International Women’s Day 2020. Women & mathematical brilliance.

By March 3, 2020 No Comments

As we celebrate International Women’s Day on the 8th March 2020, we look back at the contribution’s women have made to the vast engineering advancements & the progress the human race has made since the Industrial Revolution.

The Industrial Revolution set in motion the rapid advancement of human endeavour & technology. Technological usage in the 21stC has become an intrinsic part of everyday human life. From the moment we wake up to our Smart Phone alarms, we are bombarded with the legacies of our Engineering Forefathers & the Industrialists of the 18th & 19thC; spending our days surrounded by data, machinery & computational excellence.

However, despite a seeming lion share of our industrial heritage having been developed by men, there are plenty of women who have left their legacies & an imprint on the world we live in today.

Mathematics & the use of mathematical equations underpins modern computational capacities. However, modern computing power was not available in the times of the Industrial Revolution & only in basic format’s until the 1960’s to 1980’s & therefore traditional methods, assisted by innovation & invention, were used to write the blue prints for the future we are now all living.

With this in mind, this year Dolphin N2 are going to shine the limelight on two mathematical & computational trail blazers, without whom our world would be a very different place.

Ada Lovelace – 1815 – 1852 – English Mathematician & Computer programmer   

Ada Lovelace, born Augusta Ada Byron, Lady Byron & daughter of renowned Poet Lord Byron was an educated woman, living in vastly changing times. Being born into the time when the Industrial Revolution was transforming the landscape of Britain; she was an exception to many rules of the time.

Her passion for mathematics was spurned by being educated by renowned mathematician & logician Augustus De Morgan, the first professor of mathematics at the University of London. Having married William King, 8th Baron King in 1835, she claimed her title countess of Lovelace, when William King was created an earl in 1838.

Charles Babbbage was at the cutting edge of mathematical calculating machinery & his notion of calculating numbers with machinery first came to him in 1812/1813. His first calculating machine, the Difference Machine, was built & had a calculation capacity of eight decimals. Following Government investment in 1823, he subsequently went on to devise a calculator, the Analytical Machine,  which could calculate to twenty decimals.

Ada Lovelace became interested in Charles Babbage’s machines in 1833 & translated & annotated an article penned by the Italian Mathematician & Engineer Luigi Federico Menabrea “Notions sur la machine analytique de Charles Babbage” (1842; “Elements of Charles Babbage’s Analytical Machine”). (1)

Ada’s annotations explored the notion that the Analytical Machine, the successor to Babbage’s Difference Engine, could be programmed to compute Bernoulli numbers. The Notes included the first published description of a stepwise sequence of operations for solving certain mathematical problems & Ada has therefore often been referred to as ‘the first programmer’. (2) Ada added a footnote to her translation of Menabrea’s article. Ada emphasized the difference between Pascal’s machine, which can be compared to a calculator, & Babbage’s Analytical Machine, which can be compared to a modern day computer & have the capacity to store & remember calculations. (3)

Ada was clearly a woman way ahead of her time, as this extract from her annotations proves. Her foresight about the computational value & ability of the Analytical Machine as far back as 1843 is astonishing:

“Again, it [the Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine . . . Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent” (3)

Katherine Johnson – 1918 – 2020 – NASA Mathematician

Katherine Johnson was born in 1918 to a self-taught mathematician Father & her Mother who was a teacher. Despite having the educational support at home, Katherine Johnson, as an African-American living in Greenbrier County; was only entitled to an education to the age of twelve.

Her parents moved the family & at the age of fifteen, Katherine graduated to the West Virginia State College. Her teachers included William Schieffelin Claytor an African-American Mathematician who tailored courses specifically for the young Katherine, seeing her graduate with honours in Mathematics & French in 1937, aged only eighteen.

Following marriage, a teaching career & the birth of her three daughters, (for which she forsook academia & the place she had won at West Virginia University in Morgantow); Katherine’s journey to NASA began in 1953 when her husband moved the family to the Virginia Peninsula & Katherine began work at the all-black West Area Computing section at the National Advisory Committee for Aeronautics’ (NACA’s) Langley laboratory headed by fellow West Virginian Dorothy Vaughan (4)

Johnson’s first permanent position at Langley, in the Maneuver Loads Branch of the Flight Research Division, saw her spend four years analyzing data from flight tests & worked on the investigation of a plane crash caused by wake turbulence (4)

In 1957 the Soviet ‘Sputnik’ satellite was launched & Johnson subsequently provided mathematics for the 1958 document ‘Notes on Space Technology’, part of a compendium of lectures given by engineers Flight Research Division and the Pilotless Aircraft Research Division (PARD). Engineers from those groups formed the core of the Space Task Group, the NACA’s first official foray into space travel (4)

Once NACA had become NASA in 1958, Johnson worked on trajectory analysis for Alan Shepard’s May 1961 mission Freedom 7; the first human spaceflight made in the US. In 1960, Johnson & engineer Ted Skopinski co-authored the paper ‘Determination of Azimuth Angle at Burnout for Placing a Satellite Over a Selected Earth Position’ & she became the first woman in the Flight Research Division to receive credit as an author of a research report.

In 1962 as John Glenn prepared himself for his Friendship 7 mission, the complex orbitol flight path meant a worldwide communications network had been built to track trajectories, linking tracking stations to IBM computers in Washington, Cape Canaveral in Florida, & Bermuda. Astronauts were concerned at this point about the computational accuracy of the technologies & the computers, as they had a history of being prone to inaccuracies.

Therefore, ‘as a part of the pre-flight checklist, Glenn asked engineers to “get the girl”—Johnson—to run the same numbers through the same equations that had been programmed into the computer, but by hand, on her desktop mechanical calculating machine.  “If she says they’re good,’” Katherine Johnson remembers the astronaut saying, “then I’m ready to go.” (4)

The trust Katherine Johnson’s mathematical acumen instilled in the astronauts is incredible & ironically in a modern setting, computers would be trusted over human fallibility at every juncture.

Without Ada Lovelace’s & Katherine Johnson’s passion for numbers & mathematical computation; some of the greatest moments in technological history may never have been realised. Both women, facing prejudice not only for their sex, but also for their heritage; stood up & were counted as part of the great history of women in science, engineering & mathematics.

Written by Katy-Jane Mason for & on behalf of Dolphin N2.