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

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.


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Slapstick by Kurt Vonnegut Jnr (1976)

This is a really weird story, a madly disorientating story about twin freaks, a future dystopia, shrinking Chinese and communication with the afterlife.

The main story (pp.15-170) is narrated by the two-metre tall man, christened Wilbur Rockefeller Swain but now known as Dr Wilbur Daffodil-II Swain.

It is a morbid and depressing story. Swain is just coming up to his 101st birthday. He lives amid the ruins of New York. The rest of America has been depopulated by Albanian Flu (p.33), but New York had a special plague of its own, known as the Green Plague. Now it is almost empty, with only Swain and a handful or relatives and friends living in the overgrown ruins. To survivors on the mainland it is known only as ‘the Island of Death’.

So Slapstick is a post-apocalypse story.

As so often in fictional memoirs, two timelines run in parallel 1. The ‘present’ in which the narrator wakes up and potters round and we are introduced to the main characteristics of the post-apocalyptic world. Thus Swain starts each chapter with a bit of gossip about his current companions, his emaciated though pregnant grand-daughter Melody, and her husband Isidore, or about their best friend Vera Chipmunk-5 Zappa who keeps a farm worked by ‘slaves’.

Before 2. returning to a conventional chronological account which begins with the birth of him and his twin sister, follows them through their early life, and on to the series of events which led up to the disaster.

Vonnegut uses Vonnegutian tricks such as:

  • The entire text is broken up into very short sections, sometimes a few paragraphs, but sometimes just a few words, all divided by three asterisks in the centre of the page, creating the sense that the whole book is made of fragments glued together, a suitable feel, maybe, for post-apocalyptic fragments.
  • And just as the catchphrase ‘So it goes’ appeared on every page of Slaughterhouse-Five and ‘And so on’ capped every anecdote in Breakfast of Champions, so almost every bit of prose which tells a significant story or anecdote in this book is capped with ‘Hi ho’. At one point the narrator says he must go back through the book and delete all the ‘Hi ho’s’. Which he follows with another Hi ho. Hi ho. I think it is safe to say this use of ironically off-hand taglines has become a mannerism.

From his birth up to the age of 15, Wilbur and his twin sister, Eliza Mellon Swain, pretend to be drooling idiots. In fact they are geniuses, especially if they physically touch their heads together. When they do this they share a joint super-intelligence. But for 15 years all they do is pretend to be retards, and are locked by their parents in their posh Boston home. (They are from a super-rich family.)

This is every bit as weird as it sounds. On their fifteenth birthdays, they overhear their parents discussing sending them to separate homes and so make the startling announcement that they are not brain damaged but the reverse – hyper-intelligent and articulate young people.

This shocks their parents even more, who promptly call in a high-powered women psychiatrist who, vindictively knowing the damage it will cause them, recommends they be separated, declaring Wilbur is the clever one and Eliza is the defect.

So Wilbur is packed off to medical school and becomes a successful pediatrician, while Eliza goes to rot in a home for the mentally defective.

Cut to about ten years later when Wilbur is confronted by Eliza, who has been sprung from the home by a money-grabbing lawyer on the news that their parents have died. She is a wreck, distraught and determined on revenge as she confronts him at his grand mansion. But the moment they actually make physical contact, the old telepathic communication is revived and they have a five-day long orgy during which they tie up all the servants.

Maybe this whole plotline is intended as satirical but it comes over as a kind of poor man’s Philip K. Dick, with its dwelling on identity and reality, and sick obsession with a dead sibling (both Dick and Vonnegut had dead sisters).

Meanwhile, in the background of the story, we learn that oil has been running low, and that American science and technology has stagnated. The sky has turned yellow because of gases released by underarm deodorants. The Chinese are making all kinds of new discoveries. The West is collapsing. Americans are becoming more lonely.

Eliza takes her cut of Swain’s estate and goes to Macchu Picchu. Why? Because it

was then becoming a haven for rich people and their parasites, people fleeing social reforms and economic declines, not just in America, but in all parts of the world. (p.93)

An absurdist theme which runs through the book is that the Chinese, as part of their transformation into top economic power in the world, undertake a programme of miniaturising human beings. There are so many of them, they can only survive if they get smaller.

