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Friday 27 November 2015

Sense and Sensible Statistics

Recently I wrote about the value of the humanities classes in teaching rational thinking. Understanding why something evokes an emotional response is critical to understanding the intent of an article, i.e. how the author is trying to manipulate you. And once you have that, you can begin to step outside the emotions and think logically.

But that's only the beginning. While some of the humanities courses in schools are very good, what we really seem to be lacking almost entirely is a good course on statistics for the under 16's. Because if you take a statistical view of the world, then it's really not as bad as you might think.

Of course I don't mean that we need more emphasis on teaching mathematical techniques - yes, it's important to understand the mean and median and why the median is usually the better, but those are hardly the most important aspects. What I'm on about are the much less mathematical, more philosophical aspects of statistical measurements. You don't need any maths to understand them, but I see a great many people who just don't seem to get them at all. Yet while they're really a lot simpler to explain than the mathematical aspects, they're probably even more important. So, in no particular order :

Anecdotes Are Not Evidence

I just said, "I see a great many people". But what does that mean ? How many people ? Where ? Did I actually talk to them in detail or just form a snap judgement based on one short quote ? You see, by itself, my observation that I personally have witnessed some number of people not understanding statistical methods proves precisely nothing about how many people overall really do not understand statistical methods. Without more details (which I'll get on to in a minute) there could be any number of reasons why my casual observation is meaningless.

But anecdotes aren't unrelated to evidence. For statistics they're a sort of base unit of evidence. As long as the witness isn't lying or delusional, they do prove individual things happen. The problem is that my statement, "I see lots of people who..." strongly implies that I think there's a majority of people who behave in a certain way. And I might think that. I might very well think that. But as to whether it's really true...

Ian Richardson is infinitely more charismatic than Kevin Spacey and anyone who disagrees is objectively wrong.
All my observation can tell us is that some number of people don't understand statistical methods. Sometimes that's good enough : "I saw that man attacking that adorable kitten, officer !". You can use anecdotes to refute sweeping, overstated generalizations ("All men attack kittens.", "Ah, but I knew a man who never attacked a kitten at all !"), but not to support generalizations ("It must be true, I've seen lots of men attacking kittens"). As an estimate as to what fraction of men really attack adorable kittens, it's useless. It's extremely difficult to overcome a personal bias when we witness something happening first-hand for ourselves, especially if we see it repeatedly. Which brings us neatly on to...

Selection Effects

It's almost impossible to get everyone's opinion on any topic or analyse everything in any sample, which is why we need statistics in the first place. But questioning as many people as you can could be utterly useless if you question only specific people. If you're trying to find out how many people enjoy reading, you don't go and only ask people visiting the library, because that's just plain silly.

Of course, you can't ignore the evidence of your own eyes. You see youths being aggressive day in, day out, and it's easy to conclude that young people are aggressive. And it's even true in your experience. But if you're walking the same route each day and see the same youths, you've limited your sample. Or you might be going through a park where the local ruffians choose to congregate, so you're only seeing the dregs and not the far greater numbers of young people who are busy in school.

It's very difficult to eliminate all selection effects when collecting data. But if you don't try to do this at all, you'll end up with a very warped view of the world. Which is probably why people seem to think that most immigrants in Britain are Polish plumbers, even though they're actually highly skilled twenty-somethings.

Think Of The Big Picture

Statistical thinking cautions us to remember that while what we observe is always true, it isn't necessarily representative of what's going on everywhere. Maybe most teenagers in parks are hooligans, but most teenagers overall are just lovely. The point is that you have to be very careful about generalizing from specific observations. The more data you've got, and the wider variety of sources it comes from, the better.

For example, the media often focus on stories about individuals. Being basically empathetic creatures, we react strongly to emotional, personal stories. The trouble is that it doesn't matter how many "violent immigrant" stories you report, all you're doing is picking out anecdotes without reporting the full story. It's a bit like only reporting plane crashes - obviously, there's no story when a plane doesn't crash, because people aren't interested. But we all know planes are safe enough, we accept the small risk that comes with flying because we're at least broadly aware of how many planes don't crash.

It's harder to escape the emotional impact of a violent, personal attack. Our pattern recognition skills tell us, "That dangerous person is in some way different, therefore any people which share that difference might also be dangerous." But unless you also consider the number of such people who aren't dangerous, you are not thinking statistically. You also have to consider how people in other groups behave, otherwise you have nothing to compare with. For instance, 98% of all terrorism in the Western hemisphere is carried out by non-Muslims - which is hardly the view one gets from the media*. People like fear because it stops them from the more difficult task of actually thinking. That sells newspapers but it doesn't tell you what's really going on.

* Strictly speaking if you want to find out if Muslims are more violent, you should look at how many violent acts occur per capita by Muslims compared to all other demographics.

It also puts into perspective how some awful crimes just really aren't that much of a problem. Statistically, terrorism causes about as many annual fatalities as pregnancy, and no-one is talking about a "war on babies".

Underlying Causes

Your local observation of gangs of young ruffians consistently appearing in a local park tells you that you should be wary of those ruffians in that park. It does not, by itself, tell you that you should be wary of all parks or all youngsters. What if that park is in a city with a very high crime rate anyway ? It could be that you're seeing kids in a park because kids hang out in parks; that they're also violent could be related to the fact that the whole area has a high rate of violence in all age groups. There's nothing wrong with your specific knowledge of the area, but you're jumping the gun to assume that all parks (or all youths) are the same everywhere.

It's easy to see why we think this way : we have monkey minds in a modern world. It makes sense to run away from all tigers, because all tigers really are dangerous. The trouble is that we try to apply this thinking to far more complex, modern situations, and it's failing miserably. Instead of making us safer, it's making things more dangerous - our unfounded fears about certain groups cause us to hate them, which causes them to hate us, and the cycle of hate and violence can be difficult to break.

But even when your specific observation is borne out in more general trends, that doesn't necessarily mean anything either. Even if you did see that all kids in parks were violent, it would be silly to conclude that parks make them violent. Similarly it's plainly ridiculous to say that being tall and skinny is a sign of intelligence. Doing intelligent things, like completing a degree in mathematics, is a sign of intelligence - that you're a sexy partygoer is completely and utterly irrelevant, and really quite insulting.

