Poincaré, Cubism, Non-Euclidian Geometry and Special Relativity

Cubist Poincaré, linocut, 8" x 8" by Ele Willoughby, 2022

This is a hand-printed lino block portrait in the Cubist style of mathematician Henri Poincaré. It’s one of a variable edition printed on Japanese kozo (or mulberry paper), 8” x 8” or (20.3 cm x 20.3 cm). The latest prompt for #printersolstice is Cubism.

Diagram from Jouffret's 'Traité élémentaire de géométrie à quatre dimensions'

This print is about how movements in art can be connected with contemporary math and physics (and other sciences). Specifically, the way Cubism breaks from a single favoured perspective or absolute frame of reference and attempts to break down subjects into geometrical shapes from multiple points of view can be tied to advancements in non-Euclidian geometry in mathematics, special relativity (published by Einstein in 1905) and the revolution in early 20th century physics. Picasso and his circle were specifically introduced to the mathematics of the fourth dimension and Non-Euclidian geometry by his actuary and enthusiastic amateur mathematician friend Maurice Princet, who gave him the book 'Traité élémentaire de géométrie à quatre dimensions' (Elementary Treatise on the Geometry of Four Dimensions) by Esprit Jouffret, a popularization of Henri Poincaré's 'La Science et l'Hypothèse' (Science and Hypothesis). Jouffret's book includes many diagrams of four dimensional objects like hypercubes projected on the 2D surface of a page. Princet also spoke to Picasso about the work of polymath Henri Poincaré. Picasso realized that this approach to 4D geometry captured the how he wanted to depict two points of view simultaneously and art historians can trace the influence of this geometry in his earliest Cubist paintings. So I have made a Cubist style portrait of mathematician, physicist, engineer and philosopher of science Henri Poincaré (1854-1912).

Henri Poincaré 
(photograph published in 1913, via Wikipedia)

Pointcaré was called "The Last Universalist" since he excelled in such a wide range of mathematics including pure and applied math, mathematical physics and celestial mechanics. Chaos theory and the idea that deterministic systems can have sensitive dependance on initial conditions (colloquially known as the butterfly effect) seemed to explode on the scene with increasing applications in the 1980s but in fact some foundations were laid a century earlier by Poincaré. He was the first person to discover a deterministic system which exhibits chaos in the three-body problem (or how a system of  3 masses behave over under Newton's Law of Universal Gravitation). The three circular shapes in the background allude to the 3-body problem and the spiral is a hint at the chaos in the trajectories. He is considered a founder of the study of topology (how geometric properties are preserved under deformations) and stressed the importance of the invariance of physical laws under various transformations. Special relativity tells us that light speed is the universal speed limit, and that space and time are not absolute. As things approach this speed limit they experience length contraction and time dilation. We use Lorentz transformations to compare length and duration in differing frames of reference. It was Poincaré who wrote the Lorentz transformations in their modern form. He discovered the Lorentz transformations for velocity and the invariance of Maxwell's equations (for electricity, magnetism and light), which was vital part of special relativity. He published a short paper in 1905 which Einstein did not see until after he had published his own independent and revolutionary paper on special relativity. Poincaré also proposed gravitational waves, travelling at light speed from masses. It's hard to over-state his importance to 20th century math and physics.

Pablo Picasso, Portrait of Ambroise Vollard, spring of 1910 (Pushkin Museum, Moscow)

Poincaré himself worked quite intuitively and wrote, "It is only through science and art that civilization is of value."

One of the ways in which Special relativity is strange is that we discovered the problem of simultaneity. If there is no absolute frame of reference, there is no simultaneity; observers in different inertial frames of reference (that is going different speeds*) will not agree on the sequence of events or even whether two things happen at the same time. This problem of simultaneity, it can be argued, is exactly what interested Picasso, when he chose to paint two different points of view on the same canvas. This is the argument made by Miller, author of 'Einstein, Picasso: Space, Time and the Beauty That Causes Havoc' makes. Leonard Schlain, in 'Art & Physics' makes the case that Picasso in painting all sides of an object simultaneously as if he was seeing space as all here in the everlasting now, was depicting what a viewer would see astride a beam of light at the universal speed limit when time has reached its maximum dilation to the present (and only the present). 

