Simply Complexity (31 page)

So what
is
the best form of defense? In particular, if a system such as the body, or a computer node, or a city, or even a country, is being attacked by some unknown superbug, how should we organize our defense? Is the best form of defense to go out in search of the attacking force – hunting it down? Or is it to encircle the object we are trying to defend and just lie in wait for any attackers? Both methods have their advantages and disadvantages. But how can we model this?

At the end of
chapter 8
we mentioned this exact same problem, albeit in another context. In particular, Roberto Zarama, Juan Camilo Bohorquez and Tim Jarrett have created a sheep-dogs-wolves game to mimic an attack by unknown predators (i.e. the wolves) on a set of defenseless objects (i.e. the sheep). More specifically, they have modeled a scenario where the attacking agents (i.e. the wolves) wish to destroy the target agents (i.e. the sheep) and hence win the game. The targets are protected by defensive agents (i.e. the dogs) which we assume that we can control, at least partially. The complications arise from the fact that we don’t know how many wolves there are, nor where they are – nor do we know where the sheep are. And nor do the dogs. So do we send out the dogs to look for wolves, in the hope that the dogs can find the wolves before the wolves find the sheep? The problem with such an attacking defense strategy is that if the wolves outnumber the dogs significantly, and each dog ends up chasing a wolf, then there will be an excess number of free wolves who may simply wander up to the sheep and kill them. On the other hand, having the dogs try to track down and encircle the sheep from the outset may also cause problems – the sheep will generally change their position in time and hence the dogs would need to constantly track the sheep better than the wolves can. One false move by the dogs and the sheep are dead. Indeed, even the problem of one sheep, one dog and one wolf will be complex – it is a three-body problem, and when combined with motion on a complex network will give rise to all sorts of rich behavior.

Tim Jarrett has studied what happens in this game when the objects move on a complex network, such as the hub-and-spoke of
chapter 7
. He allows the wolves and dogs to smell other nearby animals in order to sense their direction, which effectively gives the wolves and dogs hunting abilities. He then explores two types of behavioral model for the defending objects (i.e. dogs): attacking and defensive. We will refer to these as attacking defense and defensive defense, respectively. In the case of attacking defense, the dog attempts to defend the target by attacking the attacker. In the case of defensive defense, the dog attempts to defend the target by sitting next to it. Overall Tim finds that for small numbers of dogs, sheep and wolves,
attack is the best form of defense.

This model can be extended in all sorts of interesting ways, and to many other applications. For example, one can imagine that the dogs play the role of a police force, the sheep are ordinary citizens, and the wolves are criminals. How does one then deploy a limited number of police in order to best protect the community? In the case of just a few criminals, Tim’s results suggest that the strategy of tracking down known criminals even before they have committed the next crime, would be a useful form of defense – as opposed to trying to defend directly a cross-section of the population. He is currently looking at the effects of either losing a defender, adding an attacker or corrupting a defender in order to measure the system’s robustness. For example if one allows for the possible corruption of a dog into a wolf, the best policy may be to send out dogs in a crowd of three or more.

It turns out that a very similar problem arose for the allied Navy during World War II, but in a completely different context. When convoys of ships were being sent across the Atlantic in order to supply the allies and their forces with food and machinery, the Navy had to decide how to defend these ships. These supply ships typically had no defenses of their own, and hence represent the sheep in our game. The accompanying frigates and battleships played the role of the dogs, and the role of the wolves was very vividly played by the German U-boat submarines. The Navy did not in general know where the wolves were, nor did they know how many of them there were – and yet the convoy needed to have some kind of strategy. In the end, the Navy decided to
introduce a black-box device on the ships which, every so often, would spit out instructions for random changes in course. The result became very much like a herd of sheep who start wandering semi-aimlessly across a field – or in this case, the ocean. The German U-boats would then have had a hard job tracking the boats in order to torpedo them. Complexity and conflict – hand in hand once again.

