The Rescue

Violence is totally alien to people on this planet

In the vast expanse of the South Atlantic, halfway between South Africa and South America, an ancient volcano rises from the sea. This is the main island of Tristan da Cunha, the most remote archipelago in the world, home to around 260 souls. And it’s British.

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Tristan da Cunha as seen from space

There is one policeman in the British Overseas Territory of Tristan da Cunha, and he’s pretty bored. His colleagues back in Blighty investigate crimes from burglary to murder, but for Inspector Conrad Glass a stolen bicycle would be the highlight of his year.

The fact is that on Tristan da Cunha, with its one pub and six surnames, there is hardly any crime to speak of. Everyone knows everyone else, and when Inspector Glass is called in it is generally to calm down arguments between neighbours, not to arrest and prosecute criminals.

It sounds like an ideal society, unless you are a policeman. But the relative tranquillity of these islands is not the result of any unusual virtue among the inhabitants, nor has it come about through any political genius. Rather, it is a predictable result of the capacities and limitations of the human brain.

It’s hard to commit crimes against people who you know, and harder to get away with it when everyone knows everyone’s business. Yes, there are people who will do terrible things to their closest friends and family, but these are thankfully rare. A small community isn’t guaranteed to be peaceful, but there is at least a good chance that a small enough group, with effective social sanctions to deal with issues before they become too serious and a token police service as a backstop in case they do, could come as close as possible to a crime-free ideal.

The question is, how small is small enough?

The anthropologist Robin Dunbar noted that, in apes and monkeys, there is a good correlation between the size of the neocortex relative to the rest of the brain and the size of the typical social group. The neocortex is involved in many of the higher brain functions, including sensory perception, language and conscious thought, so it’s reasonable to suppose it plays an important role in managing social relations. The correlation noticed by Dunbar suggests that the processing power of the brain sets a limit on the size of the animal’s social group, much as the processing power of your computer limits the number of browser tabs you can keep open at once.

But Dunbar went a step further. He extrapolated this correlation to humans, who have a larger relative neocortex size than any other hominid. This predicted a human group size of 148, though uncertainties in the data mean you can only really say that the group size is somewhere between 100 and 200.

Regardless of these uncertainties, a slightly rounded figure of 150 has now become known as Dunbar’s Number, and is frequently invoked to explain all kinds of social group size, from the average size of villages in the Domesday Book to the size of Army units – the average standalone unit, the company, averages about 150 soldiers.

Of course, you can be acquainted with far more than 150 people, but this does seem to be number of people with whom you can have a genuine social relationship, defined by Dunbar as people you wouldn’t feel embarrassed about joining for a drink uninvited if you happened to bump into them in a bar. Studies of social networks show that the same considerations apply in virtual space: we can have thousands of Facebook friends, but the number that we have some real connection with, as opposed to vaguely remembering from school and paying no real attention to, is limited to about this number of 150. (Speaking of which, I’ve just checked my Twitter profile and the number of people I’m following is… 151. Sorry, but one of you is going to have to go.)

So groups of one or two hundred people can all know each other, but in itself this isn’t enough to keep the peace. Roughly speaking, there’s about 5% of the population who are willing to commit the most appalling crimes in cold blood against people they know well. Some of these people have some recognised clinical condition such as sociopathy, others are just pricks. Whatever their reasons, we could expect our group of 150 people to have 7 or 8 such individuals. That may seem like quite enough dangerous criminals to have in your community, but bear in mind that whether these potential criminal proclivities translate into actual offending is highly situational. It depends on motivation – do they think they have something to gain from the crime? – opportunity – do events put them in a position where crime looks like a good idea? – and ability – even the most sociopathic three-year-old is unlikely to murder the babysitter, and the infirm elderly tend not to get into bar fights. It’s also worth noting that this figure of 7 or 8 is an average, and will fluctuate from time to time, and from population to population. The rule of thumb for counting statistics is that the standard deviation – a measure of the size of fluctuations – is the square root of the average number, so here the standard deviation would be a bit less than three. So a typical range might be 4 – 11, and it wouldn’t be terribly unlikely to sometimes be zero.

Also, some risk factors for criminality have a hereditary component. In particular, sociopathy – the lack of empathy towards others – has a heritability of around 50%. If, by whatever chance, our initial population has few of the genetic factors involved in sociopathy, then the number of potential criminals in subsequent generations may be much lower than the estimates above. (Though there is a caveat: these numbers for heritability come from recent studies on sample groups from the US: the heritability level in a radically different environment may be much higher or lower.)

So a small community may not be perfect, but it certainly seems like it’s more peaceful than the average Monday morning on the tube, never mind daily life in a high-crime inner-city estate. In which case, why don’t we all live like that?

Well, the historical development of urban civilisation is a bit long for this blog post, but the fundamental point is that larger societies are able to do more, different things, are able to advance and innovate artistically, scientifically, socially and technologically in ways that small groups simply can’t achieve. Our ancestors used stone tools for a million years, and the incremental development was so slow that an untrained eye would be hard pressed to distinguish a Lower Paleolithic axe head from a Neolithic model. By contrast, the distinction between a Roman pilum and a Heckler & Koch G36 assault rifle would be apparent to the dullest Neanderthal.

