Tuesday, November 12, 2019

Mary Somerville, the Queen of Science

Mary Somerville, linocut print 11" x 14" by Ele Willoughby, 2019
The great mathematician, writer and polymath, Mary Fairfax Somerville (1780-1872) was allowed "to grow up a wild creature," roaming in nature, wading in the sea, watching birds, collecting eggs, starfish, shells, seaweed and flowers or watching whales, with her older brother Sam when he was home from school but otherwise on her own. Second of four surviving children of Vice-Admiral Sir William George Fairfax and his second wife, Margaret Charters, the young Mary Fairfax grew up in the Scottish Borders. Though well-respected and highly ranked, her father's income was quite meagre and her pragmatic mother helped feed the family and supplement income growing vegetables, fruit and keeping cows for milk. Her easygoing if busy mother did teach her to read the Bible and Calvinist catechisms, but she was left largely to her own devices. Though her father was a Tory, she was liberal-minded and felt the French populace justified to revolt; she and her brother also refused sugar in their tea to protest the institution of slavery. She later wrote that she "resented the injustice of the world in denying all those privileges of education to my sex which were so lavishly bestowed on men." Her father returned from sea when she was 10 and declared that running wild wouldn't do and she was sent for a year of tuition at Musselburgh, an expensive boarding school where she learned writing, grammar and some French. When released she "felt like a wild animal escaped from a cage."

After her year of schooling she did spend a lot of time reading, or resentfully working on a sampler, stitching letters and numbers. Her aunt Janet disapproved of her reading and neglecting her poor sewing skills and she was sent to the village school for needlework lessons. The village school master began to visit in the evenings and teacher a bit more including how to use a globe. When she was 13 she was sent to writing school in Edinburgh during the winter months, where she finally learned arithmetic. She taught herself enough Latin to read books in their home. She confessed this to her favourite uncle Dr. Thomas Somerville, the adult in her life who didn't discourage her pursuit of ideas and learning.  He told her women had been scholars even in ancient times and read her Virgil to help her learn more Latin. She went to visit her uncle William Charters, in Edinburgh, where she was sent to dancing school to learn manners and to curtsey. She also met the Lyell family, befriending Charles, who would go on to revolutionize geology.

Mary stumbled upon mathematics unexpectedly. A young woman, whom she met when dragged to a tea party by her mother, invited her to come see her needlework and showed her a ladies' magazine with puzzles. Mary was fascinated by the mathematical puzzles and solutions the magazine published. Her new friend could only tell her these were called algebra. She sought books at home to help her decipher this but she only found a book on navigation. It did not help with algebra, but she was introduced to trigonometry and learned there was more to astronomy than stargazing. She asked her younger brother's tutor to buy her an algebra textbook and Euclid's Elements, and soon she was staying up late to read these after chores. But she ran through too many candles and her parents put a stop to this, fearing for her sanity; they like many contemporaries felt that higher learning was unnatural in a woman. She continued to study in secret.

Nicknamed "the Rose of Jedburgh" among Edinburgh socialites, her expected role was to marry and so she did. She married her distant cousin Samuel Grieg, a commissioner in the Russian navy and London-based Russian consul. They were not a good match. He held a low opinion of the abilities of women and no interest in science. Left largely alone, she began to study French and more mathematics. She was widowed within three years and left with her young toddler son Woronzow, a baby, and a small inheritance. She returned to live her parents, more independent now as a widow.

Laplace's Demon
Laplace's Demon, by Ele Willoughby 2011

She had studied plane and spherical trigonometry, conic sections and James Ferguson's Astronomy. Despite her children and household chores she ambitiously tried to read Newton's Principia.  She met intellectuals like Lord Henry Brougham, and the renown Professor of mathematics and natural history, John Playfair who encouraged her mathematical studies and introduced her to mathematician and astronomer William Wallace. She corresponded with Wallace about her mathematical problems. She made a name for herself when she was awarded a silver medal in 1811 by solving a mathematical problem posed in the mathematical journal of the Military College at Marlow. Wallace suggested she read mathematician Pierre-Simon Laplace on gravity and all physics in the decades since the Principia first appeared in 1687. Finding she understood Laplace's five-volume Mécanique Céleste (Celestial Mechanics) as well as the tutor she hired, her confidence increased, and she expanded her studies to astronomy, chemistry, geography, microscopy, electricity and magnetism, buying a "excellent little library" of math and science books at the age of 33.  She began to see that English mathematics, dominated by Newton, had stagnated and fallen behind their continental colleagues, by not adopting Leibnizian calculus.

Ada, Countess Lovelace, linocut by Ele Willoughby.
Ada is shown with Babbage's diagrams of his Difference Engine
and the equations for Bernouilli Numbers, which she showed
how to calculate mechanically in the world's first
computer program.
She was much luckier in her second marriage in 1812, to another cousin, Dr William Somerville (1771–1860). He was inspector of the Army Medical Board, and the son of her favourite aunt and uncle. Elected a member of the Royal Society, William Somerville socialized with leading intellectuals, scientists and writers of the day and was a devoted supporter of Mary's studies. She returned to reading Laplace and Newton after their honeymoon. The family (including William's illegitimate son who became close with Woronzow) moved to Hanover Square into a government house in Chelsea when William was appointed to the Chelsea Hospital in 1819. Her marriage was a very happy one, though they had a disastrous financial loss (the trusting William acted as guarantor for a relative's loan) and were devastated by the early death of three of Mary's six children; her second son from her first marriage died at nine, her first son with William died as a baby, and their first daughter Margaret died at ten. Woronzow, and their daughters Martha and Mary survived.

Caroline Herschel
Caroline Herschel, linocut by Ele Willoughby, 2014
Wallace introduced the Somervilles to astronomer F. William Herschel who discovered Uranus and worked with his sister Caroline, who discovered many comets and more. He showed them his huge reflecting telescope and his son, mathematician and polymath John Herschel became one of Mary's mentors, though ten years her junior. The Somervilles we popular and met "nothing but kindness" in scientific circles. They met many including philosopher William Wollaston, and physicists Thomas Young and Michael Faraday.  Mary become friends with mathematician Anne Isabella Milbanke, Baroness Wentworth, and mathematics tutor to her daughter, Ada Lovelace. She frequently visited polymath and inventor Charles Babbage, viewed his Calculating-machines and introduced him to Lovelace. She and Lovelace became close friends, discussing mathematics problems over tea. The couple travelled frequently to Europe, and like in London, met with the scientists and intellectuals of the day on their travels. On the continent they met polymath François Arago, physicist Jean-Baptiste Biot, mathematician Siméon Denis Poisson, and Laplace himself.  

