Mission to the Unknown

A thorn from a Varga plant. A thing part animal, part vegetable. Looks like a cactus. The poison attacks the brain. Rational thought is replaced by an overwhelming desire to kill. Eventually the poison seeps through the system and the victim is gradually transformed into a Varga.

If one of your work colleagues accidentally got themselves pricked by a nasty-looking thorn, then tried to kill you before transforming into a plant, you could be forgiven for being surprised. After all, it’s not as if it happens every day.

And there are good reasons why. Oh, the psychotic violence thing isn’t too hard, all kinds of chemicals can alter a person’s state of mind. Indeed whole industries – legal and illegal – are founded on just such self-administered manipulations, and there are plenty of drugs that have irrational bouts of violence as a side-effect.

No, it’s the whole turning into a plant bit that’s the problem. Plants and animals have fundamental differences, right down to the cellular level, from the way they extract energy from the environment to the chemicals they synthesise to keep themselves alive. The scale of the re-engineering that would be required to turn one into the other is staggering. Literally every cell would have to be changed into something new.

But let’s look at how it might be done. How do you turn a cell into a different kind of cell? It’s not easy. Even if you could somehow restructure a particular cell, the change won’t stick. You have to get right into the heart of the cell, and transform its DNA.

The chain of chemicals in your DNA contains the instructions for building and running, well, you. Every cell in your body contains a complete copy of this information. Inside your cells, tiny chemical factories run along sections of your DNA, assembling basic chemicals derived from breaking down food into constituent parts of your body. And as the cells are continually growing and dividing, they need to make copies of the DNA so that each new cell also carries this fundamental blueprint.

Although DNA is a complex chemical, it stores information in an essentially digital form. This means we can get some insight into how it works by looking at much simpler digital coding technology. A computer.

Whatever device you’re reading this on, it encodes the letter you are reading as binary numbers, strings of ones and zeroes, that are stored as electronic states within the computer’s memory. To pick a nice, simple example, let’s look at how a computer stores the word “WHO”.

In one common form of computer representation, called UTF 8-bit binary coding, every letter and character is represented by a sequence of eight ones and zeroes. So, for example, “W” is represented by the sequence 01010111, “H” by 01001000, and “O” by 01001111. This means the word “WHO”, constructed by sticking these codes together, is the sequence 010101110100100001001111.

Now let’s create a physical object that contains this code. Evolution has to make do with the raw materials available, so in that spirit let’s imagine we’re trying to do this in the fruit and veg section at Tesco.

Let’s use apricots to stand for 0, and cherries to stand for 1, stringing them together into a fruity chain of encoded information.. Our code for “WHO” then becomes ACACACCCACAACAAAACAACCCC, where “A” denotes the position of an apricot and C a cherry. To the uninitiated observer, this will just look like a particularly unsuccessful party snack, but anyone who knows the code can tell that it reads “WHO”

This is all well and good, but we want to be able to duplicate our code by some automatic process. The way nature does this with DNA goes something like this.

Take a load of tomatoes and grapes. Go along the chain of fruit, placing a tomato beside every apricot and a grape beside every cherry, sticking them to each other with a dab of jam. (You’ll probably want to use quite small tomatoes.) String your tomatoes and grapes together into another chain. You now have a more complicated double chain that looks like

dna code

You haven’t actually added any new information, though: it still just decodes to “WHO”. So why bother with all this palaver?

Well, here’s why. When it comes to reproducing this information, we can start at one end, pulling the chains apart from each other. As we do so, wherever we pull an apricot away from a tomato we attach a tomato to the exposed apricot and vice versa, and similarly for cherries and grapes. Once we’ve finished going all along the chain doing this, we end up with two separate chains that look just like the one we started with:

dna code duplicated

both of which say “WHO”.

And that’s how DNA replication works.

OK, it’s a bit more complicated than that. The fruits are chemicals called nucleobases – adenine, cytosine, thymine and guanine – the string is a chain of sugars and phosphates, the jam is a set of covalent hydrogen bonds and the whole thing is twisted into a spiral structure called a double helix – but you get the idea. (I’ve also cheated a bit by using a simple binary code – in real DNA, all four nucleobases are used in the coding on each strand.) The splitting and duplication is done by a complex chemical called DNA polymerase, and various other chemical machines also play their part. You can see a real-time simulation of the process in all its complex glory in this video – it’s really quite a remarkable piece of natural engineering.

The replication of DNA that is going on right now in all the living cells in your body is vital to making sure that you stay you. It’s remarkably accurate, only making a mistake every billion copies or so – which is just as well, because mistakes mean bits of you don’t behave the way they should, and grow into tumours and the like.

Now, if we’re going to transform you into a murderous alien vegetable, we’re going to have to interrupt this process somehow, interfere with it so the system that keeps you being you goes wrong, and instead you become something else.

The most obvious way to do this would be to introduce some kind of new chemical machine, one that would process the DNA just as the polymerase in your body does, but would add different chemicals to the exposed strands. these chemicals would have to have one end that looked like the A, C, G, and T chemicals that the DNA strand is expecting to be married up with, and another end that looked like a different A, C, G, or T, so as to create a new genetic code. Once this was done, the new imposter DNA would replicate and multiply, transforming the cellular makeup of the unfortunate victim.

It would have to be very carefully contrived. Even doing a transformation like this at all is barely conceivable, but keeping the organism alive all the way through the process would require genetic programming of astonishing ingenuity. And of course the chemical sabotage machines would have to be designed specifically to work on the target species.

There’s no way something like this is just going to evolve on some distant planet, ready and waiting for the first unwitting human who crosses its path. It would have to be deliberately genetically engineered.

But who on Earth would do such a thing? All this incredible effort only results in killing a few humans who happen to be stumbling around a jungle, an effect that could be much more straightforwardly achieved with a few claymore mines.

It would have to be done by some hostile intelligence, of prodigious scientific achievement with a penchant for grandiose, overly-complex schemes and a fanatical hatred of human beings. An alien race capable of conquering the Universe, and yet regularly brought low by an eccentric old man in a travelling phone box. The answer, surely, is staring us in the face.

The Varga plants were created by the Daleks.


Galaxy 4

What difference does it make what your form is?

The moral of many stories is that we shouldn’t judge by appearances. Beauty is only skin deep. Don’t judge a book by its cover. All that sort of thing.

But is it true?

Over the past few decades, there’s been a lot of research into beauty – how we judge it, what effects it has on the lives of those who have it, or who seriously lack it.

The main discovery is that, in a wide variety of ways, life is better if you are beautiful. Investigating exactly why this is the case leads to some interesting and tricky questions.

If we’re going to talk about beauty, the most fundamental question is whether there is really some more or less objective thing called beauty that we can meaningfully talk about. If it’s all just down to random subjective whims, then whether one person or another is called beautiful becomes simply arbitrary, and any idea of studying beauty scientifically falls apart.

The good news – or bad news, depending on your point of view – is that assessments of beauty are remarkably consistent both within and between cultures. When groups of people are given photographs of faces and asked to rate them according to attractiveness, there is a high level of agreement. This has been found in multiple studies, and it applies however experimenters vary the gender, race or culture of the people doing the rating or the people in the photographs. White American undergraduate students judge beauty in the same way as Tsimane people of the Bolivian rain forest who have had virtually no contact with Western culture.

