高校新文科建设中数理模型简化问题研究

The Simplification of Mathematical Models in the Construction of New Liberal Arts

当前许多文科领域在研究方法上越来越倾向于借助定量数理模型开展前沿研究,然而文科学习者和实务工作者数理工具基础相对薄弱,造成研究与教学和应用之间严重脱节。文章通过一个关于数理模型简化路径的思维框架发现,相对于自然语言模型、全模型、解说式模型、玩偶模型和数值模拟,数值示例可以大大降低文科数理工具门槛,同时保持科学研究的逻辑性、主要思想和发现,可以大幅度拉近“研、教、学、用”的距离。文章提出了数值示例开发的标准流程,同时认为推动数值示例开发一方面需要高素质专业学者队伍的参与,也需要相应的学术环境和资源配套。

At present, many fields of liberal arts are increasingly inclined to carry out frontier research with quantitative mathematical models in research methods. However, liberal arts learners and practitioners have relatively weak foundations in using mathematical tools, resulting in a serious disconnect between research and teaching, learning and application. Through a framework of thinking on the simplified path of mathematical models, this paper finds that compared with natural language models, full models, illustrative models, toy models and numerical simulations, numerical examples can greatly reduce the threshold of mathematical tools of liberal arts, while maintaining the logic, main ideas and discoveries of scientific research, thus greatly narrowing the gap between "research and teaching, learning and application". This paper proposes a standard process for the development of numerical examples, and provides a sample. We argue that promoting the development of numerical examples requires the participation of high-quality professional scholars on the one hand, and the corresponding academic environment and resources on the other hand.