## Saturday 18 November 2023

### On This Day in Math - November 18

Predictions can be very difficult—
— Niels Bohr

The 322nd day of the year; 322 is the 12th Lucas Number. The Lucas Sequence is similar to the Fibonacci sequence with L(1) = 1 and L(2) = 3 and each term is the sum of the two previous terms. L(n) is also the integer nearest to ${\varphi }^{n}$ This is the last day of the year that will be a Lucas Number.

322 is smallest number whose square has 6 diff digits (103684). *Derek Orr
322 is a sphenic number, which means that it is the area of  a rectangular box (parallelepiped) with prime lengths for its length, width, and height.

EVENTS

2349 B.C. Noah’s ﬂood began according to the English mathematician, William Whiston (1667–1752) who felt it was caused by a comet which passed over the equator causing extensive rains. *Claire L. Parkinson, Breakthroughs, p. 131 Whiston would follow Newton as the Lucasian Professor at Cambridge.*RMAT
An English theologian, historian, natural philosopher, and mathematician, a leading figure in the popularization of the ideas of Isaac Newton. He is now probably best known for helping to instigate the Longitude Act in 1714 (and his attempts to win the rewards that it promised) and his important translations of the Antiquities of the Jews and other works by Josephus (which are still in print). He was a prominent exponent of Arianism and wrote A New Theory of the Earth.
In 1710 he lost the professorship and was expelled from the university as a result of his unorthodox religious views. Whiston rejected the notion of eternal torment in hellfire, which he viewed as absurd, cruel, and an insult to God. What especially pitted him against church authorities was his denial of the doctrine of the Trinity, which he believed had pagan origins.
He was an early advocate, along with Edmond Halley, of the periodicity of comets; he also held that comets were responsible for past catastrophes in Earth's history. In 1736, he caused widespread anxiety among London's citizens when he predicted the world would end on 16 October that year because a comet would hit the earth. William Wake as Archbishop of Canterbury officially denied this prediction to calm the public.

A portrait of William Whiston with a diagram demonstrating his theories of cometary catastrophism, described in A New Theory of the Earth

1690 First use of catenary According to E. H. Lockwood (1961) and the University of St. Andrews website, this term was first used (in Latin as catenaria) by Christiaan Huygens (1629-1695) in a letter to Leibniz dated November 18, 1690. *Earliest Known Uses of Some of the Words of Mathematics The English word catenary is usually attributed to Thomas Jefferson (but see below****), who wrote in a letter to Thomas Paine on the construction of an arch for a bridge"I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to be a very scientifical work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the catenary is in perfect equilibrium."  (Dec. 23, 1788) *Jeff Miller  (Paine had previously used the term "catenarian" in earlier letter to Jefferson. (Sept. 15, 1788).
****Miller's web site now includes a single previous use of Catenary in English in 1725 in Lexicon Technicum: Or, An Universal English Dictionary of ARTS and SCIENCES: Fourth Edition Volume I*****

1752 Goldbach writes Euler with conjecture that every odd number greater than 3 is the sum of an odd number and twice a square (he allowed 02). Euler would reply that it was true for the first 1000 odd numbers, and then later to confirm it for the first 2500. A hundred years later, German mathematician Moritz Stern found two contradictions, 5777 and 5993. The story appears in Alfred S. Posamentier's Magnificent Mistakes in Mathematics, (but gloriously, has a mistake for the date, using 1852, but such a wonderful book can forgive a print error.)

1812 Jean Victor Poncelet , a military engineer, was captured while Napoleon’s army was retreating from Moscow. He proﬁted from this enforced leisure (until his release in June 1814) by resuming his study of mathematics. While there he did important work on projective geometry. *VFR
He is considered a reviver of projective geometry, and his work Traité des propriétés projectives des figures is considered the first definitive text on the subject since Gérard Desargues' work on it in the 17th century. He later wrote an introduction to it: Applications d'analyse et de géométrie.

1825 Birbeck writes to Gilmer regarding the application for professor at U Va of Charles Bonnycastle, son of John Bonneycastle.  “The name of Bonnycastle must be well known in America, and if known, must be highly valued; and the son I am persuaded will extend the fame of the parent.