What’s particularly striking about beauty, though, is what is called the halo effect. We tend to ascribe good properties to beautiful people, even when these properties have nothing to do with physical appearance. Beautiful people are perceived to be happier and more socially desirable, better spouses and better parents. They are considered to be more trustworthy, more intelligent, and better at their jobs.

These effects are not confined to the laboratory. Beautiful people have higher salaries and higher status jobs, are more likely to be married, do better in exams at school and university, and if they stand for office are more likely to be elected.

On the face of it, this seems unjust. Why should a pretty face get you a better job?
Lets establish a few key points. First, there are actually two effects going on here – the “beauty premium” and the “ugliness penalty”. Both of these matter – on every measure where people who are notably good-looking do better, people who are notably plain or unattractive do worse. It is the combination of these two effects that drives inequalities related to physical appearance, and generally speaking the ugliness penalty usually turns out to be larger than the beauty premium. Being pretty is certainly an advantage – but if you’re a munter you’re screwed.

Next, this turns out not to be a gendered issue. For the most part, the beauty premium and the ugliness penalty affect men as well as women, and often they are both somewhat more important for men. This is certainly surprising, given that the beauty of women is so much more emphasised than the beauty of men, not just in Western culture, but across the world. There are a few instances in which there are consequences of beauty that only seem to apply to women, but these are very much the exception.

But what if there’s something going on here besides mere prejudice? What if beautiful people really are better?

It’s easy to see how beauty could be a genuinely relevant advantage in some jobs, like modelling or acting, and it’s hardly surprising that good-looking people in these professions can command higher fees, all else being equal. Also, the halo effect can directly enhance performance in some jobs. An experiment into soliciting charitable donations found that attractive charity workers were able to gather substantially more donations. (If you break down the figures, it turns out that the effect in this case is down to men being more likely to give money when asked by pretty young women.) The effect may be irrational, but even so if you are in the business of raising money for charity it would make rational sense to favour attractiveness when hiring and retaining staff.

What’s more surprising is that the premium for beauty doesn’t seem to bear much relationship to the relevance of physical appearance to the job. In one striking study, it was found that the beauty premium for prostitutes is pretty much the same as that for the general population – and of all the jobs where you would think attractiveness would be a bonus, surely that would be it.

So is there some general quality, that has something to do with beauty, and is advantageous across job roles of all types? Possibly.

You see, if there’s one quality that is an advantage no matter what job you are doing, all else being equal, it is intelligence. And it turns out there is a correlation between intelligence and beauty. As with most of these other effects, there is both a beauty premium and an ugliness penalty when it comes to measurements of intelligence, and the ugliness penalty is a substantially bigger effect.

We can find corroboration of this in educational attainment. Beautiful people do better in exams. Not just in face-to-face exams, where you could imagine the examiner might be influenced by the good looks of the student, but in written examinations as well.

It seems, therefore, that beautiful people are just a bit, well, better than their ugly counterparts. Time to ditch the stereotypes of pretty airheads. But can we find some way to explain this?

There are two basic kinds of theory in beauty studies. There is the biological theory, in which beauty is favoured because it is a signal of genetic fitness, and people prefer to mate with partners who have good genes, and there is the cultural theory, in which beauty is a matter of conformity to arbitrary societally-defined standards.

These two theories make different, testable predictions. The biological theory predicts that assessments of beauty should be similar across different cultures, while the cultural theory predicts that these assessments should vary significantly from culture to culture. As we have seen above, the data here supports the biological theory and contradicts the cultural theory. That’s not to dismiss cultural influences entirely – for example, although an explicit emphasis on female beauty is found in all cultures, this is particularly strong in Western culture. However, these differences appear to be second-order effects.

But when you try to drill down into the biological theory, to figure out exactly how beauty relates to genetic health, it all gets a bit foggy. The established indicators of beauty, such as symmetrical features and clear skin, don’t relate all that well to any significant genetic health factors. There is some indication that attractiveness may be linked to a better immune system, and a moderate association with longevity, but none of this evidence is terribly strong. The ugliness penalty does show up in this data as well, with a correlation between below average looks at age 17 and poorer health in later adulthood, but none of this comes close to touching on factors like intelligence and leadership. One can imagine that there might be some correlation linking beauty, genetic health and intelligence, but imagining doesn’t make it so, and thus far there is no solid evidence base for any such link.

One way out of this morass might be that genetic factors are amplified by upbringing. We know that attractive children are more favourably judged than their ugly peers, just as with adults. Might it be that this means they are better treated as they grow up, developing more self-confidence and thus greater abilities in learning and leadership? As with the previous theories, this “internalisation theory” sounds plausible enough. The problem is that, when self-perception is measured, beautiful people have only slightly more positive self-images than average, an effect which is dwarfed by the size of the effect of their beauty on how they are perceived by others. It is difficult to see how such a weak effect could be driving the clear advantages of attractiveness.

So it seems that, statistically at least, not only are beautiful people better treated by society, this better treatment is somewhat merited. Meanwhile, the ugly are doubly disadvantaged. But we have no simple explanation for this – it seems likely that there is some biological basis, but establishing what it is and disentangling the various effects of genetics, culture and upbringing will take some doing.

It’s not the most satisfying conclusion, but we can take comfort in one logical consequence of all this mass of data. This blog is aimed at a non-specialist audience, it is true, but nevertheless at readers of above average intelligence and educational attainment. Which means its readers are statistically likely to be better-looking than average as well.

Good for you, you gorgeous bastards.

The Time Meddler

The whole course of history changed in one single swoop.

When you start thinking about time travel, you pretty quickly get to the central and most difficult question: can you change the past?

Say by whatever means I have travelled to the past and found my grandfather when he was a teenager. I point a loaded gun at his head and pull the trigger. (This always seems to come down to killing grandfathers. If time travel is ever invented, will we start killing our grandchildren in pre-emptive self-defence?) What happens next?

What happens physically is that the hammer of the gun strikes the firing pin, this in turn strikes the rear of the cartridge, setting off a rapid exothermic chemical reaction in the propellant. The pressure of the resulting hot gas accelerates the bullet out of the end of the gun barrel in the direction of my grandfather’s head. On impact, the bullet penetrates my grandfather’s skull and enters his brain, where it decelerates and spins, transferring energy and momentum to the brain tissue and disrupting the physical structure of the brain, before exiting through the other side of the skull. This damage to the brain causes my grandfather’s central nervous system to shut down, quickly leading to the irrevocable cessation of his respiratory and circulatory systems.

In short, he dies.

The important point about this sequence of events is that every step along the way depends only on the physical conditions right then and there. How the gun came to be pointing at my grandfather’s head, the date of manufacture of the bullet, the history of the chemicals in the propellant – none of these things matter.

And this is the essence of the Grandfather Paradox. The laws of physics are local, each step following on from the step before, and yet, looked at globally, the result seems contradictory. How can I kill my grandfather, if killing him means I can never be born?

Physicists investigating the theory of time travel have a simpler – and less bloodthirsty – model that captures the same essential point. Imagine a region of spacetime that somehow functions as a time machine. Exactly how it works is not the issue, so long as it has the property that an object can enter it at a time t2 and emerge at an earlier time t1.

