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## Sunday, 15 October 2017

### On the Shoulders of...

Those who have learned to walk on the threshold of the unknown worlds, by means of what are commonly termed par excellence the exact sciences, may then, with the fair white wings of imagination, hope to soar further into the unexplored amidst which we live - Ada Lovelace

Earlier this week was Ada Lovelace Day and, after my last outing, which was emotionally draining and took some recovery, I thought I'd do something a little more pleasant and cobble together a quick tribute to women in STEM to celebrate. I started, some time ago, to write a post about the unsung heroes of science. It's a massive topic, for fairly obvious reasons, but even I didn't realise just how massive. Just in researching one of the people I'd intended to write about, it quickly became apparent that a post was simply insufficient to even begin to broach the subject, and the idea has burgeoned into a book, or possibly a series of books. Almost all of the people that I wanted to include in that post were women, not least because, despite genuinely Earth-shattering contributions to the sciences, they seem to be equally Earth-shatteringly under-reported which, in my opinion, is nothing short of criminal. It's a sad and damning testament to the attitude of society that most of the women here are hardly known outside scientific circles.

Research in science, technology, engineering and mathematics has traditionally been dominated by men. This is not, as one might think, because these aren't suitable topics for girls, or because girls shouldn't worry their pretty little heads about them, despite what you may have heard. Some of the most important people in the history of these fields have been, and continue to be, women. Still they're horribly under-represented in these areas of academia.

Don't let that put you off, though. It can be hard, but only you, by taking up these subjects and excelling in them as we know you can, can make the difference and begin to erode the dominance of men. You can do this, by being the difference you (and we) want to see in the world.

So here's my little tribute to the awesome women who've made essential contributions, to science especially, as that's what I know best. Let it stand as a flavour of what's to come.

I'm going to start with one of the great heroes of physics and mathematics.

Amalie Emmy Noether was born in Erlangen, Germany in 1882, and her story is one of those that should inspire, yet she's little known outside the sciences. The daughter of an autodidactic mathematician, Max Noether, whose own contributions to mathematics were substantial, most notably in algebraic geometry, Emmy originally qualified as a teacher of English and French. She decided, however, to pursue the study of mathematics, and attended Erlangen University. At that time, women were allowed to study at university only at the discretion of the professors delivering the courses. Eventually finishing her dissertation in 1907, she worked at Erlangen for the next seven years without pay.

In 1915, David Hilbert and Felix Klein invited her to the University of Göttingen, then a world-renowned centre of mathematical research. Because of objections by faculty of the philosophy department, she gave lectures under Hilbert's name for four years - again unpaid - until the approval of her habilitation in 1919, which allowed her to become a doctoral supervisor. Emmy didn't actually get paid for her lectures until the creation of a special title 'algebra lecturer' in 1923.

Noether went on to have major impact on various fields in mathematics and physics, notably abstract algebra, topology, Galois theory, and many other areas. I'll briefly come back to this to show just how profound her influence was, and how that influence still impacts discoveries being made today.

Her biggest contribution was a unification of disparate concepts in physics, collectively known as 'conservation laws'. Anybody who's done any study in physics at any level at all has come across these, but it's worth a little unpacking. First, though, on the route to understanding, we need to talk about symmetry. This takes us a little off course but I think it's worth it, because it will give greater clarity later on.

Symmetry is one of the most important concepts we discuss, not just in STEM, but outside it as well. Art, architecture, music... However, it also plays massively important roles in biology, chemistry and all areas of nature. Where it takes on the deepest meaning, however, is in modern physics.

We all remember, I'm sure, learning about symmetry in maths class. For some of us, that requires a pretty long memory. It's not a difficult concept to grasp in its most basic terms.

Picture a square. Draw lines that bisect it exactly, and you can see the lines of symmetry. We think of it as all the places you can fold it exactly in two. This is a good guide to symmetry, but it doesn't really capture the essence of what symmetry is. Think, instead, of each of those lines as an axis about which the square can be rotated and still look exactly the same when you're done. This also applies to rotation about the axis going from front to back through the centre of the square.

Now pick the square up, move it one metre to the right, and drop it again. You'll see that, aside from its location, it looks exactly the same as it did in the original location. This is also a feature of symmetry.

In the jargon, changes to a system are known as 'transformations'. A symmetry, then, is any instance of a transformation that has no effect on the outward result. This is going to become important, as we explore other, slightly less obvious symmetries.