The excellent Spurious Correlations website is full of examples of this, although my favourite has to be this one :

Does eating more chocolate increase your chances of winning a Nobel prize ? Probably not. First, we could turn it around. It doesn't make a lot of sense to say that a few academics winning Nobel prizes causes the whole populace to eat more chocolate, so you can't assume the reverse is true. There could be any number of common reasons why both chocolate consumption and Nobel prize winnings increase simultaneously. In poor countries the population are starved of all foods, so they aren't healthy and have little time to spend on science, while the reverse is true in richer countries. There's a very strong selection effect at work here : why only look at chocolate ? What's the correlation like with other foods ?

Determining what the underlying cause really is is difficult. Ideally you perform an analysis where you see how one variable correlates with lots of other variables, not just one. If you find a correlation and there's a physical mechanism to cause it and no other variable seems to correlate as well, then maybe you've found something interesting.

Ask ALL The Questions !

If a study is focused on a very narrow area, you might think that you can get away with asking very short, simple questions. Not necessarily. You might be introducing a selection effect and miss something very important that's going on. If you're monitoring library usage and find that it's dropping, you don't just ask people whether the chairs are uncomfortable. Ideally you want as much data as possible, so that you can consider both causes you consider likely and unlikely on an equal footing.

Then there's the hugely complicated topic of asking the right questions in the right way. I'm not going to go into this one save to mention this brilliant Yes Minister scene which shows why it's so important :

You've also got to ask the same questions, even if they're not ideal. If you ask people, "Do you like pork pies ?" in Hull and, "Are pork pies your favourite food ?" in Doncaster you will inevitably get different results. This is an even bigger problem when it comes to international studies, since different countries don't always cooperate to get public opinion in the same way. For example, recently there was a claim that America is a less violent place than Britain, which is revealed as pure nonsense when you realise that the two countries have very different definitions of violent crime.

Outliers Are More Noticeable

Selection effects are constantly at work in human memory. We only notice events, we don't notice non-events. A plane that doesn't crash isn't memorable. An immigrant who never breaks the law doesn't stand out. Negative outliers are perhaps even more memorable, because it's safer to remember danger than it is to remember the examples of success. The thing to remember with media stories is that in general, stories only make the news because they're unusual. For that reason, be extremely wary of judging whether anything the media is reporting is typical of what's usually going on. And also be acutely aware that because of this, the media are feeding you a series of unusual events, which will inevitably bias your memory and impressions of what usually happens.

Oddly enough, while it's always possible to point to events in which people were killed, it's not always possible to say when lives are saved - at least not specific, personal examples. It's easy to say when someone dies of heart disease. It's impossible to point to individuals who never get heart disease in the first place because, say, of changes in food regulations or campaigns for healthy eating.

One of my schoolteachers taught me a classic example of what happened when the British government decided to stop moving the clocks back an hour in winter. Campaigners said this would prevent unnecessary deaths in the evening (i.e. schoolchildren walking home in the dark getting hit by cars). And it did. There was also an increase in the number of deaths in the morning, but it was less than the decrease in the evening. So statistically, lives were saved.

But was the media full of stories of children who were, inexplicably, not dead ? No, because you have no idea who was saved by this, but it's very easy to find examples of children killed in the morning, when it was now darker. Of course, you really have no idea who exactly was killed as a result of this either - they might have been run over anyway. Really it makes no more sense to interview the parents of one dead child and say, "this is an example of this law killing children" than it does to to interview the parents of one child who's not dead and say, "this is an example of the law saving lives".

This kind of statistical thinking can seem cold, even cruel and inhuman. In situations like this it's important to remember that we're dealing with probabilities and risk, not individuals. You might think it's a choice of saying, "I want to kill lots more children in the evening and a few less in the morning" or "I want to kill a lot less children in the evening and a few more in the morning", so that basically it boils down to how much killing you want to do - you do not have the luxury of a good choice here.

It's true, but of course altering risk is not the same as either lining up people for a firing squad or rescuing them from a hungry shark. You'll never know who was saved and who was not - you have to go on the numbers, because that's all you've got. You can't avoid taking risks. You can only control which risks you take.


Unlikely events still happen by chance. If something has a 1 in 10,000 chance of occurring, you can expect that it will occur if the requisite scenario actually does happen 10,000 times. So if you get 10,000 people to flip a coin ten times and one them comes down heads ten times in a row, it's not because one of the people was psychic.

Measuring how statistically significant an event is - the probability that it didn't happen by chance - can be mathematically complicated. It also relies on accounting for those all-important selection effects. Be especially wary of the phenomenon of small number statistics. The smaller your sample, the greater the chance that it can appear to show a trend where actually none exists. For example, if you ask a million people if they like cheese and 600,000 say yes, the result is far more decisive than if you poll ten people and nine of them said yes.

The point is that you should be cautious when an unlikely event happens because it might have happened by chance anyway. Weather prediction is a good example. You can never attribute an individual very hot summer to global warming, because it might have happened anyway. A run of three hot summers is also difficult, because the Earth has been around an awful long time so has probably had umpteen bouts of three hot summers in a row. At what point you can start to say, "this is significant" you'll need to call in a climate expert.


So can these few simple lessons really make you happier ? Possibly. It certainly teaches caution : just because you feel something is true from your own experience doesn't mean that it really is. To be more accurate, personal experience is not a good guide to general trends. Without having experienced other situations, you don't know what selection effects are at work. So anecdotes can tell you something about individual situations, but they're nearly useless when it comes to the big picture. Even your general impressions about what's going on in the world at large are coloured by a media for whom selling emotional but statistically irrelevant stories is de rigueur.

I shall return to the "generation of spoiled idiots" in a moment, but the main point is that we don't often stop to think about how much worse things could be. This is what I call the Grandparent Paradox (nothing to do with the time-travelling Grandfather Paradox). Grandparents are old, experienced people, and experience is valuable. Yet despite having survived World War II, my grandmother was convinced the world was getting worse. Yeah, really, worse than say, being bombed by Nazi Germany, or having to live in a world where women couldn't do equal work for equal pay, homosexuality was illegal, and being an abject racist was just normal.