Now imagine shooting a billiard ball into the time machine at t2. It emerges at t1, as expected. But what if you arrange billiard ball’s trajectory at t2 such that, when it comes out at t1, it strikes its earlier self, deflecting it away from the time machine such that it never enters it at t2 after all?

At this point, there are basically three responses.

1. Time Travel Is Impossible

This neatly gets around all the problems by simply saying that the setup is impossible in the first place. You just can’t build a time machine, and that’s that.

While elegant, this response does have the problem that, as far as anybody can tell, the laws of physics that are currently known do not rule out time travel. So this answer is in effect saying “some as yet undiscovered law of physics will one day prove me right”, which is entirely possible, but not terribly satisfactory. I mean, you could say that about anything.

2. Only Self-Consistent Time Travel Is Possible

In this case, the ball is not deflected away from the time machine at all. Instead, when the ball emerging from t1 strikes its earlier self, it deflects the earlier ball just enough so that, when it enters the time machine at time t2, it is travelling at just the right angle and speed to deflect its earlier self into the time machine such that it emerges travelling at just the right angle and speed to deflect its earlier self into the time machine such that it emerges travelling at just the right angle and speed… and so on.

In the context of attempted grand-patricide, the scenario would be something like this. The bullet strikes my grandfather in the head, he collapses and I get back into my time machine cackling diabolically. But the shot does not kill him – he recovers, but is never quite the person he was, and suddenly the mild mental disabilities that had always afflicted him ever since I could remember but which the family never spoke about are all explained.

This gets rid of the contradictions, but it can’t help but seem a little contrived. Some influence must act across all of history to prevent actions that would otherwise be physically possible, and it’s not at all clear what that could be. We have the same problem as in the previous response, only much worse. It’s not so difficult to imagine that we will discover a law of physics that rules out time travel – it’s harder to imagine the kind of as yet unknown force that could act in this remarkable way.

3. Divergent Timelines

We looked at the many-worlds hypothesis in the last post. It’s the idea that, whenever an event has multiple possible outcomes, all of these outcomes occur simultaneously in different universes, with the universe splitting at the point of measurement. This is an attempt to explain the odd behaviour of measurements in quantum mechanics, the physical theory of microscopic systems, but it turns out that it can also resolve the apparent paradoxes of time travel.

In this many worlds or branching universes picture, there is no problem with you shooting your grandfather. Well, apart from the usual legal and moral issues involved in shooting anyone in cold blood, but we’re assuming here that you’re fine with those. The universe simply branches into two – one branch containing your grandfather’s slowly cooling corpse, the other containing you standing there with a jammed pistol and an awkward expression on your face while your granddad runs pell-mell from a freakish encounter that he never speaks of to anyone.

Your path through divergent timelines is shown in red, from your birth, to going back in time and killing your grandfather, to whatever you do next, you murdering swine.

Your path through divergent timelines is shown in red, from your birth, to going back in time and killing your grandfather, to whatever you do next, you murdering swine.

But if you do this, are you really changing the past? Or have you just travelled into different universe that always existed, in which your grandfather was shot by some passing maniac when he was young and you were never born, while the universe in which you were born, stepped into a time machine and were never heard from again carries on existing?

In the many worlds view of time travel, it is the latter. Going back to the simpler experiment with the billiard ball, the you in universe A sees the ball vanish into the time machine, never to be seen again, while the you in universe B tries to shoot the ball into the time machine but is frustrated when an identical ball appears and knocks into it in mid-flight, and is left with two billiard balls rolling around on the floor.

So we’ve achieved a self-consistent physical picture in which time travel exists without paradoxes, but at the expense of ditching – or at least heavily modifying – our intuitive ideas about what it means to change the past.

To see the implications of this, imagine that you are poised, gun aimed, ready to shoot your poor innocent grandfather, when some grumpy old bugger comes storming out of a police box and disarms you with a whack of his cane. “You can’t be allowed to change history,” he declares, “and it’s up to me to stop you!” But this aggressive senior citizen hasn’t stopped you changing history at all. All he has done is prevent you from moving from one universe to another, forcing you to remain in one where your grandfather lived through a perplexing and frightening event in his youth. There are still universes out there where your grandfather died in his teens, in which you do not exist at all.

So is there any point in trying to stop someone from changing the past? Well, no more than there is any point in doing anything. All possible futures might happen, but they do not all happen with equal probability, and from each choice branches off a cascade of universes, branches upon branches, and the higher the probability of an outcome, the more versions of the universe will spring from it. Perhaps the best and worst of all possible worlds exist simultaneously, but the number of different versions of their inhabitants, and the number of times their joy or suffering is duplicated across the universes, depends on how likely each outcome is.

As a time traveller, you have no more or less responsibility than anyone else to try to make a better future more probable. There is nothing intrinsically special about the history that you are familiar with – just because William won the Battle of Hastings in your history book doesn’t mean you shouldn’t give Harold a helping hand should you turn up in 1066. But the time traveller may have some insight into the consequences of their actions that is denied to the rest of us, some reason to think a particular outcome will be better or worse, some moral drive to make as many universes as possible as good as they can be.

A frequent time traveller, with vast experience of traversing a multitude of histories, might even take on the task of visiting key decision points, influencing the outcome as far as possible, saving at least some timelines from future horrors. Such a person would be special indeed, using knowledge of the future to bend whole universes towards their vision of a better life. One might almost call them a Lord of Time.

The Chase

They cannot escape! Our time machine will soon follow them. They will be exterminated! Exterminated! Exterminated!

So… how exactly do you chase someone through time and space?

There’s a quite straightforward way of going about this, which is unfortunately entirely unlike what we actually see in this story. However, it’s worth looking at anyway, as it will illustrate some ideas that will be useful for understanding the more complicated answer later on.

Space and time are not separate things – they are combined into a four-dimensional environment called spacetime. (Not the most imaginative name, I’ll admit.) As you travel through spacetime, you trace out what is called a world line, which is just a trajectory consisting of all the points you move through. Even sitting on your backside reading this blog you trace out a world line: as you orbit round the Sun and move forward in time, your worldline is a segment of a spiral.

Worldline of the Earth (red) orbiting the Sun (blue). Time is on the vertical axis. (Image credit: www.cleonis.nl)

Worldline of the Earth (red) orbiting the Sun (blue). Time is on the vertical axis. (Image credit: http://www.cleonis.nl)

So it seems that chasing someone through time is much the same as chasing someone through space. You just need to find the path they’ve taken – their worldline – and follow it a bit faster.

Except that isn’t really going to work, is it? You can’t go faster than me and still stay on the same worldline, as the worldline is defined by the speed of my movement through spacetime. Change your velocity, and you start travelling along a different worldline.

And anyway, a worldline isn’t like a trail of footprints. If a point on my worldline is “At the front door of the British Museum, 2:30 pm on Sunday 2 March 2014”, then if you go to that point on my worldline there’s no need for any chasing – I’m already there, that’s what a worldline means. You’ve got me, and the chase is over before it has even begun.

No, the way to catch me is to find out some point in spacetime where I am going to be, and arrange to be there at the same time. In other words, to make our worldlines intersect. If, for example, you know I am in the habit of popping into the British Museum around 2:30 on a Sunday afternoon, you hang around there as unobtrusively as possible until I show up. No chasing involved.

