Things Change Numbers Remain

Things Change Numbers Remain According to Ancient Beliefs. Who would believe that numbers are more permanent than figures of solid geometry?  Pythagoras and Plato did. Five regular polyhedrons prove the point.  Our current civilization thinks numbers are only an adjective., thinking that  they simply define quantity.

Things Change Numbers Remain in Their Duality

These geometrical figures change into their dual figure. The numbers of behind their faces and corners trade places:  The 8 faces of the octahedron become the 8 corners of the cube. Eight corners of the cube become the 8 faces of the octahedron.

In geometry, any of the above Platonic solids, the polyhedron is associated with a second dual figure.  In duality the number of  vertices of one solid correspond to the number of faces faces of its dual figure.  Only edges on both dual figures the same .[1]  As described in the picture above:  The 8 vertices of the cube become the 8 faces of the octahedron.  The cube and octahedron both retain 12 edges. Duality proves beyond doubt that numbers remain constant even if the shape of the geometrical figure changes.

What is the Meaning of This Geometrical Duality?

Because numbers between dual figures are constant while the figures themselves are not, numbers are more real and permanent than figures of solid geometry.

Pythagoras’ most important belief was that the physical world was mathematical and that numbers were the real reality.[2] 

Certainly, if one takes into account duality, at its deepest level, reality is mathematical in nature, rather than geometrical. Numbers become the constant.  Solids can appear and turn into their dual figure. Have fun discussing this point with your friends!

Internal link: Dozen Appears on the Ancient 3 x 3 Number Grid

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