Polished aluminium on hardboard on six painted plywood panels, with two additional panels, overall: 1829 x 7315 x 279 mm (72 x 288 x 11 in); each panel 1829 x 914 x 279 mm (72 x 36 x 11 in)
First panel (from left) inscribed by the artist on back in black oil paint with arrows ‘á PANEL á’, in grey oil paint ‘<SPARE>’, and in black oil paint ‘1’ top centre, in black oil paint ‘mm’ lower centre
Second panel inscribed by the artist on back in black oil paint ‘MM’ centre
Third panel inscribed by the artist on back in black oil paint with arrows ‘á 3 á’ top centre, ‘MM’ lower centre
Fourth panel inscribed by the artist on back in black oil paint with arrows ‘á 4 á’ top centre, ‘MM’ lower right
Fifth panel inscribed by the artist on back in black oil paint ‘Mary Martin’ lower centre
Sixth panel inscribed by the artist on back in black oil paint ‘Mary Martin’ lower centre
Seventh panel inscribed by the artist on back in black oil paint ‘Mary Martin’ lower centre
Eighth panel inscribed by the artist on back in black oil paint with arrows ‘á 8 á’ top centre, inscribed in another hand in pencil ‘Mary MARTIN | 8’ lower centre
Presented by the Friends of the Tate Gallery 1970
Estate of Mary Martin; from whom acquired by Friends of the Tate Gallery 1970
Soundings Three, Signals Gallery, London, August-September 1966 (16)
Rosc ‘67, Royal Dublin Society, Dublin, November-December 1967 (69, right half only; reproduced upside down)
Mary Martin, Axiom Gallery, London, February-March 1968 (7, one half only)
Konstruktive Kunst: Elemente und Prinzipien, Nuremberg Biennale, April-August 1969 (Mary Martin I)
Series, Tate Gallery, London, December 1977-January 1978 (3, reproduced)
Mary Martin, Tate Gallery, London, October-November 1984 (34, reproduced p.29)
Times, September 1966
Spectator, 2 September 1966
Mary Martin, ‘Statement’, December 1967, in Alan Bowness, ‘The Constructive Art of Mary Martin, Studio International, vol.175, no.898, March 1968, p.121
Alan Bowness, ‘The Constructive Art of Mary Martin, Studio International, vol.175, no.898, March 1968, p.125, reproduced
Paul Overy, ‘Mary Martin’s “Inversions”’, Art and Artists, vol.3, no.7, October 1968, pp.34-5, reproduced
Paul Overy, ‘Mary Martin and Kenneth Martin’, Art and Artists, vol.5, no.8, November 1970, p.30
Tate Gallery Report 1970-2, London 1972, pp.143-5, reproduced
Colin Naylor and Genesis P-Orridge (eds.), Contemporary Artists, London 1977, p.620
Mary Rose Beaumont, ‘Mary Martin’, Arts Review, vol.36, no.20, 26 October 1984, p.544
The ninety-six reflective metal planes of Inversions extended Mary Martin’s characteristic unit onto a monumental scale. The eight base boards are each six feet high and three feet wide. The relief area is three feet high and occupies the full width of the central six panels (forming a square on each). It is set two feet up from the lower edge and a foot from the top of the base board, which, with the outer panels, serves as the ‘open plane’. Inversions was thus architectural in ambition even if it was not made for a permanent site. In her ‘Statement’ of December 1967, Martin wrote about the potential of the angled reflective unit in the construction of ‘superpatterns’ - extended variations of basic patterns. She added: ‘I made one large work in 1966 (Inversions), which combined both reflections and open planes’. These concerns were central to her approach. In a contemporary text, ‘Reflections’, she used emotive language to assert:
Establishment of the surface is a primary move, since the parting from and clinging to a surface is the essence of the relief. Then that space which lies between the surface and the highest point becomes a sphere of play, or conflict, between opposites, representing the desire to break away and the inability to leave the norm. It is for this reason that the base is made important in size. In recent work, using half-cubes, the depth of the relief is dictated by the area of the base of the chosen unit. ... The appearance of the work should be that of an object set upon a wall, if it is not a development of the wall itself.
