Structure and Dynamics of Working Language
Abstract
Language works in the sense of basic physics- it directs energy transfer, leading to the displacement of material objects in space. Abstractly speaking, language includes the DNA that directs biological life, natural languages like English that direct our social interactions, and the high-level programming languages that direct our technology. In all cases, language is selected for its expressive power, communicative success, and ease of processing. We claim that category theory is one of society’s most impressive instances of these features to date. It offers schemas for handling arbitrarily complex grammatical constructions in a staggering variety of application areas. As it continues to be operationalized in compositional programming libraries such as AlgebraicJulia for scientific and industrial use, category theory will play an increasing role in coordinating humanity’s efforts toward solving its biggest problems. But category theory can also be used to study the dynamics of this process itself. Robust control of material resources demands a symbol system and compositional grammar that fits with the structural and combinatorial possibilities of those material resources. The dynamics—a gears-level description of how compositional language actually directs physical activity—seems to be a compilation process, akin to howdependent type theory is compiled into intermediate languages like C, then to Assembly, then to machine code, which directs coordinated changes to the voltage-levels on a huge array of transistors. But how can we mathematically account for this process in general, not just as it pertains to computers, but abstractly so that it also makes sense for other domains, such as systems biology. With this grant we aim to clarify the multi-scale and substrate-independent process of constructing and operationalizing languages. We will use category theory, e.g. an approach to categorical systems theory using polynomial functors, to describe the structure and dynamics of working language. We will also treat categorical constructions—to the extent that they are operationalized in the real world as working systems with material consequences—as an interesting test case of how efficient language actually accomplishes its aims.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 06, 2024
- Source ID
- FA95502310376
Entities
People
- David Spivak
Organizations
- Air Force Office of Scientific Research
- United States Air Force