Maxwell's Demon
Maxwell's Demon, linocut
by Ele Willoughby

Mary began experimenting and published her first paper on "The magnetic properties of the violet rays of the solar spectrum", in the Proceedings of the Royal Society in 1826. Her results were praised and reproduced by others but ultimately shown to be incorrect, which crushed her confidence in performing her own experiments. The truth is that finding small errors in experimental design and correcting and improving them is part of the normal process of science. She was the first woman to publish scientific results under her own name. Had she not been a woman and an outsider, she might have realized she had no reason to feel embarrassed. In 1829, Sir David Brewster, inventor of the kaleidoscope, wrote that Mary Somerville was "certainly the most extraordinary woman in Europe - a mathematician of the very first rank with all the gentleness of a woman".

Antoine et Marie-Anne Paulze Lavoisier,
linocut with collaged washi,
2018 by Ele Willoughby
Meanwhile, her acquaintance Lord Brougham asked her to translate Laplace's Mécanique Céleste into English for the Society for the Diffusion of Useful KnowledgeHe even visited her in person to try and persuade her. She agreed on the condition she could work in secret and that it could be more technical than he had intended, for she felt the need to introduce the British public to Leibnizian calculus so they could understand Laplace. This became a labour of love, not just a translation, but an expanded version explaining all the mathematics of gravity and celestial mechanics that Laplace assumed the reader should intuit, and additional pertinent topics, under the title of The Mechanism of the Heavens. It took her three years. Brougham refused to publish it, deeming it too technical for his audience. William was determined her work would not go to waste and he brought the book to their friend geologist Charles Lyell's publisher John Murray. Murray eventually agreed to publish it (after John Herschel reviewed the manuscript and found it virtually flawless) in 1831, when Mary was 50. It sold well, made her famous and became the standard textbook for undergraduates at University of Cambridge until the 1880s. As Mary had been denied access to a university education as a woman this was very gratifying. In France, her book was so well received that Biot wrote to her to say colleagues were pestering him to hurry up his review of the book for the Journal des Savants. The next year when they travelled to Paris they were celebrated and made new scientific friends including physicist André-Marie Ampère and Marie-Anne Paulze Lavoisier Rumford (widow of and assistant to the famous chemist Antoine, and now also widow of the physicist Count Rumford). Mary Somerville was elected an honourary member of the Royal Astronomical Society along with Caroline Herschel. They were first two women admitted in any way, even if only honourary members of the society. She was also elected honorary member of the Royal Irish Academy, of the Bristol Philosophical Institution and the Société de Physique et d'Histoire Naturelle de Genève in 1834 and the British Crown granted her a pension of £200 a year for her contributions to science and literature. The pension was very timely, as the Somervilles' financial problems meant they quietly relied on the extra income she was able to earn (something not deemed appropriate for a middle class woman).

Her next book On the Connexion of the Physical Sciences (1834) was even grander in scope, connecting and summarizing the physical sciences of physics and astronomy with geography and meteorology. This book sold 15,000 copies establishing her reputation as amongst the elite of scientific authors. It was her publisher John Murray's most successful science book until Darwin published The Origin of Species in 1859. The book went through nine editions and she updated it for the rest of her life, even pointing out in the third edition that the challenges in calculating the position of Uranus hinted at the existence of  further possible undiscovered planets. She wrote that perhaps even the mass and orbit of this hypothetical planet could be deduced from observations of Uranus. Somerville's insight inspired British astronomer John Couch Adams who was able to mathematically predict the existence of Neptune in 1846. In his review of Connexion, polymath William Whewell introduced a new term he coined: 'scientist.' Many claim he praised her as the first scientist, but in fact he thought she was superior to his utilitarian designation, a "real person of science," a proper natural philosopher and a great writer in contrast with other popularizers of science.

Though she had many male scientist friends and mentors, as a woman she was usually barred from  scientific societies. Her husband presented her papers to the Royal Society on her behalf, as did John Herschel. Their friend Arago presented her results on light and chemistry to the French Academy of Science. Faraday praised her explanations of his work, which was cutting edge research at the time of the publication of Connexion. Throughout her career, she had great instincts and open-mindedness about new ideas. She supported her friend Thomas Young's controversial wave theory of light, a real paradigm shift. Young explained his famous double-slit experiment by building on his French friend Augustin-Jean Fresnel's explanation of the diffraction of light in terms of waves and Christian Huygen's idea of the propagation of wavefronts of light, at a time when Biot and Laplace were still expounding on the particle nature of light. Likewise, she hinted at the revolution to come with the next generation of physicists who showed how seemingly disparate forces could be combined. Mary wrote, "Various circumstances render it more than probable that, like light and heat, [electricity] is a modification or vibration of that subtle ethereal medium, which, in a highly elastic state, pervades all space," which inspired the subsequent investigations by Hans Christian Ørsted (also written Oersted) and Michael Faraday. Mary noted that mariners observe lightening affects compasses. She described American John Henry's electromagnet, able to hold a ton of metal. And she traced the history of electrical and magnetic investigations since Coulomb. Later, the great physicist James Clerk Maxwell who combined the forces of electricity and magnetism in his laws for light, cited Somerville's book On the Connexion of the Physical Sciences for its hints of connections between light and magnetism, electricity and light, colour, electricity and magnetism and heat. He praised her insight and took the time to carefully explain why her experiment using violet light to magnetize a needle had failed. Mary may not have succeeded in establishing the connection between light and magnetism, but in searching for it she was on the vanguard of contemporary research.

