Virtual Enterprises
Ted Goranson

Virtual Enterprises and Ethnomathematics

Investigations of cross-cultural mathematical practices, such as those by Helen Verran, Donald Crow and Paulus Gerdes point to the existence of many systems of abstraction in different cultures, including fundamental variations in mathematical reasoning. Societies evolve different ways of conceptualizing their world and concerns, sometimes quite different from each other. Researchers have shown that groups in Africa mathematically reason in ways that are different from the prevailing paradigm. The study of this phenomenon is called “ethnomathematics.”

Scholars are still discovering a vast range of indigenous reasoning systems. Previously thought to be quaint folk traditions, they are now finding that these are often sophisticated, complete representational reasoning systems. Like all else in terms of cultural diversity, these are disappearing at an alarming rate — faster than some can even be identified and understood.

An emerging notion is that many of these systems likely have practical merit against contemporary problems. Some of these systems are every bit as sophisticated as the mathematics taught in the West, and might be leverageable for practical, analytical use. They are not regarded as useful because they have no persistent representations that can be passed in artifacts; they lack “communication technologies.” But they may be valuable if they can be tapped and integrated into enterprises.

Ask any mathematician why a problem seems intractable and she will respond that it is because the right abstractions have not yet been found. As a result, theoretical mathematicians spend their lives increasing the ways that the world can be abstracted, while practical mathematicians labor to match these abstract systems to problems. Having a variety of abstractions makes innovation possible, but only if they can be used.

In the same way, business also thrives when many pockets of expertise work on the same product from different angles, each expert using their own conceptual toolkit while contributing to a collective endeavor. Consider the aerospace case, where many engineers work on the same jet engine but use highly specialized abstractions: heat flow versus tensile strength, for example. In pharmaceutical research, breakthroughs are directly related to the novelty in how a biomolecular phenomenon is modeled. Novel approaches to mathematical abstraction could expand the context for problem-solving, and in the best case plug directly into new product development.

Advanced virtual enterprises as a matter of definition can allow for and even encourage partners with these novel ways of thinking.

We speculate that in Central Africa, novel indigenous abstraction systems still exist, and can be preserved in a virtual enterprise context. This may not be true, and it may not be desirable to attempt in a project designed to be a clean demonstration. But it is a topic worthy of serious consideration.

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