Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?

~Edward Lorenz

Title of paper presented at the 139th Annual Meeting of the American Association for the Advancement of Science (29 Dec 1979)*TIS

The 106th day of the year; The sum of the first 106 digits of pi is prime. Amazingly, I could use this same numerical idea for tomorrow.

106^{106}-105^{105} (a number of 215 decimal digits)is prime.

There are 106 distinct mathematical trees with ten vertices.

Hundred, West Virginia was named for Henry Church and his wife, the first settlers who lived to be 109 and 106. Hundred is the only place in the United States with this name.

M 106 in Michigan runs almost to Hell, literally, ending on M-36 just a few miles northwest of Hell, Michigan in the Pinckney State Recreational Area. If you came this far, you might as well stop by "Hell in a Handbasket Country Store", which used to be the Post Office for Hell, but now mail is delivered from Pinckney. Plan ahead, you might want to be there for Hellfest. They have an auto show, but only for hearses, and are in the Book of World Records for the longest Hearse parade in the world. And there is a US Weather Station there, to tell you just how hot it is in Hell. (And just in case you wondered, even in southern Michigan, occasionally Hell does freeze over.)

1178 BC Homer records the events of a solar eclipse. This may have marked the return of Odysseus, legendary King of Ithaca, to his kingdom after the Trojan War. The date is surmised from a passage in Homer's Odyssey, which reads, "The Sun has been obliterated from the sky, and an unlucky darkness invades the world." This happens in the context of a new moon and at noon, both necessary preconditions for a full solar eclipse. In 2008, to investigate, Dr Marcelo O. Magnasco, an astronomer at Rockefeller University, and Constantino Baikouzis, of the Observatorio Astrónomico de La Plata in Argentina, looked for more clues. Within the text, they interpreted three definitive astronomical events: there was a new moon on the day of the slaughter (as required for a solar eclipse); Venus was visible and high in the sky six days before; and the constellations Pleiades and Boötes were both visible at sunset 29 days before. Since these events recur at different intervals, this particular sequence should be unique: the doctors found only one occurrence of this sequence while searching between 1250 and 1115 BC, the 135-year spread around the putative date for the fall of Troy. It coincided with the eclipse of April 16, 1178 BC.*Wik

837 Comet Halley passed 3.2 million miles from Earth, About 13x the lunar distance. *David Dickinson @Astroguyz (This is the closest to Earth in history. It is recorded widely, and was almost certainly an event in every culture on the planet.)

Its tail may have stretched 60 degrees across the sky. It was recorded by astronomers in China, Japan, Germany, the Byzantine Empire, and the Middle East;[65] Emperor Louis the Pious observed this appearance and devoted himself to prayer and penance, fearing that "by this token a change in the realm and the death of a prince are made known."

image: Halley's comet 1986

1610 George Fugger in a letter to Kepler debunks Galileo's claim to inventing the telescope. Fugger, in Venice, a member of the famous banking family who worked as an ambassador for the Holy Roman Empire, wrote to his correspondent Johannes Kepler in Prague, about Galilei’s eye catching demonstrations in Italy:

"The man [Galilei] [...] intends to be considered the inventor of that ingenious spy-glass, despite the fact that some Dutchman, on a trip here through France, brought it here first. It was shown to me and others, and after Galilei saw it, he made others in imitation of it and, what is easy perhaps, made some improvements to what was already invented." In his next paragraph Zuidervaart makes very clear that the accusation was false and that Galileo had not claimed the invention. *Huib J. Zuidervaart, The ‘true inventor’ of the telescope. A survey of 400 years of debate, Royal Netherlands Academy of Arts and Sciences, Amsterdam

The original Galileo telescope, which is preserved today at the Museo Galileo in Italy.