In 1848 she published her most popular book,  Physical Geography, which was the first textbook on the subject in English. It went through six editions in her lifetime, was used until the early 20th century and won her the Victoria Gold Medal of the Royal Geographical Society in 1869. Physical Geography was influential, ignoring political divisions and viewing humanity as a part of nature, but a part able to affect its environment, emphasizing interconnectedness and interdependencies. While she was working on this book, she was initially discouraged by German naturalist Alexander von Humboldts publication of his first volume of Kosmos (1845), which covered similar subject matter but John Hershel encouraged her to continue and as she wrote, follow  "the noble example of Baron Humboldt, the patriarch of physical geography." She takes her readers through the place of the Earth in the solar system, its structure, features of land and water, formation of mountains, volcanoes, oceans, lakes and rivers, and what impacts temperature, electricity, magnetism and the auroras before turning to the distribution of life. Impressed, Humboldt himself wrote to her, "You alone could provide your literature with an original cosmological work." Her book also precipitated some backlash because her discussion of geology contradicted the biblical estimate of the age of the Earth, but she wrote, "facts are such stubborn things." Four years later, the Somerville family, Mary and William and their daughters Martha and Mary, moved to Italy for health reasons and because the cost of living was lower.

William Somerville died at 89 in 1860 and then her son Woronzow died suddenly, at age 60, in 1865, sending Mary into a deep grieving period. So when Maxwell published his theory of electromagnetism in 1865, Mary was preoccupied with grieving and took little notice of this monumental work she helped presage and inspire. Now in her 80s, she began work on her memoir. Mary had always put her fame and scientific credibility to work to support causes she believed in, including women’s suffrage, arguing that science was too often used for military purposes, the antivivisection movement and drawing attention to the way human activity was causing animal extinctions. A lifelong lover of birds, she had a pet mountain sparrow which would sleep on her arm as she wrote. She noted the decline in "feathered tribes" of Europe who would be "avenged by the insects." In 1866 when philosopher and economist John Stuart Mill organized a massive petition to Parliament to give women the right to vote, he asked Mary Somerville to be the first to sign. She was a member of the General Committee for Woman Suffrage in London, and petitioned London University unsuccessfully to grant degrees to women (noting that in France, Emma Chenu had been granted an MA in mathematics and a Russian lady, likely Sofia Kovalevski, had also taken a degree). She viewed her final book as a mistake. Published at age 88 in 1869, On Molecular and Microscopic Science, a popularization of science book, it was not as well received as her previous works, but was nonetheless sold well. She explained the latest thinking on atoms and molecules and revealed the lifeforms discovered with the microscope. But, she felt her time would have been better used if devoted more purely to mathematics, and began working to catch up on the latest mathematics research and returned to work on her 246-page manuscript on curves and surfaces. She enjoyed her old age and was glad to keep her faculties, work on mathematics and take an interest in current affairs until her own death, expressing only regret that she would not live to see results of scientific expeditions underway or the abolition of the slave trade. She died on November 28, 1872, while working on a mathematical paper on Hamilton's quaternions, approaching her 92nd birthday. Her obituary in The Morning Post read, "Whatever difficulty we might experience in the middle of the nineteenth century in choosing a king of science, there could be no question whatever as to the queen of science." Her daughter Martha edited her autobiography, Personal Recollections, from Early Life to Old Age (1873), and it was published posthumously.

In my portrait, I've shown Somerville with diagrams from her first two books, emphasizing the importance of her impact on astronomy and physics, and highlighting some of the cutting edge science she presented (like connections between electricity and magnetism, and Young's Double Slit Experiment).

References
Mary Somerville, Mechanism of the Heavens, London: John Murray 1831
Mary Somerville, On the Connexion of the Physical Sciences London: John Murray 1834 
Mary Somerville, PERSONAL RECOLLECTIONS FROM EARLY LIFE TO OLD AGE OF MARY SOMERVILLE WITH Selections from her Correspondence BY HER DAUGHTER, MARTHA SOMERVILLE.  London: John Murray, 1874

Robyn Arianrhod, Seduced by Logic: Émilie du Châtelet, Mary Somerville and the Newtonian Revolution, OUP, New York, 2012
James Secord, 'Mary Somerville's Vision of Science' Physics Today 71, 1, 46 (2018); doi: 10.1063/PT.3.3817
'Mary Somerville', Britanica, accessed November 2019 
Mary Sommerville, Wikipedia, accessed November 2019

Friday, November 1, 2019

Rear Admiral and Mathematician Grace Hopper Teaching Computers Something Like English

Grace Hopper, linocut on 11" x 14" Japanese kozo paper, 2019, by Ele Willoughby
The first modern computers were loud, room-sized monsters, essentially a collection of relays (electrical switches) patched together with electrical cords. Each "switch" could be one (1) or off (0) and could represent data (an input value) or an action applied to these data.  To talk to the computer, to tell it to do anything with these values, you needed to speak in machine code, in the natural language of the computer itself of zeroes and ones - and each machine had its one structure and associated code. The story of how these giant computing machines went from a rare, complex tool available only research scientists at a few select university or government labs to ubiquitous, multipurpose portable tools we carry with us everywhere and use daily, depends in part on the idea we could, and should, develop machine-independent programming languages and that these could be based on English. This revolutionary idea was popularized by American computer scientist and US Navy rear admiral Grace Brewster Murray Hopper (née Murray December 9, 1906 – January 1, 1992).

Born in on the Upper West Side of New York City, the eldest of three children, she was the sort of curious child who dismantled alarm clocks to discover how they work; she was seven when she was caught, having already taken seven clocks apart, and her mother limited her future exploration to working with a single clock. Her father owned an insurance business. She took after her mother, herself a mathematician. She was admitted to Vassar College at 17 and completed a Bachelor's degree in math and physics. By 1930, she had completed her Master's at Yale and married New York University comparative literature professor Vincent Foster Hopper (1906–1976). She began teaching at Vassar in 1931. By 1934, she completed her PhD on "New Types of Irreducibility Criteria" under the supervision of Øystein Ore at Yale. Unusually for a mathematics professor, she insisted her students write well; her first assignment would be an essay on her favourite formula. She felt studying mathematics without the ability to communicate math was pointless. Her own ability to translate real world problems into mathematics and math into English would serve her well throughout her career.