Earlier art historians, and in fact Einstein when asked, argued that Cubism wasn't connected to relativity or non-Euclidian geometry but I think each under appreciated the other. The art historians argued the artists had no knowledge of Einstein, or Minkowski (who combined space and time into the 4D spacetime), equations or pure math. Einstein preferred earlier classical painting and argued "This new artistic 'language' has nothing in common with the Theory of Relativity" but then, he felt contemporary art and music had both degenerated. If we are less literal, I think the connection between the two movements is quite clear. There is no absolute frame of reference and both art and physics were revolutionized by this realization.

Schlain makes a further argument connecting Cubism with relativity but noting that colours also change with speed, as length contracts (including the wavelengths or colours we would observe), and colours would be merge as what is in front and behind become one. He argues we would be left with neutrals at the speed of light: white (of white light), black (of its absence),  and muddy tones of mixed colours brown and grey. These are precisely the colours Picasso and Braque used in their early Cubist paintings, and the colours of my palette for my portrait of Poincaré.

*without acceleration and/or far from large masses, so we can ignore general relativity

References

William B. Ashworth, Jr., Scientist of the Day - Esprit Jouffret, Linda Hall Library blog, March 15, 2021.

Arthur I. Miller, Henri Poincaré the unlikely like between Einstein and Picasso, The Guardian, July 17, 2021

Did Picasso know about Einstein?, Physics World, November 1, 2002

Leonard Schlain, Art & Physics, Quill William Morrow, New York, 1991

Henri Poincaré, Wikipedia, accessed January, 2022

Prints inspired by art history

I am trying to participate in the #PrinterSolstice again this year. They have created a series of prompts for each of 13 weeks starting with the (northern hemisphere) winter solstice. This year the themes are based on 20th century movements in art. It's been challenging to find time; we're once again sheltering at home and schools have gone remote here. Facilitating remote school takes a lot of my time and I cannot print at the same time, though I can plan, draw and carve. 

We started with Abstract Expressionism, which is really outside my wheelhouse, since my prints are representational. But it gave me a chance to work intuitively to create a mono print with scraps of lino.

monoprint by Ele Willoughby, 2022

Next was Art Deco. I looked at a lot of Art Deco artworks. The frequent clamshell motif and the keyhole shape in Art Nouveau works, plus seeing a number of mermaid illustrations reminded me I had long wanted to illustrate the story of Mélusine, the legendary half-fairy ancestor of the House of Lusignan and royals including the Plantagenets, whose lower half became a serpent when she bathed. She marries a nobleman but insists he must never observe her in the bath; of course he does, and she leaves him - so the keyhole shape works just right to tell the story! There are many versions, like most folklore. Sometimes she has two tails, or a fishtail or wings. There are different versions of her name and various stories are found in different regions especially France, Luxembourg and the Low Countries. I first learned of her from Manuel Mujica Láinez’s The Wandering Unicorn, which tells her story through the centuries. Her story also appears in A.S. Byatt’s Possession amongst many other places from operas to video games.

Mélusine linocut, 8" x 10" by Ele Willoughby, 2022

These art history prompts have been a challenge to link to my art practice. I've  been seeking a connection to things like science art. The third prompt was Bauhaus. In looking at Bauhaus paintings I was reminded of nothing so much as Feynman diagrams, and the exuberance action on the quantum scale, so I decided to combine quantum physics with the Bauhaus vocabulary of lines, shapes and colour palette. 

I was thinking more of the paintings of Kandinsky than the regular geometric shapes in Bauhaus design: a welter of black straight, wavy and curly lines, stripes of colour, triangles, circles and concentric rings and washes of pale colour, often on a cream coloured background. 

The Feynman diagrams are a tool of particle and quantum physics to both denote a particle interaction and also can be used to make calculations of probabilities and physical properties. Straight lines denote particles (quarks and leptons like electrons). Wavy lines denote photons. Curly lines are gluons and the dotted line is a Higgs particle. I wanted to include an electron spontaneously giving off a virtual photo and particle-antiparticle pairs, production of a Higgs particle, one diagram of the sort of we see if we smash protons together, and one hilariously named penguin diagram (in this instance producing a gluon).

