Peter,
Yes, it has been awhile. I had prepared my paper for another purpose, but then found it could be applied to this years' FQXi essay contest. In the response to my first essay comment I stated, If we use the premise that specific mathematical structures, such as arithmetic, geometry, algebra, etc., were developed to solve a type of problem, there is nothing mysterious about that. Basically, what we possess is incomplete information as to why certain mathematical structures were originally developed; algebra and geometry are examples. As man began to quantize the characteristics of the environment in which he lived, additional mathematical processes were developed to assist in the process.
Your essays' final statement is right on the mark, Mathematics itself then works nicely to local domain limits but is easily misused and we can't assume algorithms which work also accurately model nature. The importance of improving breadth of input and or deriving initial conceptions unimpeded by prior assumptions emerges.
Unfortunately, it seems our scientific establishment revels in using prior assumptions and or creating an assumption that has no basis in fact. Astronomers use of dispersion measure (DM) is a good example. DM assumes there is a uniform electron density throughout the universe. This assumption ignores the existence of gravity, which tends to aggregate everything that possesses mass. Everything should be denser as one gets closer to a large aggregation of particles.
I do not trust many of the conclusions radio astronomers make when they ignore the fact that their listening point is inside the Suns' heliosphere, which some studies indicate is a very energetic medium that produces many electromagnetic emissions. I produced the following paper, "Cosmic Dust, Refraction and Emissivity" after reading about the BICEP debacle. http://vixra.org/abs/1411.0103
I refer to the Suns' heliosphere as Van Allen Belts on steroids.
I was tempted to put the following statement in my original paper, but I knew that would never get past peer review, "Every intelligent species in the universe, after discovering the relationships identified in the triangle pair concept, structured their scientific units of measure based upon the units revealed in the concept." Strangely, my original IEEE published paper is getting attention from a particular corporation.