Geometry of Language
LANGUAGE OF GEOMETRY
‘Geometry likewise lies beneath the content of our writing. Language has a verbal geometry, and writing necessitates a crafting of space. Geometric space and form are implicit in language’s body, and geometry can be used as a tool to enhance the powerful modes of communication of which language is capable.’ – Arielle Saiber
While many authors over the course of literary history have noted and consciously elaborated the relationship between geometry and language, few have done so as comprehensively and explicitly as the sixteenth-century polymath Giordano Bruno. Giordano Bruno (1548-1600): philosopher, poet, playwright, mnemonist, and magus.’ – Arielle Saiber
The Flower and the Serpent
‘Shakespeare with his clever hidden geometries opens up unending vistas of multiple mirrors, kaleidoscopic images, broken shards of fractal images that unfold and unfurl as our imagination sweeps in and out of them, as we find and loose ourselves in his creations, as each successive generation interacts and reinvents his text’ - Ismail Serageldin
Geometry is not just a collection of shapes but an understanding of relations among shapes and related calculations as well. Did Man discover the relations and became capable of changing shapes to each other? Nature was not able to give him such ability on itself. This ability was what created geometry.
This would imply that geometric knowledge and patterns had deep roots in time and in the daily lives of humans. An understanding of the procedures during which geometric patterns evolve, the mechanisms of their evolution and the position they occupied in humans’ minds may help decode their meanings in later periods.
Geometric patterns constitute an important part of the most ancient writing systems of the Old World in the Sind valley, Iran and Mesopotamia. Some of the geometric shapes can be found in the Palaeolithic petroglyphs of these countries as well as other parts of the world.
Sierpinski Gasket - Zipf's Law
Zipf's law is an empirical law formulated using mathematical statistics that refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions.
For example, Zipf's law (Sierpinski’s Gasket) states that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table. Thus the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc., the rank-frequency distribution is an inverse relation. For example, in the Brown Corpus of American English text, the word "the" is the most frequently occurring word, and by itself accounts for nearly 7% of all word occurrences (69,971 out of slightly over 1 million). True to Zipf's Law, the second-place word "of" accounts for slightly over 3.5% of words (36,411 occurrences), followed by "and" (28,852).