Dóra Maurer @ Tate Modern

This is a lovely FREE exhibition on the third floor of Tate Modern. It is the first UK survey to celebrate Dóra Maurer’s five-decade career, bringing together 35 works, ranging from:

  • her conceptual photographic series
  • the experimental films
  • her colourful graphic works
  • and the striking large geometric paintings

Potted biography

Dóra Maurer was born in 1937 in Budapest, capital of Hungary. She was a child during the Second World War and grew up in a society dominated by the Soviet-supported Communist Party. She came to adulthood just after the failed Hungarian Rising of 1956 led to Russian tanks being sent in to repress the uprising and demands for greater democracy.

It was during the 1960s that Maurer emerged as part of a generation of neo-avant-garde Hungarian artists who produced highly experimental work in parallel to the ‘official’ art system of the socialist regime.

Photographs

She trained as a graphic artist and printmaker in the 1950s and quickly began pushing the medium to its limits in her early works. She had an eye informed by questions of design and layouts.

From early on her main interest was in movement, displacement, perception and transformation. The exhibition includes a set of photographs she and a colleague took of each other across the courtyard of a tenement building as they moved along the gallery thus creating a series of variations. Another set shows a series of hand gestures: same hand, infinite variation of gestures, titled, in a suitably technocratic way, Reversible and Changeable Phases of Movements No.6.

She was interested in taking shapes and patterns and subjecting them to set changes and transformations, a fascination which resulted in probably her best known work, Seven Twists.

Seven Twists V (1979) by Dóra Maurer © Dóra Maurer

Experimental films

One room is devoted to five of her experimental films. This short clip gives you a feel.

She’d wanted to experiment with films since the late 1960s but didn’t have access to the equipment. Then in 1973 the state film organisation made its facilities available to artists and, voom! she was off.

Again she is playing with repetition, variation, and displacement. Relative Swingings splices together three separate strands of film to create a dizzying disorientation, shot in her own flat, some of the scenes more or less static, others made by lying on the floor and swinging the camera back and forth to create a blurred image of the ceiling.

Repetition with distortions

In 1974 she placed a coil of wire under a thin metal printing plate and pressed down so that it left a mark on the plate. The plate was inked and a print was made. The coil was then placed under the same plate and pressed down and a new print was made. Doing this in succession recorded what she called ‘phases of displacement’.

Traces of a Circle (1974) by Dóra Maurer. Tate

As her work became more geometric and abstract, Maurer explored system-based painting and the way in which geometric forms are affected by colour and perception. Some of these were exercises set for her students for she was now teaching in the Creativity Exercises Circle.

The third room explores her large-scale experiments with repetition and distortion. The most striking example is a set of four rectangular wooden panels suspended from the ceiling and part covered in mirrors, with a distinct gap between them, titled 4 out of 3. It’s the four panels hanging in mid-air at the right of this photo.

Installation view of Dóra Maurer at Tate Modern. Photo by Matt Greenwood

As you walk around, or as you observe other people walking round, they enter the reflective surface of the mirrors and leave them. It’s a simple, unpretentious and beguiling invention. Note its relationship with the coloured squares hanging on the wall behind it  (5 out of 4), which clearly show the way Maurer takes a pattern and then subjects it to variations and displacements.

The Schloss Buchberg commission

In 1983 Maurer was awarded a commission for a site-specific project at Schloss Buchberg, near Vienna. For this she needed to think big, big spaces to cover, and an opportunity to play with colour. As she covered corners, curves and vaulted ceilings she began to appreciate the three-dimensional visual distortions they created on two-dimensional designs.

In the late 1970s Maurer had developed personal rules and techniques for producing varied shapes (such as 5 out of 4 and 4 out of 3, above) which included the strict use of just eight specific colours.

The Schloss Buchberg commission prompted her to expand her colour palette and experiment with three-dimensional affects, playing with perspective and perception. Thus some of her new works in the 1980s require the visitor to stand in just the right place in order to appreciate the optical illusion being created. In this respect she reminds me a bit of Bridget Riley’s Op Art.

Installation view of Dóra Maurer at Tate Modern. Photo by the author

The huge colour shapes

The show culminates in the fifth room with a display of Maurer’s most recent works, half a dozen enormous bright colour paintings with no frames, which are just coloured shapes mounted on the walls.

These are, quite simply, marvellous. Who would have thought there was still the scope to create objects which are, in a sense, so simple, but yet so inspiring. They are entirely flat – the impression of curving, of shape and shadow is created by varying the colours.

Stage II (2016) by Dóra Maurer. Photo by the author

Somewhere there’s a reference to Matisse’s late cutouts, but Maurer has reached this point entirely by herself, and by following a fascinating evolution through successive theories and experiments with shape and variation, with pattern and displacement, which the exhibition has traced so well.

Dora is still alive and producing new work at the ripe age of 82. May she long continue to do so. This is a really fascinating exhibition which leads to a completely unexpected and uplifting conclusion. Lovely!

Promotional video

Curator

  • Juliet Bingham, Curator International Art and Carly Whitefield, Assistant Curator Film

Related links

Reviews of other Tate exhibitions

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 several 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, in a mathematical 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. This is a wonderfully illuminating read.

1. The Natural Order

Thus Stewart begins the book by describing just some of nature’s multitude of 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)

Stewart trots through the history of major mathematical discoveries: Kepler discovers that the planets move not in circles but in ellipses. That the nature of acceleration is ‘not a fundamental quality, but a rate of change’. Then 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. These are, respectively, applied and pure mathematics.

Stewart 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, mathematics well done, whatever its source and no matter how abstract its origin, 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 nature doesn’t use numbers as such – she uses 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. Pattern appears wherever we look.

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 numbers, the series is known as integers. Positive and negative numbers taken together 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 to isolate out the initial variables.

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

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, the understanding of which underpinned the invention of radio, radar, TV etc – taking in descriptions of the contributions from Michael Faraday, James Clerk Maxwell, Heinrich Hertz and Guglielmo Marconi.

Stewart makes the point that mathematical theory tends to start with the simple and immediate and grow ever-more complicated. This is because of a basic principle, which is that 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 clear 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 starting point, cataclysmic differences may eventually emerge.

Stewart goes on to explain 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 Stewart 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 easily stated laws and functions – and we see water dropping off taps or flowerheads all the time – and yet the intermediate steps between principle and real world embodiment, are mind-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. He calls it morphomatics.


Related links

Reviews of other science books

Chemistry

Cosmology

The Environment

Genetics and life

Human evolution

Maths

Particle physics

Psychology

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