Nature’s Numbers by Ian Stewart (1995)

Stewart is a mathematician and prolific author, having written over 40 books on all aspects of maths, as well as publishing guides to the maths used in Terry Pratchett’s Discworld books, authoring half a dozen textbooks for students and co-authoring a couple of science fiction novels.

He writes in a marvellously clear style, but more importantly, he is interesting: he sees the world in an interesting way and manages to convey the wonder and strangeness and powerful insights which seeing the world in terms of patterns and shapes, numbers and maths, gives you.

He wants to help us see the world as a mathematician sees it, full of clues and information which can lead us to deeper and deeper appreciation of the patterns and harmonies all around us.

1. The Natural Order

Thus he begins the book by describing just some of nature’s patterns: the regular movements of the stars in the night sky; the sixfold symmetry of snowflakes; the stripes of tigers and zebras; the recurring patterns of sand dunes; rainbows; the spiral of a snail’s shell; why nearly all flowers have petals arranged in one of the following numbers 5, 8, 13, 21, 34, 55, 89; the regular patterns or ‘rhythms’ made by animals scuttling, walking, flying and swimming.

2. What Mathematics is For

Mathematics is brilliant at helping us to solve puzzles. it is a more or less systematic way of digging out the rules and structures that lie behind some observed pattern or regularity, and then using those rules and structures to explain what’s going on. (p.16)

Kepler discovers the planets move in ellipses. The nature of acceleration, ‘not a fundamental quality, a rate of change’. Newton and Leibniz invent calculus to help us work out rates of change.

Two of the main things that maths are for are 1. providing the tools which let scientists understand what nature is doing 2. providing new theoretical questions for mathematicians to explore further. Applied and pure mathematics.

He mentions one of the oddities, paradoxes or thought-provoking things that comes up in many science books which is the eerie way that good mathematics, whatever its source, eventually turns out to be useful, to be applicable to the real world, to explain some aspect of nature. Many philosophers have wondered why. Is there a deep congruence between the human mind and the structure of the universe? Did God make the universe mathematically and implant an understanding of maths in us? Is the universe made of maths?

Stewart’s answer is simple and elegant: he thinks that nature exploits every pattern that there is, which is why we keep discovering patterns everywhere. We humans express these patterns in numbers, but it isn’t the numbers nature uses – it’s the patterns and shapes and possibilities which the numbers express, or define.

Mendel noticing the numerical relationships with which characteristics of peas are expressed when they are crossbred. The double helix structure of DNA. The computer simulation of the evolution of the eye from an initial mutation providing for skin cells sensitive to light, published by Daniel Nilsson and Susanne Pelger in 1994.

Resonance = the relationship between periodically moving bodies in which their cycles lock together so that they take up the same relative positions at regular intervals. The cycle time is the period of the system. The individual bodies have different periods. The moon’s rotational period is the same as its revolution around the earth, so there is a 1:1 resonance of its orbital and rotational period.

Mathematics doesn’t just analyse, it can predict, predict how all kinds of systems will work, from the aerodynamics which keep planes flying to the amount of fertiliser required to increase crop yield to the complicated calculations which keep communications satellites in orbit round the earth and therefore sustain the internet and mobile phone networks.

Time lags: the gap between a new mathematical idea being developed and its practical implementation can be a century or more: it was 17th century interest in the vibration of a violin string which led, three hundred years later, to the invention of radio, radar and TV.

3. What Mathematics is About

The word ‘number’ does not have any immutable, God-given meaning. (p.42)

Numbers are the most prominent part of mathematics and everyone is taught arithmetic at school, but numbers are just one type of object that mathematics is interested in.

The invention of numbers. Fractions. Some time in the Dark Ages the invention of 0. The invention of negative numbers, then of square roots. Irrational numbers. ‘Real’ numbers.

Whole numbers 1, 2, 3… are known as the natural numbers. If you include negative whole number, the series is known as integers. Positive and negative numbers are known as rational numbers. Then there are real numbers and complex numbers. Five systems in total.

But maths is also about operations such as addition, subtraction, multiplication and division. And functions, also known as transformations, rules for transforming one mathematical object into another. Many of these processes can be thought of as things which help to create data structures.

Maths is like a landscape with similar proofs and theories clustered together to create peaks and troughs.

4. The Constants of Change

Newton’s basic insight was that changes in nature can be described by mathematical processes. Stewart explains how detailed consideration of what happens to a cannonball fired out of a cannon helps us towards Newton’s fundamental law, that force = mass x acceleration.

Newton invented calculus to help work out solutions to moving bodies. Its two basic operations – integration and differentiation – mean that, given one element – force, mass or acceleration – you can work out the other two. Differentiation is the technique for finding rates of change; integration is the technique for ‘undoing’ the effect of differentiation.

Calculating rates of change is a crucial aspect of maths, engineering, cosmology and many other areas.

5. From Violins to Videos

A fascinating historical recap of how initial investigations into the way a violin string vibrates gave rise to formulae and equations which turned out to be useful in mapping electricity and magnetism, which turned out to be aspects of the same fundamental force, understanding which underpinned the invention of radio, radar, TV etc, taking in contributions from Michael Faraday, James Clerk Maxwell, Heinrich Hertz and Giulielmo Marconi.

Stewart makes the point that mathematical theory tends to start with the simple and immediate and grow ever-more complicated. This is because you have to start somewhere.

6. Broken Symmetry

A symmetry of an object or system is any transformation that leaves it invariant. (p.87)

There are many types of symmetry. The most important ones are reflections, rotations and translations.

7. The Rhythm of Life

The nature of oscillation and Hopf bifurcation (if a simplified system wobbles, then so must the complex system it is derived from) leads into a discussion of how animals, specifically animals with legs, move, which is by staggered or syncopated oscillations, oscillations of muscles triggered by neural circuits in the brain.

This is a subject Stewart has written about elsewhere and is something of an expert on. The seven types of quadrupedal gait are: the trot, pace, bound, walk, rotary gallop, transverse gallop, and canter.

8. Do Dice Play God?

Stewart’s take on chaos theory.

Chaotic behaviour obeys deterministic laws, but is so irregular that to the untrained eye it looks pretty much random. Chaos is not complicated, patternless behaviour; it is much more subtle. Chaos is apparently complicated, apparently patternless behaviour that actually has a simple, deterministic explanation. (p.130)

19th century scientists thought that, if you knew the starting conditions, and then the rules governing any system, you could completely predict the outcomes. In the 1970s and 80s it became increasingly unclear that this was wrong. It is impossible because you can never define the starting conditions with complete certainty.

Thus all real world behaviours are subject to ‘sensitivity to initial conditions’. From minuscule divergences at the start point, cataclysmic differences may eventually emerge.

He then explains the concept of phase space developed by Henri Poincaré: this is an imaginary mathematical space that represents all possible motions in a given dynamic system. The phase space is the 3-D place in which you plot the behaviour in order to create the phase portrait. Instead of having to define a formula and worrying about identifying every number of the behaviour, the general shape can be determined.

Much use of phase portraits has shown that dynamic systems tend to have set shapes which emerge and which systems move towards. These are called attractors.

9. Drops, Dynamics and Daisies

The book ends by drawing a kind of philosophical conclusion.

Chaos theory has all sorts of implications but the one he closes on is this: the world is not chaotic; if anything, it is boringly predictable. And at the level of basic physics and maths, the laws which seem to underpin it are also schematic and simple. And yet what we are only really beginning to appreciate is how complicated things are in the middle.

It is as if nature can only get from simple laws (like Newton’s incredibly simple law of thermodynamics) to fairly simple outcomes (the orbit of the planets) via almost incomprehensibly complex processes. To end, Stewart gives us three examples of the way apparently ‘simple’ phenomena in nature derive from stupefying complexity:

  • what exactly happens when a drop of water falls off a tap
  • computer modelling of the growth of fox and rabbit populations
  • why petals on flowers are arranged in numbers derived from the Fibonacci sequence

In all three cases the underlying principles seem to be resolvable into laws and functions – and we see water dropping off taps or flowerheads all the time – and yet the intermediate steps are bogglingly complex.

Coda: Morphomatics

He ends the book with an epilogue speculating, hoping and wishing for a new kind of mathematics which incorporates chaos theory and the other elements he’s discussed – a theory and study of form, which takes everything we already know about mathematics and seeks to work out how the almost incomprehensible complexity we are discovering in nature gives rise to all the ‘simple’ patterns which we see around us.


Related links

Reviews of other science books

Cosmology

Environment / human impact

Genetics

  • The Double Helix by James Watson (1968)

Maths

Particle physics

Psychology

  • Irrationality: The Enemy Within by Stuart Sutherland (1992)

Maths ideas from John Allen Paulos

There’s always enough random success to justify anything to someone who wants to believe. (Innumeracy, p.33)

It’s easier and more natural to react emotionally than it is to deal dispassionately with statistics or, for that matter, with fractions, percentages and decimals. (A Mathematician Reads the Newspaper p.81)

I’ve just read two of John Allen Paulos’s popular books about maths, A Mathematician Reads the Newspaper: Making Sense of the Numbers in the Headlines (1995) and Innumeracy: Mathematical Illiteracy and Its Consequences (1998).

My reviews tended to focus on the psychological, logical and cognitive errors which Paulos finds so distressingly common on TV and in newspapers, among politicians and commentators and every walk of life for the simple reason that I didn’t understand the way he explained most of his mathematical arguments.

I also criticised the style and presentation of the books which I found meandering, haphazard and so that much harder to follow, specially since he was packing in so many difficult mathematical concepts.

Looking back at my reviews I realise I missed out large chunks of the mathematical concepts he describes (sometimes at length, sometimes only in throwaway references). This blog post is designed to simply list and define the mathematical principles which he describes and explains in these two books. They appear in the same order as they appear in the books.

1. Innumeracy: Mathematical Illiteracy and Its Consequences (1988)

The multiplication principle If some choice can be made in M different ways and some subsequent choice can be made in B different ways, then there are M x N different ways the choices can be made in succession. If a woman has 5 blouses and 3 skirts she has 5 x 3 = 15 possible combinations. If I roll two dice, there are 6 x 6 = 36 possible combinations.

If, however, I want the second category to exclude the option which occurred in the first category, the second number is reduced by one. If I roll two dice, there are 6 x 6 = 36 possible combinations. But the number of outcomes where the number on the second die differs from the first one is 6 x 5. The number of outcomes where the faces of three dice differ is 6 x 5 x 4.

If two events are independent in the sense that the outcome of one event has no influence on the outcome of the other, then the probability that they will both occur is computed by calculating the probabilities of the individual events. The probability of getting two head sin two flips of a coin is ½ x ½ = ¼ which can be written (½)². The probability of five heads in a row is (½)5.

The probability that an event doesn’t occur is 1 minus the probability that it will occur. If there’s a 20% chance of rain, there’s an 80% chance it won’t rain. Since a 20% chance can also be expressed as 0.2, we can say there is a 0.2 chance it will rain and a 1 – 0.2 = 0.8 chance it won’t rain.

Binomial probability distribution arises whenever a procedure or trial may result in a ‘success’ or ‘failure’ and we are interested in the probability of obtaining R successes from N trials.

Dirichlet’s Box Principle aka the pigeonhole principle Given n boxes and m>n objects, at least one box must contain more than one object. If the postman has 21 letters to deliver to 20 addresses he knows that at least one address will get two letters.

Expected value The expected value of a quantity is the average of its values weighted according to their probabilities. If a quarter of the time a quantity equals 2, a third of the time it equals 6, another third of the time it equals 15, and the remaining twelfth of the time it equals 54, then its expected value is 12. (2 x ¼) + (6 x 1/3) + (15 x 1/3) + (54 x 1/12) = 12.

Conditional probability Unless the events A and B are independent, the probability of A is different from the probability of A given that B has occurred. If the event of interest is A and the event B is known or assumed to have occurred, ‘the conditional probability of A given B’, or ‘the probability of A under the condition B’, is usually written as P(A | B), or sometimes PB(A) or P(A / B).

For example, the probability that any given person has a cough on any given day may be only 5%. But if we know that the person has a cold, then they are much more likely to have a cough. The conditional probability of someone with a cold having a cough might be 75%. So the probability of any member of the public having a cough is 5%, but the probability of any member of the public who has a cold having a cough is 75%. P(Cough) = 5%; P(Cough | Sick) = 75%

The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.

For example, if a fair coin (where heads and tails come up equally often) is tossed 1,000,000 times, about half of the tosses will come up heads, and half will come up tails. The heads-to-tails ratio will be extremely close to 1:1. However, if the same coin is tossed only 10 times, the ratio will likely not be 1:1, and in fact might come out far different, say 3:7 or even 0:10.

The gambler’s fallacy a misunderstanding of probability: the mistaken belief that because a coin has come up heads a number of times in succession, it becomes more likely to come up tails. Over a very large number of instances the law of large numbers comes into play; but not in a handful.

Regression to the mean in any series with complex phenomena that are dependent on many variables, where chance is involved, extreme outcomes tend to be followed by more moderate ones. Or: the tendency for an extreme value of a random quantity whose values cluster around an average to be followed by a value closer to the average or mean.

Poisson probability distribution measures the probability that a certain number of events occur within a certain period of time. The events need to be a) unrelated to each other b) to occur with a known average rate. The Ppd can be used to work out things like the numbers of cars that pass on a certain road in a certain time, the number of telephone calls a call center receives per minute.

Bayes’ Theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if cancer is related to age, then, using Bayes’ theorem, a person’s age can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person’s age.

Arrow’s impossibility theorem (1951) no rank-order electoral system can be designed that always satisfies these three “fairness” criteria:

  • If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
  • If every voter’s preference between X and Y remains unchanged, then the group’s preference between X and Y will also remain unchanged (even if voters’ preferences between other pairs like X and Z, Y and Z, or Z and W change).
  • There is no “dictator”: no single voter possesses the power to always determine the group’s preference.

The prisoner’s dilemma (1951) Two criminals are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. The prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

  • If A and B each betray the other, each of them serves two years in prison
  • If A betrays B but B remains silent, A will be set free and B will serve three years in prison (and vice versa)
  • If A and B both remain silent, both of them will only serve one year in prison (on the lesser charge).
Prisoner's dilemma graphic. Source: Wikipedia

Prisoner’s dilemma graphic. Source: Wikipedia

Binomial probability Binomial means it has one of only two outcomes such as heads or tails. A binomial experiment is one that possesses the following properties:

  • The experiment consists of n repeated trials
  • Each trial results in an outcome that may be classified as a success or a failure (hence the name, binomial)
  • The probability of a success, denoted by p, remains constant from trial to trial and repeated trials are independent.

The number of successes X in n trials of a binomial experiment is called a binomial random variable. The probability distribution of the random variable X is called a binomial distribution.

Type I and type II errors Type I error is where a true hypothesis is rejected. Type II error is where a false hypothesis is accepted.

Confidence interval Used in surveys, the confidence interval is a range of values, above and below a finding, in which the actual value is likely to fall. The confidence interval represents the accuracy or precision of an estimate.

Central limit theorem In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a “bell curve”) even if the original variables themselves are not normally distributed. OR: the sum or average of a large bunch of measurements follows a normal curve even if the individual measurements themselves do not. OR: averages and sums of non-normally distributed quantities will nevertheless themselves have a normal distribution. OR:

Under a wide variety of circumstances, averages (or sums) of even non-normally distributed quantities will nevertheless have a normal distribution (p.179)

Regression analysis here are many types of regression analysis, at their core they all examine the influence of one or more independent variables on a dependent variable. Performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other. In order to understand regression analysis you must comprehend the following terms:

  • Dependent Variable: This is the factor you’re trying to understand or predict.
  • Independent Variables: These are the factors that you hypothesize have an impact on your dependent variable.

Correlation is not causation a principle which cannot be repeated too often.

Gaussian distribution Gaussian distribution (also known as normal distribution) is a bell-shaped curve, and it is assumed that during any measurement values will follow a normal distribution with an equal number of measurements above and below the mean value.

The normal distribution is the most important probability distribution in statistics because it fits so many natural phenomena. For example, heights, blood pressure, measurement error, and IQ scores follow the normal distribution.

Statistical significance A result is statistically significant if it is sufficiently unlikely to have occurred by chance.

2. A Mathematician Reads the Newspaper: Making Sense of the Numbers in the Headlines

Incidence matrices In mathematics, an incidence matrix is a matrix that shows the relationship between two classes of objects. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y. The entry in row x and column y is 1 if x and y are related (called incident in this context) and 0 if they are not. Paulos creates an incidence matrix to show

Complexity horizon On the analogy of an ‘event horizon’ in physics, Paulos suggests this as the name for levels of complexity in society around us beyond which mathematics cannot go. Some things just are too complex to be understood using any mathematical tools.

