Depth beyond depth was revealed to me - the Byss and Abyss.
I saw - as one might see the transit of Venus or even the Lord Mayor's Show
- a quantity passing through infinity and changing its sign from plus to minus.
I saw exactly why it happened and why the tergiversation
was inevitable but it was after dinner
and I let it go.
The 124th day of the year;124 =σ( 1! * 2! * 4!) *Prime Curios (The sigma function of a positive integer n is the sum of the positive divisors of n)
124 is also an Odious number: a number with an odd number of 1's in its binary expansion.(just recently, it occurred to me that it would be more appropriate if an Odious number, had an odd number of "0's")
124 in base two is expressed as 1111100.
124 in base five is a repdigit, 444, which means it's one less than 5^3 (students new to studying bases should observe that a repdigit of (n-1) which is k units long in base n, will always be (n^k)-1. [like 99 in base 10 is 10^2-1]
and ±1 ± 2 ± 3 ± 4 ± 5 ± 6 ± 7 ± 8 ± 9 ± 10 ± 11 ± 12 = 0 has 124 solutions (collect the whole set) *Math Year-Round @MathYearRound
And for Algebra students, 124 is divisible by four so it is the difference of two squares of numbers that differ by 2, and since 124 / 4 = 31, the numbers must straddle 31, 32² - 30² = 124.
Several More math facts for this date at https://mathdaypballew.blogspot.com/
The Letters were written to the wealthy Augsburg Magistrate Mark Welser (1558-1614), a well-known patron of the new sciences, in responses to Christoph Scheiner's own Letters on Sunspots, published through Wesler in 1612.
Galileo and Scheiner were later to quarrel bitterly over priority of discovery of sunspots; in fact the first recorded sunspot observation is on 8 December 1610 by the Englishman Thomas Harriott (1560-1621), and the first publication by Johann Fabricius.
The title page of Galileo's letters, published by Wesler, is shown below. The lynx depicted on the Title page indicates Galileo's membership in the Lincean academy (Accademia dei Lincei, for the "sharp-eyed")
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1675 Charles II orders Royal Greenwich Observatory be built to solve Longitude problem. * Nat. Maritime Museum@NMMGreenwich
1694 David Gregory and Newton disagree on "kissing numbers" during Gregory's visit to Newton in Cambridge. Newton asserted that 12 was the maximum number of spheres that could be placed touching around a central sphere. Gregory held out that a 13th was possible. Kepler had shown a completely rigid arrangement of 12 spheres around one in his Six-cornered Snow Flakes. His method is called a hexagonal packing. But Newton and Gregory both knew that placing the surrounding 12 spheres at the vertices of an icosahedron around the central sphere, there was enough space to move the balls around, In fact, any two balls could be moved around and interchanged while all twelve balls were still in contact with the central one. The maximum "kissing number" is known for the first four dimensions, but beyond that only the eighth (240) and twenty-fourth(196,560) are exactly known. *Plus Math, *Wik (Newton was right, but it wasn't proven until 1953.) If you want to take up the challenge, in the fifth dimension the "kissing number" is known to be 40 <= k <=44.
1756 A letter from John Elliot, a young naval officer, to his father.
"There is no News here worth troubling you with, only the discovery of the longitude by a Hanovarien, it is perform’d by an Observation of the Moon & any fix’d Star by knowing there distance at a given place & observing there difference at Sea given the difference of time[. T]he obs[ervatio]n is simple & easey but the Calculation is extreamly perplexd. I had this from a Man that is making the Instrument."
The Hanovarien mentioned is Tobias Mayer. *Richard Dunn, Board of Longitude Project, Royal Museums Greenwich
1780 The American Academy of Arts and Sciences, the first national arts and sciences society in the U.S., was founded on this date in Boston “to cultivate every art and science which may tend to advance the interest, dignity, honor and happiness of a free, independent and virtuous people.” James Bowdoin was the first president. *VFR [The original incorporaters were later joined by Benjamin Franklin, George Washington, Thomas Jefferson, Charles Bulfinch, Alexander Hamilton, and John Quincy]*TIS
1885 On September 5, 1885, Scientific American published a photograph depicting a “streak of real ‘Jersey lightning,’” taken by William Nicholson Jennings (1860-1946) at 10:30 p.m. on the first of August that same year. Captured on the roof of Jennings’ house in North Philadelphia and later reproduced as a lantern slide, the photograph reveals a flash of lightning traveling diagonally from the upper left corner of the frame to the horizon, illuminating the tops of trees and a line of row house roofs in the foreground. Regional and national newspapers soon proclaimed Jennings as the first to successfully photograph lightning with a camera.
