Understanding Linguistic Geometry
A disambiguation of different approaches sharing this name
Academic Acknowledgment
We respectfully acknowledge that the term “Linguistic Geometry” has been used in academic literature prior to our project. Most notably, Dr. Boris Stillman pioneered work under this name in the 1990s in the field of artificial intelligence and strategic problem-solving. While our domain was registered in 2011, we recognize and honor the precedence of earlier academic work. Our approach represents a distinct interpretation focused on the geometric and topological structures inherent in natural language itself.
Stillman's Linguistic Geometry (1990s-present)
Focus: Artificial Intelligence, Strategic Problem-Solving, Game Theory
Dr. Boris Stillman developed Linguistic Geometry as a mathematical approach to solving complex strategic problems, particularly in domains like chess, military operations, and robotic navigation. This approach uses linguistic-like constructions to generate efficient strategies in large-scale systems.
Learn more →Kandasamy et al.'s Linguistic Geometry (2022)
Focus: Social Network Analysis, Linguistic Variables
This approach, developed by W.B. Vasantha Kandasamy, K. Ilanthenral, and Florentin Smarandache, uses linguistic terms instead of numerical values to model social problems and networks. It replaces traditional mathematical measurements with qualitative linguistic descriptions.
Published by Editorial Global Knowledge, 2022
Our Approach: Structural Linguistic Geometry (2011-present)
Focus: Language Structure, Topology, Geometric Visualization
Our approach draws inspiration from various sources, including the 2016 science fiction film “Arrival” directed by Denis Villeneuve, based on Ted Chiang's novella “Story of Your Life” (1998). In this work, the fictional Heptapod language employs circular, non-linear orthographic symbols that encode complete semantic units geometrically. This cinematic representation of language as geometric form resonates with our exploration of how natural language structures can be understood through geometric and topological concepts.
We apply mathematical frameworks from topology, category theory, and differential geometry to analyze syntax, semantics, and morphology, seeking to understand the spatial and structural properties inherent in human language.
This website, established with the domain registered in 2011, represents our ongoing exploration of these ideas, viewing language as a geometric space where meaning emerges from structural relationships.
Our Vision: Language as Geometric Form
The conceptual framework presented in “Arrival” (Paramount Pictures, 2016), wherein the alien Heptapod species employs a non-linear, circular writing system (Heptapod B) that represents complete thoughts as unified geometric forms, provides a compelling artistic parallel to our research objectives. In the film's narrative, these semasiographic symbols encode temporal and semantic information simultaneously through their geometric structure—a concept that aligns with our investigation into how human language might be understood through geometric and topological frameworks.
Note: “Arrival” and its linguistic concepts are fictional works created for entertainment purposes. Our academic research is independent and draws from established mathematical and linguistic theories.
Our approach investigates:
- • How syntactic transformations can be modeled as continuous deformations in topological space
- • The geometric properties of semantic fields and conceptual spaces
- • Morphological processes as transformations in linguistic manifolds
- • The possibility of non-linear representations of linguistic meaning
Mathematical Foundations of Heptapod B
The development of the Heptapod language in “Arrival” involved significant mathematical and computational expertise. Stephen Wolfram, creator of Mathematica and author of A New Kind of Science, was consulted during production. His son, Christopher Wolfram, played a key role in generating the visual representations of the Heptapod logograms using Mathematica to procedurally generate the alien script's circular inkblot-style symbols.
Characteristics of Heptapod B
In the film's fictional framework, Heptapod B exhibits several properties that resonate with our research into linguistic geometry:
- Non-linear and Semasiographic: The written form conveys meaning without representing sound, encoding entire thoughts as unified geometric forms.
- Holistic Composition: Each logogram requires knowing the complete thought before beginning to write—a reflection of non-linear temporal perception.
- Mathematical Consistency: The symbols were generated using computational methods to ensure linguistic and visual coherence across the film.
The innovative approach to language design in “Arrival” demonstrates how mathematical and computational methods can create compelling representations of non-linear communication systems.
This fictional exploration of language as geometric form—where meaning emerges from spatial relationships rather than linear sequences—provides an imaginative parallel to our academic investigation into the topological and geometric properties of natural language structures.
References & Acknowledgments
Film: Villeneuve, D. (Director). (2016). Arrival [Film]. Paramount Pictures. Based on “Story of Your Life” by Ted Chiang.
Source Material: Chiang, T. (1998). “Story of Your Life.” In Stories of Your Life and Others. Tor Books.
Linguistic Geometry (AI): Stillman, B. (1990s-present). Various publications on Linguistic Geometry in artificial intelligence and strategic planning.
Linguistic Geometry (Social Networks): Kandasamy, W.B.V., Ilanthenral, K., & Smarandache, F. (2022). Linguistic Geometry and its Applications. Editorial Global Knowledge.
All trademarks and copyrights are the property of their respective owners. References to “Arrival” and related concepts are for academic discussion and comparative analysis only.