Monthly Archives: October 2015

Women in Science: Emmy Noether

The first in my Women in Science series has to be Emmy Noether, described by Einstein himself as “the most significant creative mathematical genius thus far produced since the higher education of women began”. She’s easily one of my favourite physicists of all time, even though she only has one major contribution to physics: Noether’s Theorem.

From Wikipedia

Of course, when Einstein produced that quote, the higher education of women had not been around for very long, so it’s not a very crowded competition for “most significant creative mathematical genius”. I’m also not qualified to judge how good most of her work is, since it exists well outside my area of expertise, in abstract, pure maths. Noether’s Theorem, however, deserves explaining in detail, along with a brief discussion of her life and times.

Born in 1882 in the German town of Erlangen, her father, Max, was also a mathematician. This proved to be invaluable in getting her career started, as she was able to work as an academic under her father’s name, thereby avoiding restrictions on women holding academic positions. She received her PhD in 1907 and worked thereafter in academia until her death, but wouldn’t be paid for her academic work until 1923. 

She faced constant institutional sexism in every institution she worked at for decades. When two of the great mathematicians of their day, David Hilbert and Felix Klein (of the Hilbert Hotel and Klein Bottle respectively), tried to recruit her to teach at the University of Göttingen in 1915, they faced opposition from other faculty members. Hilbert, an interesting character in and of himself, responded with a quote I rather enjoy, “I do not see that the sex of the candidate is an argument against her admission as privatdozent [lecturer]. After all, we are a university, not a bath house.” Again, when at Göttingen, she lectured under Hilbert’s name.

Noether did research at Göttingen until 1933. This was, of course, the year that Hitler became Chancellor, and Noether was (you guessed it) Jewish. The expulsion of Jewish academics from university positions was among the first of Hitler’s antisemitic policies to be enacted in Germany. She was by no means the only one affected by this — a decent fraction of the Manhattan Project was staffed by German Jewish exiles. Noether was noted by many of her colleagues for being particularly courageous at this time, and for providing comfort for them. Like many of her colleagues, she moved to America. Specifically, she accepted a post at Bryn Mawr College in Pennsylvania. It was her last position — she died in 1935. She was 53.


That’s her story. I want to talk a bit about her Theorem, because it is truly remarkable. It came out of the study of General Relativity, but applies to all theoretical physics. The reason it’s so revered is because it provides a deep, profound connection between two of the most important concepts in physics — conservation laws and symmetries.

A conservation law is a law of physics which states that, for a given system, something is conserved. Energy is the most famous example — it can be neither created nor destroyed, only converted from one form to another. If one system loses energy, that must mean another system has gained the equivalent amount. There are, of course, many other conservation laws. Momentum is one, angular momentum is another, as are more exotic ones like charge, lepton number, parity, and more.

Conservation laws are loved by physicists because they impose constraints on what physical systems can do, making them easier to predict. Particle physics, for example, uses conservation of momentum to tell how many particles are involved in a given interaction. This is how the neutrino was discovered: they noticed certain decays weren’t conserving momentum, and so concluded that an undetected particle was carrying some away. You can use conservation of energy to do this:

From Cosmos: A Spacetime Odyssey, 2014


Neil deGrasse Tyson didn’t flinch because he knew energy would be conserved — the pendulum couldn’t swing further than his nose because it didn’t have enough energy to do so, and had no way to gain it.

Symmetries are another concept beloved by physicists. We love to study symmetric systems because they’re a lot easier to study! If a system looks exactly the same after you transform it in some way, then if you can describe it in one state, you can also describe it in the transformed state equally well. For a concrete example: if I tell you that a ball is perfectly symmetric, and that one square inch on it is green, then the rest of it must be green, too, otherwise it wouldn’t be perfectly symmetric! For many non-symmetric systems, we often describe them as being symmetric, plus a correction term for any asymmetry. Asymmetries are aberrations we need to handle delicately, most of the time.

The green ball is an example of rotational symmetry. If you rotate that ball through any angle, about any axis, it will look the same. There are other symmetries associated with other transformations. The laws of physics are the same at any point in space (we assume), so you can move your experiment anywhere in space and not be able to tell — this is translational symmetry. The same applies to time — we assume physics has been and will be the same at all points in time, giving us time translational symmetry. Symmetries are also of great use to particle physicists, who use symmetry considerations to derive theoretical results. The mathematical study of symmetries is called group theory, and the theoretical underpinning of particle physics is built on that.

