Empire of the SUM: It All Adds Up / Wall Street Journal Book Review


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Belinda Lanks
Aug. 21, 2023 6:11 pm ET


In 1976, Steve Wozniak sold his HP-65 programmable calculator for $500 to start a computer company with Steve Jobs.

It wasn’t a huge sacrifice. As a calculator engineer at Hewlett-Packard, he knew that the HP-67 was on its way and, with his employee discount, he could buy one for $370. His more highly prized gadget was the HP-35—the world’s premier scientific calculator and his inspiration for going to work at HP in the first place.

The HP-35 was a technological wonder. Until its appearance in 1972, pocket calculators performed only addition, subtraction, multiplication and division. The $395 HP-35 packed advanced functions like logarithms, sines and cosines into a relatively affordable, user-friendly package. Suddenly a computer’s worth of power could fit into anyone’s pocket.

In “Empire of the Sum: The Rise and Reign of the Pocket Calculator,” Keith Houston surveys the engineering advances that led to that moment and the human drive to solve equations faster and smarter.


Mr. Houston, whose previous books explored punctation and symbols (“Shady Characters,” 2013) and the history of books (“The Book,” 2016), begins by looking back to when humans started counting using the tools at our immediate disposal: our fingers. The earliest archaeological evidence of counting is a baboon fibula incised with notches indicating the number of whatever its owner wanted to track.

That 42,000-year-old tally stick, discovered in 1973 in a cave near South Africa’s border with Swaziland, “marks the point at which we began to delegate our memories to external devices,” Mr. Houston writes.

As civilizations progressed, they moved on from anatomical calculators, conferring numerical values to objects. The Sumerians, for instance, developed tokens whose varied shapes and sizes corresponded to smaller or larger quantities. But the biggest leap forward was the abacus, the first purpose-built calculator, invented in Mesopotamia or Greece between three and five millennia ago. The abacus made solving complicated equations possible, but getting results still required mental gymnastics.

Some shortcuts finally arrived in the 17th century courtesy of John Napier, a Scottish landowner, astrologer and mathematician. His invention: logarithms, a quick means of multiplying or dividing numbers through addition and subtraction. Not long after he published his revelation in 1614, logarithms became the basis for at least two important physical tools. Edmund Gunter placed them on a wooden rule to help seafarers with navigational calculations. Then William Oughtred produced his easier-to-use linear sliding rules, which, with a few later modifications, became the trusty and enduring slide rule.

As some mathematicians sought to simplify equations, others tried to automate them. Blaise Pascal was the first, in 1645, to build and sell a mechanical adding machine. Using gears similar to those of a clock, his Pascaline was an elegant metal box featuring windows for displaying a running total. Unfortunately, it didn’t do much more than add whole numbers, and its cost made it inaccessible to most.

Over the next 200 years, more machines with greater functionality were introduced, the most important of which was Charles Xavier Thomas’s mid-19th-century arithmometer. None, however, would be as convenient or portable as a slide rule—until the Curta, a pepper mill-like mechanical gadget designed by the Austrian engineer Curt Herzstark during World War II.

In a book that’s long on technical details and short on compelling anecdotes, Mr. Houston’s profile of Herzstark is a notable highlight. As a salesman for his family’s factory manufacturing unwieldy calculators, Herzstark heard his customers’ calls for a truly portable machine. Not long after Herzstark hatched the idea for one, however, German troops annexed Austria.

As the son of a Jewish father and Christian mother, Herzstark was sent to Buchenwald. There he supervised a factory of inmates fabricating rocket parts and repairing looted calculating machines. As Herzstark later recounted, his manager urged him to pursue his Curta side project, promising: “If it is really worth something, then we will give it to the Fuhrer as a present after we win the war. Then, surely, you will be made an Aryan.”

When Buchenwald was liberated in April 1945, Herzstark took his blueprints with him and eventually produced the Curta. It was a palm-size engineering marvel but a commercial failure.

The rest of Mr. Houston’s intermittently fascinating account is a creation story of tech breakthroughs begetting first-of-their-kind digital calculators. For a moment, relays made their way into calculators. The less finicky vacuum tube enjoyed an even briefer moment.

Transistors then hit the scene, as showcased in Olivetti’s 1965 flagship Programma 101. The Italian typewriter manufacturer was already renowned for its design excellence, and the P101 programmable megacalculator was no exception. It was the first user-centric desktop PC, and were it not for a series of business missteps, Olivetti might have beat Apple to the punch.

The year the P101 launched, Texas Instruments decided to enter the calculator market with its big innovation, the microchip. The company had industrial and military customers for its chips, but to expand demand it needed to sell them to consumers. The idea: an electronic calculator that could fit in one’s pocket.

The resulting prototype didn’t quite live up to expectations—it was the size of a paperback and weighed 3 pounds—but it laid the groundwork for the smaller, lighter gadgets to come, notably Busicom’s first truly pocketable calculator in 1971 and Hewlett-Packard’s HP-35 in 1972.

The era of calculator mania had begun, and throughout the late ’70s and ’80s calculators were everywhere, as standalones and as combinations with other electronics, including clock radios, digital watches and even synthesizers.

The pocket calculator’s heyday would be brief compared with that of the slide rule it replaced. Even scientific calculators grew cheaper and profit margins waned. HP, despite Mr. Wozniak’s pleas to build a personal computer, refused to take the risk, only to see calculators absorbed into PCs, palmtops and, finally, smartphones.

The pocket calculator sublimed, becoming “everywhere and nowhere at once,” Mr. Houston writes. “The calculator is dead; long live the calculator.”