Zahlen, bitte! Solomon W. Golomb and an octillion IT systems

What is the most common algorithm used by computers, smartphones, things on the Internet of Things, and many other devices? The computer scientist and physicist Stephen Wolfram asked himself this question in 2016, not in one of the many books he regularly publishes, but in a kind of obituary for a friend, the mathematician Solomon Wolf Golomb.

After his studies, Golomb had published a paper in July 1955 on linear feedback shift registers (LFSR), those useful circuits that can be used to generate pseudo-random number sequences. Wolfram calculated how often such LFSRs are used in computers, in communication via RFID, WiFi, Bluetooth, or in the GPS process and came up with the remarkable figure of one octillion, or 10⁴⁸. Since Golomb's death, another zillion has probably been added.

Zahlen, bitte!

In this section, we present amazing, impressive, informative and funny figures ("Zahlen") from the fields of IT, science, art, business, politics and, of course, mathematics every Tuesday. The wordplay "Zahlen, bitte!" for a section about numbers is based on the ambiguity of the German word "Zahlen." On one hand, "Zahlen" can be understood as a noun in the sense of digits and numerical values, which fits the theme of the section. On the other hand, the phrase "Zahlen, bitte!" is reminiscent of a waiter's request in a restaurant or bar when they are asked to bring the bill. Through this association, the section acquires a playful and slightly humorous undertone that catches the readers' attention and makes them curious about the presented numbers and facts.

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Initial research into secure satellite communication

With his rough calculation, Stephen Wolfram wanted to draw attention to the fact that the “pure” mathematics that Sol Golomb was working on at Harvard in the 1950s did indeed have practical uses. Golomb was already working as an advanced student during semester breaks at the Martin Company, which was developing space rockets for the Vanguard project. In this context, the question arose as to how communication with the rocket and later with the transported satellites could be secured.

In 1955, Colomb published the report “Sequences with Randomness Properties,” which Wolfram describes as the founding document of the theories on feedback shift registers. When the US satellite Explorer 1 reported from space a year later, after the Sputnik shock in 1957, this was also a triumph for Sol Golomb. At the time, he was employed as a mathematician at the Jet Propulsion Laboratory (JPL) and was responsible for secure communication.

After the successful satellite mission, he became head of a new department at JPL, the Information Processing Group. He managed and calculated the Venus radio astronomy experiment, which was used at JPL to determine the distance between the Earth and our nearest neighbor more precisely. JPL had installed antennas for space observation in the Mojave Desert, the arrangement of which Golomb had calculated using his Golomb ruler.

Witty reflections on contact with extraterrestrials

Along the way, Golomb thought about what would happen if humanity came into contact with other life forms. Fluent in nine languages (including Chinese and Japanese), the scientist published his ideas under the title “Extraterrestrial Linguistics” and mocked that the US government would surely set up a Cosmic Intelligence Agency (CIA) to monitor the aliens. He wrote, “To serve mankind, we must endeavor to find out whether they want us served baked or fried.” (“To serve mankind', we must endeavor to ascertain whether they wish to serve us baked or fried.”)

The first edition of his work Shift Register Sequences was published in 1967. By this time, Sol Golomb had returned to university, specifically to the University of Southern California (USC), with which he remained closely associated throughout his life. Together with his friend Edwyn Berlekamp, he founded the company Cyclotomics, which supplied NASA with communication programs, but he was not interested in commercial ventures.

This also applied to the Linkabit Company, which he co-founded and which would later become Qualcomm. When the Swedish company Ericsson hit Qualcomm with a series of patent lawsuits in the mid-1990s and filed numerous Swedish documents, it was Sol Golomb who, as an expert witness, managed to get Ericsson to give in: he had married the Swede Bodil Rygaard in 1955 and naturally spoke Swedish and Norwegian - and was also an expert in the interpretation of runic characters.

Sol Golomb lived and worked at USC in various ways from 1963 to 2016. With his essay Forty Years After Sputnik, he made fun of the scientists who wanted to separate the “one” mathematics from applied mathematics. Internationally, as a devout Jew who regularly read the Torah in the synagogue, he was particularly interested in exchanging ideas with scientists from Israel, as demonstrated by his collaboration with his students Abraham Lempel and Jacob Ziv.

Throughout his life, Golomb was a great fan of board games and puzzles of all kinds. With his research on Tetraminos and Pentaminos, he is sometimes considered the inventor of Tetris, but that is a story in itself.

(mho)