Thursday, August 9, 2018

Mary Golda Ross, mathematician, aerospace engineer and the Space Race

Mary Golda Ross, linocut handprinted on Japanese kozo paper, 11" x 14", 2018 by Ele Willoughby
Today would have been Mary Golda Ross' 110 birthday. Known as Gold to her family, Mary Golda Ross (1908-2008) was a mathematician, aeronautical engineer, philanthropist and Cherokee “hidden figure” of the space race. Great-great-granddaughter of Chief John Ross, longest-serving chief of the Cherokee Nation who was forced to lead his people on the long march known as Trail of Tears, Ross attributed her success in math to the Cherokee tradition of encouraging equal education for boys and girls. She went to Northeastern State Teacher’s College in Tahlequah, Oklahoma and earned a bachelor’s in math by the time she was 20. She taught science and math in rural schools through the Depression then got her Master’s at the University of Colorado, taking the opportunity to also take as many astronomy classes as she could. She aimed to put her education to work to try to help Indigenous people by working as a statistician with the Bureau of Indian Affairs, until she was reassigned as an advisor to girls at the Santa Fe Indian School.

When WWII broke out her father suggested she find a technical job in California. Lockheed Martin hired her as mathematician in 1942, troubleshooting the P-38 Lighting fighter plane (as shown). She knew already that her interest was in interplanetary flight, but didn’t mention it in 1942 for fear that her credibility would be questioned. As it turned out, she was indeed farsighted. After the war Lockheed Martin sent her to UCLA to study engineering and celestial mechanics. She was one of the 40 engineers selected to start Skunk Works, their Advanced Development Program, an in-house top-secret think tank. She was the only woman and only Indigenous person and much of her work there remains classified! The engineers were working long hours, often to 11 pm at night, during the rush of the Space Race. Some of her work included
feasibility studies of ballistic missile and other defense systems. More interesting to me is her work on the pressure from ocean surface waves would effect submarine-launched vehicles; the effect of pressure from ocean surface waves on the seafloor was central to my own doctoral research. She worked on preliminary design concepts for interplanetary travel, crewed and uncrewed space flights and the earliest plans for orbiting satellites. She worked on the Agena rocket, so important to the Apollo moon mission (shown in my portrait), the Polaris reentry vehicle and was an author of the NASA Flight Handbook Vol. III about flight to Mars and Venus.

After retiring in 1973, she devoted her time to recruiting and mentoring women and Indigenous people to engineering. At 96 she participated in the opening ceremony for the National Museum of the American Indian, wearing her first traditional Cherokee dress made by her niece, and she left the museum $400,000 upon her death.


Erin Blakemore, 'This Little-Known Math Genius Helped America Reach the Stars : It’s time for Mary Golda Ross to be remembered as an aerospace pioneer,', March 29, 2017

What's My Line? - Andy Griffith; Jack Lemmon [panel] (Jun 22, 1958)

Mary G. Ross, wikipedia, accessed July 11, 2018

Ariel Sandburg, Remembering Mary Golda Ross, The Michigan Engineer News Center, June 14, 2017

Cherokee Almanac: Mary Golda Ross, YouTube, June 13, 2015

Graham Lee Brewer, Rocket Woman, Oklahoma Today Magazine, July/August 2018

Kara Briggs, Cherokee rocket scientist leaves heavenly gift, Cherokee Pheonix, 12/18/2008 07:22 AM

Jenny Howard, Meet Mary Golda Ross, one of the First Native Americans in Engineering,, May 17, 2018, accessed July 11, 2018

"Mary G. Ross blazed a trail in the sky as a woman engineer in the space race, celebrated museum". The National Museum of the American Indian. 2009-10-07. Retrieved July 11, 2018

"The Cherokee Nation Remembers Mary Golda Ross, the First Woman Engineer for Lockheed". Cherokee Nation. 2008-05-13. Retrieved July 11, 2018

"Mary Golda "GOLD" Ross (1908 - 2008)". Find A Grave Memorial. Retrieved July 11, 2018.


Wednesday, July 4, 2018

Margaret Cavendish and The Blazing World

This is a linocut portrait of Margaret Lucas Cavendish, Duchess of Newcastle-upon-Tyne (1623 – 1673), 17th-century English aristocrat, philosopher, poet, scientist, fiction-writer, and playwright shown with her imaginary world from her strange science fiction novel 'The Blazing World' which she appended to her scientific treatise 'Observations upon Experimental Philosophy'. Cavendish is an odd addition to my collection of portraits of scientists, as a self-taught, die-hard royalist aristocrat, and firm anti-empiricist, but her publications on gender, power, manners, scientific method, and philosophy cannot be ignored. She wrote six books on Natural Philosophy and was the first woman admitted to a meeting of the Royal Society, and as such was a part of the contemporary world of science. Plus, this delightfully eccentric woman combined her natural philosophy with science fiction, and wrote herself into the story. The lino block portrait is handprinted on Japanese kozo (or mulberry paper) 11" x 14" with some collaged washi papers.

