{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T15:59:15Z","timestamp":1790783955935,"version":"4.1.0"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,4]],"date-time":"2022-01-04T00:00:00Z","timestamp":1641254400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>The purpose of the paper is to extend the general theory of translation to texts written in the same language and show some possible applications. The main result shows that the mutual mathematical relationships of texts in a language have been saved or lost in translating them into another language and consequently texts have been mathematically distorted. To make objective comparisons, we have defined a \u201clikeness index\u201d\u2014based on probability and communication theory of noisy binary digital channels-and have shown that it can reveal similarities and differences of texts. We have applied the extended theory to the New Testament translations and have assessed how much the mutual mathematical relationships present in the original Greek texts have been saved or lost in 36 languages. To avoid the inaccuracy, due to the small sample size from which the input data (regression lines) are calculated, we have adopted a \u201crenormalization\u201d based on Monte Carlo simulations whose results we consider as \u201cexperimental\u201d. In general, we have found that in many languages\/translations the original linguistic relationships have been lost and texts mathematically distorted. The theory can be applied to texts translated by machines. Because the theory deals with linear regression lines, the concepts of signal-to-noise-ratio and likenss index can be applied any time a scientific\/technical problem involves two or more linear regression lines, therefore it is not limited to linguistic variables but it is universal.<\/jats:p>","DOI":"10.3390\/info13010020","type":"journal-article","created":{"date-parts":[[2022,1,7]],"date-time":"2022-01-07T01:15:26Z","timestamp":1641518126000},"page":"20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Linguistic Mathematical Relationships Saved or Lost in Translating Texts: Extension of the Statistical Theory of Translation and Its Application to the New Testament"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6506-4238","authenticated-orcid":false,"given":"Emilio","family":"Matricciani","sequence":"first","affiliation":[{"name":"Dipartimento di Elettronica, Informatica e Bioingegneria, Politecnico di Milano, 20133 Milan, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"936","DOI":"10.4236\/ojs.2020.106055","article-title":"A Statistical Theory of Language Translation Based on Communication Theory","volume":"10","author":"Matricciani","year":"2020","journal-title":"Open J. Stat."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"373","DOI":"10.4236\/ojs.2019.93026","article-title":"Deep Language Statistics of Italian throughout Seven Centuries of Literature and Empirical Connections with Miller\u2019s 7 \u2213 2 Law and Short-Term Memory","volume":"9","author":"Matricciani","year":"2019","journal-title":"Open J. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Elmakias, I., and Vilenchik, D. (2021). An Oblivious Approach to Machine Translation Quality Estimation. Mathematics, 9.","DOI":"10.3390\/math9172090"},{"key":"ref_4","unstructured":"Proshina, Z. (2008). Theory of Translation, Far Eastern University Press. [3rd ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1080\/13520520009615581","article-title":"Discourse analysis as part of translator training","volume":"7","author":"Trosberg","year":"2000","journal-title":"Curr. Issues Lang. Soc."},{"key":"ref_6","unstructured":"Warren, R. (1989). The Art of Translation: Voices from the Field, Northeastern University Press."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1075\/target.19.1.06wil","article-title":"A corpus-Based study of the verb observar in English-Spanish translations of biomedical research articles","volume":"19","author":"Williams","year":"2007","journal-title":"Target. Int. J. Transl. Stud."