 "More bad news", she'd say, having just read the latest edition of the Daily "we supported Hitler" Mail. As though the assassination of the Tazenikistani Royal Family (or some such) was somehow impinging on her own need to turn up the heating to a level able to roast a turkey, set the telly on full volume and go off on racist rants for no apparent reason (with hindsight the Daily Mail probably had a lot to do with that).

Statistical thinking means you don't lose your head because something awful happened. Awful things happen all the time, and they probably always will. What they don't indicate is that things are getting worse - you have to look at numbers over time for that. "I see this happening more and more" means precisely diddly-squat without numbers.

Over the last century we've gone from a situation in which racism was normal to, if far from gone, then at least being hated by the majority of people. We're living longer. Our standard of living is immeasurably higher. Women and minorities have equal rights, if not yet equal treatment. And yes, progress hasn't been linear, but inferring that the apocalypse is round the corner because something bad just happened is just dumb.

The other notable quote my gran used to say was that my generation couldn't possibly have fought the Nazis. How she came to this conclusion was anyone's guess, never mind the ridiculous notion about how people "were nicer in those days." It's not my generation that put up signs in pubs saying, "No blacks or Irish". Similarly, the idea that we're a generation of "spoiled idiots" does have a base emotional appeal, but is it really true ?

That's probably the internet meme I hate the most, because every single damn thing about it is wrong. First, I've never seen this in any school playground*. Cardiff, Arecibo, Prague... nope, not happening. Show me the evidence that this does happen and I'll believe you. Second, what's wrong with kids playing with smartphones and not playing sport ? I freakin' HATED sport ! I'd have wounded small puppies for the chance to get out of  P.E. lessons and play with a handheld computer. Why the hell would it have been better for me to suffer ? Kids having access to more advanced technology is a good thing. That's how technological progress is supposed to work.

* Of course, all my anecdote proves is that kids don't avoid sports in every school.

Our continual raising of our own expectations is a mixed blessing. We're continually driven for self-improvement : racism isn't considered normal any more, and homophobia is heading the same way. The downside is that whenever things do get worse we tend to forget how far we've come overall, and because we continually shift the goalposts we're never happy.

Grandparents, in my experience, also seem to have a view that that the modern world is a more dangerous place. "Oh we were allowed to wander off by ourselves when I was six, and we could eat dog poop if we wanted and it never did me any harm", they say. Sure you were. That doesn't mean the world or dog poop was safer (or that medical advice was wrong*) - it could just mean that your parents were stupider, or less well-informed, or didn't love you as much, or just weren't paying attention, or in fact were better at parenting because they let you have more fun. The idea that the world has become more dangerous is only one possible explanation, and just because you see a lot more media reports about murderers doesn't mean there are more murderers around.

* Yeah, you may have gotten away with not washing your hands once in a while. Cleanliness doesn't guarantee survival any more than dirtiness guarantees death - all you're doing is altering the risk. Some changes can't be seen on an individual level - they require a much larger statistical view. There's also a selection effect here : of course it did you no harm, because those people who it did harm are dead and can't complain about it.

The main lesson of statistics isn't that you should jump around in some kind of orgasmic ecstasy about how great the world it, because large aspects of the world are pretty darn crappy. But it reminds us that while we don't live in a Utopia, we do live in something that's infinitely better than many alternatives. We've escaped warlords and petty kings and absolute monarchies and emperors, serfdom and slavery and the workhouse. True, the world isn't what it once was - the only constant is change. But in so many ways, that change has been for the better. I think if we grew up learning about these basic statistical effects, we'd all be a lot more rational. And maybe - just maybe - we'd all be a little bit happier too.

Monday 16 November 2015

Scapegoats and Statistics

I know, I know - every half-wit on the internet has their own opinion on the recent terrorist atrocities in Paris. Personally I find the commentary by Google's Yonatan Zunger to be probably the closest to the truth. If I might make a humble effort to simplify this (but you should really read it yourself), it would be something like this : the causes of terrorism are complicated and cannot be attributed only, or even mostly, to religion - other factors, such as poverty, war, and government collapse are all to blame. I would also strongly urge, nay insist you also read this article on the cause of the Arab Spring.

Zunger further contends that Muslims haven't integrated into some European societies because they have been prevented from doing so by laws and prejudice. Whereas Charlie Hebdo provoked violent terrorism from some Muslims, The Life of Brian merely provoked anger from some Christians. This wasn't because Christianity is innately more peaceful, but because Christians didn't really feel threatened by Monty Python. They weren't "integrated" into society, they were and are society.

Some Muslims do not feel like that. They don't see satire as satire; they see it as part of a much larger attack not just on their beliefs, but on them. That is not to say they are correct, only that if they felt truly a part of society, they wouldn't react violently to legitimate criticism. Which is evidenced by a surprisingly small proportion (albeit a majority) of Muslims who believe that violence in response to cartoons is never justified. Maybe they feel this way because as Zunger suggests, they are constantly excluded from society and "their" extremist element reacts in the same way extremist elements react in all groups.

Because I know full well that I am not an expert on international politics or psychology, I am going to try and limit the scope of this post as much as possible. I do not want to examine in detail the cause of or the solutions to the problem. Instead I have only one point to make with this post : terrorist attacks caused by Muslims are not occurring because the instigators are Muslims.

There are an estimated 2-6 million Muslims living in France today. Since 2000, there have been a total of 14 terrorist attacks, nine or ten by Muslim extremists, involving a total of perhaps twenty individuals. Twenty ! Out of maybe five million Muslims ! Islamic terrorists are outnumbered by innocent Muslims by something like two hundred thousand to one*. Fearing Muslims makes no sense.

* EDIT : As rightly pointed out in the comments below, the number of extremists may be somewhat higher than that, especially given that around 1,000 individuals have left France to join ISIS in the Middle East. Still, the number of individuals who have remained within France and actually want to hurt France is vanishingly small.

Let that ratio sink in. It's exactly equivalent to saying that you wouldn't visit Luxembourg or Rouen or Swansea or Venice because you'd heard there was one murderer present. Or better yet, to say, "Sir, before you enter this establishment, I have to check if you're from Venice."

