Arms and insecurity

During the last 25 years of his life, Richardson's main scientific interest was the study of the causes of war. To most people, any attempt to apply the methods of mathematics to such a complex social phenomenon appears doomed from the start. The two books which he wrote on the subject failed to find a publisher during his lifetime and it was not until seven years after his death that they were published with the help of a subsidy from the Littauer Foundation. (In fact, both books had to be reprinted and the royalties more than covered the subsidy.)

The first, entitled Arms and Insecurity, is an attempt to produce a mathematical theory of arms races. The mathematics used is not very hard and can be explained to anyone who has done a couple of years of calculus. (If you have not, just skip this part of the discussion.) Consider two nations who spend at a rate x(t) and y(t) (measured, for example, in dollars per year) on armaments at time t. The first nation will tend to increase its expenditure in response to the perceived threat of the expenditure of its rival, but will be restrained by the burden that its own expenditure represents. The greater y(t) is, the greater the rate of increase of x(t) but the greater x(t) is, the smaller the increase.

How safe?

In the early days of railways, there was no means of communicating between different parts of the line and trains were run on a time-interval basis. After the passage of a train, a danger signal would be shown for five minutes (say) to prevent another train following too closely. For the next five minutes a caution signal was displayed to indicate that any following train should slow down and finally a clear signal would be shown. If a train had to stop between signalling points, the guard was supposed to run back to warn the following train. (The book from which this account is taken remarks that ‘accidents were not as frequent as might be expected’.)

Gradually, as experience was gained and technology permitted, improvements were made. Points and signals were mechanically inter-locked so that the signals could only show clear if the points were correctly set. The invention of the electric telegraph allowed signalmen to communicate and led to the replacement of time-interval by space-interval working under the block system. The line was divided into blocks and when a train passed the signalman at the beginning of a block, he placed his signals at danger until informed by the signalman at the other end that the train had left the block. Since only one train can be in any one block at any one time, collisions are, in some sense, ‘impossible’.

Why are we not all called Smith?

In Section 15.1 we saw that the question of whether the Turing bombes would work depended on whether an effectively random process in which ‘mother statements’ give rise to a certain random number of ‘daughter statements’ which in turn give rise to ‘granddaughter statements’ and so on would die away quickly or give rise to a family containing all (or almost all) possible statements. The bombe problem is complicated by several special features and, though I hope that the discussion of the next two sections will shed some light on it, I shall concentrate on simpler but related problems.

Sir Thomas Browne wrote ‘Generations pass while some trees stand and old families last not three oaks’. (The quotation is taken from Kendall's fascinating papers [114] and [115].) Less concisely, Galton wrote:

Introduction

We have discussed in some detail the integrated natural entities of Levels 1, 2 and 3, in the physical range; and those of Levels 4, 5 and 6 in the biological range. So we now come to the social range: there are the one-mother family societies at Level 7, the multifamily societies at Level 8, and the societies of sovereign states at Level 9 (Fig. 7.1).

The zoological species with which this chapter is primarily concerned are those where the adult actively aids the young after hatching or birth. These species can be regarded as truly social species. However, the words social and society can be used with many different meanings. Some biologists may regard a group of plants growing together, and of the same species as constituting a society. The word actively, as used above, implies the use of respirational energy.

According to the evidence of fossils and isotopic dating, the first animals where the adult actively aided the young, after hatching or birth, were the early mammals. These lived about 200 million years ago. Similar societies of birds appeared about 150 million years ago. And the earliest social insect, found only recently, dates from about 100 million years ago.

There have been fascinating recent studies of the social behaviour of, for example, chimpanzees, orang-utans, baboons and other primates, of lions, tigers, wild dogs, seals, elephants, herring gulls, jackdaws and rooks, of certain fish and of bees, ants and termites.

At a given integrative level are there only a few lightweight members, many middleweight members, and only a few heavyweights? That is the kind of symmetrical or ‘normal’ distribution which is often encountered or assumed in the study of statistics. Or will some or all of the integrative levels show some other kind of distribution?

