Sources page biographical material

6.AJ. GEOMETRIC ILLUSIONS
There are a great many illusions. This will only give some general studies and some specific sources, though the sources of many illusions are unknown.
An exhibition by Al Seckel says there are impossible geometric patterns in a mosaic floor in the Roman villa at Fishbourne, c75, but it is not clear if this was intentional.

Anonymous 15C French illustrator of Giovanni Boccaccio, De Claris Mulieribus, MS Royal 16 Gv in the British Library. F. 54v: Collecting cocoons and weaving silk. ??NYS -- reproduced in: The Medieval Woman An Illuminated Book of Postcards, HarperCollins, 1991. This shows a loom(?) frame with uprights at each corner and the crosspieces joining the tops of the end uprights as though front and rear are reversed compared to the ground.

Seckel, 2002a, below, p. 25 (= 2002b, p. 175), says Leonardo da Vinci created the first anamorphic picture, c1500.

Giuseppe Arcimboldo (1537-1593). One of his paintings shows a bowl of vegetables, but when turned over, it is a portrait. Seckel, 2000, below, fig. 109, pp. 120 & 122 (= 2002b, fig, 107, pp. 118 & 120), noting that this is the first known invertible picture, but see next entry.

Topsy turvy coin, mid 16C. Seckel, 2002a, fig. 65, p. 80 (omitted in 2002b), shows an example which shows the Pope, but turns around to show the Devil. Inscription around edge reads: CORVI MALUM OVUM MALII.

Robert Smith. A Compleat System of Opticks in Four Books. Cambridge, 1738. He includes a picture of a distant windmill for which one cannot tell whether the sails are in front or behind the mill, apparently the first publication of this visual ambiguity. ??NYS -- cited by: Nicholas J. Wade; Visual Allusions Pictures of Perception; Lawrence Erlbaum Associates, Hove, East Sussex, 1990, pp. 17 & 25, with a similar picture.

L. A. Necker. LXI. Observations on some remarkable optical phœnomena seen in Switzerland; and on an optical phœnomenon which occurs on viewing a figure of a crystal or geometrical solid. Phil. Mag. (3) 1:5 (Nov 1832) 329-337. This is a letter from Necker, written on 24 May 1832. On pp. 336-337, Necker describes the visual reversing figure known as the Necker cube which he discovered in drawing rhomboid crystals. This is also quoted in Ernst; The Eye Beguiled, pp. 23-24]. Richard L. Gregory [Mind in Science; Weidenfeld and Nicolson, London, 1981, pp. 385 & 594] and Ernst say that this was the first ambiguous figure to be described.

See Thompson, 1882, in 6.AJ.2, for illusions caused by rotations.

F. C. Müller-Lyer. Optische Urtheilstusehungen. Arch. Physiol. Suppl. 2 (1889) 263-270. Cited by Gregory in The Intelligent Eye. Many versions of the illusion. But cf below.

Wehman. New Book of 200 Puzzles. 1908. The cube puzzle, p. 37. A 'baby blocks' pattern of cubes, which appears to show six cubes piled in a corner one way and seven cubes the other way. I don't recall seeing this kind of puzzle in earlier sources, though this pattern of rhombuses is common on cathedral floors dating back to the Byzantine era or earlier.

James Fraser. British Journal of Psychology (Jan 1908). Introduces his 'The Unit of Direction Illusion' in many forms. ??NYS -- cited in his popular article in Strand Mag., see below. Seckel, 2000, below, has several versions. On p. 44, note to p. 9 (= 2002b, p. 44, note to p. 9), he says Fraser created a series of these illusions in 1906.

H. E. Carter. A clever illusion. Curiosities section, Strand Mag. 378 (No. 219) (Mar 1909) 359. An example of Fraser's illusion with no indication of its source.

James Fraser. A new illusion. What is its scientific explanation? Strand Mag. 38 (No. 224) (Aug 1909) 218-221. Refers to the Mar issue and says he introduced the illusion in the above article and that the editors have asked him for a popular article on it. 16 illustrations of various forms of his illusion.

Lietzmann, Walther & Trier, Viggo. Wo steckt der Fehler? 3rd ed., Teubner, 1923. [The Vorwort says that Trier was coauthor of the 1st ed, 1913, and contributed most of the Schülerfehler (students' mistakes). He died in 1916 and Lietzmann extended the work in a 2nd ed of 1917 and split it into Trugschlüsse and this 3rd ed. There was a 4th ed., 1937. See Lietzmann for a later version combining both parts.] II. Täuschungen der Anschauung, pp. 7-13.