Gondoliers : you just can't trust 'em.
And yes, there have been protests in which large numbers of Muslims said really, really stupid things. But how many of them acted on that ? Practically none.

"But," you might say, "you just said that most of the attacks were carried out by Muslims. Doesn't that mean that we should hold Muslims in greater suspicion when looking for terrorists, even if it is only a tiny minority that commit terrorism ?"

No. You still haven't grasped the scale of how very, very few terrorists there are. The numbers are so low it makes no sense to be more suspicious of Muslims than any other group. If you have an event at which you're concerned about terrorism, you need security procedures that detect terrorists. If you resort to using someone's religion to determine if they're more likely to be a terrorist or not, you've basically admitted you have no idea what you're doing.

Let's consider the terrorist attacks in France in the 20th century :
1900 - 1950 : Five attacks, all politically motivated, none by Muslims.
1950 - 1975 : Seven attacks, all politically motivated, none by Muslims.
1975 - 2000 : Fifty one attacks, thirty two by Muslim extremists (how many were French and how many were foreigners is unclear).

The attacks by non-jihadists include a wide variety of causes, from mental illness to various ideologies such as communism and nationalism. So jihadists form the largest single group responsible for French terror attacks in the 20th and 21st centuries. And they have escalated in recent years : i.e. there was a time not so long ago when Muslim terrorism was just not a thing. EDIT : It's worth bearing in mind that when considering the number of attacks overall in Europe (unfortunately I don't have data for France alone) - that is, the attempts that were foiled - the number of attacks by Islamists is negligible compared to those by other causes.

Something grimly interesting emerges when reading the list : the stochastic nature of the attacks. 1994 saw no less than nine Jihadist attacks, whereas from 1997-2003 there were none. If merely being Muslim caused a propensity toward violence, we might expect to see a more consistent level of violence. In fact it tends to occur in bursts, often caused by organizations. There are a few lone extremists, but they are by far the minority.

Similarly, while the anti-religious ilk are quick to point out that the Crusades and Inquisition as being agents of Christian medieval terror (quite correctly), we don't often think of the Catholics as being violent terrorists today. But it does happen. You might not like Catholic ideology, but few people worry about the Catholics plotting to blow up Parliament, because Catholic terrorism is just so vanishingly rare. Yes, once it was considered a serious threat. It isn't any more, even though Catholicism has hardly gone away. So Catholicism looks to be very unlikely as the root cause of terrorism.

Sometimes antitheists say to me, "Just because a theist donated money to charity doesn't mean you can infer that theism is a good thing." That's very true. And by exactly the same token, just because some theists kill people doesn't mean you can infer that theism is a bad thing either. Since theism can cause people to do both good and bad things, to judge whether theism is a good or bad thing you'd need at the very least a statistical estimate of how many good and bad things (whatever those are) theists and non-theists commit. Do you have one ? No, you don't. You only have anecdotes. This is not a sensible way to judge religion or the religious.

Right, yes, as opposed to, say, poverty and oppression. This is an example of sciolism : giving an opinion on something well outside one's area of expertise. I suppose I'm doing it too, of course.
When certain Irish republicans were waging a campaign of terror against the United Kingdom, no-one said they were doing it because they were Irish (except for racist bigoted idiots). Nor was believing in an independent Ireland cited as the cause of the violence. It was what they were trying to use violence to achieve, but it wasn't what made them violent. Rather it was their unquestioning devotion to that cause and the extremist belief that anything they did was justified that made them violent.

When a Christian murders someone, should we automatically assume that it was Christianity that made them do it ? Does anyone honestly think that during every single murder, someone who happens to believe in God is thinking, "Jesus told me it's OK !", or that Christian thieves rob houses because they think the Angel Gabriel commanded them to ? Is it not at least plausible that in some cases, religious people do evil things for reasons completely unrelated to their religion ? Poverty seems a far more likely cause of theft, anger a more likely cause of murder, than a book telling people not to kill or steal.

Maybe, just maybe, hungry people steal food because they're hungry. That they happen to follow a religion can have nothing to do with it.

Murderous people can always come up with an ideology to "justify" murdering people, be it religious or otherwise (communism comes to mind). If it wasn't religion, it would probably be something else. Lunatic idiots will always be lunatic idiots.

Not that it's quite as simple as that though. True, sometimes religion can turn good people into evil people -  the Aztecs surely weren't all born with a desire to rip out people's hearts, but they did so on a massive scale to appease their gods. Yes, this was due to religion - a very specific kind of ultra-extreme religion into which people were brutally indoctrinated. Aztec religion was a form of extremism in itself. It wasn't the belief in the gods that made them sacrifice human beings on an industrial scale, it was the belief that those gods needed to be fed human hearts to keep the world from ending.

ISIS are equally extremist. It isn't the belief in Allah that's making them kill. It's because they are, when you get right down to it, a bunch of nutjobs - unlike the millions upon millions of Muslims who are absolutely no threat to anybody.

Terrorism exploits two things : fear (please read), and our terrible natural skills at analysing statistics. We are not designed to think statistically. If anything, quite the reverse : we have evolved to see more threats than there really are, because escaping threats that aren't there is far safer than not spotting threats that are there.

The total number of fatalities due to terrorism (of all causes) in France in the whole of the 20th and 21st centuries is 305. Even if all of those had occurred during a single year, as an individual you should be more scared of hot weather. Literally. The 2003 heatwave is estimated to have killed over 14,000 people in France alone. Yes, terrorism is evil and yes, we should try to stop it. But with a French population of over 60 million, the chances of any individual being killed in a terrorist attack in France are close to nil. EDIT : You are far, far more likely to drown, die because of nasty weather or a transport accident or because you fell over, than by a terrorist attack of any motivation. Statistically, terrorism is not much more dangerous than getting pregnant. 

The conclusion from this is inescapable : it does not make sense for us to feel unsafe. Our reactions are driven by gut emotions, which are there for a very good reason but are not logical. In the jungle, almost all tigers are dangerous, so it makes sense to run away from them. In modern European cities, practically no Muslims are dangerous, but our hyper-inflated pattern recognition abilities tell us otherwise.