Margaret Cavendish and the Blazing World linocut 11" x 14", 2018, by Ele Willoughby
Margaret was born the youngest of eight children of Thomas Lucas, a wealthy aristocrat and royalist who died when she was two. She spent a lot of time with her siblings and had no real education, though she had access to scholarly libraries and she began writing at a young age, at a time when this was considered quite unusual for a woman. She also learned from her brother John, a philosopher and natural philosopher and founding member of the Royal Society. Margaret was unusual in many ways and full of contradictions. She was bashful yet flirtatious, accused of using speech full of 'oaths and obscenity' yet concerned about decorum and propriety, fame-seeking and ambitious,  society phenomenon considered to bold for a woman, proto-feminist yet an "arch-conservative" monarchist. In 1641, the royalist Lucas family were attacked by the Puritan neighbours and fled to Oxford where King Charles I held his court. Left without a dowry, she convinced her mother and Elizabeth Leighton Lucas to let her become one of Queen's Ladies-in-Waiting (to Queen Henrietta Maria the Catholic wife of the soon to be executed King Charles I, known at the time as 'Queen Mary')  in 1643 and then accompanied her upon her exile to France in 1644 (during the First English Civil War). This was a move she regretted. She was too shy to speak much and was mistaken for a fool, but she preferred this to risking being found wanton or rude. She suffered from what she called melancholia. She wanted to quit but her mother convinced her this would be disgraceful and to stay for two years, until such time as she married William Cavendish, then Marquis of Newcastle, later named Duke. A widower 30 years her senior, William Cavendish seems to have been a remarkably good match for her, and both of them wrote about their love for and pride in the other. William reportedly liked her bashfulness and became her writing tutor, supported her writing, paid for her work to be published and defended her when contemporaries doubted her authorship. He was her great supporter and defender, a patron of the arts and brother to noted scholar Charles Cavendish. Margaret was unable to conceive a child (though William had two sons from his first marriage). Without children or an estate, Margaret filled her time writing. Margaret's most successful publication was her biography of her husband, The Life of the Thrice Noble, High and Puissant Prince William Cavendishe.

As a 'royalist delinquent' (a Royalist who fought against Parliament during the English Civil War) her husband's estate was sequestered by parliament and was to be sold. She tried returning to England with her brother-in-law to benefit from the sale, but was denied and returned to France after a year and a half to be with her husband. In 1660, with the Restoration of the Stuart monarchy, Margaret and William were able to return to England and ultimately settled in Welbeck, where Margaret worked on publishing her writing and increasing her knowledge and skills.

Margaret Cavendish by Pieter Louis van Schuppen, c. 1655-1658. Frontispiece to
Grounds of Natural Philosophy, London 1668.
At a time when women published anonymously, if at all, Cavendish published over a dozen works in her own name. She choose to reinvent herself through fashion, seeking to be and look unique arguing that clothes oppressed women. She wrote a memoir to ensure later generations would have a true account of her lineage and life and in her bid to achieve everlasting fame. She wrote about natural philosophy, atoms, nature personified, macro and microcosms, other worlds, death, battle, hunting, love, honour, employing poetry, prose, epistles and plays. She was one of the earliest advocates for animals and opponents of animal testing. Her writing was defensive, excusing her errors as due to her youth and ignorance, imploring detractors to keep silence, and nonetheless asking that if her writing was successful that she benefit and gain fame for it. Between her being a female author, woman engaged with science, her eccentricities and theatrical dress-sense, she was nicknamed "Mad Marge" by contemporaries, but along with her detractors, she had her supporters and she was taken seriously enough to be the first woman invited to attend meeting of the Royal Society.

