calculen

Calculen is a fictional mathematical framework described in speculative mathematics and science fiction. It presents a universal calculus for reasoning about computation, information flow, and dynamic systems. The term is not part of mainstream mathematics, but it appears in theoretical thought experiments as a formalism that emphasizes compositionality, modularity, and abstraction.

In the imagined formalism, calculen is built from a small set of primitive notions: a set of states S, a set of operations O, and a transition function or relation T that describes how states evolve under operations. Often a measurement or observation function M: S → R assigns numerical values to states. Computations are represented as expressions built by composing operations, and their meaning is given by evaluating the resulting state through T and possibly by extracting values via M.

Theoretical features commonly attributed to calculen include recursive definitions, compositional semantics, and support for concurrent or interleaved execution. Some treatments describe calculen as a parametric framework that can instantiate various known calculi, such as lambda calculus or finite automata, by choosing appropriate state sets, operations, and evaluation rules.

In fiction and thought experiments, calculen is used to explore questions about determinism, simulability, and the limits of computation, as well as to model complex systems in a compact, algebraic way. See also: Calculus, Automata theory, Formal methods, Computational models.