From the excellent Spurious Correlations.
The real danger comes from our reaction to the terrorist attacks. If we give in to hate and start discriminating against European Muslims, we will make the problem worse. ISIS will say, "look how they hate you" and more people will join their cause, not because they are Muslim but because they are hated. I agree with Zunger that in the Middle East, military action may be the only way to stop ISIS - but it will utterly fail in the long-term if we don't also look at the underlying causes. The challenge in Europe is to differentiate any foreign military intervention from the treatment of Muslim citizens of Europe.

A few months ago I probably would have agreed with most people that Muslims need to be more vocal about distancing themselves from terrorists. Now I'm not so sure. Maybe all our insistence that they stand up and differentiate themselves is just another way of excluding them from European society, potentially creating a problem where none existed. Maybe the answer isn't less tolerance, but more.

Saturday 14 November 2015

Fear : A Short Exploration In Mostly Memes

What is is that we fear ? According to Batman :

Knowledge and understanding aren't perfect weapons against fear. Some fears are pure, irrational instinct that are almost impossible to overcome. A few are genuinely hilarious unless you happen to be one of the afflicted.

But often we can overcome fear through knowledge. Which is why sometimes there's only one thing to fear :

Sheldon teaches us that fear is indeed a pretty scary thing. Why is that ? The Bene Gesserit have the answer :

Fear can make us stupid. It does not permit us to think, only to feel. Why can this be dangerous ? For that we turn to master Yoda :

But what's the point of being afraid if all it does is cause such awful problem ? Doctor Who says :

And maybe, says the Doctor/Clara (it's a closed timelike curve so we don't know where the information originally came from) :

Which is why, if the choice is to be a coward or killer, there's only one answer :

But most of us aren't so wise and strong. That's what makes fear such a potent weapon of the manipulator. Extremist politicians (right and left) thrive on fear because fear is the mind-killer. "The [insert ethnic or religious group that happens to be currently out of favour] are responsible for this atrocity ! Yes, all of them, not just the terrorists !" And because people have died, fear is a natural response and easy to provoke. We want to lash out, to find someone to blame so we can feel safe again. Fear makes us stupid. We forget about all the legions of ethnic/religious group members that are just like us. We forget about all the ethnic/religious groups we used to fear but have successfully integrated with.

The problem isn't the blacks, or the Irish, or the gays, or the Catholics, or the French, or the Syrians, or the Scots, or the Muslims, or the whole of religion. It is extremism of any ideology. I do not fear any of those groups. I fear those who would have us believe in simple solutions to complicated problems, who want to stop us from thinking. But to those who would say that it's all the fault of the Muslims, or religion itself, I say this :

The Muslims don't scare me. Those who want to discriminate against Muslims, to treat them as sub-human on the basis that some of them are nasty people scare me. Those who think that atheism is a defence against extremism scare the crap out of me. But in the end :

You cannot blame whole groups of people for the actions of individuals. It's never made any sense, and it never will.

Friday 13 November 2015

When Worlds Collide : Science In Society

What Is Science, Anyway ?

Science, someone told me recently, is a business. This bold assertion made me too angry to respond because I've seen first-hand what happens if you try and run an observatory as a business, and it just plain doesn't work. Science is not a business. Nor is it art, or politics, or journalism, or a religion, or anything else. It's it's own thing, but like most enterprises it does have some aspects of all of those. Today I'm going to explore a few of those and look at how science and other endeavours relate to each other.

Is science a religion ? Actually screw this one, I can't be bothered.

I've written far too much to bother repeating myself as to why science isn't dogmatic to go through all that again. Simply put, if you think science clings fervently to its beliefs, you are deluded. Nor does religion refuse to admit its mistakes either, though both religious fundamentalists and individual, highly intelligent scientists can and do sometimes behave like this. No amount of devout atheism will save you from being a blithering idiot - or, more to the point, from having any irrational beliefs at all. But I really don't want to dwell on this today, so just go and watch the movie Contact. Don't worry, I'll wait. Just don't bother bringing this up in the comments because I'm not in the mood, OK ?

Fair enough. What about the arts ?

You might not necessarily think that science has much in common with art either, but you'd be wrong. As explained previously, the humanities courses can be an essential tool in developing rational thinking. I'll get to the most obviously relevant form of this - journalism - in a minute, but even the purely creative arts share important aspects with science. And I don't mean the more obvious overlap of scientific illustrations, which have to be able to inform as well as (in a sense) entertain - I mean something much more fundamental.

Problem solving is not so very different to creativity. This is especially important in theoretical physics, where thinking up radically new concepts is the key to making breakthroughs, but it's also essential to be able to come up with new ways of analysing data or doing new tricks with old technology. Finding new interpretations of old data is also tantamount to being creative.

These similarities mean that sometimes the process of doing both science and the arts can be very similar. Both require large amounts of time to do nothing but thinking (and in the case of science at least, an awful lot of background reading). Inspiration can't be forced - you cannot make people have new ideas. You can, however, encourage them. Science and art are both sometimes highly elaborate forms of play, to explore the question, "what if I did it this way...", or better yet, "what does this button do ?" Such thinking intrinsically demands a liberal, reasonably informal atmosphere. Insisting that people are at their desks during some particular set of hours and only talk to each other during scheduled meetings makes absolutely no damn sense whatsoever.

And art and science sometimes both require large amounts of trial and error and sheer patience. Scientific productivity is hard to measure in any case (more on that later), but it simply cannot be evaluated at all on hourly, daily, or even weekly timescales.  Above all, both require the freedom to fail - to spend years on something that may very well be utterly useless without worrying that it might end careers if nothing useful turns up*.

* Recent example - this project took a full seven years to complete, and it could easily have been the case that we would have found nothing interesting whatsoever. So you can take your hourly timesheets and file them where the sun does not shine, thanks.

You might say, "Well, in science a negative result is always useful, and in art, paintings that people hate today might be seen as masterpieces eventually." And that's partially true. Sometimes results in science also aren't recognized as significant until centuries after their inception. And, sometimes, like terrible works of art, they are just god-awful and done by people who are simply very, very stupid.