Thus it is that a lot later in the book, Swain is visited by the Chinese ambassador who is only a few inches tall (the size of Wilbur’s thumb, p.101). Piling absurdity on absurdity, he is named Fu Manchu. He asks Swain to take him to the family mausoleum in which are hidden the various writings Swain and Eliza did when their heads were together and they were a super-genius. Swain doesn’t understand why, but some of these writings are of immense importance to the Chinese – now the leading scientific and technological country in the world.

A second major idea has to do with gravity. When Swain describes life in post-apocalyptic America, he has dropped hints about there being a problem with gravity, that it varies from day to day like the weather, with some days of heavy gravity, some of light. This is, apparently, caused by scientific experiments by the Chinese, though by this stage nobody in America understands what or how or has the power to stop it.

The first time gravity changes is on the day Swain picks up a telegram at his local post office which tells him that Eliza is dead, crushed under an avalanche on Mars (p.106). Mars? Yes she had tipped off the Chinese about the secret documents hidden in the mausoleum and, as a reward, was transported to the new Chinese colony on Mars. Ill-fatedly, as it turns out.

As he walks out onto the steps outside his local post office, gravity changes – for just a minute or so it is doubled, quintupled, and Wilbur falls through the wooden steps he’s standing on, people fall through ladders, chairs, and flimsy flooring. Bridges and tall buildings collapse, elevators plummet to the ground and so on.

The Gravity Shift only lasts a minute or so but undermines the confidence of Americans even more than the failing oil supply and yellow sky.

It is against this backdrop of America’s economic, scientific and political decline, that Swain runs for president on a platform of radically reorganising society. He decides the problem with Americans is they are lonely and isolated. He comes up with a scheme whereby all Americans will be given new middle names by computer. The number of names will be calculated so that each new ‘family’ has about 10,000 members. I.e. if something happens to you there will be 9,999 other ‘family members’ you can call on.

He runs for senator, then president, on the slogan of ‘Lonesome no more’ – which is the sub-title of this book (p.112).

It is hard not to think that this plotline – the satire on American loneliness – is a separate short story or plot idea which Vonnegut has bolted onto the weird story of two twin giants who are cruelly separated. Chucking in Chinese miniaturisation, and the notion that the Earth’s gravity can be played with, as additional sweeties.

By this stage we learn that, because of the end of oil and technology, America has collapsed as a political entity. There are no more printing presses, no more radio or TV – because there is no more fuel (p.117). it has been replaced by warlords which control territories like Michigan or Dakota – hence the King of Michigan, the Great Lake pirates, and other satirical names the narrator casually mentions in passing.

(In a satirical touch, the only way to power the computer which doles out new middle names to the population of America, is by systematically burning all the paper archives in the White House and Congress.)

(In another satirical touch he throws in the fact that the new religion which the general crisis gives rise to is the Church of Jesus Christ the Kidnapped.)

Also, by this stage, Wilbur tells us he has become addicted to some kind of tranquiliser named tri-benzo-Deportamil, which helps him to cope with all the ups and downs of his life with equanimity.

Vonnegut devotes an extensive passage to describing his happiness at visiting a lodge of his own ‘family’, the Daffodils, in Indiana, how kind and welcoming they are. And to explaining how his successful family plan meshes or overlaps with the numerous small wars which the King of Michigan and so on are fighting against each other.

In fact there is a satirical scene where Swain is summoned by the grandiose young King of Michigan who wishes him to solemnly sign a document reversing the famous Louisiana Purchase of 1803 and handing over rule of what was then the vast territory in the centre of the USA over the king. Fine, thinks Swain, and signs.

Epilogue

At this point the memoir written by Wilbur Swain comes to an abrupt end. It is succeeded by an epilogue tying up loose ends.

This takes the story from the meeting with the King of Michigan to his death.

Swain had been contacted by a woman who had discovered a way of contacting the dead. An old farmer arranged a bucket and antique pipe in just such a way atop a defunct particle accelerator (no more electricity; hadn’t worked for years) and, to his surprise, began hearing voices out of the pipe.