She became bored with an unexciting marriage and found teaching math less fulfilling than she hoped. When the US entered WWII she was on partial leave from Vassar, spending a year studying finite difference methods for solving partial differential equations with Richard Courant at New York University. She saw a way to change her life. At age 34, Hopper tried to enlist in the Navy, but was rejected. She was deemed too old, and a petite woman, her weight to height ratio was too low; further her job as a mathematician and professor at Vassar was considered valuable to the war effort.
Though Vassar promoted her to associate professor in 1941 she obtained a leave of absence. She persisted with her goal and got a special exemption for being 15 pounds (6.8 kg) below the Navy minimum weight of 120 pounds (54 kg) and volunteered for the the United States Navy Reserve women's branch (WAVES) in 1943. By 1945, she had divorced her husband, but chose to retain her husband's family name.

After graduating top of her class at the Naval Reserve Midshipman's School at Smith College in Massachusetts, she was assigned to the Bureau of Ships Computation Project at Harvard University as a lieutenant, junior grade. Howard H. Aiken, physicist and computing trailblazer, who had been a professor was now leading a team there as a commander in the Navy. His team was working on programming the giant IBM Automatic Sequence Controlled Calculator (ASCC), an electromechanical computer known as the Mark I. Hopper said she had to learn the languages of the different scientists and engineers whose problems they were running on the machine, the languages of the managers, and of the programmers, and her facility with these different modes of communication was why Aiken assigned her to write the first computer programming manual. Despite her doubt about writing a book, she produced a 561-page volume starting with a history of computing machines from Charles Babbage to the present. Like her forebearer Ada Lovelace, she saw the potential of a computer controlled by separate punch tape instructions (what we now know as software) rather than the need to reconfigure the machine hardware itself. Aiken had originally bristled at the thought of a woman on the team, but soon made Hopper primary programmer and his top deputy. She became known as irreverent, brilliant, sharp-tonged but a good collaborator. Together, Aiken and Hopper co-authored three papers on the Mark I. After the war, she requested to transfer to the regular Navy, but her request was declined due to her age. She opted nonetheless to remain at Harvard as Navy reserve research fellow under a Navy contract, until 1949, despite the offer of a full professorship at Vassar.

While working on the Mark I, Hopper perfected the use of the subroutine, the way programmers use a specific chunk of code to perform a specific task again and again, such as taking the sinusoid or logarithm of a value. This a concept Ada Lovelace wrote about in her Notes on the Analytical Engine.  She began thinking about the way to take her library of subroutines and enable its use on any machine, if her source code could be translated to machine code (which is machine-specific) by using a compiler.

Famously, while working on the Mark II, she and her colleagues had to do some literal "debugging" when a dead moth was discovered in a relay. The term "bug" already existed in engineering, but the process of systematical detecting and removing problems in computer programs came to be known as debugging partially because of this specific wayward moth and Hopper delighted to telling the story of the actual bug. It was dutifully recorded by taping its corpse labelled "First actual case of bug being found," in the log book dated September 9, 1947.

The Harvard Mark I, II and III, were reliable machines based on electromechanical relays, but these were slow. Hopper's work had help make these machines the most easily programmed but she recognized that the new electronic devices using vacuum tubes were so much faster, that easy of programming and reliability were not enough. Also, it became clear that she would not be promoted or granted tenure at Harvard. She left her post to join the Eckert–Mauchly Computer Corporation where she worked on the development of UNIVAC I, the first general purpose electronic digital computer design, made for business. When the company was taken over by Remington Rand in 1950, she was appointed UNIVAC director of Automatic Programming Development. She became convinced that since people were far better at writing English than in symbols, that they ought to be able to write programs in English and that the computer themselves should translate this into machine code. It took her three years to convince others. She wrote her first paper on compilers (now known as link-loaders, the tool computers use to translate English-like computer programs into machine code) and had developed a functional link-loader the A-0 in 1952, all while her peers thought computers could only do arithmetic. As a mathematics professor she realized only, "[v]ery few people are really symbol manipulators. If they are they become professional mathematicians, not data processors. It's much easier for most people to write an English statement than it is to use symbols. So I decided data processors ought to be able to write their programs in English, and the computers would translate them into machine code. That was the beginning of COBOL, a computer language for data processors. I could say 'Subtract income tax from pay' instead of trying to write that in octal code or using all kinds of symbols." Promoted to the company's first director of automatic programming, her department released some of the first compiler-based programming languages, including MATH-MATIC and FLOW-MATIC. In 1959, she was a technical consultant to the Conference on Data Systems Languages (CODASYL) where she and colleagues defined the new language COBOL (an acronym for COmmon Business-Oriented Language), extending on FLOW-MATIC and IBM's language COMTRAN. COBOL became a major computer language in data processing and even persists today as legacy code.

She sadly retired from the Navy Reserve at age 60, as required in 1967, at the rank of commander but was recalled to active duty in 1968 and served as the director of the Navy Programming Languages Group in the Navy's Office of Information Systems Planning. She retired again in 1971, but was again recalled in 1972. She became a captain in 1973. During the 70s she argued for the move away from giant centralized computers to networks of small, distributed machines. She worked on standards for computer systems, components and programming languages like FORTRAN and COBOL. In 1983 she was promoted to commodore and remained on active duty several years beyond mandatory retirement by special approval of Congress. In 1985 the rank commodore was renamed rear admiral making her one of few women to achieve that rank. She final retired in 1986 as the the oldest active-duty commissioned officer in the United States Navy at age 79. She then worked as a senior consultant to Digital Equipment Corporation (DEC) until her death at age 85 in 1992, lecturing on the history of computers in full dress uniform. By the end of her life she was a very well-recognized figure, earning more than 40 honourary degrees, many awards and had many things named in her honour. She became the first woman to win the National Medal of Technology, the highest technology award in the US. At the ceremony she said, “If you ask me what accomplishment I’m most proud of, the answer would be all the young people I’ve trained over the years; that’s more important than writing the first compiler.” After her death, the Navy commissioned the U.S.S. Hopper, a guided missile destroyer, and in 2016 Hopper was posthumously received the Presidential Medal of Freedom.

In my portrait I've shown her as she was in WWII in front of the Harvard Mark I, with a little nod to the famous "first" computer bug. I am the sort of nerd who actually looks up the actual moth recorded and then put some thought into species that may have fit the size and colour of the moth found at Harvard.

