Step 1 in the paradigm transition: Start with magnetic tetrahedron.

Dial back about 350 years and one of Descartes' messages was, "Start with the cube".  From there flows a lot of abstract math that turns out to have uncanny connections to features in physical reality.  Why? So far, we don't have a clear understanding why that is. 

Dial back about 100 years and we notice that Descartes' classical start is straining under the load.  Time has gone from being absolute to relative, and the mechanistic world turns out to be composed of  inner fundamentals of shimmering multiple states.

Dial back, say, 50 to  70 years and a person named R. Buckminster Fuller,  among other things, said, "Start with tetrahedron" and he went on to develop geodesic domes, the dymaxion map, and to predict the structure and existence of what have since become known as  "fullerenes" which are important in chemistry and nano-technology.

Dial back about 25 years and this author idly differentiated  Fuller's structural perspective by asking "What  do you get when you build a tetrahedron out of magnets. In effect  saying, "Start with a magnetic tetrahedron".

The outcome unfolds in an interesting manner.  There are five ways  to align four rod magnets along the radii of a tetrahedron. That is, immediately, one is dealing  directly with structurally  similar but energetically different multiple states.  Moreover, there are two ways to form states which have the same look and feel locally, but which differ in their  relative function within the enfolding field. As well, some of the states exhibit variable mass-density.  And these features are ALL   expressed in haptic, analog mathematically  "terms" which deliver physical intuition with absolutely NO abstract math pre-requisite. 

"Why is this?", one may  wonder.