Monday, November 25, 2019

Nudibranchs and other November

Linocut Glaucus atlanticus by Ele Willoughby, 2019
Astro goodies at RCI Science Black Hole event
A little update on some November activities... Saturday, I joined some lovely SciArt makers for a market at the RCI Science black hole event at U of T. It was great to see and meet so many friendly SciArt/SciComm faces. It was a busy weekend in this family, which also saw a couple of parties (for holidays and birthdays). This week, our son turns 6! It seems impossible, but it's another busy week so we can celebrate him. When not working on my ongoing series of women in STEM, I took the time to make a few wee linocuts of delightful, varied and beautiful nudibranchs, the colourful slugs of the sea, for #Nudivember.

This year, I'm only doing small markets, so if you're looking for minouette items, check out my minouette shop (and 20% off during Cyber Week!) or find me on December 7, from 12 pm to 3 pm at Gotomago, 1231 Woodbine Ave (near O'Connor).
Spanish Shawl nudibranch by Ele Willoughby, 2019

Doris chrysoderma the Lemon Lolly Doris, bt Ele Willoughby, 2019

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).

Mary Somerville, Mechanism of the Heavens, London: John Murray 1831
Mary Somerville, On the Connexion of the Physical Sciences London: John Murray 1834 

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.

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