On the other hand there are plenty of pictures of Jesus, but very few that could be described as "a very hairy monkey in an ill-fitting tunic", so maybe this one wasn't such a waste after all.
The point is that sometimes there's just no way to know in advance if your research will be a load of tripe or lead to the invention of electrical power. To invest only in research you believe is more likely to have practical benefits is the sign of a small mind bereft of vision. You cannot innovate without taking risks. With science, the payoffs - electricity, radio, television, communications satellites, hurricane prediction, the internet, fewer diseases, greater food production, cheap global travel - are so stupendously important that I'm continually amazed by the ongoing need to justify science expenditure at all. It just makes no sense to me whatsoever. Perhaps it's because these things are such an integral part of our daily lives that we don't often think of them as scientific advances.

And no, I don't care about the typo.
Of course science isn't quite the same as the arts. Scientific freedom of thought has to be constrained by observational evidence, whereas the imagination of an artist has no such limits. Scientists can question whether the observations were done correctly, but that's as far as you can go - if your theory predicts that a plane will fly and it doesn't, well that's tough on you. Art on the other hand has no such clear objective measurement.

Journalism then.

Good journalism is the search for truth, no matter how unpleasant it may be or how many people want to stop you from exposing it (excepting perhaps cases where that might endanger innocent people). Similarly, good science is about the search for truth no matter how crazy it might seem or how opposed it may be to any and all ideologies.

Bad journalism, on the other hand, is all about making a sale : telling people what they want to hear or what evokes such a strong emotional reaction that they can't help but feel it's correct. It's much more about who than what or why. Similarly, bad science is about only going for easy, non-controversial results, never considering alternative ideas, interpreting the evidence to mean what you already think it should mean, and deliberately trying to agree or disagree with specific people rather than their ideas.

Sorry Augustine, but that's total rubbish. If it was true we wouldn't have people still claiming the Earth is frickin' flat or refusing to use vaccines. Maybe natural selection will kill off those idiots eventually, but it's a slow and unnecessary process. Bad journalism and bad science (and bad science communication) can be immensely damaging practises.

Good science is a lot like good journalism. The major difference is that science isn't about people, it's about specific things and general trends : the ability to say, "if I do this, given these conditions, then that will always happen." Journalism, on the other hand is usually only about discovering what happened in the past in a very specific circumstance, rather than what might happen next. Journalist's predictions are (often simply because the number of variables is so large) only speculation, even if they are very well-informed speculation, whereas established scientific results are always true. Heating up lead to ~350 C will always melt it - unlike in politics, it doesn't matter what the mood of the experimenter was or whether they'd gained enough support of their peers.

There's also a curious difference between science and journalism when it comes to impartiality. It's usually the job of a journalist to communicate the findings of experts to the public rather than present their own opinions, at least when it comes to making predictions. But it is not always the job of a scientist to be impartial. Scientists are supposed to be objective, which is not the same thing.

Suppose some imbecile of a politician decides that astrology really works. It's the job of a journalist to interview both the politician, scientists, and possibly members of the public to inform people what those groups believe, not to decide who's right and who's wrong. But it is exactly the job of a scientist to decide what's right and what's wrong, to tell you what the evidence says. When the case is a decisive as this, being impartial is not being objective at all, because astrology objectively doesn't work. It doesn't matter if you disagree, you're wrong. Science is not a democratic process.

Not quite true : you do need people's opinions on facts, but we'll get back to that soon.
It's the job of a scientist to form an opinion based on the evidence. As usual it all comes back to this : the beliefs of science are evidence-based and provisional. But for established results which have mountains of evidence (or even irrefutable proof) backing them up, objectivity and impartiality could not be further apart : a scientist who believes the Earth is flat is an oxymoron.

When it comes to cutting-edge research, however, it's another story entirely. Scientists should, of course, try and assess the evidence in an unbiased way. But that does not mean they shouldn't form an opinion about it, only that they should be prepared to change that opinion given different evidence. Of course, when there is very good opposing evidence to an idea, scientists should be honest enough to state, "this is my opinion, but for an alternative you should talk to that guy." But you cannot expect scientists not to express their opinions at all, which brings us neatly on to the next area.

Tuesday 10 November 2015

Keenan's Ring

Or, Galaxies Behaving Badly...

I've been itching to write this post for a while. They say the first one's always the hardest, and that's certainly true of astrophysical papers. Much toil has gone into this over the last year or so on the paper alone, but the results are not only very interesting, they're also pretty.

If we could see the hydrogen gas in the galaxy M33, it would appear around five times larger than the full Moon.
The super-short version is that we've found a new hydrogen cloud (not shown above, you'll have to keep reading for that) near to the Triangulum galaxy. It's the largest, most massive cloud that's been found there in over 30 years, and it's ring shaped. We have no idea why it's a ring, let alone what the cloud actually is. A giant starless galaxy ? A huge shell of hydrogen somehow thrown out of the galaxy ? Nothing seems to work. But to understand why this is so difficult to explain, read on.

(Note that I could have given this the clickbaiting title of "Arecibo Scientists Baffled By Giant Hydrogen Cloud" or, "Find Out Why Astronomers Can't Explain This Huge Celestial Ring" or even, "One Young Scientist Went Looking For Galaxies And You Won't Believe What Happened Next". But I didn't, because I am not a moron.)

As usual, the first part is an introduction. If you'd rather skip straight to the new results, scroll down to the "Hydrogen Hunting" section.

Trouble in the Neighbourhood

At first glance, our Local Group of galaxies is a somewhat dull place. Our Milky Way is like a great galactic introvert, hanging out with just a couple of close friends (Andromeda and Triangulum - also known as M31 and M33) and steering clear of heaving nightclubs like the Virgo cluster. Or so you might think.

The Local Group (left) compared to the nearest rich galaxy cluster (Virgo, right). The field of view - about 6 million light years - is the same in each case; the galaxy sizes have been exaggerated by a factor of twenty. Galaxy images come from the Sloan Digital Sky Survey. Small galaxies in the Local Group are shown as faint transparent fuzzy patches. You can just about see Andromeda flying past, but good luck spotting the tiny Triangulum.
But look a little closer and the Local Group turns out to be less of a fancy soiree and more of a rowdy house party. True, there are only three giant galaxies, whereas the Virgo cluster has many hundreds (possibly thousands). If you count smaller (dwarf) galaxies, the Local Group still only has around a hundred at most - it's nowhere near as crowded as a cluster, but we haven't got to the good stuff yet.

