On Complexity and the Prospects for Scientific Advancement

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.

随着复杂系统、网络科学与人工智能等领域的兴起，学界已投入诸多努力对科学本身开展建模研究。在本研究中，我们提出一种相关建模方法，用于刻画知识复杂度对科学发展前景的影响。更具体而言，我们聚焦于如下问题：知识网络的拓扑复杂度能够在多大程度上影响科学发展前景。当知识被表征为复杂网络后，我们将其一个子网络——核心子网络（nucleus）——视作该网络当前已被认知的部分。与核心子网络邻接的节点相对数量，以及该数量与连接核心子网络与网络其余部分的边数之比，被分别用作科学发展潜力与此类科学进展实现效率的量化指标。我们分别在埃尔德什-雷尼（Erdos-Renyi）随机网络与巴拉巴西-阿尔伯特（Barabasi-Albert）模型中，分析了不同规模的核心子网络场景。出人意料的是，两类模型得到的结果几乎无显著差异，这表明在本研究的建模框架下，知识网络的复杂度或许对科学发展前景的影响微乎其微。