Alex’s Adventures In Numberland by Alex Bellos (2010)

Alexander Bellos (born in 1969) is a British writer and broadcaster. He is the author of books about Brazil and mathematics, as well as having a column in The Guardian newspaper. After adventures in Brazil (see his Wikipedia page) he returned to England in 2007 and wrote this, his first book. It spent four months in the Sunday Times bestseller list and led on to five more popular maths books.

It’s a hugely enjoyable read for three reasons:

1. Bellos immediately establishes a candid, open, good bloke persona, sharing stories from his early job as a reporter on the Brighton Argus, telling some colourful anecdotes about his time in Brazil and then being surprisingly open about the way that, when he moved back to Britain, he had no idea what to do. The tone of the book is immediately modern, accessible and friendly.
2. However this doesn’t mean he is verbose. The opposite. The book is packed with fascinating information. Every single paragraph, almost every sentence contains a fact or insight which makes you sit up and marvel. It is stufffed with good things.
3. Lastly, although its central theme is mathematics, it approaches this through a wealth of information from the humanities. There is as much history and psychology and anthropology and cultural studies and philosophy as there is actual maths, and these are all subjects which the average humanities graduate can immediately relate to and assimilate.

Chapter Zero – A Head for Numbers

Alex meets Pierre Pica, a linguist who’s studied the Munduruku people of the Amazon and discovered they have little or no sense of numbers. They only have names for numbers up to five. Also, they cluster numbers together logarithmically i.e. the higher the number, the closer together they clustered them. Same thing is done by kindergarten children who only slowly learn that numbers are evenly spaced, in a linear way.

This may be because small children and the Munduruku don’t count so much as estimate using the ratios between numbers.

It may also be because above a certain number (five) Stone Age man needed to make quick estimates along the lines of, Are there more wild animals / members of the other gang, than us?

Another possibility is that distance appears to us to be logarithmic due to perspective: the first fifty yards we see in close detail, the next fifty yards not so detailed, beyond 100 yards looking smaller, and so on.

It appears that we have to be actively taught when young to overcome our logarithmic instincts, and to apply the rule that each successive whole number is an equal distance from its predecessor and successor i.e. the rational numbers lies along a straight line at regular intervals.

More proof that the logarithmic approach is the deep, hard-wired one is the way most of us revert to its perspective when considering big numbers. As John Allen Paulos laments, people make no end of fuss about discrepancies between 2 or 3 or 4 – but are often merrily oblivious to the difference between a million or a billion, let alone a trillion. For most of us these numbers are just ‘big’.

He goes on to describe experiments done on chimpanzees, monkeys and lions which appear to show that animals have the ability to estimate numbers. And then onto experiments with small babies which appear to show that as soon as they can focus on the outside world, babies can detect changes in number of objects.

And it appears that we also have a further number skill, that guesstimating things – the journey takes 30 or 40 minutes, there were twenty or thirty people at the party, you get a hundred, maybe hundred and fifty peas in a sack. When it comes to these figures almost all of us give rough estimates.

To summarise:

• we are sensitive to small numbers, acutely so of 1, 2, 3, 4, less so of 5, 6, 7, 8, 9
• left to our own devices we think logarithmically about larger numbers i.e lose the sense of distinction between them, clump them together
• we have a good ability to guesstimate medium size numbers – 30, 40, 100

But it was only with the invention of notation, a way of writing numbers down, that we were able to create the linear system of counting (where every number is 1 larger than its predecessor, laid out in a straight line, at regular intervals).

And that this cultural invention enabled human beings to transcend our vague guesstimating abilities, and laid the basis for the systematic manipulation of the world which followed

Chapter One – The Counter Culture

The probable origins of counting lie in stock taking in the early agricultural revolution some 8,000 years ago.

We nowadays count using a number base 10 i.e. the decimal system. But other bases have their virtues, especially base 12. It has more factors i.e. is easier to divide: 12 can be divided neatly by 2, 3, 4 and 6. A quarter of 10 is 2.5 but of 12 is 3. A third of 10 is 3.333 but of 12 is 4. Striking that a version of the duodecimal system (pounds, shillings and pence) hung on in Britain till we finally went metric in the 1970s. There is even a Duodecimal Society of America which still actively campaigns for the superiority of a base 12 counting scheme.

Bellos describes a bewildering variety of other counting systems and bases. In 1716 King Charles XII of Sweden asked Emmanuel Swedenborg to devise a new counting system with a base of 64. The Arara in the Amazon count in pairs, the Renaissance author Luca Paccioli was just one of hundreds who have devised finger-based systems of counting – indeed, the widespread use of base 10 probably stems from the fact that we have ten fingers and toes.

He describes a complicated Chinese system where every part of the hand and fingers has a value which allows you to count up to nearly a billion – on one hand!

The Yupno system which attributes a different value for parts of the body up to its highest number, 33, represented by the penis.

Diagram showing numbers attributed to parts of the body by the Yupno tribe

There’s another point to make about his whole approach which comes out if we compare him with the popular maths books by John Allen Paulos which I’ve just read.