Two of the most important of these symmetries were first formalised by Galileo Galilei, famed for dropping balls from the Leaning Tower of Pisa (although this tale is almost certainly apocryphal) and for getting into hot water with the church for suggesting that the Earth wasn't the centre of the universe. He noted that any experiment conducted facing East, to pick a direction at random, should yield precisely the same results as the same experiment conducted facing West, or indeed any other direction. You should easily be able to see the parallel here, and precisely why this is the same kind of symmetry as rotating that square about any given axis. As one might expect, this is a case of rotational symmetry in precisely the same way.

The second of these important insights was that an experiment conducted in Pisa should yield exactly the same result as the same experiment conducted in Rome. This is a slightly different kind of transformation, so it isn't immediately obvious how this relates to symmetry. In this case, we're looking at an instance of what's known in the jargon as 'translational symmetry', and it exactly reflects the act of picking up the square and moving it a metre.

The first one of these to appreciate is probably conservation of momentum, as it's one we all have some experience of. This law is expressed in Newton's First Law of Motion thus:
In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
This is, of course, the modern statement of it, as Newton's original formulation is problematic, especially in dealing with rigid bodies, deformable bodies and other things such as non-inertial frames, but this is what we're all familiar with. Mathematically, it can be expressed (for completeness) in the form:

$\sum F=0 \Leftrightarrow \dfrac {dv}{dt} = 0$

This assumes a constant non-zero mass. In natural language, if the vector sum of all forces acting upon a body is zero, then the velocity of the body remains constant. Remember that velocity is a vector quantity, meaning that it has both magnitude and direction, thus the velocity can change even while the speed - a scalar quantity having only magnitude - remains unchanged.

Confused? Wondering what all this has to do with symmetry?

Enter Emmy Noether.

David Hilbert, widely regarded as probably the most influential mathematician of the early 20th century, along with Felix Klein, formulator of the Klein bottle, one of the possible solutions to the topology of the universe, invited Noether to Göttingen to help the to understand Einstein's General Theory of Relativity, as her expertise in invariance, they hoped, would help them to grapple with it. Hilbert had noted that conservation of momentum seemed to be violated by it, because it suggested that gravitational energy could gravitate. Noether resolved this apparent paradox and, along with it, provided one of the fundamental tools of modern theoretical physics. Along the way she laid the groundwork for what ultimately became the research that won this year's Nobel prize for physics; gravitational waves.

What Noether did, in a nutshell, was to unify all symmetries under a single framework and, in so doing, tied them all together, along with all conservation laws. In particular, her first theorem shows that every single differentiable symmetry was a manifestation of some conservation law, and vice versa.

"Well," you might say, "so what?"

It's difficult to express just how important this idea is. It's especially important because symmetries and the breaking thereof are among the most important concepts in physics. Why do we inhabit a universe dominated by matter? CPT symmetry violation. Why can nothing travel faster than lightspeed?  Lorentz invariance symmetry. Rotational symmetry is conservation of angular momentum, the same principle that relates the orbital velocity of the moon to the area of the wedge swept out in a given period of time. Translational symmetry is conservation of momentum, the same principle underpinning Newton's First Law above. Here's a table of exact conservation laws and their respective symmetries.

It really is impossible to overestimate the contribution Emmy Noether made to modern physics and, frankly, I could carry on in this vein for hours (and that's without even leaving her first theorem, which is a tiny portion of her contribution), but I really must crack on, because there are still quite a few to talk about. I'm not going to cover any of them in quite this detail, but Emmy was worth it, and it's a travesty that her name is so little-known outside academic circles. As far as I know, no complete biography of her exists for adults, only two children's books. I highly recommend finding out about her and her many contributions to science and mathematics.

So, let's move on and look at some other amazing women in science.

Next up, somebody whose influence on the modern world is difficult to calculate. Her work was not only the foundation of the nuclear age, it ultimately killed her. I'm talking, of course, about the most successful person in the history of the Nobel foundation's prizes for science, Madame Marie Curie.

Thankfully, this is at least a name that most are familiar with. Born in Poland, then a kingdom of the Russian Empire, to two teachers, Marie studied initially in the famous 'Flying University', an underground academic establishment rooted in traditional Polish scholarship and resistant to the ideologies of first the Prussian and later the Russian authorities.