The science fiction author Charlie Stross recently tried to establish what would be the minimum population required to maintain a technological civilisation of the level we have today. It’s about having enough people for the division of labour and specialisation that makes our society possible. It’s about having people who can build all the things we use, people who can maintain them, extract the raw materials needed for manufacture, distribute them throughout the population. It’s having educators who can train the population in complex tasks, farmers who can provide raw foodstuffs, butchers, bakers and sandwich makers who ensure the population is fed, artists, actors and writers who create the vital cultural life of the society, through simple entertainment or deep reflection. It’s about the bin collectors and sewage workers who stop us all drowning in filth, the clinicians and support staff who keep us healthy and care for the sick. It’s even about the politicians and bureaucrats who keep the whole thing working, and the emergency services who step in when it doesn’t.

Stross comes up with an estimate of about a hundred million people. This is roughly the number of people who would have to settle some alien planet before it could be a self-sufficient technological society like the one its people have just left. It’s a bit of a hand-wavey number, to be honest, but even if it’s too high by a factor of ten or a hundred, it still tells us that if a technological civilisation is to survive, it must be of a substantial size – much too large to be peaceful in the way that tiny populations can achieve.

So what of the Didonians? We are assured they are a peaceful people, and that they numbered only about a hundred – few enough that Bennett could reasonably think he had wiped them out by attacking one small ceremony. But with such small numbers, there is no way they could develop a “new ray” for use in construction. Indeed, even the elaborate spike traps in the cave would probably be beyond them: their design and construction would require significant division of labour and surplus resources.

Mind you, if they’re such a peaceful people… who are the spike traps for?

 

The Dalek Invasion of Earth

They dare to tamper with the forces of creation?

Diagram of Earth's interior

Interior of the Earth (courtesy of openlearningworld.com)

The inner core of the Earth is a ball of solid iron about 2400 km across – 2/3 the size of the Moon. Its temperature is 5400 °C – about the same as the surface of the Sun. And it’s freezing.

When the Earth first formed, its interior was molten all the way through. Gradually it cooled, and the centre solidified. Although still incredibly hot by human standards – iron melts at about 1500 °C in the open air – the high pressure caused by the weight of all the Earth pressing down upon the core raises its melting point so that it freezes solid even at these sunlike temperatures. The interior is still cooling, and the solid inner core is slowly growing as the lowest layers of molten iron in the outer core freeze onto it.

Now freezing releases heat. If that seems an odd statement, think of it this way. You have to put in heat to melt a solid, using energy to break the molecular bonds. So if you reverse the process, as a liquid freezes that same heat must be given up.

That’s important in the Earth’s core. The heat released by freezing at the boundary between the inner and outer cores drives convection currents that make the liquid outer core roil and swirl restlessly.

Iron, of course, is a magnetic material, and all that circulation of liquid iron generates a powerful magnetic field. This field reaches to the surface of the Earth and far beyond into deep space. It allows seafarers to navigate with a magnetic compass, shields our planet from the full anger of the Sun, and channels the solar wind to the polar caps to create the shimmering curtains of the aurora.

As we move up through the outer core, the pressure drops and the temperature decreases. Once we get about 3500 km out from the centre, we hit another boundary. Above this depth, the composition changes. We are too high up for the heavy iron that sank towards the centre. Instead we have something more like ordinary rock, predominantly silicates, but under temperatures and pressures that are far from ordinary. This is not the flowing fluid of the outer core : neither is it the crystalline solid of the inner core or the crust. Instead it is an incredibly viscous, slowly flowing material called the mantle.

To get a handle on how this stuff behaves, we can look at the world’s longest-running scientific experiment – the pitch drop experiment.

Tar pitch is about the most viscous substance in human experience. To get an idea of what this means, go into the kitchen. Fill a glass with water, and stir it. Easy, isn’t it? That’s because water had low viscosity. Now try stirring a jar of honey. That’s a lot harder – the viscosity of honey is about ten thousand times that of water. If you have some peanut butter, give that a stir. It’s about 25 times more viscous than honey, and about the most viscous thing you’re likely to have lying around.

Tar pitch is a million times more viscous than peanut butter.

The original pitch drop experiment started at the University of Queensland in Brisbane in 1927, and is still going strong. It’s quite simple, really: a funnel is filled with tar pitch, and a drop slowly forms at the bottom of the funnel as the tar flows out, eventually dropping off, and then a new drop forms. They’ve recorded a drop every eight years or so. Just recently, a similar experiment at Trinity College Dublin was the first to record a drop falling on camera. (The Queensland experiment missed filming its most recent drop because the camera was offline.)

Mantle is ten trillion times more viscous than tar. Ten million trillion times more viscous than peanut butter.

So it’s incredibly stiff, but still more like tar than ordinary rock: it has no crystalline structure, and flows, however slowly, under pressure.

That lot makes up the bulk of planet Earth. On the outside edges there are some details: mantle that flows more readily thanks to the low pressure near the surface and, floating on top of it, some solid plates of cold, brittle rock on which various biological organisms live out their brief, meager lives.