Social range

Level 9: Societies of sovereign states

For plotting the diagram of Fig. 14.1 the information used was from the 1971 data sheet of the Population Reference Bureau in Washington. The conspicuous result is that about three-quarters of all states consist of less than 20 million people. These include for instance Sweden, Switzerland, Sudan, Somalia, Senegal, Syria, Saudi Arabia, Singapore and El Salvador, to mention just a few.

Most of the other quarter have populations between 20 and 200 million, including for instance the United Kingdom, France, Germany, Spain, Italy, Egypt, Canada and Japan. Only the United States, Russia, India and China had populations in the range beyond 200 million. So the long thin tail to the right of Fig. 14.1 is hardly to be distinguished from the zero baseline; and for that reason the baseline itself has not been drawn in. (In recent years the population of China has of course grown to more than 800 million, indeed by 1990 to more than a thousand million; and India itself might reach that population by the year 2000.)

The vertical axis shows the relative frequency or number of nations along different sections of the horizontal scale.

Introduction

As indicated in Chapter 1, the first three major integrative levels are those of fundamental particles, atoms and molecules. These constitute the physical range of integrated natural entities.

A hydrogen atom consists of two fundamental particles. Most of any atom's mass resides in its small central nucleus. The nucleus of a hydrogen atom consists of a single proton. This has a positive electrical charge, which counterbalances the negative charge of the electron which circles or orbits around the nucleus (Fig. 4.1a). Each atom of the other chemical elements has more than one electron orbiting the centre. And apart from hydrogen atoms, the central nucleus of all normal atoms contains two or more protons together with two or more neutrons. Neutrons have a mass similar to that of protons, but they are electrically neutral, hence their name.

When a sunbeam enters a room one can speak of the arrival of electromagnetic waves, of such and such wavelength and frequency. Or alternatively one can speak of tiny particles streaming in, which have been given the name photons. In some contexts photons are not classed as fundamental particles, but in our new classification photons are definitely regarded as members of Level 1; so it is convenient here also to regard them as fundamental particles. Physicists sometimes regard photons as having no weight or mass; or no mass when not moving. But when moving, as in a beam of light, each photon does have a mass which can be calculated from knowing the wavelength or frequency of the light concerned.

This book, about the various sciences, is addressed primarily to students and general readers. Apart from my main duties of lecturing in biology at Brunei University in West London, for many years I gave short courses of lectures plus discussion on the fundamental findings of science. It was for groups of first-year undergraduates whose main disciplines varied widely. And the following pages lean heavily on that teaching experience. Hence almost any student or general reader is likely to find them quite intelligible.

The topics covered certainly range widely, from small fundamental particles up to the large and complex societies of sovereign states. There is also a brief outline of the main evolutionary developments since the beginning of the Earth, more than four thousand million years ago.

After having established, objectively, nine major levels of organisation, several new types of quantitative study become possible for the first time. These are reported in Chapters 10 to 15.

During the 1930s I studied at Cambridge, and then worked there on biological research. In 1940 I learnt that I was about to join the Royal Corps of Signals, in the Army. At that time I knew very little about telecommunications, though later, as it happens, I ran the War Office Wireless Demonstration Section, giving instructional talks and demonstrations to all ranks up to Brigadier.

However in 1940, to remedy my ignorance I went into Heffer's bookshop in Cambridge, and there, from the shelves, was able to purchase a couple of useful textbooks. One was the Admiralty Handbook of Wireless Telegraphy.

The concept of integrative levels was one which I introduced, stimulated by various predecessors, in the Herbert Spencer Lecture which I gave at Oxford in 1937, over half a century ago.

Several dozen authors have subsequently used the idea of different integrative levels. Their discrimination of integrative levels has often used the ‘compositional criterion’; but the present work by my old friend Max Pettersson is unique in also introducing a ‘duality criterion’, for the discrimination of major levels. One of the agreeable results of this is that we now find an excellent match between the relatively static hierarchy of things present today, and the evolutionary progression to more and more complex entities which has occurred on Earth during the past 4000 million years.

Having established a series of nine major integrative levels, various quantitative studies have now become possible for the first time. Perhaps most or all of the twenty or so newly discovered quantitative conclusions will be found to remain valid. For readers a generation or two hence, it will be very interesting to notice how much further such studies have developed and ramified.