The Today in Science claims an earlier occurrence on May 4 of the previous year. " In 1884, the first photograph of a lightning flash made in the U.S. was made by W. C. Gurley of the Marietta Observatory, Ohio. The flash was about 3 miles away." I don't have a picture of that one (but am willing to post one if someone can find it) so Jennings gets the plug. The observatory in Marietta is named for William Chamberlain Gurley, its first director.
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1935 Albert Einstein, in a letter to the New York Times, writes, "In the judgement of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began". *Dwight E. Neuenschwander, Emmy Noether's Wonderful Theorem
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1989, the space probe Magellan was carried in the cargo bay by the STS-30 Space Shuttle Atlantis mission launched from Kennedy Space Center in Florida. The space probe was named after the 16th-century Portuguese explorer Ferdinand Magellan. This was the first planetary spacecraft to be released from a shuttle in Earth orbit. It arrived at its planned polar orbit around Venus on 10 Aug 1990, which it circled once every 3-hr 15-min. As the planet rotated slowly beneath it, Magellan collected radar images of the surface in strips about 17-28 km (10-17 mi) wide and radioed back the information. Its mission included taking other measurements. On 11 Oct 1994, it was directed towards the surface, collecting data until it burned up in the atmosphere.*TIS
1995 Commodore Bought By German Company:
German electronics company Escom AG paid $10 million for the rights to the name, patents and intellectual property of Commodore Electronics Ltd. A pioneer in the personal computer industry, Commodore halted production in 1994 and declared bankruptcy. Escom AG planned to resume production of Commodore personal computers, including its most recent model, the Amiga. The company later sold its Amiga rights. *CHM
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2000 A rare conjunction occurs on the New Moon including all seven of the traditional celestial bodies known from ancient times up until 1781 with the discovery of Uranus. The May 2000 conjunction consisted of: the Sun and Moon, Mercury, Venus, Mars, Jupiter, and Saturn. *Wik
2011 Star Wars Day, as told to me by a student..."May the Fourth be with you."
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1806 Sir William Fothergill Cooke (4 May 1806 – 25 June 1879) English inventor who worked with Charles Wheatstone in developing electric telegraphy. Of the pair, Cooke contributed a superior business ability, whereas Wheatstone is generally considered the more important of the two in the history of the telegraph. After Cooke attended a demonstration of the use of wire in transmitting messages, he began his own experiments with telegraphy (1836) and formed a partnership with Wheatstone. Their first patent (1837) was impractical because of cost. They demonstrated their five-needle telegraph on 24 July 1837 when they ran a telegraph line along the railway track from Euston to Camden Town able to transmit and successfully receive a message. In 1845, they patented a single-needle electric telegraph. *TIS
1825 T(homas) H(enry) Huxley (4 May 1825 – 29 June 1895) was an English biologist , known as "Darwin's Bulldog" for his promotion of Darwinism which led him to an advocacy of agnosticism (a word he coined). At the age of 12 he was reading advanced works on geology, and by early adolescence he recorded the results of simple self-conducted experiments. As a ship's assistant surgeon on HMS Rattlesnake he studied marine specimens by microscope. During the 1850's he published papers on animal individuality, the cephalous mollusks (ex. squids), the methods of paleontology, and the methods and principles of science and science education. *TIS
Though Clifford never constructed a full theory of spacetime and relativity, there are some remarkable observations he made in print that foreshadowed these modern concepts: In his book Elements of Dynamic (1878), he introduced "quasi-harmonic motion in a hyperbola". He wrote an expression for a parametrized unit hyperbola, which other authors later used as a model for relativistic velocity. Elsewhere he states,
The geometry of rotors and motors ... forms the basis of the whole modern theory of the relative rest (Static) and the relative motion (Kinematic and Kinetic) of invariable systems.
