On This Day in Math - February 2

 

Smooth shapes are very rare in the wild
  but extremely important in the ivory tower and the factory.

~Benoit Mandelbrot

The 33rd day of the year; among the infinity of integers, there are only six that can not be formed by the addition of distinct triangular numbers. The largest of these is 33. What are the other five?

33 = 1!+2!+3!+4! *jim wilder @wilderlab

33 is the smallest n such that n, n+1 and n+2 are all semi-primes, the products of two primes. *Bob S McDonald

The 33 letter Dutch word nepparterrestaalplaatserretrappen is the longest palindrome I know in any language. It means fake stairways from the ground floor to the sun lounge, made of steel plate. The shorter word "saippuakauppias" for a soap vendor is the longest single word palindrome in the world that is in everyday use. *Wiktionary

10³³ is the largest known power of ten that can be expressed as the power of two factors neither of which contains a zero. 10³³ = 2³³ 5³³ = 8,589,934,592 x 116,415,321,826,934,814,453,125 *Cliff Pickover @pickover

 A fun problem given to Fibonacci at the contest before Frederic II  Three men, A, B, and C possess a sum of money w with shares in the ratio 1:2:3.  A takes away x and deposits half of it with man D. B takes away y and deposits 1/3 of it with D.  C takes away the rest, z, and deposits 1/6 of it with D.  The ratio of each persons money in D's hands is now 3:2:1.   Fibonacci showed there were many solutions, but one of the solutions involves 33.  Please share your solutions. 

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EVENTS

*Wik 

1673 From Hooke's Diary: Sir Jonas More; Cox here: compleated arithmeticall engin in ye contrivance for a product of 20 places. He would present the "engin" to the Royal Society three days later.*‏@HookesLondon This "Cox" is most likely Christopher Cock, the designer of instruments who is believed to have made the microscope used by Hooke his observations for his beautiful Micrographia. These microscopes were compound lens instruments, which suffered greatly from spherical aberration.

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1823 Gauss completes the “Gauss-Markov Theorem.” *VFR
In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator of the coefficients is given by the ordinary least squares (OLS) estimator. *Wik

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1826 Mary Somerville’s work was first read by the Royal Society. It became the first paper by a female author to be published in the Philosophical Transactions.

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1841 The earliest recorded observance of Groundhog day in America was on this day in the diary of Morgantown, Pa. storekeeper,James Morris:

"Last Tuesday, the 2nd, was Candlemas day, the day on which, according to the Germans, the Groundhog peeps out of his winter quarters and if he sees his shadow he pops back for another six weeks nap, but if the day be cloudy he remains out, as the weather is to be moderate."

entry for Feb 4th *Wik

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1851 “You are invited to come to see the Earth turn, tomorrow from three to five, at Meridian Hall of the Paris Observatory.” Foucault sent these handwritten invitations to all the known scientists in Paris. *Amir D Aczel, Pendulum, pg 93

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1883 Preliminary meeting of the Edinburgh Mathematical Society

*Proceedings of the Edinburgh Mathematical Society, Volumes 1-4

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1962, eight of the nine planets lined up for the first time in 400 years.*TIS  On May 12,2011 six planets  (Mercury, Venus, Jupiter, Mars, Uranus and Neptune, were essentially in a line. All the planets will not be aligned (at least as closely as they can get) until sometime in the 29th century. 

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1977  Radio Shack officially begins creating TRS-80 computer.  It is one of the earliest mass-produced and mass-marketed retail home computers. By 1979, the TRS-80 had the largest selection of software in the microcomputer market. Until 1982, the TRS-80 was the best-selling PC line, outselling the Apple II series by a factor of five according to one analysis. *Wik  

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2004 Google does a doodle in honor of Gaston Julia's 111th birthday, but a day early by my calculation. My records show his birthday is Feb 3. (It's me vrs Google, choose sides people.)

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BIRTHS

1522 Lodovico Ferrari (2 Feb 1522 in Bologna, Italy - 5 Oct 1565) Italian mathematician who was the first to find an algebraic solution to the biquadratic, or quartic, equation (an algebraic equation that contains the fourth power of the unknown quantity but no higher power).*TIS  born in Bologna, Italy. In 1536 he was sent to live with Girolamo Cardano, who taught him Latin, Greek, and mathematics. He collaborated with Cardano in research on third and fourth degree equations. *VFR He began as the servant of Cardano but was extremely bright, so Cardano started teaching him mathematics. Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published. While still in his teens, Ferrari was able to obtain a prestigious teaching post after Cardano resigned from it and recommended him. Ferrari eventually retired young (only 42) and quite rich. He then moved back to his home town of Bologna where he lived with his widowed sister Maddalena to take up a professorship of mathematics at the University of Bologna in 1565. Shortly thereafter, he died of white arsenic poisoning, allegedly murdered by his greedy sister.*Wik

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1766 Timofei Fedorovic Osipovsky (February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary.
He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds.
His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik

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1786 Jacques Philippe Marie Binet (2 Feb 1786 in Rennes, Bretagne, France - 12 May 1856 in Paris, France) investigated the foundations of matrix theory which was to set the scene for later work by Cayley and others. He discovered the rule for multiplying matrices in 1812 and it is almost certainly for this that he will be remembered rather than his other work.
He did, however, write a number of important papers which were influential in the development of mathematics, in particular he wrote Mémoire sur les intégrales définies eulériennes in 1840. The following year he wrote on number theory, making a contribution to the theory of the Euclidean algorithm. *SAU
He is also remembered for Binet's formula expressing Fibonacci numbers in closed form, which is named in his honor, although the same result was known to Abraham de Moivre a century earlier.
\(F(n) = \frac{(1+\sqrt{5})^2-(1-\sqrt{5})^2}{2^n\sqrt{5}} \)

