Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a main inspirational source for Plato and platonism.
Later resurgence of ideas similar to those held by the early Pythagoreans are collected under the term Neopythagoreanism.
The Pythagoreans were called mathematikoi, which means "those that study all1"
To say it is easy in knowing where to begin, is a understatement of what has been an enormous struggle to define the world around me. Indicative of the complications of how one may have seen this world in regards to the "views of a Synesthesist," would have taxed most "science minds" if they had "this inkling" of the complexity this brings to science. Think about what is implied here when one refers to "studying it all?"
So as I lay in the twilight hours of the mind's rest period, there are these things that I am asking of myself, as to how I may point to what is comparative in the "geometric views of science" and what is comparative to the views of that science in relation to examples given of the Synesthesist who sees from a certain position.
Again, my mind falls back in the history of humanities evolution and while the distinctiveness of sectors of that past history, it would not be unkind to draw from that history and present the question of what a Synesthesist might have seen in relation to the numbers?
Create and play with the most beautiful, hypnotic light illusions you have ever seen.
I seen the above in relation to Lubos's post. It would be nice to offer the "equation correlations" to these "colour displays" in string theory?:)
Numbers
Are you quicker then I then to see that numbers may have had the colour attached to their very nature, that "all things" then my have had this basis of "music" and "colour association" thrown "into the mix/cross over points"" to call it the Pythagorean?
So imagine being strapped with the job to start from some place, and move any mind to consider the complexity of "departing euclidean views" to meld with the "non-euclidean reality" assigned our everyday species to "what is natural" from straight lines and such. Has now moved to a dynamical world of "Faraday lines" Gauss's role as "teacher of Gaussian Co-ordinates" to views of his student, "Riemann?"
This equation provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found.
Should one be so crude as to see that straight lines can have a "greater implication of design" that one would not have seen, had they not understood Gauss's work? That if you moved yourself to natures's domain, how many lines are really that straight?
Ask your self then what is natural and what was man-made? That these straight lines are indeed an order to mankind's "ode to building and living," while there are these "other worldly visions" supplied in the "non euclidean realm" existed free from man's definition of nature.
8.6 On Gauss's Mountains
One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean. It's certainly true that Gauss acquired geodetic survey data during his ten-year involvement in mapping the Kingdom of Hanover during the years from 1818 to 1832, and this data included some large "test triangles", notably the one connecting the those three mountain peaks, which could be used to check for accumulated errors in the smaller triangles. It's also true that Gauss understood how the intrinsic curvature of the Earth's surface would theoretically result in slight discrepancies when fitting the smaller triangles inside the larger triangles, although in practice this effect is negligible, because the Earth's curvature is so slight relative to even the largest triangles that can be visually measured on the surface. Still, Gauss computed the magnitude of this effect for the large test triangles because, as he wrote to Olbers, "the honor of science demands that one understand the nature of this inequality clearly". (The government officials who commissioned Gauss to perform the survey might have recalled Napoleon's remark that Laplace as head of the Department of the Interior had "brought the theory of the infinitely small to administration".) It is sometimes said that the "inequality" which Gauss had in mind was the possible curvature of space itself, but taken in context it seems he was referring to the curvature of the Earth's surface. 2
The Interior Probabilities Manifests as Colour
How foolish would I be then to tell you that "Heaven' Ephemeral Qualities," are coloured to the degrees that "gravity defines itself in time?" That "model building" had to take place, so that the understanding of where this gravity explains itself, could find correlations to humans experiencing "durations of time" within in the living of day to day.
Again I move one back to what this "egg of fluttering does" as of physiological consequent, as the correlations of those same colours manifest in the qualities of those same thought patterns. Those experiences mapped to MRI imaging are condensible features "in the physical" do not explain the "Ephemeral Quality" assigned to each of these regions. Had one knew how to switch around the "value of consciousness" to the condensible feature as brain matter, one would have known about the happenings taking place "outside" of our bodies.
It is here to then that I take from the "metaphysical realm" and bring it into the relations of what is happening in the physical brain. While history has shown groups who gathered to see what was happening, saw "human experiencing" as they went through these colour modes.
1 Hemmenway, Pryia – Divine Proportion pp66, Sterling Publishing, ISBN 1-4027-3522-7
2 Reflections on Relativity8.6 On Guass's Mountain