Lietzmann, Walther. Wo steckt der Fehler? 3rd ed., Teubner, Stuttgart, (1950), 1953. (Strens/Guy has 3rd ed., 1963.) (See: Lietzmann & Trier. There are 2nd ed, 1952??; 5th ed, 1969; 6th ed, 1972. Math. Gaz. 54 (1970) 182 says the 5th ed appears to be unchanged from the 3rd ed.) II. Täuschungen der Anschauung, pp. 15-25. A considerable extension of the 1923 ed.

Williams. Home Entertainments. 1914. Colour discs for the gramophone, pp. 207-212. Discusses several effects produced by spirals and eccentric circles on discs when rotated.

Gerald H. Fisher. The Frameworks for Perceptual Localization. Report of MOD Research Project70/GEN/9617, Department of Psychology, University of Newcastle upon Tyne, 1968. Good collection of examples, with perhaps the best set of impossible figures.

Pp. 42 47 -- reversible perspectives.

Pp. 56 65 -- impossible and ambiguous figures.

Appendix 6, p.190 -- 18 reversible figures.

Appendix 7, pp. 191 192 -- 12 reversible silhouettes.

Appendix 8, p. 193 -- 12 impossible figures.

Appendix 14, pp. 202 203 -- 72 geometrical illusions.

Harvey Long. "It's All In How You Look At It". Harvey Long & Associates, Seattle, 1972. 48pp collection of examples with a few references.

Bruno Ernst [pseud. of J. A. F. Rijk]. (Avonturen met Onmogelijke Figuren; Aramith Uitgevers, Holland, 1985.) Translated as: Adventures with Impossible Figures. Tarquin, Norfolk, 1986. Describes tribar and many variations of it, impossible staircase, two pronged trident. Pp. 76 77 reproduces an Annunciation of 14C in the Grote Kerk, Breda, with an impossible perspective. P. 78 reproduces Print XIV of Giovanni Battista Piranesi's "Carceri de Invenzione", 1745, with an impossible 4 bar.

Diego Uribe. Catalogo de impossibilidades. Cacumen (Madrid) 4 (No. 37) (Feb 1986) 9 13. Good summary of impossible figures. 15 references to recent work.

Bruno Ernst. Escher's impossible figure prints in a new context. In:  H. S. M. Coxeter, et al., eds.; M. C. Escher -- Art and Science; North Holland (Elsevier), Amsterdam, 1986, pp. 124 134. Pp. 128 129 discusses the Breda Annunciation, saying it is 15C and quoting a 1912 comment by an art historian on it. There is a colour reproduction on p. 394. P. 130 shows and discusses briefly Bruegel's "The Magpie on the Gallows", 1568. Pp. 130 131 discusses and illustrates the Piranesi.

Bruno Ernst. (Het Begoochelde Oog, 1986?.) Translated by Karen Williams as: The Eye Beguiled. Benedikt Taschen Verlag, Köln, 1992. Much expanded version of his previous book, with numerous new pictures and models by new artists in the field. Chapter 6: Origins and history, pp. 68-93, discusses and quotes almost everything known. P. 68 shows a miniature of the Madonna and Child from the Pericope of Henry II, compiled by 1025, now in the Bayersche Staatsbibliothek, Munich, which is similar in form to the Breda Annunciation (stated to be 15C). (However, Seckel, 1997, below, reproduces it as 2 and says it is c1250.) P. 69 notes that Escher invented the impossible cube used in his Belvedere. P. 82 is a colour reproduction of Duchamp's 1916-1917 'Apolinère Enameled' - see 6.AJ.2. Pp. 83-84 shows and discusses Piranesi. Pp. 84-85 show and discuss Hogarth's 'False Perspective' of 1754. Reproduction and brief mention of Brueghel (= Bruegel) on p. 85. Discussion of the Breda Annunciation on pp. 85-86. Pp. 87-88 show and discuss a 14C Byzantine Annunciation in the National Museum, Ochrid. Pp. 88-89 show and discuss Scott Kim's impossible four-dimensional tribar.