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1793 William Hopkins FRS (2 February 1793 – 13 October 1866) was an English mathematician and geologist. He is famous as a private tutor of aspiring undergraduate Cambridge mathematicians, earning him the sobriquet the senior-wrangler maker.
Before graduation, Hopkins had married Caroline Frances Boys (1799–1881) and was, therefore, ineligible for a fellowship. He instead maintained himself as a private tutor, coaching the young mathematicians who sought the prestigious distinction of Senior Wrangler. He was enormously successful in the role, earning the sobriquet senior wrangler maker and grossing £700-800 annually. By 1849, he had coached almost 200 wranglers, of whom 17 were senior wranglers including Arthur Cayley and G. G. Stokes. Among his more famous pupils were Lord Kelvin, James Clerk Maxwell and Isaac Todhunter.
He also made important contributions in asserting a solid, rather than fluid, interior for the Earth and explaining many geological phenomena in terms of his model. However, though his conclusions proved to be correct, his mathematical and physical reasoning were subsequently seen as unsound.In 1833, Hopkins published Elements of Trigonometry and became distinguished for his mathematical knowledge.
There was a famous story that the theory of George Green (1793–1841) was almost forgotten. In 1845, Lord Kelvin (William Thomson, a young man in 1845) got some copies of Green's 1828 short book from William Hopkins. Subsequently, Lord Kelvin helped to make Green's 1828 work famous according to the book "George Green" written by D.M. Cannell. *Wik It is known that he gave one copy of Green's book  to Liouville, founder and editor of a popular French Mathematical Journal.

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1849 Leopold Bernhard Gegenbauer (2 Feb 1849 - 3 June 1903) was an Austrian mathematician who gave his name to a sequence of orthogonal polynomials. He gave the well-known asymptotic estimate 6n/π² for the number of square-free integers not exceeding n.*SAU

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1881 Gustav Herglotz (2 February 1881 – 22 March 1953) was a German mathematician. He is best known for his works on the theory of relativity and seismology. From 1925 (until becoming Emeritus in 1947) he again was in Göttingen as the successor of Carl Runge on the chair of applied mathematics. One of his students was Emil Artin.
Herglotz made contribution in many fields of applied and pure mathematics. The Theorem of Herglotz is known in differential geometry, and he also contributed to number theory. He worked in the fields of celestial mechanics, theory of electrons, special relativity (where he developed a theory of elasticity), general relativity, hydrodynamics, refraction theory. *Wik

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1882 Joseph Henry Maclagen Wedderburn (2 Feb 1882 in Forfar, Angus, Scotland -  9 Oct 1948 in Princeton, New Jersey, USA) studied at Edinburgh, Leipzig, Berlin and Chicago. He returned to Scotland to work at Edinburgh but then moved to a post at Princeton where he spent the rest of his career except for a break for service in World War I. He made far-reaching discoveries in the theory of rings, algebras and matrices. He became an honorary member of the EMS in 1946. *SAU

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1893 Cornelius Lanczos (2 Feb 1893 - 25 June 1974) worked on relativity and mathematical physics and invented what is now called the Fast Fourier Transform. *SAU

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1896 Kazimierz Kuratowski (2 Feb 1896 in Warsaw, Russian Empire (now Poland) - 18 June 1980 in Warsaw, Poland) He worked in the area of topology and set theory. He is best known for his theorem giving a necessary and sufficient condition for a graph to be planar.*SAU

Kuratowski's theorem: "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K₅ (the complete graph on five vertices) or K_3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three)."  (in simpler, but less exact terms, 

it can be drawn in such a way that no edges cross each other."
Math Historian V F Rickey calls this "the most cited theorem in graph theory."

The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is K_3,3 (below). The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other.(1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917)  (see June 21)
I have a short blog with two other proofs that this is impossible that should be appropriate for high school students.  

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1897 Gertrude Blanch (2 Feb, 1897 (sometimes 1898) - 1 Jan,1996) was an American mathematician who did pioneering work in numerical analysis and computation. After the war, Blanch's career was hampered by FBI suspicions that she was secretly a communist. Their evidence for this seems scarce, and included, for example, the observation that she had never married or had children. In what must have been a remarkable showdown, the diminutive fifty-year-old mathematician demanded, and won, a hearing to clear her name.
Subsequently, she worked for the Institute for Numerical Analysis at UCLA and the Aerospace Research Laboratory at Wright-Patterson Air Force Base in Dayton, Ohio. She was one of the founders of the ACM.
She published over thirty papers on functional approximation, numerical analysis and Mathieu functions. In 1962, she was elected a Fellow in the American Association for the Advancement of Science.
Blanch retired in 1967 at the age of 69, but continued working under a consulting contract for the Air Force for another year. Thereafter she moved to San Diego and continued to work on numerical solutions of Mathieu functions until her death in 1996, concentrating on the use of continued fractions to achieve highly accurate results in a small number of computational steps. This work has not been published. The Gertrude Blanch Papers, 1932-1996 are stored at the Charles Babbage Institute, University of Minnesota, Minneapolis. *Wik

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1903 Bartel Leendert van der Waerden (2 Feb 1903 - 12 Jan 1996) This famous algebraist is best known for his book Moderne Algebra, but has, more recently, done interesting work on the history of ancient mathematics. *VFR