Feynman Diagram Bauhaus, linocut, variable edition, 8" x 10" by Ele Willoughby, 2022

Looking at all these prints as I try to plan ahead and link them to my art practice and science art I am reminded of Leonard Shlain's book Art and Physics. It should be around here somewhere but I can't find it on my bookshelves. (Aside: this house needs a librarian.) In the book Schlain linked major movements in art with advancements in physics. I am not sure I can agree with his thesis that movements in art presaged new physics (which feels like it violates causality to me) but I greatly enjoyed the book. Others have drawn parallels between art and physics and it's clear that both math and physics were an influence of some of these major modern movements in art. In fact, this has been true for centuries; consider for instance the development of artistic perspective, or the camera obscura. One of the obvious connections is between cubism and the math of the fourth dimension and the physics of relativity. So that is something I'm thinking about for an upcoming print.

Some of the other prompts (colour field, Dadaism, Fauvism, Harlem Renaissance, Minimalism and surrealism) are less obvious for me, but I'm thinking ahead. Op Art is rather clearly related to mathematics. I have a scientific idea for Conceptual art and the seed of an idea for Pop Art. Stay tuned for more!

Somewhat sinister holiday cards

 I decided to add to my collection of darker yuletide folklore cards, to go with the Yule Cat and made:

linocut Krampus card by Ele Willoughby, 2021

 

The relief print on each card shows Krampus, the scary horned counterpart to Santa of Alpine folklore, complete with birch rods, and naughty child in a basket.  The origins of this character are debated but there are traditional parades called the Krampuslauf or Krampus run, where young men dressed as Krampus and attempt to scare the audience with their antics in many Alpine towns, and  Krampus is featured on holiday greeting cards called Krampuskarten (which often read "Gruss von Krampus" or "Greetings from Krampus"). Krampus is usually hairy, horned, has cloven feet, a lolling long tongue and fangs. The bundle of birch branches or ruten links back to pagan times.

linocut Mari Lwyd card by Ele Willoughby, 2021

This lino block printed card shows Mari Lwyd, a traditional Welsh hobby horse in a field. As part of a wassailing tradition from South Wales, a hobby horse made of a horse skull on a pole, decorated with buttons and ribbons, with sack cloth shrouding the poll and porter is carried through the local area at Christmas time. The men performing with Mari Lwyd at dusk and into the night would request entrance to houses through song, and if admitted must be given food and drink. 

The name Mari Lwyd (pronounced "lood") might come from Holy Mary or grey mare. The source of the tradition is debated but can be linked to various British hooded animal traditions.

linocut Joulupukki, or the Yule Goat, card by Ele Willoughby, 2021

The relief print on each card shows the Yule Goat, Joulupukki of Finland, carrying his parcels, staff with lantern, and bedecked with bells and ribbons in this nighttime scene. Each card is 4.25" by 5.75" (11 cm by 15 cm) and the envelopes are 5.12" x 7.12" (13.5cm x 18.5 cm).

Joulupukki is a Finnish Christmas figure whose name translates as Yule or Christmas Goat. Pukki comes from the Teutonic root "bock", which is a cognate of the English "buck", and means "billy-goat". There is an old tradition of men dressing as a goat at Yule in Finland. These nuuttipukki were evil spirits who would go from house to house demanding gifts and leftovers from the Yule feast. But over time the concept of nuutipukki merged with the idea of Santa Claus and became the benevolent Joulupukki who gave out gifts, rather than claim them, to well-behaved children. But in some areas, nuuttipukki still make visits on Nuutinpäivä, or St. Knut's Day, January 13. 

Yule goats (Julbocken) are common in Nordic countries, as small decorative straw or wicker ornaments decorated with red ribbon or giant ones like the Gävle goat in Sweden, a frequent target of arson. Some argue they are linked to Thor, who rode in a goat-pulled chariot. But others argue it is even more ancient and links to proto-Slavic beliefs where Koliada or Yule honors the god of the fertile sun and the harvest who was represented by a white goat. So Koliada festivals always had a person dressed as a goat, often demanding offerings in the form of presents.

linocut Perchta card by Ele Willoughby, 2021

This linocut card shows Perchta or Berchta (or Bertha in English), a figure from Alpine folklore, who visits during the 12 days of Christmas. Her name may come from "the bright one" or the German word for the feast of the Epiphany and her history is linked to white robbed goddesses like Holda who oversaw spinning and weaving or the goddess Frigg and she emerged from Germanic and Celtic traditions in the Early Middle Ages. She has two forms, both shown in my print: young and beautiful and as white as snow, or an old crone with a long knife and often a beak-like nose. She sometimes has one large, possibly goose foot. Jacob Grimm (of fairy tale fame) thought this indicated she was a shapeshifter or swan maiden. She is associated with birch trees and looked over the forest and wildlife. She was said to visit homes during the 12 days of Christmas and enforce cultural taboos, such as not spinning on holidays. If young people were good (and completed duties like spinning their flax or wool) she would leave a silver coin. But if not, she would slit their bellies open and stuff them with straw or refuse! Between the beautiful and ugly forms of Perchta I include a spindle. In her beautiful form she was known as Grandmother Winter, the bringer of snow

Some legends associate her with the Wild Hunt, and claim she rides through the night sky with her Perchten. 

