RTD info logoMagazine on European Research

Special Issue - March 2004
  SHAPES, STRUCTURES, OBJECTS  -  The enigma of knots

Engaging mathematicians ans psychoanalysts, fascinating astrophysicists and biologists, knots are also evident in the history of art. Examples of an 'eternal' symbol.

Jorge Eielson, Nodo, 1973. Courtesy Galleria d'Arte Niccoli, Parma
Jorge Eielson, Nodo, 1973. Courtesy Galleria d'Arte Niccoli, Parma
In mathematical terms, a knot is a closed curve. It can intertwine, crossing over or under itself. A simple circle is also a knot. Knot theory is a field of topology   – or the study of the geometrical properties of an object which remain unchanged by continuous changes in shape or size, providing nothing is severed. Mathematicians seek to discover whether or not an apparently complex knot can be simply untied, whether two apparently different knots are the same, and how to classify knots. It is an area of research that is also of interest to biologists who frequently observe knotted molecules through the lenses of their electronic microscopes. 

The physical and concrete knot has long been a subject of fascination for the artist. Unlike the abstract knot, given a little patience it can always be untied. It may take some time to unravel its mysteries, discover the loose end and follow it through its many twists and turns. But a solution can always be found. The Peruvian artist Jorge Eilson has been working on the knot for the past 40 years. For him it is the metaphor for life itself – from the DNA sequence to the tangle of nerves and neurons. 'Our whole existence,' he writes, 'is the story of a structure which, to survive, must continually invent a network of information and interactive relationships to widen its horizons.'  

Two ways of presenting the Borromean Rings, the heraldic symbol of the Borromea family at the time of the Renaissance, at the Castello Sforzesco in Milan (IT). On the left, the interlacing is wrong; the 'real' rings are on the right. No one ring links with any other within the Borromean Rings, yet the group that they form cannot be unknotted. If one of the three rings is cut, three separate rings are obtained. These rings can also be seen on stone sculptures in Gotland, an island off the coast of Sweden, which are believed to date from around the ninth century. They can also be found in the form of a triangle in northern Scandinavia. A representation of the Borromean Rings in the form of 'Odin's triangle’ or 'the knot of the slain' can also be found in this region.  Matemilano exhibition, MilanTwo ways of presenting the Borromean Rings, the heraldic symbol of the Borromea family at the time of the Renaissance, at the Castello Sforzesco in Milan (IT). On the left, the interlacing is wrong; the 'real' rings are on the right. No one ring links with any other within the Borromean Rings, yet the group that they form cannot be unknotted. If one of the three rings is cut, three separate rings are obtained. These rings can also be seen on stone sculptures in Gotland, an island off the coast of Sweden, which are believed to date from around the ninth century. They can also be found in the form of a triangle in northern Scandinavia. A representation of the Borromean Rings in the form of 'Odin's triangle’ or 'the knot of the slain' can also be found in this region.  Matemilano exhibition, Milan


Two ways of presenting the Borromean Rings, the heraldic symbol of the Borromea family at the time of the Renaissance, at the Castello Sforzesco in Milan (IT). On the left, the interlacing is wrong; the 'real' rings are on the right. No one ring links with any other within the Borromean Rings, yet the group that they form cannot be unknotted. If one of the three rings is cut, three separate rings are obtained. These rings can also be seen on stone sculptures in Gotland, an island off the coast of Sweden, which are believed to date from around the ninth century. They can also be found in the form of a triangle in northern Scandinavia. A representation of the Borromean Rings in the form of 'Odin's triangle’ or 'the knot of the slain' can also be found in this region. Matemilano exhibition, Milan