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Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
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
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
Table of contents
1 Introduction
2 Intermediate
3 ConclusionsConclusionsBibliography
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
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
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
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.
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
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
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
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
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
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
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
The Reduction
R (e, ⋆)
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
The Reduction
R (e, ⋆)
Final Result
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
Reduced networks
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
Reduced networks
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
Reduced networks
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
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
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
Reduced networks
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
Conclusions
Conclusions
Alessio Ansuini Complexity of NS
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
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
Complexity of
NS
Alessio
Ansuini
Introduction
Intermediate
Conclusions
Conclusions
Bibliography
Acknowledgments
Thank you !
Alessio Ansuini Complexity of NS
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