References
Gilbert, Lynn (1981). Women of Wisdom: Grace Murray Hopper. Lynn Gilbert, Inc.
Software Bug, Wikipedia, accessed October 2019 
Grace Hopper, Wikipedia, accessed October 2019 
COBOL, Wikipedia, accessed October 2019   
Harvard Mark IWikipedia, accessed October 2019   
Walter Isaacson, Grace Hopper, computing pioneer, The Harvard Gazette, December 3, 2014
Grace Murray Hopper (1906-1992): A legacy of innovation and service, Yale News, February 10, 2017

Tuesday, October 8, 2019

Mathematician Maryam Mirzakhani for Ada Lovelace Day 2019

This 11" x 14" (27.9 cm x 35.6 cm) hand-printed linocut portrait shows the late, great, mathematician Maryam Mirzakhani, the only woman to ever win the Fields Medal, along with several of her diagrams and doodles she used to work out her mathematical ideas. The print is made in blues and reds on white Japanese kozo (or mulberry paper).

Awarded every four years to 2 to 4 mathematicians under the age of 40, the Fields Medal, sometimes known as the mathematician's Nobel Prize, is one of the highest and most prestigious awards a mathematician can receive. It has been award 60 times since 1936; to 59 men and 1 woman, Iranian mathematics professor at Standford University Maryam Mirzakhani (12 May 1977 – 14 July 2017) who won in 2014. Mirzakhani's research included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry, and she the Fields award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".

Born in Tehran, her mathematical ability showed young. She attended the Tehran Farzanegan School, part of the National Organization for Development of Exceptional Talents (NODET). She won the gold medal for mathematics in the Iranian National Olympiad, in both of her final two years of high school, which allowed her to bypass the national college entrance exams. In 1994, Mirzakhani won the gold medal level in the International Mathematical Olympiad in Hong Kong, scoring 41 out of 42 points. Here too, she was both the first woman and first Iranian to do so. The following year she became the first Iranian student to achieve a perfect score and to win two gold medals in the International Mathematical Olympiad in Toronto. She and her friend  Roya Beheshti Zavareh were the first women to compete and won gold and silver, respectively, in the Iranian National Mathematical Olympiad. The two attended a conference for gifted students and former Olympiad competitors in Ahvaz in March 1988, and were riding the bus back to Tehran which was involved in an accident, and fell off a cliff, killing seven passengers. They were some of the few survivors of this nation tragedy.  Years later, the pair went on to collaborate on the text 'Elementary Number Theory, Challenging Problems' which was published in 1999.

She earned her Bachelor of Science in mathematics from Sharif University of Technology in 1999, and in the process received recognition from the American Mathematical Society for her work in developing a simple proof for a theorem of Schur. She went on to earn a PhD in 2004 from Harvard University, where she worked under the supervision of the Fields Medalist Curtis T. McMullen. She became a research fellow of the Clay Mathematics Institute and a professor at Princeton University before being hired as a professor at Standford in 2009.

In 2008, Mirzakhani married Jan Vondrák, a Czech theoretical computer scientist and applied mathematician who currently is an associate professor at Stanford University. Together they had a daughter named Anahita, who described her mother's work as "painting" because of her habit of solving problems by doodling shapes, diagrams and formulae all over huge sheets of paper. A self-described "slow" mathematician, Mirzahani said "you have to spend some energy and effort to see the beauty of math." My portrait incorporates images based on her doodles, as well as some diagrams from published papers to illustrate both her creative mental world and her contributions to mathematics.

On 14 July 2017, Mirzakhani died of breast cancer at the age of 40. Upon her death, several Iranian newspapers broke taboo and published photographs of Mirzakhani with her hair uncovered, drawing international attention. The International Council for Science has agreed to declare Maryam Mirzakhani's birthday, 12 May, as International Women in Mathematics Day in her memory.

References
Maryam Mirzakhani, Wikipedia, accessed October 2019
Fields Medal, Wikipedia, accessed October 2019
Krishnadev Calamur, Math's Highest Honor Is Given To A Woman For The First Time, NPR, August 2014
Elizabeth Manus, Maryam Mirzakhani, Fields Winner, Doodler
The Beautiful Mathematical Explorations of Maryam Mirzakhani, Quanta Magazine, July 2017

Mirzakhani, Maryam. “Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces.” Inventiones mathematicae 167 (2006): 179-222. DOI:10.1007/s00222-006-0013-2
Mirzakhani, Maryam. “Ergodic Theory of the Earthquake Flow.” (2010). DOI:10.1093/imrn/rnm116
 


Ada Lovelace, 3rd edition
Ada, Countess Lovelace, 3rd edition linocut by Ele Willoughby
Today is the 11th annual international day of blogging to celebrate the achievements of women in technology, science and math, Ada Lovelace Day 2019 (ALD19). I'm sure you'll all recall, Ada, brilliant proto-software engineer, daughter of absentee father, the mad, bad, and dangerous to know, Lord Byron, she was able to describe and conceptualize software for Charles Babbage's computing engine, before the concepts of software, hardware, or even Babbage's own machine existed! She foresaw that computers would be useful for more than mere number-crunching. For this she is rightly recognized as visionary - at least by those of us who know who she was. She figured out how to compute Bernouilli numbers with a Babbage analytical engine. Tragically, she died at only 36. Today, in Ada's name, people around the world are blogging.
You can find my previous Ada Lovelace Day posts here. 


Tuesday, October 1, 2019

6th Annual Etsy: Made in Canada Toronto

minouette table at Etsy: Made in Canada Toronto (photo: Peter Power)

This Saturday we held our 6th annual Etsy: Made in Canada Toronto. A huge thank you to all the visitors who came out and stopped by the minouette table at the show! It's great to meet you all in person. As the captain of the Toronto Etsy Street Team, I spent months on this show with a team of organizers from TEST and 416Hustler and it's so gratifying to see thousands of people come out and support local artists and artisans and vintage sellers. Thanks especially to my fellow organizers! I love seeing all my fellow makers too... only being so busy stops me from spending all my earnings at the other tables!