A typical interaction at CERN. You can use symmetry considerations and conservation laws to get lots of data about the particles from this kind of event.


Now we finally get to Noether’s Theorem. According to the theorem, every conservation law is associated with a symmetry, and vice versa. It’s a theorem, meaning it’s derived from mathematical results, and is provably true. The mathematics is very involved, but essentially, if there is a system you can transform without changing it, it must have an associated conserved quantity. The best example is energy, which is associated with time invariance. If a system doesn’t change over time, then its energy must be conserved. At a fundamental level, the reason for conservation of energy is time invariance, under Noether’s Theorem.

Similarly, conservation of momentum is associated with translational invariance. If you can take a system and move it anywhere without it changing, then momentum must be conserved. (This makes sense if you think about the opposite — when moving a system does change it, it must mean something’s in the way in its new position. Whatever that is, it’ll affect the system in some way, changing its momentum.) Also, conservation of angular momentum associates with rotational invariance. Those are the simplest examples, but there are countless others.

Noether’s theorem allows you to describe conservation laws, but it also allows you to derive new ones. Just observe any symmetries a system has, and then give a name to whatever the conserved quantity associated with it is. Once you know that quantity is conserved, you can use it as an experimental tool to make powerful predictions about the system’s properties. Similarly, if you see a quantity not being conserved, that gives you information about asymmetries inherent in the system.

As I hope you can see, we like conservation laws, and we like symmetries, so to have a fundamental connection between them, as outlined in Noether’s Theorem, is quite amazing. It’s also a really powerful theoretical tool that can be used to derive all sorts of amazing results. It’s easily one of the most important theorems in theoretical physics, as it’s one of those rare results that applies to all areas of physics. I’ve even heard it compared to Pythagoras’ Theorem in terms of importance. Noether was an unparalleled genius, and I hope an appreciation of the beauty and elegance of her most famous theorem can help you appreciate that.

Women in Science

Science is a man’s world. Sadly, the historical forces which keep women out of the sciences still exist today. The clearest example of this is at Imperial College, where I did my undergraduate degree. Students there speak in hushed tones of The Ratio, that infamous spectre that haunts college life. The Ratio states that for every woman at the college, there are two men. The reason for this is that Imperial College is solely for science, engineering and medicine, and these are all male-dominated fields.

Imperial. Ahh, good times.

Within departments the stories are different. Medicine, for example, has an encouraging near-parity of genders, and a couple of life sciences courses have a slight imbalance in favour of women. Physics, however, sits glumly down at four men for every woman, roughly speaking, and computing roughly averages a dismal nine in most years. And that’s just the students.Throughout my degree I only had one female lecturer (out of over 40), for example. I don’t want to single Imperial out entirely. It’s exceptional only because it’s only a science, engineering, and medicine university. In the equivalent departments across the country and world, the story is the same.

I don’t believe for a second that this is all because women intrinsically ‘like science’ less than men. Frankly the kind of people who do believe that are not worth engaging with. More needs to be done at every level, from nurseries to committees appointing new professors, to equalise The Ratio at every university in the world. It’s a daunting task, but a vital one. The actual reason women are not choosing science, and why women are not reaching the highest levels of scientific careers as much as men are, has to be explained at a cultural and societal level. When expressed like this, it’s a clear problem that needs to be solved.

The LEGO ACADEMICS Twitter account tweets updates from the Lego scientists at the Lego Research Institute, whilst also fighting the idea that science isn’t for girls!

For some reason we still live in a world where calling oneself a feminist is seen as controversial by some. I don’t want to wildly speculate on psychology too much, but from my perspective it seems as though the reason men (and it is mostly men) choose to reject the word and all that it implies is because it would mean forcing them to accept that where they are in life isn’t solely the result of their skill and effort, but is also partly due to privileges they were born with that they have no control over. “Check your privilege” is a clichéd term these days, but it exists for a reason.