In 1666 she wrote Observations upon Experimental Philosophy. Philosophically, she rejected Aristotle and favoured the Stoics. She argued against Cartesian dualism. She had no education in science or natural philosophy, though her brother was a founder of the Royal Society, her interest was supported by her husband and brother-in-law, and she socialized with her husband's tutor Thomas Hobbes. Like Hobbes, she rejected the idea of incorporeal souls. She thought minds are material and matter could think. Unlike Hobbes, she envisioned a vitalistic nor mechanistic world. While in France they gathered an intellectual circle (known as the Cavendish or Newcastle circle) which included English philosopher Thomas Hobbes,  Henry More, and natural philosopher Kenelm Digby and Walter Charleton, and French philosophers and mathematician René Descartes, Pierre Gassendi  and Marin Mersenne. This circle in turn was in communication with fellow intellectuals throughout Europe. She herself corresponded with physicist Christiaan Huygens, philosopher  and Joseph Glanvill and botanist John Evelyn. She chose to engage with and write about the science and scientists of her time to the best of her abilities. She argued strongly for the use of clear and plain English when writing about science and complained that natural philosophy contained difficult words and unfamiliar expressions. She chose to avoid such writing in her desire to communicate clearly and broadly. Appended to this work was one of the earliest science fiction novels, a sort of imaginative complement to the science: The Description of a New World, Called The Blazing-World, better known as The Blazing World, a fantasy, utopian satire.

The story tells of a young woman from the Kingdom of Esfi, who is kinapped by pirates and then escapes to another world via a portal at the North Pole. This other world is called the Blazing World and is inhabited by animal-people (bird-men, fish-men, fox-men, bear-men, ape-men, ant-men, fly-men, worm-men, louse-me and more) obsessed with telescopes and microscopes, a means by which Cavendish satirizes the Royal Society and the work of Robert Hooke (who had recently published his Micrographia). The lady becomes the Empress by marriage there. As Empress she grows frustrated with their use of telescopes since they seem to only be a cause of arguments and first bans them but relents and orders them to keep them in their schools, rather than introduce any "disturbances in State, or Government." She is likewise underwhelmed by their microscopic observations and considers these technological tools "false informers". The Empress seeks a scribe to read her write her own religious texts. She rejects famous philosophers Aristotle, Pythagoras, Plato, Galileo or Hobbes, who would be too “self-conceited”  to agree and develops a telepathic relationship mediated by spirits with none other than... Margaret Cavendish! The Duchess and Empress become platonic lovers and travel to each other's worlds. Like later science fiction, the Blazing World includes some imagined technology and science which can appear far-sighted in hindsight, like the air-powered engines, flying machines, elaborate submarines (which could remotely measure ocean depth) or the concept of an infinite universe. But, it also contains common contemporary misconceptions like the idea that insects are spontaneously generated or that alchemy might work. The work also features without judgment homosexuality, androgyny and polyamory. My print shows the Empress (the only personnage in the Blazing World allowed to wear gold) surrounded by the fish, ape, birds, bears, worm, and fly-men scholars, complete with telescope, microscope and a louse-man in a submarine.

She challenged the idea of man's dominion over nature and argued that animals possessed intelligence. She employed the sceptical tools of science to attack natural philosophy and question its methods as well as argue for recognition of women's intellectual capacity. She attacked the empirical methods of Robert Hooke and Robert Boyle and once referred to such experimentalists as “Boys that play with watry Bubbles.” She attacked Descartes' flawed vortex theory. She attacked male-dominated science in general. She conceived that shape plays a role in the reaction of atoms - an idea more familiar to modern-day scientists than her contemporaries (though her version of atomic theory also combined some medieval ideas about the elements). She made publications on the contemporary concepts of atomic theory, magnetism and heat. She also combined speculation and fantasy with some of her confused ideas about natural philosophy, but her output was no more muddled than that of male contemporaries considered scientific prodigies. Unlike her contemporaries, her ideas about atoms had no requirement for God or theology to explain the world, and in fact her ideas of infinite populated words both without and within (for instance on a lady's earring) were a bit dangerous in her time. Though I am an experimentalist and fan of Hooke and her think her radical scepticism is misplaced, I believe that questioning the limits of empirical methods and knowledge is of the utmost importance.

Amongst some less charitable things, Virginia Wolf wrote of Cavendish, "One cannot help following the lure of her erratic and lovable personality as it meanders and twinkles through page after page. There is something noble and Quixotic and high-spirited, as well as crack-brained and bird-witted, about her. Her simplicity is so open; her intelligence so active; her sympathy with fairies and animals so true and tender. She has the freakishness of an elf, the irresponsibility of some non-human creature, its heartlessness, and its charm."

More recently, Margaret Cavendish has been studied as an early feminist, though her pleas for the need for education of women and defense of their abilities is combined with a great deal of criticism of other women. As she inserted herself into The Blazing World, she's also delightfully being called the original Mary Sue.