So that about wraps it up for The Chase. Except… what we’ve just described isn’t how the Tardis travels through time and space at all. Far from tracing out a single worldline in four-dimensional spacetime, it disappears here and appears there, travelling in between through some exotic other space, sometimes called a vortex.

To get an idea of how that might work, look back at the post on the very first episode, An Unearthly Child. There we saw the idea that two points in four-dimensional space-time can be connected by a five-dimensional tunnel. (Admittedly this involves manipulations of unknown complexity with forms of exotic matter that are not currently known to exist, but we can presume the Doctor’s people have long since mastered such implementation details.) The Tardis travels in space and time, not by following a continuous worldline from one spacetime event to another, but by creating a corridor through the fifth dimension and taking a short-cut through that.

So can the Daleks chase the Tardis through the same 5-d tunnel? Again, this brings up the same problem as in the 4-d case. The opening to the tunnel is a spacetime event, and to enter the tunnel you have to go through that spacetime event. As Tardis and its crew are also at that event, you’ve already caught them. Or to put it another way, the tunnel presumably opens and closes just long enough for the Tardis to vanish into it and zoom off to its new destination. If the Daleks turn up five minutes later, they’re too late and just have to whirl around bitching at each other.

Or do they? Perhaps there’s something extra we can add to this model that makes The Chase plausible [1] after all.

Any change in the geometry of spacetime creates ripples – usually called gravitational waves. These are very faint, and have only ever been observed indirectly. Some exquisitely sensitive instruments have been built over the last couple of decades to try to detect these waves as they pass across the Earth, with a view to seeing the signs of distant astronomical events, like the collision of black holes, that are invisible to telescopes. So far these efforts have been unsuccessful, but physicists continue to strive.

It’s reasonable to suppose that opening up this 5-d tunnel would also create such waves. Indeed, it would be surprising if it did not. We don’t know anything about this fifth dimension that the Tardis apparently travels through, but let’s assume it’s geometrically well-behaved, and that opening this corridor through it similarly creates ripples in the fifth dimension. The Doctor’s Time Path Detector can evidently register these disturbances, and presumably the Daleks have something similar.

Now we have all we need. The Daleks can detect these ripples, and set up their own 5-d corridor close to the one the Tardis is using. These ripples will die off the further away they get from their source, just like the ripples on a pond when you chuck a stone in, so the Daleks will want to keep their corridor as close as possible to the Doctor’s, so that they can be sure of arriving close to the end-point of his journey. For practical purposes, it’s natural to focus on the time displacement between the two end points, although obviously there is some spatial displacement as well, hence the Doctor’s repeated remarks that the Daleks are only so many minutes behind them. The more often the Daleks do this, the more precisely they will be able to calibrate their instruments, the more they can minimise the displacement between their arrival point and the Doctor’s – and so they effectively catch up with every trip the Tardis takes. It all seems to fit quite nicely.

There’s just one problem. In our model, there’s nothing to prevent the Daleks turning up a few minutes before the Tardis, and setting up an ambush, ready to exterminate our intrepid time travellers the moment they step out of their box. So why don’t they?

Perhaps the answer can be found, not in relativity, but in quantum mechanics.

One of the most strange and perplexing issues in quantum mechanics – the theory that describes the behaviour of microscopic objects such as atoms, electrons and so on – is what’s called the quantum measurement problem. It goes something like this.

The reason why quantum mechanics is called quantum mechanics is that, when you get right down to the microscopic level, variables like energy and spin that describe a particle’s motion cannot take on a continuous range of values, but can only have a limited number of very precise values. It’s as if your car could go at 40 or 50 miles per hour, but not any speed in between – and if you wanted to accelerate you would have to jump instantly from 40 to 50 without ever going at 41, 42 or 43 miles per hour. These discrete units were historically called quanta, hence quantum mechanics.

Now, whenever you measure a quantum mechanical system, you find it in one or other of its possible quantum states. In our quantum car, whenever you look at the speedometer you find it sitting at 40 or 50 mph. But very often systems exist in some mixture of the possible states. Our car might, for example, be in a state of one half 40 mph, one half 50 mph. That doesn’t mean the speedometer shows 45. It means that, on average, half the time you look at the speedometer you see it reading 40, the other half of the time you see it reading 50.

Now if the car goes past a speed camera set to trigger if the car is going over 45 mph, you will get a speeding ticket half the time, on average – as long as you don’t look at the speedometer. If you do look at the speedometer just as the car enters the speed trap, if you see it reading 40 you definitely won’t get a ticket, if you see it reading 50 you definitely will.

This is a bit weird, but it has been confirmed by a multitude of precise experiments, so it’s the way the world is. (Experiments on beams of electrons and the like, not improbable motor vehicles.) Somehow, when we measure a quantum system, we change it, forcing it out of its mixed state and into one of its pure states.

Exactly what is going on here has intrigued and baffled physicists and philosophers for more than eighty years. One interpretation – the most orthodox – has it that the act of measurement itself causes the quantum state to randomly assume one of its pure values. Looking at the speedometer forces the car to be going at either 40 or 50 mph, and then you either get a ticket or you don’t. Another interpretation, known as the many-worlds interpretation, holds that all the possible results of the measurement happen simultaneously, but in different universes, with each act of measurement spawning a new set of parallel worlds. Looking at the speedometer results in two versions of you in two versions of the car, one going at 40, the other at 50, and in one of these worlds you get a speeding ticket while your more fortunate self in the other world drives on without a care in the world. Lucky bastard.

We’ll have a lot more to say about parallel worlds in future episodes. For now, suffice to say that, in the universe of Doctor Who, the many-worlds interpretation is definitely correct. And since quantum interactions are happening all the time, every instant is spawning new sets of alternate universes.

So what does this lengthy digression have to do with The Chase? Well, remember the question we had a few paragraphs back – why don’t the Daleks arrange to arrive a few minutes before the Doctor and his chums and ambush them? The answer is now clear. For every set of universes in which the Tardis arrives at a particular place and time, there is a set of universes in which it does not. The Daleks have to arrive after the Doctor so they can be sure he is going to arrive at all. Otherwise they risk ending up in one of those other universes, hanging around in awkward silence until the embarrassment gets too much and they pile back into their spacetime craft to give it another go.

So there you have it. Should you ever find yourself tasked by an implacable manager with chasing after an old git in a phone box that can travel anywhere in time and space, I hope you will find this elementary guidance useful. No warranty is expressed or implied. Good luck.

1. You know what I mean.

The Space Museum

You dropped a glass, and it came together again in your hands?

If you drop your glass of water and it shatters all over the floor, you’ll be a bit annoyed. But f it then spontaneously reassembles and jumps back up into your hand, you won’t be relieved to have your drink back. You’ll be thoroughly freaked out. Things like that just don’t happen.

This is why it’s usually easy to tell if a video recording is being played forwards or backwards. Smashed glasses reassembling, clouds of smoke rushing into narrow chimneys, pulped meat and bread emerging from mouths and assembling into pristine burgers – all of these tell us instantly that the video is being rewound. And if we were to see them in real life, we would know that time was running in reverse.

