# Positional Value and Linguistic Recursion

@article{Kadvany2007PositionalVA, title={Positional Value and Linguistic Recursion}, author={John Kadvany}, journal={Journal of Indian Philosophy}, year={2007}, volume={35}, pages={487-520} }

The confluence of linguistic and mathematical thought in ancient India pro vides a unique view of how modern mathematics and computation rely on linguistic and cognitive skills. The linchpin of the analysis is the use of posi tional notation as a counting method for ancient and modern arithmetical procedures. Positional notation is a primary contribution from India to the development of modern mathematics, and in ancient India bridges mathe matics to Indian linguistics. Panini's grammar, while… Expand

#### 13 Citations

Indistinguishable from Magic: Computation is Cognitive Technology

- Computer Science
- Minds and Machines
- 2010

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. Expand

āṇ ini grammar is the earliest known computing language

- 2014

Pāṇini’s fourth (?) century BCE Sanskrit grammar uses rewrite rules guided by an explicit and formal metalanguage. The metalanguage makes extensive use of auxiliary markers, in the form of Sanskrit… Expand

Pāṇini's Grammar and Modern Computation

- Computer Science
- 2016

While Pāṇini's Sanskrit grammar is computationally limited, the metalanguage through which his formalism is defined can be directly used to define any rule-based system by mimicking standard formal language definitions as an extension of the grammatical system proper. Expand

Recursion and the Language Faculty On the Evolution of the Concept in Generative Grammar

- Computer Science
- 2011

It is argued that two different perspectives need to be distinguished, which directly relate to distinct vantage points of earlier generative frameworks on the one hand and the Minimalist program on the other. Expand

The First Textbook of Calculus: Yuktibhāṣā

- 2007

In 1832, Charles M. Whish, an Englishman who had worked for the East India Company, presented to the Royal Asiatic Society of Great Britain and Ireland an account1 of the contents of four palm leaf… Expand

Recovering permutations over a deletion channel

- 2017

A d-deletion channel C will take a sent message, remove up to d symbols, and then contract the resulting message before delivery. We consider the problem of finding a permutation σ acting on [n] so… Expand

StegCure: a comprehensive steganographic tool using enhanced LSB scheme

- Computer Science
- 2008

An overview of steganography on GIF image format is presented in order to explore the potential of GIF in information hiding research and the enhancement of the Least Significant Bits (LSB) insertion techniques from the most basic and conventional 1 bit to the LSB colour cycle method is explained. Expand

Incorporating Ideas from Indian History in the Teaching and Learning of a General Place Value System

- Engineering
- 2012

.................................................................................................................................. i Dedication… Expand

StegCure: an amalgamation of different steganographic methods in GIF image

- Computer Science
- 2008

An overview of steganography on GIF image format is presented in order to explore the potential of GIF in information hiding research by using an amalgamation of three different Least Significant Bit (LSB) insertion algorithms that is able to perform steganographic method. Expand

Effect of Noise on image steganography based on LSB insertion and RSA encryption

- Computer Science
- 2012

By matching data to an image, there is less chance of an attacker being able to use steganalysis to recover the data and Before hiding the data in an image the application first encrypts in it, which is superior to that used by current steganography tools. Expand

#### References

SHOWING 1-10 OF 41 REFERENCES

Contrasting Applications of Logic in Natural Language Syntactic Description

- 2005

Formal syntax has hitherto worked mostly with theoretical frameworks that take grammars to be generative, in Emil Post’s sense: they provide recursive enumerations of sets. This work has its origins… Expand

Universals: Studies in Indian Logic and Linguistics

- Sociology
- 1988

This collection of articles and review essays, including many hard to find pieces, comprises the most important and fundamental studies of Indian logic and linguistics ever undertaken. Frits Staal is… Expand

A Reader on the Sanskrit Grammarians

- History
- 1972

The achievements of Pānini and the Indian grammarians, beginning nearly 2500 years ago, have never been fully appreciated by Western scholars--partly because of the great technical difficulties… Expand

Lexicalization and Language Change

- Sociology
- 2005

Lexicalization, a process of language change, has been conceptualized in a variety of ways. Broadly defined as the adoption of concepts into the lexicon, it has been viewed by syntacticians as the… Expand

Lexicalization and Language Change: Frontmatter

- Sociology
- 2005

Lexicalization, a process of language change, has been conceptualized in a variety of ways. Broadly defined as the adoption of words into the lexicon, it has been viewed by some as the reverse… Expand

CONSTRUCTING A LANGUAGE: A USAGE-BASED THEORY OF LANGUAGE ACQUISITION

- Psychology
- Studies in Second Language Acquisition
- 2004

CONSTRUCTING A LANGUAGE: A USAGE-BASED THEORY OF LANGUAGE ACQUISITION. Michael Tomasello. Cambridge, MA: Harvard University Press, 2003. Pp. viii + 388. $45.00 cloth. Michael Tomasello has an… Expand

Dedre Gentner and Susan Goldin-Meadow (eds): Language in Mind: Advances in␣the Study of Language and Thought.

- Philosophy, Computer Science
- Minds and Machines
- 2006

The present collection of articles by cognitivescientists and linguists makes latest approaches and research in cognitive linguistics undergo test by posing one of the original questions of the discipline—the Sapir-Whorf Hypothesis that contemplatest the possible inﬂuence of language on thought. Expand

The universal history of numbers : from prehistory to the invention of the computer

- Mathematics
- 2001

PART ONE. Chapter 1: Historical Summary of Arithmetic, Numerical Notation, and Writing Systems. chapter 2: From the Particular to the General: Arithmetic Leads to Algebra. Chapter 3: From Calculation… Expand

Contributions to the history of Indian mathematics

- Mathematics
- 2005

I. Introductory Overview Mathematics in Ancient and Medieval India R. Sridharan II. Ancient Period Sanskrit Prosody, Pingala Sutras and Binary Arithmetic R. Sridharan. Shedding Some Localic and… Expand

Computation: Finite and Infinite Machines

- Engineering
- 1967

From the Preface (See Front Matter for full Preface)
Man has within a single generation found himself sharing the world with a strange new species: the computers and computer-like machines.… Expand