Etsy: Made in Canada Toronto, September 28, 2019 (photo: Peter Power)
Checking out the Newfoundland and Labrador print at Etsy: Made in Canada Toronto (photo: Peter Power)


Thursday, August 22, 2019

Émilie du Châtelet and the Foundations of Physics


Émilie du Châtelet linocut, 11" x 14", by Ele Willoughby, 2019

This is a hand-printed portrait of Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (1706-1749), a natural philosopher, mathematician and physicist, inspired by contemporary portraits, and shows her along with her diagrams. Each 11" x14" (27.9 cm x 35.6 cm) linocut print is printed on lovely, delicate, Japanese paper. The diagrams are from Principes Mathématiques de la Philosophie Naturelle, a two-volume translation and commentary of Newton’s Principia, published in 1759 in French in Paris.

While historically she was merely remembered as Voltaire's lover, she in fact was not only responsible for all his ideas about physics but was the first to postulate the conservation of total energy (which includes kinetic and other forms of energy combined). Further, she found the relationship between kinetic energy, mass and velocity of an object. Before translating Newton, she published her magnum opus Institutions de Physique (or Foundations of Physics) in 1740 and within a mere two years it had been translated into many languages and republished. Debate raged at the time about how the measure the force of an object and how to formulate conservation principles. She was an active participant in this dispute known as the vis viva debate. There was a schism between the Newtonians in England and the continental philosophers who followed Leibniz, particularly in German-speaking regions; she wanted the best of both while contemporaries viewed Newton and Leibniz' work as fundamentally opposed interpretations of the world. Institutions de Physique covered philosophy, space, time, matter, laws of nature and gravity including Galileo's results and Newton's more general work. In Principes Mathématiques de la Philosophie Naturelle, she combined Newton's text with Leibniz' more elegant formulation of calculus, pushing physics forward. She was recognized during her lifetime by the greatest thinkers of the day including renowned mathematicians such as Johann II Bernoulli and Leonhard Euler, her works were translated into other languages and discussed in scholarly journals and represented in (or even plagerized by) the Encyclopédie of Denis Diderot and Jean le Rond D'Alembert. She made a large impact on contemporary physics and philosophy.

Fronstispiece from Algorotti's
Il Newtonianismo Per Le Dame, 1737 Venice
After much goading and many years, Newton finally published the bulk of his understanding of mechanics and his famous three laws in Philosophiæ Naturalis Principia Mathematica, known simply as the Principia, in 1687 with two further corrected editions in in 1713 and 1726. As the title implies, the text is written in Latin. Though he had to derive the concepts of calculus to complete the work, it's largely absent from the text in favour of the geometrical approaches to infinitessimal calculus. So Émilie du Châtelet's work does not simply represent a translation - she reorganized the work using Leibniz' calculus, wrote commentaries and explanations and most importantly, added her own discoveries about kinetic energy. To this day, du Châtelet's version is the standard French translation of the Principia and modern translators still rely on Émilie's translation.

She taught herself mathematics, and then was tutored in algebra and calculus by Moreau de Maupertuis, a member of the Academy of Sciences (who had been trained by mathematician Johann Bernoulli, who also taught Leonhard Euler).  Then she turned to his protégé mathematician Alexis Clairaut, author of Clairaut's equation and Clairaut's theorem, who became a life-long friend, and other top French mathematicians. On one occassion she was ejected from Café Gradot, where men held intellectual discussions, for being a woman. So, she had some men's clothing made and boldly returned. She became a world authority on Newtonian mechanics, at a time when few imagined a woman capable or even interested in such a thing. Émilie's impact on continental physics, and bringing Newton's Principia to Europe (and to those in England more able to read French than Latin) cannot be overstated.

She was aristocrat who not only dedicated herself to knowledge, writing about physics and experimentation, she enjoyed clothing and could be extravagant. She loved fashion, gambling and jewellery.  She used her mathematics ability to devise successful gambling techniques, when she needed money for books as a teen. Voltaire was known to call her Madame Newton-Pompom-du Châtelet for the pompoms she wore. His own writings on physics were written in collaboration with her and often quoted her word for word. It wasn't long before her skills and interest far exceeded his own. She had some insight into the relationship between light, colour and heat, long before a modern understanding of energy. At the time, scholars debated whether kinetic energy or momentum was the pertinent thing - we now know that both are important, yet distinct. She leaned towards Leibniz' ideas on the subject, which shows how she was at the cutting edge of contemporary physics knowledge and debate.

She translated Mandeville's The Fable of the Bees into French and used the preface to denounce the prejudice that prevented women from access to a proper education. Nonetheless, a product of her time, she focused more on her daughter's marriage prospects and her son's education. She had to fight to be taken seriously and deal with sexism from even the well-meaning; she and contemporary part-time Bolognese physics professor Laura Bassi were not impressed when their friend Algarotti wrote a rather patronizing popularization of Newton's physics called (I wish I were kiding) Newtonianism for the Ladies. Worse, the frontispiece of his book shows a man speaking to a lady who suspiciously ressembles du Châtelet, implying he had explained Newtonianism to her. Her short-term mathematics tutor Samuel König, a student fo Mauterpuis, also tried to undermine her by claiming responsibility for Institutions de Physique. This lead to her estrangement from Mauterpuis. Ironically König later fell out with Euler and accused Mauterpuis of having plagerized him.


The story of her long-lasting relationship with Voltaire is quite fascinating, a relationship she pursued with the knowledge and blessing of her husband, Marquis Florent-Claude du Chastellet-Lomont (Châtelet is the modernized spelling of Chastellet). She first met Voltaire as a child at one of her father's salons. They became close when she re-entered society after the birth of her children. She invited Voltaire to live at their country house, a refuge for him when he was in disfavour, and there they worked together on their publications and set up a lab. They both submitted essays to the 1738 Paris Academy prize contest on the nature of fire; neither won (they lost to Euler) but they both earned honourable mention and their essays were published by the Academy. Hence, du Châtelet because the first woman to have a scientific paper published by the Academy. Eventually their relationship became a comfortable, platonic collaboration. At age 42, she began a new affair with the poet Jean François de Saint-Lambert. She feared she could not survive her subsequent unplanned pregnancy. Six days after the birth of a daughter, on 10 September 1749, at Lunéville, she suffered a fatal pulmonary embolism. Voltaire, her husband and final lover Saint-Lambert were all at her bedside with she died.

