The Rise of Pocket Calculators: A Mathematical Journey Through History
In the late 1970s and early 1980s, digital watches with built-in calculators were all the rage among schoolchildren. These sleek devices not only allowed kids to do maths on their wrists but also play popular games like Space Invaders. However, what many may not realize is that pocket calculators were the result of centuries of human innovation and progress, as outlined in Keith Houston’s book, Empire of the Sum.
In this book, Houston takes readers on a fascinating mathematical history tour, tracing the development of number systems, slide rules, mechanical calculators, and microchips. Throughout the pages, he introduces us to brilliant inventors and thinkers such as Thomas Edison, Isaac Newton, Blaise Pascal, and Katherine Johnson, who have each played a significant role in shaping the world of mathematics.
One interesting revelation from the book is that different cultures have varied approaches to counting. While most societies, including ours, use a base-10 system due to our ten fingers, this is not true for all. The Sumerians, for example, used a base-60 system, which is still reflected in the way we measure time with twelve hours, sixty minutes, and sixty seconds. Another example is the Indigenous Melanesian people of the Torres Straits Islands, who employed a base-19 system that accounted for various body parts beyond the fingers.
Houston delves into the ancient Babylonian, Greek, and Chinese cultures, where abacuses, the forerunners of calculators, were used. These bead-based calculators lasted for centuries, even continuing into the 1970s in Japanese schools. Slide rules, which operated on the principle of adding the logarithmic equivalents of numbers to multiply them, also enjoyed a long life, beginning in the 17th century and still being available in the 1980s.
While these early calculating devices were innovative and allowed for complex calculations, they had their limitations. Slide rules, for instance, heavily relied on the user’s eyesight and often led to oversimplified solutions. As a result, structures such as bridges were built stronger and more expensively than necessary, and vehicles consumed more fuel than required.
The book also sheds light on the significant role played by mechanical calculators and the computers who used them. These human calculators, mostly women, tackled massive mathematical tasks, such as producing tables of mathematical values during the Great Depression. Among them was Curt Herzstark, who invented the portable Curta Type I mechanical calculator while imprisoned at the Buchenwald concentration camp. Unfortunately for Herzstark, the rise of electronic calculators rendered his invention obsolete soon after.
The second half of the book focuses on the rapid development of electronic calculators, first utilizing vacuum tubes and relays, and later transistors and microchips. Companies like Texas Instruments and Casio competed fiercely in this technological landscape, leading to cross-pollination and advancements in calculator technology. Notably, algorithms created for bomber aircraft navigational systems found their way into the first pocket scientific calculator, HP-35, launched by Hewlett-Packard in 1972.
Empire of the Sum concludes with the advent of the computer spreadsheet program. Before programs like VisiCalc, accountants used physical spreadsheets to track debits and credits. However, the introduction of computational interfaces allowed users to input numbers and perform calculations effortlessly, making computers indispensable and overshadowing pocket calculators.
While the rise of computers and smartphones led to a decline in pocket calculators’ popularity, they still find utility in various settings, from classrooms to home applications on smartphones. As Houston aptly remarks, The calculator is dead, long live the calculator. Throughout history, pocket calculators played a profound role, and their impact was nothing short of remarkable.
In Empire of the Sum, Keith Houston beautifully encapsulates the journey of pocket calculators, reminding us of their legacy and the incredible advancements they brought to the world of mathematics.