J. Richard Block & Harold E. Yuker. Can You Believe Your Eyes? Brunner/Mazel, NY, 1992. Excellent survey of the field of illusions, classified into 17 major types -- e.g. ambiguous figures, unstable figures, ..., two eyes are better than one. They give as much information as they can about the origins. They give detailed sources for the following -- originals ??NYS. These are also available as two decks of playing cards.

W. E. Hill. My wife and my mother-in-law. Puck, (6 Nov 1915) 11. [However, Julian Rothenstein & Mel Gooding; The Paradox Box; Redstone Press, London, 1993; include a reproduction of a German visiting card of 1888 with a version of this illusion. The English caption by James Dalgety is: My Wife and my Mother-in-law. Cf Seckel, 1997, below.] Ernst, just above, cites Hill and says he was a cartoonist, but gives no source. Long, above, asserts it was designed by E. G. Boring, an American psychologist.

G. H. Fisher. Mother, father and daughter. Amer. J. Psychology 81 (1968) 274-277.

G. Kanisza. Subjective contours. SA 234:4 (Apr 1976) 48-52. (Kanisza triangles.)

Al Seckel, 1997. Illusions in Art. Two decks of playing cards in case with notes. Deck 1 -- Classics. Works from Roman times to the middle of the 20th Century. Deck 2 -- Contemporary. Works from the second half of the 20th Century. Y&B Associates, Hempstead, NY, 1997. This gives further details on some of the classic illusions -- some of this is entered above and in 6.AU and some is given below.

10: Rabbit/Duck. Devised by Joseph (but notes say Robert) Jastrow, c1900. Seckel, 2000, below, p. 159 (= 2002b, p. 156), says Joseph Jastrow, c1900.

10: My Wife and My Mother-in-Law, anonymous, 1888. However, in an exhibition, Seckel's text implies the 1888 German card doesn't have a title and the title first occurs on an 1890 US card. Seckel, 2000, below, p. 122 (= 2002b, p. 120), says Boring took it from a popular 19C puzzle trading card.

Al Seckel, 2000. The Art of Optical Illusions. Carlton, 2000. 144 well reproduced illusions with brief notes. All figures except 69-70 are included in Seckel, 2002b.

J. Richard Block. Seeing Double Over 200 Mind-Bending Illusions. Routledge, 2002. Update of Block & Yuker, 1992.

Edgar Rubin. Rubin's Vase. 1921. This is the illusion where there appears to be a vase, but the outsides appear to be two face profiles. [Pp. 8-11.] But Seckel, 2000, above, p. 122 (= 2002b, p. 120), says Rubin's inspiration was a 19C puzzle card.

My wife and my mother-in-law. P. 17 says Hill's version may derive from a late 1880s advertising postcard for Phenyo-Caffein (Worcester, Massachusetts), labelled 'My Girl & Her Mother', reproduced on p. 17.

P. 18 has G. H. Fisher's 1968 triple image, labelled 'Mother, Father and Daughter-in-Law'.

P. 44 says that Rabbit/Duck was devised by Joseph Jastrow in 1888.

Al Seckel, 2002a. More Optical Illusions. Carlton, 2002. 137 well reproduced illusions with brief notes, different than in Seckel, 2000, above. All figures except 65-66, 86-87, 95-95, 137 are included in Seckel, 2002b, but with different figure and page numbers.

Al Seckel, 2002b. The Fantastic World of Optical Illusions. Carlton, 2002. This is essentially a combination of Seckel, 2000, and Seckel, 2002a, both listed above. The Introduction is revised. Figures 69-70 of the first book and 65-66, 86-87, 94-95, 137 of the second book are omitted. The remaining figures are then numbered consecutively. The page of Further Reading in the first book is put at the end of this combined book.
Here I make some notes about origins of other illusions, but I have fewer details on these.
The Müller-Lyer Illusion -- <-> vs >---< was proposed by Zollner in 1859 and described by Johannes Peter Müller (1801-1858) & Lyer in 1889. This seems to be a confusion, as the 1889 article is by F. C. Müller-Lyer, cf above. Lietzmann & Trier, p. 7, date it as 1887.

The Bisection Illusion -- with a vertical segment bisecting a horizontal segment, but above it -- was described by Albert Oppel (1831-1865) and Wilhelm Wundt (1832-1920) in 1865.

