Sources page biographical material

6.AJ.2. TRIBAR AND IMPOSSIBLE STAIRCASE
Silvanus P. Thompson. Optical illusions of motion. Brain 3 (1882) 289-298. Hexagon of non overlapping circles.

Thomas Foster. Illusions of motion and strobic circles. Knowledge 1 (17 Mar 1882) 421-423. Says Thompson exhibited these illusions at the British Association meeting in 1877.

Pearson. 1907. Part II, no. 3: Whirling wheels, p. 3. Gives Thompson's form, but the wheels are overlapping, which makes it look a bit like an ancestor of the tribar.

Marcel Duchamp (1887-1968). Apolinère Enameled. A 'rectified readymade' of 1916-1917 which turned a bedframe in an advertisement for Sapolin Enamel into an impossible figure somewhat like a Penrose Triangle and a square version thereof. A version is in the Philadelphia Museum of Art and is reproduced and discussed in Ernst; The Eye Beguiled, p. 82. (Duchamp's 'readymades' were frequently reproduced by himself and others, so there may be other versions of this.)

Oscar Reutersvård. Omöjliga Figure [Impossible Figures -- In Swedish]. Edited by Paul Gabriel. Doxa, Lund, (1982); 2nd ed., 1984. This seems to be the first publication of his work, but he has been exhibiting since about 1960 and some of the exhibitions seem to have had catalogues. P. 9 shows and discusses his Opus 1 from 1934, which is an impossible tribar made from cubes. (Reproduced in Ernst, 1992, p. 69 as a drawing signed and dated 1934. Ernst quotes Reutersvård's correspondence which describes his invention of the form while doodling in Latin class as a schoolboy. A school friend who knew of his work showed him the Penroses' article in 1958 -- at that time he had drawn about 100 impossible objects -- by 1986, he had extended this to some 2500!) He has numerous variations on the tribar and the two pronged trident. An exhibition by Al Seckel says Reutersvård had produced some impossible staircases, e.g. 'Visualized Impossible Bach Scale', in 1936-1937, but didn't go far with it until returning to the idea in 1953.

Oscar Reutersvård. Swedish postage stamps for 25, 50, 75 kr. 1982, based on his patterns from the 1930s. The 25 kr. has the tribar pattern of cubes which he first drew in 1934. (Also the 60 kr.??)

L. S. & R. Penrose. Impossible objects: A special type of visual illusion. British Journal of Psychology 49 (1958) 31 33. Presents tribar and staircase. Photo of model staircase, which Lionel Penrose had made in 1955. [Ernst, 1992, pp. 71-73, quotes conversation with Penrose about his invention of the Tribar and reproduces this article. Penrose, like the rest of us, only learned about Reutersvård's work in the 1980s.]

Anon.(?) Don't believe it. Daily Telegraph (24 Mar 1958) ?? (clipping found in an old book). "Three pages of the latest issue of the British Journal of Psychology are devoted to "Impossible Objects."" Shows both the tribar and the staircase.

M. C. Escher. Lithograph: Belvedere. 1958.

L. S. & R. Penrose. Christmas Puzzles. New Scientist (25 Dec 1958) 1580 1581 & 1597. Prob. 2: Staircase for lazy people.

M. C. Escher. Lithograph: Ascending and Descending. 1960.

M. C. Escher. Lithograph: Waterfall. 1961.

Oscar Reutersvård, in 1961, produced a triangular version of the impossible staircase, called 'Triangular Fortress without Highest Level'.

Joseph Kuykendall. Letter. Mad Magazine 95 (Jun 1965) 2. An impossible frame, a kind of Penrose rectangle.

S. W. Draper. The Penrose triangle and a family of related figures. Perception 7 (1978) 283 296. ??NYS -- cited and reproduced in Block, 2002, p. 48. A Penrose rectangle.

Uribe, op. cit. above, gives several variations, including a perspective tribar and Draper's rectangle.

Jan van de Craats. Das unmögliche Escher-puzzle. (Taken from: De onmogelijke Escher-puzzle; Pythagoras (Amsterdam) (1988).) Alpha 6 (or: Mathematik Lehren / Heft 55 -- ??) (1992) 12-13. Two Penrose tribars made into an impossible 5-piece burr.