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DEATHS

1704 Guillaume François Antoine, Marquis de l'Hôpital (?, 1661, Paris – February 2, 1704, Paris) was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his treatise on the infinitesimal calculus, entitled Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes. This book was a first systematic exposition of differential calculus. Several editions and translations to other languages were published and it became a model for subsequent treatments of calculus. or a while, he was a member of Nicolas Malebranche's circle in Paris and it was there that in 1691 he met young Johann Bernoulli, who was visiting France and agreed to supplement his Paris talks on infinitesimal calculus with private lectures to l'Hôpital at his estate at Oucques. In 1693, l'Hôpital was elected to the French academy of sciences and even served twice as its vice-president. Among his accomplishments were the determination of the arc length of the logarithmic graph, one of the solutions to the brachistochrone problem, and the discovery of a turning point singularity on the involute of a plane curve near an inflection point.
L'Hôpital exchanged ideas with Pierre Varignon and corresponded with Gottfried Leibniz, Christiaan Huygens, and Jacob and Johann Bernoulli. His Traité analytique des sections coniques et de leur usage pour la résolution des équations dans les problêmes tant déterminés qu'indéterminés ("Analytic treatise on conic sections") was published posthumously in Paris in 1707. *Wik

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1769 Robert Smith (1689 – 2 February 1768) was an English mathematician and music theorist. In his will Smith left £3500 South Sea stock to the University of Cambridge. The net income on the fund is annually divided equally between the Smith's Prize and the stipend of the Plumian Professor.
Smith was probably born at Lea near Gainsborough, the son of the rector of Gate Burton, Lincolnshire. After attending Queen Elizabeth's Grammar School, Gainsborough (now Queen Elizabeth's High School) he entered Trinity College, Cambridge, in 1708, and becoming minor fellow in 1714, major fellow in 1715 and senior fellow in 1739, was chosen Master in 1742, in succession to Richard Bentley. From 1716 to 1760 he was Plumian Professor of Astronomy, and he died in the Master's Lodge at Trinity.
In February 1719 he was elected a Fellow of the Royal Society
Besides editing two works by his cousin, Roger Cotes, who was his predecessor in the Plumian chair, he published A Compleat System of Opticks in 1738, which gained him the sobriquet of Old Focus, and Harmonics, or the Philosophy of Musical Sounds in 1749.
Smith never married but lived with his unmarried sister Elzimar (1683–1758) in the lodge at Trinity College. Although he is often portrayed as a rather reclusive character, John Byrom's journal shows that in the 1720s and 1730s Smith could be quite sociable. Yet ill health, particularly gout, took its toll and severely inhibited his academic work and social activities. He died at the lodge on 2 February 1768, and on 8 February he was buried in Trinity College Chapel, the funeral oration being delivered by Thomas Zouch.

According to the Oxford Dictionary of National Biography, Smith helped to spread Isaac Newton's ideas in Europe and "Newton's successes in optics and mechanics dominated Smith's scientific career". Bishop was a Christian that although did not publish theological works, wrote a Zachary Grey's response to the Examination of the Fourteenth Chapter of Newton's Observations on Daniel. *Wik

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1950 Constantin Carathéodory (or Constantine Karatheodori) (13 September 1873 – 2 February 1950) was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory. His work also includes important results in conformal representations and in the theory of boundary correspondence. In 1909, Carathéodory pioneered the Axiomatic Formulation of Thermodynamics along a purely geometrical approach. *Wik  He is the only modern Greek mathematician “who does not suffer by comparison with the famous names of Greek antiquity.” *VFR.

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1911 Hugues Charles Robert Méray (November 12, 1835, Chalon-sur-Saône, Saône-et-Loire - February 2, 1911, Dijon) was a French mathematician. He is noted as the first to publish an arithmetical theory of irrational numbers. His work did not have much of a role in the history of mathematics because France, at that time, was less interested in such matters than Germany.*Wik

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1965 George Neville Watson (31 Jan 1886 in Westward Ho!, Devon, England - 2 Feb 1965 in Leamington Spa, Warwickshire, England) studied at Cambridge, and then taught at Cambridge and University College London before becoming Professor at Birmingham. He is best known as the joint author with Whittaker of one of the standard text-books on Analysis. Titchmarsh wrote of Watson's books, "Here one felt was mathematics really happening before one's eyes. ... the older mathematical books were full of mystery and wonder. With Professor Watson we reached the period when the mystery is dispelled though the wonder remains." *SAU

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1970 Bertrand Arthur William Russell (18 May 1872 - 2 Feb 1970) (3rd earl)  was a Welsh mathematical logician, analytical philosopher and writer. He worked to establish foundations of mathematics and developed contemporary formal logic. He is known for Russell's paradox (concerning the set of all sets that are not members of themselves), his theory of types, and his contributions to the first-order predicate calculus. He believed in logicism, the theory that mathematics was in some important sense reducible to formal logic. With Alfred Whitehead, he co-authored Prinicpia Mathematica (1910). Russell is regarded as one of the most important logicians of the twentieth century. He was active in social and political campaigns, and advocated pacifism and nuclear disarmament. The Nobel Prize for Literature was awarded to Russell in 1950 *TIS

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2005 Edward Maitland Wright (13 Feb 1906 in Farnley, near Leeds, England - 2 Feb 2005 in Reading, England) was initially self-taught in Mathematics but was able to go and study at Oxford. He spent a year at Göttingen and returned to Oxford. He was appointed to the Char at Aberdeen where he stayed for the rest of his career, eventually becoming Principal and Vice-Chancellor of the University. He is best known for the standard work on Number Theory he wrote with G H Hardy. One of Wright's first papers, published in 1930, was on Bernstein polynomials. Also among his early work was a series of three papers titled Asymptotic partition formulae. The third in the series Asymptotic partition formulae, III. Partitions into kth powers was published by Acta Mathematica in 1934.  *SAU