1879  After the death of Maxwell, George Stokes writes to offer Lord Rayleigh the position of head of the Cavendish Laboratory in Cambridge.  *Memoir and scientific correspondence of the late Sir George Gabriel Stokes, pg 227

1883 At noon on this day the telegraphic time signals sent out daily from the Naval Observatory at Washington, D.C., were changed to standard time, a system adopted on the initiative of the American Railway Association. Standard time was suggested for the U.S. in 1869 by Charles Ferdinand Dowd, a schoolmaster from Saratoga, N.Y., but was not adopted then. He suggested dividing the continent into four time zones each one hour or ﬁfteen degrees of longitude wide. Standard Railroad Time had four time zones, Eastern, Central, Western, and Paciﬁc. *VFR
(before this change, "Clocks in New York City were 1 minute 1 second behind Albany, but 10 minutes 27 seconds ahead of Baltimore. So the railroads decided to adopt a variation of the idea first advanced in 1869 by a New York schoolmaster, Charles F. Dowd, to divide the continent into four time belts, each 15 degrees of longitude, or one hour, wide. "
"Some citizens grumbled about ''railroad tyranny'' and tampering with ''God's time.'' The Mayor of Bangor, Me., deplored the change as an ''attempt to change the immutable laws of God Almighty.'' The Indiana Sentinel lamented, ''The sun is no longer boss of the job.'' *New York Times, 20 Nov. 1983.)
On April 1 of 1967, The Uniform Time Act divided the United States into eight time zones; Eastern, Central, Mountain, Pacific, Yukon, Alaska, Hawaii, and Bering.  *FFF, pg 149
Mr. Dowd, the schoolmaster and time innovator, died two decades after the switch to standard time. He was hit by a train.

1915 On the third Tuesday of November, Einstein entered the Prussian Academy of Sciences, and erased a planet from the solar system. A planet witnessed dozens of times, so often they had calculated its orbit. In the first of two papers on his General Theory of Relativity, he showed that his calculations perfectly explained the strange behavior of Mercury. For years the inability of Newtonian Physics had been unable to explain the behavior, and they looked for (and found?) Vulcan, Mercury's close "companion". With Einstein's theory, his calculations proved Vulcan did not exist. *Thomas Levenson "The Hunt for Vulcan."

1963 The first push-button telephone goes into service. @yovisto
The first electronic push-button system with Touch-Tone dialing was offered by Bell Telephone to customers in Carnegie and Greensburg, Pennsylvania.
Western Electric experimented as early as 1941 with methods of using mechanically activated reeds to produce two tones for each of the ten digits. But the technology proved unreliable and it was not until long after the invention of the transistor when the technology matured. On 18 November 1963 the Bell System in the United States officially introduced dual-tone multi-frequency (DTMF) technology under its registered Touch-Tone® mark. Over the next few decades Touch-Tone service replaced traditional pulse dialing technology and it eventually became a world-wide standard for telecommunication signaling.
The now standard layout of the keys on the Touch-Tone telephone was the result of research of the human-engineering department at Bell Laboratories in the 1950s under the leadership of South African-born psychologist John Elias Karlin (1918–2013), who was previously a leading proponent in the introduction of all-number-dialing in the Bell System. This research resulted in the design of the DTMF keypad that arranged the push-buttons into 12 positions in a 3-by-4 position rectangular array, and placed the 1, 2, and 3 keys in the top row for most accurate dialing.[18] The remaining digits occupied the lower rows in sequence from left to right, however, placing the 0 into the center of the fourth row, while omitting the lower left, and lower right positions. These two positions were later assigned to the asterisk and pound key when the keypad was expanded for twelve buttons in 1969. *Wik

1991 IBM and Siemens AG Announce 64M DRAM Chip Prototype : IBM and Siemens AG announce they have developed a prototype 64 megabyte DRAM chip. This development was in line with Moore’s Law which predicts a doubling of the number of transistors etched into silicon every 18 months. *CHM

BIRTHS

1839 August (Adolph Eduard Eberhard) Kundt (18 Nov 1839; 21 May 1894)  was a German physicist who developed a method (1866) to determine the  velocity of sound in gases and solids. He used a closed glass tube into  which a dry powder (such as lycopodium) has been sprinkled. The source  of sound in the original device was a metal rod clamped at its centre  with a piston at one end, which is inserted into the tube. When the rod  is stroked, sound waves generated by the piston enter the tube. If the  position of the piston in the tube is adjusted so that the gas column is  a whole number of half wavelengths long, the dust will be disturbed by  the resulting stationary waves forming a series of striations, enabling  distances between nodes to be measured. *TIS

