Cognitive Langlands
The Cognitive Langlands is a research program that studies how different cognitive systems can be related through shared structural patterns. It draws inspiration from the Langlands correspondence in mathematics, which links distant fields through common invariants. In Mahākāla’s work, the same idea is applied to cognition: to identify how perception, reasoning, and computation can be mapped onto one another through geometry.
Within Mahākāla, the Cognitive Langlands provides the conceptual foundation for cross-domain research. It links the Cognitive Automaton to broader scientific and philosophical questions about the nature of thought, intelligence and consciousness. By studying how different cognitive systems can be mapped through geometry, the framework builds a coherent method for exploring the continuity between perception and computation.
Research Agenda
/ Foundational Research
Focuses on how cognitive organization emerges from spatial and topological relations. Cognitive processes are expressed through measurable transformations that define their embedded and embodied geometry. This establishes the conceptual and mathematical basis for understanding cognition as structured organization rather than symbolic representation.
/ Correlates
Looks into neuroscience, cognitive science, and related fields to identify processes that exhibit geometric or topological organization. Focuses on how neural populations encode information through patterns of connectivity and oscillation, and how these patterns correspond to perception, attention, and decision-making, amongst others.
/ Computational Modeling
Parallel efforts focus on building computational environments that reproduce these structural patterns in synthetic systems. By designing models that adapt through transformations of their internal geometry, the program aim to test how structural coherence influences learning, adaptation, and reasoning across contexts.
/ Cross-Domain Correspondence
Another line of work investigates correspondences between biological, computational, and physical systems. By identifying common invariants across these domains, Mahākāla develops methods for translating findings from one field into another, supporting cumulative progress toward a unified understanding of cognition.
/ Applied Development
The agenda extends to practical applications, where insights from structural cognition guide the design of adaptive tools, interpretive AI systems, and experimental interfaces. These initiatives test how geometric organization supports stability, generalization, and understanding in environments that change or evolve over time.