Nobody would deny that Einstein was a genius. But it turns out that he was a slightly tortured genius – tortured by something for which he had earlier been awarded the Nobel Prize. That something is
Quantum Physics
. It turns out that although we know of Einstein most typically through his work on space-time and relativity, he was actually awarded the Nobel Prize for his work on explaining the so-called photoelectric effect. Einstein’s great insight was to explain this effect – whereby particles called electrons are emitted from a metal using light – by means of quantum physics. In so doing, he revolutionized the understanding of our world.

The story of this discovery is as follows. People had shown that if light is shone onto a piece of metal, the light can kick particles called electrons out of it. Maybe that doesn’t seem so surprising? After all, light has energy. And surely the brighter the light, the more energy it has, and the more particles it will kick out. After all, if I shake something like a tree harder and harder, more leaves are going to drop off. But this is not what was observed.

At first scientists had tried using a very dim red light, but it did not liberate any particles. One would therefore imagine that sending in light of any other color but with the same low brightness, would also have no effect. That is not what happened. In
particular, they found that dim blue light did liberate particles even though dim red light did not. So the energy of light has something to do with color. And here comes the real surprise – turning up the brightness of the red light has absolutely no effect at all. Even if the most intense red light you can imagine is falling on the metal, no particles come off. And yet a very dim blue light
is
enough to release particles. So what is going on?

The explanation that Einstein gave is that instead of thinking of the effect of light as a shaking motion (or in technical jargon, a wave), whereby the brighter the light the more vigorous the shaking, it is instead more akin to a stream of objects like balls. So throwing light on a metal is like throwing balls at a coconut-shy in a fairground. The light is the stream of balls – and the electrons in the metal that you are trying to kick out, are the coconuts. The red light then behaves like very lightweight balls – balls that are too light to dislodge a coconut even if you throw twenty in rapid succession. In other words, it doesn’t matter how many of those lightweight balls you throw at the coconut, the coconut won’t move. The same happens with the light on the metal. Red light is made up of lightweight balls, or rather packets or “quanta” of energy – a stream of them acts like a stream of lightweight bullets. Hence if we fire a steady stream of these red light quanta at the metal, none of them is individually energetic enough to dislodge the particles inside. It doesn’t matter how rapidly we send them, they are never going to do the job. By contrast, blue light is made up of balls which are relatively heavyweight in terms of their energy. In short, each individual quantum of blue light carries a lot of energy. So even if we fire only one at the metal, it can dislodge a particle – just as we would be able to dislodge the coconut with a single accurate throw of a heavyweight ball.

This effect of light appearing as packets or “quanta” of energy is a direct manifestation of Quantum Physics. In fact everything in our world exists as quantum objects like the balls of light – and we give all of them the generic name of quantum particles. This is all very surprising, and explaining this won Einstein the Nobel Prize. But that is where his problems began. It turns out that although an individual quantum particle is clearly quite a strange object, two or more are positively weird. In fact Einstein
labelled the special quantum properties of a collection of two quantum particles, as “spooky”. He was right to call them spooky, as we will show in the next section. However Einstein never accepted this spookiness and effectively spent much of the rest of his life trying to show that Nature couldn’t possibly be that spooky. And because technology at the time couldn’t test out the experiments that he had thought up to challenge Quantum Physics, they just remained as arguments in his brain – or so-called thought experiments. Since these thought experiments couldn’t be carried out in practice, the arguments became philosophical and hence were never resolved while he was alive. And like all unresolved things, this must have left Einstein feeling very uneasy.

Fortunately, recent advances in optical technology have enabled Einstein’s thought experiments to be performed in a laboratory. However, unfortunately for Einstein, these experiments have shown quite conclusively that Quantum Physics is correct and that Einstein was wrong to dismiss its spookiness. In short, Nature is indeed very spooky.