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2011 Rodney Hill FRS (11 June 1921 – 2 February 2011) was an applied mathematician and a former Professor of Mechanics of Solids at Gonville and Caius College, Cambridge.
In 1953 he was appointed Professor of Applied Mathematics at Nottingham University. His 1950 The Mathematical Theory of Plasticity forms the foundation of plasticity theory. Hill is widely regarded as among the foremost contributors to the foundations of solid mechanics over the second half of the 20th century. His early work was central to founding the mathematical theory of plasticity. This deep interest led eventually to general studies of uniqueness and stability in nonlinear continuum mechanics, work which has had a profound influence on the field of solid mechanics—theoretical, computational and experimental alike—over the past decades. Hill was the founding editor of the Journal of the Mechanics and Physics of Solids, still among the principal journals in the field.
His work is recognized worldwide for its concise style of presentation and exemplary standards of scholarship. Publisher Elsevier, in collaboration with IUTAM, established a quadrennial award in the field of solid mechanics, known as the Rodney Hill Prize, first presented at ICTAM in Adelaide in August 2008. The prize consists of a plaque and a cheque for US$25,000. Its first recipient is Michael Ortiz, for his contribution to nonconvex plasticity and deformation microstructures (California Institute of Technology, USA).
He won the Royal Medal in 1993 for his contribution to the theoretical mechanics of soil and the plasticity of solids and was elected a Fellow of the Royal Society in 1961. He was awarded an Honorary Degree (Doctor of Science) by the University of Bath in 1978. *Wik

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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

Roman Numeral Fractions?

 Just browsing through an old Recreations in Mathematics by Dr H. E. Licks (not real name, see below) and discovered something I had wondered about, but never seen, an example of fractions of a unit in Roman engineering.  And if you think regular Roman numerals are complex to deal with, check these fractions.  

 I knew they had symbols of some measures that were themselves fractions, ounces (uncia-12th), inches (uncia), and digits (digitus), for example.  You've probably heard of the first two, but digits seems less well known.

But if you had to guess, you'd probably guess finger, and be right.  The Romans, like many of us today used 12 inches in a foot (pes), but they also adopted a Greek fraction of 1/16th of a foot, called digitus.  While reading the previously mentioned book, I found a whole new set of symbols to represent fractional parts of these named units attributed to Frontinus, a 97 AD Water Commissioner about water flow in roman pipes (fistula) .  

Pipes, it seems, were expressed by their diameter in digits, divided into 12th parts of a digit.  The symbol - was for a twelfth part of a digit, two of them, = would be 2/12,  adding more beside these , == could be four-twelfths. He represented The half unit was represented by an  S , 6/12, and more bars added  to make 7 through 11 twelfths.  Another symbol was introduced for the 24th part of a digit, which looked greatly like the Pound Sterling symbol, for which I substitute L.  There was even another for the 288th (a twelfth of a twenty-fourth) part of a digit (that's 1/128th of 1/16 of an inch, a little less than .0005 ".  This symbol was represented by something resembling the reverse of a Euro symbol, or the Latin Capital open O, Ɔ, with a little extra line in the back.

The standard flow measure, a quinaria, was the amount from a 1 1/4 digit pipe, (or I =-) .  His example of something called a fifty pipe has (diametri digitos) diameter of 7 digits + 1/2 + 5/12 +1/24 + 5/228, which my symbols would write as VII S ==-  L ƆV .  The V after the 288ths to mean five of them makes you  wonder why he would not have done that with the twelfths.

Dr Licks writes, "Perhaps the awkward notation retarded the development of mathematics among the Romans."

Frontinus' document was translated by Clemens Herschel in 1889 from whence Dr Licks wroteLies, Damned Lies, and Something About StatisticsthisLies, Damned Lies, and Something About Statisticsearly part of his book.  

Regular readers of my blog have met the Dr H E Licks annually in earl February in the Events portion:

1880 On 10 February 1880, an article ran in the Daily Times (of Bethlehem, Pennsylvania) describing a remarkable invention recently demonstrated by a local inventor, Dr. H.E. Licks. The invention allowed images to be transmitted by telegraph. In other words, it resembled what people today would recognize as a television. However, Licks called his invention a "diaphote," from the Greek dia meaning "through" and photos meaning "light".
Despite the excitement it generated, the diaphote turned out to be a hoax. However, it wasn't until 1917 that "Dr. H.E. Licks" revealed the hoax in a book, Recreations in Mathematics. Licks himself is believed to have been the pseudonym of Mansfield Merriman (1848-1925), a professor of engineering at Lehigh University. *Museum of Hoaxes

On This Day in Math - February 1

 

Some physicists describe gravity in terms of ten dimensions all curled up. But those aren't real words—just placeholders, used to refer to parts of abstract equations.
~Scott Adams

The 32nd day of the year; 32 is conjectured to be the highest power of two with all prime digits. *Number Gossip (Could 27 hold the similar property for powers of three?)

Also, 131 is the 32nd prime and the sum of the digits of both numbers is 5. 32 & 131 is the smallest n, P(n) with this property.
32=11+22+33$$
32 = 1¹ + 2² + 3³ 31 + 32 = 3³ + 1³ + 3³ + 2³ *Jim Wilder @wilderlab

A Fermat prime is a prime number of the form 22n+1${\mathrm{2^(}}^{{\mathrm{2^}}^{\mathrm{n) }}}+ 1$ and five are known (3, 5, 17, 257, 65537). Their product is 232−1${\mathrm{2^}}^{32}-1$
[David Marain pointed out that the products of the first n are all expressible in 2ⁿ-1 form, 3x5=24−1,3x5x17=28−1$3x5={\mathrm{2^}}^4-1,3x5x17={\mathrm{2^}}^8-1$, and 3x5x7x257=216−1$3x5x7x257={\mathrm{2^}}^{16}-1$ ]

On an 8x8 chessboard, the longest closed non-crossing knight's path is 32 moves.

