Exploring fundamental patterns in Nature
In high school I majored in art and music and yet hung out with the math, science and computer geeks. Being among other things a visual learner art was an obvious choice at the time. One of my favorite artists then and now is M.C. Escher. My art often embodied geometry and symmetry and really I enjoyed visualizing mathematical relationships and to me it was just "art". Yet I could handle even enjoy geometry and trigonometry because I could associate something real and discernible, the visual structures, the lines, angles and the shapes with the attendant mathematical symbols.
Once the math courses were more "advanced" mainly calculus and higher algebra the visual structures all but disappeared from the curriculum and gave way to practically all symbolic mathematics and introduced the abstract concept of the infinitesimal. More on this elsewhere. So to this day I pursue visual art often with underlying geometric structure and symmetries.
At the time I did not realize there was a very import area of study called visual mathematics.
At the time I did not realize there was a very import area of study called visual mathematics.
I have been pursuing self directed studies starting in high school and immersed myself in the work of Buckminster Fuller who's "Synergetic geometry" based on geodesics and the closest packing of spheres gave rise to the isotropic vector matrix AKA, "natures coordinate system" which was based on observable structures in nature. As an artist trained in the skill of observation this offered an alternative to the Cartesian co-ordinate system and the increasingly abstract mathematics associated with it. More on this elsewhere.
HSM Coxeter was a major influence. For him mathematics and music were intimately related, as he mentioned in a 1962 article on "Mathematics and Music" in the Canadian Music Journal. I was fascinated by his work on regular polytopes and higher-dimensional geometries. He championed the classical approach to geometry, in a period when the tendency was to approach geometry more and more via algebra.
He met Maurits Escher and his work on geometric figures inspired some of Escher's works, particularly the Circle Limit series based on hyperbolic tessellations and also inspired some of the innovations of Buckminster Fuller.
He met Maurits Escher and his work on geometric figures inspired some of Escher's works, particularly the Circle Limit series based on hyperbolic tessellations and also inspired some of the innovations of Buckminster Fuller.
The poly radial matrix I have developed is based on an extension of the regular polytope symmetry and the bi-radial matrix. Both will be described elsewhere.
Further investigations into fundamental patterns and coordinate systems were influenced on the physics side of things by David Bohm and his concept of "Wholeness and The Implicate order" which helped me make connections between the detailed geometric models I've developed to physics, particularly the concept of the "quantum potential". The work of Lee Smolin from the Perimeter Institute helped me make connections between this detailed geometry and quantum gravity and in the basic correlation between geometry and time. Wolfram's "New Kind of Science" has been influential as well in correlating the detailed geometry with physics, understanding the concept of "connection algorithms" and in the area of cellular automatons which in large measure appear related to synchrographics. This web site is a brief survey of various related projects.
Further investigations into fundamental patterns and coordinate systems were influenced on the physics side of things by David Bohm and his concept of "Wholeness and The Implicate order" which helped me make connections between the detailed geometric models I've developed to physics, particularly the concept of the "quantum potential". The work of Lee Smolin from the Perimeter Institute helped me make connections between this detailed geometry and quantum gravity and in the basic correlation between geometry and time. Wolfram's "New Kind of Science" has been influential as well in correlating the detailed geometry with physics, understanding the concept of "connection algorithms" and in the area of cellular automatons which in large measure appear related to synchrographics. This web site is a brief survey of various related projects.