References
Project Vox, Duke University, accessed August, 2019
Émilie du Châtelet, Wikipedia, accessed August, 2019
Philosophiæ Naturalis Principia Mathematica, Wikipedia, accessed August, 2019
Robyn Arianrhod, Seduced by Logic: Émilie du Châtelet, Mary Sommerville and the Newtonian Revolution, Oxford University Press, 2012
Cynthia J. Huffman, Mathematical Treasure: Émilie du Châtelet’s Principes Mathématiques, Convergence (January 2017)

Thursday, August 15, 2019

Ancient Korean Astronomer Queen - Queen Seondeok of Silla

Queen Seondeok of Silla, linocut with chine collé, 9.25" x 12.5", 2019 by Ele Willoughby 
This handprinted lino block print is a portrait of Queen Seondeok of Silla or 선덕여왕 sometimes written Sonduk or Sondok (c. 595 ~ 610 - 647), reigned as 27th ruler of Silla, one of the Three Kingdoms of Korea, from 632-647, who brought about a rise in Buddhism and a renaissance in culture and science as well as building the Cheomseongdae moon and star-gazing observatory. Each print is printed on Japanese papers, and is 12.5 inches by 9.25 inches (31.7 cm by 23.5 cm).

Known for her intelligence, wisdom and benevolence, stories survive of her curiosity and cleverness even as a child. When her father the King was gifted peony seeds and a painting of peonies from China she remarked that it was a pity the lovely flowers had no scent. The astonished adults asked her how she knew; she had noted that the painting of the flower did not show bees or butterflies and had corrected deduced that they were unscented. One story recounts how she predicted an attack from the neighbouring Baekche kingdom by noting the sounds of frogs at the gate.

She was introduced to astronomy by her tutor and tried to discuss it with the Chinese ambassador but was rebuffed as Confucianism discouraged educating women. Then she predicted the occurrence and duration of a solar eclipse which angered him and he persuaded her father to stop her studies. Seondeok wrote the following on a votive jar dedicated to her grandmother:

Will I ever know the truth about the stars?

I’m too young to engage in theories about our Universe.

I just know that I want to understand more. I want to know all

I can. Why should it be forbidden?*


But when her father died without a male heir she became Queen as the first female sovereign in ancient Korea. During this turbulent time, the southern Korean peninsula was divided into three competing kingdoms of Silla, Goguryeo and Baekche and Seondeok was able to combine diplomacy, forging alliances with Tang China, with military might to weather rebellion and threats from other her neighbours during her reign. After lifting peasants’ taxes for a year and helping orphans and elderly, she set to work building a 9m tall moon and star-gazing tower Cheomseogdae. The bottle-shaped stone observatory still survives today, and is the oldest standing observatory in East Asia, and perhaps the world. The capital became a centre of culture and science; mathematics, astronomy and astrology flourished. The observatory is believed to have been the centre of an entire scientific district.

The building itself represented knowledge; the number of stones represents days of the year (scholars differ on whether it contains 362 or 365 large stones representing days in the solar or lunar year). The stones appear in 27 courses (for Seondeok, the 27th ruler) with 12 courses above and below the window entrance for the months of the year and these sum to 24, the number of solar terms in a year (24 points in traditional East Asian lunisolar calendars that matches a particular astronomical event or signifies some natural phenomenon). Including the stylobate, or platform on which it was built, gives 28 courses and 28 symbolizes the 28 constellations of East Asia. The addition of the two-tier top brings us to 30, the number of days in a month. The tower itself is a gnomon of a sundial and the window captures the sun’s rays on the interior floor at spring and autumn equinoxes. Astronomy was of vital importance as it governed agriculture and contemporary scientists produced detailed star charts. Astrology influenced political decisions of the day. Thus observations at Cheomseongdae were of utmost importance to Silla.


References
*Gabriella Bernardi, 'The unforgotten sisters: Sonduk, the astronomer queen.' Cosmos magazine, 28 March 2018

Hong-Jin Yang, 'Historical Astronomy of Korea', Korean Astronomy Olympiad, Korean Astronomical Society, 2012

K.P.Kulski, 'The Tower of the Moon and Stars: Queen Seondeok of Silla,' Unbound, 2017

Mark Cartwright, Cheomsongdae, Ancient History Encyclopedia, 2016

Mark Cartwright, Queen Seondeok, Ancient History Encyclopedia, 2016

Queen Seondeok of Silla, wikipedia, accessed August, 2019

Cheomseongdae, wikipedia, accessed August, 2019

Category of Astronomical Heritage: tangible immovableCheomseongdae observatory, Republic of Korea, UNESCO Portal to the Heritage of Astronomy, accessed August, 2019

Wednesday, May 22, 2019

Cecilia Payne-Gaposchkin and the Most Abundant Elements in the Sun, Stars and Universe

Cecilia Payne-Gaposchkin, linocut 9.25" x 12.5" on ivory kozo paper by Ele Willoughby 2019
This is a 9.25" x 12.5" (23.5 cm by 31.7 cm) 3-layer linocut print on ivory Japanese kozo (or mulberry paper) showing the great astrophysicist Cecilia Payne-Gaposchkin in front of the sun with a solar absorption spectrum. Cecilia Payne-Gaposchkin (1900-1979) was a trailblazer for women in astronomy and discovered that hydrogen and helium are the most common elements in the universe.

For the first quarter of twentieth century, astronomers believed that Earth and Sun were much the same, made of the same distribution of elements, differentiated only by temperature. Nuclear fusion, the source of solar energy had yet to be discovered, and scientists looked at the entire spectrum of light emitted to try and determine the nature of star stuff. Physicists were beginning to use spectroscopy to identify the elements of which things are made. It turns out that with stars, which are hot and full of excited atoms, rather than emission spectra, it is absorption spectra, like rainbows crossed with bar codes, which are the most useful. Light is emitted from stars at a broad range of frequencies (and those within the visible range we see as different colours), but there are specific stripes which are missing (or absorbed) because they exactly match the energy difference between two quantum mechanical states of their constituent atoms.  Each element has its own ‘bar code’ of absorption lines. The lines of common metals like silicon and carbon are seen in the sun’s absorption spectrum which lead scientists to think it star stuff was the same as Earth stuff.

