View source for The Swallow's Tail

{{Short description|1983 painting by Salvador Dalí}}
{{Use dmy dates|date=April 2020}}
{{Infobox artwork
| image_file=The_Swallowtail.jpg
| backcolor=#FBF5DF
| image_size=400px
| title=The Swallow's Tail — Series on Catastrophes
| artist=[[Salvador Dalí]]
| year=1983
| medium=[[Oil painting|Oil on canvas]]
| height_metric=73
| width_metric=92.2
| height_imperial=28.7
| width_imperial=36.3
| metric_unit=cm
| imperial_unit=in
| museum=[[Dalí Theatre and Museum]]
| city=[[Figueres]]
}}

'''''The Swallow's Tail — Series of Catastrophes''''' ({{langx|fr|La queue d'aronde — Série des catastrophes}}) was [[Salvador Dalí]]'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 space|four-dimensional phenomena]], there are seven possible equilibrium surfaces, and therefore seven possible discontinuities, or "elementary catastrophes": [[Catastrophe theory#Fold catastrophe|fold]], [[Catastrophe theory#Cusp catastrophe|cusp]], [[Catastrophe theory#Swallowtail catastrophe|swallowtail]], [[Catastrophe theory#Butterfly catastrophe|butterfly]], [[Catastrophe theory#Hyperbolic umbilic catastrophe|hyperbolic umbilic]], [[Catastrophe theory#Elliptic umbilic catastrophe|elliptic umbilic]], and [[Catastrophe theory#Parabolic umbilic catastrophe|parabolic umbilic]].<ref>{{cite book|author=Thom, René|year=1972|title=''Structural stability and morphogenesis. an outline of a general theory of models'', (D.H.Fowler, trans.) (Reading, Mass. London. Benjamin. 1975). Originally published in French as ''Stabilité structurelle et morphogénèse''|publisher=Westview Press |isbn=0201406853}}</ref> "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]] and the instrument's [[sound hole|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]]: ∫."<ref name="King">{{cite book|last1=King|first1=Elliott|editor1-last=Ades|editor1-first=Dawn|editor-link1=Dawn Adès|title=Dali|date=2004|publisher=Bompiani Arte|location=Milan|pages=418–421 |isbn=0847826732}}</ref>{{long quote|date=June 2019}}

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".<ref>Dalí, Salvador, 'Gala, Velásquez and the Golden Fleece' (9 May 1979).  Reproduced in-part in: {{cite book|author=Descharnes, Robert|year=1984|title=''Dalí, the Work, the Man''|publisher= New York: Harry N. Abrams |page=420 |isbn=0810908255}} Originally published in French as ''Dalí, l'oeuvre et l'homme'' (Lausanne: Edita, 1984).</ref>  He also recollected his first and only meeting with René Thom, at which Thom purportedly told Dalí that he was studying [[tectonic plate]]s; this provoked Dalí to question Thom about [[Gare de Perpignan|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": <math>V = x^5 + ax^3 + bx^2 + cx,</math> 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 (singularity)|cusp]].<ref name="King" />

==See also==
* [[List of works by Salvador Dalí]]
* [[1983 in art]]

==References==
{{Reflist|30em}}

{{Salvador Dalí}}
{{Mathematical art}}
{{Authority control}}

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