In contemporary alpine festivals she is accompanied by an entourage, the Perchten, either beautiful and bright Schönperchten who bring luck or ugly Schiachperchten with fangs, tusks and horse tails (resembling Krampus) who are supposed to drive out ghosts and demons. She is viewed as the one who rewards generosity and punishes bad behaviour. 

Bioluminescent Firefly Squid and some borbs

 A couple of other recent prints which actually came from the weird and wonderful AI-generated #Botober2021 art prompts for "Firefly squid" (a surprisingly normal suggestion for an actual existing animal) and "impossibly cute pudgy birds".

Firefly Squid, linocut, 8" x 8" by Ele Willoughby, 2021

This is a linocut print of the firefly squid (Watasenia scintillans), also called sparkling enope squid or hotaru-ika in Japan. These tiny squid live at depth (200 to 400 m) and they are bioluminescent and emit blue light from photophores. The print shows the squid against a white background so you can see the whole animal and then its reflection is shown against dark blue so you can see how its bioluminescence would appear underwater with fluorescent blue spots. Each print is 8" x 8" (20.3 cm x 20.3 cm) on white Japanese kozo (or mulberry) paper. When they spawn on the shores of Japan visitors come to see the blue glow and they are a boon to fishermen who collect the dying squid. 

 

Tufted titmouse linocut holiday card by Ele Willoughby, 2021

 

The Icelandic Yule Cat Jólakötturinn

So every year for several years now, a lot of artists do all the Inktober daily art prompts, and there are now a whole slough of various prompts. There are even a fairly large number of #sciart prompts. I thought I would do the "AI weirdness" neural net generated prompts by Janelle Shane called #Botober2021. I think the only way to manage daily brand new art is to keep it low key, so I'm keeping it simple, posting to Twitter (@minouette) and my Instagram stores (@the.minouette) only. Mainly there's pen and ink sketches. I am going to try and fit in a couple of linocuts. There's an upcoming prompt which made recall a mythological creature I have previously considered. I rather like all the various holidays (many pagan and ancient) which coincide roughly with Christmas time and how some of them are more spooky than festive, as we, in the northern hemisphere, approach the solstice and the longest nights. The prompt is "way too much cat" and what came to mind was the Icelandic Yule Cat, Jólakötturinn.

Linocut print Yule Cat, by Ele Willoughby, 2021

The first written accounts of Jólakötturinn, enforcer of good behaviour leading up to Christmas, date to the 19th century but the stories of the monster cat likely date to the Dark Ages. In Iceland, good children who did their chores received new clothes, but the lazier ones risked meeting the giant Yule Cat, who towered over houses. If there were no new clothes amongst their gifts the Yule Cat would eat them! The Yule Cat was intended to also inspire generosity and encourage giving clothing to the less fortunate.

I have added a couple of sets of hand printed Yule Cat cards to my shop. I think I might get some digitally printed so I can make more cards.

You can find Bjork singing a carol about Jólakötturinn here, and if you haven't already done so, do yourself a favour, and check out Luke Pearson's Hilda graphic novels or the animated Netflix series - where you'll also find the Yule Cat and other trolls and Yule lads from Icelandic folklore.

Isabella Aiona Abbott, First Lady of Limu and the Seaweeds of the Central Pacific