This passage makes reference to biquaternions, though Clifford made these into split-biquaternions as his independent development. The book continues with a chapter "On the bending of space", the substance of general relativity. Clifford also discussed his views in On the Space-Theory of Matter in 1876.
1862 Alice Liddell (4 May 1852 – 16 November 1934), subject of the Alice in wonderland stories. 4 May is also probably the date on which the mad hatter's tea party took place. Charles Wells suggested to me that perhaps that was the date on which young Alice and Charles Dodgson went for a row with her dad and Dodgson first told the tale. There are, Charles points out, two references to the date being the fourth (the white rabbit for instance has a watch that tells the date, not the time and asks Alice the date) and two referring to the month of May . It turns out that that boat ride was on July 4 of 1862. There is however evidence in the book that Dodgson intended to make the story on Alice's date of birth. In that year, for example, the date of her birth there was exactly two days difference between solar and lunar time. Thus the Hatter's response to the date, "Two days wrong" perhaps. Anyway, a novel idea (bad pun) Charles, and thanks for the comment.
1876 Heinrich Jung (4 May 1876 in Essen, Germany - 1953 in Halle, Germany) was a German mathematician who worked on algebraic functions. *SAU
1918 George Francis Carrier (May 4, 1918 – March 8, 2002) was an engineer and physicist, and the T. Jefferson Coolidge Professor of Applied Mathematics Emeritus of Harvard University. He was particularly noted for his ability to intuitively model a physical system and then deduce an analytical solution. He worked especially in the modeling of fluid mechanics, combustion, and tsunamis.
Born in Millinocket, Maine, he received a master's in engineering degree in 1939 and a Ph.D. in 1944 from Cornell University with a dissertation in applied mechanics entitled Investigations in the Field of Aeolotropic Elasticity and the Bending of the Sectorial-Plate under the supervision of J. Norman Goodier. He was co-author of a number of mathematical textbooks and over 100 journal papers.
Carrier was elected to the American Academy of Arts and Sciences in 1953, the United States National Academy of Sciences in 1967, and the American Philosophical Society in 1976. In 1990, he received the National Medal of Science, the United States' highest scientific award, presented by President Bush, for his contributions to the natural sciences.
He died from esophageal cancer on March 8, 2002. *Wik
George Carrier was considered to be one of the best applied mathematicians the United States ever produced. He loved applied mathematical problems developing complex mathematical models, which he solved with ingenious approximations and asymptotic results.*SAU
1926 David Allan Bromley (4 May 1926; 10 Feb 2005 at age 78) was a Canadian-American physicist who was considered the “father of modern heavy ion science” for his pioneering experiments on both the structure and dynamics of atomic nuclei. He was a leader in developing particle accelerators detection systems and computer-based data acquisition and analysis systems. While at Atomic Energy of Canada (1955-60) he installed the first tandem Van Der Graaff accelerator. He was founder and director (1963-89) of the A.W. Wright Nuclear Structure Laboratory at Yale University, which has produced more experimental nuclear physicists than any other facility. During this time he became active on numerous national and international science policy boards. From 1980-89, he was a member of the White House Science Council.*TIS
1932 Edward Nelson (May 4, 1932 – September 10, 2014) was an American mathematician. He was professor in the Mathematics Department at Princeton University. He was known for his work on mathematical physics and mathematical logic. In mathematical logic, he was noted especially for his internal set theory, and views on ultrafinitism and the consistency of arithmetic. In philosophy of mathematics he advocated the view of formalism rather than platonism or intuitionism. He also wrote on the relationship between religion and mathematics.
Edward Nelson was born in Decatur, Georgia, in 1932. He spent his early childhood in Rome where his father worked for the Italian YMCA. At the advent of World War II, Nelson moved with his mother to New York City, where he attended high school at the Bronx High School of Science. His father, who spoke fluent Russian, stayed in St. Petersburg in connection with issues related to prisoners of war. After the war, his family returned to Italy and he attended the Liceo Scientifico Giovanni Verga in Rome.