Nonlinear complexity Complex systems often have nonlinear behavior, meaning they may respond in different ways to the same input depending on their state or context. In mathematics and physics, nonlinearity describes systems in which a change in the size of the input does not produce a proportional change in the size of the output.

The Banzhaf power index is a power index defined by the probability of changing an outcome of a vote where voting rights are not necessarily equally divided among the voters or shareholders. To calculate the power of a voter using the Banzhaf index, list all the winning coalitions, then count the critical voters. A critical voter is a voter who, if he changed his vote from yes to no, would cause the measure to fail. A voter’s power is measured as the fraction of all swing votes that he could cast. There are several algorithms for calculating the power index.

Vector field may be thought of as a rule f saying that ‘if an object is currently at a point x, it moves next to point f(x), then to point f(f(x)), and so on. The rule f is non-linear if the variables involved are squared or multiplied together and the sequence of the object’s positions is its trajectory.

Chaos theory (1960) is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. “Chaos” is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems, there are underlying patterns, constant feedback loops, repetition, self-similarity, fractals, self-organization, and reliance on programming at the initial point known as sensitive dependence on initial conditions.

The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state, e.g. a butterfly flapping its wings in Brazil can cause a hurricane in Texas.

Linear models are used more often not because they are more accurate but because that are easier to handle mathematically.

All mathematical systems have limits, and even chaos theory cannot predict even relatively simple nonlinear situations.

Zipf’s Law states that given a large sample of words used, the frequency of any word is inversely proportional to its rank in the frequency table. So word number n has a frequency proportional to 1/n. Thus the most frequent word will occur about twice as often as the second most frequent word, three times as often as the third most frequent word, etc. For example, in one sample of words in the English language, the most frequently occurring word, “the”, accounts for nearly 7% of all the words (69,971 out of slightly over 1 million). True to Zipf’s Law, the second-place word “of” accounts for slightly over 3.5% of words (36,411 occurrences), followed by “and” (28,852). Only about 135 words are needed to account for half the sample of words in a large sample

Benchmark estimates Benchmark numbers are numbers against which other numbers or quantities can be estimated and compared. Benchmark numbers are usually multiples of 10 or 100.

Non standard models Almost everyone, mathematician or not, is comfortable with the standard model (N : +, ·) of arithmetic. Less familiar, even among logicians, are the non-standard models of arithmetic.

The S-curve A sigmoid function is a mathematical function having a characteristic “S”-shaped curve or sigmoid curve. Often, sigmoid function refers to the special case of the logistic function shown below

and defined by the formula:

This curve, sometimes called the logistic curve, appears to describe the growth of entities as disparate as Mozart’s symphony production, the rise of airline traffic, and the building of Gothic cathedrals (p.91)

Differential calculus the study of rates of change, rates of rates of change, and the relations among them.

Algorithm complexity gives on the length of the shortest program (algorithm) needed to generate a given sequence (p.123)

Chaitin’s theorem states that every computer, every formalisable system, and every human production is limited; there are always sequences that are too complex to be generated, outcomes too complex to be predicted, and events too dense to be compressed (p.124)

Simpson’s paradox (1951) a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined.

The amplification effect of repeated playing the same game, rolling the same dice, tossing the same coin.


Related links

Reviews of other science books

Cosmology

Environment / human impact

Genetics

  • The Double Helix by James Watson (1968)

Maths

Particle physics

Psychology

  • Irrationality: The Enemy Within by Stuart Sutherland (1992)

Jessa Fairbrother: Constellations and Coordinates @ the Photographers’ Gallery

If you visit the Photographer’s Gallery (just off Oxford Street, in central London) the main exhibitions on the upper floors are well signposted, but it’s easy to overlook the existence of the print room exhibition space down in the basement.

Here they display works by up-and-coming photographers which you can not only admire but buy. (They also have a back catalogue of works by other photographers associated with the gallery, which you can order as prints, framed or unframed.)

The print room is currently hosting a small but beautifully formed exhibition, the first major solo show of British artist Jessa Fairbrother, titled Constellations & Coordinates.

Constellation 6 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers' Gallery

Constellation 6 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers’ Gallery. £1,750 + VAT, including frame

Jessa takes stylish black and white photos of herself posing naked, in a range of positions suggestive of ballet or yoga, poses which are always dynamic, in which her body, bent forward or backward with outstretched arms expresses a powerful sense of yearning, stretching, reaching, straining. The sense that it is just a body is emphasised by the fact that in every single photo her head is turned away, her face almost always hidden, we certainly never see her eyes and so, in that basic sense, never engage with her self or soul. Instead we are confronted with the (female) body as living sculpture, arranged and posed so as to emphasise patterns and arrangements.

(Quite apart from all other considerations I wonder where she got the ideas for all these positions, they’re surprisingly varied and yet at the same time have a kind of formal unity. They don’t seem haphazard and are the opposite of casual. They’re not exactly religious but they radiate a sense of discipline, the sense of a range of hieratic poses being worked through methodically. From a book of yoga postures, or stretching exercises?)

Anyway, what lifts the photos from being just very attractive nude studies is the fact that Jessa then embroiders the prints to create the sense of swirling, whirling patterns of minuscule dots or holes. Imagine a lace doily. Then imagine a lace doily superimposed over a photo of a naked woman. That’s the effect.

Constellation 9 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers' Gallery

Constellation 9 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers’ Gallery. £1,750 + VAT, including frame

One series of ten or so photos is titled Constellations, the other series is titled Coordinates. What’s the difference? The Constellations are in black and white, the Coordinates are in colour. To quote the gallery guide:

In Constellations (2018), Fairbrother punctures the surface of the print creating intricate lace like patterns around the photographed figure, inspired by religious icons and ancient sculptures of female deities. The raised pattern also echoes braille embossing, suggesting a more tactile consideration of the work and alternative readings.

Coordinates (2019) emerged from a fascination with the systems we employ to make sense of the world. Fairbrother uses a needle and thread to trace her own emotional topography by sewing directly on to the photography of her own body, revealing hidden contour lines.

So in the black and white ones a needle or some kind of implement is used to perforate the print and create the intricate curving abstract patterns of tiny holes across the surface of the print – while in the colour ones, coloured thread is sewn into the print in order to create ovals, bands, halos and triangles made up of hundreds of tiny flowerhead shapes. In both types the flat surface of the original print is damaged, manipulated, altered, to create a new work.

Coordinate VII 2019 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers' Gallery

Coordinate VII 2019 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers’ Gallery. £2,150 + VAT, including frame

The use of colour does at least two things.

One, quite obviously, is that it makes the basic component, the image of the naked female body, a lot more candid, brutal, realistic. The black and white photos distance the image, giving her body the abstract beauty of Greek sculpture, plain, white, marmoreal, detached and also somehow dated – any black and white image carrying the suggestion that it is historic, distant, from the past, any stylish black and white nude evoking, for me at any rate, memories of Man Ray’s wondrous nudes from the 1930s.

This sense of distance, of detachment, is echoed or emphasised by the nature of Fairbrother’s decoration of the black and white shots. The stippled effect of the doily patterns is muted and subdued, understated, with two results: the patterns blend in with the white surface of the body – from even a little distance away they begin to disappear; you have to lean right in to enjoy the amazing detail of the patterns. Connected to this is the way the patterns are more extensive; because they are more subtle they can afford to cover almost her entire body ( see Constellation 9, above).

The colour works in the Coordinates series make a sharp contrast in every way to these elements. Colour photography is a lot less forgiving, a lot more explicit of detail. Thus – to highlight an apparently trivial detail – in the colour photos you can see Fairbrother’s moles. You can see the rosy colour of her nipples, the brown shade of her pubic hair, the way her white belly and chest give way to the pink or rose colouring of her neck and throat.

In other words, her body has lost the abstract, statue-like quality it had in the black and white shots. It is very much the body of a young white woman, alive, now.

The second impact of colour is the way the use of coloured thread as the medium of patterning makes a startling difference from the mute, understated quality of the stippling in the black and white photos.

The patterns made up (mostly) of coloured flower or star shapes really dominate the images. They risk making the images seem too hectic or busy. Looking at them again and again I can see that Fairbrother has had to be much more sparing of the coloured patterning. Less is more.

Whereas in a piece like Constellation 9 (above) almost every inch of her body is covered in patterning, you can see how in a piece like Coordinate VII (above) very little of her body is covered with the flower shapes. Because the colour patterning is so much more dominant, a new equilibrium, a new dynamic has to be established between the power of the body and the power of the design.

This maybe explains why, in the colour works, the main focus of the pattern is not on her body. Instead, the colour ones tend to feature abstract patterns emerging from, or surrounding her body.

These are of three types: first of all the circular halo of flower shapes surrounding her head (as in Coordinate VII , above). Then there are the ones where an isosceles triangle of flower patterns is bursting from or superimposed from her shoulders or chest or stomach.

Coordinate VIII 2019 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers' Gallery

Coordinate VIII 2019 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers’ Gallery. £2,150 + VAT, including frame

And the final type is where her body is placed within a large oval of flowers which fills the picture and reminds me of an old-fashioned Victorian or Edwardian picture frame.

In all of these oval frame pictures Fairbrother is upright and facing away from us, stretching out her arms and leaning forward. Maybe she discovered that the oval frame required symmetry, and so didn’t go with the other, mostly asymmetrical, poses which she uses in almost all the other works.

Coordinate XII 2019 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers' Gallery

Coordinate XII 2019 by Jessa Fairbrother © Jessa Fairbrother. Courtesy of the Photographers’ Gallery. £2,650 + VAT, including frame

In all the colour shots it is also noticeable that although her body has some decoration on it, it’s nowhere near as much as the all-over stippling of the black and white works. It’s almost as if the use of colour decoration calls into being a different way of seeing, or of thinking about shapes and patterns. It’s almost as if the harshness of colour, as a photographic medium, requires or invokes or inspires or suits a correspondingly harsher geometry.

Thoughts

I think these are marvellous. I was entranced. They attract on multiple levels. At a most obvious level Fairbrother has a very attractive, sexy body. As a heterosexual man I acknowledge that I enjoyed the sight of it very much. At a slightly higher level, I was fascinated by the variety of poses. I do stretching exercises at the gym, and could imaginatively feel my way into many of the positions and poses she adopts and was intrigued by their source: did she just make them up?

Beyond that, as I noticed that you never see her face I realised that she was deliberately refusing what you might call a human, emotional, candid encounter, the kind we all have when we see someone’s eyes and assess their thoughts and feelings in a million ways. The consistent choice not to show her face amounts to an aesthetic decision to distance her self from her body, to make her body into an expressive medium, a tool for her art, an object to be arranged for aesthetic effect.

And then I was fascinated by the way that the choice between black and white or colour created a whole cascade of stylistic and aesthetic consequences – which can be summarised as ‘black and white subtle, zoomorphic and sensuous’, ‘colour more brutal, geometric, shiny, brash’.

As has probably become clear by now, I preferred the black and white works titled Constellation, finding them subtler, more understated and, once you leaned in to really look, full of far more rich and complex patterns than the colour ones. But I can also appreciate how the colour ones would suit a different mood, more energetic and brassy. They are more dynamic in the aesthetic sense, meaning there is a greater range of colour, tone and image (colour itself being a form of energy, and the nearly regular geometric shapes of circle, oval and triangle possessing a dynamically mathematical energy). But – now I look yet again – I think in many of the colour ones she is actually moving, tossing her head back so her hair swings backwards.

Different styles for different moods.

Like all great ideas this perforation and embroidering of photographs is stunningly simple, once someone has done it and shown it to you. What a great idea, and how brilliantly she has executed it. Deeply enjoyable.


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Dave Heath: Dialogues with Solitudes @ the Photographers’ Gallery

‘The fact that I never had a family, a place or a story that defined me, inspired a need in me to join the community of mankind. I did so by inventing a poetic form linking this community, at least symbolically, in my imagination, through this form.’ (Dave Heath)

This is the first major UK exhibition dedicated to the work of American photographer Dave Heath (1931-2016).

New York City, 1960 by Dave Heath © Dave Heath / Courtesy of Howard Greenberg Gallery, New York, and Stephen Bulger Gallery, Toronto

New York City, 1960 by Dave Heath © Dave Heath / Courtesy of Howard Greenberg Gallery, New York, and Stephen Bulger Gallery, Toronto

Heath started taking photos towards the end of his stint in the Korean War (1950-53). All his photos from Korea ignore battlefield heroics, firefights, explosions and hardware – instead showing the average grunt as isolated individuals caught in moments of thought, looking down, looking sad.

Korea, 1953 by Dave Heath © Dave Heath, Courtesy Howard Greenberg Gallery, NYC

Korea, 1953 by Dave Heath © Dave Heath, Courtesy Howard Greenberg Gallery, NYC

And this is the sensibility he brought back to civilian life. Of the 109 photos on display here, I only saw three where the subject is smiling or laughing. The other hundred and six show individuals or couples looking moody, intense, sullen, lost in thought. Inhabitants of solitude. Aficionados of introspection.

Elevated in Brooklyn, New York City, 1963 by Dave Heath © Dave Heath / Courtesy of Howard Greenberg Gallery, New York, and Stephen Bulger Gallery, Toronto

Elevated in Brooklyn, New York City, 1963 by Dave Heath © Dave Heath / Courtesy of Howard Greenberg Gallery, New York, and Stephen Bulger Gallery, Toronto

Even the handful of photos which aren’t of people, but of buildings or the sidewalk, manage to make them look lost in thought and downbeat. The result is tremendously atmospheric if, on occasion, a bit samey.

Biography

The downbeat tone was set early in Heath’s life. He was born in Philadelphia in 1931 to very young parents who abandoned him at the age of four after which he was sent to a series of foster homes before being placed in an orphanage. From then on he carried a sense of loss and abandonment which he projected, very successfully, onto everything around him.

Heath became interested in photography as a teenager, and joined an amateur camera club. He read the photo essays in Life magazine and cites one in particular as having a decisive impact on his future. Bad Boy’s Story by Ralph Crane depicted the emotional experiences of a young orphan not unlike young Heath.

In a flash Heath realised that photography could be a means of self-expression, a way of shaping the external world to fit his experiences, and a way of connecting to others.

In his early twenties he set about becoming an expert in photographic techniques, taking courses in commercial art, working in a photo processing lab, and studying paintings at the Philadelphia Museum of Art. His stint in the army as a machine gunner interrupted his career for a few years, but crystallised his approach to subject matter, his skill at capturing a wide range of people in moments of thought and vulnerability.

On his return, Heath developed this aptitude for capturing an ‘inner landscape’, seeking out the lonely and lost and fragile on the streets of big city America. Most of the photographs on display here were taken on the streets of Chicago and New York (where he moved to in 1957).

Heath’s subjects seem eerily detached from their physical context, shot either singly or in couples, but always intensely aware of – almost physically projecting – their isolation.

Washington Square, New York, 1960 by Dave Heath © Dave Heath / Collection Torosian, courtesy Howard Greenberg Gallery, New York, and the Stephen Bulger Gallery, Toronto

Washington Square, New York, 1960 by Dave Heath © Dave Heath / Collection Torosian, courtesy Howard Greenberg Gallery, New York, and the Stephen Bulger Gallery, Toronto

Heath is quoted as saying:

My pictures are not about the city but from the city. I’ve always seen it as a stage and I’ve always seen the people in the streets as being actors, not acting out a particular play or story, but somehow being the story itself…

It would be wrong to think that all his photos are close-ups of alienated individuals or couples. There’s more variety than that. At the busy end of the spectrum there’s a photo of a crowd gathering round a policeman in Central Park guarding the spot where a suicide has been discovered. At the other end of the spectrum, sometimes he picked out just details, lost property, street detritus, close-ups of parts of people’s bodies, which manage to convey a tremendous sense of loss and abandonment.

California, 1964 by Dave Heath © Dave Heath / Courtesy of Howard Greenberg Gallery, New York, and Stephen Bulger Gallery, Toronto

California, 1964 by Dave Heath © Dave Heath / Courtesy of Howard Greenberg Gallery, New York, and Stephen Bulger Gallery, Toronto

Heath’s photos capture that eerie moment in American history just before the 1960s exploded, just around the time JFK was assassinated and Civil Rights began to become an enormous, society-sundering issue and then, of course the growing opposition to the Vietnam War.

He had always been interested in exploring how individual photos could be tied together into sequences which created something larger than the sum of its parts. Heath once wrote that ‘the central issue of my work is sequence’ and thought that the rhythm of images arranged in collages or montages created a deeper and more complex psychological state than a single image.