But if you were to look at a video recording made through a sufficiently powerful microscope, one that could see the basic interactions of particles that make up all these events, there would be no way to tell which was the forward playback and which was the reverse. Whether atom A knocks into atom B or vice versa, whether an atom loses energy by emitting a photon, or gains energy by absorbing one, all these processes are equally possible. The fundamental laws of physics – quantum field theory, general relativity – work equally well if time is reversed.

In theory, then, there is no reason why your dropped glass shouldn’t repair itself. All that needs to happen is that all the air molecules displaced by the broken pieces of glass should flow back and strike the fragments, giving just enough force to move them back the way they came, and similarly for all the drops of water, then for the glass molecules at the fractures to all move at the same time so as to repair the damage, enabling the glass to hold the water that is flowing back into it, and finally for the air molecules moved out of the way as the glass fell to move back and lift the glass back up into your hand. Cheers.

None of this would violate the microscopic laws of physics. So why doesn’t it happen? Why do we see such a difference between time going forward and backward?

Well, there is one set of physical laws that make a distinction between past and future. These are the laws of thermodynamics. In particular, the second law of thermodynamics states that, in an isolated system, entropy – a property related to energy and temperature – can increase or remain unchanged, but can never decrease. The significance of this is that entropy is a measure of the useful work that a system can do. The lower the entropy, the more capacity there is for the system to do work. As entropy increases, the system is less and less able to do anything.

For example, imagine you have an insulated box at -20 C – well below freezing point. You can use this to make ice cubes. Just fill an ice cube tray with water, pop it in the box, and wait for the water to freeze. Let’s assume this box is perfectly insulated, so heat doesn’t leak in through the walls, and you are able to open and close the door quickly enough that the inside doesn’t heat up while you’re doing it. Even so, this box is not going to be able to make ice cubes forever. Every tray of water you put in transfers some heat to the inside of the box, so every time you take a tray of ice cubes out the inside of the box will be slightly hotter. If you have a thermometer measuring the interior temperature, you will be able to see the temperature rising: -49, -48, -47… Even if you haven’t bothered with that, you will notice that each tray of water takes longer to freeze than the last one, as the temperature difference between the box and the water gets smaller.

Eventually, if you have a hell of a lot of gin and tonics to make and thus a massive demand for ice, you will notice that the water stops freezing at all, as the inside of the box has finally got above freezing point. Your box is now useless, and your gin and tonics will be sadly lacking. If you still have all the ice cubes around, you could try to cool the box back down by stuffing them back inside it, but at best you’ll manage to melt all your ice, get the box back to -20 C and be no better off than you were before you started. In fact, you probably won’t even be able to do this much. The ice will have warmed up and melted a bit while it was sitting around outside, and so some of your cooling power has been lost forever.

This is the remorseless march of entropy. As time goes on, temperature differences are smoothed out and thermal systems can do less and less work. Indeed, one of the many versions of the second law simply states that heat flows from higher temperatures to lower temperatures, but never the other way around.

At this point, some of you may be saying “But I have a box like that in my kitchen, and it provides me with ice for my G&Ts whenever I want!” Yes, but if you stick your hand round the back of it you will notice it’s warm on the outside. That’s because your freezer box is attached to an electric heat pump, and the entropy it generates by emitting heat into your kitchen allows it to maintain your ability to make ice.

The laws of thermodynamics were first codified during the industrial revolution in order to describe large-scale phenomena like hot gases pushing pistons – a vital application of science to emerging technology. As scientists began to realise that matter was made up of microscopic particles – atoms – the question arose of how the behaviour of these particles gave rise to the laws that govern the visible world. Eventually it would become clear that the laws of thermodynamics are about much more than steam engines and freezers: they are fundamental to the workings of the Universe, the nature of life, and the march of time itself.

The key to all this is a branch of physics called statistical mechanics. The idea behind this is that it is humanly impossible to calculate all the movements and collisions of the atoms even in something so simple as a box full of gas – and also pointless, as we can’t measure all these motions anyway. But by figuring out the average behaviour of the atoms, we can calculate quantities we can measure, such as pressure and temperature, and figure out how they change.

The second law of thermodynamics flows very naturally from this sort of calculation. Take a simple system, like the box of gas from the previous paragraph. As the atoms of gas move around inside the box, they randomly move through all the possible configurations of the system. These possible configurations could have all the atoms evenly distributed, or all of them concentrated into one corner, or all of them at the top of the box and none at the bottom, or whatever. They key point is that there are lots and lots of ways the gas can be evenly distributed, and relatively few ways it can be arranged in just one part of the box. So if the gas is already evenly distributed, it is overwhelmingly likely to stay that way, and if it is put into one of these special configurations it will quickly diffuse out and become evenly distributed once more.

It turns out that this is exactly equivalent to the second law of thermodynamics. The gas all in one corner is a low-entropy state, and the evenly distributed gas is a high-entropy state. The low-entropy system will spontaneously transform into the high-entropy system, while the high-entropy system will stay as it is.

But it also shows how the second law matters for any kind of physical system. A highly ordered system -say, a glass full of water – will readily become a less ordered system – say, a load of broken glass in a puddle – but not the other way around. There are many more ways for glass and water to be arranged in a mess on the floor than there are for them to be arranged as a container full of refreshing beverage.

The second law is also essential for life. As far as thermodynamics is concerned, life ingests low-entropy substances (high-frequency light, plants, animals), uses them to build up low-entropy structures (leaves, muscles, memories) and excretes high-entropy waste products (low-frequency light, poo, more poo). Ultimately, all life on Earth depends on the fact that the entropy of radiation is inversely proportional to its temperature. The Earth absorbs light from the Sun that has a temperature of 5500 C, and emits radiation at a temperature of about 20 C. The entropy difference is what powers all life on this planet.

So the arrow of time points from low entropy to high entropy. This implies that the Universe must have begun in a low-entropy state, from which it is gradually emerging as entropy rises. Is this true?

The further we look out into the Universe, the further back in time we are looking. Light from a galaxy a million light years away has taken a million years to reach us, which means we are seeing the galaxy now as it was a million years ago. So if it is really true that the thermodynamic arrow of time points in the direction of increasing entropy, then surely the further back we look into space, the lower the entropy should be.

But that’s not what we see at all. The oldest and most distant radiation we can detect is the cosmic microwave background radiation, or CMBR. Just after the Big Bang, all the matter in the Universe was in the form of a hot plasma, a gas made up of subatomic particles because it is too hot for atoms to survive. These days, space is cold and dark, with rock, gas and dust orbiting around the scattered stars and galaxies. This is because, as the Universe expanded, it cooled, and when the temperature had dropped enough the plasma formed into atoms of hydrogen, helium and other light elements. The time when this happened is called the recombination time, and it was about four hundred thousand years after the Big Bang – around thirteen billion years ago.


The cosmic microwave background radiation, as mapped by the COBE spacecraft

The CMBR is the light that was emitted by the hot plasma at the recombination time. It is the oldest light we can ever see. Looking back at the CMBR is like looking at the Sun – we can see the light given off at the surface, but nothing within it. Unlike the Sun’s light, the CMBR is primarily in the microwave part of the spectrum. It was visible light when it was emitted, but the expansion of the Universe in the intervening thirteen billion years has stretched out the light waves, shifting them to higher and higher wavelengths until now they are only detectable by very sensitive radio telescopes.