She later moved to Paris, following her sister Bronislawa, and completed her studies. She was a pioneer in the study of radioactive materials and discovered two new elements, both radioactive. The second of these, radium, became ubiquitous in commerce, because it was luminescent. It found its way into paints used on watch and clock faces, all kinds of beauty products, and even toothpaste. This, of course, was before it was properly understood how damaging radiation is to living cells.

Curie was the first woman to win a Nobel prize and the first person to win two - still the only woman to have done so, which is fairly damning in and of itself. She also remains the only person to have won Nobel prizes in two different scientific disciplines, sharing the 1903 physics prize with her husband Pierre and physicist Henri Becquerel, whom we met briefly in Calilasseia's wonderful guest post on radiometric dating, and winning the 1911 prize for chemistry in her own right. Indeed, Curie's family won a total of five Nobel prizes between them, making them a remarkable family by any measure.

She was a pioneer in isolating radioactive elements, coined the term 'radioactivity', developed mobile X-Ray technology for field hospitals during World War I, and founded the Curie Institutes in Paris and Warsaw. These are still pioneering centres of medical research to this day.

Curie died in France in 1934 of aplastic anaemia, a direct result of her research in radiation and her work in field hospitals during the war. The influence of her work underpins much of the modern world, not least in nuclear weapons and energy, as well as having huge relevance in areas such as the aforementioned radiometric dating.

Next up, something of an oddity that many will have heard of in a completely different context.

Hedy Lamar was an Austrian actress and one of the most popular leading ladies in Hollywood in the thirties and forties. She starred alongside some of the biggest names in the history of film, including Clark Gable, Spencer Tracy, George Sanders and Bob Hope.

What's not widely known about her is that she was also something of an inventor. Largely autodidactic, she dabbled in quite a few things. She attempted to invent a tablet that, when dissolved in water, could carbonate water. She made improvements to stop lights, and she did some self-study in aerodynamics which aided Howard Hughes in improving his aircraft designs, being largely responsible for the earliest curved wing designs to aid efficiency.

During WWII, she learned that the torpedoes in use at the time, radio controlled, could be fairly easily jammed, which meant that they could be driven off course and fail to hit their targets. Borrowing on knowledge she'd picked up from her first marriage to Austrian arms manufacturer Friedrich Mandl, she had the idea of a frequency-hopping system that would allow torpedoes to modulate their control frequencies, thereby hampering attempts to jam them. With her friend, pianist George Antheil, she developed a miniaturised pianola mechanism with radio signals. This device was patented in 1942, although implementation was problematic, so it wasn't used during the war. However, an updated version of the same device appeared on US Navy ships from 1962.

In 1997, she was co-recipient of the Electronic Frontier Foundation Pioneer Award along with Antheil, and they were both inducted posthumously into the National Inventors Hall of Fame in 2014.

I'm going to move on to another pioneer of modern science that has sadly been largely overlooked.

Since the publication of Darwin's epic work in 1859 that identified the process that directs evolution, and the work by Gregor Mendel in quantifying heredity, the race was on to identify the precise mechanism which drove the inheritance of traits. Only a decade later, in 1869, Friedrich Miescher, a Swiss surgeon, isolated a 'microscopic substance' in the nuclei of cells in pus from discarded bandages. Due it's source, he named it 'nuclein'. Less than a decade later again, Albrecht Kossel isolated nucleic acid and identified the five primary nucleobases. Then in 1919, Phoebus Levene, a Lithuanian born American, pinned down the nucleotide unit of base, phosphate and sugar.

Discoveries proceeded at a pace until, in 1952, Alfred Hershey and Martha Chase - the latter being yet another overlooked name in science but for whom we have insufficient space here - finally confirmed the role of DNA in heredity. Only a year later, Francis Crick and James Watson, working at the famed Cavendish laboratory in Cambridge, published work identifying the helical structure of DNA.

It's fairly well-known by now that their work would have been impossible without the input of somebody else, then working as a research associate in X-Ray crystallography at King's College, London. That researcher is, of course, Rosalind Franklin. This is, at least, a name that most will have encountered. It was her imaging studies and, in particular, one image, photo 51, that gave them the much-needed clue. It's been suggested that this picture was actually taken from her drawer without her knowledge by Maurice Wilkins, though there is some doubt as to the veracity of this claim. It's certainly the case that it was Franklin's work, and especially a lecture she delivered in November 1951 at King's College, dealing with two forms of the DNA molecule and in which she specified the water content of the molecule - critical to molecular stability - and the fact that the phosphates were located to the outside of the molecule, were crucial to all later constructions.