1673 “I conjecture that Mr. Collins himself does not speak of these summations of inﬁnite series because he brings forward the example of the series 1/2, 1/3, 1/4, 1/5, 1/6, ... which if it is continued to inﬁnity cannot be summed because the sum is not ﬁnite, like the sum of the triangular numbers, but inﬁnite. But now I am cramped by the space of my paper.” Leibniz to Oldenburg, indicating some hint of a distinction between convergent and divergent series. [The Correspondence of Henry Oldenburg, 9, pp. 599–600.] *VFR

1705 Newton knighted by Queen Anne at Trinity College. [DSB 10, 83] *VFR

1811 Wilhelmine Reichard launched to her first solo flight in a gas balloon, thus becoming Germany`s

very first female balloonist. The first recorded manned flight was made in a hot air balloon built by the Montgolfier brothers on 21 November 1783, starting in Paris and reaching a height of almost 200 meters. The very first woman to fly in a ballon followed only 8 months after the first manned flight on June 4, 1784, when opera singer Élisabeth Thible took her place with Mr. Fleurant on board a hot air balloon christened La Gustave in honour of King Gustav III of Sweden. Another early woman balloonist was Jeanne Geneviève Labrosse, who became the first woman to ascend solo in 1798 and, on October 12, 1799, the first woman to make a parachute descent (in the gondola), from an altitude of 900 meters. But also disaster is not far ahead. Ballooning was a risky business for the pioneers. When Marie Madeleine Sopie Blanchard ascended in her hydrogen balloon to watch a firework on July 6, 1819, she should become the first woman to lose her life while flying. Her craft crashed on the roof of a house and she fell to her death. *yovisto.

**1816** Gauss writes to his friend H. C. Schumacker that he had independently discovered the Arithmetic-Geometric mean as a youth of 14 in 1791. The agM (as Gauss would write it, first appeared in a memoir by Lagrange. At about the time of this letter, Gauss would write a paper describing many of his discovered properties of the agM, however it would not be published until after his death. *Gert Almkvist and Bruce Berndt, Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary (The title is also the table of contents?)

The geometric mean of n numbers, , is just the nth root of their product,

The Geometry of the Geometric and arithmetic mean

**1912 **Harriet Quimby of Coldwater, Michigan, the first American woman to earn a pilot's license, becomes the first woman to fly an airplane across the English Channel. Her accomplishment received little media attention, however, as the sinking of the Titanic ocean liner the day before riveted the interest of the public and filled newspapers.

The Vin Fiz Company, a division of Armour Meat Packing Plant of Chicago, recruited Quimby as the spokesperson for the new grape soda, Vin Fiz in April 1912. Her distinctive purple aviator uniform and image graced many of the advertising pieces of the day.

**1938** The ﬁrst William Lowell Putnam competition was held. It was won by the team of three from the University of Toronto. Irving Kaplansky was one of the team members. For the history of this now famous exam for undergraduates, see AMM, 72(1965), p. 474. *VFR

**1959** "LISP" Language Unveiled:

The programming language that provided the basis for work in artificial intelligence, LISP, has its first public presentation. Created by John McCarthy, LISP offers programmers flexibility in organization and it or its descendants are still used in the AI development environment.*CHM

**2014** Steve Colyer pointed out to me that every day this week when written in the conventional US mo/day/year is a palindrome. Today is 41614, etc. May of next year will have the same relation for a week

**2022 ** in 2012 a new world record distance for paper airplane throw: Joe Ayoob, a former Cal Quarterback, throws a John Collins paper airplane design, (which was named Suzanne), officially breaking the world record by 19 feet, 6 inches. The new world record was 226 feet, 10 inches. The previous record is 207 feet and 4 inches set by Stephen Kreiger in 2003. *ESPN

1495 Peter Apian (16 Apr 1495; 21 Apr 1552 at age 56)German astronomer and geographer, also known as Petrus Apianus, whose major work was Instrumentum sinuum sivi primi mobilis (1534), in which he gave tables of his calculations of sines for every minute, with a decimal division of the radius. *TIS Apian remained in Ingolstadt until his death. Although he neglected his teaching duties, the university evidently was proud to host such an esteemed scientist. Apian's work included in mathematics—in 1527 he published a variation of Pascal's triangle, and in 1534 a table of sines— as well as astronomy. In 1531, he observed a comet and discovered that a comet's tail always point away from the sun. (Girolamo Fracastoro also detected this in 1531, but Apian's publication was the first to also include graphics.) He designed sundials, published manuals for astronomical instruments and crafted volvelles ("Apian wheels"), measuring instruments useful for calculating time and distance for astronomical and astrological applications.*Wik