This radiation was first detected in 1965 by Penzias and Wilson – quite by accident, as an annoying hiss in their radio detection equipment – and was swiftly recognised as confirmation of the then-controversial Big Bang theory of cosmology. Perhaps an even more important and profound observation, however, was in 1992, when the COBE spacecraft mapped the structure of the entire CMBR, showing us not only a picture of the entire Universe in its primordial state, but also the tiny fluctuations in the plasma that would eventually grow into stars and galaxies, planets and people.

And it’s those tiny fluctuations that are the problem, as far as the thermodynamic arrow of time is concerned. They are a problem precisely because they are so tiny. The COBE observations showed that, thirteen billion years ago, the Universe was in a state of complete thermal equilibrium to within one part in one hundred thousand. This means the entire cosmos was at the same temperature, around 3000 degrees, with only minute variations.

The thing is, thermal equilibrium like this is a high-entropy state. The highest, in fact. All thermodynamic systems will tend towards thermal equilibrium, just as a ball on a hill tends towards rolling downwards. And when the system reaches thermal equilibrium, like the ball reaching the bottom of the hill, it stops.

So there’s a paradox. For time to work the way it does, the Universe must have started in a low-entropy state. But from the CMBR it looks like entropy in the early Universe was about as high as it can be. Does this mean all our ideas about time are wrong?

Not quite. We haven’t taken into account the fact that the Universe is expanding. This prevents the contents of the Universe from remaining in global thermal equilibrium, as the volume they occupy is increasing too quickly for them to be able to thermodynamically adjust. For an example of how this can work, consider a Universe consisting only of radiation and dust – a commonly-used model for the real Universe after the recombination time, when the CMBR was emitted. As the  Universe expands, it cools. But these two components of the Universe cool at different rates. Matter cools more quickly than radiation. This creates a temperature difference, pulling the entire Universe out of thermal equilibrium. In other words, as the Universe expands, its entropy decreases.

So Vicki’s glass smashes because the Universe is expanding. Or to be a little more precise, a smashable object like Vicki’s glass only exists because the Universe is expanding. And the same goes for our experience of time, our laying down of memories, the measurable difference between the past and the future. All of these phenomena, however mundane, ultimately depend upon the structure of the Universe itself.

But what happens when all the glasses have smashed, when all the stars have burnt out, when entropy finally wins as the Second Law assures us it must? Will time come to an end?

It depends what you mean by time. However much the Universe expands, however old it gets, it will always be a four-dimensional structure with time as one of its coordinates. However, at some point in the far distant future, the subjective experience of time will indeed cease.

The scenario is this. Eventually all the stars will have collapsed into black holes, and these black holes will have absorbed all the other matter in the Universe. But that is not the end. Black holes eventually evaporate, shrinking as they give off radiation until they vanish entirely. So eventually there will be nothing left in the Universe except photons, particles of light. Now, according to the Special Theory of Relativity, for any particle moving at the speed of light every event is simultaneous. To a photon, there is no such thing as time. So when there is nothing left but photons, there will be nothing in the Universe that can experience time, nothing that can be aware of one event happening before or after another. Time will have come to an end.

And the Universe will carry on expanding. Forever.

The Crusade

Why are we here in this foreign land if not to fight? The Devil’s horde, Saracen and Turk, posses Jerusalem and we will not wrest it from them with honeyed words.

A truism of military science, frequently attributed to General Omar Bradley, is that amateurs study strategy, but professionals study logistics.

Certainly, the technological demands of modern warfare make careful logistical planning absolutely critical to any military campaign. Guns need ammunition, tanks need fuel and spare parts, aircraft need frequent servicing by highly trained specialists, and if these necessities are not available at the right time, in the right place, in the right quantity, no amount of courage, grit or righteousness will make up for it.

Modern supply lines can stretch for hundreds or even thousands of miles, with precisely manufactured materiel crossing continents and oceans to reach the soldiers on the front line. If those supply lines are cut, or if they fail to operate according to plan, the front line soldiers are doomed.

Before the modern age, an army was a much more autonomous creature. Supplies would be carried on carts and pack animals, and as they were used up they would be replaced from the local area. This could be done by means of compulsory purchase  (legal in principle, but rife with corruption), extortion, or straight up theft. Pack animals would graze on fields or eat locally-acquired fodder, soldiers would scavenge or appropriate their food, and whatever ammunition and spare parts the army was likely to need could be carried along with it. An army’s survival in the field did not depend on a long supply train to a distant homeland.

The corollary of this was that an army that could not supply itself would collapse. Sometimes this happened inadvertently, such as in the Thirty Years War when parts of Germany were picked over again and again by different hordes of unpaid, disaffected mercenaries until there was nothing left to scavenge. And sometimes it was deliberate, when an army would destroy crops and poison wells to prevent an enemy’s advance onto its territory. These scorched earth tactics, as they became known, have a long and inglorious history, from the nomadic Scythians defending their homelands from the Persian army of Darius the Great, to the Russian’s successful defence against Napoleon in 1812. Such tactics are prohibited now by the Geneva Conventions, as they are so devastating to the civilian population. (A few countries, such as the United States, Israel, Iran and Pakistan, have failed to ratify this protocol. Not that they’re likely to get involved in any wars.)

We can see these points in action in the Third Crusade, when King Richard I of England (alongside Philip II of France) led his army to the Holy Land. Jerusalem and most of the surrounding region was under the control of Muslim forces led by the Islamic hero Saladin. The fall of Jerusalem had prompted the leading Christian rulers of Europe to muster great armies and attempt to regain the Holy City and reverse this religious calamity.

Map of the Third Crusade

Map of the Third Crusade. Click to enlarge. (image credit: alexandcalebcrusades.wikispaces.com)

This was a massive undertaking. Never before had an army of such size travelled such a distance by sea. Over a hundred ships, carrying 14,000 people, 5,000 horses, armour, weapons and miscellaneous baggage as well as food and water, travelling for over five months. The sheer financial chicanery required just to finance this vast fleet was a once-in-a-generation activity, not to be readily repeated.

But Richard’s real problems started when he got to the Holy Land. Saladin undertook a scorched earth strategy, designed to limit the crusaders’ movements and ability to fight, and to encourage them to slink off home to Europe. His forces poisoned wells, burnt crops and stripped the region of food for both man and beast.

Issues of supply and logistics thus dominated Richard’s campaign from the start, and they would only get worse. After fighting a victorious battle to retake the coastal town of Acre, returning it to crusader hands, Richard had to secure the key port of Jaffa in order to keep his army supplied for any subsequent advance on Jerusalem.

This involved a long march down the barren coast, stripped bare by the Muslim forces. Richard’s conduct of that march was one of his major military successes. The key strength of the crusader armies was the heavy mounted knights, attracted by the opportunity to combine religious pilgrimage with bloody slaughter. The Muslim forces under Saladin were light skirmishers, unable to directly withstand the full force of the European cavalry, but more than capable of picking them off piecemeal through fast, harrying manoeuvres. To the heavy knights, fighting these lighter forces was like trying to punch a cloud of mosquitoes with a fist.

