Applying tangles in the social and political sciences

• Applicant: Professor Dr. Reinhard Diestel
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 573843776

The publication of my recent monograph, Tangles (CUP 2024), has led to a number of inquiries from scholars in the social and political sciences, who would like to apply tangles in their respective fields. Such applications will require on-going mathematical support not only at the level of how to use the software that we have made available, but also at the mathematical level when dealing with particulars of the applied project, where an adaptation of tangle theory may be needed to accommodate them. I intend to use this project to fund a particular young scientist who knows all three pillars of such tangle applications intimately, because he has contributed to them all: the mathematical theory of tangles, their algorithms, and the software implementation of those algorithms. The following collaborations on concrete projects are already underway: Tangle-based constitution of citizens' councils, Tangle analysis of data recently collected in a co-operative study and Tangle analysis of decision-making in economics. In addition, we plan to develop generic tangle applications based on AI support, as follows. One aspect for which I received particularly positive feedback from social scientists following the publication of my Tangles book is that tangles facilitate a paradigm shift in the process of establishing new explanations of social phenomena. The standard method here is to formulate hypotheses, and then to test these empirically. Tangles, by contrast, can detect structure in data that leads to new explicit descriptive results directly, without requiring them to be advanced as a hypothesis first, and tested later. Social studies in which such unknown structures can be detected need to be large, though: not only in terms of numbers of participants, but also in the number of questions they ask. This is because in the absence of any favoured hypothesis to test, they have to establish sufficiently diverse data to detect unknown phenomena as structure in their body of answers - wherever these may be found and whichever data they may combine. Our aim, therefore, is to use AI-based virtual studies instead: 'studies' that are grounded in real data collected over many years, but which can ask an unlimited number of 'questions' without incurring any major costs. We plan to conduct such a sociological study. We shall thus compute the tangles of AI-generated returns for a social questionnaire designed by an expert, who will evaluate our results.

• DFG Programme: Research Grants