We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Indistinguishable from Magic: Computation is Cognitive Technology.
- Authors
Kadvany, John
- Abstract
This paper explains how mathematical computation can be constructed from weaker recursive patterns typical of natural languages. A thought experiment is used to describe the formalization of computational rules, or arithmetical axioms, using only orally-based natural language capabilities, and motivated by two accomplishments of ancient Indian mathematics and linguistics. One accomplishment is the expression of positional value using versified Sanskrit number words in addition to orthodox inscribed numerals. The second is Pāṇini’s invention, around the fifth century BCE, of a formal grammar for spoken Sanskrit, expressed in oral verse extending ordinary Sanskrit, and using recursive methods rediscovered in the twentieth century. The Sanskrit positional number compounds and Pāṇini’s formal system are construed as linguistic grammaticalizations relying on tacit cognitive models of symbolic form. The thought experiment shows that universal computation can be constructed from natural language structure and skills, and shows why intentional capabilities needed for language use play a role in computation across all media. The evolution of writing and positional number systems in Mesopotamia is used to transfer the thought experiment of “oral arithmetic” to inscribed computation. The thought experiment and historical evidence combine to show how and why mathematical computation is a cognitive technology extending generic symbolic skills associated with language structure, usage, and change.
- Subjects
ARITHMETIC; AXIOMS; LINGUISTICS; HINDU mathematics; THOUGHT experiments
- Publication
Minds & Machines, 2010, Vol 20, Issue 1, p119
- ISSN
0924-6495
- Publication type
Article
- DOI
10.1007/s11023-010-9185-z