His book below with volvelles on both pages, from The Newberry Library, Chicago

Astronomicum Caesareum by Peter Apian |

1753 Sir Hans Sloane (16 Apr 1660; 11 Jan 1753 at age 92) (Baronet) British physician and naturalist whose collection of books, manuscripts, and curiosities formed the basis for the British Museum in London. By the time he died, Sloane had amassed one of the world's largest and most varied collections of natural history specimens. His passion for the collection and his concern for its future upkeep after his death led him to write a will which clearly stated that it must "remain together and not be separated." He offered it to the British nation, requesting in return a sum of £20,000 for his heirs. Parliament accepted, and King George II gave his royal assent 7 Jun 1753. Thus the British Museum was created and eventually its sister institution, the British Museum of Natural History. *TIS He also invented Hot Chocolate. Sloane encountered cocoa while he was in Jamaica, where the locals drank it mixed with water, and he is reported to have found it nauseating. However, he devised a means of mixing it with milk to make it more pleasant. When he returned to England, he brought his chocolate recipe back with him. *Wik The myth that Sloan had invented the process of Hot Chocolate, which is still strongly promoted in the shops in Chelsea that feature this product, is a myth. See James Delbourgo's Article on Sloan and Cocoa here. Skipping to page 78 for details of the history of Chocolate in use around Europe in the 17th century. It had been used for much longer by the natives of South America with some apparent religious or spiritual relationship. A book of recipes was published in England for Hot Chocolate in 1662, when Sloane would have been not quite two years old.

1682 John Hadley (16 Apr 1682; 14 Feb 1744 at age 61) British mathematician and inventor who perfected methods for grinding and polishing telescope lenses. Hadley improved the reflecting telescope (first introduced by Newton in 1668) and produced the first of its kind having sufficient accuracy and power to be useful in astronomy. It had a 6 inch mirror. He is also known for the reflecting octant (1730) used at sea to measure the altitude of the Sun or a celestial body above the horizon to within one second of arc. It was the ancestor of the modern nautical sextant. He was a prominent member of the Royal Society, of which he was vice-president from 21 Feb 1728. John Hadley was the older brother of George Hadley.*TIS

1728 Joseph Black (16 Apr 1728; 6 Dec 1799 at age 71)Scottish chemist and physicist who experimented with "fixed air" (carbon dioxide), discovered bicarbonates and identified latent heat. He lectured in chemistry, anatomy at the University of Glasgow, while also a physician. From heated magnesia alba (magnesium carbonate), Black collected a gas, carbon dioxide, different from common air. He published Experiments Upon Magnesia Alba, Quicklime, and Some Other Alcaline Substances (1756). Carbon dioxide was also released by fermentation, respiration, and burning charcoal so he assumed it was in the atmosphere. He also observed that ice melts without change of temperature, due to heat that becomes "hidden" - latent heat - and determined "specific heat" for heated of materials.*TIS

The world's first ice-calorimeter, used in the winter of 1782–83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in various chemical changes, calculations which were based on Joseph Black's prior discovery of latent heat.

**1823 Ferdinand Gotthold Max Eisenstein** (16 Apr 1823; 11 Oct 1852 at age 29)

German mathematician whose work covered a range of topics including the theory of elliptic functions, and quadratic and cubic forms, which led to cyclotomy, the reciprocity theorem for cubic residues, and also theorems for quadratic and biquadratic residues from partition of prime numbers. *TIS Gauss said of him, "There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein."

**1838 Ernest Gaston Joseph Solvay **(16 April 1838 – 26 May 1922) was a Belgian chemist, industrialist and philanthropist.

