100 Essential Things You Didn't Know You Didn't Know Page 16

  Let’s look at the set-up of the San Francisco Zoo’s tiger enclosure shown above. The wall was 3.8 metres high, but the tiger is bulky and its centre would have to clearfn1 about 4.3 metres to get cleanly over the wall because Siberian tigers are about 1 metre high at the shoulder. (We will neglect the possibility that it clings on and scrambles over the wall – always likely though.) This gives V2 = 9.8(4.3 + √(18.5 + 100)) = 148.97 (m/s)2, so V is 12.2 m/s.

  This is within the launch-speed capability of a tiger, and so it could indeed have cleared the wall. Raise the wall to 5.5 metres so the tiger needs to raise its centre by 6 metres to clear the wall and the tiger needs to launch at 13.2 metres per second to clear the wall. As the Director said, ‘Obviously now that something’s happened, we’re going to be revisiting the actual height.’

  fn1 In these problems the projectile is taken to be a mass of negligible size located at its centre (a so-called ‘point’ mass). Of course, a tiger has a very significant size and is in no sense a point. However, we shall neglect this and treat the tiger as if it had its whole mass located at its centre.

  75

  How the Leopard Got His Spots

  Then the Ethiopian put his five fingers close together . . . and pressed them all over the Leopard, and wherever the five fingers touched they left five little black marks, all close together . . . Sometimes the fingers slipped and the marks got a little blurred; but if you look closely at any Leopard now you will see that there are always five spots – off five black fingertips.

  Rudyard Kipling, ‘How the Leopard Got His Spots’

  Animal markings, particularly on big cats, are some of the most spectacular things we see in the living world. These patterns are by no means random, nor are they determined solely by the need for camouflage. The activators and inhibitors that encourage or block the presence of particular pigments flow through the embryonic animal in accord with a simple law that dictates how their concentrations at different points depend on the amount of production of that pigment by chemical reactions and the rate at which it spreads through the skin. The result is a wavelike spread of signals, which will activate or suppress different colour pigments. The resulting effects depend on several things, like the size and shape of the animal and the wavelength of the pattern waves. If you were to look at a large area of skin surface, then the peaks and troughs of these waves would create a regular network of hills and valleys of different colours. The appearance of a peak occurs at the expense of the inhibiting tendency, and so you get a pronounced stripe or spot against a contrasting background. If there is a maximum concentration that is possible in a particular place, then the build-up of concentration will eventually have to spread out, and spots will merge, turning into patches or stripes.

  The size of the animal is important. A very small animal will not have room for many ups and downs of the pigment-activating wave to fit along and around its body, so it will be one colour, or perhaps manage to be piebald like a hamster. When the animal is huge, like an elephant, the number of ups and downs of the waves is so enormous that the overall effect is monochrome. In between the big and the small, there is much more scope for variety, both from one animal to the next and over an animal’s body. A cheetah, for example, has a spotty body but a stripy tail. The waves create separate peaks and troughs as they spread around the large and roughly cylindrical body of the cheetah, but when they spread to the thin cylindrical tail they were much closer together and merged to create the appearance of stripes. This tendency gives a very interesting mathematical ‘theorem’ that follows from the behaviour of the colour concentration waves on animals bodies: animals with spots can have striped tails but striped animals cannot have spotted tails.

  76

  The Madness of Crowds

  The future belongs to crowds.

  Don Delillo, Mao II

  If you have ever been in a huge crowd, at a sports event, a pop concert or a demonstration, then you may have experienced or witnessed some of the strange features of people’s collective behaviour. The crowd is not being organised as a whole. Everyone responds to what is going on next to them, but nonetheless the crowd can suddenly change its behaviour over a large area, with disastrous results. A gentle plodding procession can turn into a panic-stricken crush with people trying to move in all directions. Understanding these dynamics is important. If a fire breaks out or an explosion occurs near a large crowd, how will people behave? What sort of escape routes and general exits should be planned in large stadiums? How should religious pilgrimages of millions of worshippers to Mecca be organised so as to avoid repeating the deaths of hundreds of pilgrims that have occurred in the past, as panic generates a human stampede in response to overcrowding?

  One of the interesting insights that informs recent studies of crowd behaviour and control is the analogy between the flow of a crowd and the flow of a liquid. At first one might think that understanding crowds of different people, all with different potential responses to a situation, and different ages and degrees of understanding of the situation, would be a hopeless task, but surprisingly, this is not the case. People are more alike than we might imagine. Simple local choices can quickly result in an overall order in a crowded situation. When you arrive at one of London’s big rail termini and head down to the Underground system, you will find that people descending will have chosen the left- (or right-) hand stair, while those ascending will keep to the other one. Along the corridors to the ticket barriers the crowd will organise itself into two separate streams moving in opposite directions. Nobody planned all that or put up notices demanding it: it arose as a result of individuals taking their cue from what they observed in their close vicinity. This means that they act in response to how people move in their close vicinity and how crowded it is getting. Responses to the second factor depend a lot on who you are. If you are a Japanese manager used to travelling through the rush hour on the Tokyo train system, you will respond very differently to a crush of people around you than if you are a tourist visitor from the Scottish Isles or a school group from Rome. If you are minding young or old relatives, then you will move in a different way, linked to them and watching where they are. All these variables can be taught to computers that are then able to simulate what will happen when crowds congregate in different sorts of space and how they will react to the development of new pressures.