A master printer – so good that other photographers asked him to make their prints for them – Heath also crafted handmade books and experimented with multimedia slide presentations. All this thinking and experimentation culminated in the book which is considered his masterpiece, A Dialogue with Solitude, published in 1965.

A Dialogue With Solitude

A Dialogue with Solitude was conceived in 1961 but not published till 1965. Heath chose 82 of his best or most characteristic photographs taken between 1952 and 1962 and grouped them into ten chapters dedicated to variations on the theme of solitude, being: violence, love, childhood, old age, poverty, war, race and death.

Each one is preceded by a short quote from a literary giant including: Matthew Arnold, James Baldwin, T.S. Eliot, William Hazlitt, Herman Hesse, Rilke, Yeats and so on. In other words, all the names you’d meet in a basic undergraduate course in comparative literature – or at least before the explosion of feminist and black and queer studies added a lot more women and marginalised writers to the canon.

The book is commemorated here by a wall-seized display which places scores of photos next to the bookish quotes, to create a sort of immersive visual and literary experience.

Installation view of Dave Heath: Dialogues with Solitudes at the Photographers Gallery, showing the wall-sized display of photos and texts from the book, Dialogue with Solitude. Photo by the author

Installation view of Dave Heath: Dialogues with Solitude at the Photographers Gallery, showing the wall-sized display of photos and texts from the book, Dialogue with Solitude. Photo by the author

In the opinion of the writer whose wall label accompanies this display, Francesco Zanot:

The primacy of montage and sequencing in Heath’s work is made obvious. The result has nothing to do with linear narration, but rather resembles a vast poem, rhapsodic and tormented. Heath merges together on the space of a page references as refined as they are distant from one another. The book, then, becomes the ideal medium by which to carry out a reflection both through and upon photography.

Thoughts

I liked the Korean War photos best. Soldiers in a war really have got something to be pissed off about. Guys lying on their bunks or sitting on a crate smoking a fag reminded me of all the crappy labouring jobs I’ve had, and how it feels when you get a break and five minutes to just sit staring into space, too tired to think about anything, too tired or too mind numblingly bored to say or do or think anything.

The photos of sad people in Philadelphia and Chicago and New York are undoubtedly atmospheric and poignant, beautifully composed and printed with a grainy effect that carries the viewer back back back to a historic era.

And yet… and yet…. I think I’ve seen too many photographs of unhappy Americans recently – the hundred or more photos by Diane Arbus currently at the Hayward Gallery, or the long career of Dorothea Lange devoted to documenting American misery and injustice, celebrated at the Barbican last summer, or the enormous brightly coloured images of alienation and being lost in the crowd created by Alex Prager.

Upstairs at the Photographers’ Gallery, right now, the works of Mark Ruwedel don’t feature any people but they, also, convey a tremendous sense of loss and abandonment via pictures of run-down shacks in the desert or the abandoned sites of military tests.

Abandonment, loneliness, isolation, solitude, unhappiness. These seem to be the default subjects of American art photographers.

Washington Square, New York City, 1960 by Dave Heath © Dave Heath / Courtesy of Howard Greenberg Gallery, New York, and Stephen Bulger Gallery, Toronto

Washington Square, New York City, 1960 by Dave Heath © Dave Heath / Courtesy of Howard Greenberg Gallery, New York, and Stephen Bulger Gallery, Toronto

Independent movies

Off to one side of the main display rooms is a dark room where you can watch clips from cult independent films from the 1960s, contemporary with Heath’s works, which also focus on theme of solitude. These include:

1. Portrait of Jason by Shirley Clarke (1966), Jason being ‘a gay African-American hustler and aspiring cabaret performer’.

2. Salesman by Albert and David Maysles and Charlotte Mitchell Zwerin (1968) a creepy depiction of slimy American salesman.

3. The Savage Eye by Ben Maddow, Sidney Meyers and Joseph Strick (1960)

Interview with Senior Curator, Karen McQuaid

Curators

  • Curated by Diane Dufour, Director of LE BAL.
  • Senior Curator for the Photographers’ Gallery, Karen McQuaid

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Deutsche Börse Photography Foundation Prize 2019 @ the Photographers’ Gallery

The Deutsche Börse Photography Foundation Prize

The Deutsche Börse Photography Foundation Prize acknowledges an international photographer for an outstanding body of work that has been exhibited or published in Europe in the previous twelve months. Projects are recognised for their major achievements and innovations in the field of photography and contemporary culture.

The DBPFP19 exhibition aims both to highlight and give platform to four very diverse artistic practices, which simultaneously display innovative, committed and engaged approaches to photography

Each year a long list is drawn up and then the panel of judges whittles it down to a list of four finalists. The winner of the £30,000 prize will be announced at a special award ceremony held at The Photographers’ Gallery on 16 May 2019.

N.B.

Note two things:

  1. books Several of the projects originated as books and the book versions are on display in display cases and can be bought separately at the Photographers Gallery shop. For exhibition purposes the books are dismantled and various elements of them blown-up, printed and variously displayed on the gallery walls, but it’s worth bearing in mind the bookish origins of most of the projects.
  2. projects The prize is not narrowly about photography, it is much more broadly about ‘achievements in the field of contemporary culture’, a very wide and loose definition.

This year’s four short-listed artists are:

1. Laia Abril for the publication On Abortion (Dewi Lewis Publishing, November 2017)

2. Susan Meiselas for the exhibition Mediations (exhibited at the Jeu de Paume, Paris, 6 February–30 May 2018)

3. Arwed Messmer for the exhibition RAF – No Evidence / Kein Beweis (exhibited at ZEPHYR|Raum für Fotografie, Mannheim, 9 September – 5 November 2017)

4. Mark Ruwedel for the exhibition Artist and Society: Mark Ruwedel (16 February–16 December 2018 at Tate Modern, London)

1. On Abortion by Laia Abril

Laia Abril was born in Spain in 1986 (aet. 33).

Over five years Abril has compiled a multi-layered, visual history of abortion. Her display starts with a row of photos of early contraceptive  devices and abortion equipment, so that you slowly move past a series of images of gruesome-looking implements which have been used to perform abortions through the ages.

Illegal Instrument Kit (2018) by Laia Abril © Laia Abril

Illegal Instrument Kit (2018) by Laia Abril © Laia Abril

The next wall features photographic portraits Abril has made of women who tell their traumatic stories of being denied abortions in their native countries, or the risks they undertook to travel to another country to have one.

Portrait of Marta, 29, Poland by Laia Abril © Laia Abril, 2018

Portrait of Marta, 29, Poland by Laia Abril © Laia Abril, 2018

Each of these start b&w portraits is accompanied by the subject’s story. This is Marta’s:

“On January 2, 2015, I travelled to Slovakia to have an abortion. [In Poland, abortion is illegal except in cases of sexual assault, serious foetal deformation, or threat to the mother’s life] I was too scared to take DIY abortion pills alone. What if something went wrong? So I decided to get a surgical abortion in a clinic abroad. I felt upset about borrowing money for the procedure, and lonely and frustrated because I couldn’t tell anyone what was happening. The hardest part was facing my boyfriend, who opposes abortion. All the same, I felt stronger and more mature afterwards.”

The damage done to individuals by lack of access to legal, safe and free abortion services is indicated by this grid of nine women who all died because of botched abortions or because abortions were denied them by the state, even in cases of extreme medical emergency.

Installation view of On Abortion by Laia Abril. Photo by the author

Installation view of On Abortion by Laia Abril. Photo by the author

At the end of the final wall is an information panel which lists some of the attacks, arson and murders carried out by anti-abortion activists in America over the past few decades.

The project, in the words of the curators:

addresses the marginalised position of women in past and contemporary societies, whilst exposing the many social triggers, stigmas and taboos that still persist around abortion and female health.

Towards the end is this strikingly clear, bright image.

Hippocratic Betrayal by Laia Abril © Laia Abril, 2018

Hippocratic Betrayal by Laia Abril © Laia Abril, 2018

The story behind it is:

“In February 2015, a 19-year-old woman took abortion pills in Sao Bernardo do Campo, Brazil, then went to hospital with abdominal pain. After treatment, her doctor called the police, who handcuffed her to the bed and forced her to confess. In Brazil, abortion is illegal under most circumstances and doctors are known to break their confidentiality code in order to denounce women who try it. Patients accused of attempting abortion have been detained in hospitals for weeks and even months.”

My opinion

A close reading of the criteria and aims of the exhibition suggest there is a tension – or a spectrum – running between pure photography-as-art at one end and photography subordinated to ‘committed and engaged’ achievements in contemporary culture at the other.

Of the four projects, Abril’s seems to me the most obviously political, certainly the most ‘committed and engaged’ and, what’s more, on a highly emotive and often harrowing subject.

On that basis – if the judges give weight to the ‘committed and engaged’ criterion – I’d be surprised if Abril doesn’t win.

2. aka Kurdistan by Susan Meiselas

Meisalas was born in the USA in 1948 (aet. 71).

She is an internationally acclaimed documentary photographer who’s been working for five decades, whose subjects have included war, human rights and cultural conflicts such as the sex industry and the visual representation of women.

She takes an immersive approach, spending long periods of time with her subjects. In addition to photographs, she produces essays and artworks, audio and film installations.

Meiselas has been working on a long-term project titled Kurdistan: In the Shadow of History, offering a multi-layered history of the Kurds. It has not been a happy history. The Kurdish people are spread across an area which overlaps the four states of south-east Turkey, northern Syria, northern Iraq and eastern Iran, what were once described to me as four of the most brutal regimes on earth.

Map of Kurdistan © The Washington Times

Map of Kurdistan © The Washington Times

It was seeing reports of Saddam Hussein’s genocidal attacks on the Kurds in the late 1980s that inspired Meiselas to visit the area in the early 1990s. Here she began to document the atrocities committed by the Hussein regime, including mass executions, tortures and rape.

Taymour Abdullah, 15, the only survivor of village execution, shows his bullet wound, Arbil, Northern Iraq, December, 1991 by Susan Meiselas © Susan Meiselas

Taymour Abdullah, 15, the only survivor of village execution, shows his bullet wound, Arbil, Northern Iraq, December, 1991 by Susan Meiselas © Susan Meiselas

Thus began a process which has continued for the past thirty years, with Meiselas continuing to work with Kurdish diasporic communities to document their experiences and gather visual evidence – documents, family photos, maps, mementos and personal stories – to give shape to a collective memory of Kurdistan.

Destroyed village along the Hamilton Road, Northern Iraq, 1991 by Susan Meiselas © Susan Meiselas

Destroyed village along the Hamilton Road, Northern Iraq, 1991 by Susan Meiselas © Susan Meiselas

The work itself consists of two walls of colour photographs showing destroyed villages, exhumed graves, and family members mourning the dead.

Another wall has been turned into an enormous map of the Middle East and Europe, into which pins have been driven at locations where Kurdish diasporas exist (London, Berlin) and from these pins hang photos, documents, brochures and pamphlets telling their stories, complete with photos of themselves, family members alive and dead and so on. A sort of archive of memories.

And, on the fourth wall there is a film installation which, on parallel screens, intersperses photos Meiselas has taken with historic photos and footage of people and places from the region, alongside personal testimony from Kurdish survivors as well as Meiselas herself.

Installation view of Kurdistan by Susan Meiselas. Photo by the author

Installation view of Kurdistan by Susan Meiselas. Photo by the author

My opinion

Between 1987 and 1991 I worked on Channel Four’s international affairs TV programme. I was the assistant producer in charge of stories from Asia, defined as all the countries from Japan to Israel and including the two most populous nations on earth, China and India.

But it was the Middle East which kept making the news and my stint coincided with the end of the Iran-Iraq War (20 August 1988) and the first Gulf War (2 Aug 1990 – 28 Feb 1991).

During this time I got to know quite a bit about the Kurds and their culture. In fact, on one occasion I was driven to a ‘safe house’ in West London to meet Jalal Talabani, leader of the Patriotic Union of Kurdistan who was at that point on the run from Saddam Hussein’s assassins, for an interview and to persuade him to appear on British TV to put the case for Kurdish independence. He agreed so I was his minder and organiser for that appearance. Later, he went on to be elected the first post-Saddam President of Iraq, serving from 2006 to 2014.

I remember to this day producing the section of the show which covered Saddam’s gassing of the village of Halabja on March 16, 1988. At least 5,000 people died as an immediate result of the chemical attack and an estimated further 7,000 people were injured or suffered long term illness. What a bastard he was. That weekend I produced the part of the show where we interviewed a poison gas expert describing the effects on the body of the nerve agents Tabun and Sarin – the burning lungs, the seared skin, the agonising pain as you go blind – and then a regional expert explaining why Saddam launched the attack and what he hoped to gain (to terrorise the local Kurdish population into stopping their support for the Kurdish peshmerga guerrillas who had recently taken control of the region).

The full history of the Kurds is long and complicated. Just the story of the past thirty years, from the persecutions of Saddam, through the chaos of the Iraqi Civil War, and then the eruption of ISIS into Kurdish territory in 2014, right up to last week’s news that Kurdish forces played a key role in taking the final ISIS stronghold in Syria – is a tortuously complicated story which requires a lot of explaining.

So I know a bit about Kurdish political history, I’ve met Kurdish political leaders and regional analysts, I’ve been following developments there for 30 years or so – but I felt ambivalent about this display. Gathering the stories of Kurdish survivors is clearly an important contribution to their oral history. Bringing the story of this brutally repressed people to a wider audience is obviously a very worthwhile cause.

And yet I felt ambivalent about the actual products which you see on display, the layout and content of the exhibition. Take the photos of men showing off the scars from beatings and tortures they received from Saddam’s forces – or of Middle Eastern women standing next to a mass grave of their menfolk. These are stock images of stock subjects.

Villagers watch exhumation at a former Iraqi military headquarters outside Sulaymaniyah, Northern Iraq, 1991 by Susan Meiselas © Susan Meiselas

Villagers watch exhumation at a former Iraqi military headquarters outside Sulaymaniyah, Northern Iraq, 1991 by Susan Meiselas © Susan Meiselas

Obviously a project like this is well-intentioned and has involved a lot of people in numerous forms of collaboration, in telling their often harrowing stories of persecution or uplifting stories of survival.

But, in my experience, accounts like this run the risk of making the horrors of war and genocide in this region seem like inexplicable nightmares, unless and until you make the hard effort to understand the Realpolitik which lies behind them.

The twin drawback of lots of ‘political’ art is that, whatever its good intentions, it tends to rely heavily on images, and on the testimony of the kinds of people who are available to give testimony, who are keen to have their stories heard. Thus it is easy to take photos of weeping mothers and bleak-eyed family members around a mass grave – and it is easy to take extensive accounts of how this or that family survived the attack on their village, the gassing, the roundups for interrogation, made a long trek into the mountains or managed to flee the region altogether.

But the risk is that these sad images and sad stories have the tendency to create an over-simplified dichotomy between the good and the bad, dividing people into sheep and goats. On the one hand are the inexplicable evil bastards who rape and torture and murder and gas and exterminate (represented here by stock photos of defaced images / posters/ paintings of Saddam) – on the other, the weeping mothers and crying children and shell-shocked men standing beside mass graves which are only now being opened up to reveal their grim contents.

But people aren’t black and white, people are a complex mix and if 20th century history teaches us anything, it is that ordinary boring people can be bullied and persuaded to do, and accept, almost anything.

To be more specific, the Kurds themselves are divided into many factions. They have created numerous militias and fighting forces which have proved themselves very effective and with whom the West, in particular America, has allied itself over the past 20 years – but which are themselves no angels.

The area is riven by religious, ethnic, nationalistic, political and militia-based divisions which look set to destabilise it for the foreseeable future.

And, once you’ve gotten familiar with the subject, the stories you really want to hear are not the stories of the men, women and children who escaped to make new lives in Berlin and London, it is the thinking of the leaders, the generals and the politicians who created this mess. It’s in the minefield jungle of conflicting nationalistic and security aims that some kind of compromise and peace has to be thrashed out.

If you want to understand why this kind of thing happens, and are genuine about trying to prevent it happening again, then listening to lots of weeping women isn’t enough. You need to undertake a thorough study of the landscape, the geography and climate and natural resources of the area (because half the time it comes down to fighting over natural resources – water, oil, farmable land), and then of the long, bitter histories of the warring peoples who have lived there.

Only then do atrocities like this become at least comprehensible, and only as they become comprehensible and analysable, can you gather the evidence and arguments to try and stop them happening again. There’s no way to avoid inexplicable atrocity. But if the atrocity turns out to be explicable – if it can be seen as part of a way of government based on terror, as a way of controlling fierce ethnic divisions – then at least that’s a start to thinking about how the international community should deal with governments based on terror, and begins to provide suggestions on how to police ethnic divisions.