1844 Albert Wangerin (November 18, 1844 – October 25, 1933) worked on potential theory, spherical functions and differential geometry.*SAU He wrote an important two volume treatise on potential theory and spherical functions. Theorie des Potentials und der Kugelfunktionen I was published in 1909 and Theorie des Potentials und der Kugelfunktionen II was published in 1921. Wangerin functions are named for him.
He was also known for writing of textbooks, encyclopaedias and his historical writings.*Wik

1872 Giovanni Enrico Eugenio Vacca (18 November 1872 – 6 January 1953) was an Italian mathematician, Sinologist and historian of science.
Vacca studied mathematics and graduated from the University of Genoa in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved to Turin and became an assistant to Giuseppe Peano. In 1899 he studied, at Hanover, unpublished manuscripts of Gottfried Wilhelm Leibniz, which he published in 1903. Around 1898 Vacca became interested in Chinese language and culture after attending a Chinese exhibition in Turin. He took private lessons of Chinese and continued to study it at the University of Florence. Vacca then traveled to China in 1907-8 and defended a PhD in Chinese studies in 1910. In 1911, he became a lecturer in Chinese literature at the University of Rome. In 1922, he moved to Florence and taught Chinese literature and language at university until 1947.
The interests of Vacca were almost equally split between mathematics, Sinology and history of science, with a corresponding number of papers being 38, 47 and 45. In 1910, Vacca developed a complex number iteration for pi. *Wik

1887 Gustav Theodor Fechner (19 Apr 1801, 18 Nov 1887) German physicist and philosopher who was a key figure in the founding of psychophysics, the science concerned with quantitative relations between sensations and the stimuli producing them. He formulated the rule known as Fechner’s law, that, within limits, the intensity of a sensation increases as the logarithm of the stimulus. He also proposed a mathematical expression of the theory concerning the difference between two stimuli, advanced by E. H. Weber. (These are now known to be only approximately true. However, as long as the stimulus is of moderate intensity, then the laws will give us a good estimate.) Under the name “Dr. Mises” he also wrote humorous satire. In philosophy he was an animist, maintaining that life is manifest in all objects of the universe. *TIS

1897 Patrick M.S. Blackett (18 Nov 1897; 13 Jul 1974) English scientist who won the Nobel Prize for Physics in 1948 for his discoveries in the field of cosmic radiation, which he accomplished primarily with cloud-chamber photographs that revealed the way in which a stable atomic nucleus can be disintegrated by bombarding it with alpha particles (helium nuclei). Although such nuclear disintegration had been observed previously, his data explained this phenomenon for the first time and were useful in explaining disintegration by other means. *TIS

1900 George Bogdanovich Kistiakowsky (November 18, 1900 – December 7, 1982) was a Ukrainian-American physical chemistry professor at Harvard who participated in the Manhattan Project and later served as President Dwight D. Eisenhower's Science Advisor.
Born in Kiev in the old Russian Empire, Kistiakowsky fled Russia during the Russian Civil War. He made his way to Germany, where he earned his PhD in physical chemistry under the supervision of Max Bodenstein at the University of Berlin. He emigrated to the United States in 1926, where he joined the faculty of Harvard University in 1930, and became a citizen in 1933.
During World War II, he was the head of the National Defense Research Committee (NDRC) section responsible for the development of explosives, and the technical director of the Explosives Research Laboratory (ERL), where he oversaw the development of new explosives, including RDX and HMX. He was involved in research into the hydrodynamic theory of explosions, and the development of shaped charges. In October 1943, he was brought into the Manhattan Project as a consultant. He was soon placed in charge of X Division, which was responsible for the development of the explosive lenses necessary for an implosion-type nuclear weapon. He watched an implosion weapon that was detonated in the Trinity test in July 1945. A few weeks later a Fat Man implosion weapon was dropped on Nagasaki.
From 1962 to 1965, he chaired the National Academy of Sciences's Committee on Science, Engineering, and Public Policy (COSEPUP), and was its vice president from 1965 to 1973.
In later years he was active in an antiwar organization, the Council for a Livable World. Kistiakowsky severed his connections with the government in protest against the US involvement in the war in Vietnam. In 1977, he assumed the chairmanship of the Council for Livable World, campaigning against nuclear proliferation. He died of cancer in Cambridge, Massachusetts, on December 17, 1982. His body was cremated, and his ashes were scattered near his summer home on Cape Cod, Massachusetts. His papers are in the Harvard University archives.*Wik

