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Memorial Day, Solomon Golomb

May 30, 2016

Today, Monday, May 30, 2016, is Memorial Day in the United States. This holiday is observed on the last Monday in May of each year, and it's the traditional start of the summer vacation period. While originally conceived as a day to honor war dead, it's a day in which people remember their departed friends and family members, sometimes visiting grave sites to place flowers. Military veteran's graves are typically marked by a small American flag.

Cemetary at the National Shrine of the North American Martyrs, Auriesville, New York
Cemetery at the National Shrine of the North American Martyrs, Auriesville, New York. (Photo by the author, released under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 license. Click for larger image)

May 1, 2016, marked the death at age 83 of the prominent American mathematician, Solomon Wolf Golomb (May 30, 1932 – May 1, 2016). Golomb, who was the son and grandson of rabbis from Vilnius, Lithuania, was awarded his B.S. degree in mathematics from Johns Hopkins University at age eighteen.[1] His mathematical specialty was number theory, writing a doctoral dissertation at Harvard University in 1957 on the distribution of the prime numbers.

Golomb worked on communication theory at a summer job at the Glenn L. Martin Company, which sparked his interest in shift register sequences and steered him away from pure to applied mathematics.[1] After a Fulbright sabbatical at the University of Oslo, Golomb joined Caltech's Jet Propulsion Laboratory where he worked further on communications. Although recruited by UCLA, Golomb became a professor of electrical engineering in 1963 at the University of Southern California, where he was a Distinguished University Professor at his death.[1]

Solomon Golomb (left) in 1961
Solomon Wolf Golomb (left) in 1961 when he was assistant chief of the Communications Systems Research Section of NASA's Jet Propulsion Laboratory. He is shown with colleague mathematicians, Leonard Baumert and Marshall Hall, Jr., holding a representation of a Hadamard matrix of 92 rows and columns. The existence of this matrix, with utility in constructing communication code, was discovered by the team using an IBM 7090 mainframe computer, programmed by Baumert. (NASA/JPL image.)

Golomb investigated maximal length shift registers that serve as pseudorandom number generators important to many computer applications, such as numerical simulation and cryptography. He also invented Golomb coding, a lossless compression method. His advances in communications coding techniques allowed the compression needed to relay signals from the Mars Spirit and Opportunity rovers and to recover radar signals bounced from the surface of Venus in 1961.[1]

My favorite among Golomb's many mathematical constructions is the Golomb ruler, an integer-marked ruler that has no two pairs of marks the same distance apart. A moment's reflection will reveal that such a ruler can give accurate measures of many different lengths by translation. Some Golomb rulers, called perfect Golomb rulers, can measure all integer distances up to their length. This is only true for Golomb rulers of length four, or less. The web site, distributed.net, hosts a massively parallel search effort for long Golomb rulers.

Figure caption
A Golomb ruler of order 16 and length 177. This ruler, discovered by James B. Shearer in 1986, has divisions at 0, 1, 4, 11, 26, 32, 56, 68, 76, 115, 117, 134, 150, 163, 168, and 177. (Created using Inkscape. Click for larger image.)

Golomb's intellectual prowess extended into many areas, He spoke several languages, invented a hybrid of chess and checkers in 1948 called "cheskers," and his variant of dominoes, called pentomino, is said to have inspired Tetris.[1] Golomb wrote many recreational mathematics articles. He was a regular columnist of the IEEE Information Theory Society Newsletter, writing "Golomb's Puzzle Column;" author of a puzzle for each issue of the Johns Hopkins Magazine in a column called "Golomb's Gambits;" contributor to Scientific American's Mathematical Games column; and a contributor to Word Ways: The Journal of Recreational Linguistics.

Among his honors and awards is his appointment to the Viterbi Chair in Communications at USC in 1999.[1] The chair is named after another communications pioneer, Andrew Viterbi, Qualcomm co-founder, who met Golomb at JPL.[1] Golomb was awarded the 2016 Franklin Institute Benjamin Franklin Medal in Electrical Engineering, and he was one of only twelve recipients of the 2013 National Medal of Science.[1]

Golomb was elected to the National Academy of Engineering in 1976; additionally, he was elected to the National Academy of Sciences in 2003. He was a fellow of the American Academy of Arts and Sciences, the American Mathematical Society, the Society for Industrial and Applied Mathematics, the American Association for the Advancement of Science, and the Institute of Electrical and Electronics Engineers.[1] He was recipient of the 2000 IEEE Richard W. Hamming Gold Medal, the Lomonosov Medal of the Russian Academy of Sciences, the Kapitsa Medal of the Russian Academy of Natural Sciences, and a medal from the US National Security agency.

Said Andre Viterbi at Golomb's death, "We've lost a great mind. A great heart and a great sense of humor. The universe will miss him as much as we will."[1] USC President, C. L. Max Nikias, stated that
"Professor Golomb was truly a giant in the field of mathematics and engineering... He was an exceptionally imaginative thinker, and so many enduring innovations and highly creative games - including polyominoes and pentomino - emerged from his inimitable genius. But beyond the innumerable accomplishments, Professor Golomb was also a dear friend and colleague, having served on USC's faculty for more than half a century. Indeed, he helped transform our university into the world-class institution it is today."[1]

Since this is Memorial Day, I've gleaned from Wikipedia some memorable STEM field items of historical significance that occurred on May 30, as follows. Quite a few of these are not familiar to me, although I immediately recognized Eugène Catalan, Hannes Alfvén, Julius Axelrod, Marissa Mayer, Leó Szilárd, and Rosalyn Yalow.

1966 – Launch of Surveyor 1, the first US spacecraft to land on an extraterrestrial body; namely, the Moon.
1971 – Launch of Mariner 9 to map 70% of the surface of Mars.

1423 – Georg von Peuerbach, German mathematician and astronomer (died 1461).
1768 – Georg Amadeus Carl Friedrich Naumann, German mineralogist and geologist (died 1873).
1814 – Eugène Charles Catalan, Belgian-French mathematician (died 1894).
1908 – Hannes Alfvén, Swedish physicist, engineer, and Nobel laureate (died 1995).
1912 – Julius Axelrod, American biochemist and Nobel laureate (died 2004).
1912 – Erich Bagge, German physicist (died 1996).
1955 – Jacqueline McGlade, English-Canadian biologist, and ecologist.
1963 – Helen Sharman, English chemist and astronaut.
1975 – Marissa Mayer, American computer scientist, CEO of Yahoo!

1901 – Victor D'Hondt, Belgian mathematician (born 1841).
1926 – Vladimir Steklov, Russian mathematician and physicist (born 1864).
1946 – Louis Slotin, Canadian physicist and chemist (born 1910).
1964 – Leó Szilárd, Hungarian-American physicist and engineer (born 1898).
1995 – Lofty England, English-Austrian engineer (born 1911).
2006 – David Lloyd, New Zealand biologist (born 1938).
2009 – Ephraim Katzir, Israeli biophysicist, 4th President of Israel (born 1916).
2011 – Rosalyn Sussman Yalow, American physicist and Nobel laureate (born 1921).
2012 – Andrew Huxley, English physiologist, biophysicist, and Nobel laureate (born 1917).


  1. Marc Ballon and Daniel Druhora, "In memoriam: Solomon Golomb, communications technology pioneer, 83," University of Southern California Press Release, May 9, 2016 .

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