Pythagoras

To the Greeks the world was built up from the four elements of the Pythagorean system, fire, air, water and earth. These were linked to the four humours, black bile, yellow bile, phlegm and sanguine. The Pythagoreans had a geometrical conception of the world, presumably derived in some way from the Egyptians' arts of survey.


The 6-faced CUBE represented the dry, cold qualities of EARTH

 "The Pythagoreans erected a system of plane geometry in which were formulated the principle theorems which concern parallels, triangles, quadrilateral and regular polygonal figures and angles. They discerned many important properties of prime numbers and progressions." (Singer, 1941, pp20-21).
They also reached a concept of irrational numbers, e.g. 'pi' (3.1415...). Their mystical view of the sphere as the perfect figure led to a conception of the earth and the heavenly bodies as spheres.

From the triangle and the square Greek philosophers developed the concept of the triangular-faced ideal solids as the basic atoms of all things. Fire was composed of four-faced tetrahedra, earth of six-faced cubes, air of eight-faced octahedra and water of twenty-faced icosohedra.

Here we find perhaps the earliest known example of the use of technological conceptions to reflect on the nature of the world and the mind. The geometry as a projection of the mind into an ordering process for accurate measurement and division of land, reflects back and provides a basis for thinking about philosophical questions of becoming and essence. As Singer says:


The 4-faced TETRAHEDRON represented the dry, hot qualities of FIRE		 "The human mind, it must be supposed, is somehow attuned to the processes of nature. We live in a world that is susceptible of mathematical expression." (Singer, 1941, p19).