True to form, Saladin’s forces continually harassed the crusaders as they marched down the coast, attempting to draw them inland and destroy them. But Richard was wise to this, and kept his army moving in strict formation with iron discipline.

This would have been impossible, for all Richard’s undoubted force of personality, if the army had not been able to sustain itself in inhospitable surroundings. Richard’s answer was to have a fleet of ships sail down the coast, keeping pace with the army on land. These were able to keep Richard’s army supplied, and the crusaders not only took Jaffa, they were able to rout Saladin’s army along the way when it tried to mount a decisive assault at Arsuf.

Once Jaffa was secured, Richard had a key strategic decision to take. Should his army attempt to retake Jerusalem as well, or consolidate its gains in the coastal towns? Again, logistics was the key consideration. Marching inland to Jerusalem would cause increasing problems of supply the farther the crusaders got from the port of Jaffa, but even so there was a reasonable prospect of reaching Jerusalem and fighting a successful battle there. The political pressure was on Richard to take the Holy City back from the Muslims, and if supply of provisions had been his only problem he may well have taken the chance.

However, an attack on Jerusalem posed a logistical problem unique to the Crusades. Although the crusading knights were by no means the whole of the army – the  footsoldiers and archers were commoners following their lords on the campaign – they were a critical component of its strength, and the common soldiers were tied to their particular lords and would come and go with them. This meant that any mediaeval king on campaign had to keep his nobility on board, or see his army evaporate.

The problem was that the crusading knights were primarily interested in reaching Jerusalem and praying in the Church of the Holy Sepulchre, which they believed stood on the site of Christ’s crucifixion. Once that was done, it was mission accomplished as far as they were concerned. Their crusading oath would be fulfilled, and they could return to their own lands back home. Most of the knights had no desire to stay in the Holy Land any longer than necessary, as a long absence could see their own estates go to ruin in their absence.

So taking Jerusalem was a possibility, but holding it was not. Richard could expect the bulk of his forces to scurry off home as soon as they had performed their Christian duties, and his victory in Jerusalem would be short-lived indeed. He might achieve a symbolic victory, but Saladin would ensure that the city fell again to the Muslims in short order.

So instead, Richard remained encamped at Jaffa, engaged in a protracted series of negotiations with Saladin. The discussions were wide-ranging, at one point even including the suggestion that Richard might marry his own sister to Saladin’s brother in return for substantial territories in Palestine and the return of the True Cross. In the end, a deal was done that allowed Christians limited access to the Holy City, Richard strengthened the defences of the coastal towns, and the crusaders sailed off home.

The Crusader States – Outremer – limped on for another century, but these fundamental logistic problems meant they could never really secure themselves or flourish. If transport from Europe to the Holy Land had been faster and cheaper, if more knights had been willing to settle permanently instead of returning home as soon as they could manage to excuse themselves, then the history of the Middle East might have been very different. As it stands, however, these fundamental technological and political limitations would prove to be more important than any great leader or famous victory in battle. As the professionals know, logistics will always win out in the end.

The Web Planet

Why question me? Surely you can see our movements.

Each of us has a characteristic repertoire of movements. You can recognise loved ones just by the way they walk. Actors use different styles of movement to create different characters. Some of these can become iconic, instantly triggering off a complex of ideas, emotions and cultural signifiers. There are basic, gross movements that are common to they way any man walks down a street, but if one of them is Charlie Chaplin twirling an umbrella and the other is John Travolta swinging a paint can, the different personalities are immediately recognisable, and the emotional and cultural connotations are widely different.

It’s important in science fiction drama too. If human actors are to represent alien beings, then finding new styles of movement suitable to the extraterrestrial race in question is essential, if they are not to look simply like a scattering of awkward suburbanites at an unsuccessful fetish party. Wise producers will hire choreographers to work with the actors, giving each species its own palette of movements unique to itself, making each group of aliens seem coherent in itself but distinct from any other.

But what is a style of movement? We can all recognise it, but can we break it down into its elements? Quantify it? Analyse it?

Beauchamp-Feuillet notation (image credit: Judith Appleby)

Beauchamp-Feuillet notation (image credit: Judith Appleby)

The first project to have a go at pinning down the component elements of dance was commissioned by Louis XIV in the late 17th century. There had been dance treatises before then, elaborate descriptions of how particular dances should be performed (sometimes with stroppy comments about how they should certainly not be performed), but the notation that ballet master Pierre Beauchamp devised for His Majesty was the first to use abstract symbols instead of prose descriptions accompanied by realistic drawings.

This Beauchamp-Feuillet notation, as it became known after Raoul Auger Feuillet popularised it in his many published books of choreography, was an elegant, if initially forbidding, system of swirling lines and sudden angles that represented the motions and transitions of dance just as a set of dots and lines can describe the notes and rhythms of music. It remained in widespread use for a century, before being superseded by a variety of alternative systems.

Benesh Movement Notation (image credit: Juliette Kando)

Benesh Movement Notation (image credit: Juliette Kando)

There are two in wide use today. The Benesh Movement Notation represents body positions on a five-line stave similar to that used in standard musical notation, allowing music and dance notation to be more easily integrated, while Rudolf Laban’s “Labanotation” looks more like geometric abstract art than music, but does have the advantage that it can be used to describe any kind of bodily movement in space and time, not just dance moves.

Rudolf Laban and his Labanotation

Rudolf Laban and his Labanotation

This idea has been developed further, in Eshkol-Wachman movement notation. Like its predecessors, this breaks down movements into primitive elements, but it uses an elaborate system of three-dimensional polar coordinates to locate these motions in space, with techniques for rotating and translating sequences of movements so that they can be directly compared. This allows the truly invariant characteristics of movements to be calculated.

The applications go far beyond the world of dance. It has been used in a host of animal studies, allowing scientists to establish the movements that are characteristic of particular animals, study how these movements change due to illness or injury, and compare the ways different species of animal move. In one example, Tammy Ivanco and her colleagues from the University of Lethbridge, Canada, used Eshkol-Wachman notation to quantify the different ways that rats and opossums reach for food, and were able to relate the more complex movements of the rats’ hands and arms to their relatively more elaborate brains and nervous systems.

It may even prove useful in studying the human brain. Autism is not generally diagnosed until a child is around three years old, while Asperger’s Syndrome is diagnosed much later – typically around the age of six or seven, but it can remain undiagnosed into the teenage years. Osnat Teitelbaum and her colleagues at the University of Florida analysed video recordings of infants moving about, and by using the Eshkol-Wachman system were able to determine certain movement styles that were characteristic of children who would later be diagnosed with autism or Asperger’s Syndrome. These were things like asymmetric crawling, where the infant would not crawl in the efficient manner of most babies, moving diagonally opposite limbs together, but would instead move in clumsier ways, such as with one foot stepping while another crawls, or a particular way of falling forward or back from a sitting position without using the reflexive motions of the arms that neurotypical infants would protect themselves with. This work led them to develop a simple motion-based test for autism and Asperger’s Syndrome in infants, whereby the child is held and the waist and slowly tilted from side to side. If the infant does not manage to keep their head vertical, an autistic spectrum disorder may be present.