Swain, still nominally president although now with few if any powers over a disintegrated country, is told about this and invited to try it. He manages to get through to his sister Eliza, who tells him the afterlife is dreadful. Swain can hear a babble of people coughing, shouting and farting in the background. Eliza says the afterlife is like a badly managed Turkey Farm. She begs him to die and join her. The device for communicating with the dead is known as ‘the Hooligan’ after the name of the farmer who accidentally created it. (p.160-164)

Convinced that she needs his help, and in a hurry to die, Swain persuades the pilot of the helicopter (Captain Bernard O’Hare – sharp-eyed Vonnegut readers might remember that Bernard O’Hare plays an important role in his 1962 novel Mother Night) which flew him to the Daffodil reunion in Indiana (and is himself a member of the Daffodil family) to fly him to Manhattan, long since known as ‘the Island of Death’ because of the mysterious epidemic which wiped out almost its entire population.

Hovering over the empty, overgrown avenues, Swain climbs down a rope ladder and onto the balcony of the Empire State Building, whose staircase he proceeds to walk down. But instead of quickly dying, in the ruined lobby of the building Swain is kidnapped by some ‘Raspberries’ a really primitive clan of humans who live by eating nuts, and berries and whatever they can forage.

As it happens these people have unwittingly stumbled on an antidote to the Green Death, namely fish from the rivers either side of Manhattan which are so polluted that some of the rare chemicals in them act as antidotes.

Now the narrator now tells us that the flu which killed everyone was caused by an invasion of microscopic Martians, whose invasion was repelled by antibodies in the systems of the survivors (p.163). While the Green Death was caused by microscopic Chinese floating through the air who were peace-loving but were invariably fatal to normal-sized human who inhaled or ingested them (p.164).

Swain proceeds to live on derelict Manhattan for a very, very long time. Back around the time when he used the Hooligan and sold Louisiana to the King of Michigan, his last few pills of tri-benzo-Deportamil ran out and he went mental. He had to be tied down for five days in the farmhouse, but managed – in the impossible way characteristic of this narrative – to have sex and impregnate the wife of the old farmer.

She had a son.

He had a daughter, who was packed off to join the seraglio of the King of Michigan who was, by this time, a disgusting old man.  She managed to escape and set off East towards New York to try and track down the mythical grandfather her dad had told her about. Her name is Melody Oriole-2. She was helped along the odyssey by strangers who gave her a baby pram, a candlestick, a compass and an umbrella. And one who rowed her across to the Island of Death.

And that’s how Swain was reunited with his grand-daughter and came to be chatting about her at the start of the book’s 49 chapters. He has his drunken 102nd birthday, organised for him by his old friend Vera Chipmunk-5 Zappa, and drops dead.

Thoughts

It’s a short book (170 pages) but with enough ideas in it to blow anyone’s mind.

Whether any of them – plausible, fantastical, surreal, satirical – are any good, was hard to tell. I was so dazed by the relentless nonsensicality of much of the narrative that it was difficult to take a view. Is it a farrago of rubbish, which a summary of the plot might lead you to think? Or, as a friend of mine who’s a Vonnegut fan thinks, one of his best books?

I couldn’t work out if the four or five hours it took me to read it were time well spent or not.

I think it feels to me like a last hurrah of the absurdist approach, and typographical experimentation, which took off in Slaughterhouse-Five. But then Cat’s Cradle also has an end-of-the-world, post-apocalyptic setting. In fact, both books consist of the memoir of one of the few people who survived the end of the world.

And when I saw how his next novel, Jailbird, reverts to a much more conventional layout and prose style, and realistic subject matter, this adds to the sense that Slapstick is like the fagged-out hangover of the absurdist approach which characterised its three predecessors.


Related links

Kurt Vonnegut reviews

Other science fiction reviews

1888 Looking Backward 2000-1887 by Edward Bellamy – Julian West wakes up in the year 2000 to discover a peaceful revolution has ushered in a society of state planning, equality and contentment
1890 News from Nowhere by William Morris – waking from a long sleep, William Guest is shown round a London transformed into villages of contented craftsmen

1895 The Time Machine by H.G. Wells – the unnamed inventor and time traveller tells his dinner party guests the story of his adventure among the Eloi and the Morlocks in the year 802,701
1896 The Island of Doctor Moreau by H.G. Wells – Edward Prendick is stranded on a remote island where he discovers the ‘owner’, Dr Gustave Moreau, is experimentally creating human-animal hybrids
1897 The Invisible Man by H.G. Wells – an embittered young scientist, Griffin, makes himself invisible, starting with comic capers in a Sussex village, and ending with demented murders
1898 The War of the Worlds – the Martians invade earth
1899 When The Sleeper Wakes/The Sleeper Wakes by H.G. Wells – Graham awakes in the year 2100 to find himself at the centre of a revolution to overthrow the repressive society of the future
1899 A Story of the Days To Come by H.G. Wells – set in the same future London as The Sleeper Wakes, Denton and Elizabeth defy her wealthy family in order to marry, fall into poverty, and experience life as serfs in the Underground city run by the sinister Labour Corps