Paulos clearly sees the need to leaven his explanations of comparative probability and Arrow’s Theorem and so on with lighter material and so his strategy is to chuck into his text things which interest him: corny jokes, anecdotes about baseball, casual random digressions which occur to him in mid-flow. But al his examples clearly 1. emanate from Paulos’s own interests and hobby horses (especially baseball) and 2. they are tacked onto the subjects being discussed.

Bellos, also, has grasped that the general reader needs to be spoonfed maths via generous helpings of other, more easily digestible material. But Bellos’s choice of material arises naturally from the topic under discussion. The humour emerges naturally and easily from the subject matter instead of being tacked on in the form of bad jokes.

You feel yourself in the hands of a master storyteller who has all sorts of wonderful things to explain to you.

In fourth millennium BC, an early counting system was created by pressing a reed into soft clay. By 2700 BC the Sumerians were using cuneiform. And they had number symbols for 1, 10, 60 and 3,600 – a mix of decimal and sexagesimal systems.

Why the Sumerians grouped their numbers in 60s has been described as one of the greatest unresolved mysteries in the history of arithmetic. (p.58)

Measuring in 60s was inherited by the Babylonians, the Egyptians and the Greeks and is why we still measure hours in 60 minutes and the divisions of a circle by 360 degrees.

I didn’t know that after the French Revolution, when the National Convention introduced the decimal system of weights and measures, it also tried to decimalise time, introducing a new system whereby every day would be divided into ten hours, each of a hundred minutes, each divided into 100 seconds. Thus there were a very neat 10 x 100 x 100 = 100,000 seconds in a day. But it failed. An hour of 60 minutes turns out to be a deeply useful division of time, intuitively measurable, and a reasonable amount of time to spend on tasks. The reform was quietly dropped after six months, although revolutionary decimal clocks still exist.

Studies consistently show that Chinese children find it easier to count than European children. This may be because of our system of notation, or the structure of number names. Instead of eleven or twelve, Chinese, Japanese and Koreans say the equivalent of ten one, ten two. 21 and 22 become two ten one and two ten two. It has been shown that this makes it a lot simpler and more intuitive to do basic addition and subtraction.

Bellos goes on to describe the various systems of abacuses which have developed in different cultures, before explaining the phenomenal popularity of abacus counting, abacus clubs, and abacus championships in Japan which helps kids develop the ability to perform anzan, using the mental image of an abacus to help its practitioners to sums at phenomenal speed.

Chapter Two – Behold!

The mystical sense of the deep meaning of numbers, from Pythagoras with his vegetarian religious cult of numbers in 4th century BC Athens to Jerome Carter who advises leading rap stars about the numerological significance of their names.

Euclid and the elegant and pure way he deduced mathematical theorems from a handful of basic axioms.

A description of the basic Platonic shapes leads into the nature of tessalating tiles, and the Arab pioneering of abstract design. The complex designs of the Sierpinski carpet and the Menger sponge. And then the complex and sophisticated world of origami, which has its traditionalists, its pioneers and surprising applications to various fields of advanced science, introducing us to the American guru of modern origami, Robert Lang, and the Japanese rebel, Kazuo Haga, father of Haga’s Theorem.

Chapter Three – Something About Nothing

A bombardment of information about the counting systems of ancient Hindus, Buddhists, about number symbols in Sanskrit, Hebrew, Greek and Latin. How the concept of zero was slowly evolved in India and moved to the Muslim world with the result that the symbols we use nowadays are known as the Arabic numerals.

A digression into ‘a set of arithmetical tricks known as Vedic Mathematics ‘ devised by a young Indian swami at the start of the twentieth century, Bharati Krishna Tirthaji, based on a series of 16 aphorisms which he found in the ancient holy texts known as the Vedas.

Shankaracharya is a commonly used title of heads of monasteries called mathas in the Advaita Vedanta tradition. Tirthaji was the Shankaracharya of the monastery at Puri. Bellos goes to visit the current Shankaracharya who explains the closeness, in fact the identity, of mathematics and Hindu spirituality.

Chapter Four – Life of Pi

An entire chapter about pi which turns out not only to be a fundamental aspect of calculating radiuses and diameters and volumes of circles and cubes, but also to have a long history of mathematicians vying with each other to work out its value to as many decimal places as possible (we currently know the value of pi to 2.7 trillion decimal places) and the surprising history of people who have set records reciting the value if pi.

Thus, in 2006, retired Japanese engineer Akira Haraguchi set a world record for reciting the value of pi to the first 100,000 decimal places from memory! It took 16 hours with five minute beaks every two hours to eat rice balls and drink some water.

There are several types or classes of numbers:

• natural numbers – 1, 2, 3, 4, 5, 6, 7…
• integers – all the natural numbers, but including the negative ones as well – …-3, -2, -1, 0, 1, 2, 3…
• fractions
• which are also called rational numbers
• numbers which cannot be written as fractions are called irrational numbers
• transcendent numbers – ‘a transcendental number is an irrational number that cannot be described by an equation with a finite number of terms’

The qualities of the heptagonal 50p coin and the related qualities of the Reuleux triangle.

