Linking language to geometry

“Now if the ancient orators, wishing to place from day to day the parts of the speech which they had to recite, confided them to frail places as frail things, it is right that we, wishing to store up eternally the eternal nature of all things which can be expressed in speech … should assign to them eternal places” — Giulio Camillo, L’idea del Theatro

Daily life is filled with experiences; happenings occur and we observe and describe them as we reflect on events and communicate with others our perceptions and evaluations of those events. For this we use language, initially spoken and with the invention of letters eventually written as well. The events we experience are occasionally evaluated as carrying some negative emotional charge. This charge can be processed using descriptions and inferences. Psychologically this can be seen as verbally describing emotional parts of experiences allowing us to prevent future occurrences of the emotional parts of experiences by way of the understanding of their emergence. Neurally this can be seen as the iterative and hierarchical explaining away of residual nervous impulses by returning predictions of those residuals (predictive coding; Huang et al., 2011, free energy principle; Friston, 2010). Geometrically this can be seen as the homeostatizing of perturbations on a toroidal model of the sensory manifold. But residuals of nervous impulses are not always completely explained away, and perturbations are not always completely homeostatized. Both unexplained residuals of nervous impulses and remaining perturbations may emanate as language, returning us to the psychological level of verbal descriptions. A difficulty emerges in that these verbal descriptions themselves may carry emotional charge and can be seen as parts of experienced events. We could continue to iteratively describe verbally the events and our descriptions of those events, and indeed the nervous system iteratively attempts to explain away residuals of nervous stimuli, and generally perturbations are continuously homeostatized. Yet, we may reach a level of continued emotional perturbation, the rate of which exceeds the rate of homeostatizing, and emotionally charged nervous impulses may leave residuals unexplained by the returning of predictions, while psychologically we may reach a state of repeated verbal description of emotional evaluations. This potentially escalating process whereby an event leads to a buildup of perturbations, unexplained residuals, repeated verbal descriptions, can be finalized by a series of inferences linking language to geometry. First, symbolize the experienced emotionally charged event in combination with its subsequent descriptions using a word or an abbreviation of multiple words, in written form. Then, count the number of letters of that word or abbreviation. Then, compute the number of possible permutations of the word and divide by two to arrive at all possible mirrored pairs of the word. Then for every possible pair perform the following series of inferences; associate each letter of the word to a point, the points lying equidistantly on a straight line, forming a straight line of the length equal to the number of letters minus one. Then infer a mirrored version of the word opposite the word, also associated to the same number of points forming a line perpendicular to the first, at a distance equal to the distance of the first line, forming a square. Then, infer a fifth point perpendicular to the plane of the square and at some distance away from its center, forming a five-point pyramid. Then, duplicate and mirror the pyramid, the two touching at their bases, forming an octahedron. Then, shift the two pyramids into each other until their apexes meet. Then, infer the point at which their apexes meet to open; thus rotate their bases in opposite directions, and turn them into circles, opening the middle and arriving at an hourglass-shape. Further expand the middle to arrive at a cylinder. This cylinder contains one of the possible pairs of the permuted words which served to symbolize the initial sequence of emotionally charged events. We can cylinderize all possible pairs and pack the cylinders using closest circle packing, iteratively by taking 2, 3, 4, 5, 6, 7, or 11 cilinders, packing them into their closest packing configuration, and cylinderizing by starting at the pyramidal step of the previously described process. The final cylinder can then be extended in either direction, expanding its circumference, folding outwardly around itself, meeting itself into a torus. The torus forms the model on which we subsequently continue to homeostatize perturbations. As such, by linking language to geometry it’s possible to undo experienced events of their emotional charge through a series of geometrical inferences, finally restoring the toroidal model of the sensory manifold used to further homeostatize perturbations.


Korzybski, A. K. (1933) Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. Lancaster, Pa., New York City, The International Non-Aristotelian Library Publishing Company, The Science Press Printing Company.

Perelman, G. (2008) Ricci flow with surgery on three-manifolds. arXiv:math/0303109.