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. While
efforts 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 the
real 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 not
introduced 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.