This one is a bit out there in left field, and hope it doesn't draw too much flak.
Intended more for the "Mathematically Adept" out there ... which I am not.
Please understand that I am not a mathematician ... but after poking around, I wonder if there are some avenues that might offer more useful outcomes than others. To that end, here goes ...
Challenge: Is it possible to define an instantiation of Hilbert Space as an embodiment of Fuller's Isotropic Vector Matrix System ?
Is there anyone out there that knows enough about Hilbert Spaces to offer a "rigorous but suitable for layman" explanation of whether
- the non-orthogonal 4-vector space defined by Buckminster Fuller's Vector Equilibrium (Isotropic Vector Matrix System), where each vector can only be a +ve multiple of the directional unit vectors
could be mapped, using a Hilbert Space, such that a 2-way reversible mapping function would be defined for transforming to and from that IVM Space and Cartesian Space?
I may have misunderstood the end-application of Hilbert Spaces, and may have put forward an unrealistic problem, or may have made an invalid association between Hilbert Spaces and the IVM System, but I felt it was worth a try putting that problem out there for consideration.
Thank you for taking the time to consider and to offer a "layman's" explanation as to its feasibility ... or lack thereof.
Eric
member of Geodesic Help Group