Belgian industrial chemist who invented the Solvay Process (1863), a commercially viable ammonia-soda process for producing soda ash (sodium carbonate), widely used in the manufacture of such products as glass and soap. Although a half-century before, A.J. Fresnel had shown (1811) that sodium bicarbonate could be precipitated from a salt solution containing ammonium bicarbonate, many engineering obstacles had to be overcome. Solvay's successful design used an 80 foot tall high-efficiency carbonating tower in which ammoniated brine trickled down from above and carbon dioxide rose from the bottom. Plates and bubble caps helped create a larger surface over which the two could react forming sodium bicarbonate. *TIS

In 1911, he began a series of important conferences in physics, known as the Solvay Conferences, whose participants included Max Planck, Ernest Rutherford, Maria Skłodowska-Curie, Henri Poincaré, and (then only 32 years old) Albert Einstein. A later conference would include Niels Bohr, Werner Heisenberg, Max Born, and Erwin Schrödinger.*Wik

The portrait of participants to the first Solvay Conference in 1911. Ernest Solvay is the third seated from the left. Solvay was not present at the time the photo was taken, so his photo was cut and pasted onto this one for the official release.

**1867 Wilbur Wright **(16 Apr 1867 - 30 May 1912) American inventor and aviator, who with his brother Orville, invented the first powered airplane, Flyer, capable of sustained, controlled flight (17 Dec 1903). Orville made the first flight, airborn for 12-sec. Wilbur took the second flight, covering 853-ft (260-m) in 59 seconds. By 1905, they had improved the design, built and and made several long flights in Flyer III, which was the first fully practical airplane (1905), able to fly up to 38-min and travel 24 miles (39-km). Their Model A was produced in 1908, capable of flight for over two hours of flight. They sold considerable numbers, but European designers became strong competitors. After Wilbur died of typhoid in 1912, Orville sold his interest in the Wright Company in 1915.*TIS

1894 Jerzy Neyman (16 Apr 1894; 5 Aug 1981 at age 87) Russian-American mathematician who was one of the principal architects of modern theoretical statistics. His papers on hypothesis testing (1928-33) helped establish the subject. During 1934-38, he gave a theory of confidence intervals (important in the analysis of data); extended statistical theory to contagious distributions, (for interpretation of biological data); wrote on sampling stratified populations (which led to such applications as the Gallup Poll); and developed the model for randomised experiments (widely relevant across the fields of science, including agriculture, biology, medicine, and physical sciences). His later research applied statistics to meteorology and medicine. In 1968 he was awarded the prestigious National Medal of Science.*TIS

**1921**

**Marie Maynard Daly**(April 16, 1921 – October 28, 2003) American biochemist who was the first African-American woman to receive a Ph.D. in Chemistry (1947). Her postdoctoral research at the Rockefeller Institute included studying the composition and metabolism of components of cell nuclei, determining the base composition of deoxypentose nucleic acids, and calculating the rate of uptake of labeled glycine by components of cell nuclei. Seven years later, she took a university position. She taught biochemistry and researched the metabolism of the arterial wall and its relationship to aging, hypertension, and atherosclerosis. Later, she studied the uptake, synthesis, and distribution of creatine in cell cultures and tissues. She retired in 1986. *TIS

1446 Sometimes given as the date of the Death of the architect Filippo Brunelleschi, who helped develop a systematic theory of mathematical perspective. He is especially noted for his design of the Duomo in Florence. More Commonly given date is the 15th

1756 Jacques Cassini (18 Feb 1677; 16 Apr 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

1788 Comte Georges-Louis Leclerc de Buffon (7 Sep 1707, 16 Apr 1788 at age 80) French naturalist who formulated a crude theory of evolution and was the first to suggest that the earth might be older than suggested by the Bible. In 1739 he was appointed keeper of the Jardin du Roi, a post he occupied until his death. There he worked on a comprehensive work on natural history, for which he is remembered, Histoire naturelle, générale et particulière. He began this work in 1749, and it dominated the rest of his life. It would eventually run to 44 volumes, including quadrupeds, birds, reptiles and minerals. He proposed (1778) that the Earth was hot at its creation and, from the rate of cooling, calculated its age to be 75,000 years, with life emerging some 40,000 years ago.*TIS He is remembered in mathematics for a question he asked more than any questions he answered. Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry. The solution, in the case where the needle length, l, is not greater than the width of the strips, can be used to design a Monte Carlo-style method for approximating the number π. *Wik p= 2l/(πt)

