The Complex Number Calculator
A plywood board, two relays salvaged from a dumpster, strips cut from a tobacco tin, batteries, and light bulbs. Who would have thought that these makeshift materials assembled by George R. Stibitz in his kitchen in 1937 would mark our history of computing? This mathematician at Bell Telephone Laboratories (Bell Labs) had just noticed a parallel between the positions of telephone relays and binary notation. His domestic tinkering gave birth to a one-bit binary adder.
Stibitz’s evenings turned into circuit design sessions for other arithmetic operations. In 1938, he presented his work to Thornton Fry, head of the laboratory’s mathematics section. Fry raised a practical question: could these relay calculators handle complex numbers? This task was then mobilizing an army of human computers at Bell Labs.
Stibitz tackled the challenge head-on. The plans were completed by February 1938. He partnered with Sam Williams, an engineer specializing in switching systems. Their collaboration bore fruit in 1939 with the completion of the Complex Number Calculator.
The machine shone through its technical innovations. It used a binary-coded decimal system with four relays per decimal digit. It processed numbers up to eight decimal digits, with two additional internal digits to limit rounding errors. Its structure comprised two distinct calculation units: one for the real part of complex numbers, the other for the imaginary part.
The user interface constituted a revolution in itself. The machine was hidden in a closet, accessible only for maintenance. Users worked at three operator stations scattered throughout the Bell Labs building on West Street in New York. Each station had a keyboard for input and a teleprinter for displaying results. This configuration represents the first use of remote terminals in computing history.
The multiplication keys, as well as the division key, activated subroutines of about a dozen steps. These executed complex operations using the two calculation units, which worked exclusively on real numbers. This architecture already foreshadowed the modern notion of subroutines.
On September 11, 1940, the Complex Number Calculator was unveiled to the public at a meeting of the American Mathematical Society at Dartmouth College. For the occasion, a console was modified to communicate with the computer via a long-distance telephone line. Participants, including the famous Norbert Wiener (founding father of cybernetics), submitted problems on the keyboard. The data traveled to the relay equipment in New York, and the results returned to the teleprinter in less than a minute. This demonstration inaugurated remote control of a computer, heralding the data transmission that would explode in the 1960s.
The Complex Number Calculator served until 1949, with remarkable reliability. During World War II, the network design groups, its primary users, ran it almost continuously from 8 a.m. to 9 p.m., six days a week. The machine had not been designed for such a regime. Built as a demonstration model before the war, it lacked self-checking features and contact protection standard in telephone exchanges. The war prevented the construction of a more robust second machine. Toward the end of the conflict, it had to be shut down for two days to replace worn relay contacts.
The legacy of the Complex Number Calculator is immense. It proved the feasibility of automatic calculations with reliable electromechanical components. Its success spawned other relay calculators at Bell Labs during the war: the Model II in 1943, capable of iterative operations, then the Models III and IV in 1944-1945, more powerful with approximately 1,400 relays and seven teleprinter units each.
These machines established fundamental principles still present in modern computing: the use of binary for calculations, the separation between calculation unit and user interface, the notion of subroutines, and remote access to computing resources. Bell Labs’ relay calculators continued to operate efficiently 13 to 15 years after the war, some remaining in service well after the arrival of the first commercial electronic computers.
The Complex Number Calculator, born in a kitchen, showed that complex mathematical tasks could be automated reliably. Its influence extended to automatic telephone message accounting systems, where similar calculators processed detailed call billing. This machine represents an essential link between mechanical calculators and our computers.