Chapter Five – The x-factor

The origin of algebra (in Arab mathematicians).

Bellos makes the big historical point that for the Greeks (Pythagoras, Plato, Euclid) maths was geometric. They thought of maths as being about shapes – circles, triangles, squares and so on. These shapes had hidden properties which maths revealed, thus giving – the Pythagoreans thought – insight into the secret deeper values of the world.

It is only with the introduction of algebra in the 17th century (Bellos attributes its widespread adoption to Descartes’s Method in the 1640s) that it is possible to fly free of shapes into whole new worlds of abstract numbers and formulae.

Logarithms turn the difficult operation of multiplication into the simpler operation of addition. If X x Y = Z, then log X + log Y = log Z. They were invented by a Scottish laird John Napier, and publicised in a huge book of logarithmic tables published in 1614. Englishman Henry Briggs established logarithms to base 10 in 1628. In 1620 Englishman Edmund Gunter marked logarithms on a ruler. Later in the 1620s Englishman William Oughtred placed two logarithmic rulers next to each other to create the slide rule.

Three hundred years of dominance by the slide rule was brought to a screeching halt by the launch of the first pocket calculator in 1972.

Quadratic equations are equations with an x and an x², e.g. 3x² + 2x – 4 = 0. ‘Quadratics have become so crucial to the understanding of the world, that it is no exaggeration to say that they underpin modern science’ (p.200).

Chapter Six – Playtime

Number games. The origin of Sudoku, which is Japanese for ‘the number must appear only once’. There are some 5 billion ways for numbers to be arranged in a table of nine cells so that the sum of any row or column is the same.

There have, apparently, only been four international puzzle crazes with a mathematical slant – the tangram, the Fifteen puzzle, Rubik’s cube and Sudoku – and Bellos describes the origin and nature and solutions to all four. More than 300 million cubes have seen sold since Ernö Rubik came up with the idea in 1974. Bellos gives us the latest records set in the hyper-competitive sport of speedcubing: the current record of restoring a copletely scrambled cube to order (i.e. all the faces of one colour) is 7.08 seconds, a record held by Erik Akkersdijk, a 19-year-old Dutch student.

A visit to the annual Gathering for Gardner, honouring Martin Gardner, one of the greatest popularisers of mathematical games and puzzles who Bellos visits. The origin of the ambigram, and the computer game Tetris.

Chapter Seven – Secrets of Succession

The joy of sequences. Prime numbers.

The fundamental theorem of arithmetic – In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers.

The Goldbach conjecture – one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that, Every even integer greater than 2 can be expressed as the sum of two primes. The conjecture has been shown to hold for all integers less than 4 × 1018, but remains unproven despite considerable effort.

Neil Sloane’s idea of persistence – The number of steps it takes to get to a single digit by multiplying all the digits of the preceding number to obtain a second number, then multiplying all the digits of that number to get a third number, and so on until you get down to a single digit. 88 has a persistence of three.

88 → 8 x 8 = 64 → 6 x 4 = 24 → 2 x 4 = 8

John Horton Conway’s idea of the powertrain – For any number abcd its powertrain goes to abcd, in the case of numbers with an odd number of digits the final one has no power, abcde’s powertrain is abcde.

The Recamán sequence Subtract if you can, unless a) it would result in a negative number or b) the number is already in the sequence. The result is:

0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11….

Gijswijt’s sequence a self-describing sequence where each term counts the maximum number of repeated blocks of numbers in the sequence immediately preceding that term.

1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 1, …

Perfect number A perfect number is any number that is equal to the sum of its factors. Thus 6 – its factors (the numbers which divided into it) are 1, 2 and 3. Which also add up to (are the sum of) 6. The next perfect number is 28 because its factors – 1, 2, 4, 7, 14 – add up to 28. And so on.

Amicable numbers A number is amicable if the sum of the factors of the first number equals the second number, and if the sum of the factors of the second number equals the first. The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110. Added together these make 284. The factors of 284 are 1, 2, 4, 71 and 142. Added together they make 220!

Sociable numbers In 1918 Paul Poulet invented the term sociable numbers. ‘The members of aliquot cycles of length greater than 2 are often called sociable numbers. The smallest two such cycles have length 5 and 28’

Mersenne’s prime A prime number which can be written in the form 2n – 1 a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, … and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, …

These and every other sequence ever created by humankind are documented on The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane’s. This is an online database of integer sequences, created and maintained by Neil Sloane while a researcher at AT&T Labs.

Chapter Eight – Gold Finger

The golden section a number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

Phi The number is often symbolized using phi, after the 21st letter of the Greek alphabet. In an equation form:

a/b = (a+b)/a = 1.6180339887498948420 …

As with pi (the ratio of the circumference of a circle to its diameter), the digits go on and on, theoretically into infinity. Phi is usually rounded off to 1.618.

The Fibonnaci sequence Each number in the sequence is the sum of the two numbers that precede it. So the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The mathematical equation describing it is Xn+2= Xn+1 + Xn.

as the basis of seeds in flowerheads, arrangement of leaves round a stem, design of nautilus shell and much more.