Margaret Cavendish died suddenly on 15 December 1673 and was buried in Westminster Abbey. Before his death, two years later, her devoted husband gathered all the poems he had written in her honour and letters to celebrate her and published them as Letters and Poems in Honour of the Incomparable Princess, Margaret, Dutchess of Newcastle. In her own words, in the introduction of The Blazing World, she wrote, "That though I cannot be Henry the Fifth, or Charles the Second; yet I will endeavour to be, Margaret the First: and, though I have neither Power, Time, nor Occasion, to be a great Conqueror, like Alexander, or Caesar; yet, rather than not be Mistress of a World, since Fortune and the Fates would give me none, I have made One of my own."

Margaret Cavendish, Duchess of Newcastle-upon-Tyne, wikipedia, accessed July 3, 2018
The Blazing World, wikipedia, accessed July 3, 2018
Lisa T. Sarasohn, 'A Science Turned Upside Down: Feminism and the Natural Philosophy of Margaret Cavendish, Huntington Library Quarterly, Vol. 47, No. 4 (Autumn, 1984), pp. 289-307
Published by: University of Pennsylvania Press, DOI: 10.2307/3817365, Stable URL:
Duchess of Newcastle Margaret Cavendish, The Poetry Foundation, accessed July 3, 2018
Roberts, Jennifer Sherman. "Everyone, We Need to Talk About 17th-Century Badass Writer Margaret Cavendish". The Mary Sue. Retrieved July 4, 2018.
Cavendish (1623-1673), Margaret Cavendish, Duchess of Newcastle-Upon-Type, Project Vox, accessed July 4, 2018. 
Christine Corbett Moran, A Description of A New World, Called the Blazing-World, Margaret Cavendish, Medium, accessed July 4, 2018
Margaret Cavendish, Duchess of Newcastle, The Description of a New World, Called the Blazing-World, London: Printed by A. Maxwell, 1668.
Margaret Cavendish's The Blazing World (1666), skullinthestars blog post for January 2, 2011, accessed July 4, 2018
Eric Karl Anderson, The Blazing World of Margaret Cavendish, thelonesomereader blog post for March 9, 2018, accessed July 4, 2018

Wednesday, June 13, 2018

Interstital Intro - My portraits of Canadian Women in STEM

Featuring artwork by me, Cheryl Hamilton and Paige Blumer, Curiosity Collider's artshow Interstitial: Science Innovations by Canadian Women is on exhibit until June 22. Since I was unable to attend the Opening in Vancouver, they asked me to share a short video introduction to me and my artwork. So now, I'm sharing the video with you. Comes complete with a peek inside my studio and some of the artwork you could find there. I think I was so focused on pronouncing "electrophoresis" that I slipped up on the more common "geneticist", but it tells about the work.

The exhibit is open from 11 am to 6 pm from Tuesday to Saturday until June 22 at The Beaumont Studios gallery spaces, located at 316/326 West 5th Street, Vancouver, BC, V5Y 1J0.

Thursday, June 7, 2018

Redbud and the Bees

Redbud and the Bees, 18" x 24", linocut with collaged washi papers by Ele Willoughby, 2018
Proof of my Eastern Carpenter Bee linocut and block
I've been working on a new artwork about urban wildlife. Creature Conserve is a non-profit outreach organization which brings artists and scientists together to "foster sustained and informed support for animal conservation," and they posted a call for artists for their Urban Wildlife: Learning to Co-exist exhibit at the Rhode Island School of Design (RISD) at the end of July and through August. Because of my on-going work on native bees, the first thing I thought about were bees in the city. The exhibit aims to get artists to collaborate with scientists and use their artworks to explore the biology and ecology of species and the way they interact with humans. Specifically, artists are invited to explore themes of how ecosystems change in time and space, how wildlife and humans may displace each other homes, the visibility or invisibility of wildlife in the city, the rhythms of animal life and their health. I'm well aware of how our native bees have been displaced and their ranges have changed through time, and also how they can be invisible to people in the city, who often are only aware of the existence of honeybees and maybe bumblebees, so I thought they would be an apt choice.

