Hi Jonathan,
I'm glad you found answers to your questions on RG. The essay question was 'what is fundamental' -- so I chose the most fundamental feature of my research, a 1-dimension model of spacetime, with no appeal to the conventional 1 1 formulation that treats time as another dimension continuous with space rather than an integrated quantity.
My research program ultimately aims to show that complex systems are scalable by self-similar harmonic interactions to the least oscillation in the least dimension. This has obvious applications to quantum fields, quantum computing, quantum gravity and anything taken to be "quantum" vs. "classical". The domains are not demarcated -- Ramanujan's 24 modes of vibration are point coordinates encoded in 4 dimensions, 6 modes for each dimension, as every 3-dimension point has 6 coordinates. Because 24 is what Ramanujan called "highly composite" with divisors 1, 2, 3, 4, 6, 8, 12 and 24, we see (also from my previous research, ICCS2006) that the limit of 4 dimensions is 23 1, derived from summing the cardinal points of successive dimensions 0 - 4, zero dimensions having 1 point, 1 dimension having 3 points. You can see from the figure in the paper that indeed the least 1-dimension line segment has 3 points.
I've attached a figure showing my derivation of 23 1 points in 4 dimensions.
Do you see why it would be so hard to introduce my mathematical methods in 9 pages or less?
This is virgin territory and like Pascal, I haven't found the time to "make this short". Important though, is to accept Ramanujan's result and recognize that 1 point goes to infinity, because the integer 4 is a rare exception (the other is 36) to a general rule that the last index of a highly composite number is always 1. (See Kanigel, The Man Who Knew Infinity, Washington Square publishers 1991, p.236)
The invariance of dimension is a third necessary element, assuring reversibility.
Thanks for the score. Will get to your essay.
Best,
TomAttachment #1: 1_Dimension_Cardinal_Points.pdf