1901 The First Men in the Moon by H.G. Wells – Mr Bedford and Mr Cavor use the invention of ‘Cavorite’ to fly to the moon and discover the underground civilisation of the Selenites
1904 The Food of the Gods and How It Came to Earth by H.G. Wells – scientists invent a compound which makes plants, animals and humans grow to giant size, prompting giant humans to rebel against the ‘little people’
1905 With the Night Mail by Rudyard Kipling – it is 2000 and the narrator accompanies a GPO airship across the Atlantic
1906 In the Days of the Comet by H.G. Wells – a comet passes through earth’s atmosphere and brings about ‘the Great Change’, inaugurating an era of wisdom and fairness, as told by narrator Willie Leadford
1908 The War in the Air by H.G. Wells – Bert Smallways, a bicycle-repairman from Kent, gets caught up in the outbreak of the war in the air which brings Western civilisation to an end
1909 The Machine Stops by E.M. Foster – people of the future live in underground cells regulated by ‘the Machine’ until one of them rebels

1912 The Lost World by Sir Arthur Conan Doyle – Professor Challenger leads an expedition to a plateau in the Amazon rainforest where prehistoric animals still exist
1912 As Easy as ABC by Rudyard Kipling – set in 2065 in a world characterised by isolation and privacy, forces from the ABC are sent to suppress an outbreak of ‘crowdism’
1913 The Horror of the Heights by Arthur Conan Doyle – airman Captain Joyce-Armstrong flies higher than anyone before him and discovers the upper atmosphere is inhabited by vast jellyfish-like monsters
1914 The World Set Free by H.G. Wells – A history of the future in which the devastation of an atomic war leads to the creation of a World Government, told via a number of characters who are central to the change
1918 The Land That Time Forgot by Edgar Rice Burroughs – a trilogy of pulp novellas in which all-American heroes battle ape-men and dinosaurs on a lost island in the Antarctic

1921 We by Evgeny Zamyatin – like everyone else in the dystopian future of OneState, D-503 lives life according to the Table of Hours, until I-330 wakens him to the truth
1925 Heart of a Dog by Mikhail Bulgakov – a Moscow scientist transplants the testicles and pituitary gland of a dead tramp into the body of a stray dog, with disastrous consequences
1927 The Maracot Deep by Arthur Conan Doyle – a scientist, engineer and a hero are trying out a new bathysphere when the wire snaps and they hurtle to the bottom of the sea, there to discover…

1930 Last and First Men by Olaf Stapledon – mind-boggling ‘history’ of the future of mankind over the next two billion years
1938 Out of the Silent Planet by C.S. Lewis – baddies Devine and Weston kidnap Ransom and take him in their spherical spaceship to Malacandra aka Mars,

1943 Perelandra (Voyage to Venus) by C.S. Lewis – Ransom is sent to Perelandra aka Venus, to prevent a second temptation by the Devil and the fall of the planet’s new young inhabitants
1945 That Hideous Strength: A Modern Fairy-Tale for Grown-ups by C.S. Lewis– Ransom assembles a motley crew to combat the rise of an evil corporation which is seeking to overthrow mankind
1949 Nineteen Eighty-Four by George Orwell – after a nuclear war, inhabitants of ruined London are divided into the sheep-like ‘proles’ and members of the Party who are kept under unremitting surveillance