My redbud linocuts on various pink washi papers
I remembered the urbanredbud citizen science project here in Toronto. Local U of T doctoral candidate Charlotte de Keyzer is working with the public to gather data on flowering times of Eastern redbud trees (Cercis canadensis) and their pollinators using bee nest boxes and traps. She and her collaborators are particularly interested in how climate change and urbanization effect these trees and specifically the timing of their emergence and peak activity. Eastern redbud were not really known in Toronto even 30 years ago, but between climate change and its growing popularity as an ornamental landscape tree, they have became fairly common in the city and important for urban bee diversity. Local wild bees are attracted to this early flowering tree covered in pink flowers, and some also use its leaves in building their nests. Since the project addresses changes in the environment over time because of climate change and urbanization, and since it seeks to engage the public, I thought it might be a good fit and that Charlotte de Keyzer might be open to collaborating with me, and indeed she was! I asked her some questions about which bees they observe in their traps, hoping to connect this to my existing collection of native bee lino blocks, and told her about the aims and themes of the exhibit. It turns out that redbud trees are indeed popular with some of my own favourite (and previously depicted) native bees. Their early results show that amongst the most common bee visitors in Toronto foraging on redbuds are Osmia lignaria (blue orchard bee), Colletes inaequalis (polyester bee), and Xylocopa virginica (eastern carpenter bee). Leafcutters also use the leaves to build nests (though they do not yet have information on which species of leafcutter are actually doing the cutting). In my artwork I show flowering redbud branches, the small blue O. lignaria, a Megachile relativa leafeater bee (I took the liberty of simply choosing this local bee) at the top along with a telltale round hole in a leaf, and the X. virginica in the middle.

It was Charlotte's suggestion that I focus on the eastern carpenter bee. Like the redbuds themselves, the eastern carpenter bee is at the northernmost end of its range, which is advancing northward with climate change and aided by urbanization (because cities are warmer due to the urban heat island effect, which likely helps them survive our winters). In fact, since people are planting redbud trees in their gardens, we're inadvertently aiding migration of both tree and bee. She points out that "redbuds are now starting to naturalize in ravines and woodlots across southern Ontario." What brings the X. virginica into conflict with its human neighbours is that female carpenter bees of course, build nests by boring holes into untreated wood structures, including outdoor furniture and buildings. Thus these bees are often considered pests by home owners and we are still working on 'learning to co-exist.' To emphasis this conflict, I printed weathered wood with round holes like thoses bored by eastern carpenter bees.

If you live in Toronto and own or know of a nearby redbud tree, you too can take part in the urbanredbud citizen science project. Check it out here.

I got a lot of positive feedback on my linocut of the redbud before I added the bees, so I think I will also make a simpler piece of the tree branches alone. 

Wednesday, June 6, 2018

Mathematician Emmy Noether, Symmetries and Conservation Laws

Emmy Noether, linocut, 11" x 14", Ele Willoughby, 2018
Emmy Noether (1882-1935, pronounced NER-ter) has long been on my "to do" list of scientist portraits. Noether's Theorem is one of the most fundamental and profound theories in physics and I think it's impossible to overstate its importance. In some ways it's astonishing that Noether's Theorem wasn't discovered until one century ago in 1918 and in some ways its true import wasn't clear until much later. The theorem is so powerful that I struggled with how I could depict it visually. It can be written in many different ways. I could have reproduced her actual equations as her paper is widely available in the original German and in English translation. But, my goal with my art is to communicate science, and even writing a single equation cuts the potential audience. I hope that expressing ideas visually through geometry is more accessible to more people. So, in my portrait, I chose to depict a young Emmy in front of a blackboard with a more simple formulation of her theorem and three specific applications of it, shown schematically, using pictures and geometry. In simple terms, Noether's theorem shows us that any symmetry of a system (say, a given problem in physics, like a ball rolling or a molecule or a solar system or the universe itself) implies a conservation law.

The three examples I give are probably the best known, but just give a hint of the power of this theorem. If you do an experiment and then move three steps to the right and repeat it, you usually expect the same results. In general, a lot of things will have this translational symmetry. Noether's Theorem shows that if you get the same result in two reference frames which are shifted from one another, your system conserves momentum (p with an arrow, as a vector quantity). Thus, we have conservation of momentum in any inertial frame of reference. That means that any place where we don't have to worry about any significant differences from acceleration or gravity, we can solve physics problems by simply knowing that the total momentum never changes. In my print I show a set of x, y, z axes moved (translated) to get a new set of axes x', y' and z' and then the quantity p. Similarly, if your system doesn't care if you rotate it or how it's oriented in space, the conserved quantity is angular momentum (L with an arrow, as a vector quantity); hence in my print, I show a set of x, y, z axes rotated x', y' and z' along with conserved quantity L. Your system itself doesn't need to be symmetric. A lumpy asteroid conserves angular momentum every bit as much as a planetary system made of perfect spheres. If it's irrelevant to results whether you do your experiment at 3:00 or 6:25 then your system has a time symmetry and conserves energy (E). This method of using observed symmetries of something and then finding things which are invariant allows us to easily solve all sorts of problems in physics. Further, using observed symmetries of the Universe allows us to know which things are invariant, know more about the nature of reality and assess any new theories by checking whether they also produce the same conserved quantities.*

Here's a nice video which talks about Noether's Thereom.

