Show HN: Neural network that uses no floating-point and says "I don't know" (github.com)

A new mathematical system called "Void Mathematics" has been introduced, which entirely eliminates the concept of infinity from its operations. This revolutionary approach asserts that all mathematical processes are finite, with every operation costing one unit of a finite budget and generating heat. Uniquely verified in Coq, Void Mathematics operates under a single admitted axiom and introduces a third truth value, "BUnknown," for scenarios where resources are insufficient to make a decision. It challenges the conventional reliance on infinity by demonstrating that in reality, as experienced by artificial intelligence, computation and resources are inherently limited. The significance of this system for the AI/ML community lies in its potential to reshape our understanding of computational mathematics and its applications. It suggests a new framework to model finite computational systems, resource-bounded intelligence, and quantum phenomena from first principles. The implications extend to how we conceive of consciousness and intelligence itself, emphasizing that care and meaning arise when resources are limited. With features like arbitrary precision and budgeted complexity, Void Mathematics proposes a fresh outlook on how mathematics aligns with the physical world, providing tools for advancements in AI that focus on realistic and finite representations.