Numeraarisissa

Numeraarisissa is a speculative concept in mathematics and worldbuilding that describes a nontraditional numeration system. In Numeraarisissa, numbers are not fixed symbols but compositions of interacting units called numeraries that reside in a structured space called the numeraarium. The framework is used in thought experiments and fictional settings to explore how alternative representations of quantity influence arithmetic, logic, and computation. It is not part of standard number theory.

Key features and structure

- Numeraries: contextual units that carry weight and state, capable of interaction with other numeraries.

- The numeraarium: the abstract space where numeraries combine and evolve under defined rules.

- Representation: numbers are finite sums of numeraries with coefficients drawn from a fixed alphabet, rather than a single glyph.

- Arithmetic: addition and multiplication are defined as morphisms in the numeraarium, with carry and interaction rules that may depend on state or context.

Origins and usage

The term emerged in speculative mathematics and science fiction discourse in the early 21st century and has since appeared in worldbuilding and puzzle communities. There is no universally accepted formalism, and different writers or researchers propose varying axioms and operations. As a result, Numeraarisissa serves mainly as a thought experiment about the nature of numerals, representation, and the relationship between symbols and meaning.

Examples and comments

A simple representation might express a number as N = a1*r1 + a2*r2, where r1 and r2 are fixed numeraries with weights, and a1, a2 are digits from a defined set. Different rule choices yield different arithmetic behaviors and representations, illustrating how numeral systems shape computation and reasoning.

See also

Numeral system, Numeration, Base notation, Mathematical fiction.