Chapter Nine – Chance Is A Fine Thing

A chapter about probability and gambling.

Impossibility has a value 0, certainty a value 1, everything else is in between. Probabilities can be expressed as fractions e.g. 1/6 chance of rolling a 6 on a die, or as percentages, 16.6%, or as decimals, 0.16…

The probability is something not happening is 1 minus the probability of that thing happening.

Probability was defined and given mathematical form in 17th century. One contribution was the questions the Chevalier de Méré asked the mathematical prodigy Blaise Pascal. Pascal corresponded with his friend, Pierre de Fermat, and they worked out the bases of probability theory.

Expected value is what you can expect to get out of a bet. Bellos takes us on a tour of the usual suspects – rolling dice, tossing coins, and roulette (invented in France).

Payback percentage if you bet £10 at craps, you can expect – over time – to receive an average of about £9.86 back. In other words craps has a payback percentage of 98.6 percent. European roulette has a payback percentage of 97.3 percent. American roulette, 94.7 percent. On other words, gambling is a fancy way of giving your money away. A miserly slot machine has a payback percentage of 85%. The National Lottery has a payback percentage of 50%.

The law of large numbers The more you play a game of chance, the more likely the results will approach the statistical probability. Toss a coin three times, you might get three heads. Toss a coin a thousand times, the chances are you will get very close the statistical probability of 50% heads.

The law of very large numbers With a large enough sample, outrageous coincidences become likely.

The gambler’s fallacy The mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future (or vice versa). In other words, that a random process becomes less random, and more predictable, the more it is repeated.

The birthday paradox The probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. (These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.) In other words you only need a group of 23 people to have an evens chance that two of them share a birthday.

The drunkard’s walk

The difficulty of attaining true randomness and the human addiction to finding meaning in anything.

The distinction between playing strategy (best strategy to win a game) and betting strategy (best strategy to maximise your winnings), not always the same.

Chapter Ten – Situation Normal

Carl Friedrich Gauss, the bell curve, normal distribution aka Gaussian distribution. Normal or Gaurrian distribution results in a bell curve. Bellos describes the invention and refinement of the bell curve (he explains that ‘the long tail’ results from a mathematician who envisioned a thin bell curve as looking like two kangaroos facing each other with their long tails heading off in opposite directions). And why

Regression to the mean – if the outcome of an event is determined at least in part by random factors, then an extreme event will probably be followed by one that is less extreme. And recent devastating analyses which show how startlingly random sports achievements are, from leading baseball hitters to Simon Kuper and Stefan Szymanski’s analysis of the form of the England soccer team.

Chapter Eleven – The End of the Line

Two breakthroughs which paved the way for modern i.e. 20th century, maths: the invention of non-Euclidean geometry, specifically the concept of hyperbolic geometry. To picture this draw a triangle on a Pringle. it is recognisably a triangle but all its angles do not add up to 180°, therefore it defies, escapes, eludes all the rule of Euclidean geometry, which were designed for flat 2D surfaces.

Bellos introduces us to Daina Taimina, a maths prof at Cornell University, who invented a way of crocheting hyperbolic surfaces. The result looks curly, like curly kale or the surface of coral.

Anyway, the breakaway from flat 2-D Euclidean space led to theories about curved geometry, either convex like a sphere, or hyperbolic like the pringle. It was this notion of curved space, which paved the way for Einstein’s breakthrough ideas in the early 20th century.

The second big breakthrough was Georg Cantor’s discovery that you can have many different types of infinity. Until Cantor the mathematical tradition from the ancient Greeks to Galileo and Newton had fought shy of infinity which threatened to disrupt so many formulae.

Cantor’s breakthrough was to stop thinking about numbers, and instead think of sets. This is demonstrated through the paradoxes of Hilbert’s Hotel. You need to buckle your safety belt to understand it.

Thoughts

This is easily the best book about maths I’ve ever read. It gives you a panoramic history of the subject which starts with innumerate cavemen and takes us to the edge of Einstein’s great discoveries. But Bellos adds to it all kinds of levels and abilities.

He is engaging and candid and funny. He is fantastically authoritative, taking us gently into forests of daunting mathematical theory without placing a foot wrong. He’s a great explainer. He knows a good story when he sees one, and how to tell it engagingly. And in every chapter there is a ‘human angle’ as he describes his own personal meetings and interviews with many of the (living) key players in the world of contemporary maths, games and puzzles.

Like the Ian Stewart book but on a vastly bigger scale, Bellos makes you feel what it is like to be a mathematician, not just interested in nature’s patterns (the basis of Stewart’s book, Nature’s Numbers) but in the beauty of mathematical theories and discoveries for their own sakes. (This comes over very strongly in chapter seven with its description of some of the weirdest and wackiest number sequences dreamed up by the human mind.) I’ve often read scientists describing the beauty of mathematical theories, but Bellos’s book really helps you develop a feel for this kind of beauty.

