Approximate reasoning and the ethnomathematics of cooking

Abstract

Several methods of approximate reasoning are known, and many remain to be discovered across domains. Some are tied to reasoning with uncertainty. The developments over the last fifty years or so in the development of approximate reasoning methods, and their application across multiple STEM domains, suggest that it is necessary to introduce them early in school. Whileefforts towards building the infrastructure for the process have been limited, the bigger question is “What should be introduced?”. If concepts are always approximated in real life, then how should they be done mathematically? If thereal numbers are not always necessary to approximate concepts or even quantities, then how should they be approximated, and what should be taught in schools? Specifically, functional representations of approximate reasoning are notintroduced early. This additionally impedes diversity, ethnomathematical explorations, learning from experience, and through models. The objective of this research is to explain the problem with a focus on the ethnomathematics of cooking, and associated haptic methods. Further, it is argued through the context that of the many approaches to approximate reasoning, intrusive methods are best avoided, and that general rough sets is better suited for modeling such knowledge. Intrusive methods, such as those based on fuzzy or probability theory, are those that indulge in an excess of unjustified numeric assumptions. This builds on earlier work of the present author on modeling approximate reasoning. Her axiomatic approach to granularity are additionally applicable to approximate recipes that possess desired properties. In the contexts of ethnomathematical discourse involving haptic reasoning (as in cooking), it is shown that such an approach can model the essence of context without oversimplifications or outright dismissal of the efforts involved. Further, it has the potential to help in inventing expressive structured languages for the ethnomathematics, and associated model eliciting activities. Distinct facets of three specific contexts are theoretically explored to illustrate aspects of the reasoning, and meta aspects.