EVENTS

1634 Descartes writes from Deventer in Holland to Father Marin Mersenne and explains that he had retracted his book, The World, which supported the Copernican theory, “thus losing four years of my work in order to give full obeisance to the Church…. I do not dare publish my own sentiment.” Ironically it would be a decision by the Dutch Protestant theologians to declare his writings as “atheistic” that led to his leaving Holland to accept a position in Sweden which led to his death. *VFR (See 1650 below)

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1650 Descartes contracted a chill, while tutoring Queen Christina of Sweden, which developed into inflammation of the lungs. 10 days later he was dead at age 53. *J. F. Scott, The Scientific World of Rene Descartes, p. 6.

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1673 (1672 os) Leibniz, during his first visit to London, exhibited his calculating machine to the Royal Society. *VFR Called the Stepped Reckoner, it as the first machine that could do all four arithmetic operations. It was about this time that Leibniz says he met Pell at the house of Robert Boyle and during a discussion of sequences and series Leibniz was informed that this work had been done by Nicholas Mercator. (with hints at plagiarism from Mouton.)

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1891 The first bimagic square (the numbers form a magic square, and when the numbers are replaced by their squares, they still form a magic square) in the world by G. Pfeffermann in France. Created in 1890, this 8x8 square was published in a french magazine "Les Tablettes du Chercheur" January 15, 1891, with only half of the numbers shown as a problem for the readers. The solution, and so the full first bimagic square, was published in the next issue of "Les Tablettes du Chercheur", February 1st 1891. Here is the original puzzle and the solution. *The Magic Encyclopedia ™ DataBase The famous Edouard Lucas (1842-1891), who was a writer of articles in Les Tablettes, wrote that this first bimagic square was a "very remarkable square". He would go on to prove that no 3x3 bimagic square could exist, even with non-consecutive digits, and that no 4x4 could be created with consecutive digits. Unfortunately he also died that same year (see link above) in as the result of a most unusual accident. 8x8 is still the smallest order bimagic square that can be formed with consecutive digits.
 

The lower image shows the squares of the digits in the first square.  images from *http://www.multimagie.com

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1894 Nature magazine covers Newcomb's speech to the New York Mathematical Society. On 28 December, 1893, Simon Newcomb had given a speech to the Society with comments on the fourth dimension; "It is a perfectly legitimate exercise .... if we should not stop at three dimensions in geometry, but construct one for space having four... and there is room for an indefinite number of universes". He also called his speculations on the fourth dimension, "the fairlyland of geometry."
The speech appears a short time later on February 1, 1894 in Nature. His comments would also be commented on in H. G. Wells, Time Machine. "But some philosophical people have been asking ... - Why not another direction at right angles to the other three? ... Professor Simon Newcomb was expanding on this only a month or so ago." *Alfred M. Bork, The Fourth Dimenson in Nineteenth-Century Physics, Isis, Sept 1964 pg 326-338

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1911, Thomas Jennings was found guilty with the first use of fingerprint evidence in the U.S. He was convicted at the Criminal Court of Cook County for killing Clarence B. Hiller. Upon appeal, 21 Dec 1911, the Illinois Supreme Court ruled the evidence was admissible. Two months later, Jennings was executed on 16 Feb 1912. *TIS  I have since read of a case in New York City (trial on Jan 12, 1911) in which fingerprint evidence found at the site of a crime was used to identify suspects and when investigated, they were found in possession of the stolen goods.  However “The prisoners broke down…and pleaded to burglary in the third degree.”  The Sun Newspaper noted “It was the first conviction by the finger print method obtained in this country.” *http://daytoninmanhattan.blogspot.com

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1972, the first scientific hand-held calculator (HP-35) was introduced for $395 by Hewlett-Packard. (Wikipedia gives this price as $795, either way, YIKES!) Its model number came from having 35 keys. It was the first hand-held calculator able to perform logarithmic and trigonometric functions with one keystroke. The red LED display could give scientific notation up to 10 digits mantissa and 2 digits exponent. The price was reduced several times, eventually to $195. By Feb 1975 (when production of the model was discontinued), 300,000 had been sold. The numbers and functions for calculations were entered in "Reverse Polish Notation" (RPN), which used an "ENTER" key but needed no parentheses or "=" key. Its size was 79 mm x 147 mm x 34 mm (3.1" x 5.8" x 1.4"), ran on rechargeable batteries, and its electronics used several integrated circuits.*TIS

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1991 Sun Microsystems Starts JavaTM Technology.
Mike Sheridan, James Gosling, and Patrick Naughton of Sun Microsystems, Inc. start to develop JavaTM technology. It grew out of a Sun project in embedded control called *7 (Star Seven). Naughton focused on Aspen graphics system, Gosling on programming language ideas, Sheridan on business development.*CHM

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2003 The seven-member crew of STS-107 died when the Columbia orbiter disintegrated during reentry into the Earth's atmosphere. STS-107 was the 113th flight of the Space Shuttle program, and the final flight of Space Shuttle Columbia. The mission launched from Kennedy Space Center on 16 January 2003, and during its 16 days in orbit conducted a multitude of international scientific investigations.