I liked the idea of the enormous map with the pamphlets hanging from it as a thing, as an object – but then I love maps of any kind.

The film projections included lots of evocative old photos of Kurdish peasants taken in the late 19th or early 20th century.

All of the photos are taken with great clarity and all-too-vividly capture the horrible traumatic experiences of the victims.

And partly because the room is darkened to allow us to see the projections, the whole thing has a powerful sensaround feel to it.

And maybe all of this, maybe even the mere existence of a people called the Kurds, will come as news to a lot of the gallery goers.

But for me, personally, I didn’t think this display explains to any visitor why the history of the Kurds has been so troubled, exactly what challenges they face, and the best ways forward to some kind of peaceful solution.

3. RAF – No Evidence / Kein Beweis by Arwed Messmer

If women protesting against illiberal abortion laws, and the sorry plight of the Kurds are both likely to prompt sympathy – or righteous anger – from the enlightened gallery-goer, then this project by Arwed Messmer is much more problematic.

To state the facts:

The Red Army Faction (German: Rote Armee Fraktion), also known as the Baader-Meinhof Gang was a West German far-left militant organization founded in 1970. Key early figures included Andreas Baader, Gudrun Ensslin, Horst Mahler and Ulrike Meinhof. The West German government as well as most Western media and literature considered the Red Army Faction to be a terrorist organization.

The Red Army Faction carried out a series of bombings, assassinations, kidnappings, bank robberies and shoot-outs with police over the course of three decades. Their activity peaked in late 1977, which led to a national crisis that became known as the “German Autumn”. The RAF has been held responsible for thirty-four deaths, including many secondary targets, such as chauffeurs and bodyguards, as well as many injuries throughout its almost thirty years of activity.

RAF No Evidence/Kein Beweis (2017) by Arwed Messmer © Arwed Messmer: research, concept and editing; source: German Federal Archives, 2018

RAF No Evidence/Kein Beweis (2017) by Arwed Messmer © Arwed Messmer: research, concept and editing; source: German Federal Archives, 2018

Messmer’s display derives from a massive book, a copy of which is available to leaf through on a table in his exhibition room. According to the Photographers’ Gallery:

Messmer’s project repurposes images, documents and other source materials commonly used in police investigations and crime-scene reconstructions that he researched in German state and police archives. Messmer’s new and surprising ‘narrative’ examines how images once used as evidence in criminal cases can now provide a unique insight into our understanding of history. The installation highlights the early period between 1967 to 1977, showcasing images from the student protests in 1968, police re-enactments and an extensive collection of investigative, forensic and documentary photographs ranging from the mundane to the surreal.

RAF No Evidence/Kein Beweis (2017) by Arwed Messmer © Arwed Messmer: Compilation design and editing of the photographic material. Source: AM_PHS_SCHUPO_FILM 1933_19A_20A Berlin Police Historical Collection Kurfürstendamm, Berlin, 12.04.1968

RAF No Evidence/Kein Beweis (2017) by Arwed Messmer © Arwed Messmer: Compilation design and editing of the photographic material. Source: AM_PHS_SCHUPO_FILM 1933_19A_20A Berlin Police Historical Collection Kurfürstendamm, Berlin, 12.04.1968

In the German Autumn of 1977, I was 16 and punk rock was exploding across England. (It wasn’t the only thing that was exploding: here is a list of all the IRA attacks carried out in 1977 – long, isn’t it? If you didn’t live through that era you can’t imagine what it was like to turn on the evening news and read about a new terrorist attack in Northern Ireland, mainland Britain or Europe every night.)

The Clash’s first single White Riot was released in March that year and it seemed a completely appropriate soundtrack to an era of street disorder, to the terrorist shootings, bombings and assassinations which were the routine background to our lives. Baader, Ensslin and other members of the group had been arrested and imprisoned as early as 1972 but this didn’t stop other members of the extended group carrying out terrorist acts throughout the 1970s.

On 17 October 1977, in what came to be called the ‘Death Night’, Ensslin, Baader and Jan-Carl Raspe were found hanged in their cells at Stammheim Prison. The press ran features about the gang and I pinned atmospheric black-and-white photos of these university-educated would-be revolutionaries up on my bedroom wall, along with all the other symbols of the political chaos of the time.

As to Messmer’s display, this is on four walls of one room. On wall is dominated by an enormous blow-up of a black and white photo of student protester Benno Ohnesorg lying dead having been shot by Germany police during a student demo in June 1967, one of the increasingly violent events which crystallised the belief among some students that they, too, needed to take up arms in order to overthrow the West German capitalist, imperialist, patriarchal state.

Installation view of RAF – No Evidence / Kein Beweis by Arwed Messmer showing the bog photo of the death of Benno Ohnesorg and, on the bench in the foreground, the enormous book which the display is based on. Photo by the author

Installation view of RAF – No Evidence/Kein Beweis by Arwed Messmer showing the bog photo of the death of Benno Ohnesorg and, on the bench in the foreground, the enormous book which the display is based on. Photo by the author

Along the next wall are full-length mug shots of twenty or so student activists protesting at the state funeral of Reichstag President Paul Löbe in August 1967. They’re dressed in all kinds of comical outfits, some wearing make-up, so that it looks more like a parade of clowns and hippies than dangerous radicals. It was still the late ’60s. Hey, hey we’re the Monkees.

RAF No Evidence/Kein Beweis, 2017 by Arwed Messmer © Arwed Messmer: research, concept and editing; source: Berlin Police Historical Collection, 2018

RAF No Evidence/Kein Beweis, 2017 by Arwed Messmer © Arwed Messmer: research, concept and editing; source: Berlin Police Historical Collection, 2018

Jump forward ten long years to the period just before the Death Night.

The most evocative or eerie or disturbing element in the display, while at the same time being strangely banal, is an entire wall of photos taken inside the cells of Meinhof and Baader at Stammheim Prison at the time of their deaths.

What struck me was how comfy the cells look, with toothbrushes and rolling tobacco lying about and the walls packed with shelves full of books. It looks a lot like my son’s room at university, only tidier.

I noticed books by the usual suspects lying around, works by Marx and Lenin, of course, and then by the supposedly ‘softer’ Western Marxists such as Gramsci, Lukacs and Walter Benjamin.

Freedom through armed, anti-imperialist struggle.

Compared to other prison cells I’ve read about, compared to the Nazi death camps or the barracks in Russian gulags, this looks like the lap of luxury: hot and cold running water, as many books as you want and even – to my amazement – record players (I noticed a copy of Bob Dylan’s Blonde on Blonde in Meinhof’s cell).

RAF – No Evidence/Kein Beweis by Arwed Messmer showing the wall of photos depicting the inside of the Baader - Meinhof cells at Stammheim Prison

RAF – No Evidence/Kein Beweis by Arwed Messmer showing the wall of photos depicting the inside of the Baader – Meinhof cells at Stammheim Prison

My opinion

Does this installation offer a:

new and surprising ‘narrative’ [which] examines how images once used as evidence in criminal cases can now provide a unique insight into our understanding of history?

As with the Meiselas, I felt the display gave you the opposite of history and the opposite of understanding. I appreciate the aesthetic unity of the project; I appreciate in particular the visual uniformity of style and subject matter of the prison cell photos. Having them cover two walls does create a real sense of claustrophobia (tempered, as I’ve mentioned, by envy at their cracking book collection).

But the installation as a whole doesn’t, I think, begin to convey the mad craziness of the times and the power and persuasiveness of the anti-capitalist, anti-imperialist, student slogans which rang on in universities across the western world and continued to inspire the plane hijackings, the kidnapping and assassination of bankers and industrialists, or just the random acts of violence which dominated the decade.

The most illuminating thing I’ve read about the terrorist movements which raged through the 1970s are the relevant chapters of The Seventies Unplugged by Gerard DeGroot (2010). It’s a popular and non-scholarly book, but it’s impact lies in the interviews with ex-members of the terrorist groups in Italy, France and Germany who, to a man, feel nothing but shame and regret for the harm, damage and deaths they caused. The chapter in it about the Red Army Faction (pp.111-121) will tell you more about their motivation, their activities, and the regrets of the former members than anything in this display.

4. Artist and Society by Mark Ruwedel

Ruwedel was born in 1954 in America (thus two of the four entrants are Americans). His is the most straightforward display. After the bewilderingly complex moral, social and political issues raised by the multimedia installations, it’s quite a relief to come to a display in a photography exhibition which consists simply of… photographs.

Classic black and white photos of American landscapes and the American scene.

“Typical American House“, Nevada Test Site, Yucca Flat, Apple II Test Site, 1995 by Mark Ruwedel © Mark Ruwedel, 2018

‘Typical American House’, Nevada Test Site, Yucca Flat, Apple II Test Site, 1995 by Mark Ruwedel © Mark Ruwedel, 2018

The four walls of this room display beautifully composed, nicely framed, richly evocative black and white photos of a) abandoned houses in the desert b) the relics of military testing in the desert c) distinctively American houses lining Sunset Boulevard in Los Angeles, and d) rivers running through ravines.

Hells Canyon (1999) by Mark Ruwedel © Mark Ruwedel, 2018

Hells Canyon (1999) by Mark Ruwedel © Mark Ruwedel, 2018

Reading the wall labels you discover these images are indeed collected into sets which have names:

  • Dusk a series showing empty houses and shacks in the bleak empty desert under the twilight sky
  • Pictures from Hell awe-inspiring landscapes which generations of settlers evocatively named Helltown, Devils Gardens, Hells Hollow or Devils Land
  • We All Loved Ruscha his homage to the artist Ed Ruscha, which recreates shots included in Ruscha’s 1966 book, Every Building on the Sunset Strip
  • Crater which depicts nuclear test sites in Nevada

I like going on long walks in the country, and I’ve been a fan of land artists like Richard Long from the moment I learned about them in the 1980s, and I am a big fan of the J.G. Ballard aesthetic of how Western civilisation is already living amidst its own ruins – so I warmed most of all to Ruwedel’s shots of eerily deserted bomb test sites.

Ruined old shacks in the desert I’ve seen loads of times; picturesque photos of canyons you can see in tourist promos for America’s national parks etc… but the strange metal and concrete shapes built by military forces for reasons long forgotten and long since abandoned… they do it for me every time.

Nevada Test Site 1995 by Mark Ruwedel © Mark Ruwedel, 2018

Nevada Test Site 1995 by Mark Ruwedel © Mark Ruwedel, 2018

Not to be outdone by the bookish competition, Ruwedel is also interested in the craft of photographic printing and the photograph-as-object, and this is demonstrated by a number of his hand-made artist’s books which are on show in a glass display case. Stylish.

My opinion

If the prize were awarded solely of the basis of photography – on a photographer’s skill in choosing great visual subjects, on the quality of composition, the framing, and the creation of atmosphere, I think Ruwedel would win the Deutsche Börse Photography Foundation Prize hands down.

But it isn’t. A ‘committed and engaged approach’ is a key criterion for winning the prize, and seen from a political-cultural perspective Ruwedel is the weakest entrant.

The Messmer project is, in my opinion, the next weakest in that the images he has dug up from the archives are certainly intriguing and often striking (the mugshots of 1967 protesters dressed as clowns and freaks) but you had to know a bit about the subject matter first for it to really make sense.

The Susan Meiselas I have already discussed at length, and I suppose is worthy, thorough, deeply engaged, but – in my opinion – flawed.

Which leaves Laia Abril as the likely winner, for several reasons. One is the universal applicability of her subject – the politics of sexual reproduction, the issue of control of women’s bodies, by definition affects at least half the world’s population.

But it’s not just about the emotive subject matter, and her evident commitment to it. It’s also about her skill as a photographer. The emotion Abril gets into the gaunt, haunted portraits of her abortion-traumatised women makes a lasting impact that grows in the memory. Just that one photo of handcuffs attached to a metal bedstead is hard to forget, both as a story, and because it is such a skillful visual composition.

Altogether, regarded as a socio-political art project, I think Abril’s one really does show the fullest, most rounded breadth and depth – ranging from photos of the horrible implements used in back street abortions, to the stark images of women affected by repressive legislation here and now.

If I were a gambling man, I’d bet that Abril will win the prize on 16 May.

Curator

Curated by Anna Dannemann from The Photographers’ Gallery.


Related links

Reviews of other photography exhibitions

A Mathematician Reads the Newspaper: Making Sense of the Numbers in the Headlines by John Allen Paulos (1995)

Always be smart. Seldom be certain. (p.201)

Mathematics is not primarily a matter of plugging numbers into formulas and performing rote computations. It is a way of thinking and questioning that may be unfamiliar to many of us, but is available to almost all of us. (p.3)

John Allen Paulos

John Allen Paulos is an American professor of mathematics who came to wider fame with publication of his short (130-page) primer, Innumeracy: Mathematical Illiteracy and its Consequences, published in 1988.

It was followed by Beyond Numeracy: Ruminations of a Numbers Man in 1991 and this book, A Mathematician Reads the Newspaper in 1995.

Structure

The book is made up of about 50 short chapters. He explains that each one of them will take a topic in the news in 1993 and 1994 and show how it can be analysed and understood better using mathematical tools.

The subjects of the essays are laid out under the same broad headings that you’d encounter in a newspaper, with big political stories at the front, giving way to:

  • Local, business and social issues
  • Lifestyle, spin and soft news
  • Science, medicine and the environment
  • Food, book reviews, sports and obituaries

Response

The book is disappointing in all kinds of ways.

First and foremost, he does not look at specific stories. All the headlines are invented. Each 4 or 5-page essay may or may not call in aspects of various topics in the news, but they do not look at one major news story and carefully deconstruct how it has been created and publicised in disregard of basic mathematics and probability and statistics. (This alone is highly suggestive of the possibility that, despite all his complaints to the contrary, specific newspaper stories where specific mathematical howlers are made and can be corrected are, in fact surprisingly rare.)

The second disappointment is that, even though these essays are very short, they cannot stay focused on one idea or example for much more than a page. I hate to say it and I don’t mean to be rude, but Paulos’s text has some kind of attention deficit disorder: the essays skitter all over the place, quickly losing whatever thread they ever had in a blizzard of references to politics, baseball, pseudoscience and a steady stream of bad jokes. He is so fond of digressions, inserts, afterthoughts and tangents that it is often difficult to say what any given essay is about.

I was hoping that each essay would take a specific news story and show how journalists had misunderstood the relevant data and maths to get it wrong, and would then show the correct way to analyse and interpret it. I was hoping that the 50 or so examples would have been carefully chosen to build up for the reader an armoury of techniques of arithmetic, probability, calculus, logarithms and whatever else is necessary to immediately spot, deconstruct and correct articles with bad maths in them.

Nope. Not at all.

Lani ‘Quota Queen’ Guinier

Take the very first piece, Lani ‘Quota Queen’ Guinier. For a start he doesn’t tell us who Lani ‘Quota Queen’ Guinier is. I deduce from his introduction that she was President Clinton’s nomination for the post of assistant attorney general for civil rights. We can guess, then, that the nickname ‘quota queen’ implies she was a proponent of quotas, though whether for black people, women or what is not explained.

Why not?

Paulos introduces us to the Banzhaf power index, devised in 1965 by lawyer John F. Banzhaf.

The Banzhaf power index of a group, party or person is defined to be the number of ways in which that group, party or person can change a losing coalition into a winning coalition or vice versa. (p.10)

He gives examples of companies where three or four shareholders hold different percentages of voting rights and shows how some coalitions of shareholders will always have decisive voting rights, whereas others never will (these are called the dummy) while even quite small shareholders can hold disproportionate power. For example in a situation where three shareholders hold 45%, 45% and 10% of the shares, the 10% party can often have the decisive say. In 45%, 45%, 8% and 2% the 2% is the dummy.

He then moves on to consider voting systems in some American states, including: cumulative voting, systems where votes don’t count as 1 but are proportionate to population, Borda counts (where voters rank the candidates and award progressively more points to those higher up the rankings), approval voting (where voters have as many votes as they want and can vote for as many candidates as they approve of), before going on to conclude that all voting systems have their drawbacks.

The essay ends with a typical afterthought, one-paragraph coda suggesting how the Supreme Court could end up being run by a cabal of just three judges. There are nine judges on the U.S. Supreme Court. Imagine (key word for Paulos), imagine a group of five judges agree to always discuss issues among themselves first, before the vote of the entire nine, and imagine they decide to always vote according to whatever the majority (3) decide. Then imagine that a sub-group of just three judges go away and secretly decide, that in the group of five, they will always agree. Thus they will dictate the outcome of every Supreme Court decision.

So:

1. I had no idea who Lani ‘Quota Queen’ Guinier was or, more precisely, I had to do a bit of detective work to figure it out, and still wasn’t utterly sure.