Her male colleagues Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener described Noether as the most important woman in the history of mathematics - a compliment which betrays the biases of the times in comparing her only to those of the same sex. She was quite simply, one of the most important mathematicians period, and her impact on physics was tremendous. (My portrait betrays my own biases, focusing on the physics of Noether's Theorem, rather than her contributions to mathematics... but there you are. I'm a physicist by training, not a mathematician).

Born in Erlangen, Germany, Emmy Noether initially planned to teach girls English and French, rather than follow in her father's footsteps and become a professor of mathematics. But ultimately, she choose to study mathematics at the University of Erlangen, where he was a lecturer. Pursuing mathematics was unconventional for a woman; the university had recently declared that mixed-sex education would "overthrow all academic order" and as one of 2 female students (out of 986) she was only able to audit classes at the discretion of professors. She nonetheless managed to pass the graduation exam in 1903 and was granted a degree. She spent the winter semester at the University of Göttingen attending lectures from astronomer Karl Schwarzschild and mathematicians Hermann Minkowski, Otto Blumenthal, Felix Klein, and David Hilbert, before returning to Erlanger. She completed a dissertation supervised by Paul Gordan, On Complete Systems of Invariants for Ternary Biquadratic Forms (1907) using the "computational" approach to invariants, later superseded by Hilbert's more abstract and general approach. She later referred to this well-received thesis and the first few similar papers as "crap". She continued to work at the university for 7 years, but as a woman she was excluded from an academic position and in fact forced to worked without pay.

In 1915 she was recruited to come to the renown University of Göttingen and work with famed mathematicians David Hilbert and Felix Klein. However, some philologists and historians in the philosophical department protested that a woman must not become a Privatdozent, an additional post-doctoral rank required in Germany and certain other European nations to act as a university professor. Famously, a faculty member protested "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?" but Hilbert defended her indignantly, with one of my favourite lines in response to such entrenched academic sexism: "I do not see that the sex of the candidate is an argument against her admission as privatdozent. After all, we are a university, not a bath house." There she still faced hurdles and had to rely on her family to support her financially, as she was unpaid and could only lecture under Hilbert's name until 1919  despite already having published her eponymous Noether's Theorem in 1918! After Einstein published his theory of general relativity in 1915 and Noether responded by applying her invariance work to some of its complexities and this eventually lead her to prove her famous theorem. As Einstein wrote when he read her paper, "Yesterday I received from Miss Noether a very interesting paper on invariants. I'm impressed that such things can be understood in such a general way. The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff."

The end of WWI and German Revolution of 1918-1919 lead to social change and increased rights for women. Her habilitation was approved and she obtained the rank of Privatdozent in 1919. Three years later she was promoted to an untenured professor (nicht beamteter ausserordentlicher Professor) but her work remained unpaid until the next year when she was finally granted a special position (Lehrbeauftragte für Algebra).
Until 1919 she focused on theories of algebraic invariants and number fields. While her incredible contribution to physics had already occurred in 1918, mathematicians remember her for her central role in the 20th century revolution in mathematics, the development of abstract algebra, and her prolific work including Ring Theory from 1920 to 1926, as well as Noetherian rings, Noether groups, Noether equations, Noether modules and more. Her revolutionary 1921 paper Theory of Ideals in Ring Domains is considered a classic and objects which satisfy the ascending chain condition are named Noetherian, in her honour. In the final stage of her career, she focused on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. She was a leader in the strong University of Göttingen math department until 1933. Her colleague Dutch mathematician B. L. van der Waerden made her work the foundation of the second volume of his influential 1931 textbook, Moderne Algebra; it was typical of her to allow students and colleagues to receive credit for her ideas. She supervised more than a dozen doctoral students. She was known for her patient guidance but insistence on accuracy. van der Waerden wrote that she was, "Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all." She learned to live frugally, having gone so long without a salary, and took no concern about her manners, housework or appearance. She used her lecturers as a time for spontaneous discussions of the latest mathematics with students and a place to explore ideas (many of which would become major publications of those students). She spent the winter of 1928–29 at Moscow State University, working with P. S. Alexandrov. She was interested in and supportive of the Russian Revolution and her political opinions got her evicted from her lodging back in Germany when students there complained of living with "a Marxist-leaning Jewess". In 1932, she won the received the Ackermann–Teubner Memorial prize for her contributions to mathematics, which came with 500 Reichsmarks and she gave the plenary address at the 1932 International Congress of Mathematicians in Zürich, a sign of her international stature in the field. Colleagues complained that she was however never elected to the Göttingen Gesellschaft der Wissenschaften (academy of sciences) or promoted to full professor. Within a year Nazi Germany moved to dismiss her and all Jewish academics from university positions. The German Student Association, aided by one of Noether's own former students, a privatdozent named Werner Weber, led the attack on Jews at the University of Göttingen. She merely laughed when students showed up dressed as Hilter's brownshirts. Dedicated to her students, she invited them to her home to discuss math and their plans for the future. Herman Weyl wrote "Emmy Noether—her courage, her frankness, her unconcern about her own fate, her conciliatory spirit—was in the midst of all the hatred and meanness, despair and sorrow surrounding us, a moral solace." Emmy Noether was able to find a position at Bryn Mawr College in Pennsylvania in 1933, where she finally gained the appreciation she deserved. In 1934 she lectured at the Institute for Advanced Study in Princeton, but remarked that she was not welcome at the "men's university, where nothing female is admitted." Tragically, she died 4 days after surgery to remove an ovarian cyst in 1935 when she was only 53.

