# White lab coats, pink tutus and camouflage fatigues

In this post I contemplate the effects of stereotypes and biases. I hope that this will encourage you to examine these ideas too. I promise I’ll get back to more science soon.

Just over a week ago, I helped with an outreach event for year nine students. Some of the astrophysics PhD students and I ran an interactive lecture on gravity and its importance in astrophysics. These type of events are fun: you get to teach some physics to a (usually) enthusiastic audience, and hopefully inspire them to consider studying the subject. I also get to play with our Lycra Universe. I think it’s especially important to show students what a university environment is like and have them interact with real scientists. It is important to counter the stereotype that studying science means that you’ll spend all day in a lab wearing a white lab coat. (Although that would be cool. I’d want goggles too, and maybe a doomsday device).

This event was to promote the studying of STEM subjects. That’s science, technology, engineering and mathematics, because there’s nothing like an acronym to make things accessible. It is often argued that we need more people trained in STEM subjects for the economy, industry, or just so we can finally get pizza over the Internet. I like to encourage people to study these areas as I think it’s good to have a scientifically-literate population. Also, because science is awesome! The event was aimed specifically at encouraging a group who are under-represented at university-level STEM, namely girls.

There has been much written on gender and subject choice. I would recommend the Closing Doors report by the Institute of Physics. I will not attempt to unravel this subject. In all my experience, I have never noticed any difference in aptitude between genders. I don’t believe that the ability to pee standing up gives any advantage when studying physics—one could argue for a better understanding of parabolic motion, but anyone who has paid attention to the floor in the gents (I advise against this), knows this is demonstrably not the case. I assume the dominant factors are social pressures: a vicious circle of a subject becoming more associated with one gender, which makes people feel self-conscious or out of place studying it. Also: there are always bigots. It’s a real shame to be potentially missing out on capable scientists. There have been many attempts to try to counter this trend, to break the cycle—some of them truly awful.

Good arguments have been made that the gender segregation of toys pushes girls away from science and technology from an early age. (For some reason, there seems to be a ridiculous idea that women can only relate to things that are pink). It makes sense to me that if only boys get the chemistry sets and construction toys, then they are going to be more numerous in the STEM subjects. The fact that a few female LEGO scientists merits coverage in nation newspapers, the BBC, etc. shows something isn’t quite right.

We are all influenced by our childhoods, and this got me thinking: I know of negative impacts for women from these gender biases, what are they for men? If women are under-represented in engineering, maths and physics, then men must be under-represented somewhere else to balance things: namely English, biology (conspicuous amongst the STEM subjects) and languages. We are short of male teachers and nurses. It seems that men are pushed away from caring careers or those with emphasis on communication.

The lack of men in certain professions is a problem, although I would say less so than the continued under-representation of women at senior positions (say as professors, CEOs or members of government). I was about to relax, since I hadn’t uncovered yet another unconscious bias to add to the list. Then I checked the news. I don’t know what’s in the news when you’re reading this, but at the time it was conflict in Ukraine, Iraq and Israel–Palestine—I assume things are much better in the future? One thing that struck me was that the combatants in the photos were almost exclusively men. It then occurred to me that for every girl who plays with a ballerina doll, there is a boy who plays with an action figure with a weapon. I’m not as naive as to suggest it’s a simple as growing up to be exactly like your toys (I, regrettably, am neither a dinosaur nor a cuddly elephant), but perhaps it is worth keeping in the front of our mind what identities we associate with each gender and how we project these onto children. I don’t want to say that being a ballerina isn’t a good vocation or hobby, or that being a soldier is a bad career. (Curiously, I believe that some of the requirements to be a good ballet dancer or soldier overlap, say discipline, determination, physical fitness and, perhaps, empathy). However, I think it is dangerous if we raise girls who primarily aspire to be pretty, and boys who resolve conflict through violence (men are both more likely to be victims of homicide and suicide).

In conclusion, stereotypes can be damaging, be it that scientists are all socially-awkward comic-book geeks as in The Big Bang Theory, that men can’t talk about their feelings, or that women must be mothers. There is a balance between the genders: by assigning one quality to a particular gender, you can push the other away. Mathematical ability shouldn’t be masculine and compassion shouldn’t be feminine. This is not a new idea, but conveniently coincides with Emma Watson’s wonderful speech for the UN as part of the HeForShe campaign. Cultural biases might be more significant than you think, so give them some extra attention. Sexism hurts everyone, so let’s cut it out and all go play with some LEGO.

The Big Bang Theory‘s popularity has been credited with encouraging more students to take physics. The cast reflects traditional stereotypes: the men are physicists, an astronomer and an engineer, the women are two biologists and Penny.

# How big is a black hole?

Physicist love things that are simple. This may be one of the reasons that I think black holes are cool.

