conclusions alessio ansuini bibliography 1 physics ...€¦ · hurford, j. (1987), “language and...

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The complexity of numeral systems

The Complexity of Numeral Systems

PhD Student: Alessio Ansuini1

Supervisor: Vittorio Loreto1

1Physics Department–“Sapienza” University of Rome

October 21, 2009

Alessio Ansuini Complexity of NS

Complexity of

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Table of contents

1 Introduction

2 Intermediate

3 ConclusionsConclusionsBibliography

Alessio Ansuini Complexity of NS

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Numeral systems

What are numeral systems ?

Numeral systems in natural languages are a “ system ofnames which have been given to numbers in the variouslanguages of the world [...] ” (Hurford 1987)

A writing system for expressing numbers, that is amathematical notation for representing numbers of a givenset, using graphemes or symbols in a consistent manner.

Alessio Ansuini Complexity of NS

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Defining the complexity of numeral systems

Linguistics

Hurford in “Artificially growing a numeral system”.

Hammarstrom “Complexity in Numeral Systems with anInvestigation into Pidgins, Pidgincreoles and Creoles”

What can we do as physicists and why

Language and cognitive networks. Representation of therelationships between the elements of language.

Semiotic dynamics and the Statistical Mechanics of socialsystems.

This work wants to be a contribution in the field of languagenetworks.

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Network representation of a Numeral System

Triple

Figure: The Triple T (x). y is an elementary symbol, z is composed.

Alessio Ansuini Complexity of NS

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Building networks from the data

Example

four-teen 4 × 10; quatre-vingt dix (4 × 20) + 10

Figure: How to build networks from data

Alessio Ansuini Complexity of NS

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Topological properties

Degree distribution

0 5 10 15 20 25 30 35 40

k

1e-05

0.0001

0.001

0.01

0.1

P(k)

Figure: The degree distributionbase 4; N = 105

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The Reduction

R (e, ⋆)

Alessio Ansuini Complexity of NS

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The Reduction

R (e, ⋆)

Final Result

Alessio Ansuini Complexity of NS

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Reduced networks

Alessio Ansuini Complexity of NS

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Reduced networks

Alessio Ansuini Complexity of NS

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Reduced networks

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The complexity of positional systems

2 4 6 8 10 12 14 16 18 20 22 24 26 28

base (B)

20

25

30

35

40

45

50

55

60

65

70

com

plex

ityKC

Figure: The descriptional complexity K and C.Alessio Ansuini Complexity of NS

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Reduced networks

Alessio Ansuini Complexity of NS

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Conclusions

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Alessio Ansuini Complexity of NS

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Bibliography

Hurford, J. (1987), “Language and Number: the emergence ofa cognitive system.” Oxford: Basil Blackwell.Dehaene S. (1997)“The Number sense:: How the Mind CreatesMathematics .” London, Penguin.

Alessio Ansuini Complexity of NS

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Acknowledgments

Thank you !

Alessio Ansuini Complexity of NS