No one wants to hear that simply by existing where they are they are unwittingly contributing to a system that (for example) discourages women from being scientists, and denies them the success they deserve in the sciences. However, there is a lot of truth to that idea. It sucks, but it’s the world we live in, and denying it doesn’t help anyone, not even the denier in the long term. Heck, even me writing this blog post is a symptom of the problem — I’m using my privileges as a man in science to assert my position on the issue, instead of promoting an equivalent female voice. This is why I care strongly about these causes, and why we need to work towards a more egalitarian scientific community. Or, to put it bluntly, this is why we need to “smash the patriarchy”.

One of the ways we can help achieve these goals is by acknowledging the historical contribution women have made to the sciences. True, for historical reasons, the overwhelming majority of scientists have been men, and the overwhelming majority of significant scientific discoveries have been made by men, but there are many, many women who have made amazing contributions over the centuries. Many of these women have been obscured in some ways, or overshadowed by male colleagues. A few have even been denied Nobel Prizes. With all this in mind, I’m going to make a semi-regular effort to document here some stories from women in science throughout the centuries, and maybe even from some contemporary ones! I hope you enjoy it!

The Science Communicators (2)

Last week I talked about science communication. As promised, this week I’m making a list of the various web-based science communication outlets I’m subscribed to.

1. Numberphile, Sixty Symbols, Periodic Videos, etc. The three listed here are by far my favourite. They’re listed together because they’re all part of the herculean efforts of one man, the hard-as-nails Brady Haran. Brady is a video journalist with no formal training as a scientist. In these channels, and others, he interviews scientists to try to get them to explain tricky concepts from their fields. Numberphile is for maths, and has explanations of everything from the Riemann Hypothesis to Klein Bottles. Sixty Symbols is physics, Periodic Videos is chemistry (geddit?) etc. etc.

Image from Brady Haran @
Brady interviewing Professor Sir Martyn Poliakoff

What I love about Brady’s videos is his skill as an interviewer. Whenever the scientist is explaining something I know about, I’m always amazed by how Brady always seems to ask exactly the right question to prompt the interviewee to explain the concept in the most clear way possible. When it’s about something I don’t know about, Brady’s question is usually exactly what I was wondering about this weird new thing. He has an inquisitive mind, but no formal scientific training, making him the ideal person to drag scientists out of their offices into the limelight. If there’s one (set of) channel(s) you check out from this blog post, make it Brady’s.

2. Veritasium is run by Derek Muller, a physics graduate who also has a PhD in physics education. Derek has a knack for pedagogy, and along with general videos explaining physics concepts in clear ways, he has two other cool tricks up his sleeve: firstly, he uses vox pops to see what the average person on the street believes about whatever he’s trying to explain. By highlighting the inaccurate preconceived notions we all have about things, he can dislodge them from our brains more easily, and replace them with the right ideas. Secondly, Derek often sets up puzzle videos, where he waits a week to reveal the answers. Interactivity is always better for making difficult concepts stick in the brain, and I’ll admit to having been stumped by more than one of them.

3. Crash Course is not entirely science-oriented, but deserves a mention nonetheless. Created by the famous Vlog Brothers, John and Hank Green, Crash Course is a collection of short lecture series about a wide range of topics, from World History to Astronomy to Economics to Chemistry. The target audience is high school classrooms, and is meant to be only a brief introduction to the topics they cover, but I can’t stress enough how much I’ve learned from these courses. The World History one, for example, totally changed the way I looked at a lot of historical events, and at the subject as a whole. Definitely worth a watch.

PHIL PLAIT presents the Crash Course Astronomy series, for example

4. SciShow. Created by Vlog Brother The Younger (Hank Green) and company, SciShow is a mix of science news in the vein of IFLS, and science explanation like Veritasium, along with other science goodies. The news aspect is what I like most about it — the news is well-curated and excellently reported. SciShow is the place to go for regular, quality science news.

5. Vi Hart is an exceptionally talented thing-explainer, focusing and specialising in maths. Her unique style and clear, layman-friendly explanations make for entertaining videos, that sometimes even become genuinely moving and heartfelt. Maths is a thing many people express love for, but it’s also a thing few people have a talent for conveying their love for to others. Vi Hart is one of the few who can do that, and she does it well. Sadly she seems to not be making videos as frequently these days, but her back-catalogue is definitely worth a look anyway.