Zollner's Illusion -- parallel lines crossed by short lines at 45^o, alternately in opposite directions -- was noticed by Johann K. F. Zollner (1834-1882) on a piece of fabric with a similar design.

Hering's Illusion -- with parallel lines crossed by numerous lines through a point between the lines -- was invented by Ewals Hering (1834-1918) in 1860.

6.AJ.1 TWO PRONGED TRIDENT
I have invented this name as it is more descriptive than any I have seen. The object or a version of it is variously called: Devil's Fork; Three Stick Clevis; Widgit; Blivit; Impossible Columnade; Trichometric Indicator Support; Triple Encabulator for Tuned Manifold; Hole Location Gage; Poiyut; Triple-Pronged Fork with only Two Branches; Old Roman Pitchfork.
Oscar Reutersvård. Letters quoted in Ernst, 1992, pp. 69-70, says he developed an equivalent type of object, which he calls impossible meanders, in the 1930s.

R. L. Gregory says this is due to a MIT draftsman (= draughtsman) about 1950??

California Technical Industries. Advertisement. Aviation Week and Space Technology 80:12 (23 Mar 1964) 5. Standard form. (I wrote them but my letter was returned 'insufficient address'.)

Hole location gage. Analog Science Fact • Science Fiction 73:4 (Jun 1964) 27. Classic Two pronged trident, with some measurements given. Editorial note says the item was 'sent anonymously for some reason' and offers the contributor $10 or a two year subscription if he identifies himself. (Thanks to Peter McMullen for the Analog items, but he doesn't recall the contributor ever being named.)

Edward G. Robles, Jr. Letter (Brass Tacks column). Analog Science Fact • Science Fiction 74:4 (Dec 1964) 4. Says the Jun 1964 object is a "three-hole two slot BLIVIT" and was developed at JPL (Jet Propulsion Laboratory, Pasadena) and published in their Goddard News. He provides a six-hole five-slot BLIVIT, but as the Editor comments, it 'lacks the classic simple elegance of the Original.' However, a letter of inquiry to JPL resulted in an email revealing that Goddard News is not their publication, but comes from the Goddard Space Flight Center. I have had a response from Goddard, ??NYR.

D. H. Schuster. A new ambiguous figure: a three stick clevis. Amer. J. Psychol. 77 (1964) 673. Cites Calif. Tech. Ind. ad. [Ernst, 1992, pp. 80-81 reproduces this article.]

Mad Magazine. No. 93 (Mar 1965). (I don't have a copy of this -- has anyone got one for sale?) Cover by Norman Poiyut (?) shows the figure and it is called a poiyut. Miniature reproduction in: Maria Reidelbach; Completely Mad -- A History of the Comic Book and Magazine; Little, Brown & Co., Boston, 1991, p. 82. Shows a standard version. Al Seckel says they thought it was an original idea and they apologised in the next issue -- to all of the following! I now have the relevant issue, No. 95 (Jun 1965) and p. 2 has 15 letters citing earlier appearances in Engineering Digest, The Airman (official journal of the U.S. Airforce), Analog, Astounding Science Fact -- Science Fiction (Jun 1964, see above), The Red Rag (engineering journal at the University of British Columbia), Society of Automotive Engineers Journal (designed by by Gregory Flynn Jr. of General Motors as Triple Encabulator Tuned Manifold), Popular Mechanics, Popular Science (Jul 1964), Road & Track (Jun 1964). Other letters say it was circulating at: the Engineering Graphics Lab of the University of Minnesota at Duluth; the Nevada Test Site; Eastman Kodak (used to check resolution); Industrial Camera Co. of Oakland California (on their letterhead). Two letters give an impossible crate and an impossible rectangular frame (sort of a Penrose rectangle).

Sergio Aragones. A Mad look at winter sports. Mad Magazine (?? 1965); reprinted in: Mad Power; Signet, NY, 1970, pp. 120 129. P. 124 shows a standard version.

Bob Clark, illustrator. A Mad look at signs of the times. Loc. cit. under Aragones, pp. 167 188. P. 186 shows standard version.

Reveille (a UK weekly magazine) (10 Jun 1965). ??NYS -- cited by Briggs, below -- standard version.

