It seems almost absurd now, but cosmologists once assumed that galaxies of a given type were all the same and didn’t change. Because of this assumption, galaxies were used as a redshift or light-based yardstick to measure distances in the universe. But what if some galaxies were intrinsically redder than others? Little to no thought was given to their origins, compositions, or evolution until Beatrice Tinsley came along.
Beatrice saw galaxies as changing bodies of stars. She believed that they grew, evolved, and died because they’re made of stars, and that’s what their star populations did. To lump all galaxies together and use them as a standard candle was an oversimplification. Beatrice created the first computer model of a galaxy to prove her point and in doing so, she founded the field of galaxy evolution.
If you’ve never heard of Beatrice, don’t feel bad. Just as her career was really beginning to take off, she developed cancer and died shortly after her 40th birthday. Though her life was short, her influence on cosmology is long-reaching. Continue reading “Beatrice Tinsley And The Evolution Of Galaxies”→
If you were to create a short list of women who influenced software engineering, one of the first picks would be Margaret Hamilton. The Apollo 11 source code lists her title as “PROGRAMMING LEADER”. Today that title would probably be something along the line of “Lead software engineer”
Margaret Hamilton was born in rural Indiana in 1936. Her father was a philosopher and poet, who, along with grandfather, encouraged her love of math and sciences. She studied mathematics with a minor in philosophy, earning her BA from Earlham College in 1956. While at Earlham, her plan to continue on to grad school was delayed as she supported her husband working on his own degree from Harvard. Margaret took a job at MIT, working under Professor Edward Norton Lorenz on a computer program to predict the weather. Margaret cut her teeth on the desk-sized LGP-30 computer in Norton’s office.
Hamilton soon moved on to the SAGE program, writing software which would monitor radar data for incoming Russian bombers. Her work on SAGE put Margaret in the perfect position to jump to the new Apollo navigation software team.
The Apollo guidance computer software team was designed at MIT, with manufacturing done at Raytheon. To say this was a huge software project for the time would be an understatement. By 1968, over 350 engineers were working on software. 1400 man-years of software engineering were logged before Apollo 11 touched down on the lunar surface, and the project was lead by Margaret Hamilton. Continue reading “Margaret Hamilton Takes Software Engineering To The Moon And Beyond”→
When she was four years old, Nancy Grace Roman loved drawing pictures of the Moon. By the time she was forty, she was in charge of convincing the U.S. government to fund a space telescope that would give us the clearest, sharpest pictures of the Moon that anyone had ever seen. Her interest in astronomy was always academic, and she herself never owned a telescope. But without Nancy, there would be no Hubble.
Goodnight, Moon
A view of the Milky Way from Reno, Nevada. Via Lonely Speck
Nancy was born May 16, 1925 in Nashville, Tennessee. Her father was a geophysicist, and the family moved around often. Nancy’s parents influenced her scientific curiosities, but they also satisfied them. Her father handled the hard science questions, and Nancy’s mother, who was quite interested in the natural world, would point out birds, plants, and constellations to her.
For two years, the family lived on the outskirts of Reno, Nevada. The wide expanse of desert and low levels of light pollution made stargazing easy, and Nancy was hooked. She formed an astronomy club with some neighborhood girls, and they met once a week in the Romans’ backyard to study constellations. Nancy would later reminisce that her experience in Reno was the single greatest influence on her future career.
By the time Nancy was ready for high school, she was dead-set on becoming an astronomer despite a near-complete lack of support from her teachers. When she asked her guidance counselor for permission to take a second semester of Algebra instead of a fifth semester of Latin, the counselor was appalled. She looked down her nose at Nancy and sneered, “What lady would take mathematics instead of Latin?”
Everyone loves a hero. Save someone from a burning building, and you’ll get your fifteen minutes of fame. That’s why I’m always surprised that more people don’t know Norman Borlaug, who would have celebrated his 104th birthday on Sunday. He won the Nobel prize in 1970 and there’s good reason to think that his hacking efforts saved about a billion people from starving to death. A billion people. That’s not just a hero, that’s a superhero.