2. This is a very sketchy introduction to the issue of democratic voting systems. This is a vast subject, which Paulos skates over quickly and thinly.

Thus, in these four and a bit pages you have the characteristic Paulos experience of feeling you are wandering all over the place, not quite at random, but certainly not in a carefully planned sequential way designed to explore a topic thoroughly and reach a conclusion. You are introduced to a number of interesting ideas, with some maths formulae, but not in enough detail or at sufficient length to really understand them. And because he’s not addressing any particular newspaper report or article, there are no particular misconceptions to clear up: the essay is a brief musing, a corralling of thoughts on an interesting topic.

This scattergun approach characterises the whole book.

Psychological availability and anchoring effects

The second essay is titled Psychological availability and anchoring effects. He explains what the availability error, the anchor effect and the halo effect are. If this is the first time you’ve come across these notions, they’re powerful new ideas. But I recently reread Irrationality by Stuart Sutherland which came out three years before Paulos’s book and spends over three hundred pages investigating these and all the other cognitive biases which afflict mankind in vastly more depth than Paulos, with many more examples. Next to it, Paulos’s three-minute essay seemed sketchy and superficial.

General points

Rather than take all 50 essays to pieces, here are notes on what I actually did learn. Note that almost none of it was about maths, but general-purpose cautions about how the news media work, and how to counter its errors of logic. In fact, all of it could have come from a media studies course without any maths at all:

  • almost all ‘news’ reinforces conventional wisdom
  • because they’re so brief, almost all headlines must rely on readers’ existing assumptions and prejudices
  • almost all news stories relate something new back to similar examples from the past, even when the comparison is inappropriate, again reinforcing conventional wisdom and failing to recognise the genuinely new
  • all economic forecasts are rubbish: this is because economics (like the weather and many other aspects of everyday life) is a non-linear system. Chaos theory shows that non-linear systems are highly sensitive to even minuscule differences in starting conditions, which has been translated into pop culture as the Butterfly Effect
  • and also with ‘futurologists’: the further ahead they look, the less reliable their predictions
  • the news is deeply biased by always assuming human agency is at work in any outcome: if any disaster happens anywhere the newspapers always go searching for a culprit; in the present Brexit crisis lots of news outlets are agreeing to blame Theresa May. But often things happen at random or as an accumulation of unpredictable factors. Humans are not good at acknowledging the role of chance and randomness.

There is a tendency to look primarily for culpability and conflicts of human will rather than at the dynamics of a natural process. (p.160)

  • Hence so many newspapers endlessly playing the blame game. The Grenfell Tower disaster was, first and foremost, an accident in the literal sense of ‘an unfortunate incident that happens unexpectedly and unintentionally, typically resulting in damage or injury’ – but you won’t find anybody who doesn’t fall in with the prevailing view that someone must be to blame. There is always someone to blame. We live in a Blame Society.
  • personalising beats stats, data or probability: nothing beats ‘the power of dramatic anecdote’ among the innumerate: ‘we all tend to be unduly swayed by the dramatic, the graphic, the visceral’ (p.82)
  • if you combine human beings’ tendency to personalise everything, and to look for someone to blame, you come up with Donald Trump, who dominates every day’s news
  • so much is happening all the time, in a world with more people and incidents than ever before, in which we are bombarded with more information via more media than ever before – that it would be extraordinary if all manner or extraordinary coincidences, correspondences and correlations didn’t happen all the time
  • random events can sometimes present a surprisingly ordered appearance
  • because people imbue meaning into absolutely everything, then the huge number of coincidences and correlations are wrongfully interpreted as meaningful

Tips and advice

I was dismayed at the poor quality of many of the little warnings which each chapter ends with. Although Paulos warns against truisms (on page 54) his book is full of them.

Local is not what it used to be, and we shouldn’t be surprised at how closely we’re linked. (p.55)

In the public realm, often the best we can do is to stand by and see how events unfold. (p.125)

Chapter three warns us that predictions about complex systems (the weather, the economy, big wars) are likely to be more reliable the simpler the system they’re predicting, and the shorter period they cover. Later he says we should be sceptical about all long-term predictions by politicians, economists and generals.

It didn’t need a mathematician to tell us that.

A lot of it just sounds like a grumpy old man complaining about society going to the dogs:

Our increasingly integrated and regimented society undermines our sense of self… Meaningless juxtapositions and coincidences replace conventional narratives and contribute to our dissociation… (pp.110-111)

News reports in general, and celebrity coverage in particular, are becoming ever-more self-referential. (p.113)

We need look no further than the perennial appeal of pseudoscientific garbage, now being presented in increasingly mainstream forums… (p.145)

The fashion pages have always puzzled me. In my smugly ignorant view, they appear to be so full of fluff and nonsense as to make the astrology columns insightful by comparison. (p.173)

Another aspect of articles in the society pages or in the stories about political and entertainment figures is the suggestion that ‘everybody’ knows everybody else. (p.189)

Sometimes his liberal earnestness topples into self-help book touchy-feeliness.

Achieving personal integration and a sense of self is for the benefit of ourselves and those we’re close to. (p.112)

But just occasionally he does say something unexpected:

The attention span created by television isn’t short; it’s long, but very, very shallow. (p.27)

That struck me as an interesting insight but, as with all his interesting comments, no maths was involved. You or I could have come up with it from general observation.

Complexity horizon

The notion that the interaction of human laws, conventions, events, politics, and general information overlap and interplay at ever-increasing speeds to eventually produce situations so complex as to appear unfathomable. Individuals, and groups and societies, have limits of complexity beyond which they cannot cope, but have to stand back and watch. Reading this made me think of Brexit.

He doesn’t mention it, but a logical spin-off would be that every individual has a complexity quotient like an intelligence quotient or IQ. Everyone could take a test in which they are faced with situations of slowly increasing complexity – or presented with increasingly complex sets of information – to find out where their understanding breaks off – which would become their CQ.

Social history

The book was published in 1995 and refers back to stories current in the news in 1993 and 1994. The run of domestic political subjects he covers in the book’s second quarter powerfully support my repeated conviction that it is surprising how little some issues have changed, how little movement there has been on them, and how they have just become a settled steady part of the social landscape of our era.

Thus Paulos has essays on:

  • gender bias in hiring
  • homophobia
  • accusations of racism arising from lack of ethnic minorities in top jobs (the problem of race crops up numerous times (pp.59-62, p.118)
  • the decline in educational standards
  • the appallingly high incidence of gun deaths, especially in black and minority communities
  • the fight over abortion

I feel increasingly disconnected from contemporary politics, not because it is addressing new issues I don’t understand, but for the opposite reason: it seems to be banging on about the same issues which I found old and tiresome twenty-five years ago.

The one topic which stood out as having changed is AIDS. In Innumeracy and in this book he mentions the prevalence or infection rates of AIDS and is obviously responding to numerous news stories which, he takes it for granted, report it in scary and alarmist terms. Reading these repeated references to AIDS made me realise how completely and utterly it has fallen off the news radar in the past decade or so.

In the section about political correctness he makes several good anti-PC points:

  • democracy is about individuals, the notion that everyone votes according to their conscience and best judgement; as soon as you start making it about groups (Muslims, blacks, women, gays) you start undermining democracy
  • racism and sexism and homophobia are common enough already without making them the standard go-to explanations for social phenomena which often have more complex causes; continually attributing all aspects of society to just a handful of inflammatory issues, keeps the issues inflammatory
  • members of groups often vie with each other to assert their loyalty, to proclaim their commitment to the party line and this suggests a powerful idea: that the more opinions are expressed, the more extreme these opinions will tend to become. This is a very relevant idea to our times when the ubiquity of social media has a) brought about a wonderful spirit of harmony and consensus, or b) divided society into evermore polarised and angry groupings

Something bad is coming

I learned to fear several phrases which indicate that a long, possibly incomprehensible and frivolously hypothetical example is about to appear:

‘Imagine…’

Imagine flipping a penny one thousand times in succession and obtaining some sequence of heads and tails… (p.75)

Imagine a supercomputer, the Delphic-Cray 1A, into which has been programmed the most complete and up-to-date scientific knowledge, the initial condition of all particles, and sophisticated mathematical techniques and formulas. Assume further that… Let’s assume for argument’s sake that… (p.115)

Imagine if a computer were able to generate a random sequence S more complex than itself. (p.124)

Imagine the toast moistened, folded, and compressed into a cubical piece of white dough… (p.174)

Imagine a factory that produces, say, diet food. Let’s suppose that it is run by a sadistic nutritionist… (p.179)

‘Assume that…’

Let’s assume that each of these sequences is a billion bits long… (p.121)

Assume the earth’s oceans contain pristinely pure water… (p.141)

Assume that there are three competing healthcare proposals before the senate… (p.155)

Assume that the probability of your winning the coin flip, thereby obtaining one point, is 25 percent. (p.177)

Assume that these packages come off the assembly line in random order and are packed in boxes of thirty-six. (p.179)

Jokes and Yanks

All the examples are taken from American politics (President Clinton), sports (baseball) and wars (Vietnam, First Gulf War) and from precisely 25 years ago (on page 77, he says he is writing in March 1994), both of which emphasise the sense of disconnect and irrelevance with a British reader in 2019.

As my kids know, I love corny, bad old jokes. But not as bad as the ones the book is littered with:

And then there was the man who answered a matchmaking company’s computerised personals ad in the paper. He expressed his desire for a partner who enjoys company, is comfortable in formal wear, likes winter sports, and is very short. The company matched him with a penguin. (pp.43-44)

The moronic inferno and the liberal fallacy

The net effect of reading this book carefully is something that the average person on the street knew long ago: don’t believe anything you read in the papers.

And especially don’t believe any story in a newspaper which involves numbers, statistics, percentages, data or probabilities. It will always be wrong.

More broadly his book simply fails to take account of the fact that most people are stupid and can’t think straight, even very, very educated people. All the bankers whose collective efforts brought about the 2008 crash. All the diplomats, strategists and military authorities who supported the Iraq War. All the well-meaning liberals who supported the Arab Spring in Egypt and Libya and Syria. Everyone who voted Trump. Everyone who voted Brexit.

Most books of this genre predicate readers who are white, university-educated, liberal middle class and interested in news and current affairs, the arts etc and – in my opinion – grotesquely over-estimate both their value and their relevance to the rest of the population. Because this section of the population – the liberal, university-educated elite – is demonstrably in a minority.

Over half of Americans believe in ghosts, and a similar number believes in alien abductions. A third of Americans believe the earth is flat, and that the theory of evolution is a lie. About a fifth of British adults are functionally illiterate and innumerate. This is what Saul Bellow referred to as ‘the moronic inferno’.

On a recent Radio 4 documentary about Brexit, one contributor who worked in David Cameron’s Number Ten commented that he and colleagues went out to do focus groups around the country to ask people whether we should leave the EU and that most people didn’t know what they were talking about. Many people they spoke to had never heard of the European Union.

On page 175 he says the purpose of reading a newspaper is to stretch the mind, to help us envision distant events, different people and unusual situations, and broaden our mental landscape.

Is that really why he thinks people read newspapers? As opposed to checking the sports results, catching up with celebrity gossip, checking what’s happening in the soaps, reading interviews with movie and pop stars, looking at fashion spreads, reading about health fads and, if you’re one of the minority who bother with political news, having all your prejudices about how wicked and stupid the government, the poor, the rich or foreigners etc are, and despising everyone who disagrees with you (Guardian readers hating Daily Mail readers; Daily Mail readers hating Guardian readers; Times readers feeling smugly superior to both).

This is a fairly entertaining, if very dated, book – although all the genuinely useful bits are generalisations about human nature which could have come from any media studies course.

But if it was intended as any kind of attempt to tackle the illogical thinking and profound innumeracy of Western societies, it is pissing in the wind. The problem is vastly bigger than this chatty, scattergun and occasionally impenetrable book can hope to scratch. On page 165 he says that a proper understanding of mathematics is vital to the creation of ‘an informed and effective citizenry’.

‘An informed and effective citizenry’?


Related links

Reviews of other science books

Cosmology

Environment / human impact

Genetics

  • The Double Helix by James Watson (1968)

Maths

Particle physics

Psychology

  • Irrationality: The Enemy Within by Stuart Sutherland (1992)

Innumeracy by John Allen Paulos (1988)

Our innate desire for meaning and pattern can lead us astray… (p.81)

Giving due weight to the fortuitous nature of the world is, I think, a mark of maturity and balance. (p.133)

John Allen Paulos is an American professor of mathematics who won fame beyond his academic milieu with the publication of this short (134-page) but devastating book thirty years ago, the first of a series of books popularising mathematics in a range of spheres from playing the stock market to humour.

As Paulos explains in the introduction, the world is full of humanities graduates who blow a fuse if you misuse ‘infer’ and ‘imply’, or end a sentence with a dangling participle, but are quite happy to believe and repeat the most hair-raising errors in maths, statistics and probability.

The aim of this book was:

  • to lay out examples of classic maths howlers and correct them
  • to teach readers to be more alert when maths, stats and data need to be used
  • and to provide basic rules in order to understand when innumerate journalists, politicians, tax advisors and other crooks are trying to pull the wool over your eyes, or are just plain wrong

There are five chapters:

  1. Examples and principles
  2. Probability and coincidence
  3. Pseudoscience
  4. Whence innumeracy
  5. Statistics, trade-offs and society

Many common themes emerge:

Don’t personalise, numeratise

One contention of this book is that innumerate people characteristically have a strong tendency to personalise – to be misled by their own experiences, or by the media’s focus on individuals and drama… (p.1)

Powers

The first chapter uses lots of staggering statistics to get the reader used to very big and very small numbers, and how to compute them.

1 million seconds is 11 and a half days. 1 billion seconds is 32 years.

He suggests you come up with personal examples of numbers for each power up to 12 or 13 i.e. meaningful embodiments of thousands, tens of thousands, hundreds of thousands and so on to help you remember and contextualise them in a hurry.

A snail moves at 0.005 miles an hour, Concorde at 2,000 miles per hour. Escape velocity from earth is about 7 miles per second, or 25,000 miles per hour. The mass of the Earth is 5.98 x 1024 kg

Early on he tells us to get used to the nomenclature of ‘powers’ – using 10 to the power 3 or 10³ instead of 1,000, or 10 to negative powers to express numbers below 1. (In fact, right at this early stage I found myself stumbling because one thousand means more to me that 10³ and a thousandth means more than more 10-3 but if you keep at it, it is a trick you can acquire quite quickly.)

The additive principle

He introduces us to basic ideas like the additive principle (aka the rule of sum), which states that if some choice can be made in M different ways and some subsequent choice can be made in N different ways, then there are M x N different ways these choices can be made in succession – which can be applied to combinations of multiple items of clothes, combinations of dishes on a menu, and so on.

Thus the number of results you get from rolling a die is 6. If you roll two dice, you can now get 6 x 6 = 36 possible numbers. Three numbers = 216. If you want to exclude the number you get on the first dice from the second one, the chances of rolling two different numbers on two dice is 6 x 5, of rolling different numbers on three dice is 6 x 5 x 4, and so on.

Thus: Baskin Robbins advertises 31 different flavours of ice cream. Say you want a triple scoop cone. If you’re happy to have any combination of flavours, including where any 2 or 3 flavours are the same – that’s 31 x 31 x 31 = 29,791. But if you ask how many combinations of flavours there are, without a repetition of the same flavour in any of the cones – that is 31 x 30 x 29 = 26,970 ways of combining.

Probability

I struggled with even the basics of probability. I understand a 1 in five chance of something happening, reasonably understand a 20% chance of something happening, but struggled when probability was expressed as a decimal number e.g. 0.2 as a way of writing a 20 percent or 1 in 5 chance.

With the result that he lost me on page 16 on or about the place where he explained the following example.

Apparently a noted 17th century gambler asked the famous mathematician Pascal which is more likely to occur: obtaining at least one 6 in four rolls of a single die, or obtaining at least one 12 in twenty four rolls of a pair of dice. Here’s the solution:

Since 5/6 is the probability of not rolling a 6 on a single roll of a die, (5/6)is the probability of not rolling a 6 in four rolls of the die. Subtracting this number from 1 gives us the probability that this latter event (no 6s) doesn’t occur; in other words, of there being at least one 6 rolled in four tries: 1 – (5/6)= .52. Likewise, the probability of rolling at least one 12 in twenty-four rolls of a pair of dice is seen to be 1 – (35/36)24 = .49.

a) He loses me in the second sentence which I’ve read half a dozen times and still don’t understand – it’s where he says the chances that this latter event doesn’t occur: something about the phrasing there, about the double negative, loses me completely, with the result that b) I have no idea whether .52 is more likely or less likely than .49.