Don Mackey. Optical illusion. Skywriter (magazine of North American Aviation) (18 Feb 1966). ??NYS -- cited by Conrad G. Mueller et al.; Light and Vision; Time-Life Books Pocket Edition, Time-Life International, Netherlands, 1969, pp. 171 & 190. Standard version with nuts on the ends.

Heinz Von Foerster. From stimulus to symbol: The economy of biological computation. IN: Sign Image Symbol; ed. Gyorgy Kepes; Studio Vista, London, 1966, pp. 42-60. On p. 55, he shows the "Triple-pronged fork with only two branches" and on p. 54, he notes that although each portion is correct, it is impossible overall, but he gives no indication of its history or that it is at all new.

G. A. Briggs. Puzzle and Humour Book. Published by the author, Ilkley, 1966. Pp. 17-18 shows the unnamed trident in a version from Adcock & Shipley (Sales) Ltd., machine tool makers in Leicester. Cites Reveille, above. Standard versions.

Harold Baldwin. Building better blivets. The Worm Runner's Digest 9:2 (1967) 104 106. Discusses relation between numbers of slots and of prongs. Draws a three slot version and 2 and 4 way versions.

Charlie Rice. Challenge! Op. cit. in 5.C. 1968. P. 10 shows a six prong, four slot version, called the "Old Roman Pitchfork".

Roger Hayward. Blivets; research and development. The Worm Runner's Digest 10 (Dec 1968) 89 92. Several fine developments, including two interlaced frames and his monumental version. Cites Baldwin.

M. Gardner. SA (May 1970) = Circus, pp. 3 15. Says this became known in 1964 and cites Mad & Hayward, but not Schuster.

D. Uribe, op. cit. above, gives several variations.

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.
6.AJ.3. CAFÉ WALL ILLUSION
This is the illusion seen in alternatingly coloured staggered brickwork where the lines of bricks distinctly seem tilted. I suspect it must be apparent in brickwork going back to Roman times.
The illusion is apparent in the polychrome brick work on the side wall inside Keble College Chapel, Oxford, by William Butterfield, completed in 1876 [thanks to Deborah Singmaster for observing this].

Lietzmann & Trier, op. cit. at 6.AJ, 1923. Pp. 12-13 has a striking version of this, described as a 'Flechtbogen der Kleinen'. I can't quite translate this -- Flecht is something interwoven but Bogen could be a ribbon or an arch or a bower, etc. They say it is reproduced from an original by Elsner. See Lietzmann, 1953.

Ogden's Optical Illusions. Cigarette card of 1927. No. 5. Original ??NYS -- reproduced in: Julian Rothenstein & Mel Gooding; The Paradox Box; Redstone Press, London, 1993 AND in their: The Playful Eye; Redstone Press, London, 1999, p. 56. Vertical version of this illusion.

B. K. Gentil. Die optische Täuschung von Fraser. Zeitschr. f. math. u. naturw. Unterr. 66 (1935) 170 ff. ??NYS -- cited by Lietzmann.

Nelson F. Beeler & Franklyn M. Branley. Experiments in Optical Illusion. Ill. by Fred H. Lyon. Crowell, 1951, p. 42, fig. 39, is a good example of the illusion.

Lietzmann, op. cit. at 6.AJ, 1953. P. 23 is the same as above, but adds a citation to Gentil, listed above.

Leonard de Vries. The Third Book of Experiments. © 1965, probably for a Dutch edition. Translated by Joost van de Woestijne. John Murray, 1965; Carousel, 1974. Illusion 10, pp. 58-59, has a clear picture and a brief discussion.

Richard L. Gregory & Priscilla Heard. Border locking and the café wall illusion. Perception 8 (1979) 365 380. ??NYS -- described by Walker, below. [I have photos of the actual café wall in Bristol.]

Jearl Walker. The Amateur Scientist: The café wall illusion, in which rows of tiles tilt that should not tilt at all. SA 259:5 (Nov 1988) 100 103. Good summary and illustrations.
6.AJ.4. STEREOGRAMS
New section, due to reading Glass's assertion as to the inventor, who is different than other names that I have seen.
Don Glass, ed. How Can You Tell if a Spider is Dead? and More Moments of Science. Indiana Univ Press, Bloomington, Indiana, 1996. Now you see it, now you don't, pp. 131-132. Asserts that Christopher Tyler, of the Smith-Kettlewell Eye Research Institute, San Francisco, is the inventor of stereograms.