Sat, Nov 15, 2008
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INTEGRAVITY - a New Concept
Project: Polytopia
Il y a des choses que l'intelligence seule est capable de chercher, mais que, par elle-même, elle ne trouvera jamais. Ces choses, l'instinct seul les trouverait ; mais il ne les cherchera jamais.

„There are some things that only the intellect is able to seek, but which it will never find by itself. Those things could only be found by instinct, but it shall never seek them.”


Artwork by the author

As the chairman of the Symmetry Society, Szaniszló Bérczi astutely remarked, the spidron nest is really simply a way to cut a cube into two symmetrical halves of equal volume. That is why those halves can be fitted together to create space-filling structures. However, he also saw immediately that this cutting of the cube is different to the usual truncations and concave and convex cutting methods. He felt it was unusual that the well-known polyhedron, what’s more also the icosahedron and the other regular solids can be cut into halves in this manner using surfaces consisting of diminishing sequences of triangles that can also be laid out in the plane. At the Symmetry Festival held in the August of 2003 in Budapest, the Lithuanian-British mathematician and educator Paul Gailiunas also noted that other space-filling structures could be obtained if the external angles of the spidron nests were varied. He is a great expert of space-filling and has published several scientific papers about the subject. He even recommended some specific angles that would allow bodies to be composed of less than eight nests that would be different to the spidrohedrons I had produced. His idea led to the birth of several new structures, one of which does fill space with its copies. A lucky misunderstanding also allowed us to find spidron nests with more spidron arms that became the starting point of further new research and the discovery of new surfaces and space-filling polyhedra. Of those, I would like to mention specifically the ten-sided nests that cut the quasi-crystals discovered some 25 years ago into two symmetrical pieces, which can then be used to build very strange non-periodic labyrinths. The discovery was made using an idea by the American mathematician and artist Marc Pelletier at one of our spidron meetings. Later, the so-called Spidron Team not only created innumerable new structures, mobiles and polyhedra but also entered subfields of great interest for the scientific community and produced novel concepts there. To give a few examples, we have had serious queries from quantum physicists who believe that the new concept of “spidron movement” could serve as a model for the recently described quantum gravity theory. In recent months, I have had discussions with an employee of NASA in Hungary, who specifically requested us to present the mathematical model of the pulsating and deforming spidron nests and the process of spidron rings breaking off at increasing intervals at their next meeting in Houston, because – as he said – NASA are interested in all mathematical models that may be suitable for the description of physical or even cosmic processes. But I encountered a similar degree of interest from representatives of the energy sciences, optical crystal physics, nanotechnology and other material sciences, too. The team of people working with the spidron continues to grow and even during the most recent months we have reached so many surprising results and conclusions that we decided to continue the work and maintain our relationship indefinitely. Luckily, the tools provided by modern information technology make this relatively simple. Week by week, new solutions, ideas and proposals are born in the universe of the spidron, which we go on to discuss at regular annual meetings and we support each other in making every seed of an idea flourish. The ideas that appear in individual subfields are quite easily adapted to other, even rather remote fields. The present history of the spidron is characterized by this transdisciplinarity, supported by a solid foundation of basic research in mathematics and geometry, which also allows the concepts to be translated for the representatives of the various subfields of science.

Artwork by the author

Those last thoughts lay increasing emphasis on the scientific aspects of the spidrons while they may bring into question their justification in the fields of design and art. However – as the very example of the spidrons so clearly demonstrates – today science infiltrates the toolkits of object formation, industrial and artistic thinking as well as realization, “production” and manufacture increasingly, and to an unprecedented extent. One of our works in progress is being produced for a bar in a Vienna hotel. The final object has been modeled virtually with great exactitude, but the language we have used to do so was the language of mathematics. For the carpentry workshop that is going to complete the work, the entire project is defined by a table containing the data and angles of connection of the many similar triangles of different sizes that make it up along with some colour codes to indicate the methods of construction and materials. Such integrated works bring together the knowledge and culture of several millennia, from Pythagoras and Leonardo da Vinci through János Bolyai and János Neumann to Roger Penrose, John Conway, Zaha Hadid, Gábor Bachman and Santiago Calatrava. The works that result from that sort of integrative work are rendered possible by the scientific and technical achievements of the age, hence we could use a new term to describe them. The 21st century has brought a world of integrated works and products. I would be pleased to introduce the concept of integravitism for the scientific and cultural processes of recent years. The term does not denote a style or a movement, but rather the stream of products incessantly generated by contiguous research and development that gravitates into a unity, created by the simultaneous appearance of technological progress, disciplines in dialogue, direct communication and global problems (and the global objectives that appeared alongside them) – and the need to respond to them. The works maturing in such workshops can only seem inhuman monstrosities of our modern, alienated world to the superficial observer. Their very character implies that they cannot really be individual products. The spidrons themselves are clearly a present center of gravity of integravity.

Artwork by Rinus Roelofs

Sat, Nov 15, 2008  Permanent link

Sent to project: Polytopia
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