He received his Ph.D. in 1955 from the University of Chicago, where he worked with Irving Segal. He was a member of the Institute for Advanced Study from 1956 to 1959. He held a position at Princeton University starting in 1959, attaining the rank of professor there in 1964 and retiring in 2013.
In 1950, Nelson formulated a popular variant of the four color problem: What is the chromatic number, denoted 𝜒{\displaystyle \chi }, of the plane? In more detail, what is the smallest number of colors sufficient for coloring the points of the Euclidean plane such that no two points of the same color are unit distance apart? We know by simple arguments that 4 ≤ χ ≤ 7. The problem was introduced to a wide mathematical audience by Martin Gardner in his October 1960 Mathematical Games column. The chromatic number problem, also now known as the Hadwiger–Nelson problem, was a favorite of Paul Erdős, who mentioned it frequently in his problems lectures. In 2018, Aubrey de Grey showed that χ ≥ 5.
Shirley Ann Mathis was born in Bainbridge, Georgia. She received a B.A. in chemistry from Paine College in 1954, graduating summa cum laude. While also teaching chemistry at Spelman College, McBay earned an M.S. in chemistry (1957) and M.S. in mathematics (1958) from Atlanta University. In 1964, she earned a United Negro College Fund Fellowship, sponsored by the IBM Corporation, that allowed her to study at the University of Georgia and earn a Ph.D. in mathematics in 1966. Her Ph.D. was advised by Thomas Roy Brahana with a dissertation on The Homology Theory of Metabelian Lie Algebras.
McBay spent 15 years at Spelman College as a faculty member and administrator. McBay's leadership at Spelman led to the creation of the division of natural sciences and an increase in an emphasis on the sciences at the institution. She served as chairman of the division until 1975 and as associate academic dean at Spelman from 1973 to 1975. During this time, she created pre-freshman summer programs to increase interest in science majors, which led to the creation of a chemistry department and the renovations of existing science buildings.
She left Spelman in 1975 and took a position at the National Science Foundation for five years. While at the National Science Foundation, she became program director of the Minority Institutions Science Improvement Program. She then worked for ten years at MIT as the dean for student affairs. Thirty months of this time included being the director of the QEM Project, a study of minority education problems. The QEM Project was the impetus for the Quality Education for Minorities (QEM) Network that McBay founded and was president of from 1990 to 2016.
In December 2021, the University of Georgia's Science Library was renamed the Shirley Mathis McBay Science Library in her honor.
Her husband, chemistry professor Henry C. McBay, died in 1995. The couple had married in 1954. McBay died from complications of diabetes on November 27, 2021, in Los Angeles, at the age of 86. *Wik
1677 Isaac Barrow (Oct 1630, 4 May 1677) died of an overdose of drugs probably opium. Neil Middlemiss pointed out that the original source of this information may be Aubrey's "Brief Lives" wherein he claims, "his pill (an opiate)...he took it excessively at Mr. Wilson's...and 'twas the cause of his death."
Barrow had taken opiates with fasting previously in Constantinople when suffering from fever. Over dosing on opiates may have been somewhat common in the period, a tweet from
Isaac Barrow was an English Christian theologian, and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's, and Newton went on to develop calculus in a modern form. In 1662 he was made professor of geometry at Gresham College, and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge. During his tenure of this chair he published two mathematical works of great learning and elegance, the first on geometry and the second on optics. In 1669 he resigned his professorship in favor of Isaac Newton . *Wik
I just learned from a tweet from @mathshistory that Barrow was the "first to recognize that integration and differentiation are inverse operations" He is buried in the Chapel at Trinity College.
1750 William Morgan, FRS (?26 May 1750– ?4 May 1833: several history sites give different dates for his birth and death, both in old style snd new style. I picked one pair.) was a Welsh physician, physicist and statistician, who is considered the father of modern actuarial science. He is also credited with being the first to record the "invisible light" produced when a current is passed through a partly evacuated glass tube: "the first x-ray tube".