He goes on to give another example: if 20% of drinks dispensed by a vending machine overflow their cups, what is the probability that exactly three of the next ten will overflow?

The probability that the first three drinks overflow and the next seven do not is (.2)x (.8)7. But there are many different ways for exactly three of the ten cups to overflow, each way having probability (.2)x (.8)7. It may be that only the last three cups overflow, or only the fourth, fifth and ninth cups, and so on. Thus, since there are altogether (10 x 9 x 8) / (3 x 2 x 1) = 120 ways for us to pick three out of the ten cups, the probability of some collection of exactly three cups overflowing is 120 x (.2)x (.8)7.

I didn’t understand the need for the (10 x 9 x 8) / (3 x 2 x 1) equation – I didn’t understand what it was doing, and so didn’t understand what it was measuring, and so didn’t understand the final equation. I didn’t really have a clue what was going on.

In fact, by page 20, he’d done such a good job of bamboozling me with examples like this that I sadly concluded that I must be innumerate.

More than that, I appear to have ‘maths anxiety’ because I began to feel physically unwell as I read that problem paragraph again and again and again and didn’t understand it. I began to feel a tightening of my chest and a choking sensation in my throat. Rereading it now is making it feel like someone is trying to strangle me.

Maybe people don’t like maths because being forced to confront something you don’t understand, but which everyone around you is saying is easy-peasy, makes you feel ill.

2. Probability and coincidence

Having more or less given up on trying to understand Paulos’s maths demonstrations in the first twenty pages, I can at least latch on to his verbal explanations of what he’s driving at, in sentences like these:

A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence. (p.22)

It would be very unlikely for unlikely events not to occur. (p.24)

There is a strong general tendency to filter out the bad and the failed and to focus on the good and the successful. (p.29)

Belief in the… significance of coincidences is a psychological remnant of our past. It constitutes a kind of psychological illusion to which innumerate people are particularly prone. (p.82)

Slot machines light up and make a racket when people win, there is unnoticed silence for all the failures. Big winners on the lottery are widely publicised, whereas every one of the tens of millions of failures is not.

One result is ‘Golden Age’ thinking when people denigrate today’s sports or arts or political figures, by comparison with one or two super-notable figures from the vast past, Churchill or Shakespeare or Michelangelo, obviously neglecting the fact that there were millions of also-rans and losers in their time as well as ours.

The Expected value of a quality is the average of its values weighted according to their probabilities. I understood these words but I didn’t understand any of the five examples he gave.

The likelihood of probability In many situations, improbability is to be expected. The probability of being dealt a particular hand of 13 cards in bridge is less than 1 in 600 billion. And yet it happens every time someone is dealt a hand in bridge. The improbable can happen. In fact it happens all the time.

The gambler’s fallacy The belief that, because a tossed coin has come up tails for a number of tosses in a row, it becomes steadily more likely that the next toss will be a head.

3. Pseudoscience

Paulos rips into Freudianism and Marxism for the way they can explain away any result counter to their ‘theories’. The patient gets better due to therapy: therapy works. The patient doesn’t get better during therapy, well the patient was resisting, projecting their neuroses on the therapist, any of hundreds of excuses.

But this is just warming up before he rips into a real bugbear of  his, the wrong-headedness of Parapsychology, the Paranormal, Predictive dreams, Astrology, UFOs, Pseudoscience and so on.

As with predictive dreams, winning the lottery or miracle cures, many of these practices continue to flourish because it’s the handful of successes which stand out and grab our attention and not the thousands of negatives.

Probability

As Paulos steams on with examples from tossing coins, rolling dice, playing roulette, or poker, or blackjack, I realise all of them are to do with probability or conditional probability, none of which I understand.

This is why I have never gambled on anything, and can’t play poker. When he explains precisely how accumulating probabilities can help you win at blackjack in a casino, I switch off. I’ve never been to a casino. I don’t play blackjack. I have no intention of ever playing blackjack.

When he says that probability theory began with gambling problems in the seventeenth century, I think, well since I don’t gamble at all, on anything, maybe that’s why so much of this book is gibberish to me.

Medical testing and screening

Apart from gambling the two most ‘real world’ areas where probability is important appear to be medicine and risk and safety assessment. Here’s an extended example he gives of how even doctors make mistakes in the odds.

Assume there is a test for cancer which is 98% accurate i.e. if someone has cancer, the test will be positive 98 percent of the time, and if one doesn’t have it, the test will be negative 98 percent of the time. Assume further that .5 percent – one out of two hundred people – actually have cancer. Now imagine that you’ve taken the test and that your doctor sombrely informs you that you have tested positive. How depressed should you be? The surprising answer is that you should be cautiously optimistic. To find out why, let’s look at the conditional probability of your having cancer, given that you’ve tested positive.

Imagine that 10,000 tests for cancer are administered. Of these, how many are positive? On the average, 50 of these 10,000 people (.5 percent of 10,000) will have cancer, and, so, since 98 percent of them will test positive, we will have 49 positive tests. Of the 9,950 cancerless people, 2 percent of them will test positive, for a total of 199 positive tests (.02 x 9,950 = 199). Thus, of the total of 248 positive tests (199 + 49 = 248), most (199) are false positives, and so the conditional probability of having cancer given that one tests positive is only 49/248, or about 20 percent! (p.64)

I struggled to understand this explanation. I read it four or five times, controlling my sense of panic and did, eventually, I think, follow the argumen.

However, worse in a way, when I think I did finally understand it, I realised I just didn’t care. It’s not just that the examples he gives are hard to follow. It’s that they’re hard to care about.

Whereas his descriptions of human psychology and cognitive errors in human thinking are crystal clear and easy to assimilate:

If we have no direct evidence of theoretical support for a story, we find that detail and vividness vary inversely with likelihood; the more vivid details there are to a story, the less likely the story is to be true. (p.84)

4. Whence innumeracy?

It came as a vast relief when Paulos stopped trying to explain probability and switched to a long chapter puzzling over why innumeracy is so widespread in society, which kicks off by criticising the poor level of teaching of maths in school and university.

This was like the kind of hand-wringing newspaper article you can read any day of the week in a newspaper or online, and so felt reassuringly familiar and easy to assimilate. I stopped feeling so panic-stricken.

This puzzling over the disappointing level of innumeracy goes on for quite a while. Eventually it ends with a digression about what appears to be a pet idea of his: the notion of introducing a safety index for activities and illnesses.

Paulos’s suggestion is that his safety index would be on a logarithmic scale, like the Richter Scale – so straightaway he has to explain what a logarithm is: The logarithm for 100 is 2 because 100 is 102, the logarithm for 1,000 is 3 because 1,000 is 103. I’m with him so far, as he goes on to explain that the logarithm of 700 i.e. between 2 (100) and 3 (1,000) is 2.8. Since 1 in 5,300 Americans die in a car crash each year, the safety index for driving would be 3.7, the logarithm of 5,300. And so on with numerous more examples, whose relative risks or dangers he reduces to figures like 4.3 and 7.1.

I did understand his aim and the maths of this. I just thought it was bonkers:

1. What is the point of introducing a universal index which you would have to explain every time anyone wanted to use it? Either it is designed to be usable by the widest possible number of citizens; or it is a neat exercise on maths to please other mathematicians and statisticians.

2. And here’s the bigger objection – What Paulos, like most of the university-educated, white, liberal intellectuals I read in papers, magazines and books, fails to take into account is that a large proportion of the population is thick.

Up to a fifth of the adult population of the UK is functionally innumerate, that means they don’t know what a ‘25% off’ sign means on a shop window. For me an actual social catastrophe being brought about by this attitude is the introduction of Universal Credit by the Conservative government which, from top to bottom, is designed by middle-class, highly educated people who’ve all got internet accounts and countless apps on their smartphones, and who have shown a breath-taking ignorance about what life is like for the poor, sick, disabled, illiterate and innumerate people who are precisely the people the system is targeted at.

Same with Paulos’s scheme. Smoking is one of the most dangerous and stupid things which any human can do. Packs of cigarettes have for years, now, carried pictures of disgusting cancerous growths and the words SMOKING KILLS. And yet despite this, about a fifth of adults, getting on for 10 million people, still smoke. 🙂

Do you really think that introducing a system using ornate logarithms will get people to make rational assessments of the risks of common activities and habits?

Paulos then goes on to complicate the idea by suggesting that, since the media is always more interested in danger than safety, maybe it would be more effective, instead of creating a safety index, to create a danger index.

You would do this by

  1. working out the risk of an activity (i.e. number of deaths or accidents per person doing the activity)
  2. converting that into a logarithmic value (just to make sure than nobody understands it) and then
  3. subtracting the logarithmic value of the safety index from 10, in order to create a danger index

He goes on to say that driving a car and smoking would have ‘danger indices’ of 3.7 and 2.9, respectively. The trouble was that by this point I had completely ceased to understand what he’s saying. I felt like I’ve stepped off the edge of a tall building into thin air. I began to have that familiar choking sensation, as if someone was squeezing my chest. Maths anxiety.

Under this system being kidnapped would have a safety index of 6.7. Playing Russian roulette once a year would have a safety index of 0.8.

It is symptomatic of the uselessness of the whole idea that Paulos has to remind you what the values mean (‘Remember that the bigger the number, the smaller the risk.’ Really? You expect people to run with this idea?)

Having completed the danger index idea, Paulos returns to his extended lament on why people don’t like maths. He gives a long list of reasons why he thinks people are so innumerate a condition which is, for him, a puzzling mystery.

For me this lament is a classic example of what you could call intellectual out-of-touchness. He is genuinely puzzled why so many of his fellow citizens are innumerate, can’t calculate simple odds and fall for all sorts of paranormal, astrology, snake-oil blether.

He proposes typically academic, university-level explanations for this phenomenon – such as that people find maths too cold and analytical and worry that it prevents them thinking about the big philosophical questions in life. He worries that maths has an image problem.

In other words, he fails to consider the much more obvious explanation that maths, probability and numeracy in general might be a combination of fanciful, irrelevant and deeply, deeply boring.

I use the word ‘fanciful’ deliberately. When he writes that the probability of drawing two aces in succession from a pack of cards is not (4/52 x 4/52) but (4/52 x 3/51) I do actually understand the distinction he’s making (having drawn one ace there are only 3 left and only 52 cards left) – I just couldn’t care less. I really couldn’t care less.

Or take this paragraph:

Several years ago Pete Rose set a National League record by hitting safely in forty-four consecutive games. If we assume for the sake of simplicity that he batted .300 (30 percent of the time he got a hit, 70 percent of the time he didn’t) and that he came to bat four times a game, the chances of his not getting a hit in any given game were, assuming independence, (.7)4 – .24… [at this point Paulos has to explain what ‘independence’ means in a baseball context: I couldn’t care less]… So the probability he would get at least one hit in any game was 1-.24 = .76. Thus, the chances of him getting a hit in any given sequence of forty-four consecutive games were (.76)44 = .0000057, a tiny probability indeed. (p.44)

I did, in fact, understand the maths and the working out in this example. I just don’t care about the problem or the result.

For me this is a – maybe the – major flaw of this book. This is that in the blurbs on the front and back, in the introduction and all the way through the text, Paulos goes on and on about how we as a society need to be mathematically numerate because maths (and particularly probability) impinges on so many areas of our life.

But when he tries to show this – when he gets the opportunity to show us what all these areas of our lives actually are – he completely fails.

Almost all of the examples in the book are not taken from everyday life, they are remote and abstruse problems of gambling or sports statistics.

  • which is more likely: obtaining at least one 6 in four rolls of a single die, or obtaining at least one 12 in twenty four rolls of a pair of dice?
  • if 20% of drinks dispensed by a vending machine overflow their cups, what is the probability that exactly three of the next ten will overflow?
  • Assume there is a test for cancer which is 98% accurate i.e. if someone has cancer, the test will be positive 98 percent of the time, and if one doesn’t have it, the test will be negative 98 percent of the time. Assume further that .5 percent – one out of two hundred people – actually have cancer. Now imagine that you’ve taken the test and that your doctor sombrely informs you that you have tested positive. How depressed should you be?
  • What are the odds on Pete Rose getting a hit in a sequence of forty-four games?

Are these the kinds of problems you are going to encounter today? Or tomorrow? Or ever?

No. The longer the book went on, the more I realised just how little a role maths plays in my everyday life. In fact more or less the only role maths plays in my life is looking at the prices in supermarkets, where I am attracted to goods which have a temporary reduction on them. But I do that because they’re labels are coloured red, not because I calculate the savings. Being aware of the time, so I know when to do household chores or be somewhere punctually. Those are the only times I used numbers today.

5. Statistics, trade-offs and society

This feeling that the abstruseness of the examples utterly contradicts the bold claims that reading the book will help us with everyday experiences was confirmed in the final chapter, which begins with the following example.

Imagine four dice, A, B, C and D, strangely numbered as follows: A has 4 on four faces and 0 on two faces; B has 3s on all six faces; C has four faces with 2 and two faces with 6; and D has 5 on three faces and 1 on three faces…

I struggled to the end of this sentence and just thought: ‘No, no more, I don’t have to make myself feel sick and unhappy any more’ – and skipped the couple of pages detailing the fascinating and unexpected results you can get from rolling such a collection of dice.

This chapter goes on to a passage about the Prisoner’s Dilemma, a well-known problem in logic, which I have read about and instantly forgotten scores of times over the years.

Paulos gives us three or four variations on the idea, including:

  • Imagine you are locked up in prison by a philanthropist with 20 other people.

Or:

  • Imagine you are locked in a dungeon by a sadist with 20 other people.

Or:

  • Imagine you are one of two drug traffickers making a quick transaction on a street corner and forced to make a quick decision.

Or:

  • Imagine you are locked in a prison cell, and another prisoner is locked in an identical cell down the corridor.

Well, I’m not any of these things, I’m never likely to be, and I am not really interested in these fanciful speculations.

Moreover, I am well into middle age, have travelled round the world, had all sorts of jobs in companies small, large and enormous – and I am not aware of having ever been in any situation which remotely resembled any variation of the Prisoner’s Dilemma I’ve ever heard of.

In other words, to me, it is another one of the endless pile of games and puzzles which logicians and mathematicians love to spend all day playing but which have absolutely no impact whatsoever on any aspect of my life.

Pretty much all of his examples conclusively prove how remote mathematical problems and probabilistic calculation is from the everyday lives you and I lead. When he asks:

How many people would there have to be in a group in order for the probability to be half that at least two people in it have the same birthday? (p.23)

Imagine a factory which produces small batteries for toys, and assume the factory is run by a sadistic engineer… (p.117)

It dawns on me that my problem might not be that I’m innumerate, so much as I’m just uninterested in trivial or frivolous mental exercises.

Someone offers you a choice of two envelopes and tells you one has twice as much money in it as the other. (p.127)

Flip a coin continuously until a tail appears for the first time. If this doesn’t happen until the twentieth (or later) flip, you win $1 billion. If the first tail occurs before the twentieth flip, you pay $100. Would you play? (p.128)

No. I’d go and read an interesting book.

Thoughts

If Innumeracy: Mathematical Illiteracy and Its Consequences is meant to make its readers more numerate, it failed with me.

This is for a number of reasons:

  1. crucially – because he doesn’t explain maths very well; or, the way he explained probability had lost me by about page 16 – in other words, if this is meant to be a primer for innumerate people it’s a fail
  2. because the longer it goes on, the more convinced I became that I rarely use maths, arithmetic and probability in my day today life: whole days go by when I don’t do a single sum, and so lost all motivation to submit myself to the brain-hurting ordeal of trying to understand his examples

3. Also because the structure and presentation of the book is a mess. The book meanders through a fog of jokes, anecdotes and maths trivia, baseball stories and gossip about American politicians – before suddenly unleashing a fundamental aspect of probability theory on the unwary reader.

I’d have preferred the book to have had a clear, didactic structure, with an introduction and chapter headings explaining just what he was going to do, an explanation, say, of how he was going to take us through some basic concepts of probability one step at a time.

And then for the concepts to have been laid out very clearly and explained very clearly, from a number of angles, giving a variety of different examples until he and we were absolutely confident we’d got it – before we moved on to the next level of complexity.

The book is nothing like this. Instead it sacrifices any attempt at logical sequencing or clarity for anecdotes about Elvis Presley or UFOs, for digressions about Biblical numerology, the silliness of astrology, the long and bewildering digression about introducing a safety index for activities (summarised above), or prolonged analyses of baseball or basketball statistics. Oh, and a steady drizzle of terrible jokes.

Which two sports have face-offs?
Ice hockey and leper boxing.

Half way through the book, Paulos tells us that he struggles to write long texts (‘I have a difficult time writing at extended length about anything’, p.88), and I think it really shows.