1950 I, Robot by Isaac Asimov – nine short stories about ‘positronic’ robots, which chart their rise from dumb playmates to controllers of humanity’s destiny
1950 The Martian Chronicles – 13 short stories with 13 linking passages loosely describing mankind’s colonisation of Mars, featuring strange, dreamlike encounters with Martians
1951 Foundation by Isaac Asimov – the first five stories telling the rise of the Foundation created by psychohistorian Hari Seldon to preserve civilisation during the collapse of the Galactic Empire
1951 The Illustrated Man – eighteen short stories which use the future, Mars and Venus as settings for what are essentially earth-bound tales of fantasy and horror
1952 Foundation and Empire by Isaac Asimov – two long stories which continue the future history of the Foundation set up by psychohistorian Hari Seldon as it faces attack by an Imperial general, and then the menace of the mysterious mutant known only as ‘the Mule’
1953 Second Foundation by Isaac Asimov – concluding part of the ‘trilogy’ describing the attempt to preserve civilisation after the collapse of the Galactic Empire
1953 Earthman, Come Home by James Blish – the adventures of New York City, a self-contained space city which wanders the galaxy 2,000 years hence powered by spindizzy technology
1953 Fahrenheit 451 by Ray Bradbury – a masterpiece, a terrifying anticipation of a future when books are banned and professional firemen are paid to track down stashes of forbidden books and burn them
1953 Childhood’s End by Arthur C. Clarke a thrilling narrative involving the ‘Overlords’ who arrive from space to supervise mankind’s transition to the next stage in its evolution
1954 The Caves of Steel by Isaac Asimov – set 3,000 years in the future when humans have separated into ‘Spacers’ who have colonised 50 other planets, and the overpopulated earth whose inhabitants live in enclosed cities or ‘caves of steel’, and introducing detective Elijah Baley to solve a murder mystery
1956 The Naked Sun by Isaac Asimov – 3,000 years in the future detective Elijah Baley returns, with his robot sidekick, R. Daneel Olivaw, to solve a murder mystery on the remote planet of Solaria
1956 They Shall Have Stars by James Blish – explains the invention – in the near future – of the anti-death drugs and the spindizzy technology which allow the human race to colonise the galaxy
1959 The Triumph of Time by James Blish – concluding story of Blish’s Okie tetralogy in which Amalfi and his friends are present at the end of the universe

1961 A Fall of Moondust by Arthur C. Clarke a pleasure tourbus on the moon is sucked down into a sink of moondust, sparking a race against time to rescue the trapped crew and passengers
1962 A Life For The Stars by James Blish – third in the Okie series about cities which can fly through space, focusing on the coming of age of kidnapped earther, young Crispin DeFord, aboard New York
1962 The Man in the High Castle by Philip K. Dick In an alternative future America lost the Second World War and has been partitioned between Japan and Nazi Germany. The narrative follows a motley crew of characters including a dealer in antique Americana, a German spy who warns a Japanese official about a looming surprise German attack, and a woman determined to track down the reclusive author of a hit book which describes an alternative future in which America won the Second World War
1968 2001: A Space Odyssey a panoramic narrative which starts with aliens stimulating evolution among the first ape-men and ends with a spaceman being transformed into galactic consciousness
1968 Do Androids Dream of Electric Sheep? by Philip K. Dick In 1992 androids are almost indistinguishable from humans except by trained bounty hunters like Rick Deckard who is paid to track down and ‘retire’ escaped andys
1969 Ubik by Philip K. Dick In 1992 the world is threatened by mutants with psionic powers who are combated by ‘inertials’. The novel focuses on the weird alternative world experienced by a group of inertials after a catastrophe on the moon

1971 Mutant 59: The Plastic Eater by Kit Pedler and Gerry Davis – a genetically engineered bacterium starts eating the world’s plastic
1973 Rendezvous With Rama by Arthur C. Clarke – in 2031 a 50-kilometre long object of alien origin enters the solar system, so the crew of the spaceship Endeavour are sent to explore it
1974 Flow My Tears, The Policeman Said by Philip K. Dick – America after the Second World War is a police state but the story is about popular TV host Jason Taverner who is plunged into an alternative version of this world where he is no longer a rich entertainer but down on the streets among the ‘ordinaries’ and on the run from the police. Why? And how can he get back to his storyline?

1981 The Golden Age of Science Fiction edited by Kingsley Amis – 17 classic sci-fi stories from what Amis considers the Golden Era of the genre, namely the 1950s
1982 2010: Odyssey Two by Arthur C. Clarke – Heywood Floyd joins a Russian spaceship on a two-year journey to Jupiter to a) reclaim the abandoned Discovery and b) investigate the enormous monolith on Japetus
1987 2061: Odyssey Three by Arthur C. Clarke* – Spaceship Galaxy is hijacked and forced to land on Europa, a moon of the former Jupiter, but the thriller aspects are only pretexts for Clarke’s wonderful descriptions of landing on Halley’s Comet and the evolution of wild and unexpected new forms of life on Europa

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