He won the Copley Medal in 1789, for his two papers on the values of Reversions and Survivorships, printed in the last two volumes of the Philosophical Transactions of the Royal Society, in the field of actuarial science:
"On the Probabilities of Survivorships Between Two Persons of Any Given Ages, and the Method of Determining the Values of Reversions Depending on those Survivorships", 1788–1794
"On the Method of Determining, from the Real Probabilities of Life, the Value of a Contingent Reversion in Which Three Lives are Involved in the Survivorship". Philosophical Transactions of the Royal Society of London, vol. 79 (1789) pp. 40–54
He was elected a Fellow of the Society, in May of the following year.
Advised by Joseph Priestley, a family friend, he developed an interest in scientific experimentation and is credited with being the first to record the "invisible light" produced when a current is passed through a partly evacuated glass tube: "the first x-ray tube"*Wik
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1859 Joseph Diaz Gergonne (19 June 1771 Nancy, France—4 May 1859 Montpellier, France)... Finding problems getting his mathematics papers published, Gergonne established his own mathematics journal, the first part appearing in 1810. The Journal was officially called the Annales de mathématiques pures et appliquées but became known as Annales de Gergonne . Gergonne's mathematical interests were in geometry so it is not surprising that it was this topic which figured most prominently in his journal. In fact many famous mathematicians published in the twenty-one volumes of the Annales de Gergonne which appeared during a period of twenty-two years. In addition to Gergonne himself (who published around 200 articles), Poncelet, Servois, Bobillier, Steiner, Plücker, Chasles, Brianchon, Dupin, Lamé, Galois and many others had papers appear in the Journal. Gergonne provided an elegant solution to the Problem of Apollonius in 1816. This problem is to find a circle which touches three given circles. Gergonne introduced the word polar and the principle of duality in projective geometry was one of his main contributions. *SAU
1880 Milan (Rastislav) Stefánik (July 21, 1880 – May 4, 1919) Slovakian astronomer and general who, with Tomás Masaryk and Edvard Benes, from abroad, helped found the new nation of Czechoslovakia by winning much-needed support from the Allied powers for its creation as a post-WWI republic, (1918-19). Before the war, the famous observatory in Meudon near Paris sent a scientific expedition to the 4810m high Mont Blanc. He joined the expedition, which was paid for by the French government to go to the roof of Europe.*TIS
1936 Alfred Cardew Dixon (22 May 1865 in Northallerton, Yorkshire, England - 4 May 1936 in Northwood, Middlesex, England) Alfred Dixon graduated from London and Cambridge and then had professorial appointments in Galway and Belfast. He worked on ordinary and partial differential equations. *SAU
1974 Otton Marcin Nikodym (13 Aug 1887 in Zablotow, Galicia, Austria-Hungary (now Ukraine) - 4 May 1974 in Utica,New York, USA) On 2 April 1919, the Polish Mathematical Society was founded by sixteen mathematicians - among them Otton Nikodym. In 1924, under strong pressure from Sierpinski, Nikodym agreed to take his doctoral examination at Warsaw University. It seems he did not care much for the title or publication - his response to Sierpinski's persuasion was, "Am I going to be any wiser because of that?"
Nikodym's name is mostly known in measure theory (e. g. the Radon-Nikodym theorem and derivative, the Nikodym convergence theorem, the Nikodym-Grothendieck boundedness theorem), in functional analysis (the Radon-Nikodym property of a Banach space, the Frechet-Nikodym metric space, a Nikodym set), projections onto convex sets with applications to Dirichlet problem, generalized solutions of differential equations, descriptive set theory and the foundations of quantum mechanics. *SAU
2001 Anne Anastasi (19 Dec 1908, 4 May 2001 at age 92) American psychologist known as the "test guru," for her pioneering development of psychometrics, the measurement and understanding of psychological traits. Her seminal work, Psychological Testing (1954), remains a classic text in the subject. In it, she drew attention to the ways in which trait development is influenced by education and heredity. She explored how variables in the measurement of those traits include differences in training, culture, and language. In 1972, she became the first woman to be elected president of the American Psychological Association in half a century. For her accomplishments, she was awarded the National Medal of Science in 1987.*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
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