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''The Swallow's Tail — Series of Catastrophes'' () was
Salvador Dalí Salvador Domingo Felipe Jacinto Dalí i Domènech, Marquess of Dalí of Púbol (11 May 190423 January 1989), known as Salvador Dalí ( ; ; ), was a Spanish Surrealism, surrealist artist renowned for his technical skill, precise draftsmanship, ...
's last painting. It was completed in May 1983, as the final part of a series based on the mathematical catastrophe theory of René Thom.


History and description

Thom suggested that in four-dimensional phenomena, there are seven possible equilibrium surfaces, and therefore seven possible discontinuities, or "elementary catastrophes": fold,
cusp A cusp is the most pointed end of a curve. It often refers to cusp (anatomy), a pointed structure on a tooth. Cusp or CUSP may also refer to: Mathematics * Cusp (singularity), a singular point of a curve * Cusp catastrophe, a branch of bifu ...
, swallowtail,
butterfly Butterflies are winged insects from the lepidopteran superfamily Papilionoidea, characterized by large, often brightly coloured wings that often fold together when at rest, and a conspicuous, fluttering flight. The oldest butterfly fossi ...
, hyperbolic umbilic, elliptic umbilic, and parabolic umbilic. "The shape of Dalí's Swallow's Tail is taken directly from Thom's four-dimensional graph of the same title, combined with a second catastrophe graph, the s-curve that Thom dubbed, 'the cusp'. Thom's model is presented alongside the elegant curves of a
cello The violoncello ( , ), commonly abbreviated as cello ( ), is a middle pitched bowed (sometimes pizzicato, plucked and occasionally col legno, hit) string instrument of the violin family. Its four strings are usually intonation (music), tuned i ...
and the instrument's f-holes, which, especially as they lack the small pointed side-cuts of a traditional f-hole, equally connote the mathematical symbol for an integral in
calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...
: ∫." In his 1979 speech, ''Gala, Velázquez and the Golden Fleece'', presented upon his 1979 induction into the prestigious Académie des Beaux-Arts of the Institut de France, Dalí described Thom's theory of catastrophes as "the most beautiful aesthetic theory in the world".Dalí, Salvador, 'Gala, Velásquez and the Golden Fleece' (9 May 1979). Reproduced in-part in: Originally published in French as ''Dalí, l'oeuvre et l'homme'' (Lausanne: Edita, 1984). He also recollected his first and only meeting with René Thom, at which Thom purportedly told Dalí that he was studying tectonic plates; this provoked Dalí to question Thom about the railway station at Perpignan, France (near the Spanish border), which the artist had declared in the 1960s to be the center of the universe. Thom reportedly replied, "I can assure you that Spain pivoted precisely — not in the area of — but exactly there where the Railway Station in Perpignan stands today". Dalí was immediately enraptured by Thom's statement, influencing his painting ''Topological Abduction of Europe — Homage to René Thom'', the lower left corner of which features an equation closely linked to the "swallow's tail": V = x^5 + ax^3 + bx^2 + cx, an illustration of the graph, and the term ''queue d'aronde''. The seismic fracture that transverses ''Topological Abduction of Europe'' reappears in ''The Swallow's Tail'' at the precise point where the y-axis of the swallow's tail graph intersects with the S-curve of the
cusp A cusp is the most pointed end of a curve. It often refers to cusp (anatomy), a pointed structure on a tooth. Cusp or CUSP may also refer to: Mathematics * Cusp (singularity), a singular point of a curve * Cusp catastrophe, a branch of bifu ...
.


See also

* List of works by Salvador Dalí * 1983 in art


References

{{DEFAULTSORT:Swallow's Tail, The Paintings by Salvador Dalí 1983 paintings Mathematics and culture Singularity theory Mathematical artworks Musical instruments in art Collection of the Dalí Theatre and Museum