Wednesday, April 25, 2018

Positive Futurism

I have yet to share Quadray Coordinates with either Jesuit or Central Catholic.  You might suppose, given my background as a Catholic school teacher, that I'd be posting theses on their doors or something.  Actually St. Mary's would be the most apropos, as most similar to St. Dominic Academy.

As it is, I've been promulgating said alternative basis vector bouquet with Linus Pauling House (ISEPP), IEEE (indirectly through Portland Center Stage), Saturday Academy and the Systems Science folks at Portland State.

What's so special about Quadrays?  We start with four vectors from the origin (0,0,0,0) to the four corners of a regular tetrahedron, with addresses (1,0,0,0), (0,1,0,0) (0,0,1,0) and (0,0,0,1). It's pretty easy to see that, from these, one may develop a spanning set, not including rotation as one of the necessary operations.  We appreciate change in direction is distinct from a change in length.

In ordinary XYZ math, three basis vectors (1,0,0) (0,1,0) and (0,0,1) are helpless to reach 7/8ths of space minus help from their counterparts, the rotated versions.  Vector negation (180 degree rotation) is primitive to this space such that -i, -j, -k are linearly dependent, not independent, of their mirrors.

In the Quadray system, we're fine with rotation e.g. -(1,0,0,0) = (-1,0,0,0) = (0,1,1,1) but don't need it to span space with our original four basis vectors.  Any point is a linear combination of the original four, with at least one of them passive i.e. not involved.

By anchoring this caltrop in some Philosophy of Mathematics, we open three doors at once:

(A) Wittgenstein's philosophy of mathematics, based on "language games", comes to life and
(B) we're right where we need to be vis-a-vis the CCP sphere packing and
(C) we've established a context for a Concentric Hierarchy of polyhedrons

All twelve combinations of {2,1,1,0} e.g. (2,0,1,1)(0,2,1,1) and so on, point to the vertices of the cuboctahedron, twelve spheres around one.  We're ready to give all CCP ball centers positive integer coordinates.

I've also been in touch with Eastern Orthodox, "the other Christians" outside the Euro-Anglo Catholic-Protestant axis.  My essay on how an RT on RT would signal a connection with New England Transcendentalism showed up in Medium some time ago.

Some readers understand how (C) links us to a lot of positive futurism, including a brilliant critique of Corporate Personhood (Grunch of Giants).  I setup the website to keep those memes alive.

I don't really need to bring my work to the Quakers as I'm already identified as a Friend.  However at QuakerQuaker you'll find me reaching out to Sufi schools.  Having attended the 1999 Parliament for World Religions in Cape Town (when my wife Dawn got to visit with the Dalai Lama in Durban), I'm quite used to Ecumenism.