Crick and Watson received the 1962 Nobel prize for chemistry. The rules of the Nobel society prohibit posthumous awards and, sadly, Franklin had died of ovarian cancer in 1958, aged only 37 years old. To be fair to Crick and Watson, both men acknowledged that Franklin should have received a Nobel for her contribution, had it been worn prior to her death.

It's worth noting that her work also included major contributions to the structure of viruses, among other things, and that these contributions were at least recognised in her lifetime.

Next, another favourite of mine, and again at least one that many have heard of although, I suspect, that's more to do with how the discovery that made her famous was initially interpreted.

Born in County Armagh, Northern Ireland, Jocelyn Bell first became interested in astronomy while her father, an architect, was working on Armagh Planetarium. Unfortunately, girls weren't allowed to study science, but her parents were having none of that, and just as well. Jocelyn went on to study physics and, as a post-graduate, was working on a radio telescope that she'd worked on the construction of with her thesis advisor, Antony Hewish. While analysing data sets, she discovered a strange repeating signal that, due to its regularity, was thought to be of non-natural origin, much like the submarine pulsing in The Hunt For Red October. Once terrestrial sources were ruled out, this left only extra-terrestrial intelligence as a candidate, because no natural source was known that could emit a signal with such regularity. The source of the discovery was dubbed LGM-1 - 'little green men'. Of course, as we now know,  this turned out to be a previously unobserved type of star, a pulsar, which is a star made primarily of neutrons, rotating rapidly and beaming out radio jets, hence the regularity of the radio pulses.

Hewish was awarded the 1979 Nobel prize for physics (along with astronomer Martin Ryle), for his work in the development of radio aperture synthesis that made the discovery possible, but Bell was excluded from the award. She went on to have a distinguished career and, despite the exclusion, has no regrets about it.

Just room for one more, and this is a really special one.

During the fifties and sixties, the US and the USSR were locked in a war of ideology. This war played out on many fronts, but perhaps the front on which they waved their todgers about the most was the space race.

Now, getting to space, even low-Earth orbit, is no trivial matter. The technological challenges in this were absolutely colossal. The Germans had made a good deal of headway in rocketry during WWII, and of course many of the scientists, not least Werner von Braun, the father of rocketry, had ended up in the employ of the Americans, so the foundations were pretty much in place.

What's not immediately obvious to a non-scientist is the enormous amount of mathematics involved, in calculating trajectories, mass to fuel-mass ratios to ensure sufficient fuel not just to get off the planet but also to return safely.

This is where our next hero comes in.

Katherine Johnson, in her own words 'grew up counting everything'. She showed a gift for mathematics even as a young girl in Greenbrier County W.Va. Her parents arranged for her to attend high school in a neighbouring county, as Greenbrier didn't offer public schooling to African-Americans beyond 8th grade. She graduated high school at 14, and earned degrees in mathematics and French by 18 at West Virginia State College. After teaching for two years in a black public school, she entered a graduate programme at West Virginia University in Morgantown, the first African-American woman to do so, though she became pregnant after a year and dropped out.

In 1958, she heard at a family event that the organisation that would eventually become NASA were hiring mathematicians, She applied and was taken on as a 'human computer'. This was extremely advanced work, plotting trajectories, and she was responsible in large part for the success of the American space programme. Most of this was in a time when segregation was still rife, in a sphere dominated by men.

Johnson was awarded the Presidential Medal of Freedom in 2015 by Barack Obama.

I'll leave it there, other than to say she wasn't alone in this journey, much of which can be seen in the fantastic Hidden Figures, starring Taraji P. Henson as Johnson.

Finally, I'm just going to list some of the incredible women who've contributed to STEM fields with some of their achievements, many of which have gone largely unnoticed by the general public.

Henrietta Leavitt - Discovered the relationship between the period and luminosity of cepheid variable stars. This discovery allowed them to be used as 'standard candles', meaning that they could be used for distance calculations beyond the limits of parallax, and eventually paved the way for Hubble's observation that the universe is expanding.

Lise Meitner - Co-led the team, along with Otto Hahn, that discovered fission of uranium under absorption of an additional neutron. Her work with Hahn, and further work with Otto Frisch, was the foundation of our understanding of fission, and led directly to the nuclear bomb and fission reactors used in the generation of power un nuclear power stations. Element number 109 in the periodic table is named after her. She also wasn't included in the nomination for the Nobel prize granted for this work, the 1944 prize for chemistry that was awarded to Hahn.