  Crowds seem to have three phases of behaviour, just like a flowing liquid. When the crowding is not very great and the movement of the crowd is steady in one direction – like the crowd leaving Wembley Stadium for Wembley Park Underground station after a football match – it behaves like a smooth flow of a liquid. The crowd keeps moving at about the same speed all the time and there is no stopping and starting.

  However, if the density of people in the crowd grows significantly, they start pushing against one another and movement starts to occur in different directions. The overall movement becomes more staccato in character, with stop-go behaviour, rather like a succession of rolling waves. The gradual increase in the density of bodies will reduce the speed at which they can move forward, and there will be attempts to move sideways if people sense that things might move forwards faster that way. It is exactly the same psychology as cars swopping lanes in a dense, slow-moving traffic jam. In both cases it sends ripples through the jam, which cause some people to slow and some people to shift sideways to let you in. A succession of those staccato waves will run through the crowd. They are not in themselves necessarily dangerous, but they signal the possibility that something much more dangerous could suddenly happen.

  The closer and closer packing of people in the crowd starts to make them behave in a much more chaotic fashion, like a flowing liquid becoming turbulent, as people try to move in any direction so as to find space. They push their neighbours and become more vigorous in their attempts to create some personal space. This increases the risk of people falling, becoming crushed together so closely that breathing is difficult or children becoming detache
d from their parents. These effects can start in different places in a big crowd and their effects will spread quickly. The situation rapidly snowballs out of control The fallers become obstacles over which others fall. Anyone with claustrophobia will panic very quickly and react even more violently to close neighbours. Unless some type of organised intervention occurs to separate parts of the crowd from other parts and reduce the density of people, a disaster is now imminent.

  The transition from smooth pedestrian flow to staccato movement and then crowd chaos can take anything from a few minutes to half an hour, depending on the size of the crowd. It is not possible to predict if and when a crisis is going to occur in a particular crowd, but, by monitoring the large-scale behaviour, the transition to the staccato movement can be spotted in different parts of a big crowd and steps taken to alleviate crowding at the key pressure points that are driving the transition where chaos will set in.

  77

  Diamond Geezer

  I have always felt a gift diamond shines so much better than one you buy for yourself.

  Mae West

  Diamonds are very remarkable pieces of carbon. They are the hardest naturally occurring materials.

  The most sparkling properties of diamonds, however, are optical, because diamond has a huge refractive index of 2.4, compared with that of water (1.3) or glass (1.5). This means that light rays are bent (or ‘refracted’) by a very large angle when they pass through a diamond. More important still, light that is shone onto a diamond surface at an angle more than just 24 degrees from the vertical to the surface will be completely reflected and not pass through the diamond at all. This is a very small angle – for light shone through air on water this critical angle is about 48 degrees from the vertical, and for glass it is about 42 degrees.

  Diamonds also spread colours in an extreme fashion. Ordinary white light is composed of a spectrum of red, orange, yellow, green, blue, indigo and violet light waves, which travel at different speeds through the diamond and get bent by different angles (red the least, violet the most) as white light passes through a transparent medium. Diamond produces a very large difference between the greatest and the least bending of the colours, called its ‘dispersion’, and this creates the remarkable ‘fire’ of changing colours when light passes through a well-cut diamond. No other gem stones have such a large dispersive power. The challenge presented to the jeweller is to cut a diamond so that it shines as brightly and colourfully as possible in the light it reflects back into the eye of the beholder.

  The cutting of diamonds is an ancient practice that has gone on for thousands of years, but there is one man who contributed more than anyone to our understanding of how best to cut a diamond and why. Marcel Tolkowsky (1899–1991) was born in Antwerp into a leading family of diamond cutters and dealers. He was a talented child and after graduating from college in Belgium was sent to Imperial College in London to study engineering.fn1 While still a graduate student there, in 1919 he published a remarkable book entitled Diamond Design, which showed for the first time how the study of the reflection and refraction of light within a diamond can reveal how best to cut it so as to achieve maximum brilliance and ‘fire’. Tolkowsky’s elegant analysis of the paths that are followed by light rays inside a diamond led him to propose a new type of diamond cut, the ‘Brilliant’ or ‘Ideal’, which is now the favoured style for round diamonds. He considered the paths of light rays coming straight at the top flat surface of the diamond and asked for the angles at which the back of the diamond should be inclined so as to completely internally reflect the light at the first and second internal reflections. This will result in almost all the incoming light passing straight back out of the front of the diamond and produce the most brilliant appearance. In order to appear as brilliant as possible, the outgoing light rays should not suffer significant bending away from the vertical when they exit the diamond after their internal reflections. The three pictures overleaf show the effects of too great, and too small, an angle of cut compared to an optimal one which avoids light-loss by refraction through the back faces and diminished back-reflection.