*NASA

The Columbia Accident Investigation Board determined the failure was caused by a piece of foam that broke off during launch and damaged the thermal protection system components (reinforced carbon-carbon panels and thermal protection tiles) on the leading edge of the left wing of the orbiter. During re-entry the damaged wing slowly overheated and came apart, eventually leading to loss of control and disintegration of the vehicle. The inflight photo at right was from a roll of unprocessed film recovered among the debris.

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2012 a fireball over central Texas wowed thousands of onlookers in the Dallas-Fort Worth area. *Wik
"It was brighter and long-lasting than anything I've seen before," reports eye-witness Daryn Morran. "The fireball took about 8 seconds to cross the sky. I could see the fireball start to slow down; then it exploded like a firecracker artillery shell into several pieces, flickered a few more times and then slowly burned out." Another observer in Coppell, Texas, reported a loud double boom as "the object broke into two major chunks with many smaller pieces." There would be over seven different "fireball" events in the month, NASA's Meteoroid Environment Office called that, "about normal".

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2023   On Feb.1, comet C/2022 e3 (ZTF) will make its closest approach to Earth. It will come within 28 million miles (42 million kilometers) of our home planet. This close approach is its first flyby to Earth in 50,000 years.  Look for a bright green object in the sky.

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BIRTHS

1561 Henry Briggs (Feb ? 1561, 26 Jan 1630) English mathematician who constructed the decimal-based common (Briggsian) logarithms that use base 10, and popularized them in Europe. John Napier had already introduced “natural” logarithms (1614) that use the base e (2.71...) [I think this is an error. Napier's log tables were not base e, nor any other particular base as they produced smaller log values for larger numbers, with log(10⁷=0.]. Briggs visited Napier in 1616, and they agreed on the merit of using base 10 {with log(1)=0}. By 1624, Briggs had calculated logarithm tables to 14 decimal places, published in Arithmetica Logarithmica. These tables vastly simplified the task of mathematicians, astronomers and other scientists making otherwise long and tedious calculations. Briggs was professor of astronomy at Oxford from 1619. He is also credited with developing the modern method of long division. Briggs was strongly opposed to astrology, at a time when it was otherwise widely accepted by many scholars, including Napier. *TIS
A story is told that when Briggs first journeyed to Scotland to meet Napier, after he was shown into the room they stood in silence for almost a quarter of an hour, "each beholding the other with admiration".

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1840 William Allen Whitworth (1 February 1840 – 12 March 1905) was an English mathematician and a priest in the Church of England.
As an undergraduate, Whitworth became the founding editor in chief of the Messenger of Mathematics, and he continued as its editor until 1880. He published works about the logarithmic spiral and about trilinear coordinates, but his most famous mathematical publication is the book Choice and Chance: An Elementary Treatise on Permutations, Combinations, and Probability (first published in 1867 and extended over several later editions). The first edition of the book treated the subject primarily from the point of view of arithmetic calculations, but had an appendix on algebra, and was based on lectures he had given at Queen's College. Later editions added material on enumerative combinatorics (the numbers of ways of arranging items into groups with various constraints), derangements, frequentist probability, life expectancy, and the fairness of bets, among other topics.
Among the other contributions in this book, Whitworth was the first to use ordered Bell numbers to count the number of weak orderings of a set, in the 1886 edition. These numbers had been studied earlier by Arthur Cayley, but for a different problem. He was the first to publish Bertrand's ballot theorem, in 1878; the theorem is misnamed after Joseph Louis François Bertrand, who rediscovered the same result in 1887. He is the inventor of the E[X] notation for the expected value of a random variable X, still commonly in use, and he coined the name "subfactorial" for the number of derangements of n items.
Another of Whitworth's contributions, in geometry, concerns equable shapes, shapes whose area has the same numerical value (with a different set of units) as their perimeter. As Whitworth showed with D. Biddle in 1904, there are exactly five equable triangles with integer sides: the two right triangles with side lengths (5,12,13) and (6,8,10), and the three triangles with side lengths (6,25,29), (7,15,20), and (9,10,17). *Wik

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1847 Eduardo Torroja Caballe (February 1, 1847 – June 1, 1918) was a Spaniard mathematician born in the city of Tarragona, Spain. His father was Juan Torroja, a Professor of Geography and History. He continued his studies at Complutense University, where he obtained the degrees of Bachelor of Science (1864), Masters of Science (1866), Architect (1869) and Doctor of Science (1873) in Mathematics.
Very early in his studies he became a disciple of Karl Georg Christian von Staudt, whose ideas of Geometry he embraced and promoted among his fellow mathematicians for the rest of his life. The strong presence of Geometry in Spain's mathematical curriculum, even to this day, can be traced back to Torroja's influence. *Wik

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1890 Jovan Karamata (February 1, 1902–August 14, 1967) was one of the greatest Serbian mathematicians of the 20th century. He is remembered for contributions to analysis, in particular, the Tauberian theory and the theory of slowly varying functions. Karamata was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts in 1946. *Wik

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1900 John Charles Burkill FRS (1 February 1900 Holt, Norfolk, England – 6 April 1993 Sheffield, England) was an English mathematician who worked on analysis and introduced the Burkill integral. He was elected a fellow of the Royal Society in 1953*Wik

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1905 Ernst Carl Gerlach Stueckelberg (February 1, 1905, September 4, 1984) was a Swiss mathematician and physicist. In 1938 he recognized that massive electrodynamics contains a hidden scalar, and formulated an affine version of what would become known as the Abelian Higgs mechanism. He also proposed the law of conservation of baryon number. In 1953 he and the mathematician Andre Petermann discovered the renormalization group.
He was awarded the Max Planck medal.*Wik