Isabella Aiona Abbott, linocut 9.25" x 12.5", by Ele Willoughby, 2021

Professor Isabella Aiona Abbott (1919-2010), was born Isabella Kauakea Yau Yung Aiona on June 20, 1919 in Hāna on Maui, the second youngest of eight children. Her Hawaiian name means "white rain of Hāna," referring to the rain which comes in from the ocean as a white mist; her friends called her Izzie, the nickname her father gave her. Her mother Annie Kailihou was Native Hawaiian schoolteacher and Izzie first learned to love seaweed while gathering it on the shore with her mother, who would cook traditional Hawaiian dishes. Her mother taught her the Hawaiian names for seaweed; those she didn’t know she called ōpala (rubbish). Her father Loo Yuen had emigrated to Hawai’i from China, at age 18, to work on the Kīpahulu sugar plantation. He completed his contract, repaid his recruitment expenses, and opened a general store (in direct competition with the plantation store). His store was quite successful and the plantation store closed. He was friendly and learned to speak Hawaiian fluently before learning English. He had six sons with his first wife before she died; a local matchmaker introduced him to Annie. Annie moved to Hana to marry Loo and they had a son and a daughter. Loo spoke Chinese with business friends, English with the kids and Hawaiian speak privately with his wife. Izzie confessed the kids all learned Hawaiian to follow what her parents were saying amongst themselves. The family moved from to Honolulu so she could access the best schools. She was allowed to choose a Chinese or American school, private or public. She opted to attend the Kamehameha School for Girls in Hawaii, a private school for students of Hawaiian ancestry, which nurtured her love of botany. She recalled growing beans for the girls to eat and visiting flower gardens where she learned scientific names for plants, as well as the Hawaiian names.  She learned that the scientific names for plants had meaning, and conveyed information about the plants, just like the Hawaiian names for plants did. She graduated in 1937.

 

While an undergraduate in biology at the University of Hawai’i she met her husband Don Abbott day one. They were seated next to each other thanks to the alphabetic seating chart. She earned her B.Sc.in 1941 and then her M.Sc. from the University of Michigan at Ann Arbor in 1942 then with her husband who studied marine invertebrates, she continued her graduate studies in algal taxonomy at the University of California Berkley.  Their passion for different areas of marine biology was always complementary. She became the first Hawaiian woman to earn a doctorate in science when she graduated at age 31 in 1950. The couple moved to Pacific Grove, California in 1950, when zoologist Don joined the Stanford faculty at their field school Hopkins Marine Station. Biology jobs were scarce, especially for women and with their anti-nepotism rules, there was no job offer for Izzie, despite having the same credentials as her husband. So she focused on raising their daughter Annie, her involvement in the community and continuing to study and cook seaweed on her own adapting recipes to use the local bull kelp (Nereocystis) in things like cake and pickles. In 1960, she became a lecturer for Stanford’s Biology department, began teaching summer courses at Hopkins and publishing scientific papers. In 1969, she won the Darbaker Prize from the Botanical Society of America. By 1972, she had shown herself to be such a productive researcher and effective teacher that she was hired as both the first person of colour to receive a full professorship at Stanford and the first woman on the biological sciences faculty, bypassing the usual preliminary steps in the tenure-track ladder. She published more than 150 research papers and is credited with the discovery of over 200 species of algae. Many species have been named in her honour including an entire red algae genus known as Abbottella, or little Abbott. In 1976, she wrote ‘The Marine Algae of California,’ considered the definitive text on the subject. She and Don were well-loved teachers, and considered “the heart” of the marine station, often housing visiting scholars, hosting colleagues and students, and feeding them Izzie’s popular seaweed-based delights. Izzie was known for allowing her gradient students freedom to choose and explore their research areas so her group studied a wide range of subjects within marine botany.

 

During this time, Abbott was diagnosed with breast cancer. Determined to survive the disease, she took the only possible cure at the time, complete mastectomy. She became a 40-year cancer survivor.

 

The Abbotts retired in 1982 and moved to Hawai’i where Izzie, hired by the University of Hawai’i developed a course in ethnobotany which lead the development of an undergraduate major in the subject. Her classes were hands-on; students were encouraged to grow plants, make baskets or bark-cloth and of course, were regularly fed limu. She wrote a small book about the edible seaweed of Hawai’i known as “limu” for the lay public, which included their scientific names, Hawaiian names, oral history of kūpuna (Hawaiian for elders) and recipes. Her culinary skills were featured in a 1987 article in Gourmet Magazine. Asked which was the most important limu, she made a case for limu kala (S. echinocarpum, on the right in my portrait. “People eat it, turtles eat it. And kala means ‘to forgive.’ It’s used in purification ceremonies like ho’oponopono (the Hawaiian reconciliation process), or if you’ve been sitting with a dead person, or if you’re going on a dangerous journey.”