Black holes form when you have something so dense that nothing can resist its own gravity: it collapses down becoming smaller and smaller. Whatever formerly made up your object (usually, the remains of what made up a star), is crushed out of existence. It becomes infinitely compact, squeezed into an infinitely small space, such that you can say that the whatever was there no longer exists. Black holes aren’t made of anything: they are just empty spacetime!

Daisy, a spherical cow, or “moo-on”. Spherical cows are highly prized as pets amongst physicists because of their high degree of symmetry and ability to survive in a vacuum. They also produce delicious milkshakes.

Black holes are very simple because they are just vacuum. They are much simpler than tables, or mugs of coffee, or even spherical cows, which are all made up of things: molecules and atoms and other particles all wibbling about and interacting with each other. If you’re a fan of Game of Thrones, then you know the plot is rather complicated because there are a lot of characters. However, in a single glass of water there may be 1025 molecules: imagine how involved things can be with that many things bouncing around, occasionally evaporating, or plotting to take over the Iron Throne and rust it to pieces! Even George R. R. Martin would struggle to kill off 1025 characters. Black holes have no internal parts, they have no microstructure, they are just… nothing…

(In case you’re the type of person to worry about such things, this might not quite be true in a quantum theory, but I’m just treating them classically here.)

Since black holes aren’t made of anything, they don’t have a surface. There is no boundary, no crispy sugar shell, no transition from space to something else. This makes it difficult to really talk about the size of black holes: it is a question I often get asked when giving public talks. Black holes are really infinitely small if we just consider the point that everything collapsed to, but that’s not too useful. When we want to consider a size for a black hole, we normally use its event horizon.

The event horizon is not actually sign-posted. It’s not possible to fix a sign-post in empty space, and it would be sucked into the black hole. The sign would disappear faster than a Ramsay Street sign during a tour of the Neighbours set.

The event horizon is the point of no return. Once passed, the black hole’s gravity is inescapable; there’s no way out, even if you were able to travel at the speed of light (this is what makes them black holes). The event horizon separates the parts of the Universe where you can happily wander around from those where you’re trapped plunging towards the centre of the black hole. It is, therefore, a sensible measure of the extent of a black hole: it marks the region where the black hole’s gravity has absolute dominion (which is better than possessing the Iron Throne, and possibly even dragons).

The size of the event horizon depends upon the mass of the black hole. More massive black holes have stronger gravity, so there event horizon extends further. You need to stay further away from bigger black holes!

If we were to consider the simplest type of black hole, it’s relatively (pun intended) easy to work out where the event horizon is. The event horizon is a spherical surface, with radius

$\displaystyle r_\mathrm{S} = \frac{2GM}{c^2}$,

This is known as the Schwarzschild radius, as this type of black hole was first theorised by Karl Schwarszchild (who was a real hard-core physicist). In this formula, $M$ is the black hole’s mass (as it increases, so does the size of the event horizon); $G$ is Newton’s gravitational constant (it sets the strength of gravity), and $c$ is the speed of light (the same as in the infamous $E = mc^2$). You can plug in some numbers to this formula (if anything like me, two or three times before getting the correct answer), to find out how big a black hole is (or equivalently, how much you need to squeeze something before it will collapse to a black hole).

What I find shocking is that black holes are tiny! I meant it, they’re really small. The Earth has a Schwarzschild radius of 9 mm, which means you could easily lose it down the back of the sofa. Until it promptly swallowed your sofa, of course. Stellar-mass black holes are just a few kilometres across. For comparison, the Sun has a radius of about 700,000 km. For the massive black hole at the centre of our Galaxy, it is 1010 m, which does sound a lot until you release that it’s less than 10% of Earth’s orbital radius, and it’s about four million solar masses squeezed into that space.

The event horizon changes shape if the black hole has angular momentum (if it is spinning). In this case, you can get closer in, but the position of the horizon doesn’t change much. In the most extreme case, the event horizon is at a radius of

$\displaystyle r_\mathrm{g} = \frac{GM}{c^2}$.

Relativists like this formula, since it’s even simpler than for the Schwarzscild radius (we don’t have to remember the value of two), and it’s often called the gravitational radius. It sets the scale in relativity problems, so computer simulations often use it as a unit instead of metres or light-years or parsecs or any of the other units astronomy students despair over learning.

We’ve now figured out a sensible means of defining the size of a black hole: we can use the event horizon (which separates the part of the Universe where you can escape form the black hole, from that where there is no escape), and the size of this is around the gravitational radius $r_\mathrm{g}$. An interesting consequence of this (well, something I think is interesting), is to consider the effective density of a black hole. Density is how much mass you can fit into a given space. In our case, we’ll consider the mass of the black hole and the volume of its event horizon. This would be something like

$\displaystyle \rho = \frac{3 M}{4 \pi r_\mathrm{g}^3} = \frac{3 c^6}{4 \pi G^3 M^2}$,

where I’ve used $\rho$ for density and you shouldn’t worry about the factors of $\pi$ or $G$ or $c$, I’ve just put them in case you were curious. The interesting result is that the density decreases as the mass increases. More massive black holes are less dense! In fact, the most massive black holes, about a billion times the mass of our Sun, are less dense than water. They would float if you could find a big enough bath tub, and could somehow fill it without the water collapsing down to a black hole under its own weight…

In general, it probably makes a lot more sense (and doesn’t break the laws of physics), if you stick with a rubber duck, rather than a black hole, as a bath-time toy.