To understand why that claim is made, you have to go back to the 1970s. The population was growing and was approaching an unprecedented four billion people. Common wisdom was that the Earth couldn’t sustain that many people. Concerns about pollution were rampant and there were many influential thinkers who felt that we would not be able to grow enough food to feed everyone.
Paul Ehrlich, in particular, was a Stanford University biologist who wrote a book “The Population Bomb.” His forecast of hundreds of millions starving to death in the 1970s and 1980s, including 65 million Americans, were taken very seriously. He also predicted doom for India and that England would not exist by the year 2000.
Here we are 40 or 50 years later and while there are hungry people all over the world, there isn’t a global famine of the proportions many people thought was imminent. What happened? People are pretty good problem solvers and Norman Borlaug — along with others — created what’s known as the Green Revolution.
When a 13-year old Marie-Sophie Germain was stuck in the house because of the chaotic revolution on the streets of Paris in 1789, she found a refuge for her active mind: her father’s mathematics books. These inspired her to embark on pioneering a new branch of mathematics that focussed on modeling the real world: applied mathematics.
Post-revolutionary France was not an easy place for a woman to study mathematics, though. She taught herself higher maths from her father’s books, eventually persuading her parents to support her unusual career choice and getting her a tutor. After she had learned all she could, she looked at studying at the new École Polytechnique. Founded after the revolution as a military and engineering school to focus on practical science, this school did not admit women.
Anyone could ask for copies of the lecture notes, however, and students submitted their observations in writing. Germain got the notes and submitted her coursework under the pseudonym Monsieur Antoine-August Le Blanc. One of the lecturers that she impressed was Joseph Louis Lagrange, the mathematician famous for defining the mathematics of orbital motion that explained why the moon kept the same face to the earth. Lagrange arranged to meet this promising student and was surprised when Germain turned out to be a woman.
Gauss and Germain
‘Le Blanc’ also corresponded with German mathematician Carl Friedrich Gauss on number theory. When Napoleon’s armies occupied the town the famous mathematician lived in, Germain enlisted a family friend in the army to check that Gauss had not been harmed. Gauss didn’t realize who had helped him out, until he discovered that ‘Le Blanc’ was Sophie Germain, he wrote to her thanking her for her concern and praising her mathematical prowess given the hurdles set before her.
“How sweet is the acquisition of a friendship so flattering and precious to my heart. The lively interest you took during this terrible war deserves the most sincere recognition….But when a person of this sex, who, for our mores and prejudices, must recognize infinitely more obstacles and difficulties than men to become acquainted with these thorny searches, knows how to get rid of these obstacles and to penetrate what they have, most hidden, must undoubtedly, she has the most noble courage, talents quite extraordinary, genius superior.”
As well as working on the thorny and theoretical problems of number theory, Germain worked on applying mathematics to real world problems. One of these was a challenge set by the Paris Academy of Science to mathematically describe the elasticity of metal plates. An experimenter called Ernest Chladni had demonstrated that a metal plate would resonate in odd ways when vibrated at certain frequencies. If you put sand on the plate, it would collect in different patterns created by the resonance of the plate, called Chladni figures. To win the prize, the solution had to predict these figures.
The Mathematics of Stress and Strain
Mathematically predicting the behavior of metal plates could make it easier to design metal objects and predict how they would behave under stress. The prize was set in 1808 but was so difficult that Germain was the only one who decided to try to solve it, as it required coming up with a whole new way to analyze and describe how materials bend and change under stress.
The first two solutions that she submitted were rejected due to mathematical errors, but the third version won her the prize in 1816. However, due to the Academy policy of not allowing women to join (and to only attend events if they were wives of members), Germain was not able to attend the ceremony where the prize was granted. She was also not allowed to attend meetings of the Academy. After the Academy failed to publish her prize-winning work, Germain had to pay to publish the work herself in 1821.