 

Offered a chance to name a research vessel by NOAA (the National Oceanographic and Atmosphic Administration) she named it The Hi’ialakai, which translates as “embracing or searching the pathways of the sea”. In 1992, she published “Lā‘au Hawai‘i”, the first comprehensive Hawaiian ethnobotany textbook covering everything from canoe-building, clothing, medicine, hula, weaponry to religion. She called it “a Western scientist’s viewpoint of the Hawaiian way of doing things,” and argued it was needed so that,  “Hawaiians are not put in second- or third-class status of Native people who don’t know anything. Hawaiian culture is unbelievably sophisticated.”

 

In 1993, she won the Charles Reed Bishop Medal. In 1997, Isabella Aiona Abbott was awarded the highest award in marine botany, the National Academy of Sciences Gilbert Morgan Smith medal. In 2005 the Honpa Hongwanji Buddhist Mission named her a Living Treasure. In 2008 the Hawaii Department of Land and Natural Resources honoured her with a lifetime achievement award from for her studies of coral reefs.

 

Isabella Aiona Abbott linocut with labelled algae species and her related publications.

 

In my print, she is surrounded by algae of the Pacific, all of which appeared in Abbott's research publications, including several species she discovered, or based on images of specimen she personally collected or whose traditional use as food she documented. From left, clockwise around to the right, these algae are:

 

Laurencia majuscula, which is a type of peppery flavoured limu used by Hawaiians as a condiment, Spatoglossum macrodontum, Feldmannia cylindica or simplex, Hincksia granulosa, Cryptopleura rosacea, Pradae weldii, Sargossum echinocarpum, an edible limu species called limu kala.

 

She died at age 91, in 2010, in her home at O’ahu.

 

 

References:

Healoha Johnston, ‘Marine Botanist Isabella Aiona Abbott and More Women to Know this Asian American and Pacific Islander Heritage Month,’ Because of Her Story, Smithsonian.com, May 3, 2021

 

I.A. Abbott, ‘Limu: An Ethnobotanical Study of Some Hawiian Seaweeds’, National Tropical Botanical Garden, Kaua‘i, Hawai‘i, 1984.

 

Danika Bense, ‘A Celebration of Women’s History and Dr. Isabella Aiona Abbott,’ Ho’oulu, UH Maui College, March 14, 2019

 

Louise Bergeron, Isabella Abbott, world-renown Standord algae expert, dies at 91, Stanford Report, December 7, 2010

 

Isabella Abbott, Wikipedia, accessed September, 2021

 

Jennifer Crites, Pioneering professor is first lady of limu, Mālamalama, The Magazine of the University of Hawai’i, October 21, 2010.

 

Long Story Short with Leslie Wilcox, with guest Isabella Abbott, PBS Hawaii, First air date June 17, 2008

 

Isabella Aiona Abbott 1919-2010, Hawai’I Women’s Suffrage Centennial Commemoration, April 28, 2020

Karli Chudeau, Science Heroes: Dr. Isabella Aiona Abbott, The Ethogram, June 29, 2021

Shannon Wianecki, Hawai’i’s First Lady of Limu, Hana Hou: The Magazine of Hawaiian Airlines, December 2019/January 2020

 

 

Optimizer of compilers, code and parallel computing trailblazer Fran Allen

 

Frances Allen, linocut 9.25" x 12.5", by Ele Willoughby, 2021

 

This is my linocut portrait of trailblazing American computer scientist Frances Elizabeth Allen (August 4, 1932 – August 4, 2020) who made foundational contributions to optimizing compilers (which translate code written in computer languages to the machine code in ones and zeroes actually used by computers), optimizing programs and parallel computing. This work has made computers and everything they do faster and more efficient. Compiler expert Graydon Hoare told the New York Times that her work is in “every app, every website, every video game or communication system, every government or bank computer, every onboard computer in a car or aircraft.” She was the first woman to become an IBM Fellow, where she worked from 1957 to 2002 and as an emeritus fellow afterwards. She was the first woman to win the prestigious A.M. Turing Award or contributions "of lasting and major technical importance to the computer field". I made this portrait for the #mathyear prompt: Turing Award.

She grew up the eldest of six kids on a farm near Lake Champlain; her mother was a teacher and her father a farmer. She went to elementary school in a one-room schoolhouse before attending a local high school and then the New York State College for Teachers where she graduated with a degree in mathematics in 1954. She worked as a teacher, back at her old high school, before returning to study at the University of Michigan for a MSc in mathematics in 1957.
 