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wilss, W. (1996). Knowledge and Skills in Translator Behaviour, John Benjamins.","DOI":"10.1075\/btl.15"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gamallo, P., Pichel, J.R., and Alegria, I. (2020). Measuring Language Distance of Isolated European Languages. Information, 11.","DOI":"10.3390\/info11040181"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1075\/dia.30.2.01bar","article-title":"An experimental study comparing linguistic phylogenetic reconstruction methods","volume":"30","author":"Evans","year":"2013","journal-title":"Diachronica"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1016\/j.physa.2010.02.004","article-title":"Measures of lexical distance between languages","volume":"389","author":"Petroni","year":"2010","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/j.physa.2013.08.075","article-title":"Comparison of directed and weighted co-occurrence networks of six languages","volume":"393","author":"Gao","year":"2014","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1007\/s11434-013-5711-8","article-title":"Language clustering with word co-occurrence networks based on parallel texts","volume":"58","author":"Liu","year":"2013","journal-title":"Chin. Sci. Bull."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.physa.2017.05.011","article-title":"From Language Identification to Language Distance","volume":"484","author":"Gamallo","year":"2017","journal-title":"Phys. A"},{"key":"ref_15","first-page":"434","article-title":"Measuring diachronic language distance using perplexity: Application to English, Portuguese, and Spanish","volume":"26","author":"Pichel","year":"2019","journal-title":"Nat. Lang. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1093\/llc\/fqv061","article-title":"Visualization in stylometry: Cluster analysis using networks","volume":"32","author":"Eder","year":"2015","journal-title":"Digit. Scholarsh. Humanit."},{"key":"ref_17","first-page":"79","article-title":"A Statistical Approach to Machine Translation","volume":"16","author":"Brown","year":"1990","journal-title":"Comput. Linguist."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Koehn, F., Och, F.J., and Marcu, D. (2003, January 27). Statistical Phrase-Based Translation. Proceedings of the HLT-NAACL 2003, Main Papers, Edmonton, AB, Canada.","DOI":"10.3115\/1073445.1073462"},{"key":"ref_19","unstructured":"Czulo, O., and Hofmann, S. (2017). Sketch of a Noisy Channel Model for the translation process. Silvia Hansen-Schirra, Empirical Modelling of Translation and Interpreting, Language Science Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Techn. J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Lavie, A., and Agarwal, A. (2007, January 23). Meteor: An Automatic Metric for MT Evaluation with High Levels of Correlation with Human Judgments. Proceedings of the Second Workshop on Statistical Machine Translation, Prague, Czech Republic.","DOI":"10.3115\/1626355.1626389"},{"key":"ref_22","unstructured":"Banchs, R., and Li, H. (2011, January 19\u201324). AM-FM: A Semantic Framework for Translation Quality Assessment. Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies, Portland, OR, USA."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10590-011-9090-0","article-title":"Apertium: A free\/open-source platform for rule-based machine translation","volume":"25","author":"Forcada","year":"2011","journal-title":"Mach. Transl."},{"key":"ref_24","unstructured":"Buck, C. (2012, January 7\u20138). Black Box Features for the WMT 2012 Quality Estimation Shared Task. Proceedings of the 7th Workshop on Statistical Machine Translation, Montreal, QC, Canada."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Assaf, D., Newman, Y., Choen, Y., Argamon, S., Howard, N., Last, M., Frieder, O., and Koppel, M. (2013, January 16\u201319). Why \u201cDark Thoughts\u201d aren\u2019t really Dark: A Novel Algorithm for Metaphor Identification. Proceedings of the 2013 IEEE Symposium on Computational Intelligence, Cognitive Algorithms, Mind, and Brain, Singapore.","DOI":"10.1109\/CCMB.2013.6609166"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Graham, Y. (2015, January 26\u201331). Improving Evaluation of Machine Translation Quality Estimation. Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing, Beijing, China.","DOI":"10.3115\/v1\/P15-1174"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Espla-Gomis, M., Sanchez-Mart\u0131nez, F., and Forcada, M.L. (2015, January 17\u201318). UAlacant word-level machine translation quality estimation system at WMT 2015. Proceedings of the Tenth Workshop on Statistical Machine Translation, Lisboa, Portugal.","DOI":"10.18653\/v1\/W15-3036"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.csl.2014.11.001","article-title":"Latest trends in hybrid machine translation and its applications","volume":"32","author":"Fonollosa","year":"2015","journal-title":"Comput. Speech Lang."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Kreutzer, J., Schamoni, S., and Riezler, S. (2015, January 17\u201318). QUality Estimation from ScraTCH (QUETCH): Deep Learning for Word-level Translation Quality Estimation. Proceedings of the Tenth Workshop on Statistical Machine Translation, Lisboa, Portugal.","DOI":"10.18653\/v1\/W15-3037"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Specia, L., Paetzold, G., and Scarton, C. (2015, January 26\u201331). Multi-level Translation Quality Prediction with QuEst++. Proceedings of the ACL-IJCNLP 2015 System Demonstrations, Beijing, China.","DOI":"10.3115\/v1\/P15-4020"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1109\/TASLP.2015.2405751","article-title":"Adequacy-Fluency Metrics: Evaluating MT in the Continuous Space Model Framework","volume":"23","author":"Banchs","year":"2015","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1162\/tacl_a_00056","article-title":"Pushing the Limits of Quality Estimation","volume":"5","author":"Martins","year":"2017","journal-title":"Trans. Assoc. Comput. Linguist."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3109480","article-title":"Predictor-Estimator: Neural Quality Estimation Based on Target Word Prediction for Machine Translation","volume":"17","author":"Kim","year":"2017","journal-title":"ACM Trans. Asian Low-Resour. Lang. Inf. Process."},{"key":"ref_34","unstructured":"Kepler, F., Tr\u00e9nous, J., Treviso, M., Vera, M., and Martins, A.F.T. (August, January 28). OpenKiwi: An Open Source Framework for Quality Estimation. Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics: System Demonstrations, Florence, Italy."},{"key":"ref_35","first-page":"200","article-title":"Automatic Evaluation of End-to-End Dialog Systems with Adequacy-Fluency Metrics","volume":"55","author":"Banchs","year":"2018","journal-title":"Comput. Speech Lang."},{"key":"ref_36","unstructured":"Yankovskaya, E., T\u00e4ttar, A., and Fishel, M. (November, January 31). Quality Estimation with Force-Decoded Attention and Cross-lingual Embeddings. Proceedings of the Third Conference on Machine Translation: Shared Task Papers, Belgium, Brussels."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Yankovskaya, E., T\u00e4ttar, A., and Fishel, M. (2019, January 1\u20132). Quality Estimation and Translation Metrics via Pre-trained Word and Sentence Embeddings. Proceedings of the Fourth Conference on Machine Translation, Florence, Italy.","DOI":"10.18653\/v1\/W19-5410"},{"key":"ref_38","unstructured":"Lindgren, B.W. (1968). Statistical Theory, MacMillan Company. [2nd ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Matricciani, E., and Caro, L.D. (2019). A Deep-Language Mathematical Analysis of Gospels, Acts and Revelation. Religions, 10.","DOI":"10.3390\/rel10040257"},{"key":"ref_40","unstructured":"Mazza, A. (1968). Studi Sulle Redazioni de I Promessi Sposi, Edizioni Paoline."},{"key":"ref_41","unstructured":"Giovanni Nencioni, N. (1993). La Lingua di Manzoni. Avviamento Alle Prose Manzoniane, Il Mulino."},{"key":"ref_42","unstructured":"Guntert, G. (2000). Manzoni Romanziere: Dalla Scrittura Ideologica Alla Rappresentazione Poetica, Franco Cesati Editore."},{"key":"ref_43","unstructured":"Frare, P. (2016). Leggere I Promessi Sposi, Il Mulino."},{"key":"ref_44","unstructured":"Papoulis, A. (1990). Probability & Statistics, Prentice Hall."},{"key":"ref_45","unstructured":"Haykin, S. (2001). Communication Systems, John Wiley & Sons. [4th ed.]."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/1\/20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:27:00Z","timestamp":1760362020000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/13\/1\/20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,4]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["info13010020"],"URL":"https:\/\/doi.org\/10.3390\/info13010020","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,4]]}}}