1901 George Horace Gallup (November 18, 1901 – July 26, 1984) was an American pioneer of survey sampling techniques and inventor of the Gallup poll, a successful statistical method of survey sampling for measuring public opinion.
Gallup was born in Jefferson, Iowa, the son of George Henry Gallup, a dairy farmer. His higher education took place at the University of Iowa. He served as a journalism professor at Drake and Northwestern for brief periods. In 1932 he moved to New York City to join the advertising agency of Young and Rubicam as director of research (later as vice president from 1937 to 1947). He was also professor of journalism at Columbia University, but he had to give up this position shortly after he formed his own polling company, the American Institute of Public Opinion (Gallup Poll), in 1935.
In 1936, his new organization achieved national recognition by correctly predicting, from the replies of only 50,000 respondents, that Franklin Roosevelt would defeat Alf Landon in the U.S. Presidential election. This was in direct contradiction to the widely respected Literary Digest magazine whose poll based on over two million returned questionnaires predicted that Landon would be the winner. Not only did Gallup get the election right, he correctly predicted the results of the Literary Digest poll as well using a random sample smaller than theirs but chosen to match it.
Twelve years later, his organization had its moment of greatest ignominy, when it predicted that Thomas Dewey would defeat Harry S. Truman in the 1948 election, by five to fifteen percentage points. Gallup believed the error was mostly due to ending his polling three weeks before Election Day.
Gallup died in 1984 of a heart attack at his summer home in Tschingel, a village in the Bernese Oberland of Switzerland. He was buried in Princeton Cemetery. *Wik

1912 Shigeo Sasaki 佐々木 (18 November 1912 Yamagata Prefecture, Japan – 14 August 1987 Tokyo) was a Japanese mathematician working on differential geometry who introduced Sasaki manifolds. *Wik

1916 Sir David Robert Bates, FRS(18 November 1916, Omagh, County Tyrone, Ireland – 5 January 1994) was an Irish mathematician and physicist.
During the Second World War he worked at the Admiralty Mining Establishment where he developed methods of protecting ships from magnetically activated mines.
His contributions to science include seminal works on atmospheric physics, molecular physics and the chemistry of interstellar clouds. He was knighted in 1978 for his services to science, was a Fellow of the Royal Society and vice-president of the Royal Irish Academy. In 1970 he won the Hughes Medal. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1974.
The Mathematics Building at Queens University Belfast, is named after him. *Wik

1923 Alan B. Shepard, Jr. (18 Nov 1923; 21 Jul 1998) Alan Bartlett Shepard, Jr. was America's first man in space and one of only 12 humans who walked on the Moon. Named as one of the nation's original seven Mercury astronauts in 1959, Shepard became the first American into space on 5 May 1961, riding a Redstone rocket on a 15-minute suborbital flight that took him and his Freedom 7 Mercury capsule 115 miles in altitude and 302 miles downrange from Cape Canaveral, FL. (His flight came three weeks after the launch of Soviet cosmonaut Yuri Gagarin, who on 12 Apr 1961, became the first human space traveler on a one-orbit flight lasting 108 minutes.) Although the flight of Freedom 7 was brief, it  was a major step for U.S. in a  race with the USSR. *TIS

1927 John Leslie Britton (November 18, 1927 – June 13, 1994) was an English mathematician from Yorkshire who worked in combinatorial group theory and was an expert on the word problem for groups. Britton was a member of the London Mathematical Society and was Secretary of Meetings and Membership with that organization from 1973-1976. Britton died in a climbing accident on the Isle of Skye. *Wik

DEATHS

1919 Adolf Hurwitz (26 March 1859 in Hildesheim, Lower Saxony, Germany
Died: 18 Nov 1919 in Zurich, Switzerland) Hurwitz studied the genus of the Riemann surface and worked on how class number relations could be derived from modular equations. Hurwitz did excellent work in algebraic number theory. For example he published a paper on a factorisation theory for integer quaternions in 1896 and applied it to the problem of representing an integer as the sum of four squares. A full proof of Hurwitz's ideas appears in a booklet published in the year of his death. This involves studying the ring of integer quaternions in which there are 24 units. He shows that one-sided ideals are principal and introduces prime and primary quaternions. *SAU

