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THE CURTA CALCULATOR looks like a pepper grinder with numerals peering out. There’s a crank on the top that whirs with reassuring precision. And anyone serious about Time-Speed-Distance rallying in the old days wanted one. By “the old days,” of course, I mean back when computers took up entire walls of office space.
History of the Curta involves the persistence of Austrian Curt Herzstark, the Buchenwald Prison Camp, the Prince of Liechtenstein, the mathematics of Gottfried Leibnitz and the entertainment of a goodly number of early sports car enthusiasts.
In 1938, Curt Herzstark obtained Deutsche Reichpatent 747073 for design of a mechanical calculator’s complemented stepped drum (more on which anon). The Nazi’s annexation of Austria in 1938 transformed the Herzstark family’s precision machine works into manufacturing military hardware, causing a hiatus in development of any calculator concept.
Curt’s father was a Jew; his mother, a Catholic-born Lutheran. And, in 1943, Curt was arrested and sent to Prague’s Pankrác Prison and then to Buchenwald Concentration Camp for “helping Jews” and “indecent contact with Aryan women.” Serving at Buchenwald as an intelligenz-slave, he was forced to reproduce the drawings describing his calculating device.
Fortunately, the Allies’s April 1945 liberation of Buchenwald came before the Nazis fully grasped the idea. Herzstark was freed and given responsibility for reconstruction of German factories in a region soon engulfed in the Soviet Zone.
Herzstark subsequently fled to Vienna, came close to enlisting a Swiss company to produce his design—and then Prince Franz Josef II of Liechtenstein played a role. The prince wanted to transform his agricultural enclave into a modern state, and he invited Herzstark to establish high-precision manufacturing in the Principality.
The first Curta prototypes were assembled in 1947 in the ballroom of Hotel Hirschen, in the town of Mauren, Liechtenstein. A building for the new company Contina AG soon followed.
Reflecting its compact dimensions, the device’s original name had been Liliput. According to Herzstark, though, the name Curta arose when a Miss Ramaker, trade correspondent of Contina AG, suggested, “This machine is the daughter of Mister Herzstark. When the father is called CURT, the daughter has to be called CURTA.”
Between 1947 and 1972, perhaps 140,000 Curta calculators were produced, about 80,000 of the Type I design and perhaps 61,000 of the slightly larger Type II. By the end of production, a Type I cost $125; a Type II, $175. By contrast, the Texas Instrument TI 2500 Datamath arrived in 1972, initially priced at $149.99, soon reduced to $119.95.
Both Curtas are capable of addition, subtraction, multiplication and division. The primary difference between a Type I and Type II is in significant figures: The Type I has 8-digit entry, a 6-digit counter and 11-digit results. The Type II operates with 11, 8 and 15 digits, respectively. To put these capabilities in perspective, my cell phone’s Utilities Calculator is a 9-digit device, though it’ll handle larger results using scientific notation.
The Curta made news in Road & Track back in October 1956: “A new and remarkable little instrument has been brought to our attention…. For you rally fiends and engineering enthusiasts it should save the day…. Our Technical Editor is all aglow!” Full disclosure: No Technical Editor was listed on the masthead; I suspect Editor John R. Bond did it all in those days.
I talked about “Crankin’ Your Curta” back in Tech Tidbits, R&T, July 2007. Briefly, “You entered digits by sliding knobs on the drum’s circumference, then cranked once to enter the number, a series of turns for multiplying it. Units, tens, hundred, etc., were handled by rotation of the knurled top ring. Pull the crank out slightly, and you got subtraction. The revolution counter and result counter—i.e., the answer—were atop the drum.”
Subtraction is of special interest, as it uses Herzstark’s patented “complemented stepped drum.” The idea of stepped drums for keeping track of numbers dates back to the 17th century and Gottfried Wilhelm Leibnitz, the German co-discoverer of calculus (Brit Isaac Newton was the other).
The idea of complemented arithmetic replaces ordinary subtraction and its “borrowing” or “regrouping” with a related addition, in this case Complements by 9s. The following example of 726 – 350 shows how it works, albeit without fully explaining why. A digit’s complement of 9 is the difference between it and 9: The complement of 3 is 6; the complement of 0 is 9.
Lurking beneath the strange “and add 1 to get the answer” is the fact that subtracting a digit is equivalent to adding its complementary digit plus 1. Algebraically, and ignoring the tens place, A – B = A + (9 – B ) + 1. This idea of Complements of 9 may sound like Rube Goldberg gone wild, but indeed, it’s how even today’s digital devices perform subtraction.
These seem fair prices for celebrating Curt Herzstark, Prince Franz Josef II of Liechtenstein, Gottfried Leibnitz and Contina AG’s Miss Ramaker. ds
© Dennis Simanaitis, SimanaitisSays.com, 2016