IBM Research was recruiting and Allen needed to pay off student loans so she took the job. They wanted  their employees to learn and use FORTRAN (FORmula TRANslation, the first and newly introduced high-level programming language).  With her teaching experience and some basic computing courses under her belt, she was assigned to teach FORTRAN while simultaneously learning it herself. She said she had to teach these unhappy scientists (who were skeptical that a high-level language could work as well as assembly code) and became enamored with FORTRAN and its possibilities for productivity and performance. As Grace Hopper argued, "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." Her goal became to make those compilers, the translators, more efficient. Allen had intended to return to her first love, teaching high school math, but instead stayed with IBM for 45 years. 

In 1959 Allen managed the compiler-optimization teams for Harvest and Stretch, IBM's first transitorized 100 kW supercomputer. With its 2048 kB of memory the goal was to make it 100 times faster than contemporary machines! While it was not a hit with clients (as it apparently still took 18 hours to produce a 24-hour weather forecast), it impressed the National Security Agency. Allen was then assigned to the Harvest project for code breaking (of messages from the Soviet Union intercepted by American spies) and she spent a year leading an NSA team on classified projects. Harvest was such a success, thanks to Allen's optimization of the compiler, it was used for 14 years despite the pace of technological innovation. She also worked on the Alpha computer language which could run on Stretch and could create new alphabets beyond the system-defined alphabets. She  In '62 she moved from the IBM facility in Poughkeepsie to Yorkton Heights, where she worked on further supercomputer (ACS-1) and language projects (PL/I). She collaborated with John Cocke on a series of fundamental papers about compiler optimization to improve how higher level languages are translated to machine code. The diagrams in the portrait are from their crucial 1971 paper, 'A Catalogue of Optimizing Transformations'. Their work introduced the concept of using such graph-theoretical structures to encode a program content in order to efficiently and automatically understand how its parts function together and find ways to optimize code.

She did a sabbatical at NYU in 1971 and was thence an adjunct professor there, and a sabbatical at Stanford in 1977. From 1980 to 1995 she led IBM's parallel computing team, developing tools which became broadly used in commercial compilers in personal computers, and developing software for their Blue Gene project. She became the first woman IBM Fellow in 1989. In 1995 she was named president of the IBM Academy of Technology, an internal steering group for the company. In this role she focused on mentoring and women in tech. After her retirement in 2002 she remained as an Emeritus Fellow and continued to work on programs encouraging women and girls to work in computing.

She was a fellow of the IEEE, the AAAS, the American Philosophical Society, the Association for Computing Machinery and the Computer History Museum. She was elected to the National Academy of Sciences. In 1997 she won the IEEE Computer Society Charles Babbage Award and was inducted in the Women in Technology Hall of Fame. She won the IEEE Computer Society Computer Pioneer Award in 2004. She won the Association for Women in Computing Augusta Ada Lovelace Award in 2002 and the ABIE Award for Technical Leadership from the Anita Borg Institute in 2004. In 2006, she won the Associating of Computing Machinery A.M. Turing Award,  for contributions "of lasting and major technical importance to the computer field" in recognition of her work with supercomputers.  She was the first woman to win the prestigious award in its 40 year history.

When she wasn't working she enjoyed other challenges and adventures, as an avid runner, mountain climber and participant in expeditions to the to the Artic and on the Chinese/Tibet border. 

In 2022, the IEEE will present the IEEE Frances E. Allen Medal for the first time for innovative work in computing leading to lasting impact on other fields of engineering, technology, or science.

References

Frances Allen, wikipedia, accessed September, 2021

Allen, Frances E.; Cocke, John (1971). Rustin, Randall (ed.). A Catalogue of Optimizing Transformations. Design and Optimization of Compilers. Thomas J. Watson IBM Research Center. Prentice Hall. 

Kim Lyons, Computer scientist Frances Allen, known for her work on compiling, dies at 88, The Verge,
Aug 9, 2020

Frances Allen, Allen on  joining IBM and teaching FORTRAN, Turing Awardee Clips on the A.M. Turing Award YouTube channel, posted 22 Jun 2020 

Frances Allen, Women in Technology Hall of Fame, accessed September, 2021

Ben James, Frances Allen Optimised Your Code Without You Even Knowing, Hackaday.com, August 25, 2020

Frances "Fran" Allen, A Pioneer in the World of Computing, IBM Research, accessed September, 2021.

IEEE Staff, Computer Scientist Who Made Foundational Contributions to Computing Has IEEE Medal Named in Her Honor, June 26, 2020.