The main function of this chapter will be to do a basic job of stock-taking. In the small part of the universe best known to us, the solar system, about how many are there of each of the nine main kinds of integrated natural entity? Inspecting the nine answers will suggest several general observations of wide validity.

Frequency estimates

Right from the beginning of an enquiry about the numbers of things, certain points stand out. One is that most of the mass of the solar system, nearly 99.9 per cent, resides in the Sun itself, the atomic composition of which has been reported in some detail. Another point is that the only living systems (or entities from intermediate entity upwards), which are known to occur in the solar system, are on Earth. The surface of the Earth is an extremely small habitat in comparison with the size of the whole solar system, but it is at least a place which we ourselves are able to observe closely. With regard to the photons emitted by the sun, it is proposed to include in the ‘extended solar system’ sufficient photons to bring the total number of fundamental particles up to the round number of 1060. This will be discussed further in another chapter.

Thus we can have a firm value for the total number of fundamental particles in the extended solar system at Level 1. At the other end of the series at Level 9 we have a value of about 180 societies of sovereign states.

Some definitions

One of the definitions which a dictionary gives for the word ‘entity’ is ‘a thing that exists’. A definition of ‘hierarchy’ is ‘a body classified in successively subordinate grades’. This corresponds reasonably well with what follows. The word ‘integer’ means ‘a whole’. An individual mammal is certainly a coherent entity, made up and functioning as a whole. It is an ‘integrated natural entity’, and a good representative of one of the major ‘integrative levels’ which are the primary theme of this book.

A car and a computer are not ‘natural’ but manufactured, or ‘artificial’. In comparison with a heap of scrap metal, a car is certainly an integrated entity; but an integrated artificial entity. A pebble and a planet are each ‘natural’ entities. But compare a pebble with a live mouse, of about the same size. If the pebble is broken in two, the properties of the system do not change greatly. But if a live mouse is cut into halves the properties change catastrophically because the live mouse has such a highly complex and wellintegrated structure, with properties to match. While a mouse can be thought of as an integrated natural entity, pebbles and planets (being rather low-grade aggregations of molecules and ions, etc.) could be regarded as ‘aggregational’ natural entities, a term that will not often need to be used.

Natural hierarchies

It is well known to students of chemistry and physics that molecules consist of atoms, and that atoms consist of fundamental particles.

This chapter will be mainly about the societies of sovereign states; about complex societies at Level 9. However, certain more general topics will be included.

In August 1993 the number of member states of the United Nations was 184 and as a first approximation the number of members of the UN can be taken as the current number of sovereign states in the world. Each sovereign state maintains order and governs within its own territory. It normally keeps a strict control of the movements of persons, other organisms, and artifacts (including money) across its borders. The populations of Britain, France, Germany, the United States and Japan are examples of Level 9 entities.

The society of each sovereign state is made up of the societies of settlements. And we must recognise that there is sometimes one or more important tier of government between that of our standard administrative unit and the society of the sovereign state. For instance each ‘State’ within the USA has its own influential government, but even California is not a sovereign state. It will be interesting to see whether, in the years ahead, something like a United States of Europe does emerge; or whether, on the other hand, the existing states co-operate more fully without actually fusing.

When, where, and how, did the early sovereign states arise? In the days of the first little farming villages, probably each community was more or less independent. An independent Level 8 society might be on good terms with some neighbouring villages and on bad terms with others.

By now we have covered all the more general points involved in the idea of the natural hierarchy, and of its nine major integrative levels. A number of points of detail will need to be filled in, as in Chapters 4–9, before the quantitative results of Chapters 10–14 can be attained. But before discussing atoms and molecules in Chapter 4, it seems appropriate – for the benefit of non-specialist readers – to give some idea of how large such things as atoms and molecules actually are, and how their sizes compare with those of viruses and cells. At the same time we can briefly introduce some methods of logarithmic plotting which are rather useful for the display of the weight (or mass) of various entities, and their parts, as well.