A much simpler form of notation was devised recently by Amy LaViers, an engineering postgrad at the Georgia Institute of Technology. (That’s Georgia the US state, not Georgia the former Soviet republic.) Eschewing the complexity and power of the Eshkol-Wachman notation, LaVier’s system represents two legs, each of which can adopt one of ten different poses. The sequence of poses, and the transitions between them, describe the dance.

These ten discrete states are not chosen arbitrarily. Ballet dancers perform their warm-up exercises at the barre, a handrail that they hold on to for stability as they exercise each leg in turn. The ten barre exercises are the building blocks of ballet, and it is these movements that are captured in LaVier’s finite state automaton, a computer program that moves through these different poses to create sequences of dance.

There are constraints on the movements the automaton can perform. Some of these are physical – it cannot hover with both legs off the ground like some Jedi Cossack – but others are aesthetic. Specific mathematical constraints define the style and content of the dance, and as the automaton improvises within these constraints the audience perceives the character of its motion.

The aim of this work is not to create a ballet-dancing robot. Rather, it is to find ways to make robots move with particular styles and qualities. Non-verbal communication is expected to become an important element of the human-machine interface, as machines become more mobile and autonomous. A Predator drone may have no need to appear friendly (though for PR purposes I can imagine one of its successors might), but as robots increasingly interact with humans in non-lethal contexts, their body language may be the critical factor in putting people at their ease.

In this way, the robot engineers face the same sort of challenge as a choreographer on a science fiction show. They each have to define characteristic styles of movement that their performers – actors or robots – can work within, generating arbitrary sequences of movement that remain within strict aesthetic constraints. The difference is that the choreographer wants to make the actors seem as inhuman as possible, moving with a sense of the strange and uncanny, while the engineer wants the robots to seem as human, friendly and familiar as an automaton of motors and software can be.

The Romans

The music is so soft, so delicate, that only those with keen perceptive hearing, will be able to distinguish this melodious charm of music.

Take a look at this picture:


Cards used in the Asch conformity experiments (image credit: nyenyec)

The line on the left-hand card is the same length as one of the lines on the right hand card. But which one – A, B or C?

You’re probably thinking C. But what if seven other people had answered before you, and they had all said B. Would you be so sure of your response then?

That was the situation that faced the subjects of the Asch Conformity Experiments, started by psychologist Solomon Asch in 1951. The subjects were told that they were part of a group of eight volunteers taking part in a psychological experiment, but in reality the other seven people were working for Asch, and had been instructed to all give the same, incorrect answer.

The results were striking. Three quarters of the subjects gave the incorrect answer at least once, while only a quarter consistently answered correctly. By contrast, a control experiment showed that subjects gave the right answer more than 99% of the time when they were on their own, so it was definitely the deliberately wrong answers of the seven actors that were causing people to pick the wrong line.

When Asch interviewed the participants afterwards, he found that their reasons for giving the wrong answers were varied and complex. Some of them truly believed that the group must be right, despite the evidence of their own eyes. Some were well aware that the group was wrong, but went along with the majority in order to avoid being the odd one out. And a few became convinced that there must be some inadequacy in themselves that was preventing them from seeing the correct answer.

But perhaps the most striking result came when Asch changed the experimental set-up very slightly. Instead of all of the actors giving the wrong answer, instead all but one of them did so: the other was instructed to give the correct response. In these circumstances, the conformity rate dropped drastically, to about a quarter of the previous rate. It seems it only takes one dissenter to break the spell of conformity.

This of course, if the famous climax to Hans Christian Andersen’s “The Emperor’s New Clothes”. The emperor and his courtiers have been persuaded by con men that the emperor is wearing a suit of the finest fabric, which cannot be seen by the stupid or incompetent. The emperor duly parades naked in public, showing off what he believes are his marvellous new clothes to the astonishment of the watching public, who all cheer his fine garments until a child says “But he isn’t wearing anything at all”. The cheers turn to jeers as the crowd all realise the emperor is naked, but he and his courtiers continue parading as best they can, determined to carry on the show.

The truth in Andersen’s parable was realised earlier by the great political philosopher Niccolo Machiavelli. In chapter 23 of The Prince, “How Flatterers Should Be Avoided”, Machiavelli recommends that

a wise prince ought to hold a third course by choosing the wise men in his state, and giving to them only the liberty of speaking the truth to him, and then only of those things of which he inquires, and of none others; but he ought to question them upon everything, and listen to their opinions, and afterwards form his own conclusions.

Here, Machiavelli treads a careful path between unbridled dissent that would undermine the prince’s authority, and the dangers of a court in which the prince hears only what he wishes to hear and is blinded to the truth.

But what if someone wants to encourage conformity? They may be  con men trying to sell invisible clothes, a time traveller caught impersonating a famous musician, or a politician wanting a country to support a war or acquiesce in mass surveillance. In these cases, relying on the psychology of conformism isn’t enough. After all, Solomon Asch found that a quarter of people will not succumb to the pressure to conform, and that is a dangerous level of individualism for these deceivers and authoritarians. They need to add an extra factor: a penalty for speaking out.

In Andersen’s tale, the con men claim that the cloth cannot be seen by anyone who is unfit for office or unpardonably stupid. Naturally, no one wants to be thought of in that way, so everyone pretends they can see the beautiful material. The Doctor insists that only those with keen, perceptive hearing can discern the music, but in this case he only really has to appeal to Nero’s vanity: the dangers of contradicting an impulsive dictator with the power of life and death would surely keep any subordinates quiet.

None of us in the democratic West is in much danger of being summarily executed for speaking our minds. However, there are still systems to cow dissent, and the more significant the groupthink in the ruling establishment, the more critical the political situation, the more powerful the suppressing influence that is brought to bear. People with ideas just a little outside the political mainstream are dismissed as nutters and obsessives, poorly dressed and socially undesirable. This isn’t just a way of rejecting their proposals, it’s a way of ensuring that the rest of the group gets the message: don’t take these ideas seriously, or you’ll be a social outcast too.

And when it comes to matter of war, espionage and national security (which principally means the security of the governing class, and only incidentally the security of the rest of us), well in those cases dissent becomes all the more intolerable. The British weapons inspector and scientist David Kelly endured intense pressure and public smearing when he dissented from the Government’s assessment of Iraq’s weapon stockpiles in the run-up to the 2003 invasion. Within a few days he killed himself in the woods near his home. Here was the man who spoke up to say the emperor had no clothes, and the emperor drove him to take his own life. If dissenting voices on both sides of the Atlantic had been valued instead of scorned, a disastrous war might have been avoided.

More recently, the cases of Chelsea Manning and Edward Snowden, who each punctured myths of the US security establishment, one now imprisoned, the other an exile, show the lengths to which the deep core of the state will go to suppress dissenting voices. But they might also show the value of such dissent. The current disquiet among US telecoms and hosting companies as they suddenly find potential customers wondering about their reliability, and the increasing questioning of the surveillance state, is starting to feel like a spell has been broken, and that the people are looking at the emperor with new eyes.

It’s too soon to say how these recent developments will play out. What we can say for sure, though, is that there is great wisdom in allowing ourselves to be questioned, and great danger to any society in shunning or persecuting those who question the received wisdom. The open society may seem unruly and difficult to manage, bit it will always win out over a society that refuses to question itself.

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.


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.