6. io9 (pron. eye-oh-nine) is the first full website I’ll mention here. It’s an interesting case because it features science news and science explainers, but interspersed with news of a more science-fictional nature. io9 is primarily a news & reviews site for ‘genre’ fiction — anything from books to movies to TV shows to comics and beyond, but when it was first created by Gawker Media (a frankly unfortunate relationship, given the site’s sleazy journalism history), its creator, Annalee Newitz, was insistent that the site feature science content alongside the science fiction. The tagline of the website is “we come from the future”, and it fits. By combining real and fictional science news, one is left with a pleasant taste of the future, today. A lot of the science explainers are of more quirky, out-of-the-ordinary topics, too, giving the site a unique style and voice.

7. Rationally Speaking is a podcast from New York City Skeptics. The podcast covers science, and also other areas such as philosophy, skepticism, religion, and rationalism. The host, Julia Galef, regularly interviews experts in interesting and diverse fields on topics such as “Science drives moral progress” and “Most human behavior is signalling”. Be sure to check out the archive, too, as the show used to have two hosts, and some episodes just featured the two of them talking about topics like stoicism, pseudoscience, and the Turing Test.

8. IFLScience is here for completeness. I’ve sung the praises of this particular site enough already. Go check it out!

Other notable YouTube mentions include: Smarter Every Day, Minute Physics/Minute Earth, CGP Grey, Vsauce, Kurzgesagt (In a Nutshell), and Zogg from Betelgeuse. All of these channels have various quirks, merits, interests, and ‘schticks’, and they all merit your time if you’re a science enthusiast. One final thing I’ll mention is that many of the creators of the channels I’ve mentioned are really close friends in real life, having met at VidCon a few years ago. They live all over the world, but often meet up and do crossovers. One notable one was when the creators of the Numberphile, CGP Grey, Minute Physics, Smarter Every Day and Veritasium channels did a panel event together called Random Acts of Intelligence. I mention all this because it means that following these people means following a really lovely community of science enthusiasts. And the more of them you follow, the better the experience!

On Science Communication (1)

As I mentioned before, science communication is A Big Thing these days. I’m incredibly pleased by this. There’s so many benefits to it, and only a few downsides. They’re all worth talking about, though. Let’s dig in.

I’d say science communication (in the UK at least) has never been in a bad shape, at least for as long as I can remember. Popular science books have been a popular genre for a long time, and there’s always been a decent number of TV shows and such which bring science to non-scientists. Think of how long The Sky At Night has been running, for example. Not to mention, the New Scientist magazine has been publishing in the UK for almost 60 years. If you wanted to find out what scientists were doing all day, there have always been a few ways to do so. Most importantly, though, science has always been a respected field. I think it’s fair to say that the public and the government have always considered scientists worthy of their attention, and as valid sources of knowledge in their fields (even if the government rarely acts on the recommendations of scientists).

Patrick Moore hosted The Sky At Night for over 50 years before his death in 2013

As with so many things, however, the internet has changed everything. One of the internet’s defining features is how it allows anyone to access any kind of ‘content’ they want (‘content’ is a bit of a dirty word on the internet these days) on-demand. This creates a massive variety of new niches for ‘content’ that would never have existed before. Now, if you want to find out what scientists do all day, there’s a problem of information overload. There’s almost too many places to find out! There’s an embarrassment of riches when it comes to science news and information online.

There’s more to it than that, though. There’s been a cultural shift in the way we perceive scientists and science. No greater summary of this exists than the Facebook page I Fucking Love Science. Started by Elise Andrew, a biology undergrad student in 2012, the explosively popular page (over 20 million ‘likes’ and counting) created a full-time job for her as a science communicator. The page is now backed by a website, and continues to post science news and cool science facts and images on a regular basis.

The success of the page is clearly down to the quality of the content featured on it, in part, but in my opinion a large part of the success is down to the name. The name taps into the zeitgeist surrounding science extremely effectively. Science, as the primary driving force behind so much of the modern world, is being recognised by the general public for how amazing it really is. Places like IFLS are tapping into that awe, and provide readers with a glimpse into the everyday life of people in the lab.

IFLS’s logo

There’s other examples of this trend, too. Think of how many Hollywood films have scientists and engineers as their protagonists. The most popular superhero right now arguably is Iron Man, who, yes, gets his ‘powers’ from his industrial prowess and business skills (i.e. his money), but also from his genius-level scientific intellect. Both Avengers films feature long scenes of Tony Stark just geeking out about science stuff with his buddy Bruce Banner (who, as The Incredible Hulk, also gets superpowers from science). How many kids are going to grow up wanting to be inventors just like their hero Tony Stark?

