PLEASE TAKE NOTE, THE COLLOQUIUM WILL BEGIN AT 4:00 P.M. BEGINNING IN 2014-15
DEPARTMENT OF PHILOSOPHY
THURSDAY, JANUARY 29, 2015
WATSON HALL, ROOM 517 @ 4:00 p.m.
Françoise Monnoyeur-Broitman (Linköping University, Sweden)
Title: “The Platonic Solids and Crystallography: a Lesson in the Power of Thought”
Matter has been defined in very different ways according to physical and philosophical theories through the ages. Matter was represented by elements and geometrical figures in the Greek antiquity, by metals during the flourishing time of alchemy, by mathematical extension during the scientific revolution, and by atoms, waves, energy, and photons in the most recent period.
Each theory has proposed its own model to understand the structure or main properties of matter. In the Timaeus of Plato the four elements (earth, water, air, and fire) are modeled with geometric solids chosen according to the type of triangles (isosceles or equilateral) composing their faces. Mobility and stability are the properties associated with this model: the solids made of acute angles are supposed to be more mobile than the solids with right angles. The point of interest was to represent the transformation, for instance, of water into air through fire. Plato’s scientific instruments are geometry (Pythagoras’ theorem) and perception, and his scientific values are symmetry and rationality.
Nowadays the study of matter, carried out by using advanced instruments like the electron microscope and x-ray diffraction, has helped to describe in a precise way the structure of matter. For instance, it has been shown that carbon atoms can be bonded forming different geometrical structures, and as result of each structure different materials and properties are obtained: tetrahedral (kind of cubic) structures in diamonds, hexagonal networks in graphite, and forming a spherical structure in a fullerene. While the tetrahedral structure results to be the hardest known material, the hexagonal is very soft and slippery, and the fullerene extremely elastic. The value of symmetry is fundamental to the understanding of the materials micro-structure and their properties.
In this presentation, I will analyze how Platonic solids prefigure the structures of carbon atoms. It will be shown how Plato conceived his solids to explain the movement/stability of the elements, and how hardness/softness of the material come into play in modern crystallography. In both Platonic solids and crystallography, visualization and symmetry are at the center of the discovery process.
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