For me, I think three broad conclusions emerged:

1. Most mathematicians are in it for the fun. Setting yourself, and solving, mathematical puzzles is obviously extremely rewarding. Maths includes the vast territory of puzzles and games, such as the Sudoku and so on he describes in chapter six. Obviously it has all sorts of real-world application in physics, engineering and so on, but Bellos’s book really brings over that a true understanding of maths begins in puzzles, games and patterns, and often remains there for a lifetime. Like everything else maths is no highly professionalised the property of tenured professors in universities; and yet even to this day – as throughout its history – contributions can be made by enthusiastic amateurs.

2. As he points out repeatedly, many insights which started out as the hobby horses of obsessives, or arcane breakthroughs on the borders of our understanding, and which have been airily dismissed by the professionals, often end up being useful, having applications no-one dreamed of. Either they help unravel aspects of the physical universe undreamed of when they were discovered, or have been useful to human artificers. Thus the development of random number sequences seemed utterly pointless in the 19th century, but now underlies much internet security.

On a profounder note, Bellos expresses the eerie, mystical sense many mathematicians have that it seems so strange, so pregnant with meaning, that so many of these arcane numbers end up explaining aspects of the world their inventors knew nothing of. Ian Stewart has an admirably pragmatic explanation for this: he speculates that nature uses everything it can find in order to build efficient life forms. Or, to be less teleological, over the past 3 and a half billion years, every combination of useful patterns has been tried out. Given this length of time, and the incalculable variety of life forms which have evolved on this planet, it would be strange if every number system conceivable by one of those life forms – humankind – had not been tried out at one time or another.

3. My third conclusion is that, despite John Allen Paulos’s and Bellos’s insistence, I do not live in a world ever-more bombarded by maths. I don’t gamble on anything, and I don’t follow sports – the two biggest popular areas where maths is important – and the third is the twin areas of surveys and opinion polls (55% of Americans believe in alien abductions etc etc) and the daily blizzard of reports (for example, I see in today’s paper that the ‘Number of primary school children at referral units soars’).

I register their existence but they don’t impact on me for the simple reason that I don’t believe any of them. In 1992 every opinion poll said John Major would lose the general election, but he won with a thumping majority. Since then I haven’t believed any poll about anything. For example almost all the opinion polls predicted a win for Remain in the Brexit vote. Why does any sane person believe opinion polls?

And ‘new and shocking’ reports come out at the rate of a dozen a day and, on closer examination, lots of them turn out to be recycled information, or much much more mundane releases of data sets from which journalists are paid to draw the most shocking and extreme conclusions. Some may be of fleeting interest but once you really grasp that the people reporting them to you are paid to exaggerate and horrify, you soon learn to ignore them.

If you reject or ignore these areas – sport, gambling and the news (made up of rehashed opinion polls, surveys and reports) – then unless you’re in a profession which actively requires the sophisticated manipulation of figures, I’d speculate that most of the rest of us barely come into contact with numbers from one day to the next.

I think that’s the answer to Paulos and Bellos when they are in their ‘why aren’t more people mathematically numerate?’ mode. It’s because maths is difficult, and counter-intuitive, and hard to understand and follow, it is a lot of work, it does make your head ache. Even trying to solve a simple binomial equation hurt my brain.

But I think the biggest reason that ‘we’ are so innumerate is simply that – beautiful, elegant, satisfying and thought-provoking though maths may be to the professionals – maths is more or less irrelevant to most of our day to day lives, most of the time.

Ring of Steel by Alexander Watson (2014) and multi-ethnic societies

Mutual suspicion, brinkmanship, arrogance, belligerence and, above all fear were rife in the halls of power across Europe in the summer of 1914. (p.8)

I’m very surprised that this book won the ‘2014 Guggenheim-Lehrman Prize in Military History’ and the ‘Society of Military History 2015 Distinguished Book Award’ because it is not really a military history at all.

It’s certainly an epic book – 788 pages, if you include the 118 pages of notes and 63 pages of bibliography – and it gives an impressively thorough account of the origins, development and conclusion of the First World War, as seen from the point of view of the politicians, military leaders and people of Germany and Austria-Hungary.

More social than military history

But I found it much more of a sociological and economic history of the impact of war on German and Austro-Hungarian society, than a narrative of military engagements.

Watson gives a broad outline of the German invasion of Belgium and northern France, but there are no maps and no description of any of the vital battles, of the Marne or Aisnes or Arras or Ypres. Instead he spends more time describing the impact on Belgian society of the burning of villages and the atrocities carried out by the Germans – in retaliation for what they claimed were guerrilla and francs-tireurs (free-shooter) attacks by civilian snipers.

I was specifically hoping to learn more about the famous three-week-long battle of Tannenberg between Germany and Russia on the Eastern Front, but there is no account of it at all in this book.

Instead Watson gives a detailed description of the impact on society in Galicia and East Prussia of the ruinous and repressive Russian advance. Little or nothing about the fighting, but a mass of detail about the impact on individual villages, towns and cities of being subject to Russian military administration and violence, and a lot about the impact of war on the region’s simmering ethnic tensions. I hadn’t realised that the Russians, given half a chance, carried out as many atrocities (i.e. massacring civilians) and far more forced movements of population, than the Germans did.