So what the hell are we to make of the Dalek’s plan to remove the core of the Earth? First of all, if they want to do this by drilling a hole through the crust, Bedfordshire is a terrible place to do this. You have to drill through 30 km of crust there, as opposed to less than 10 km on the ocean floor. If underwater operations are too much of a drag, somewhere like southwest Ireland would still be a lot easier.

Wherever they drill, they are going to drop some device down into the core and suck out all the molten material. Presumably through some kind of magnetic funnel, but this is the Daleks so I wouldn’t put it past them to use a giant bendy straw. However they do it, what are the effects?

The first thing this would do is reduce the pressure on the solid inner core. This is still very hot, so once the pressure drops it will start to melt. As it does so, it will be sucked out along with the outer core, leaving the Earth entirely hollow.

(Top tip : never try to find scientific information on this subject by googling “hollow earth”. You will descend into a swirling vortex of maniacs and conspiracy theorists.)

Imagine the interior of the Earth at this point. It’s a great hollow cavern 7000 km across. There’s no gravitational force. This is because a particle inside a spherical shell experiences a force towards the nearest part of the shell, and an opposite force towards the furthest part. The lesser distance of the nearest part, and the greater volume of the furthest part, exactly cancel each other out, resulting in zero net force.

And it’s hot. The inner surface is at a temperature of around 3500 °C, hot enough to glow red. Not only is it hot, but it can’t cool down, except by losing heat slowly upwards through the remaining shell of the Earth. It’s radiating heat into the vacuum inside the Earth, but any given patch of this inner surface will not only lose heat through radiation, it will also absorb radiation emitted from the rest of the surface. These two processes exactly balance each other. Like gravity, radiation follows an inverse square law, and so the same mathematics that tells us the gravitational force inside the shell is zero also tells us that there is no net loss of heat.

It’s also melting. With the removal of the core, and hence the removal of its gravitational pull, the pressure on the mantle has dropped. That pressure was the only thing keeping it solid at these high temperatures, and with the loss of that pressure it will undergo decompressive melting. Indeed, this will happen as the core is being removed, so we can expect the mantle to liquefy and be sucked out as well in its turn.

Of course, as you are removing the mantle from the inside out, you will be taking the hottest material first and gradually working outwards into progressively cooler mantle. At some point, you will reach a level where the temperature is low enough that the mantle will not melt even though the pressure has been radically reduced. Actually calculating where that point is would be a substantial research project, and one for which it would be difficult to obtain funding. We can, however, put some upper bound on the answer. The temperature at which mantle rock melts on the surface of the Earth is about 1300 °C. That corresponds to a depth of about 200 km or so. Our remaining shell of the Earth isn’t going to get thinner than this, and may stay somewhat thicker.

So by the end of all this the Daleks have removed about 90% of the Earth’s volume, leaving behind a brittle solid crust sitting on top of a thin spherical shell of ductile rock. We have to hope that this lower layer is strong enough to hold together under its own self-gravity and the weight of the crust above it, otherwise this planet is going to implode like a cheap meringue.

Even if that doesn’t happen, the consequences for life on the surface will be catastrophic. All of this planetary-scale geoengineering will at the very least cause the crust to buckle and fracture as the mantle beneath is disrupted and removed. It will be like every earthquake, every volcano and every tsunami in history hitting all at once.

With the Earth’s mass reduced by more than 90%, the surface gravity will drop by the same fraction. The Earth will be no more able to hold on to an atmosphere than the Moon – indeed, even less so, as the Moon’s surface gravity is one sixth of Earth’s. Not only will there be nothing to breath, but there will be no protection from the Sun’s hard UV and X-rays. And as if that weren’t enough, the Earth’s magnetic field will have vanished along with the liquid core, leaving the planetary surface fully exposed to the solar wind.

The surface will freeze, of course. In the absence of an atmosphere, the equilibrium temperature for the Earth is about -18 °C. The greenhouse effect may have become a threat in recent decades, but it is still the only thing that keeps our planet habitable. Given that the Daleks want to zoom the hollow Earth around in space, however, we can assume that the temperature will drop even further. Gradually the remaining mantle layer will cool, becoming brittle, and sooner or later it will be meringue time – unless the Daleks have some cunning plan for preventing this.

Quite how this zooming about is supposed to be achieved is unclear. All we know is that the Daleks intend to place some kind of power system within the hollow Earth. It will need to be anchored somehow to the inner surface to prevent it drifting out of position, otherwise it would crash into the inside of the Earth whenever the planet moved. Beyond that, it’s hard to say.

What’s even harder to discern is why the Daleks are carrying out this apparently bonkers plan. There doesn’t seem to be any practical purpose that couldn’t be achieved a lot more easily and with a lot less risk simply by building a fleet of spaceships. Such as, for example, the spaceships they used to invade Earth with in the first place. The whole scheme just seems entirely redundant. Whatever purpose it might serve, it is not one that is apparent from the story or from any rational consideration.

I reckon they’re just doing it for a laugh.