Sunday, March 26, 2017

Student Reading

At the university level, we might introduce tetravolumes in a philosophy of mathematics class, as a good example of how different language games suggest different axioms.

Imagine a tribe in which multiplication were presented differently. That's hard to "imagine" without some concrete example. This Tropical Math YT is the precursor to using three poles, say X, Y and Z. but no longer mutually perpendicular.

Non-Euclidean geometries have already legitimized branching away from Mother Goose Math into alternative territory. This might also be an Art History class where we look at Non-Euclidean geometry in Modern Art.

Remember, the meaning of '4D' depends on the namespace:
  • 4D as Time: time machine physics ala Einstein / Minkowski
  • 4D as Spatial in nD Euclidean Geometry: polytope math ala H.S.M. Coxeter
  • 4D as primitively Four Directional (tetrahedron = 4 arrow heads) in pre-Frequency a priori res extensa (American Transcendentalist with Lakota influence) 
On a plane (plain), we divide the unit circle into four quadrants with reference to the four compass directions.

In zero-G space (an ideal conceptualization) we have four directions of the tetrahedron and the four quadrants of space, per IVM "caltrop" coordinate system (so "4D" in the Lakota medicine wheel sense).

For hexahedronists, it's the three-also-six directions of the cube that make the six-spoked XYZ "jack" (so in the XYZ namespace we say space is "3D").

Storing Liquid