摘要：The spiral has been studied for the first time in the book “About the spirals”, by Archimedes （Greece, 287-212 BC）. In America, the design of spirals seems to have been used previous to Archimedes＇ time, although in the Northwest of Argentina the appearance of this figure in ceramics can be dated between the years 800 and 1,400 （AD）. The spiral is found in cave paintings, in pumpkin carvings and in pottery, particularly those painted inside of plates （pucos in Quechua language）.There can be seen simple linear spirals, double spirals and spirals filled with squares, spirals in two, facing each other symmetrically, as well as spirals joined to bodies of animals. The number of spires detected in the largest spiral is 12, a number of evidently sacred characteristics. When there are several spirals in an earthenware vessel, it can be seen that all of them spin to the same side whether it is clockwise or not. This could have been caused by the predominance of the use of either one hand or the other by the ancient artist. This paper is produced with computer methods used to design spirals in the computer, either Archimedes or the logarithmic ones. Finally, the book： “Man and his symbols” of the psychiatrist Carl Gustav Jung （1875-1961） help to understand this congruencies. In this paper, Mathematics is complemented with the Archeology of art and Psychology.

摘要：Using certain models of twistor surfaces for fields of force and the mathematical relationships that lie among fields, lines, surfaces and flows of energy, it has been designed and developed a flight electromagnetic type system based on the synergic study of their electromagnetic field geodesics to generate vehicle levitation, suspension and movement without being in contact with the surface. The idea of such work is to obtain a new flight and impulse patent of an electromagnetic vehicle by principles of super-conduction and some laws of the current like Eddy currents and principles which are very similar to mechanics of sidereal objects like galaxies or stars under models of twistor surfaces. This vehicle will be controlled by one microchip that will be programmed by conscience operators algebra of electromagnetic type that leads to the flow of Eddy currents, the iso-rotations and suspension of the special geometrical characteristics vehicle, generating also on the vehicle structure certain “magnetic conscience” that provokes all movements like succeeding to the sidereal objects in the universe.