Quantum Physics is truly the “mother of all complexities”. It underlies everything in our Universe. Everything from human cells to people, candy bars to airplanes, cell phones to baseball bats. All are made up entirely of quantum particles. We don’t notice it in our everyday lives, but it is true. But the real hard-core aspect of quantum complexity emerges when we consider an isolated group of quantum particles – for example, two quanta of light which we can think of like a pair of gloves. The analogy actually makes a lot of sense, since it turns out that a quantum of light has a handedness just like gloves. In other words, a quantum of light is either left-handed or right-handed. We call this handedness polarization, and it is because of such polarization that Polaroid sunglasses are so good at reducing glare. Reflected light from water on the road is strongly polarized in one direction, and so Polaroid sunglasses can be used to cut out that particular
direction of polarization while leaving the rest untouched. Hence we see the things around us, but we don’t see the glare.

Let’s imagine that it is a cold morning, and so you take your gloves to work. At the end of the day, we will imagine that you accidentally leave one of your gloves in the office. When you get home, there is a message on your answering machine from the receptionist saying that she has found one of your gloves. You rush to your bag, and take out the glove that you still have. It is a right-handed glove. Hence you immediately know that the glove that the receptionist has is a left-handed glove. Now, until you looked in your bag, you didn’t know whether you had lost your right-handed glove or your left-handed glove. However, this isn’t because the identity of the lost glove was some kind of hidden secret that Nature was keeping all to itself. It just reflects the fact that you yourself didn’t yet know. But the gloves knew. In other words, anyone could have found out the answer ahead of you – the information was not some kind of fundamental secret of the Universe. The fact that you yourself didn’t know is just because you hadn’t yet looked or been told.

Now let us consider the same story with a pair of “quantum gloves” – in other words, a pair of quantum particles such as two quanta of light. No store sells them – yet. But we can do a thought experiment just like Einstein. What would happen is as follows. The story is unchanged in all aspects except that until somebody looks at one of the gloves – or as scientists say, until someone measures whether one of the gloves is right-handed or left-handed – even the gloves don’t know which is which. In other words, this
is
a fundamental secret of the Universe. Nobody can know the answer as to which glove is which until somebody, somewhere, has looked at one of the gloves and hence effectively measured its handedness. As soon as somebody has done that, then the story is exactly the same as the previous one. However, until that moment of measurement, each glove is both right and left-handed at the same time. Scientists refer to this strange coexistence of both possibilities as a superposition. They also refer to the magical connection that seems to exist between the two gloves – or quantum particles – as entanglement.

Just to emphasize, we do not mean that each quantum glove is momentarily right-handed and then left-handed. We mean it is right and left-handed simultaneously. It exists in both possible worlds at the same time, like two parallel Universes. For this reason, we are looking at a type of emergent phenomenon, and hence Complexity, which is way beyond anything we have seen so far in this book. It is also very spooky.

So if the receptionist doesn’t find the quantum glove, and you never look at the other quantum glove again, the Universe will co-exist in two parallel worlds with each quantum glove being both right and left-handed. It is only when someone checks the handedness of one of the gloves that the Universe then collapses into one outcome or the other. And it does this randomly. Einstein said “God doesn’t play dice” to which the reply came “Don’t tell God what to do!” But the effect really is bizarre – so Einstein’s dis-belief reflects his deep thinking rather than any sort of lack of insight.

This complex double-life of things – indeed, everything from ice-creams to bicycles if we look hard enough – is really very strange. And it has a huge number of consequences, many of which have scientists still struggling to understand. For example, computers work by storing 1’s and 0’s. But a quantum computer would be able to store 1’s and 0’s at the same time. This has led people to deduce that a quantum computer could run faster than any normal computer ever could – so watch out Intel Corporation. Going further, one could use this double-life to create completely safe secret codes. Instead of passing around a secret password to open up a safe box, one could instead pass around collections of quantum gloves with the right-hand being a 1 and the left-hand being a 0. If anyone tries to read your password, such as the receptionist trying to look at one of the quantum gloves, you can detect this tampering simply by seeing if the other glove has “decided” to be right or left-handed.