Lengths of smaller entities

Starting from the left-hand end of a ruler, each movement to the right by a standard distance (say an inch or a centimetre) represents an additive increase of length by that standard unit. But the vertical scale in Fig. 3.1 is arranged differently. Each movement upwards, from one peg to the next peg above, represents a multiplication by a constant factor, in fact by 10, thus the distance on the scale between 1 millimetre and 1 centimetre is the same as that between 1 nanometre and 10 nanometres. We shall be using this kind of logarithmic scale frequently, so for those who wish for it, a little more information about the metric scale of lengths, and logarithmic plotting, is offered in an Appendix to this chapter.

Introduction

The biological range includes all individual living organisms, as well as many of their small and very small parts. Fig. 1.2 shows the first six levels of the natural hierarchy.

We must consider each of the three levels in detail. In the previous chapter some attention was paid to the structure and functioning of the physical range. Similarly it seems appropriate now to offer a very brief account of the structure and behaviour of organisms, cells, chromosomes and genes. It will also be interesting to enquire into the evolutionary origin of the organisation seen within ordinary cells. And we shall briefly review the range of mass of the members of each of these levels.

Level 6, multicellular organisms

When Robert Hooke in London published magnified pictures of sections through cork in 1665, he wrote of each tiny unit as a cellula (a little cell). That is how the biological term cell originated. Fig. 5.1 shows some cells, each with a nucleus, as seen in a section of tissue through the tip of a plant stem.

Aided by the new achromatic compound microscope of the 1830s, Schleiden and Schwann in Germany had by 1840 proposed that all larger plants and animals were composed of many tiny cells. Plants commonly have thick hard inert walls of cellulose around each cell (and running outside each cell's thin semi-permeable plasma membrane). Animal cells, however, are often separated only by their thin plasma membranes, so it took zoologists longer to become convinced of the cell theory.

As our ancestors and others ascended the natural hierarchy, from Level 4 to Level 9, there was acceleration, as established in Chapter 10. It will now be interesting to try and relate this newly discovered evolutionary acceleration to two other forms of acceleration about which a number of studies have already been published.

One refers both to acceleration in the increase of the number of humans on Earth and to acceleration in human cultural innovation. It will be found that a coherent picture does emerge, leading to what may be called ‘the law of ever faster change’. The topics of demographic increase and cultural innovation stand somewhat apart from our central study of the natural hierarchy. But it does seem worthwhile to notice these processes, if only briefly.

The difficulties resulting from the increasing numbers of people are force-fully discussed by, for instance, Parsons, (1971) and Ehrlich and colleagues (e.g. 1970, 1978), while another American writer, Toffler (1971), provides a moving and well-documented account of the increasing rapidity of social change.

Method of plotting

Figures 11.1 – 11.3 all use the same special axes, which have been found convenient for the data under consideration. The horizontal axis is a logarithmic scale of chronological time, referring to the number of years before AD 2000. Thus the five markers on the right of the horizontal axis refer to the dates 1999, 1990, 1900, AD 1000 and to 8000 BC.

Introduction

Three centuries ago Archbishop Ussher of Armagh, in Ireland, made a careful quantitative study of the evidence in the Old Testament of the Bible, and concluded that the first farming or agriculture (as well as the first humans) occurred about 6000 years ago. Nowadays, as a result of many careful excavations and with isotopic dating, it is concluded that farming or agriculture first appeared before 10 000 years ago, though it was roughly in the same part of the world as the Bible suggests.

Whether or not one invokes supernatural intervention to help account for subsequent changes, since the beginning of agriculture the ways of human life have come to diverge more and more away from those of our other mammalian cousins. For one thing there has been the increase in the number, diversity and bulk of artifacts (of made things). Another general feature has been the increasing speed and distance of the movement of people, goods and information. In William Shakespeare's play A Midsummer Night's Dream, written nearly four centuries ago, a fairy messenger named Puck promises to ‘put a girdle round about the Earth in forty minutes’. In fact nowadays radio messages can reach the other side of the Earth in less than a second.

It so happens that I used to have experience of something like that, night after night. In the early part of World War II one of my army jobs, in England, was to take down news items, broadcast by radio in the morse code, from the Domei News Agency in Japan.