Watson does, it is true, devote some pages to the epic battle of Verdun (pp. 293-300) and to the Battle of the Somme (pp. 310-326), but it’s not what I’d call a military description. There are, for example no maps of either battlefield. In fact there are no battlefield maps – maps showing the location of a battle and the deployment of opposing forces – anywhere at all in the book.

Instead, what you do get is lots of graphs and diagrams describing the social and economic impact of war – showing things like ‘Crime rates in Germany 1913-18’, ‘Free meals dispensed at Viennese soup kitchens 1914-18’, ‘German psychiatric casualties in the First and Second Armies 1914-18’ (p.297) and so on. Social history.

Longer than the accounts of Verdun and the Somme put together is his chapter about the food shortages which began to be felt soon after the war started and reached catastrophic depths during the ‘Turnip Winter’ of 1916-17. These shortages were caused by the British naval blockade (itself, as Watson points out, of dubious legality under international law), but also due to the intrinsic shortcomings of German and Austro-Hungarian agriculture, compounded by government inefficiency, and corruption (all described in immense detail on pages 330-374).

So there’s more about food shortages than about battles. Maybe, in the long run, the starvation was more decisive. Maybe Watson would argue that there are hundreds of books devoted to Verdun and the Somme, whereas the nitty-gritty of the food shortages – much more important in eventually forcing the Central Powers to their knees – is something you rarely come across in British texts. He certainly gives a fascinating, thorough and harrowing account.

But it’s not military history. It’s social and economic history.

A lot later in the book Watson gives a gripping account of the German offensive of spring 1918, and then the Allied counter-offensive from July 1918 which ended up bringing the Central Powers to the negotiating table.

But in both instances it’s a very high-level overview, and he only gives enough detail to explain (fascinatingly) why the German offensive failed and the Allied one succeeded – because his real motivation, the meat of his analysis, is the social and political impact of the military failure on German and Austrian society.

Absence of smaller campaigns

Something else I found disappointing about the book was his neglect of military campaigns even a little outside his main concern with German and Austro-Hungarian society.

He gives a thrilling account of the initial Austrian attack on Serbia – which was, after all, the trigger for the whole war – and how the Austrians were, very amusingly, repelled back to their starting points.

But thereafter Serbia is more or less forgotten about and the fact that Serbia was later successfully invaded is skated over in a sentence. Similarly, although the entry of Italy into the war is mentioned, none of the actual fighting between Austria and Italy is described. There is only one reference to Romania being successfully occupied, and nothing at all about Bulgaria until a passing mention of her capitulation in 1918.

I had been hoping that the book would give an account of the First World War in the East, away from the oft-told story of the Western Front: the war in Poland and Galicia and the Baltic States he does cover, but in south-eastern Europe nothing.

The text – as the title, after all, indicates – is pretty ruthlessly focused on the military capabilities, mobilisation, economy and society of Germany and Austria-Hungary.

Ethnic tension

If there’s one theme which does emerge very clearly from this very long book it is the centrality of ethnic and nationalist divisions in the Central Powers themselves, and in the way they treated their conquered foes.

Throughout its examination of the impact of war on German and Austro-Hungarian society – on employment, women’s roles, propaganda, agriculture and industry, popular culture and so on – the book continually reverts to an examination of the ethnic and nationalist fracture lines which ran through these two states.

For example, in the food chapter, there are not only radical differences in the way the German and Austro-Hungarian authorities dealt with the crisis (the effectiveness of different rationing schemes, and so on) but we are shown how different national regions, particularly of Austria-Hungary, refused to co-operate with each other: for example, rural Hungary refusing to share its food with urban Austria.

What emerges, through repeated description and analysis, is the very different ethnic and nationalist nature of the two empires.

Germany

Germany was an ethnically homogeneous state, made up overwhelmingly of German-speaking ethnic Germans. Therefore the fractures – the divisions which total war opened up – tended to take place along class lines. Before the war the Social Democrat Party (much more left-wing than its name suggests) had been the biggest socialist party in Europe, heir to the legacy of Karl Marx which was, admittedly, much debated and squabbled over. However, when war came, Watson shows how, in a hundred different ways, German society closed ranks in a patriotic display of unity so that the huge and powerful SDP, after some debate, rejected its pacifist wing and united with all the other parties in the Reichstag in voting for the war credits which the Chancellor asked for.

Watson says contemporary Germans called this the Burgfrieden spirit of the time, meaning literally ‘castle peace politics’. In effect it meant a political policy of ‘party truce’, all parties rallying to the patriotic cause, trades unions agreeing not to strike, socialist parties suspending their campaign to bring down capitalism, and so on. All reinforced by the sense that the Germans were encircled by enemies and must all pull together.

Typical of Watson’s social-history approach to all this is his account of the phenomenon of Liebesgaben or ‘love gifts’ (pp.211-214), the hundreds of thousands of socks and gloves and scarves knitted and sent to men at the front by the nation’s womenfolk, and the role played by children in war charities and in some war work.