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1905 Emilio Gino Segrè (1 Feb 1905; 22 Apr 1989) was an Italian-born American physicist who was cowinner, with Owen Chamberlain of the United States, of the Nobel Prize for Physics in 1959 for the discovery of the antiproton, an antiparticle having the same mass as a proton but opposite in electrical charge. He also created atoms of the man-made new element technetium (1937) and astatine (1940). Technetium occupied a hitherto unfilled space in the body of the Periodic Table, and was the first man-made element not found in nature. Astatine exists naturally only in exceedly small quantities because as a decay product of larger atoms, and having a half-life of only a few days, it quickly disappears by radioactively decay to become atoms of another element.*TIS

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1905 Lloyd Viel Berkner (1 Feb 1905; 4 Jun 1967) American physicist and engineer who first measured the extent, including height and density, of the ionosphere (ionized layers of the Earth's atmosphere), leading to a complete understanding of radio wave propagation and he helped develop radar systems, especially the Distant Early Warning system. He later investigated the origin and development of the Earth's atmosphere. Early in his career, he worked on radio navigation beacons for the Airways division of the Bureau of Lighthouses (1927-28), as radio engineer on the Byrd Antarctic expedition (1928-30). Returning to the U.S. Bureau of Standards (1930-33) he studied the ionosphere using radio-pulse transmissions, then terrestial magnetism with the Carnegie Institution (1933-51). *TIS

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1907 Melba Newell Phillips (February 1, 1907 - November 8, 2004) was an American physicist and science educator. She completed her doctoral studies under J. Robert Oppenheimer and was also known for refusing to testify before a U.S. Senate Judiciary Committee's subcommittee on internal security, her actions leading to her dismissal by Brooklyn College.
Melba Phillips was born in Hazleton, Indiana. She graduated from high school at the age of 15 and went on to study Mathematics at Oakland City College, Indiana graduating in 1926. She received a master's degree in physics from Battle Creek College of Michigan in 1928 and her doctorate in physics in 1933 at the University of California, Berkeley.
Phillips's supervisor at Berkeley was J. Robert Oppenheimer, who would later become scientific head of the Allied atomic bomb effort, the Manhattan Project. Together they described the Oppenheimer-Phillips effect explaining the behavior of accelerated nuclei of radioactive hydrogen atoms in 1935. *Wik

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1916 George Whitelaw Mackey (February 1, 1916 in St. Louis, Missouri – March 15, 2006 in Belmont, Massachusetts) was an American mathematician.
Mackey's main areas of research were in the areas of representation theory, ergodic theory, and related parts of functional analysis. Earlier in his career Mackey did significant work in the duality theory of locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products.
He has written numerous survey articles connecting his research interests with a large body of mathematics and physics, particularly quantum mechanics and statistical mechanics. He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

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DEATHS

1903 Sir George Gabriel Stokes (13 Aug 1819, 1 Feb 1903)(1st Baronet) British mathematical physicist who studied viscous fluids and formulated his law of viscosity for the speed of a solid sphere falling in a fluid. Other laws and mathematical work for which he is known includes Stokes's theorem, in the field of vector analysis. Stokes also worked in optics, the wave theory of light, diffraction (1849), the ultraviolet spectrum and other spectrum analysis. He coined the word fluorescence (1852) while studying that phenomenon and was a founder of the field of geodesy with his study of variations in gravity (1849). From 1849 until his death in 1903, he held the Lucasian Chair of Mathematics at Cambridge (held earlier by Isaac Newton, and currently by Stephen Hawking). He came from a family with generations of scientists, mathematicians and engineers. *TIS

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1958 Clinton Joseph Davisson (22 Oct 1881, 1 Feb 1958) American experimental physicist who shared the Nobel Prize for Physics in 1937 with George P. Thomson of England for discovering that electrons can be diffracted like light waves, thus verifying the thesis of Louis de Broglie that electrons behave both as waves and as particles. Davisson studied the effect of electron bombardment on surfaces, and observed (1925) the angle of reflection could depend on crystal orientation. Following Louis de Broglie's theory of the wave nature of particles, he realized that his results could be due to diffraction of electrons by the pattern of atoms on the crystal surface. Davisson worked with Lester Germer in an experiment in which electrons bouncing off a nickel surface produced wave patterns similar to those formed by light reflected from a diffraction grating, and supporting de Broglie's electron wavelength = (h/p). This discovery has been applied to the study of nuclear, atomic, and molecular structure. Davisson helped develop the electron microscope which uses the wave nature of electrons to view details smaller than the wavelength of visible light.*TIS

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1961 Émile Henriot (2 July 1885 - 1 February 1961) was a French chemist notable for being the first to show definitely that potassium and rubidium are naturally radioactive.
He investigated methods to generate extremely high angular velocities, and found that suitably placed air-jets can be used to spin tops at very high speeds - this technique was later used to construct ultracentrifuges.
He was a pioneer in the study of the electron microscope. He also studied birefringence and molecular vibrations.
He obtained his DSc in physics in 1912 the Sorbonne, Paris, under Marie Curie. *Wik

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1970 Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory. He proved, using the large sieve, that there is a number K such that every even number is the sum of a prime number and a number that can be written as the product of at most K primes. See also Goldbach conjecture.
In information theory, he introduced the spectrum of Rényi entropies of order α, giving an important generalisation of the Shannon entropy and the Kullback-Leibler divergence. The Rényi entropies give a spectrum of useful diversity indices, and lead to a spectrum of fractal dimensions. The Rényi–Ulam game is a guessing game where some of the answers may be wrong.
He wrote 32 joint papers with Paul Erdős, the most well-known of which are his papers introducing the Erdős–Rényi model of random graphs. Rényi, who was addicted to coffee, invented the quote: "A mathematician is a device for turning coffee into theorems.", which is generally ascribed to Erdős. The sentence was originally in German, being a wordplay on the double meaning of the word Satz (theorem or residue of coffee). *Wik