After considering her earlier use of proportion, she suggested that it ‘is one of the contributions which the artist can make to social well-being, as anyone who has directly experienced a building by Le Corbusier will know. In recent works the unit is unchanging but the situations are permuted, again according to a system, or logic or counter-logic.’
Inversions became a grand statement based on the application of just such a logical system. The ‘pendulum permutation’ used for Diagonal on Black (collection Leonie Cohn), a companion piece to Spiral (Tate T00645), also formed the basis for Inversions. Martin started with the sequence 1 2 3 4 (each denoting a different orientation of a slope). A permutation was derived by selecting alternate numbers; beginning with the second number, jumping to the fourth and then turning back to the remaining alternate numbers (the pendulum motion): hence 1 2 3 4 gives 2 4 3 1. The permutation is then applied to the second sequence, and so on. Such a scheme was used for Permutation of Five, 1967 (Estate of the artist). However, with four numbers only three sequences can be achieved before the original is repeated and, as Paul Martin, the artist’s son, has pointed out in his analysis of Inversions, the number 3 remains in the same position. With the aid of a chart, Paul Martin explained that Mary Martin invented ‘a sliding system which produces 12 different sequences before repeating itself’; this overcame the stationary position of the 3 by carrying the opening numbers of a sequence to the end of each row. The first numbers were then passed over and a sequence fashioned by a progressive shifting of the starting point (the sliding motion); hence the twelve sequences may be listed (with numbers passed over reduced):
1 2 3 4
2 4 3 1 2
4 1 3 2 4 1
1 2 3 4 1 2 3
2 4 3 1
4 1 3 2 4
1 2 3 4 1 2
2 4 3 1 2 4 3
4 1 3 2
1 2 3 4 1
2 4 3 1 2 4
4 1 3 2 4 1 3
Three consequences of the sliding version of the pendulum permutation are worth noting. First, it determines that the 3 takes up a diagonal position which is evident in the eventual relief. Second, each 1 2 3 4 sequence arrives at a different level in the sliding system, thus affording greater variety. Third, each grouping of four sequences was located on a single panel when translated to the relief.
Martin doubled the twelve permutations of the first sequence in Inversions by reversing the two pairs of numbers arrived at in the twelfth permutation. Thus, 2 4 1 3 became 4 2 3 1 (the inversions of the title). This new sequence was used to generate another twelve permutations under the sliding system and, as Paul Martin explained, resulted in ‘the sequence of numbers for the whole relief’. Following his chart with the passed over numbers removed, it may be given as:
1 2 3 4
4 3 1 2
3 2 4 1
4 1 2 3
2 4 3 1
1 3 2 4
3 4 1 2
1 2 4 3
4 1 3 2
2 3 4 1
3 1 2 4
2 4 1 3
4 2 3 1
1 3 4 2
3 2 1 4
1 4 2 3
2 1 3 4
4 3 2 1
3 1 4 2
4 2 1 3
1 4 3 2
2 3 1 4
3 4 2 1
2 1 4 3
Just such a numerical chart by the artist for Inversions survives in the Martin archive. It accompanies a diagrammatic drawing which uses the artist’s short-hand symbols for the slopes, as explained by Paul Martin; a copy of both was furnished to the Tate by Hilary Lane in 1972. Martin translated the opening sequence 1 2 3 4 as slopes to the left, to the right, up and down; this was a standard sequence, also used on Spiral. However, the vertical numerical chart was laid on its side for its conversion into the relief, so that the orientations changed. The opening sequence became the first column, reading (from the base) down, up, right, left. This change in orientation constitutes an unspecified stage between the numerical chart and the diagram of slopes.
Kenneth Martin was consulted in 1971-2, in the course of preparation for an earlier catalogue entry on Inversions, and Hilary Lane assisted him in his replies. As well as supplying a copy of Mary Martin’s diagram, Lane summarised the pendulum permutation and the sliding system. It was suggested that Kenneth Martin had discovered the pendulum permutation ‘through a study of the works of Paul Klee’. The British Constructionists much admired Klee’s work; the English translation of his Pedagogical Sketchbook in which the pendulum is discussed, proved influential through its evocative discussion of linear progression in relation to nature.
