The Swallow's Tail
Encyclopedia
The Swallow's Tail — Series on Catastrophes was Salvador Dalí
's last painting. It was completed in May 1983, as the final part of a series based on René Thom
's catastrophe theory
.
Thom suggested that in four-dimensional phenomena, there are seven possible equilibrium surfaces, and therefore seven possible discontinuities, or "elementary catastrophes": fold, cusp, swallowtail, butterfly, 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
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
:
."
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’. 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, which the artist had declared in the 1960s as the centre 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 Thom’s equation for the ‘swallow’s tail’,
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
.
Salvador Dalí
Salvador Domènec Felip Jacint Dalí i Domènech, Marquis de Púbol , commonly known as Salvador Dalí , was a prominent Spanish Catalan surrealist painter born in Figueres,Spain....
's last painting. It was completed in May 1983, as the final part of a series based on René Thom
René Thom
René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...
's catastrophe theory
Catastrophe theory
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry....
.
Thom suggested that in four-dimensional phenomena, there are seven possible equilibrium surfaces, and therefore seven possible discontinuities, or "elementary catastrophes": fold, cusp, swallowtail, butterfly, 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
Cello
The cello is a bowed string instrument with four strings tuned in perfect fifths. It is a member of the violin family of musical instruments, which also includes the violin, viola, and double bass. Old forms of the instrument in the Baroque era are baryton and viol .A person who plays a cello is...
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
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
:
."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
DALI
DALI may refer to:* Danish Audiophile Loudspeaker Industries* The "Distance-matrix ALIgnment" algorithm used in the FSSP database on structurally similar proteins* Digital Addressable Lighting Interface* Dartmouth Assessment of Lifestyle Index...
described Thom’s theory of catastrophes as ‘the most beautiful aesthetic theory in the world’. 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
Perpignan
-Sport:Perpignan is a rugby stronghold: their rugby union side, USA Perpignan, is a regular competitor in the Heineken Cup and seven times champion of the Top 14 , while their rugby league side plays in the engage Super League under the name Catalans Dragons.-Culture:Since 2004, every year in the...
, France, which the artist had declared in the 1960s as the centre 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
Perpignan
-Sport:Perpignan is a rugby stronghold: their rugby union side, USA Perpignan, is a regular competitor in the Heineken Cup and seven times champion of the Top 14 , while their rugby league side plays in the engage Super League under the name Catalans Dragons.-Culture:Since 2004, every year in the...
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 Thom’s equation for the ‘swallow’s tail’,
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 cuspCusp (singularity)
In the mathematical theory of singularities a cusp is a type of singular point of a curve. Cusps are local singularities in that they are not formed by self intersection points of the curve....
.