On top of the social media popularity of science education, YouTube has proven to be a phenomenal source of quality science content. At last count, I’m subscribed to over 15 channels whose primary content is for science education purposes. These channels are mostly not about science news (and therefore fill a slightly different niche to IFLS), and usually feature entry-level introductions to abstract, complicated scientific concepts. Part 2 will be a long list of these videos, and other science communication sources I love.

All of these things make me very optimistic for the future of science. Hopefully, with more and more people getting interested in science, we’ll be able to break down the barriers currently keeping large numbers of people from seeing science as a worthy career choice. I’m especially hopeful that things like the visibility of people like Elise Andrews will greatly increase the number of women who choose to take up science. Sadly, science is still a very male-dominated field, but recently I’ve seen some promising proto-steps to fixing that, and this is all part of it.

As optimistic as I am about how much science content is out there for enthusiasts, there are a few nagging concerns I have. As great as it is that people are being kept up-to-date on what happens in labs, the actual reporting of this leaves a lot to be desired. For decades, tabloid papers have claimed every week that scientists (or ‘boffins’ as they’re usually called) have found that x causes cancer, but y cures it, despite only the most tenuous of correlations.

This problem has not gone away in the digital era. If anything it’s become worse. The real story is always something like ‘x has been found to correlate positively with a specific cancer given very specific conditions, and the effect is very weak; more study is needed’. Almost all science news outlets are still guilty of reporting this as the headline-grabbing ‘x causes cancer’. Frankly, I’m getting tired of this shit. It’s just not good enough any more. I’m hesitant to single out a single culprit because it’s so ubiquitous.

Presenting science as a long series of definitive proof after definitive proof of various phenomena and causative links is such a frustratingly warped view of how science actually works that I’m hesitant to even call it science. It harms everyone, including scientists. It creates the impression that only studies with positive results are worthwhile and publication-worthy, which contributes to the shameful publication bias problems endemic to many fields. It contributes to the ‘p-hacking‘ problem by suggesting that getting p<0.05 is synonymous with true, as that’s what leads to press reporting. It’s a nasty feedback loop that needs to be broken.

Christie Aschwanden's article on Fivethirtyeight is excellent and well-worth a read
Christie Aschwanden’s article on Fivethirtyeight is excellent and well-worth a read

I don’t want to end on a downer like that, so I’ll restate that in general I’m very optimistic about the future of science and science communication. Getting scientists out of the proverbial ivory tower can only be a good thing, and I hope to play a small part in doing that.

Why blog?

I suppose for one of my first blog posts here a good topic might be me answering the question “why have a blog?” There’s a few answers, so let’s unpack them.

  1. I enjoy science communication. This one is the most important. The past few years have been really phenomenal for the genre of science communication. Mention must be made, of course, of the excellent Facebook page I Fucking Love Science, but it’s only one among many. There’s never been a better time to be a science advocate, so luckily it’s always been an interest of mine, and I get to surf the wave. I love YouTube channels such as NumberphileCGP Grey, SciShow, Veritasium, MinutePhysics and others, and they’ve all really inspired me to give this science communication thing a shot. I don’t want this blog to be exclusively about science, but as it’s my day job I expect it to take up a large chunk of the writing here.
  2. I gots opinions. There’s lots of interesting things happening within the scientific community, and within the world of higher education. As a physics graduate student, I’d like to think I have something to say about these things, but I’d also like to think that in a wide range of other subject areas, like politics and movies, I have interesting things to say.
  3. I like writing in general. I’ve written for the student newspaper before, and hope to do that more in the future. For those who don’t do it professionally, writing is a great pastime, and something I hope to do more of.
  4. Yes, it does look good on a CV. I’ll just be upfront about this. Obviously any personal blog these days is going to be, in part, an exercise in that most loathsome of modern concepts — personal branding. I think anyone who runs a blog who says they don’t have this somewhere in the back of their mind is kidding someone, either you or themselves. So yes, that is a part of why I’m doing this. Not a big part; not the main part, but a part.

So with that out of the way, let’s get blogging! My ambition is to have one blog post a week, with Thursday at noon as the upload time (I find it helps to have a regular upload time for these sorts of things). Thanks for stopping by!