A History in Calculators

Justin Zobel

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Sanyo CZ-2901

While packing for a house move, I found calculators in drawers, boxes, cupboards. Almost every calculator (or organiser) I'd ever owned. All of these were machines I'd had since they were new, carefully hoarded away over my entire lifetime ... just in case. These calculators reflect the evolution of the technology, from first emergence as a mass-market product to near-terminal decline; the calculator is almost obsolete now, but once was essential. So many calculators. Here they are.

My next calculator was acquired in Form 4. The previous year I had decided that calculators were nothing but useless toys that did basic arithmetic badly: an objective, reasoned criticism that might have had something to do with several months of income spent on a dud. However, my science teacher brought to us an opportunity to buy at cost an advanced calculator that, he felt, would be of real value in our studies.

And so the class, or most of us, acquired a new Sanyo that seemed like a prop from a science fiction movie, with its curved lines, bright green display, and shiny metallic finish. I think it cost about $60, which my parents thought was a lot of money, but in compensation my mother took my GE; I selflessly explained to her how good it was, and that I had been wrong to get frustrated with it.

The Sanyo was far more sophisticated than any other calculator I'd seen. Metric conversions. Coordinate systems. Multiple memories. Buttons with four functions. Twelve digits of precision. Above all else, it used reverse Polish notation. This was a calculator for initiates; a casual user couldn't even use it to compute an elementary sum. To calculate (1+2)x3, one typed 1ENT2+3x (where “ENT” represented ENTER); this was a secret language and fluency in it meant that one had joined the cognoscenti.

In practice I found reverse Polish unintuitive and error-prone but somehow magical, and it introduced the idea of stacks, which as a result was the first programming concept I learned.

Power was a problem, though. The Sanyo took 4 double-A batteries, which only lasted about an hour, so mostly I used it with the external power supply; batteries were expensive. It replaced most of my maths tables, so it got used all the time in maths and physics homework. But early in the next school year the display started to dim and then stopped working altogether. I was upset, because it was important to me, and also frustrated, because it had become an essential tool; and because it would be so costly to replace. Such a short life! Less than a year. Those early calculators could be so frail.

An item that's missing from the collection is my copy of a book on how to use calculators. It was small, more a thick pamphlet than a book, with a glossy cover; probably it was distributed by my science teacher with the Sanyo calculators, but perhaps I bought it in the bookshop of the campus where my stepfather worked. This book was wonderful for an aspiring maths adept, but has gone the way of other similar books, such as my copies of mathematical tables — discarded so long ago that I have no recollection of what happened to it.

When I first saw this book I was skeptical, wondering what it could possibly say beyond “press the buttons in the right order”, but it was genuinely valuable. Methods for estimating the accuracy of logs and trigonometric functions, and then for correcting errors; practical tips for working round restrictions such as limits on the number of open parentheses (or stack depth in reverse Polish notation); procedures for quickly computing approximate bounds on sums of series; error minimisation by, for example, doing long multiplications as sums of logs. Some of this advice was reasonably advanced, so much so that it formed part of a second-year numerical computation subject I took at university.

A particular piece of advice, which at the time seemed to belie the whole point of having such a guide, was (paraphrased from memory) “don't use a calculator for tasks that you can easily do by hand”, on the basis that overuse of a mechanical aid undermines development of understanding. A related piece of advice was (again, paraphrased) “always check whether the answer makes sense”. I still find myself offering this same advice to students, though not in the context of calculators.

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Last updated July 2018.

This webpage was created by Justin Zobel. All images are Copyright© University of Melbourne. Photography by Lee McRae.