Later, her friend Joseph Fourier allowed her to attend meetings and presentations, but the mathematical establishment never really accepted her, or her work. In a letter to a colleague in 1826 she complained about the way they rebuffed her:
“These facts are my domain and it is to me alone that they remain hidden. That’s the privilege of the ladies: they get compliments and no real benefits.”
In the same letter, Germain complained of suffering fatigue and she was diagnosed with breast cancer shortly afterwards. She died in 1831. Her final years were spent working on a solution to Fermat’s Last Theorem, and just before her death she published a partial solution that was the basis for much research into the theorem, which was finally solved only with computer help in the late 1990s.
Although Sophie Germain never earned a degree in her lifetime, she was given an honorary degree in 1837 from the University of Göttingen at the suggestion of Gauss, who noted that
“she proved to the world that even a woman can accomplish something worthwhile in the most rigorous and abstract of the sciences and for that reason would well have deserved an honorary degree.”
The Academy that snubbed her also now offers an annual prize for mathematics in her name. Perhaps more importantly, her work formed the basis of the study of elasticity and stress in metals that allowed engineers to build larger objects and buildings. Creations such as the Eiffel tower in 1887 were directly influenced by her work, and it laid some of the groundwork for Einstein’s theory of General Relativity.
Modern scholars argue that Germain could have been more than she was: her work, they argue, was hamstrung by a limited understanding of some of the fundamental concepts that Gauss and others had described. Although her work was fundamental and important, if she had been given free access to the education that she wanted and deserved, it’s easy to imagine that she would have gone farther.
Like most accidents, it happened in an instant that seemed to last an eternity. I had been felling trees for firewood all afternoon, and in the waning light of a cold November day, I was getting ready to call it quits. There was one tiny little white pine sapling left that I wanted to clear, no thicker than my arm. I walked over with my Stihl MS-290, with a brand new, razor sharp chain. I didn’t take this sapling seriously — my first mistake — and cut right through it rather than notching it. The tree fell safely, and I stood up with both hands on the saw. Somehow I lost my footing, swiveled, and struck my left knee hard with the still-running chainsaw. It kicked my knee back so hard that it knocked me to the ground.
In another world, that would likely have a been a fatal injury — I was alone, far from the house, and I would have had mere minutes to improvise a tourniquet before bleeding out. But as fate would have it, I was protected by my chainsaw chaps, full of long strands of the synthetic fiber Kevlar.
The chain ripped open the chaps, pulled the ultrastrong fibers out, and instantly jammed the saw. I walked away feeling very stupid, very lucky, and with not a scratch on me. Although I didn’t realize it at the time, I owed my life to Stephanie Kwolek.
In 1962, John Glenn sat in his capsule waiting for his rocket engines to light-up and lift him to space. But first, he insisted that Katherine Johnson double-check the electronic computer’s trajectory calculations. While that’s the dramatic version of events given in the recent movie, Hidden Figures, the reality isn’t very far off. Glenn wasn’t sitting on the launchpad at the time, but during the weeks prior to launch, he did insist that Johnson double-check the computer’s calculations.
So who is this woman who played an important but largely unknown part of such a well-known historical event? During her long life, she was a wife, a mother, an African-American, a teacher, and a human computer, a term rarely used these days. Her calculations played a part in much of early spaceflight and in 2015, she was awarded the Presidential Medal of Freedom by President Obama. She also has a building named after her at the Langley Research Center in Hampton, Virginia.
Hamilton soon moved on to the SAGE program, writing software which would monitor radar data for incoming Russian bombers. Her work on SAGE put Margaret in the perfect position to jump to the new Apollo navigation software team.
The first two solutions that she submitted were rejected due to mathematical errors, but the third version won her the prize in 1816. However, due to the Academy policy of not allowing women to join (and to only attend events if they were wives of members), Germain was not able to attend the ceremony where the prize was granted. She was also not allowed to attend meetings of the Academy. After the Academy failed to publish her prize-winning work, 