In conclusion, black holes might be smaller (and less dense) than you’d expect. However, this doesn’t mean that they’re not very dangerous. As Tyrion Lannister has shown, it doesn’t pay to judge someone by their size alone.

# How sport is like science

Athene Donald, Professor of Experimental Physics and soon-to-be Master of my old college, Churchill, recently blogged about how athletics resembles academia. She argued that both are hard careers: they require many years of training, and even then success is not guaranteed—not everyone will reach the top to become an Olympian or a Professor—there is a big element of luck too—a career can stall because of an injury or because of time invested in a study that eventually yields null results, and, conversely, a single big championship win or serendipitous discovery can land a comfortable position. These factors can make these career paths unappealing, but still most people who enter them do so because they love the area, and have a real talent for the field.

As The Breakfast Club taught us, being into physics or sports can have similar pressures.

I find this analogy extremely appealing. There are many parallels. Both sports and academic careers are meritocratic and competitive. Most who enter them will not become rich—those who do, usually manage it by making use of their profile, either through product endorsement or through writing a book, say Stephen Hawking, or Michael Jordan (although he was still extremely well paid). Both fields have undisputed heavy-weights like Einstein or Muhammad Ali, and media superstars like Neil deGrasse Tyson or Anna Kournikova; both have inspirational figures who have overcome adversity, be they Jesse Owens or Emmy Noether, and idols whose personal lives you probably shouldn’t emulate, say Tiger Woods or Richard Feynman. However, I think the similarity can stretch beyond career paths.

Athene says that although she doesn’t participate in athletics, she does enjoy watching the sport. I’m sure many can empathise with that position. I think that this is similarly the case for research: many enjoy finding out about new discoveries or ideas, even though they don’t want to invest the time studying themselves. There are many excellent books and documentaries, many excellent communicators of research. (I shall be helping out at this year’s British Science Festival, which I’m sure will be packed with people keen to find out about current research.) However, there is undoubtedly more that could be done, both in terms of growing the market and improving the quality—reporting of science is notoriously bad. If you were to go into any pub in the country, I’d expect you’d be able to find someone to have an in-depth conversation with about how best to manage the national football team, despite them not being a professional footballer. Why not someone with similar opinions about research council funding? Can we make research as popular as sport?

Increasing engagement with and awareness of research is a popular subject, most research grants with have some mention of wider impact; however, I don’t think that this is the only goal. According to UK government research, many young students do enjoy science, they just don’t feel it is for them. The problem is that people think that science is too difficult. Given my previous ramblings, that’s perhaps understandable. However, that was for academic research; science is far broader than that! There are many careers outside the lab, and understanding science is useful even if that’s not your job, for example when discussing subjects like global warming or vaccination that affect us all. Coming back to our sports analogy, the situation is like children not wanting to play football because they won’t be a professional. It’s true that most people aren’t good enough to play for England (potentially including members of the current squad, depending upon who you ask in that pub), but that doesn’t mean you can’t enjoy a kick around, perhaps play for a local team at weekend, or even coach others. Playing sports regular keeps you physically fit, which is a good thing™; taking an interest in science (or language or literature or etceteras) keeps you mentally fit, also a good thing™.

Chocolate is also a good thing™. However, neither Nobel Prizes nor Olympic Medals are made of chocolate, something I’m not sure that everyone appreciates. I’d make the gold Olympic models out of milk chocolate, silver out of white and bronze out of dark. The Nobel Prize for Medicine should contain nuts as an incentive to cure allergies; the Prize for Economics should be mint(ed) chocolate, the Peace Prize Swiss chocolate, the Chemistry Prize should contain popping candy, and the Physics Prize should be orange chocolate (that’s my favourite).

How to encourage more people to engage in science is a complicated problem. There’s no single solution, but it is something to work on. I would definitely prefer to live in a science-literate society. Stressing applications of science beyond pure research might be one avenue. I would also like to emphasis that it’s OK to find science (and maths) hard. Problem solving is difficult, like long-distance running, but if you practise, it does get easier. I can only vouch for one side of that simile from personal experience, but since I’m a theoretician, I’m happy enough to state that without direct experimental confirmation. I guess that means I should take my own advice and participate more myself: spend a little more time being physically active? Motivating myself is also a difficult problem.