1901 Henry Augustus Rowland (27 Nov 1848, 16 Apr 1901 at age 52) American physicist who invented the concave diffraction grating, which replaced prisms and plane gratings in many applications, and revolutionized spectrum analysis--the resolution of a beam of light into components that differ in wavelength. His first major research was an investigation of the magnetic permeability of iron, steel and nickel, work which won the praise of Maxwell. Another experiment was the first to conclusively demonstrate that the motion of charged bodies produced magnetic effects. In the late 1870s, he established an authoritative figure for the absolute value of the ohm, and redetermined the mechanical equivalent of heat in the early 1880s, demonstrating that the specific heat of water varied with temperature. *TIS

**1914 George William Hill** (3 Mar 1838, 16 Apr 1914 at age 76)U.S. mathematical astronomer considered by many of his peers to be the greatest master of celestial mechanics of his time. Hill joined the Nautical Almanac Office in 1861. He computed the orbit of the moon while making original contributions to the three body problem. He introduced infinite determinants, a concept which later found application in many fields of mathematics and physics. When Simon Newcomb took over the Nautical Almanac in 1877 and began a complete recomputation of all solar system motions, Hill was assigned the difficult problem of the orbits of Jupiter and Saturn. After completing the enormous labor in ten years, he returned to his farm, where he continued his research in celestial mechanics.*TIS

Hill was the third president of the American Mathematical Society, and one of the few astronomers who contributed to pure mathematics. It was Hill's memoir on Infinite Determinants that led Henri Poincar'e to take up their study. Some years later when Poincar'e came to America Robert Simson Woodward, who would be the fifth President of the AMS, introduced him to Hill, Poincar'e is reported to have grasped his hand and announced, "You are the man I came to America to see."

**1958 Rosalind Elsie Franklin** (25 Jul 1920, 16 Apr 1958 at age 37) was an English physical chemist and X-ray crystallographer who contributed to the discovery of the molecular structure of deoxyribonucleic acid (DNA), a constituent of chromosomes that serves to encode genetic information. Beginning in 1951, she made careful X-ray diffraction photographs of DNA, leading her to suspect the helical form of the molecule, at least under the conditions she had used. When James Watson saw her photographs, he had confirmation of the double-helix form that he and Francis Crick then published. She never received the recognition she deserved for her independent work, but had died of cancer four years before the Nobel Prize was awarded to Crick and Watson. *Tis

Offer Pade' suggested, "Brenda Maddox wrote a very interesting book about Rosalind Franklin."

**1998** Alberto Pedro Calderón (September 14, 1920- April 16, 1998) was one of the leading mathematicians of the 20th century. He was born in Mendoza, Argentina. His name is associated with the University of Buenos Aires, but first and foremost with the University of Chicago, where Calderón and his mentor, the distinguished analyst Antoni Zygmund, started one of the longest (more than 30 years) and most productive collaborations in mathematical history. Together they developed the ground-breaking theory of singular integral operators, thus creating the "Chicago School of (hard) Analysis" (sometimes simply known as the "Calderón-Zygmund School"); this has been one of the most influential movements in pure mathematics, but with remarkable applications to science and engineering as well. Calderón’s work, characterized by great originality, elegance and power reshaped the landscape of mathematical analysis and ranged over a wide variety of topics: from singular integral operators to partial differential equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory to inverse problems in electrical prospection. Calderón’s work has also had a powerful impact on practical applications including signal processing, geophysics, and tomography. *Wik

**2008 Edward Norton Lorenz** (May 23, 1917 - April 16, 2008) American mathematician and meteorologist known for pointing out the "butterfly effect" whereby chaos theory predicts that "slightly differing initial states can evolve into considerably different states." In his 1963 paper in the *Journal of Atmospheric Sciences*, he cited the flapping of a seagull's wings as changing the state of the atmosphere in even such a trivial way can result in huge changes in outcome in weather patterns. Thus very long range weather forecasting becomes almost impossible. He determined this unexpected result in 1961 while running a computer weather simulation that gave wildly different results from even tiny changes in the input data. *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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