100 Essential Things You Didn't Know You Didn't Know (24 page)

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 detached 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?