Noether's theorem remains fundamental to physics, and has been especially vital to particle physics in the decades since her death. Her originality in mathematics was beyond compare and in Weyl's words she "changed the face of algebra by her work."

Emmy Noether, wikipedia article access June 6, 2018

Noether E (1918). "Invariante Variationsprobleme". Nachr. D. König. Gesellsch. D. Wiss. Zu Göttingen, Math-phys. Klasse. 1918: 235–257.

M. A. Tavel's English translation of Noether's Theorems (1918)

Matthew R. Francis, Mathematician to know: Emmy Noether, Symmetry Magazine, June 18, 2015.

Natalie Angier, The Mighty Mathematician You’ve Never Heard Of, The New York Times, March 26, 2012

*Now, if you're interested in the equation itself here's one good online explation (if say, you have most of an undergraduate degree in physics or more). A more intuitive a bit more straightforward explanation is here. The original paper is here and can be found in translation here

Monday, May 7, 2018

Interstitial: Science Innovations by Canadian Women art show

I'm very glad to announce that my portraits of Canadian women in STEM will be part of the Curiosty Collider's show Interstitial: Science Innovations by Canadian Women in this June in Vancouver! More information to come ....but B.C. friends, mark your calendars:

Industry Preview: June 7, 2018 from 11 am to 6 pm
OPENING NIGHT: June 8, 2018 from 7 pm to 2 am
The exhibit will be otherwise open from 11 am to 6 pm from Tuesday to Saturday until June 22 at The Beaumont Studios gallery spaces, located at 316/326 West 5th Street, Vancouver, BC, V5Y 1J0.

Thursday, May 3, 2018

Alice Wilson, tenacious geologist and paleontologist who persisted

Alice Wilson, linocut on collaged washi papers, 11" x 14" by Ele Willoughby, 2018
Some people are late bloomers. Some are slowed in their progress due to illness and battle serious illness throughout their life. Some scientists only pursue science a little later in life. Some experience all three. Alice Wilson did not at first study geologist, and once a geologist her employer hindered her advance, as a woman, at every stage. Nevertheless, she persisted and made her greatest achievements later and took the greatest pleasure in her career after her retirement! Her extraordinary tenacity and glorious success late in life is such a satisfying story.

Geologist and paleontologist Alice Wilson (1881-1964) was outdoorsy as a girl. Her family spent its summers canoeing, camping and collecting fossils in the limestone formations near their home in Coburg, Ontario. The Wilsons valued scholarship and science. Her father was a professor of classics at the University of Toronto. She went to the University of Toronto to study modern languages and history, as preparation for one of the few career options for women: teaching. But her ill health prevented her from finishing her degree and she withdrew in her final year. When she recovered, she decided to pursue her fossil collecting first love, got a job in the Mineralogy Division of the University of Toronto Museum, and found an entry into her career in geology.

