On Complexity and the Prospects for Scientific Advancement

Luciano Da Fontoura Costa

doi:10.1590/1806-9126-rbef-2020-0442

Luciano Da Fontoura Costa

Open Access

https://doi.org/10.1590/1806-9126-rbef-2020-0442

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Abstract

With the onset of areas such as complex systems, network science, and artificial intelligence, efforts have been invested in modeling science itself. In the present work, we report a related approach to modeling the influence of the complexity of knowledge on the respective prospects for scientific advancement. More specifically, we focus on the question of how much the topological complexity of the knowledge network can influence the prospects for scientific advancement. Once the knowledge has been represented as a complex network, we consider one of its subnetworks, the nucleus, as representing the currently known portion of that network. The relative number of nodes adjacent to the nucleus, and the ratio between this quantity and the quantity of edges interconnecting the nucleus with the remainder of the network, are taken as quantifications of the potential for scientific advancement and the efficiency with which these advances can take place. Subsequent nucleus sizes are considered in both a simpler network (Erdos-Renyi) and a more complex model (Barabasi-Albert). The results surprisingly tended to vary little between these two models, suggesting that the complexity of the knowledge network may have little effect on the prospects for scientific advancement as modeled in the present approach.

Highlights

It took a long time to be discovered and, once discovered, it took some time to be believed
As we develop our study, we will see that that the relative number of nodes (n/N ), where N stands for the total number of nodes in the knowledge network, and links (e) adjacent to the nucleus provide interesting quantifications of the respective prospects for scientific advancement
First and foremost, we have that the intrinsic topology of the overall knowledge network had little influence on the two indices r(c) and s(c), yielding similar curves for both ER and BA networks throughout. This would suggest that the topological ‘complexity’ of the overall considered network tended to have little effect on both the prospects and efficiency defined by any size of nucleus

Summary

Introduction

It took a long time to be discovered and, once discovered, it took some time to be believed. We will consider the number of adjacent links and nodes reachable from the current nucleus as possible quantifications of the prospect or potential for scientific advancement implied by the interconnections between nucleus and an the overall knowledge network. Reflecting the fact that all the universe may be fully interrelated (e.g. Bell’s theorem), especially through fields of asymptotic decay, the overall network can be, in principle, assumed to constitute a connected component This characteristic may not be required from the nucleus, as not every piece of available knowledge is taken as being interconnected while performing some particular research program, which can be developed possibly independently by different research groups or along distinct periods of time.

Scientific Prospect in ‘Simple’ and ‘Complex’ Knowledge Networks

Concluding Remarks and Prospects