It certainly explains why:

  • the blizzard of problems in coin tossing and dice rolling stopped without any warning, as he switched tone copletely, giving us first a long chapter about all the crazy irrational beliefs people hold, and then another chapter listing all the reasons why society is innumerate
  • the last ten pages of the book give up the attempt of trying to be a coherent narrative and disintegrate into a bunch of miscellaneous odds and ends he couldn’t find a place for in the main body of the text

Also, I found that the book was not about numeracy in the broadest sense, but mostly about probability. Again and again he reverted to examples of tossing coins and rolling dice. One enduring effect of reading this book is going to be that, the next time I read a description of someone tossing a coin or rolling a die, I’m just going to skip right over the passage, knowing that if I read it I’ll either be bored to death (if I understand it) or have an unpleasant panic attack (if I don’t).

In fact in the coda at the end of the book Paulos explicitly says it has mostly been about probability – God, I wish he’d explained that at the beginning.

Right at the very, very end he briefly lists key aspects of probability theory which he claims to have explained in the book – but he hasn’t, some of them are only briefly referred to with no explanation at all, including: statistical tests and confidence intervals, cause and correlation, conditional probability, independence, the multiplication principle, the notion of expected value and of probability distribution.

These are now names I have at least read about, but they are all concepts I am nowhere near understanding, and light years away from being able to use in practical life.

Innumeracy – or illogicality?

Also there was an odd disconnect between the broadly psychological and philosophical prose explanations of what makes people so irrational, and the incredibly narrow scope of the coin-tossing, baseball-scoring examples.

What I’m driving at is that, in the long central chapter on Pseudoscience, when he stopped to explain what makes people so credulous, so gullible, he didn’t really use any mathematical examples to disprove Freudianism or astrology or so on: he had to appeal to broad principles of psychology, such as:

  • people are drawn to notable exceptions, instead of considering the entire field of entities i.e.
  • people filter out the bad and the failed and focus on the good and the successful
  • people seize hold of the first available explanation, instead of considering every single possible permutation
  • people humanise and personalise events (‘bloody weather, bloody buses’)
  • people over-value coincidences

My point is that there is a fundamental conceptual confusion in the book which is revealed in the long chapter about pseudoscience which is that his complaint is not, deep down, right at bottom, that people are innumerate; it is that people are hopelessly irrational and illogical.

Now this subject – the fundamental ways in which people are irrational and illogical – is dealt with much better, at much greater length, in a much more thorough, structured and comprehensible way in Stuart Sutherland’s great book, Irrationality, which I’ll be reviewing and summarising later this week.

Innumeracy amounts to random scratches on the surface of the vast iceberg which is the deep human inability to think logically.

Conclusion

In summary, for me at any rate, this was not a good book – badly structured, meandering in direction, unable to explain even basic concepts but packed with digressions, hobby horses and cul-de-sacs, unsure of its real purpose, stopping for a long rant against pseudosciences and an even longer lament on why maths is taught so badly  – it’s a weird curate’s egg of a text.

Its one positive effect was to make me want to track down and read a good book about probability.


Related links

Reviews of other science books

Cosmology

Environment / human impact

Genetics

  • The Double Helix by James Watson (1968)

Maths

Particle physics

Psychology

  • Irrationality: The Enemy Within by Stuart Sutherland (1992)

Dorothea Tanning @ Tate Modern

This is the first large-scale exhibition of Dorothea Tanning’s work to be held in the UK for 25 years.

It brings together 100 pieces from her seven-decade-long career (she lived to be an astonishing 101 years old, 1910 – 2012) across a range of media, including oil paintings, pencil drawings, ‘soft’ sculptures, lithographs, a massive installation, and a film about her. It is as comprehensive a survey of her artistic achievement as you could wish for.

Birthday (1942) by Dorothea Tanning. Philadelphia Museum of Art © DACS 2019

Birthday (1942) by Dorothea Tanning. Philadelphia Museum of Art © DACS 2019

Tanning was born in provincial America (Galesburg, Illinois) in 1910. As soon as she was able to, she moved to New York, where she soon afterwards saw the famous Surrealism exhibition of 1936. It was a coup de foudre which changed her life. She began painting in a boldly Surrealist style and in 1939 set off to Paris to meet the leaders of the movement.

Unfortunately, Hitler had other plans, and the advent of the Second World War saw her coming straight back to New York but, happily, so did half the Surrealist artists, fleeing the Nazis. These fleeing artists included one of the leading Surrealists, Max Ernst (b.1891), who she fell in love with and married in 1946.

Surrealist paintings

The exhibition features a generous selection of the Surrealist paintings she made from the mid-1930s to the end of the 40s.

Tanning said she wanted to depict ‘unknown but knowable states’ and the pictures show humans in strange postures, or morphing into inanimate objects, or bursting into flames, or standing in deserts littered with incongruous objects, or standing in bedrooms among strange and Gothic figures, or staring into sunflowers which are changing into mirrors, or standing in front of doors opening onto other doors.

Some of these are really powerful images, although many felt to me like they were channelling existing Surrealist artists, especially Salvador Dali, the man who had crystallised the Surrealist ‘look’ in the late 1920s, introducing an immaculate finish to his oil paintings which depicted random objects or events, melting watches, elephants on stilts, melting limbs propped up by crutches and so on.

In other works you can detect the influence of Giorgio de Chirico (b.1888) with his mysterious abandoned Italian squares and brooding neo-classical architecture. In some of them you can see the Magritte who painted a man in a bowler hat with an apple in front of his face.

For example the blue skyscape at the bottom of this Surreal image of a chess game, and its startling optical illusion it gives that the rest of the painting has been draped in front of a landscape, reminds me of the deceptively simple blue skies of Magritte paintings.

Endgame (1944) by Dorothea Tanning. Courtesy Gertrud V. Parker © DACS 2019

Endgame (1944) by Dorothea Tanning. Courtesy Gertrud V. Parker © DACS 2019

But all that said, many of Tanning’s paintings do have a unique and distinctive feeling.

The recurrence of women in the paintings is nothing special in itself, since the Surrealists as a movement thought of the female as being more instinctive, irrational, closer to the unconscious and an all-purpose muse figure – so Tanning’s depictions of women with bared breasts (or herself with bared breasts) don’t cover any new ground.

But I felt that her depictions of girls do capture something unique. Pre-pubescent girls are not such a common motif in male artists, who tend, all too often, to depict shapely, nude and nubile women.

I think Tanning’s depictions of pre-pubescent girls and the depiction of women not as sex objects but as individuals – I’m struggling to put this into words, but her depiction of girls and women – did have a different and distinctive feeling, capturing something genuinely strange about a girl’s experience of the world. I thought of Angela Carter’s retelling of fairy tales from a girl’s point of view.

Eine Kleine Nachtmusik (1943) by Dorothea Tanning. Tate © DACS 2019

Eine Kleine Nachtmusik (1943) by Dorothea Tanning. Tate © DACS 2019

Prismatic style

In the 1950s Tanning and Ernst moved to Paris and this marked a seismic, comprehensive reinvention of her visual language. It is signalled in the exhibition when you walk into the next room and are confronted with the massive and staggering painting, Gate 84.

Installation photograph of Dorothea Tanning at Tate Modern, 2019

Admittedly this is from a lot later, 1984, but Gate 84 captures the massive change in style which happened in the 1950s. It depicts two girls drawn in vivid graphic style with the use of strong border lines, emerging from a background of violent flaming yellow. Dividing the painting right down the middle is part of an actual door and door jamb which has been embedded into the canvas and sticks out of the picture plane. Both the girls are wearing thigh-length dresses, the one on the left is performing an acrobatic leap so as to hit the door with outstretched hand and foot; the one on the right is more lazily sitting, with her right leg outstretched, her foot pressed flat against the door as if keeping it shut.

I visited with my wife who said this reminded her vividly of the fights she was always having with her own sister, when they were kids. And she got talking to another middle aged woman standing in front of it, who agreed that it reminded her of her childhood with two sisters, rampaging and fighting. A very female sensibility capturing something vivid and dynamic about girls’ experiences of the world.

What struck me more than anything was the chunky realism of the legs, the muscular thighs and the weight and tension in the calves and feet. The entire depiction of the human body is utterly utterly different from the rather attenuated, pallid, doll-like figures in the Surrealist paintings.

And this proved to be true of all her paintings from this point onwards. They become a) much larger and b) much much more abstract, great billowing shapes.

And yet, paradoxically, the graphic element becomes clearer. Faces and bodies and fragments of bodies appear as if out of a rampaging fog and, when they do, are often painted with strict anatomical accuracy, or even a kind of super-accuracy, a monumental accuracy. The arms and thighs and bottoms reminded me of Michelangelo.

It is like the work of a completely different artist.

Dogs of Cythera (1963) by Dorothea Tanning. The Destina Foundation, New York © DACS 2019

Dogs of Cythera (1963) by Dorothea Tanning. The Destina Foundation, New York © DACS 2019

In Dogs of Cythera, at bottom left you can make out what might be an arm going round a woman’s breast, in the centre something like the top of a shaved black skull, at bottom right another arm bent at the elbow, leading up to a hand with splayed fingers.

So there are people, or people-like objects in the painting, but quite clearly something radical and massive is going on that utterly eclipses them, or only uses them as raw material in a bigger and bewildering process.

To quote the wall label, these works mark:

a more abstracted ‘prismatic’ style of painting, and her brushwork and compositions became much looser. Where her earlier work used precise realism to present fantastical scenes, in these paintings it is colour and light that bring imaginary worlds into being. The possibilities of her medium became more important to her.

‘In looking at how many ways paint can flow onto canvas, I began to long for letting it have more freedom.’

In Tanning’s Surreal works the human body, mostly female, is often stylised, thin, elongated – or given an eerie, science fiction otherworldliness, as in this disconcerting girl being covered in flowers. The subject is set in a recognisable space with perspective to create depth and often to draw the eye to some Surrealistically disturbing detail, such as the fireplace which opens onto clear blue sky.

The Magic Flower Game (1941) by Dorothea Tanning. Private collection, South Dakota © DACS 2019

The Magic Flower Game (1941) by Dorothea Tanning. Private collection, South Dakota © DACS 2019

In this later, ‘prismatic’ style, there is no depth or perspective, there is only a great storm of cloud happening right on the surface of the canvas from which parts of one or more bodies threaten to temporarily emerge into focus before disappearing again into the tumult. The paintings vary quite a lot in feel, some lighter and airier, others really dark and stormy – but all in the same immediately recognisable style.

Inutile (1969) by Dorothea Tanning. The Destina Foundation, New York © DACS 2019

Inutile (1969) by Dorothea Tanning. The Destina Foundation, New York © DACS 2019

There are over twenty paintings in this maner, it looks like most of her output after the mid-1950s was like this, and I loved them.

Many of the Surrealist works are wonderful, inventive and mysterious but I couldn’t help the nagging through that she was working – often to marvellous effect – but in someone else’s idiom. With the ‘prismatic’ paintings it seemed to me Tanning became completely free. I loved the tremendous sense of energy they convey, the sense of muscular, lithe bodies struggling, fighting, embracing, tumbling through clouds – as different as could be from the absolutely static, dream-like, frozen tableaux of the Surrealist works.

They reminded me of the last stanza of Yeats’s poem, Near The Delphic Oracle.

Slim adolescence that a nymph has stripped,
Peleus on Thetis stares.
Her limbs are delicate as an eyelid,
Love has blinded him with tears;
But Thetis’ belly listens.
Down the mountain walls
From where pan’s cavern is
Intolerable music falls.
Foul goat-head, brutal arm appear,
Belly, shoulder, bum,
Flash fishlike; nymphs and satyrs
Copulate in the foam.

Bellies, shoulders and bums all appear momentarily our of the seething fog of these strange, visionary paintings. Some are sensual, even sexy. And in some the human figure entirely emerges to be given a surprisingly traditional and realistic treatment, like this one, Tango Lives, from 1977, which seemed to me to be channelling Degas’s studies of ballet dancers on a stage, strongly lit from below.

Tango Lives (1977) by Dorothea Tanning

Tango Lives (1977) by Dorothea Tanning

But many others convey bewilderment and confusion, and some of them seem genuinely dark and terrifying, visions of a weird hell where monsters are eating each other. More than one of the dark ones reminded me of Goya’s Saturn devouring his children in a swirling fog.

Soft fabric sculptures

And then – something completely different, again.

In the 14-minute film about her – Insomnia – which runs in the final room, Tanning herself explains that at some point in the mid-1960s she just got sick of the smell of turpentine and, by implication, of painting as a medium.

So she got a sowing machine (she is shown in the film using a classic black Singer machine) and began making soft sculptures.

She used the machine to sew together strange shapes which she stuffed with wool to become free-standing sculptures. Like the prismatic paintings they hint strongly at bodily parts – not least because many of them are made out of flesh-coloured fabric – with long tubes which could be arms flung around bulbous shapes which might be bodies. Take Nue Couchée which is made from cotton textile padded with cardboard and filled with seven tennis balls and a load of wool.

Nue Couchée (1969-70) by Dorothea Tanning. Tate © DACS 2019

Nue Couchée (1969-70) by Dorothea Tanning. Tate © DACS 2019

There’s one round pink shape with a wide crack open in the front which is lined with jagged pieces of wood, obviously a rather nightmareish face. And the biggest piece is a mysterious black pin cushion, studded with giant pins, containing strange pinnacles and spouts, as well as worrying orifices.

Pincushion to Serve as Fetish (1965) by Dorothea Tanning. Tate © DACS 2019

Pincushion to Serve as Fetish (1965) by Dorothea Tanning. Tate © DACS 2019

Tanning made it when she was living in Seillans, a hill-top town in Provence. From 1965 to about 1970 she made about twenty of these cloth sculptures.

By far the most dramatic work along these lines was an enormous room-sized installation which is in fact a life-sized model of a room, complete with open door and fireplace, but which is infested with cloth sculptures looming out of the floor and bursting from the walls – a three-dimensional, if rather dingy, homage to the Surrealist nightmares which shook her imagination all those decades earlier.

Hôtel du Pavot, Chambre 202 (1970–3) by Dorothea Tanning

Hôtel du Pavot, Chambre 202 (1970–3) by Dorothea Tanning

Conclusion

There’s also a section devoted to her work for the stage, designing Surrealist sets and costumes for collaborations with the choreographer George Balantine – and a sequence of lithographs which, to me, smacked of the covers of 1950s science fiction novels, of the more abstract, harrowing, post-apocalyptic flavour.

But overall her career can be divided very broadly into these three threads

  1. Dali-like Surrealist paintings
  2. huge billowy ‘prismatic’ paintings
  3. mysterious and unnerving soft sculptures

In light of this, I think the curators have made an excellent decision which is to mix it up.

I suspect that if they’d hung the works chronologically it might have been a bit boring, each room would have risked being a bit samey. A couple of rooms of non-stop Surrealism, one of the strange 1950s lithographs and stage designs, a couple of rooms of just prismatic paintings, and then a room or two of just soft sculptures – each space would have been limiting and samey.

Instead the curators have mixed it up, with works from the 50s, 60s, 70s and 80s all in the same room, huge oil paintings next to lithographs, early drawings next to Surrealist classics.

The net result is to create thought-provoking connections and juxtapositions of subject matter and style – in short, to foment the kind of rather dreamy, disconnected, unsettling effect which I’m sure Tanning herself would have appreciated.

Self Portrait (1944) by Dorothea Tanning © San Francisco Museum of Modern Art

Self Portrait (1944) by Dorothea Tanning © San Francisco Museum of Modern Art

The promotional video

Women curators

Dorothea Tanning is curated by Alyce Mahon, Reader in Modern and Contemporary Art History at the University of Cambridge and Ann Coxon, Curator, International Art, Tate Modern, supported by Emma Lewis and Hannah Johnston, Assistant Curators, International Art, Tate Modern.


Related links

Reviews of other Tate exhibitions

Emma Kunz: Visionary Drawings @ Serpentine Gallery

Work No. 003 by Emma Kunz Photo © Emma Kunz Zentrum

Work No. 003 by Emma Kunz Photo © Emma Kunz Zentrum

Emma Kunz (1892–1963) was a Swiss healer, researcher and artist.

Emma discovered her gifts for telepathy, prophecy and healing at an early age. She began to use her gifts at the age of 18, around the same time as she began drawing in exercise books.

Work No. 004 by Emma Kunz. Photo © Emma Kunz Zentrum

Work No. 004 by Emma Kunz. Photo © Emma Kunz Zentrum

The drawings were intended to be visions of energy fields from which she could formulate diagnoses for the patients who began to visit her, seeking help for physical and mental ailments as her reputation as a psychic and healer spread.