I've already described how the numbers and orbits of those dwarfs aren't anything like what we expected (have a look here, points 5 and 6). In short there aren't anywhere near as many dwarfs as models predict, and while they should be buzzing around the giant galaxies like a swarm of bees, they're actually orbiting in loose planes at right-angles to the discs.

So the Local Group is maybe like some sort of non-conformist hipster club where no-one tells anyone what to do. But that's just what we see in the visible light. When we look at the atomic hydrogen gas* using radio telescopes, things get even stranger - and messier.

* See link for details, but remember that atomic hydrogen can only be seen using radio telescopes - so colours are false.

Two major features dominate the group. The first, and most spectacular, is the Magellanic Stream shown above - a huge stream of hydrogen gas that runs halfway around the sky. Possibly more. Whenever observations get more sensitive, it seems we find it's even longer than we realised.

Most - possibly all - of this gas seems to have come from the Magellanic Clouds, two nearby dwarf galaxies. Exactly how the gas got into this peculiar configuration is not well understood, but probably has something to do with how the two galaxies are interacting with each other whilst orbiting the Milky Way. The stream isn't spectacular just because it's close though. At well over half a million light years, it's one of the longest hydrogen streams known.

Fading between an optical image of the Magellanic Clouds and the hydrogen data which shows the gas stream.
The second feature is another, much fainter stream linking Andromeda and Triangulum. This is another dramatic structure at 850,000 light years long. It's also one of the faintest hydrogen streams known, and was only detected by a survey of exceptionally high sensitivity and low resolution. So, unfortunately, there aren't any pretty pictures of this one.

Map of the M31-M33 stream from a paper by Braun & Thilker 2004.
So whereas the Local Group has three large galaxies and two hydrogen streams which are nothing less than awesome in extent, the Virgo cluster may have thousands of galaxies but it's only got four major streams. Looks like it's a win for the hipster house party, then. Of course the Virgo cluster has its own weirdness, but that's another story.

To understand the new results, there's one other important feature of the Local Group you need to know about. Although the main part of the Magellanic Stream doesn't go anywhere near Triangulum, a bunch of smaller clouds do. Could there be some connection between the Magellanic and the Andromeda streams ? I dunno. M33 and M31 are a lot further away than the Magellanic Clouds and the stream would have a really weird, sharp kink in it, so it could just be a complete coincidence.

Probably the best map of the stream produced to date, from a paper by Nidever et al. 2010. M33 is just above Wright's Cloud (which we'll talk about soon).

Hydrogen Hunting

Now that we've got the proper context, the new results. Most of the smaller galaxies in the Local Group are orbiting the Milky Way and Andromeda. Only one is believed to be associated with Triangulum, and that's not certain. Together with all these crazy streams (especially the M33-M31 stream), back in 2006 it seemed like a good idea to look at the hydrogen in and around M33 as part of the Arecibo Galaxy Environment Survey, AGES. This is one of the most sensitive atomic hydrogen surveys ever performed, so if there's anything interesting, AGES is what will find it.

"If all else fails, point a 300m telescope at it."
It took us five years to complete the observations - without any guarantee that we'd detect anything interesting in the end. That's the problem with a telescope that can't be steered much, but it isn't normally this bad. The difficulty was that the survey area is at the absolute northern limit of where Arecibo can see, so often we could only observe it for an hour a night. Factor in that other projects sometimes get priority, the fact that we can't see the region at all for more than half the year, and various equipment failures, and five years doesn't seem quite so bad.

Five years of stating at computer screens...
More staring at screens...
Everybody look serious now. Come on people, this is science.
Occasional bouts of madness began to set in...
... which were usually solved with late-night Dominion sessions.
Sometimes even the ALFA receiver went a little nuts and had to be taken down for repairs.
Most of the people above didn't do observations of M33. In fact most of the time we just did it by setting up a script and going home.

After all this, what did we find ? Well, firstly that the hydrogen of Triangulum is considerably more extended than what the last major survey of the area had revealed. Some of the "clouds" that ALFALFA had found turned out to just be slightly denser parts of this larger disc. Also, the disc is really quite faint - so faint, according to earlier work, it should be ionized. But it isn't. You could call it, "The Hydrogen Cloud So Large It Shouldn't Exist", if you want to clickbait it*.

* But don't. It's not the only hydrogen detection known below the ionization threshold nor the first such discovery.

Animation showing the hydrogen in M33 at different sensitivity levels. If your sensitivity isn't very good, all you'll see is the densest gas in the stellar disc. Go a bit deeper and you'll see things are a lot more extended, and part of the disc (upper right) is warped. Go as deep as AGES and you'll see that even this extended component is actually just part of something even larger.
There's one more brief digression I must make for the sake of non-regular readers. Hydrogen observations depend on frequency - that is, how fast something is moving towards or away from us. Which means our radio maps are actually 3D data cubes. They're very cool to look at (and extremely useful, as we shall see), but velocity is not the same as distance. For example some of the hydrogen in M33 has the same velocity away from us as does the hydrogen in parts of the Milky Way. So in these data cubes it can look as though the hydrogen in M33 and the Milky Way overlap each other - but in reality they're actually separated by over a million light years.

M33 is the big bright thing in the middle. Some hydrogen from the Milky Way can be seen as the big flat thing at one edge of the cube.

Anyway, although the new observations showed that some clouds weren't clouds at all, they also found new ones that pretty much exactly balanced out the numbers. Just enough to agree with how many satellite galaxies models of galaxy evolution predict there should be... but none of them have any stars !

Could these be the "missing satellites" that people have been searching for for so many years ? It's not impossible, but I doubt it. Firstly, it doesn't seem very likely that only this one galaxy happens to have the right number of companions and they just happen to be made of gas rather than stars - the model's so badly broken for other galaxies, fixing it with this one wouldn't really help. Secondly, the motions of gas in the clouds don't match the model predictions*. Thirdly, they're not distributed like the predicted "swarm of bees" at all - they're found in a distinct band. There's a hint that some of these clouds are actually linked together and part of a much larger structure.