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1976 Werner Karl Heisenberg (5 Dec 1901, 1 Feb 1976) was the German physicist and philosopher who discovered a way to formulate quantum mechanics in terms of matrices (1925). For that discovery, he was awarded the Nobel Prize for Physics for 1932. In 1927 he published his indeterminacy, or uncertainty, principle, upon which he built his philosophy and for which he is best known. He also made important contributions to the theories of the hydrodynamics of turbulence, the atomic nucleus, ferromagnetism, cosmic rays, and elementary particles, and he planned the first post-World War II German nuclear reactor, at Karlsruhe, then in West Germany. *TIS

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2003 Kalpana Chawla (March 17, 1962 – February 1, 2003) was an American astronaut and the first indian woman in space. She first flew on Space Shuttle Columbia in 1997 as a mission specialist and primary robotic arm operator. In 2003, Chawla was one of the seven crew members killed in the Space Shuttle Columbia disaster. *Wik

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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

Lies, Damned Lies, and Something About Statistics

 

In a long passed discussion about quotations on the AP Statistics news group the quotation, “There are three kinds of lies; lies, damned lies, and statistics.” came up. The quote is usually attributed to either Mark Twain or Disraili, and several nice notes regarding the veracity of the quote, and its origin, were contributed. Here are snips and direct quotes from the ones that seemed most interesting…

Chris Olsen waded in with this:
“I was reading something or other recently -- I don't remember what it was, but do remember it was a statistician writing -- and he alluded to this quote. In the following the [] are my interjections. What the statistician said was that Disraeli was arguing for or against [I kind of think against] the repeal of the Corn Laws in the English Parliament [possibly in 1846]. An individual [Robert Peel?] on the other side pointed out some sort of statistic in arguing the other side of the issue, and that is when Disraeli is alleged to have made the damn remark.“


David Bee added a source for a slightly different version of the quote:
“…on Page 242 of their compilation 'Statistically Speaking' (1996), compilers CC Gaither and AE Cavazos-Gaither have the following, attributed to Disraeli in George Seldes's 1960 book The Great Quotations: There are lies, damn lies, and church statistics.”

Rex Bogg’s contributed a link to HYPERLINK "http://www1c.btwebworld.com/quote-unquote/" Quote-Unquote , a web site with the radio articles of Nigel Rees. About the topic in question, he writes:
“Although sometimes attributed to Mark Twain – because it appears in his posthumously-published Autobiography (1924) – this should more properly be ascribed to Disraeli, as indeed Twain took trouble to do: his exact words being, ‘The remark attributed to Disraeli would often apply with justice and force: “There are three kinds of lies: lies, damned lies, and statistics”.’

On the other hand, the remark remains untraced among Disraeli’s writings and sayings and Lord Blake, Disraeli’s biographer, does not know of any evidence that Disraeli said any such thing and thinks it most unlikely that he did. So why did Twain make the attribution? A suggestion: Leonard Henry Courtney, the British economist and politician (1832-1918), later Lord Courtney, gave a speech on proportional representation ‘To My Fellow-Disciples at Saratoga Springs’, New York, in August 1895, in which this sentence appeared: ‘After all, facts are facts, and although we may quote one to another with a chuckle the words of the Wise Statesman, “Lies - damn lies - and statistics,” still there are some easy figures the simplest must understand, and the astutest cannot wriggle out of.’
It is conceivable that Twain acquired the quotation from this - and also its veiled attribution to a ‘Wise Statesman’, whom he understood to be Disraeli. 

The speech was reproduced in the (British) National Review, No. 26, in the same year. Subsequently, Courtney’s comment was reproduced in an article by J.A. Baines on ‘Parliamentary Representation in England illustrated by the Elections of 1892 and 1895’ in the Journal of the Royal Statistical Society, No. 59 (1896): ‘We may quote to one another with a chuckle the words of the Wise Statesman, lies, damn lies, and statistics, still there are some easy figures which the simplest must understand but the astutest cannot wriggle out of.’ It would be a reasonable assumption that Courtney was referring to Disraeli by his use of the phrase ‘Wise Statesman’, though the context in which the phrase is used is somewhat complicated. For some reason, at this time, allusions to rather than outright quotations of Disraeli were the order of the day (he had died in 1881). Compare the fact that the remark to an author who had sent Disraeli an unsolicited manuscript – ‘Many thanks; I shall lose no time in reading it’ – is merely ascribed to ‘an eminent man on this side of the Atlantic’ by G.W.E. Russell in Collections and Recollections, Chap. 31 (1898).

Comparable sayings: Dr Halliday Sutherland’s autobiographical A Time to Keep (1934) has an account of Sir Henry Littlejohn, ‘Police Surgeon, Medical Officer of Health and Professor of Forensic Medicine at the University [Edinburgh] ... Sir Henry’s class at 9 a.m. was always crowded, and he told us of the murder trials of the last century in which he had played his part. It was Lord Young [judge] who said, “There are four classes of witnesses - liars, damned liars, expert witnesses, and Sir Henry Littlejohn”.’ Lies, Damn Lies, and Some Exclusives was the title of a book about British newspapers (1984) by Henry Porter. ‘There are lies, damned lies ... and Fianna Fáil party political broadcasts’ - Barry Desmond MEP, (Irish) Labour Party director of elections, in November 1992.