Dorothy Vaughan - Supervisor for NASA. One of the female computers responsible for calculations involved in space missions. When her department was being disbanded, she taught herself COBOL programming language so that she could operate the newly-installed digital computers at NASA. Also a subject of the film Hidden Figures mentioned above, played by Octavia Spencer.

Mary Jackson - Engineer for NASA. One of the female computers for NASA mentioned above, and the final subject of the film Hidden Figures, played by Janelle Monáe. Can't recommend this film highly enough.

Dorothy Hodgkin - British chemist who developed X-Ray crystallography and discovered the three-dimensional structure of biomolecules, including penicillin, vitamin B12 and insulin. She was awarded the Nobel prize for chemistry in 1964.

Vera Rubin - American astronomer whose pioneering work in the rotation rates of galaxies produced the discovery of a discrepancy between observed angular motion and the theoretical predictions of General Relativity, as discussed in an Scale Invariance and the Cosmological Constant. This was one of the great paradigm shifts in our understanding of the constituents of the universe.

And finally...

Just a few words about the woman at the head of this post.

Ada Lovelace was a mathematician and logician, and the first person to recognise the potential for computers to solve analytical problems beyond mere calculation. She worked with Charles Babbage on his 'analytical engine', a mechanical computer. As the writer of the first true computer algorithm - a means for the analytical engine to compute Bernoulli numbers, she was the world's first computer programmer. In notes she prepared for a lecture on the analytical engine in Turin, she wrote:
"it 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."
I'm going to finish with some shoutouts to notable women around today who might, should things not improve considerably as one hopes they will, be the unsung heroes of the future. Here's to hoping that that doesn't happen, and that women and other minorities find their places at the table in precisely the manner they deserve. What I've represented here is a tiny taste of the incredible work that women have done in the furtherance of science, often without the recognition that any man could expect for a similar contribution. This has to change, because science progresses fastest and brings the greatest benefit when every capable mind is given licence to explore. I'm going to restrict myself to the marvellous women I follow on twitter in STEM and scicomm, and I recommend you follow them all.

I also hope that anybody reading this will leave some more names in the comments. Tell us about your favourite women in STEM, what they do, and how we can access their work.

Dr Janna Levin - Cosmologist at LIGO. Work has been historically focussed on nontrivial topologies of the universe, and implications for the size of the universe, specifically whether it's finite. Author of the marvellous Black Hole Blues and Other Songs From Outer Space, a history of LIGO from first concept to gravitational-wave detection, the discovery that won this year's Nobel in physics (unfortunately not for Dr Levin).

Dr Chanda Prescod-Weinstein - Theoretical astrophysicist working in early universe cosmology, cosmic expansion and acceleration and dark matter. Staunch advocate and mentor to minority students, and vocal activist for equality in and out of the sciences.

Dr Yana Weinstein - One of my favourite tweeps, whom we've met in several past outings (she always brings me the best WOTI*), Doctor Why is aptly named. She questions everything. Quite literally. Founding partner of Learning Scientists, who we met in Does My Class Look Big in This? along with the equally brilliant Dr Meghan Sumeracki they, with their partners Dr Cindy Nebel and Dr Carolina Kuepper-Tetzel, are behind a quiet revolution in education. Their evidence-based techniques and strategies for learning and retrieval are gently but forcefully shaking up the way we think about learning. Their techniques are being used and lauded by teachers all over the world.

Prof. Alice Roberts - Palaeopathologist, osteoarchaeologist, every other kind of biologyologist, author, TV presenter and merciless debunker of creationist woo, as well as Professor for Public Engagement in Science at Birmingham University.

Dr Katie Mack - Astrophysics research fellow focussing on dark matter at University of Melbourne.

Dr Clara Nellist - Particle physicist working on the ATLAS project at CERN.

Dr Sarah Tuttle - Instrumental astrophysicist working on novel approaches to imaging diffuse matter.

I'm going to leave this here, but I may update this with other awesome and kickass women in STEM. If this is a topic that interests you, I have another article about an amazing project bringing STEM education to young women (and young men) in Kenya, which you can find HERE.

Maybe you, too, can appear in an article like this in the future. Or maybe, just maybe, you can be the woman who doesn't need an article of this nature, because you've managed to shatter all the barriers and show that all minds are needed to better progress in science.

Thanks for reading, and don't forget to leave comments about the women in STEM fields that inspire you.

*Wrong On The Internet - somebody always is.