From about 1938, when she was in her mid-forties, Emma began making the first large-scale drawings which she continued to produce for the rest of her life.

Work No. 011 by Emma Kunz. Photo © Emma Kunz Zentrum

Work No. 011 by Emma Kunz. Photo © Emma Kunz Zentrum

She used a process she called ‘radiesthesia’. She would address a question to her divining pendulum and then record the way it swung, started and stopped onto large squares of graph paper. In this way she then converted the pendulum’s motions into meticulously worked-out and coloured-in geometric shapes, in which she discovered the answer to the original question she had posed.

Emma used mostly graphite and colour pencils, working intensely and continuously on each drawing for up to 24 hours. The lines of colouring-in are clearly visible in many of the works, much like the colouring-in of children in junior school.

She didn’t give any of the drawings titles, or date them, or go on record attributing any particular meaning to them. The numbers they now bear were attributed to them by art scholars after her death.

Work No. 012 by Emma Kunz. Photo © Emma Kunz Zentrum

Work No. 012 by Emma Kunz. Photo © Emma Kunz Zentrum

The drawings were never displayed in Emma’s lifetime, indeed it is not certain that she regarded them as art works in the traditional way at all, but continued to think of them as tools to help with healing.

Geometric abstraction became a means for structuring and visualising her philosophical and scientific research which was not only rooted to her own times and the pursuit of her own restorative practices, but also for the future.

A selection of the drawings was only exhibited in her native Switzerland in 1973, some five years after her death.

This exhibition, at the Serpentine Gallery in Hyde Park, is the first show devoted solely to Emma Kunz’s drawings to be held in the UK. It features over 60 of these calming, absorbing and intriguing works.

Work No. 013 by Emma Kunz. Photo © Emma Kunz Zentrum

Work No. 013 by Emma Kunz. Photo © Emma Kunz Zentrum

Interpretation

Emma considered the works an integral part of her approach to healing, and as emblems of her holistic worldview. As she explained:

Everything happens according to a certain regularity which I sense inside me and which never lets me rest.

The Serpentine curators agree with this spiritual interpretation. In their words:

Systematic yet expansive in their compositions, her ‘energy-field’ drawings simultaneously contain micro and macro perspectives of nature, chiming with current discourses on ecology, as well as a desire to forge meaningful connections with our environment.

AION A

Emma earned her living as a naturopath but also thought of herself as an explorer and experimenter with natural healing techniques. She made investigations into the healing properties of all manner of natural materials. She used her pendulum on the flowers in her garden which, as a result, bore unusual multiple flowerheads where single flowerheads would have been expected.

In 1941 Emma discovered in a grotto in the old Roman Quarry outside the Swiss town of Würenlos a marvellous healing rock. She gave it the name AION A. The word aion comes from the Greek and means ‘without limitation’.

Emma first demonstrated the healing power of AION A on a patient of hers, Anton C. Meier, who was seriously ill with infantile paralysis. After treatment with AION A Meier recovered, a cure Emma attributed to the rock’s ‘accumulated biodynamic energy’.

45 years later the Emma Kunz Centre was opened at the self-same Roman quarries in Würenlos. Patients can visit the centre to discover more about its healing practices and undergo cures. In 1991 a museum was opened to showcase some of Emma’s 400 drawings.

View of the Emma Kunz Centre in Würenlos, Switzerland

View of the Emma Kunz Centre in Würenlos, Switzerland

AION A, mined from the same quarry, is still sold in pharmacies in Switzerland and is used to treat a host of health issues from joint and muscular pain to inflammatory skin disorders.

I was surprised to find chunks of the rock, in attractive yellow boxes, on sale in the Serpentine Gallery shop, as well as a spray which also, apparently, captures AION A’s healing properties.

Christodoulos Panayiotou

Christodoulos Panayiotou (b.1978) is a contemporary artist hailing originally from Cyprus.

He has collaborated on a number of projects and installations at the Serpentine, and he had a major creative say in the design and hang of this exhibition.

For the most part the approach has been to hang the drawings sequentially on the Serpentine Gallery’s plain white walls. Each one exists in its own space, giving you plenty of scope to study and examine it.

But the plain, one-picture-at-a-time approach gives way in the gallery’s enormous central room to a completely different design. Here around 25 of the drawings have been piled up on the walls to create powerfully cumulative impression.

After spending some time in this big room, looking at individual works then stepping back to survey each wall as a composition, it struck me that this big, white space has the feel of a chapel. The arrangement of the works is loosely analogous to the altar of a baroque or orthodox church, packed with holy images climbing vertically up the wall and framed to left and right by secondary images of saints and apostles. Not directly similar, maybe – but that’s the kind of feel which the images, the peace and the air of reverence encourage: a mood of quiet devotion.

Installation view of Emma Kunz at the Serpentine Gallery. Photo by the author

Installation view of Emma Kunz at the Serpentine Gallery. Photo by the author

Arguably Panayiotou’s main contribution to the exhibition is the stone benches. See the bench in the photo above (on the lower right)? It was shaped from stone from the AION A quarry in Switzerland. It is made from AION A. It has healing powers.

It was Panayiotou’s ideas to have these benches carved and located around the exhibition. Each of the gallery’s rooms has a bench in it. The gallery encourages you to sit on them and, while you are feasting your eyes and resting your soul looking at Emma’s hypnotic drawings, to let the AION A do its healing work on your body.

Variety

I found the single most impressive thing about the drawings was their variety.

A generic verbal description – geometric shapes on graph paper, decorated with coloured pencils – doesn’t do them any justice. In the flesh they display an impressive variety not only of design and pattern, but of resulting visual effect.

Work No. 307 by Emma Kunz. Photo © Emma Kunz Zentrum

Work No. 307 by Emma Kunz. Photo © Emma Kunz Zentrum

Some look like spirograph diagrams and please the part of the mind which likes simple, abstract patterns. Others are highly detailed mathematical diagrams which reward close attention to the way the shapes have been worked out to their logical conclusions.

Some feature what appear to be stylised human bodies – one appeared to contain a stylised man and woman, another contains about ten human forms reduced to geometric outlines and caught in a fiendishly complex web of lines.

Others contain uncanny optical illusions, drawing you into the depths of what part of your mind insists are only two-dimensional artefacts.

And all this is just to comment on the shapes, before you consider the colours, which are themselves very varied. Some contain plain washes, others more subtle gradations of colour; some are almost bereft of colour, others feel super colour-saturated. For me the variety of coloration was as surprising as the variety of pattern, and both were endlessly fascinating.

Conclusion

Whether Emma Kunz was a great spiritual healer, a true naturopath, and did make a significant contribution to human health by discovering AION A, I leave for others to decide.

But there’s no doubting that these lovely works, whatever the precise motivation to create them, are wonderfully attractive, calming, fascinating, varied and inspiring.

Emma Kunz at her working table, Waldstatt, 1958. Photo © Emma Kunz Zentrum

Emma Kunz at her working table, Waldstatt, 1958. Photo © Emma Kunz Zentrum


Related links

Reviews of other exhibitions at the Serpentine

The Beardsley Generation @ the Heath Robinson Museum

This small but entrancing exhibition explores the impact that a radical new photographic means of reproduction (process engraving) had on the art of illustration at the end of the 19th century.

Through 50 or so drawings and 20 or so illustrated books and magazines, the exhibition brings together a treasure trove of images from what many consider the golden age of illustration which lasted from around 1890 to the early 1900s.

The Pilgrim stretched both of his hands up towards Heaven by Charles Robinson (1900)

The Pilgrim stretched both of his hands up towards Heaven by Charles Robinson (1900)

Informative

As always the exhibition is in just the one room at the Heath Robinson Museum and looks small, but there are now fewer than 20 wall panels, some quite lengthy and packed with technical, historical and biographical information, so that reading all of them almost feels like reading a small book.

A brief history of Victorian illustration techniques

In the early Victorian era, book illustrations were mostly produced from steel engravings. Artists such as George Cruikshank (some of whose prints I was looking at earlier this week, in the Guildhall Art Gallery) and Hablot Browne were expert at etching on steel. However the process was expensive, requiring the illustrations to be printed on different paper separate from the text and then bound in with the rest of the book.

By the 1850s publishers preferred to use wood engravings, with the result that master wood-engravers developed large workshops which employed many engravers. The artist presented his picture on paper or on a whitened woodblock and would hand it over to the skilled engraver. The engraver then converted the picture into a woodcut, carving away the areas that were to appear white on the final print, leaving the raised lines which would take the ink, be applied to paper, and produce the print.

Thus the engraver played a major role in interpreting the artist’s work, sketch or intention, often superimposing his own character and style on the image.

Still, it did mean you could make illustrations without having to be a skilled etcher and among the first artists to take advantage of the new medium were the pre-Raphaelites, led by Dante Gabriel Rossetti and John Everett Millais.

They were followed by a second school of artists, sometimes called the ‘Idyllic School’, which included G.J. Pinwell and Arthur Boyd Houghton, who infused their essentially realistic works with intensity and emotion.

Job's Comforters by Arthur Boyd Houghton (c.1865)

Job’s Comforters by Arthur Boyd Houghton (c.1865)

There followed in the 1870s and ’80s what the curators call ‘a period of dull realism’ which is not dwelt on. It was at the end of the 1880s that the technical innovation which the exhibition is concerned with came in, and transformed the look of British illustrations.

Process engraving

In the late 1880s process engraving replaced wood engraving. An artist’s drawing was transferred to a sheet of zinc so that areas to be printed in black were given an acid-resistant coating and white areas left exposed. The plate was then dipped in acid so that the white areas were eaten away. The plate was then attached to a block of wood which could be inserted into the block holding the type, so that illustration and text were generated together by the same printing process.

This new process required that the artist’s image be in pure blacks and whites without the kind of fine lines which had flourished in etching on steel or in wood engraving. Moreover, the artist could be confident that the line he drew would be exactly what would be presented to the reader, without the involvement of a wood engraver to enhance or (possibly) detract from it.

At a stroke, the older generation of artists who had relied on master wood-engravers to work up their rough sketches for publication was swept away and replaced by a new young generation of penmen who relished the clarity of line and space encouraged by the new technique.

The most dramatic proponent of the new look, who exploded onto the art scene like a small atom bomb, was Aubrey Beardsley (b.1872)

How La Beale Isoud Wrote to Sir Tristram from the Morte d'Arthur by Aubrey Beardsley (1892)

How La Beale Isoud Wrote to Sir Tristram from the Morte d’Arthur by Aubrey Beardsley (1892)

Beardsley was an illustrator of genius who had created an entirely new and personal visual world by the incredibly young age of 20. There are four prints and two drawings by him here, plus three book covers and books laid open to show his illustrations in situ. What a genius.

Having explained this major new development in print technology, the exhibition also explains several other influences which were swirling round at the time and contributed to the development of the ‘new look’. These included:

  • Japanese art
  • European Symbolism
  • Venetian and Renaissance art
  • with a dash of Dürer thrown in

Japanese

After the Harris Treaty of 1858 reopened trade links between the West and Japan, one of the many consequences was a flood onto the Western art market of Japanese woodblock prints.

Known in Japan as ukiyo-e or ‘pictures of the floating world’, the Japanese style was notable for not using perspective to add depth, or light and shade to create a sense of volume and space in the images. Instead the Japanese used ‘dramatic boundary lines’, i.e. clear, distinct, black lines – to create images – and then used colour, again not to create depth, but decoratively, filling in the shapes created by the lines with plain washes.

Japanese art had a profound influence on Western artists at a time when they were looking for ways to revive what had become tired traditions and to combat the rising challenge of photography.

Setting a Japanese print (in this case Nakamura Shikan II as Benkai by Utagawa Kunisada) next to the works by Beardsley allows you to immediately see the liberating impact that the Japanese habit of stylising the image has had for the European – allowing him to abandon almost all conventions of perspective and depth.

Actor Nakamura Utaemon Iii As Mitsugi’s Aunt Omine by Utagawa Kunisada (1814)

Beardsley’s best images float in an indeterminate space, bounded by extremely precise and clear lines which give his best images a wonderful clarity and dynamism. But Beardsley wasn’t alone. A greater or lesser element of simplification and stylisation characterises most of the artists working in the ‘new look’.

The last fancy of the contemporary buck for Pall Mall magazine by Edmund J. Sullivan (1900)

The last fancy of the contemporary buck for Pall Mall magazine by Edmund J. Sullivan (1900)

Symbolism

Symbolism was an art movement which swept northern Europe in the 1880s and, although its techniques remained largely realistic, in some case hyper-realistic, it applied these approaches to subject matter which was infused with obscure and semi-religious feelings.

Symbolism took images of death, yearning, loss and mystery, and showed them, no longer in the bright light of nineteenth century rationalism and optimism, but brooded over by a more modern sensibility and psychology. A drawing of Salomé by Gustave Moreau is used to exemplify the Symbolist effect.

Its influence can be seen in an illustration like this one by Charles Ricketts, which takes the well-worn subject of Oedipus and the Sphinx but drenches it in arcane symbolism – inexplicable figures and flowers adding to the sensual, erotic yet mysterious atmosphere.

Oedipus and the Sphinx (1891) by Charles Ricketts

Oedipus and the Sphinx (1891) by Charles Ricketts

Hypnerotomachia Poliphili

The exhibition lists and explores other influences including the impact of a classic printed book from Venice titled Hypnerotomachia Poliphili or The Strife of Love in a Dream, published by Albertus Manutius in 1499, and regarded as a masterpiece of typography and design by collectors.

A Garden Scene from 'Hypnerotomachia Poliphili' attributed to Francesco Colonna (c.1499)

A Garden Scene from ‘Hypnerotomachia Poliphili’ attributed to Francesco Colonna (c.1499)

Copies of Hypnerotomachia Poliphili became available in England in 1888 and influenced Edward Burne-Jones, Walter Crane, Charles Ricketts, Aubrey Beardsley and Robert Anning Bell.

List of artists in the exhibitions

The exhibition includes works by all of those illustrators and more. I counted:

  • Aubrey Beardsley – 4 prints, 2 drawings and three book and magazine covers or pages
  • Alice B. Woodward – 2 drawings
  • Louis Fairfax Muckley – 1
  • Herbert Granville Fell – 2 drawings and a watercolour
  • Alfred Garth Jones – 2
  • Thomas Sturge Moore – 1
  • Laurence Housman – 5
  • Charles de Sousy Ricketts – 2
  • Paul Vincent Woodroffe – 1
  • H.A. Eves – 1
  • Harold Edward Hughes Nelson – 1
  • Byam Shaw – 1
  • Edgar Wilson – 1
  • Cyril Goldie – 1
  • Henry Ospovat – 1
  • Robert Anning Bell – 2
  • Philip Connard – 1
  • Jessie Marion King – 3
  • James Joshua Guthrie – 2
  • Edmund Joseph Sullivan – 2
  • Charles Robinson – 3
  • William Heath Robinson – 3
  • Arthur Boyd Houghton – 1
  • Walter Crane – 1

Books on display

  • Le Morte d’Arthur illustrated by Beardsley
  • Midsummer Night’s Dream ill. by Robert Anning Bell
  • The Kelmscott Chaucer ill. by Burne-Jones
  • Poems of Edgar Allen Poe ill. by William Heath Robinson
  • Poems of John Keats ill. by Robert Anning Bell
  • Poems of John Milton ill. by Garth Jones
  • The Faerie Queene ill. by Walter Crane
  • plus illustrated versions of Shakespeare’s Sonnets, the Book of Job, the Yellow Book, and more

All the works were worth looking at closely, studying and mulling in order to enjoy the play of line and form. Many of the prints are wonderfully drawn and warmly evocative. Every one is accompanied by a wall label, and the twelve or so most important artists merit bigger wall labels which give you their full biography along with influences and major works to set them in context.

These biographical notes help you to make connections between different artists linked by having a common publisher, or working on a common publication or magazine, or who knew each other and encouraged, helped or shared ideas. The exhibition really does give you a sense of an entire generation excitedly inventing a whole new style of art.

Nostalgia

I think at least in part I respond so warmly to so many of the images is because, as a boy growing up in the 1960s, lots of the old books in my local library and the children’s books which my parents bought for me, contained just this kind of late-Victorian / Edwardian illustrations.

Looking at almost any of them creates a warm bath of half-forgotten memories of curling up in a corner and totally immersing myself in thrilling stories of Greek heroes and mermaids and pirates and pilgrims.

Tailpiece by Edgar Wilson (date unknown)

Tailpiece by Edgar Wilson (date unknown)

This is another wonderful, heart-warming and highly informative exhibition from the Heath Robinson Museum.


Related links

Other exhibitions at the Heath Robinson Museum

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