  Tolkowsky went on to consider the optimal balance between reflected brilliance and the dispersion of its spectrum of colours so as to create a special ‘fire’ and the best shapes for the different faces.20

  His analysis, using the simple mathematics of light rays, produced a recipe for a beautiful ‘brilliant cut’ diamond with 58 facets, and a set of special proportions and angles in the ranges needed to produce the most spectacular visual effects as a diamond is moved slightly in front of your eye. But you see there is more to it than meets the eye.

  In the diagram we see the classic shape that Tolkowsky recommended for an ideal cut with the angles chosen in the narrow ranges that optimise ‘fire’ and brilliance. The proportions are shown for the parts of the diamond (shown with their special names) as percentages of the diameter of the girdle, which is the overall diameter.fn2

  fn1 His doctoral thesis was on the grinding and polishing of diamonds rather than on their appearance.

  fn2 The small thickness at the girdle is given so as to avoid a sharp edge.

  78

  The Three Laws of Robotics

  For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.

  Book of Genesis

  Yesterday I saw the film I, Robot, based on the robot stories of the great science-fiction writer Isaac Asimov. In 1942 he introduced the futuristic concept of humans coexisting with advanced robots in a short story entitled ‘Runaround’. In order to ensure that humans were not destroyed or enslaved by their unerringly efficient assistants, he framed a set of ‘Laws’, which were programmed into the electronic brains of all robots as a safeguard. What those laws should be is an interesting question, not merely one of technological health and safety, but a deeper issue for anyone wondering why there is evil in the world and what steps a benevolent Deity might have taken to stop it.

  Asimov’s original three laws are modelled on the three laws of thermodynamics

  First Law: A robot may not injure a human being or, through inaction, allow a human being to come to harm.

  Second Law: A robot must obey orders given to it by human beings, except where such orders would conflict with the First Law.

  Third Law: A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.

  Later, Asimov added the ‘Zeroth Law’, again as in thermodynamics, to stand before the First Law:

  Zeroth Law: A robot may not harm humanity, or, by inaction, allow humanity to come to harm.

  The reason for this last legal addition is not hard to find. Suppose a madman had gained access to a nuclear trigger that could destroy the world and only a robot could stop him from pressing it, then the First Law would prevent the robot from acting to save humanity. It is inaction on the part of robots that is a problem with the First Law, even when the Zeroth Law is irrelevant. If my robot and I are shipwrecked on a desert island and my gangrenous foot needs to be amputated in order to save my life, will my robot be able to overcome the First Law and cut it off ? And could a robot ever act as a judge in the courts where he must hand down punishments to those found guilty by a jury?

  Should we feel safe if robots were created in large numbers with these four laws programmed into their electronic brains? I think not. It’s all a question of timing. The precedence of the Zeroth Law over the First means that the robot may kill you because you are driving a gas guzzling car or not recycling all your plastic bottles. It judges that your behaviour, if it continues, threatens humanity. It might become very concerned about its duty to act against some of the world’s political leaders as well. Asking robots to act for the good of humanity is a dangerous request. It seeks something that is not defined. There is no unique answer to the question ‘What is the good of humanity?’ No computer could exist that prints out a list of all actions t
hat are good for humanity and all actions that are harmful to it. No programme can tell us all good and all evil.

  You might feel safer without the Zeroth Law than with it. Still, there is another worrying consideration that could put you at risk from all the harmful direct actions that the First, Second and Third Laws were conceived to protect us from. Advanced robots will have complicated thoughts, thoughts about themselves and us as well as about inanimate objects: they will have a psychology. Just as with humans, this may make them hard to understand – but it may also lead them to suffer from some of the psychological problems that humans can fall victim to. Just as it is not unknown for humans to be deluded into thinking they are robots, it may be that a robot could think it was a human. In that situation it could do what it likes because it no longer believes that the Four Laws of Robotics apply to it. Closely linked to this problem would be the evolution of religious or mystical beliefs in the robot mind. What then of the Third Law? What robotic existence is it that must be preserved? The material fabric of the robot? The soul in the machine that it perceives itself to have? Or, the ‘idea’ of the robot that lives on in the mind of its maker?

  You can carry on asking questions like this for yourself, but you can see that it is not so easy to trammel the consequences of artificial intelligence by imposing constraints and rules on its programming. When that ‘something’ that we call ‘consciousness’ appears, its consequences are unpredictable, with enormous potential for good or evil, and it is hard to have one without the other – a bit like real life really.

  79

  Thinking Outside the Box

  Many people would rather die than think; in fact, most do.

  Bertrand Russell