Name
The word: Name, can be thought of as a generalized number system, which may or may not be related to certain quantity. However, by just having a name, such as , it already implied the connotation of cardinality and ordinality in a greater context. A quick way to learn what name is is to think about what are unnameable[1].
Name as a Kind of Number
In number theory, or in mathematics in general, a name can be adopted as a static or invariant symbol to represent a discrete number, or even just a discrete concept. As Keith Devlin eloquently puts it, names, or numbers, in mathematics, make invisible, visible[2]. Moreover, based on Bob Coecke's work onQuantum Natural Language Processing[3], words can be composed into sentences, and they are computable according to a set of rewrite rules, similar to numbers can be composed into mathematical expressions, and they are also computable, according to the definition of mathematical operators. {{#ev:youtube |pk49iM9OT_0 }}
Monad: Natural numbers as Functors
To model numbers in terms of relations, monad can be used as a bridge. That is based on the fact that functors can be used to represent both elements in a set and the relations of the elements in the set. In other words, the notion of representable is inalienable from the notion of functor, which carries the name of this information compression. Daniel Tubbenhauer's VisualMath also has a video on What are…monads?[4]. In the beginningof the video, he stated that monad is a way of counting.
References
- ↑ Chaitin, Gregory (November 14, 2006). Meta Math! The Quest for Omega (PDF). local page: Vintage. p. 240. ISBN 978-1400077977. , Chapter V—The Labyrinth of the Continuum, Reals are un-nameable with probability one! Page 98
- ↑ Devlin, Keith (Dec 12, 2012). 1. General Overview and the Development of Numbers. Mathematics: make the invisible visible. local page: Stanford.
- ↑ Coecke, Bob; Sadrzadeh, Mehrnoosh; Clark, Stephen (Mar 23, 2010). Mathematical Foundations for a Compositional Distributional Model of Meaning (PDF). local page: arXiv.
- ↑ Tubbenhauer, Daniel (Feb 13, 2022). What are…monads?. local page: VisualMath.