The possibility that Mary Martin made a maquette for Inversions prior to its inclusion in Soundings Three in 1966 was also raised by Kenneth Martin. None survives though a smaller white and red painted work, also called Inversions, was made the following year (Estate of the artist). In 1968 Paul Overy asserted that the Tate relief was originally commissioned by David Medalla for inclusion in the exhibition at the Signals Gallery, and this, together with the scale of the undertaking would make a maquette probable. In 1960 the artist had made studies for the large SS Oriana Reliefs (Peninsular and Oriental Steam Navigation Company). Furthermore, Inversions went beyond Martin’s usual handmade works. The ninety-six units have square bases with 9 inch sides, so that the aluminium plates measure 9 x 12 3/4 inches; the production of ninety-six of these demanded industrial machining. The plates were glued to hardboard planes attached to angled strips screwed to the base board (which must have been painted before assembly) from the reverse. This system replaced that of wooden blocks used on smaller works. Together with the use of aluminium and painted panels (instead of the steel and Formica of Spiral), this helped to reduce the increased weight, as well as structural and installation problems.
These material considerations affected the appearance of the relief. The enlargement of the angled planes opened large expanses of reflection quite different from the smaller fragmentation. Martin evidently considered this as a potential distraction and, according to Kenneth Martin, deliberately ‘softened’ the reflection ‘to bring in light and dark rather than people and things’. This was done by buffing the surface of the metal. By removing the sides of the supporting blocks, reflections behind neighbouring planes and through to others were also obtained. This introduced an open linear pattern (caused by the sides of the plates which remained unpainted) in the reflection, which contrasted with the density of the black block in the smaller works. Such effects could best have been anticipated through maquettes.
Besides the difficulties of construction generated by the size, Martin would find difficulties in displaying Inversions. On two occasions, in 1967 and 1968, only half was shown. In Dublin, in the first of these showings, it was the right half and this may coincide with the full signature on the back of those panels (fifth, sixth and seventh from the left); the other three panels with relief elements are only initialled. As its generation and the title of the work suggests, this partial display was hardly satisfactory. Nevertheless, Kenneth Martin recalled that ‘each half is self-sufficient’ although it had been ‘conceived as a whole’.
The dimensions of Inversions indicate Martin’s interest in the relation of the work to its environment and to the observer in a more overwhelming way. At six feet, the height of the overall work related to that of an average man. This was the measurement used by Le Corbusier in devising his system of proportions based on the figure, Le Modulor, in which Martin was interested; it is notable that the Martins visited both the Cité Universitaire, Paris and Ronchamp in 1964. In locating the centre of the relief area four feet from the bottom of the backing boards, Martin anticipated the hanging of the panels one foot off the ground and resulting in an alignment at an eye-level of five foot. In common with contemporary American painting, the scale of the work absorbed the observer, filling the field of vision. The next logical step in size, was taken by Martin in the Wall Construction, 1969 (University of Stirling), which extended the relief on to a truly public scale. Following the systems devised for Inversions, the Stirling construction was sixty feet long; in this context it became less a unity and more ‘a development of the wall itself’. This was the culmination of Martin’s concerns with architecture, begun a decade earlier with the environment in This is Tomorrow, 1956 and the Wall Screen at Musgrave Park Hospital, Belfast, 1957, both made with the architect John Weeks. The unitary variation of Inversions tallied with contemporary architectural concerns with mass-production and systems building, while the Stirling Wall Construction epitomised the integration of Constructionism into new types of public spaces made with new materials.
 Mary Martin, ‘Statement’, December 1967, in Alan Bowness, ‘The Constructive Art of Mary Martin, Studio International, vol.175, no.898, March 1968, p.121, also quoted in Mary Martin, exhibition catalogue, Tate Gallery, London 1984, p.14.
 Martin, ‘Reflections’ 1967, in Anthony Hill ed., DATA, Directions in Art, Theory and Aesthetics, 1968, pp.95-6, republished in Tate Gallery exhibition catalogue 1984, pp.31-3.
 Ibid., p.44.
 Kenneth Martin, conversation with Richard Morphet, summer 1971, Tate catalogue files.
 Reproduced in Tate Gallery exhibition catalogue, 1984, p.56, no.36.
 Paul Overy, ‘Mary Martin’s “Inversions”’, Art and Artists, vol.3, no.7, October 1968, p.34.
 Kenneth Martin, conversation, summer 1971.