Born in Wendover, England, in 1900, Cecilia Payne was one of three children raised by her mother Emma Leonora Helena (née Pertz) after the death of her father, barrister and historian Edward John Payne, when she was only four. She attended St. Paul’s Girls’ School and won a scholarship to Newnham College at Cambridge to read botany, physics and chemistry in 1919. She was disappointed by botany, but found phyics a "pure delight". The department at Cambridge at this time included such luminaries as J.J. Thomson, Rutherford, C.T.R. Wilson, Chadwick and Bohr. This marked the year a lecture changed her life. So impressed, she later wrote out the lecture word for word correctly, comparing it against his published text. She wrote, “My world had been so shaken that I experienced something very like a nervous breakdown.” It was no everyday lecture. She had gone to hear Sir Arthur Eddington’s account of his 1919 expedition to the island of Principe off the west coast of Africa to photograph stars with apparent positions near the sun during the solar eclipse. Eddington had produced the first experimental evidence supporting Einstein’s revolutionary General Theory of Relativity, which predicted that large masses like the sun would bend spacetime itself and that gravity would bend light changing apparent position of stars. Cecilia Payne’s imagination was captured by astronomy. She completed her studies but Cambridge did not grant women degrees until 1948 and her only option in the UK would be to become a teacher. She met Arthur Shapley, Director of the Harvard College Observatory who had just established a graduate program. Thanks to a fellowship to encourage women to study at the observatory she left the US to pursue graduate school in the US.  With Shapley’s encouragement she became the first PhD in astronomy at Radcliffe College (which is now part of Harvard).

Her 1925 thesis was "Stellar Atmospheres; a Contribution to the Observational Study of High Temperature in the Reversing Layers of Stars." Indian physicist Meghnad Saha had recently developed his ionization theory, which relates the ionization state of a gas in thermal equilibrium to the temperature and pressure. That is, he explained how those stellar “bar codes” due to ionized gas in stars relates to their temperature and pressure. Astrophysicists use the phrase “to Saha correctly” now to describe the process of interpreting stellar atmospheres. Cecilia Payne was able to Saha correctly on the Harvard collection of stellar spectra; she showed that variations in absorption lines were related to ionization state and temperature, rather than the various amounts of elements. She found the abundances of silicon and carbon were just like here on Earth, as expected, but that hydrogen and helium were vastly more abundant. Hydrogen in fact was a million times more abundant! This meant it was the most abundant element in the universe. This seemed too astonishing to be true. When defending her thesis, astronomer Henry Norris Russell, swayed by the theories of American physicist Henry Rowland, convinced her that this result was spurious. But she was right and they were wrong. Within a few years astronomer Otto Struve described her work as "the most brilliant PhD thesis ever written in astronomy" and Russell himself found independent evidence of her result. Russell published his result and though he acknowledged Payne he was often wrongly credited with this discovery.

After her doctorate, she looked at the structure of the Milky Way by studying high luminosity supergiant stars, discovering many of their unusual properties including exotic ions in their spectra. Shapley suggested that she work on photographic stellar photometry which required meticulous work to establish standard stellar magnitudes and colours. She chafed under this time-consuming assignment but she knew the work was important. It lead to her best-known work on variable stars on which she spent many years. She used the millions of observations made with her assistants to investigate stellar evolution, and published the book 'Stars of High Luminosity' in 1930.

She became an American citizen in 1931 and then while on tour in Europe, met the stateless Russian-born astrophysicist Sergei I. Gaposchkin in Germany. He had flead the soviet purges in Russia and now feared for the future in Nazi Germany. She went to Washington to help him get an American visa. The two were married in 1934. She appended his last name to her own. They had three children and worked together on the observation and analysis of all variable stars bigger than magnitude 10 (a measure of brightness). Their paper on the subject became the standard reference. Their insight into variable stars served as means of elucidating the structure of the galaxy and the role of variable stars in stellar evolution. Payne-Gaposchkin worked at Harvard for her entire career. While she was barred from a professorship as a woman, and relegated to low-paid research positions, she nonetheless was able to publish several more books including 'Variable Stars' (1938), 'Variable Stars and Galactic Structure' (1954), and 'The Galactic Novae' (1957)'. Shapley worked to improve her position and in 1938 she was given the title Astronomer, later changed at her request to Phillips Astronomer. In 1943 she was elected Fellow of the American Academy of Arts and Sciences.

Thanks in part to the efforts of Donald Menzel who became Director of the Harvard College Observatory in 1954, she became the first woman full professor from within the faculty at Harvard's Faculty of Arts and Sciences in 1956 and was finally paid a salary commensurate with her stature. She trained several graduate students who went on to eminent careers in astronomy. Eventually she became the department Chair, the first woman Chair at Harvard. She retired in 1966, but continued working as an Emeritus Professor of Harvard, as a staff member at the Smithsonian Astrophysical Observatory, editing books and journals for the next twenty years. As well as the books mentioned she published more than 150 papers, popular science books and an astronomy textbook. In 1977, she was awarded the highest honour of the American Astronomical Society, the Henry Norris Russell Lectureship. Payne-Gaposchkin was a trail-blazer and role model for women in the male-dominated field of astronomy, and one of the great scientists of the twentieth century. Late in life, she wrote:

Young people, especially young women, often ask me for advice. Here it is, valeat quantum. Do not undertake a scientific career in quest of fame or money. There are easier and better ways to reach them. Undertake it only if nothing else will satisfy you; for nothing else is probably what you will receive. Your reward will be the widening of the horizon as you climb. And if you achieve that reward you will ask no other. 




References
Wikipedia entries on Cecilia Payne-Gaposchkin (both in English and French), Meghnad Saha, the Saha ionization equation, and Absorption spectroscopy, accessed May, 2019.
Gingerich, O., Obituary - Payne-Gaposchkin Cecilia, Quarterly Journal of the Royal Astronomical Society, Vol. 23, P. 450, 1982
Smith, Elske V.P.,  Cecilia Payne-Gaposchkin, Physics Today 33, 6, 65 (1980); https://doi.org/10.1063/1.2914129