Architecture and Plate Tectonics

In its third episode ("When Knowledge Conquered Fear") the recent version of “Cosmos” by Neil deGrasse Tyson featured an interesting segment involving Robert Hooke, Edmond Halley, Isaac Newton and the discovery of gravity.  Tyson’s treatment of this subject neglected to mention Hooke’s discovery of the funicular or catenary form, which is a unique insight dependent on gravity.   Hooke’s revelation anticipates and incorporates gravity. 

Hooke revealed his discovery describing how a masonry arch works in a teasing anagram with a succinct introduction:   "The true Mathematical and Mechanical form of all Manner of Arches for building, with the true butment necessary to each of them. A Problem which no Architectonic writer hath yet attempted, much less performed. abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuux."

Hooke did not provide a translation of this anagram during his lifetime.  It was finally revealed by his executor in 1705:  "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum--As hangs a flexible cable, so inverted, stand the touching pieces of an arch."  This insight has been the essential summary of Masonry Science and arch design since its 1705 revelation.

Hooke’s use of the word “Architectonic” in the preface to his anagram is interesting if we consider its etymology and related words and phrases.  Architectonic (adj.)  1:   of, relating to, or according with the principles of architecture. 2:  having an organized and unified structure that suggests an architectural design.  From “Arch” (arch) + “tectonic” (building). 

“Plate tectonics” is a geological term used to describe the movement of rigid sections of the earth’s crust around the planet.  If an arch is considered as completely as possible, it is a sphere.  Plate tectonics may be viewed as a dynamic planetary architectonic.  Plates are divided by three types of boundaries: divergent (crust is created), subduction (crust is destroyed) and shear boundaries (crust slides against crust).

Tectonic plates slide against each other in the manner of conjugate shearing.  If the creation and destruction of crust are neglected, one is left with a series of plates which will conjugate shear around a spherical surface.  How can one design plates which will conjugate shear around a spherical surface?

Gratis deGrasse Tyson, for neglecting Hooke’s flexible cable hanging under gravity and allowing me to ramble on about arches, architects, architectonics and plate tectonics.