Then in 1909 she got a job as a museum assistant with the Geological Survey of Canada (GSC), in Ottawa, where she would work until 1946 and then maintain an office as an emeritus scientist until shortly before her death in 1964.  She was supervised by the GSC's chief paleontologist Percy Raymond and catalogued and labelled the invertebrate paleontology collections. Raymond encouraged her to complete her undergraduate degree, which she succeeded in doing in 1911, after which she was offered a permanent position with the survey - the first woman to hold a professional position there. Alice Wilson became the first female geologist in Canada, facing a series of roadblocks due to her sex. She had to fight for the right to do fieldwork, arguing to superiors that "with reference to further field work of the more strenuous type, I would like to point out that while not heavily built, I am muscularly very strong, and from earliest childhood have been accustomed to an out-of-door life both with canoe and tramping." Since she was forbidden to stay in remote field sites with male colleagues, she made a case that she could work alone during day trips which she made on foot or bicycle. Denied access to a government field vehicle provided to men she later used her own car. The GSC otherwise barred women from fieldwork until 1970. 

Her research interests focused on fossil invertebrates from the Paleozoic era (252–541 million years ago) from across Canada, and from the Ordovician era (444–485 million years ago) in her own backyard in Ontario and Quebec as well as Ordovician fauna from the Rockies and Arctic. She studied stratigraphy in Ontario and Quebec. Over the course of 50 years, she became an authority on fossils and rocks of the Ottawa - St. Lawrence Valley, as a direct response to the sexist limitations placed upon her. Her studies of the geology and paleontology around Cornwall, Ontario were vital to the construction of the St. Lawrence Seaway. She covered more than 16,000 square kilometers despite ill health, frail constitution and the limitations placed upon her.

Alice Wilson at Rigaud Mountain, Québec, May 1953, happy after retirement
(courtesy Natural Resources Canada/Photo number 165185-A)
She fought from 1915 for a decade for the right to take an education leave; paid leave was commonly awarded to her male peers. She despite repeated denials, she persisted and in 1926 she was allowed to apply for a scholarship from the Canadian Federation of University Women (CFUW), but when it was granted to her, she was again denied leave. CFUW campaigned on her behalf, even petitioning Cabinet members and eventually the GSC relented and allowed her leave. She earned her doctorate from the University of Chicago in 1929 at age 49! She returned to the GSC and was repeatedly denied promotions or the professional recognition she deserved. She had only been promoted from clerk to assistant paleontologist in 1919, and then to assistant geologist in 1926. She did not receive a raise, as was common practice, after completing her doctorate. Perhaps an unexpected champion, the government of Prime Minister R. B. Bennett was seeking a female federal civil servant to honour in 1935 and selected Wilson to become a Member of the Order of the British Empire. One suspects the GSC was shamed into action as they rapidly published her research for the first time in 10 years and gave her a promotion. Wilson became first the female Canadian Fellow of the Geological Society of America in 1936, and first female Fellow of the Royal Society of Canada in 1938. She finally was promoted from assistant to a full geologist position in 1940. By 1945, she finally was addressed by the well-earned title "Dr." Five people were hired to replace her upon her retirement! Following compulsory retirement at age 65, in 1946, she had what she thought of as the happiest stage of her career. She was afforded the opportunity to mentor protegés and share her love of geology with students and children. She taught paleontology at Carleton, wrote a children’s book about geology The earth beneath our feet. She maintained an office as emeritus scientist at the GSC until she was 82, visiting daily and continuing her fieldwork. She published more than 50 academic papers throughout her career. When she finally gave up her office, the survey's director James M. Harrison tried to disuade her but she told him that her "work was done." Alice Wilson is one of only 60 inductees in the Canadian Science and Engineering Hall of Fame. Alice Wilson is now a designated national historic person.

I’ve shown her with one of her geological maps of the Ottawa region, published at the official "end" of her career just before she retired, which was for her another beginning. Her publication in 1946, 'Geology of the Ottawa - St. Lawrence Lowland, Ontario and Quebec' was the first the first major geological publication about the region and we owe our knowledge of the area's geology and economic resources including building stone, sand, gravel, and drinking water to Wilson.


Alice Wilson, Libraries and Archives Canada, accessed May 2, 2018
Alice Wilson, The Canadian Encyclopedia, accessed May 2, 2018
Wilson, A E, Geology of the Ottawa - St. Lawrence Lowland, Ontario and Quebec, Geological Survey of Canada, Memoir 241, 1946, 66 pages (4 sheets)
Alice Evelyn Wilson 1881-1964; Canadian Science and Engineering Hall of Fame, Canada Science and Technology Museum. 
The History of the Geological Survey of Canada in 175 Objects
Trailblazer - Alice Evelyn Wilson, 1881-1964 First Woman Geologist Left her Mark in Stone 
Alice Wilson, Wikipedia, accessed May 2, 2018
Parks Canada This Week in History for Monday December 24, 2012, Nothing could stop Alice Wilson!