IDEA #96. Master a pre-electronic form of mathematical calculation: learn how to use an abacus, a slide rule, a quipu, a Curta calculator, or some other calculating device or method. Instructions can be found in libraries or the Internet, and slide rules can be found at yard sales, on Internet auction sites, or even in dusty drawers in old mathematics classrooms. There is even chisanbop, a really efficient form of calculating using just the fingers that can be learned on the Internet; it is Korean in origin, and experienced practitioners can perform chisanbop calculations almost as fast as an electronic calculator.

It is hard to believe that just two generations ago most of the electronic technology that we now use to perform mathematical calculations was unavailable to the general public. Even electric adding machines used power only to assist mechanical processes, and only the most expensive and cumbersome machines were capable of simple multiplication.

Even so, human genius in many cultures had observed certain characteristics of numbers and created hand-operated devices that could perform sophisticated and precise operations. The east Asian abacus, for example, can add, subtract, multiply, and divide in skilled hands almost as quickly as an electronic calculator; although its capacities are limited, it is still sufficient for most commercial needs. The slide rule, based on logarithmic principles, enables rapid calculation in a number of modes, depending on the design of the rule (not, incidentally, a ruler, since a slide rule is not made for measurement); during World War II virtually every complex machine short of the atomic bomb was essentially developed by engineers using only slide rules.

The Curta calculator, a rarity these days and rather expensive when one can be found, is a masterpiece of precision design and manufacture from Liechtenstein that could do virtually anything a slide rule could. But the Curta is entirely digital, taking input and yielding data in precise numbers. We are partial to the Curta if for no other reason than that its mechanical elegance is almost unsurpassed. If the youngster has access to one of these, simply handling it will be a satisfying experience.

Chisanbop (also chisenbop) made its appearance in the U.S. just as cheap electronic calculators were entering classrooms, and so a promising and capable way of teaching students to perform calculations literally by hand never quite had its day in school. Like the mechanical calculators, chisanbop provides its own education in aspects of number theory.

If the youngster is intrigued by this kind of technology, there are still other, less known systems that have been used for numerical recording and calculating, and there are also groups of enthusiasts who are determined to keep alive the skill of using them. While teachers may decry the apparent de-emphasis of “math facts” in contemporary education, the simple fact is the humans have been engaged in developing ways to make calculating “automatic” for hundreds of years.