He has three or four pages about the distinctive development of ‘nail sculptures’, figures of soldiers or wartime leaders into which all citizens in a town were encouraged to hammer a nail while making a donation to war funds. Soon every town and city had these nail figures, focuses of patriotic feeling and fundraising (pp. 221-225).

Watson is much more interested by the impact of war on the home front than by military campaigns.

Austria-Hungary

The spirit of unity which brought Germany together contrasts drastically with the collapse along ethnic lines of Austria-Hungary, the pressures which drove the peoples of the empire apart.

The Empire was created as a result of the Compromise of 1867 by which the Austrians had one political arrangement, the Hungarians a completely different one, and a whole host of lesser ethnicities and identities (the Czechs, and Poles in the north, the Serbs and Greeks and Croats and Bosnians in the troublesome south) jostled for recognition and power for their own constituencies.

Watson’s introductory chapters give a powerful sense of the fear and anxiety stalking the corridors of power in the Austro-Hungarian Empire well before the war began. This fear and anxiety were caused by the succession of political and military crises of the Edwardian period – the Bosnia Crisis of 1908, the First and Second Balkan Wars of 1911 and 1912, the rising voices of nationalism among Czechs in the north and Poles in the East.

To really understand the fear of the ruling class you have to grasp that in 1914 there was a very clear league table of empires – with Britain at the top followed by France and Germany. The rulers of Austria-Hungary were petrified that the collapse and secession of any part of their heterogenous empire would relegate them to the second division of empires (as were the rulers of Russia, as well).

And everybody knew what happened to an empire on the slide: they had before them the examples of the disintegrating Ottoman and powerless Chinese empires, which were condemned to humiliation and impotence by the Great Powers. Austria-Hungary’s rulers would do anything to avoid that fate.

But Watson shows how, as soon as war broke out, the empire instead of pulling together, as Germany had, began dividing and splitting into its component parts. Vienna was forced to cede control of large regions of the empire to the local governments which were best placed to mobilise the war effort among their own peoples.

This tended to have two consequences:

1. One was to encourage nationalism and the rise of nationalist leaders in these areas (it was via wartime leadership of the Polish Legions, a force encouraged by Vienna, that Józef Piłsudski consolidated power and the authority which would enable him to establish an independent Poland in 1918, and successfully defend its borders against Russian invasion in 1920, before becoming Poland’s strongman in the interwar period).
2. The second was to encourage inter-ethnic tension and violence.

The difference between homegeneous Germany and heterogeneous Austria-Hungary is exemplified in the respective nations’ responses to refugees. In Germany, the 200,000 or so refugees from Russia’s blood-thirsty invasion of East Prussia were distributed around the country and welcomed into homes and communities all over the Reich. They were recipients of charity from a popular refugee fund which raised millions of marks for them. Even when the refugees were in fact Polish-speaking or Lithuanians, they were still treated first and foremost as Germans and all received as loyal members of the Fatherland (pp. 178-181).

Compare and contrast the German experience with the bitter resentment which greeted refugees from the Russian invasion of the Austro-Hungarian border region of Galicia. When some 1 million refugees from Galicia were distributed round the rest of the empire, the native Hungarians, Austrians or Czechs all resented having large number of Poles, Ruthenians and, above all, Jewish, refugees imposed on their communities. There was resentment and outbreaks of anti-refugee violence.

The refugee crisis was just one of the ways in which the war drove the nationalities making up the Austro-Hungarian empire further apart (pp. 198-206).

Two years ago I read and was appalled by Timothy Snyder’s book, Bloodlands, which describes the seemingly endless ethnic cleansing and intercommunal massacres, pogroms and genocides which took place in the area between Nazi Germany and Stalin’s Russia in the 1930s.

Watson’s book shows how many of these tensions existed well before the First World War – in the Balkans they went back centuries – but that it was the massive pan-European conflict which lifted the lid, which authorised violence on an unprecedented scale, and laid the seeds for irreconcilable hatreds, particularly between Germans, Poles, Ukrainians, Russians and Jews.

The perils of multi-ethnic societies

Although I bet Watson is a fully paid-up liberal (and his book makes occasional gestures towards the issue of ‘gender’, one of the must-have topics which all contemporary humanities books have to include), nonetheless the net effect of these often harrowing 566 pages of text is to make the reader very nervous about the idea of a multinational country.

1. Austria-Hungary was a rainbow nation of ethnicities and, under pressure, it collapsed into feuding and fighting nationalities.

2. Russia, as soon as it invaded East Prussia and Galicia, began carrying out atrocities against entire ethnic groups classified as traitors or subversives, hanging entire villages full of Ukrainians or Ruthenians, massacring Jewish populations.

3. The to and fro of battle lines in the Balkans allowed invading forces to decimate villages and populations of rival ethnic groups who they considered dangerous or treacherous.

Austro-Hungarian troops hanging unarmed Serbian civilians (1915) No doubt ‘spies’ and ‘saboteurs’

In other words, everywhere that you had a mix of ethnicities in a society put under pressure, you got voices raised blaming ‘the other’, blaming whichever minority group comes to hand, for the catastrophe which was overtaking them.