* This is a debatable point though. More precisely, models predict how fast the gas should be moving within galaxies, and also how it's moving - that is, they predict it should be rotating. The observations say the motions are random. But a new paper has just been submitted saying that maybe the motions should be random after all.

Some of the clouds we detected with AGES (M33 is right in the middle, but at a different velocity so it's not visible here). Notice that there aren't any clouds in the top half of the survey area. Though it is awfully strange that the number of clouds is almost exactly enough to account for the missing satellites.

And two of the clouds are much, much bigger than the others. One of them - Wright's Cloud, which we mentioned earlier - has been known about since 1979. The most popular explanation is that it's part of the Magellanic Stream, or at least related to it in some way. Although it's not that close to the main stream, it does seem to follow those smaller clouds heading from the stream towards M33. It's a bit strange though, since Wright's Cloud is far larger than any other cloud at that distance from the Magellanic Clouds.

Now, 36 years later, we can reveal another giant cloud right next to Wright's Cloud that no-one had ever detected before. Well, that's not quite true. Parts of this new cloud had been found by ALFALFA. But our new observations were more sensitive over a larger area, and they've revealed that these clouds are actually just a small part of a much larger ring :

The centre of M33 (not shown) is just above and to the right of the ring.
We're calling this Keenan's Ring after "Princess" Olivia Keenan who discovered it and did most of the hard work of writing the paper. There isn't really any convention for naming hydrogen clouds, but if we get this in common usage it will probably stick. After all, it sounds a lot better than its catalogue designation AGESM33-31.

Map of all the clouds in the area. Keenan's Ring is at about as large as M33 and yet no-one knew about it until now.
So what the heck is it ? It all depends on how far away the cloud is, which we can't measure directly. If it's as far away as M33, then the thing is about 60,000 light years across - as big as the hydrogen of M33 itself ! And that would be seriously strange, because there's no obvious way to form a stonkin' great ring of hydrogen gas like this. Models show that you can do it through colliding galaxies, but M33 doesn't look as though it's had any kind of major collision recently. The gas in the Ring appears to be completely separate to the gas in M33.

The full data cube. Colours are arbitrary - blue was chosen to highlight the gas in the Milky Way, which fills the entire field of view. Orange shows everything else. M33 is the big orange blob in the middle. Wright's Cloud is the brightest-looking orange cloud which is cut off by the edge of the survey area. Keenan's Ring is visible, as are a bunch of other smaller clouds. The data looks noisier around the Ring and the Cloud, but this is just an artifact due to how the data was visualised.

Because this gas cloud is so dang large, could it be a giant, failed galaxy ? A tempting idea. Although M33 doesn't seem to have collided with anything recently, there is a strange "warp" in its hydrogen disc, and Keenan's Ring is on exactly the opposite side of the galaxy. Which is what you might expect if a giant object had come sailing past. Also, the densest gas in the Ring is closest to M33, suggesting that M33 is exerting a gravitational influence on it (which isn't the case for Wright's Cloud, which has a higher density in its center).

But this idea doesn't really work. Although there is a small velocity gradient (the gas on one side is moving at a different speed to that on the other) across the Ring, which is often a sign of rotation, it's far smaller than for M33 (~30 km/s compared to ~180 km/s). A galaxy as large as M33 really ought to be rotating as fast as M33 - if it isn't, then it isn't as massive, so it's far less likely to explain the warp. And if it was massive, that would make the predictions of the models of how many galaxies there are even worse, not better.

It also doesn't seem a likely coincidence that Keenan's Ring and Wright's Cloud are at almost exactly the same velocity. If Wright's Cloud is really just another part of the Magellanic Stream, then it seems probable that Keenan's Ring is as well. This, in my opinion, is the most likely explanation. But it's not without major difficulties either. Why in the world should there be two massive clouds near the end but significantly offset from the main stream ? And if it's not a coincidence that Wight's Cloud is part of the Magellanic Stream because it's so close, then surely by the same token it's at least equally likely to be associated with M33 in some way as well ?

No-one seems to have any answer to this. And it's also worth remembering that Wright's Cloud and Keenan's Ring are at different velocities to the other clouds detected in this area, suggesting that they might have different origins. Yet they're also very different to each other. Wright's Cloud is larger, much more massive, doesn't show any signs of a velocity gradient, has an irregular structure, and is denser in the centre. Keenan's Ring does have a velocity gradient (albeit a small one), is much denser on one side than the other, and is of course ring shaped.

And perhaps the most difficult question to answer applies to any scenario : why is it a ring ? A disc, well, that's fine - could be a giant galaxy, or just a cloud, whatever. An amorphous blob like Wright's Cloud - yeah, also possible, could be interacting with all the other clouds and M33, no problem. But there's no obvious reason why the gas in the middle should be missing. Where's it gone ?

Could it just be that the "ring" is a bunch of clouds which happen to line up and look like a ring ? Not likely. That would require an extremely unlikely chance alignment of clouds - there's no reason you'd expect the central region to be underpopulated just by placing clouds at random. And although the velocity gradient is small, it does have one. If it was a bunch of random clouds, you'd expect the velocity of each cloud to be different. But the velocity of the gas across the Ring varies quite smoothly from one side to the other, which you wouldn't expect if it was made of separate clouds. It's possible, but not credible.

Map showing the velocity of the gas at each point in the Ring

Honestly we really just don't know what this is. Supernovae explosion are known to blast holes in the hydrogen, but if it's close to M33 then the hole is about ten times larger than any other known holes. Nor are there any obvious star clusters (massive stars aren't thought to be able to form in isolation), so if it's inside our own galaxy the Ring would be much smaller but probably just as strange. And it would be one heck of a coincidence if this structure just happened by chance to not only be so close on the sky to Wright's Cloud but at such a similar velocity.

Like all the most interesting discoveries, this one poses a lot more questions than it answers. Which, if you ask me, makes it five years well spent.