in this example, while in reality is 312 papers, then a unit of publication is 100 papers.
- 8.
For example, the authors of this paper have presumably missed the transition to experiments.
- 9.
Here X is the mass (quantity) of researchers. It is normalized in such a way that maximal productivity is for \(X=G/2\). Both can be calibrated. For example, we know that maximal productivity, \(G^{2}/4\), is for 10 researchers in subfield. Then \(X=G/2\) corresponds to 10 researchers. A researcher lives between t and \(t+1\), so that q is measured in the units of lifetime salary, and G can be defined correspondingly.
- 10.
With the first isocline coinciding with the stable path.
- 11.
This also often happens with interdisciplinary papers.
- 12.
And they also have low incentives to do that.
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Yegorov, Y., Wirl, F. (2021). On Scientific Innovations and Constraints: A Dynamic Analysis. In: Haunschmied, J.L., Kovacevic, R.M., Semmler, W., Veliov, V.M. (eds) Dynamic Economic Problems with Regime Switches. Dynamic Modeling and Econometrics in Economics and Finance, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-030-54576-5_7
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