Unable to accept the objective truth that their armies and military commanders were simply not up to winning the war, the so-called intelligentsia of Austria-Hungary, especially right-wing newspapers, magazines, writers and politicians, declared that the only reason they were losing must be due to the sabotage and treachery of traitors, spies, saboteurs and entire ethnic groups, who were promptly declared ‘enemies of the state’.

Just who was blamed depended on which small powerless group was ready to hand, but the Jews tended to be a minority wherever they found themselves, and so were subjected to an increasing chorus of denunciation throughout the empire.

Ring of Steel is a terrible indictment of the primitive xenophobia and bloodlust of human nature. But it is also a warning against the phenomenon that, in my opinion, has been ignored by generations of liberal politicians and opinion-formers in the West.

For several generations we have been told by all official sources of information, government, ministires, and all the media, that importing large groups of foreigners can only be a good thing, which ‘enriches’ our rainbow societies. Maybe, at innumerable levels, it does.

But import several million ‘foreigners’, with different coloured skins, different languages, cultures and religions into Western Europe – and then place the societies of the West under great economic and social strain thanks to an epic crash of the financial system and…

You get the rise of right-wing, sometimes very right-wing, nationalist parties – in Russia, in Poland, in Hungary, in Germany, in Sweden and Denmark, in Italy, in France, in Britain and America – all demanding a return to traditional values and ethnic solidarity.

I’m not saying it’s right or wrong, I’m just saying the evidence seems to be that human beings are like this. This is what we do. You and I may both wish it wasn’t so, but it is so.

In fact I’d have thought this was one of the main lessons of history. You can’t look at the mass destruction of the Napoleonic Wars and say – ‘Well at least we’re not like that any more’. You can’t look at the appalling suffering created by industrialisation and say, ‘Well at least we’re not like that any more’. You can’t look at the mind-blowing racist attitudes I’ve been reading about in the American Civil War and say, ‘Well, at least we’re not like that any more’. You can’t look at the mad outbreak of violence of the First World War and the stubborn refusal to give in which led to over ten million men being slaughtered and say – ‘Well, at least we’re not like that any more’. You can’t look at the Holocaust and say – ‘Well, at least we’re not like that any more’.

We cannot be confident that human nature has changed at all in the intervening years.

Because in just the last twenty years we have all witnessed the savagery of the wars in former Yugoslavia, the Rwandan genocide, the genocide in Darfur, the failure of the Arab Springs and the civil wars in Syria and Libya, the 9/11 attacks, the wars in Iraq and Afghanistan, the rise of ISIS, the war in Yemen, the genocide of Rohingya Muslims in Myanmar prove.

If all these conflicts prove anything, they prove that —

WE ARE STILL LIKE THAT

We are just like that. Nothing has changed. Given half a chance, given enough deprivation, poverty and fear, human beings in any continent of the world will lash out in irrational violence which quickly becomes total, genocidal, scorched earth, mass destruction.

In the West, in Britain, France, Germany or America, we like to think we are different. That is just a form of racism. In my opinion, we are not intrinsically different at all. We are just protected by an enormous buffer of wealth and consumer goods from having to confront our basest nature. The majority of the populations in all the Western nations are well off enough not to want, or to allow, any kind of really ethnically divisive politics or inter-ethnic violence to take hold.

Or are they?

Because creating multi-cultural societies has created the potential for serious social stress to exacerbate racial, ethnic and nationalist dividing lines which didn’t previously exist. When I was growing up there was no such thing as ‘Islamophobia’ in Britain. 40 years later there are some 2.8 million Muslims in Britain, some 5% of the population – and I read about people being accused of ‘Islamophobia’, or Muslims claiming unfair discrimination or treatment in the media, almost every day in the newspapers.

It’s not as if we didn’t know the risks. I lived my entire life in the shadow of ‘the Troubles’ in Northern Ireland which were based entirely on ethnic or communal hatred. And now not a day goes past without a newspaper article bewailing how Brexit might end the Good Friday Agreement and bring back the men of violence. Is the peace between the ethnic groups in Northern Ireland really that fragile? Apparently so. But British governments and the mainland population have always had an uncanny ability to sweep Ulster under the carpet and pretend it’s not actually part of the UK. To turn our backs on 40 years of bombings and assassinations, to pretend that it all, somehow, wasn’t actually happening in Britain. Not the real Britain, the Britain that counts. But it was.

Anyway, here we are. Over the past 40 years or so, politicians and opinion makers from all parties across the Western world have made this multicultural bed and now we’re all going to have to lie in it, disruptive and troubled though it is likely to be, for the foreseeable future.

Conclusion

Although it certainly includes lots of detail about the how the societies of the Central Powers were mobilised and motivated to wage total war, and enough about the military campaigns to explain their impact on the home front, overall Watson’s book is not really a military history of the Central Powers at war, but much more a social and economic history of the impact of the war on the two empires of its title.

And in the many, many places where he describes ethnic and nationalist tensions breaking out into unspeakable violence, again and again, all over central and eastern Europe, Watson’s book – no doubt completely contrary to his intentions – can very easily be read as a manifesto against the notion of a multicultural, multi-ethnic society.