Time Evolution of the Symmetry of Alphabet Symbols and Its Quantification: Study in the Archeology of Symmetry
Abstract
:1. Introduction
2. Methods
Scripts Addressed in the Investigation
3. Results
3.1. Quantitative Characterization of the Symmetry of Alphabets: Shannon Measures of Symmetry of the Alphabets
3.2. Shannon Diversity Index of the Alphabets
3.3. Shannon Diversity Index of Alphabets and the Vinča Symbols
3.4. Symmetry Factor: Its Definition and Calculation for Alphabets
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Phoenician Alphabet | ||||||||
---|---|---|---|---|---|---|---|---|
Script | C1 | S1 | S2 | S3 | S4 | C4 | C2 | C43 |
1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | |
1 | 1 | 1 | 1/0 | 1/0 | 1/0 | 1 | 1/0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
1 | 1 | 1 | 1/0 | 1/0 | 1/0 | 1 | 1/0 |
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Elements of Symmetry the Phoenician Alphabet | ||||||||
---|---|---|---|---|---|---|---|---|
C1 | S1 | S2 | S3 | S4 | C4 | C2 | C43 | |
22 | 7 | 9 | 2 | 2 | 2 | 6 | 2 | |
P(Gi) | 0.423 | 0.135 | 0.173 | 0.038 | 0.038 | 0.038 | 0.115 | 0.038 |
C1 | C1 S1 | C1 S2 | C1 S1 S2 C2 | C1 S1 S2 S3 S4 C4 C2 C43 | |
---|---|---|---|---|---|
Number of letters, | 12 | 1 | 3 | 4 | 2 |
Probability, | 0.545 | 0.045 | 0.136 | 0.182 | 0.091 |
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Gilevich, A.; Frenkel, M.; Shoval, S.; Bormashenko, E. Time Evolution of the Symmetry of Alphabet Symbols and Its Quantification: Study in the Archeology of Symmetry. Symmetry 2024, 16, 465. https://doi.org/10.3390/sym16040465
Gilevich A, Frenkel M, Shoval S, Bormashenko E. Time Evolution of the Symmetry of Alphabet Symbols and Its Quantification: Study in the Archeology of Symmetry. Symmetry. 2024; 16(4):465. https://doi.org/10.3390/sym16040465
Chicago/Turabian StyleGilevich, Artem, Mark Frenkel, Shraga Shoval, and Edward Bormashenko. 2024. "Time Evolution of the Symmetry of Alphabet Symbols and Its Quantification: Study in the Archeology of Symmetry" Symmetry 16, no. 4: 465. https://doi.org/10.3390/sym16040465
APA StyleGilevich, A., Frenkel, M., Shoval, S., & Bormashenko, E. (2024). Time Evolution of the Symmetry of Alphabet Symbols and Its Quantification: Study in the Archeology of Symmetry. Symmetry, 16(4), 465. https://doi.org/10.3390/sym16040465