1928 Alexander Ziwet (February 8, 1853 -  November 18, 1928) born in Breslau. He became professor at the University of Michigan, an editor of the Bulletin of the AMS, and a collector of mathematics text who enriched the Michigan library. *VFR His early education was obtained in a German gymnasium. He afterwards studies in the universities of Warsaw and Moscow, one year at each, and then entered the Polytechnic School at Karlsruhe, where he received the degree of Civil Engineer in 1880.
He came immediately to the United States and received employment on the United States Lake Survey. Two years later he was transferred to the United States Coast and Geodetic Survey, computing division, where he remained five years.
In 1888 he was appointed Instructor in Mathematics in the University of Michigan. From this position he was advanced to Acting Assistant Professor in 1890, to Assistant Professor in 1891, to Junior Professor in 1896, and to Professor of Mathematics in 1904.
He was a member of the Council of the American Mathematical Society and an editor of the "Bulletin" of the society. In 1893-1894 he published an "Elementary Treatise on Theoretical Mechanics" in three parts, of which a revised edition appeared in 1904. He also translated from the Russian of I. Somoff "Theoretische Mechanik" (two volumes, 1878, 1879).
*Burke A. Hinsdale and Isaac Newton Demmon, History of the University of Michigan (Ann Arbor: University of Michigan Press, 1906), pp. 320-321.

1933 Robert Forsyth Scott (28 July 1849 in Leith, near Edinburgh, Scotland - 18 Nov 1933 in Cambridge, England) studied at Cambridge and was elected to a fellowship. After a short time teaching he studied to be a barrister. He spent most of his career as Bursar and Master of St John's College Cambridge. He published a book on Determinants. *SAU

1949 Frank Baldwin Jewett (5 Sep 1879, 18 Nov 1949) Frank Baldwin Jewett was the U.S. electrical engineer who directed research as the first president of the Bell Telephone Laboratories, Inc., (1925-40). Jewett believed that the best science and technology result from bringing together and nurturing the best minds. Under his tenure Bell Labs laid the foundation for a new scientific discipline, radio astronomy, and transformed movies by synchronizing sound to pictures. Bell Labs was the first to transmit television over a long distance in the U.S. and designed the first electrical digital computer. Bell Labs won its first Nobel Prize in physics for fundamental work demonstrating the wave nature of matter.*TIS

1959 Aleksandr Yakovlevich Khinchin (July 19, 1894, Kondrovo, Kaluga Oblast, Russia - November 18, 1959, Moscow, Russia) was a Russian mathematician who contributed to many fields including number theory and probability. Khinchin made significant contributions to the metric theory of Diophantine approximations and established an important result for simple real continued fractions, discovering a property of such numbers that leads to what is now known as Khinchin's constant. He also published several important works on statistical physics, where he used the methods of probability theory, and on information theory, queuing theory and mathematical analysis.*Wik

 *Niels Bohr Institute
1962 Niels Henrik David Bohr (7 Oct 1885, 18 Nov 1962) was a Danish physicist, born in Copenhagen, who was the first to apply the quantum theory, which restricts the energy of a system to certain discrete values, to the problem of atomic and molecular structure. For this work he received the Nobel Prize for Physics in 1922. He developed the so-called Bohr theory of the atom and liquid model of the nucleus. Bohr was of Jewish origin and when the Nazis occupied Denmark he escaped in 1943 to Sweden on a fishing boat. From there he was flown to England where he began to work on the project to make a nuclear fission bomb. After a few months he went with the British research team to Los Alamos in the USA where they continued work on the project. *TIS (Bohr and his brother were excellent athletes in their youth, read more here.)
Niels and his mathematician brother Harald are buried in the same grave site at the Assistens cemetery in Copenhagen. I love the youthful picture of the two brothers shown at right.

1994 Nathan Jacob Fine (22 October 1916 in Philadelphia, USA - 18 Nov 1994 in Deerfield Beach, Florida, USA) He published on many different topics including number theory, logic, combinatorics, group theory, linear algebra, partitions and functional and classical analysis. He is perhaps best known for his book Basic hypergeometric series and applications published in the Mathematical Surveys and Monographs Series of the American Mathematical Society. The material which he presented in the Earle Raymond Hedrick Lectures twenty years earlier form the basis for the material in this text.*SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell