## Monday 31 January 2022

### 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.

partI 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 wrote this early 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 - January 31

Joost Bürgi nich at Kepler  monument

The capacity to blunder slightly is the real marvel of DNA.
Without this special attribute, we would still be anaerobic bacteria
and there would be no music.

The 31st day of the year; 31 = 22 + 33, i.e., The eleventh prime, and third Mersenne prime, it is also the sum of the first two primes raised to themselves. *Number Gossip  (Is there another prime which is the sum of consecutive primes raised to themselves?  A note from Andy Pepperdine of Bath who informed me that ${2}^{2}+{3}^{3}+{5}^{5}+{7}^{7}=826699$, a prime.﻿)

There are exactly 31 positive integers which cannot be written as the sum of two distinct squares; and one of them is the number 31. Finding the 31 is not so hard, they all occur in the first six months of the year.  Proving there are no more is a little tougher.

Jim Wilder ‏@wilderlab offered, The sum of digits of the 31st Fibonacci number (1346269) is 31.

If you like unusual speed limits, the speed limit in downtown Trenton, a small city in northwestern Tennessee, is 31 miles per hour.
And the little teapot on the sign? Well, Trenton also bills itself as the teapot capital of the nation. The 31 mph road sign seems to come from a conflict between Trenton and a neighboring town which I will not name ,...but I will tell you they think of themselves as the white squirrel capital.

31 is also the smallest integer that can be written as the sum of four positive squares in two ways 1+1+4+25; 4+9+9+9.

31 is an evil math teacher number. The sequence of  the maximum number of regions obtained by joining n points around a circle by straight lines begins 2, 4, 8, 16... but for five points, it is 31.

The sum of the digits of the 31st Fibonacci number.... is 31

And 31 is also the minimal number of moves to solve the Towers of Hanoi problem with five disks.  (now wondering if there is a mathematical connection between these two ideas other than coincidence)

@JamesTanton posted a mathematical fact and query regarding 31.  31 =111(base 5) =11111(base 2) and 8191 =111(base 90) = 111111111111(base 2) are the only two integers known to be repunits at least 3 digits long in two different bases.
Is there an integer with representations 10101010..., ,at least three digits, in each of two different bases?

Which made me wonder, are there other pairs that are repdigits (all alike, but not all units) in two (or more) different bases?

EVENTS
1599 During an observation of the lunar eclipse, Tycho Brahe discovers that his predictive theory about the movement of the Moon is wrong since the eclipse started 24 minutes before his calculations predicted: he improves on his theory. On March 21 he sent a letter to Longomontanus, in which he reports his revised theory.*Wik

1671 (OS-1672) In a letter from Flamsteed to John Collins, he advises that "Mr Newton's tube is now delivered into the hands of Dr. Barrow," to be presented by him at the Royal Society. *Correspondence of Scientific Men of the Seventeenth Century.
1802 Gauss elected a corresponding member of the St. Petersburg Academy of Science. *VFR Within the year he would be offered a lucrative position at the Academy, including a generous salary, pensions, allotments for his widow and children, and free lodging and heat. In thirteen months he would refuse the offer in Russia, but in four years, the death of the Duke would prompt him to accept a position in Gottingen. *PB notes

1834 Felix Klein declines to be the successor of J. J. Sylvester at John's Hopkins.  Klein had been offered the position on December 13th of the previous year, but had demanded a salary equal to the departing Sylvester and some form of security for his family which Johns Hopkins did not meet. By October he would send notes to his family, "Gottingen is beginning to make noises."  In the spring of 1836 he took over as Professor at Gottingen (he had been their second choice). *Constance Reid, The Road Not Taken, Mathematical Intelligencer, 1978

1839, Fox Talbot read a paper before the Royal Society, London, to describe his photographic process using solar light, with an exposure time of about 20 minutes: Some Account of the Art of Photogenic Drawing or the Process by which Natural Objects may be made to Delineate Themselves without the Aid of the Artist's Pencil. He had heard that Daguerre of Paris was working on a similar process. To establish his own priority, Fox Talbot had exhibited "such specimens of my process as I had with me in town," the previous week at a meeting of the Royal Institution, before he had this more detailed paper ready to present.*TIS

1939 Hewlett-Packard founded. Their calculators use the “reverse Polish notation” devised by Jan L Lukasiewicz (see here, 1878). *VFR

1939 Joseph Ehrenfried Hofmann began his academic career as a professor of the history of mathematics at the University of Berlin. He is noted for his work on Leibniz, especially the book Leibniz in Paris, 1672–1676: His Growth to Mathematical Maturity. *VFR Leibniz in Paris 1672-1676: His Growth to Mathematical Maturity

1958 Explorer 1 was launched on January 31, 1958 at 22:48 Eastern Time (equal to February 1, 03:48 UTC because the time change goes past midnight). It was the first spacecraft to detect the Van Allen radiation belt, returning data until its batteries were exhausted after nearly four months. It remained in orbit until 1970, and has been followed by more than 90 scientific spacecraft in the Explorer series. *Wik
Actually the Van Allen radiation was detectable by the Russian’s first satellite, Sputnik.  Because the signals were sent in a secret code, it’s signal could not be received by the Russians when it was detecting the radiation of the belt.  *Frederich Pohl, Chasing Science, pg 85

1964 A publicity campaign to promote the tv show Twilight Zone, came to an end.  As part of the promotion, a 19 year old student of astrophysics at UCLA was selected to be "Miss Twighlight Zone as part of the promotion.  The young woman selected, Victoria Trimble, went on to be an outstanding astrophysicist and science historian.  *HT to Paul Halpren

------------------------------------------------------------------------------------------------------------------------
1995 AT&T Bell Laboratories and VLSI Technology announce plans to develop strategies for protecting communications devices from eavesdroppers. The goal would be to prevent problems such as insecure cellular phone lines and Internet transmissions by including security chips in devices. *CHM

2016, Since the year is a leap year beginning on a Friday, the typical calendar page for January takes six lines.  Such months are called perverse months. (The same months will be perverse in a year starting on Saturday.  2016 has three such months, Jan, July and October. 2012 had only two. It is possible for there to be four in a single year. When will that year be?  Is it possible for there to be a year with no perverse months?
There is an inverse relationship between Friday-the-thirteenths and perverse months; so what is good for the calendar makers is bad for the superstitious., so 2016 has only one Friday the 13th

 Image credit: NASA/JPL-Caltech/MSSS/TAMU
2014 The Mars rover's view of its original home planet even includes our moon, just below Earth.
The images, taken about 80 minutes after sunset during the rover's 529th Martian day (Jan. 31, 2014) are available for a broad scene of the evening sky, and a zoomed-in view of Earth and the moon.
The distance between Earth and Mars when Curiosity took the photo was about 99 million miles (160 million kilometers). * NASA

2018 The rare combination of a blue moon (generally the second full moon of a month), a Supermoon (the full moon occurring nearest to perigee when moon is closer to earth), and a total lunar eclipse occurs early in the morning (8:37 am EST). Unfortunately it was only total in the western US. It is the first such triple treat in the US since 1866. *USA Today

BIRTHS
1715 Giovanni Francesco Fagnano dei Toschi (31 Jan 1715 in Sinigaglia, Italy - 14 May 1797 in Sinigaglia, Italy) He proved that the triangle which has as its vertices the bases of the altitudes of any triangle has those altitudes as its bisectors. *VFR  Of all the triangles that could be inscribed in a given triangle, the one with the smallest perimeter is the orthic triangle. This has sometimes been called Fagnano's Problem since it was first posed and answered by Giovanni Francesco Fagnano dei Toschi. Fagnano also was the first to show that the altitudes of the original triangle are the angle bisectors of the orhtic triangle, so the incenter of the orthic triangle is the orthocenter of the original triangle.*pb
He was the son of the mathematician
Giulio Carlo Fagnano. He calculated the integral of the tangent and also proved the reduction  formula $\int {x}^{n}\mathrm{sin}xdx=-{x}^{n}\mathrm{cos}x+n\int {x}^{n-1}\mathrm{cos}xdx$

*VFR

1763 The Rt. Rev. John Mortimer Brinkley D.D. (ca. 1763 (Baptized 31 Jan,1763, Woodbridge, Suffolk – 14 September 1835, Dublin) was the first Royal Astronomer of Ireland and later Bishop of Cloyne.
He graduated B.A. in 1788 as senior wrangler and Smith's Prizeman, was elected a fellow of the college and was awarded M.A. in 1791. He was ordained at Lincoln Cathedral in the same year, and in 1792 became the second Andrews Professor of Astronomy in the University of Dublin, which carried the new title of Royal Astronomer of Ireland. Together with John Law, Bishop of Elphin, he drafted the chapter on "Astronomy" in William Paley's Natural Theology. His main work concerned stellar astronomy and he published his Elements of Plane Astronomy in 1808. In 1822 he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences. He was awarded the Copley Medal by the Royal Society in 1824. Brinkley's observations that several stars shifted their apparent place in the sky in the course of a year were disproved at Greenwich by his contemporary John Pond, the Astronomer Royal. In 1826, he was appointed Bishop of Cloyne in County Cork, a position he held for the remaining nine years of his life. Brinkley was elected President of the Royal Astronomical Society in 1831, serving in that position for two years.
He died in 1835 at Leeson Street, Dublin and was buried in Trinity College chapel. He was succeeded at Dunsink Observatory by Sir William Rowan Hamilton. *Wik

1841 Samuel Loyd (31 Jan 1841 ; died 10 Apr 1911)  was an American puzzlemaker who was best known for composing chess problems and games, including Parcheesi, in addition to other mathematically based games and puzzles. He studied engineering and intended to become a steam and mechanical engineer but he soon made his living from his puzzles and chess problems. Loyd's most famous puzzle was the 14-15 Puzzle which he produced in 1878. The craze swept America where employers put up notices prohibiting playing the puzzle during office hours. Loyd's 15 puzzle is the familiar 4x4 arrangement of 15 square numbered tiles in a tray that must be reordered by sliding one tile at a time into the vacant space. *TIS When he offered a cash prize to anyone who could solve the puzzle with 14&15 reversed, it swept the country.  To show it impossible requires only a little group theory; see W. E. Story, “Note on the ‘15’ puzzle,” American Journal of Mathematics, 2, 399–404. For samples of Loyd’s many puzzles, see Mathematical Puzzles of Sam Loyd, edited by Martin Gardner, Dover 1959 [p. xi]. *VFR
Although Lloyd popularized the puzzle in his books and articles, he most certainly did not invent it. Loyd's first article about the puzzle was published in 1886 and it wasn't until 1891 that he first claimed to have been the inventor.  The article mentioned by Story(1878) was dated prior to Loyd's first mention of the puzzle) Here is the history of the puzzle as related by Wikipedia:The puzzle was "invented" by Noyes Palmer Chapman, a postmaster in Canastota, New York, who is said to have shown friends, as early as 1874, a precursor puzzle consisting of 16 numbered blocks that were to be put together in rows of four, each summing to 34. Copies of the improved Fifteen Puzzle made their way to Syracuse, New York by way of Noyes' son, Frank, and from there, via sundry connections, to Watch Hill, RI, and finally to Hartford (Connecticut), where students in the American School for the Deaf started manufacturing the puzzle and, by December 1879, selling them both locally and in Boston, Massachusetts. Shown one of these, Matthias Rice, who ran a fancy woodworking business in Boston, started manufacturing the puzzle sometime in December 1879 and convinced a "Yankee Notions" fancy goods dealer to sell them under the name of "Gem Puzzle". In late-January 1880, Dr. Charles Pevey, a dentist in Worcester, Massachusetts, garnered some attention by offering a cash reward for a solution to the Fifteen Puzzle.
The game became a craze in the U.S. in February 1880, Canada in March, Europe in April, but that craze had pretty much dissipated by July. Apparently the puzzle was not introduced to Japan until 1889.
Noyes Chapman had applied for a patent on his "Block Solitaire Puzzle" on February 21, 1880. However, that patent was rejected, likely because it was not sufficiently different from the August 20, 1878 "Puzzle-Blocks" patent (US 207124) granted to Ernest U. Kinsey.*Wik
Play with an online version here.

1886 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

1914 Lev Arkad'evich Kaluznin (31 Jan 1914 in Moscow, Russia - 6 Dec 1990 in Moscow, Russia) Kaluznin is best known for his work in group theory and in particular permutation groups. He studied the Sylow p-subgroups of symmetric groups and their generalisations. In the case of symmetric groups of degree pn, these subgroups were constructed from cyclic groups of order p by taking their wreath product. His work allowed computations in groups to be replaced by computations in certain polynomial algebras over the field of p elements. Despite the fact that the earliest applications of wreath products of permutation groups was due to C Jordan, W Specht and G Polya, it was Kaluznin who first developed special computational tools for this purpose. Using his techniques, he was able to describe the characteristic subgroups of the Sylow p-subgroups, their derived series, their upper and lower central series, and more. These results have been included in many textbooks on group theory. *SAU

1928 Heinz Bauer (31 January 1928 – 15 August 2002) was a German mathematician.
Bauer studied at the University of Erlangen-Nuremberg and received his PhD there in 1953 under the supervision of Otto Haupt and finished his habilitation in 1956, both for work with Otto Haupt. After a short time from 1961 to 1965 as professor at the University of Hamburg he stayed his whole career at the University of Erlangen-Nuremberg. His research focus was the Potential theory, Probability theory and Functional analysis
Bauer received the Chauvenet Prize in 1980 and became a member of the German Academy of Sciences Leopoldina in 1986. Bauer died in Erlangen. *Wik

1929 Rudolf Ludwig Mössbauer (31 Jan 1929 -  14 September 2011) German physicist and co-winner (with American Robert Hofstadter) of the Nobel Prize for Physics in 1961 for his researches concerning the resonance absorption of gamma-rays and his discovery in this connection of the Mössbauer effect. The Mössbauer effect occurs when gamma rays emitted from nuclei of radioactive isotopes have an unvarying wavelength and frequency. This occurs if the emitting nuclei are tightly held in a crystal. Normally, the energy of the gamma rays would be changed because of the recoil of the radiating nucleus. Mössbauer's discoveries helped to prove Einstein's general theory of relativity. His discoveries are also used to measure the magnetic field of atomic nuclei and to study other properties of solid materials. *TIS
Rudolf Mössbauer was an excellent teacher. He gave highly specialized lectures on numerous courses, including Neutrino Physics, Neutrino Oscillations, The Unification of the Electromagnetic and Weak Interactions and The Interaction of Photons and Neutrons With Matter. In 1984, he gave undergraduate lectures to 350 people taking the physics course. He told his students: “Explain it! The most important thing is, that you are able to explain it! You will have exams, there you have to explain it. Eventually, you pass them, you get your diploma and you think, that's it! – No, the whole life is an exam, you'll have to write applications, you'll have to discuss with peers... So learn to explain it! You can train this by explaining to another student, a colleague. If they are not available, explain it to your mother – or to your cat!” *Wik

1945 Persi Warren Diaconis (January 31, 1945;  ) is an American mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards.
Diaconis left home at 14 to travel with sleight-of-hand legend Dai Vernon, and dropped out of high school, promising himself that he would return one day so that he could learn all of the math necessary to read William Feller's famous two-volume treatise on probability theory, An Introduction to Probability Theory and Its Applications. He returned to school (City College of New York for his undergraduate work graduating in 1971 and then a Ph.D. in Mathematical Statistics from Harvard University in 1974), and became a mathematical probabilist.
According to Martin Gardner, at school Diaconis supported himself by playing poker on ships between New York and South America. Gardner recalls that Diaconis had "fantastic second deal and bottom deal".
Diaconis is married to Stanford statistics professor Susan Holmes. *Wik

DEATHS
1632 Joost Bürgi (28 Feb 1552, 31 Jan 1632) Swiss watchmaker and mathematician who invented logarithms independently of the Scottish mathematician John Napier. He was the most skilful, and the most famous, clockmaker of his day. He also made astronomical and practical geometry instruments (notably the proportional compass and a triangulation instrument useful in surveying). This led to becoming an assistant to the German astronomer Johannes Kepler. Bürgi was a major contributor to the development of decimal fractions and exponential notation, but his most notable contribution was published in 1620 as a table of antilogarithms. Napier published his table of logarithms in 1614, but Bürgi had already compiled his table of logarithms at least 10 years before that, and perhaps as early as 1588.
*TIS  I posted about Burgi and his work w/ "proto" logarithms here if you would like more detail.

1903 Norman Macleod Ferrers; (11 Aug 1829 in Prinknash Park, Upton St Leonards, Gloucestershire, England - 31 Jan 1903 in Cambridge, England)  John Venn wrote of him,.. ,
the Master, Dr Edwin Guest, invited Ferrers, who was by far the best mathematician amongst the fellows, to supply the place. His career was thus determined for the rest of his life. For many years head mathematical lecturer, he was one of the two tutors of the college from 1865. As lecturer he was extremely successful. Besides great natural powers in mathematics, he possessed an unusual capacity for vivid exposition. He was probably the best lecturer, in his subject, in the university of his day.
It was as a mathematician that Ferrers acquired fame outside the university. He made many contributions of importance to mathematical literature. His first book was "Solutions of the Cambridge Senate House Problems, 1848 - 51". In 1861 he published a treatise on "Trilinear Co-ordinates," of which subsequent editions appeared in 1866 and 1876. One of his early memoirs was on Sylvester's development of Poinsot's representation of the motion of a rigid body about a fixed point. The paper was read before the Royal Society in 1869, and published in their Transactions. In 1871 he edited at the request of the college the "Mathematical Writings of George Green" ... Ferrers's treatise on "Spherical Harmonics," published in 1877, presented many original features. His contributions to the "Quarterly Journal of Mathematics," of which he was an editor from 1855 to 1891, were numerous ... They range over such subjects as quadriplanar co-ordinates, Lagrange's equations and hydrodynamics. In 1881 he applied himself to study Kelvin's investigation of the law of distribution of electricity in equilibrium on an uninfluenced spherical bowl. In this he made the important addition of finding the potential at any point of space in zonal harmonics (1881).
Ferrers proved the proposition by Adams that "The number of modes of partitioning (n) into (m) parts is equal to the number of modes of partitioning (n) into parts, one of which is always m, and the others (m) or less than (m). " with a graphic transformation that is named for him. *SAU

1934 Duncan MacLaren Young Sommerville (24 Nov 1879 in Beawar, Rajasthan, India - 31 Jan 1934 in Wellington, New Zealand) Sommerville studied at St Andrews and then had a post as a lecturer there. He left to become Professor of Pure and Applied mathematics at Victoria College, Wellington New Zealand. He worked on non-Euclidean geometry and the History of Mathematics. He became President of the EMS in 1911. *SAU

1966 Dirk Brouwer (1 Sep 1902; 31 Jan 1966) Dutch-born U.S. astronomer and geophysicist known for his achievements in celestial mechanics, especially for his pioneering application of high-speed digital computers for astronomical computations. While still a student he determined the mass of Titan from its influence on other Saturnian moons. Brouwer developed general methods for finding orbits and computing errors and applied these methods to comets, asteroids, and planets. He computed the orbits of the first artificial satellites and from them obtained increased knowledge of the figure of the earth. His book, Methods of Celestial Mechanics, taught a generation of celestial mechanicians. He also redetermined astronomical constants.*TIS

1973 Noel Bryan Slater, often cited NB Slater, (29 July 1912 in Blackburn, Lancashire, England - January 31 1973 in Hull, England) was a British mathematician and physicist who worked on including statistical mechanics and physical chemistry, and probability theory.*Wik

1995 George Robert Stibitz (30 Apr 1904, 31 Jan 1995) U.S. mathematician who was regarded by many as the "father of the modern digital computer." While serving as a research mathematician at Bell Telephone Laboratories in New York City, Stibitz worked on relay switching equipment used in telephone networks. In 1937, Stibitz, a scientist at Bell Laboratories built a digital machine based on relays, flashlight bulbs, and metal strips cut from tin-cans. He called it the "Model K" because most of it was constructed on his kitchen table. It worked on the principle that if two relays were activated they caused a third relay to become active, where this third relay represented the sum of the operation. Also, in 1940, he gave a demonstration of the first remote operation of a computer.*TIS

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

## Sunday 30 January 2022

### 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.

### On This Day in Math - January 30

God may not play dice with the universe,
but something strange is going on with the prime numbers.
~Paul Erdos **

(Not realy,Referencing Albert Einstein's famous remark that "God does not play dice with the universe", this is attributed to Erdős in "Mathematics : Homage to an Itinerant Master" by D. Mackenzie, in Science 275:759 (1997), but has also been stated to be a comment originating in a talk given by Carl Pomerance on the Erdős-Kac theorem, in San Diego in January 1997, a few months after Erdős's death. Confirmation of this by Pomerance is reported in a statement posted to the School of Engineering, Computer Science & Mathematics, University of Exeter, where he states it was a paraphrase of something he imagined Erdős and Mark Kac might have said, and presented in a slide-show, which subsequently became reported in a newspaper as a genuine quote of Erdős the next day. In his slide show he had them both reply to Einstein's assertion: "Maybe so, but something is going on with the primes.")

The 30th day of the year; 30 is the difference between 2 ,and $2^5$, so

But since 30 is also the difference between 6 and $6^2$,   then

Both the dodecahedron and the icosahedron have 30 edges. They may be positioned at a common center so that in the center of each of the 12 faces of the dodecahedron is one of the 12 vertices of the icosahedron, in the center of each of the 20 faces of the icosahedron is one of the 20 vertices of the dodecahedron, and the 30 edges of the dodecahedron and the 30 edges of the icosahedron cross each other at right angles at their midpoints. (I find this incredibly wonderful)

astounding to me, but 11+22+33...+3030 = 208492413443704093346554910065262730566475781 is prime Republic of Math ‏@republicofmath If there is another prime of this type, it will have over 20025 digits.

7! hours is 30 weeks

and from *@MathYearRound
30 = 2*3*5 (first 3 primes).
30 =${1}^{2}+{2}^{2}+{3}^{2}+{4}^{2}$(first 4 perfect squares).
30 = 1*1*2*3*5 (first 5 Fibonacci #).

EVENTS

10 BCE Solar eclipse in Iran, as reported on a cuneiform tablet from the British Museum *History of Astronomy ‏@hist_astro  (I have to admit that every time I look at this image it reminds me of the map of Michigan's lower peninsula, and that little chip up by the little finger is Grand Traverse Bay, which I see from my dining room)

1610 Galileo writes to Belisario Vinta, with notes on his long observation of the moon with a new twenty-power scope. A letter containing much of what was to appear about the Moon in Sidereus Nuncius, two months later. *Drake, Galileo at Work; 1978

1830 In a letter to Laplace, Gauss writes about a "curious problem" that he had been working on for twelve years.  He gives the limiting value of  the frequency of distribution of positive integers in the continued fraction of a random number (now called the Gauss-Kuzmin Distribution) as $lo{g}_{2}\left(1+x\right)$ . He then asks if Laplace can offer help in finding the error term. *Math World

1897 Mary Frances Winston elected to membership in the American Mathematical Society. The previous year she received her PhD at G¨ottingen, being the ﬁrst American woman to receive a PhD in mathematics at a German university. *G. B. Price, History of the Department of Mathematics of the University of Kansas, 1866–1970, p. 70

1884 Sonja Kovelevskiaya gives her ﬁrst university lecturer. This was the ﬁrst regular lecture by a woman at a research institution in any ﬁeld in modern times. [The Mathematical Intelligencer, 6(1984), no. 1, p. 29] *VFR

1925 The U.S. History of Science Society was incorporated under the laws of the District of Columbia. The ﬁrst president was Lawrence Joseph Henderson (1878–1924). The movement to form the society was begun by David Eugene Smith and today is the most important historical society in the world. *VFR

1952 Two New Primes Found with SWAC. Using the Standards Western Automatic Computer (SWAC), researchers found two new prime numbers the first time they attempted a prime-searching program on the computer. Within the year, three other primes had been found. The National Bureau of Standards funded construction of the SWAC in Los Angeles in 1950 and it ran, in one form or another, until 1967.
*CHM {The first two primes found with SWAC were M521, M607. In 1951 Ferrier used a mechanical desk calculator to find the 44 digit prime (2148+1)/17 = 20988936657440586486151264256610222593863921.
The first primes found with an electronic computer were by Miller and Wheeler (Nature, 168 (1951) 838) in 1951 when they found several new primes, including the 79 digit 180(2127-1)2+1 }

1982 First computer virus, the Elk Cloner, written by 15-year old Rich Skrenta, is found in the wild. It infects Apple II computers via floppy disk. *Wik

1988 Science News reports that Noam D. Elkies, age 21, of Harvard found four fourth-powers whose sum is another fourth-power, thereby providing a counterexample to a conjecture of Euler in 1769. (Euler's conjecture was that the sum of the first n integers each raised to the nth power can not be an nth power.) The smallest number in his counterexample had eight digits. Later Roger Frye of Thinking Machines Corporation, Cambridge, MA, found the smallest counterexample:
95,8004 + 217,5194 + 414,5604 + 414 5604 = 422,4184 .
This took some 100 hours on a Connection Machine. Can you ﬁgure out how to verify this example using your calculator (which only displays 8 or 10 digits)? [Mathematics Magazine 61 (1988), p 130; Science 239 (1988), p 464]. *VFR
(Euler's general conjecture had been proven false by L. J. Lander and T. R. Parkin in 1966 when they found a counterexample for fifth powers. Elkies had suggested the computer approach that provided the minimal solution. It is still unknown if there are counterexamples above n=5)

1990 Ruth Lawrence sends a paper on homological representations of the Hecke algebra, introducing, among other things, certain novel linear representations of the braid group, the Lawrence–Krammer representation to the journal, Communications in Mathematical Physics
*Wik

1996 Yuji Hyakutake in Japan discovered a new comet using 25x150 binoculars. The comet was designated Comet C/1996 B2 (Hyakutake). As subsequent observations of the new comet were obtained, Brian Marsden from the IAU Central Bureau was able to compute the comet's orbital elements, and these computations indicated that the comet will pass as close as 0.10 AU (9.3 million miles) from the Earth on March 25, 1996! The comet has become a bright naked-eye object and remained so in March, April and May in 1996. The comet had exceeded expectations, becoming the brightest comet since Comet West in 1976. A long tail of up to 100 degrees was reported, and small fragments have been observed to break off the main nucleus. Comet Hyakutake is indeed the Great Comet of 1996. *jpl.nasa
Hyakutake discovered C/1996 B2 while looking for C/1995 Y1, a comet he had discovered a few weeks before. He died in Kokubu, Kagoshima, in 2002 at age 51 of an aneurysm which had led to internal bleeding. *Wik

BIRTHS

1619 Michelangelo Ricci  (30 Jan 1619 in Rome, Italy - : 12 May 1682 in Rome) In 1666, he found the tangent lines to the parabolas of Fermat. *VFR Michelangelo Ricci was a friend of Torricelli; in fact both were taught by Benedetti Castelli. He studied theology and law in Rome and at this time he became friends with René de Sluze. It is clear that Sluze, Torricelli and Ricci had a considerable influence on each other in the mathematics which they studied.
Ricci made his career in the Church. His income came from the Church, certainly from 1650 he received such funds, but perhaps surprisingly he was never ordained. Ricci served the Pope in several different roles before being made a cardinal by Pope Innocent XI in 1681.
Ricci's main work was Exercitatio geometrica, De maximis et minimis (1666) which was later reprinted as an appendix to Nicolaus Mercator's Logarithmo-technia (1668). It only consisted of 19 pages and it is remarkable that his high reputation rests solely on such a short publication.
In this work Ricci finds the maximum of xm(a - x)n and the tangents to ym = kxn. The methods are early examples of induction. He also studied spirals (1644), generalized cycloids (1674) and states explicitly that finding tangents and finding areas are inverse operations (1668). *SAU

1755 Nikolai Fuss (30 Jan 1755 in Basel, Switzerland - 4 Jan 1826 in St Petersburg, Russia) was a Swiss mathematician whose most important contribution was as amanuensis to Euler after he lost his sight. Most of Fuss's papers are solutions to problems posed by Euler on spherical geometry, trigonometry, series, differential geometry and differential equations. His best papers are in spherical trigonometry, a topic he worked on with A J Lexell and F T Schubert. Fuss also worked on geometrical problems of Apollonius and Pappus. He made contributions to differential geometry and won a prize from the French Academy in 1778 for a paper on the motion of comets near some planet Recherche sur le dérangement d'une comète qui passe près d'une planète. Fuss won other prizes from Sweden and Denmark. He contributed much in the field of education, writing many fine textbooks. *SAU

1805 Edward Sang,(30 Jan 1805 in Kirkcaldy, Fife, Scotland - 23 Dec 1890) A native of Fife, Sang wrote extensively on mathematical, mechanical, optical and actuarial topics. *SAU

1865 Georg Landsberg (30 Jan 1865 , 14 Sept 1912) studied the theory of functions of two variables and also the theory of higher dimensional curves. In particular he studied the role of these curves in the calculus of variations and in mechanics.
He worked with ideas related to those of Weierstrass, Riemann and Heinrich Weber on theta functions and Gaussian sums. His most important work, however was his contribution to the development of the theory of algebraic functions of a single variable. Here he studied the Riemann-Roch theorem.
He was able to combine Riemann's function theoretic approach with the Italian geometric approach and with the Weierstrass arithmetical approach. His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
One of his most important works was Theorie der algebraischen Funktionen einer Varaiblen (Leipzig, 1902) which he wrote jointly with Kurt Hensel. This work remained the standard text on the subject for many years. *SAU

1918 Heinz Rutishauser (30 January 1918 in Weinfelden, Switzerland; 10 November 1970 in Zürich) was a Swiss mathematician and a pioneer of modern numerical mathematics and computer science. *Wik

1925 Douglas Engelbart is Born, best known for inventing the computer mouse. Engelbart publicly demonstrated the mouse at a computer conference in 1968, where he also showed off work his group had done in hypermedia and on-screen video teleconferencing. The founder of the Bootstrap Institute, Engelbart has 20 patents to his name.*CHM

DEATHS

1954 Gino Benedetto Loria (19 May 1862 in Mantua, Italy - 30 Jan 1954 in Genoa, Italy) In his day, Loria was arguably the pre-eminent historian of mathematics in Italy. A full professor of higher geometry at the University of Genoa beginning in 1891, Loria wrote the history of mathematics as a mathematician writing for other mathematicians. He emphasised this approach repeatedly in his works. For instance, in the introduction to his 'Storia delle matematiche dall'alba della civilità al tramonto del secolo XIX' (History of Mathematics from the Dawn of Civilisation to the End of the 19th Century), he stated that general history of mathematics was written "by a mathematician for mathematicians". *SAU

1977 Harry Clyde Carver (December 4, 1890 – January 30, 1977) was an American mathematician and academic, primarily associated with the University of Michigan. He was a major influence in the development of mathematical statistics as an academic discipline.
Born in Waterbury, Connecticut, Carver was educated at the University of Michigan, earning his B.S. degree in 1915, and the next year becoming an instructor in mathematics; he taught statistics in actuarial applications. At the time, the University of Michigan was only the second such institution in the United States to offer this type of course, after the pioneering Iowa State University. Carver was appointed assistant professor at Michigan in 1918, then associate professor (1921) and full professor (1936); during this period the University's program in mathematical statistics and probability underwent significant expansion.
In 1930 Carver founded the journal Annals of Mathematical Statistics, which over time became an important periodical in the field. Financial support, however, was lacking in the midst of the Great Depression; in January 1934 Carver undertook financial responsibility for the Annals and maintained the existence of the journal at his own expense. In 1935 he helped to start the Institute of Mathematical Statistics, which in 1938 assumed control over the journal; Samuel S. Wilks succeeded Carver as editor in the same year. The Institute has named its Harry C. Carver Medal after him.
With the coming of World War II, Carver devoted his energies to solving problems in aerial navigation, an interest he maintained for the remainder of his life. *Wik

1991 John Bardeen (23 May 1908, 30 Jan 1991) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS

1992 Dom George Frederick James Temple​ FRS(born 2 December 1901, London; died 30 January 1992, Isle of Wight) was an English mathematician, recipient of the Sylvester Medal in 1969. He was President of the London Mathematical Society in the years 1951-1953.[2]
Temple took his first degree as an evening student at Birkbeck College, London, between 1918 and 1922, and also worked there as a research assistant. In 1924 he moved to Imperial College as a demonstrator, where he worked with Professor Sydney Chapman. After a period spent with Eddington at Cambridge, he returned to Imperial as reader in mathematics. He was appointed professor of mathematics at King's College London in 1932, where he returned after war service with the Royal Aircraft Establishment at Farnborough. In 1953 he was appointed Sedleian Professor of Natural Philosophy at the University of Oxford, a chair which he held until 1968, and in which he succeeded Chapman. He was also an honorary Fellow of Queen's College, Oxford.
After the death of his wife in 1980, Temple, a devout Christian, took monastic vows in the Benedictine order and entered Quarr Abbey on the Isle of Wight, where he remained until his death. *Wik

1998 Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish and American mathematician born in Warsaw, Russian Empire (now in Poland) and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.
He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor was Karol Borsuk. His main interest was algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (whose names the Eilenberg–Steenrod axioms bear), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory.
Eilenberg was a member of Bourbaki and with Henri Cartan, wrote the 1956 book Homological Algebra, which became a classic.
Later in life he worked mainly in pure category theory, being one of the founders of the field. The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective modules.
Eilenberg also wrote an important book on automata theory. The X-machine, a form of automaton, was introduced by Eilenberg in 1974. *Wik

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