Mathematical Philology: Entropy Information in Refining Classical Texts' Reconstruction, and Early Philologists' Anticipation of Information Theory
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{"title"=>"Mathematical philology: Entropy information in refining classical texts' reconstruction, and early philologists' anticipation of information theory", "type"=>"journal", "authors"=>[{"first_name"=>"John L.", "last_name"=>"Cisne", "scopus_author_id"=>"36951187000"}, {"first_name"=>"Robert M.", "last_name"=>"Ziomkowski", "scopus_author_id"=>"35727271200"}, {"first_name"=>"Steven J.", "last_name"=>"Schwager", "scopus_author_id"=>"7003836735"}], "year"=>2010, "source"=>"PLoS ONE", "identifiers"=>{"pmid"=>"20084117", "doi"=>"10.1371/journal.pone.0008661", "pui"=>"358394587", "issn"=>"19326203", "sgr"=>"77649248756", "scopus"=>"2-s2.0-77649248756"}, "id"=>"86c728ef-3f23-36b8-8cab-7d62f61a7178", "abstract"=>"Philologists reconstructing ancient texts from variously miscopied manuscripts anticipated information theorists by centuries in conceptualizing information in terms of probability. An example is the editorial principle difficilior lectio potior (DLP): in choosing between otherwise acceptable alternative wordings in different manuscripts, \"the more difficult reading [is] preferable.\" As philologists at least as early as Erasmus observed (and as information theory's version of the second law of thermodynamics would predict), scribal errors tend to replace less frequent and hence entropically more information-rich wordings with more frequent ones. Without measurements, it has been unclear how effectively DLP has been used in the reconstruction of texts, and how effectively it could be used. We analyze a case history of acknowledged editorial excellence that mimics an experiment: the reconstruction of Lucretius's De Rerum Natura, beginning with Lachmann's landmark 1850 edition based on the two oldest manuscripts then known. Treating words as characters in a code, and taking the occurrence frequencies of words from a current, more broadly based edition, we calculate the difference in entropy information between Lachmann's 756 pairs of grammatically acceptable alternatives. His choices average 0.26+/-0.20 bits higher in entropy information (95% confidence interval, P = 0.005), as against the single bit that determines the outcome of a coin toss, and the average 2.16+/-0.10 bits (95%) of (predominantly meaningless) entropy information if the rarer word had always been chosen. As a channel width, 0.26+/-0.20 bits/word corresponds to a 0.790.79(+0.09) (-0.15) likelihood of the rarer word being the one accepted in the reference edition, which is consistent with the observed 547/756 = 0.72+/-0.03 (95%). Statistically informed application of DLP can recover substantial amounts of semantically meaningful entropy information from noise; hence the extension copiosior informatione lectio potior, \"the reading richer in information [is] preferable.\" New applications of information theory promise continued refinement in the reconstruction of culturally fundamental texts.", "link"=>"http://www.mendeley.com/research/mathematical-philology-entropy-information-refining-classical-texts-reconstruction-early-philologist", "reader_count"=>14, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Researcher"=>3, "Student > Ph. D. Student"=>4, "Student > Master"=>2, "Other"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Researcher"=>3, "Student > Ph. D. Student"=>4, "Student > Master"=>2, "Other"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>1, "Environmental Science"=>1, "Medicine and Dentistry"=>1, "Agricultural and Biological Sciences"=>2, "Arts and Humanities"=>3, "Social Sciences"=>1, "Computer Science"=>2, "Immunology and Microbiology"=>1, "Linguistics"=>1, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Social Sciences"=>{"Social Sciences"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>2}, "Computer Science"=>{"Computer Science"=>2}, "Linguistics"=>{"Linguistics"=>1}, "Environmental Science"=>{"Environmental Science"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>3}}, "reader_count_by_country"=>{"United States"=>1, "Luxembourg"=>1, "Spain"=>1}, "group_count"=>1}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/430832"], "description"=>"<div><p>Philologists reconstructing ancient texts from variously miscopied manuscripts anticipated information theorists by centuries in conceptualizing information in terms of probability. An example is the editorial principle <em>difficilior lectio potior</em> (DLP): in choosing between otherwise acceptable alternative wordings in different manuscripts, “the more difficult reading [is] preferable.” As philologists at least as early as Erasmus observed (and as information theory's version of the second law of thermodynamics would predict), scribal errors tend to replace less frequent and hence entropically more information-rich wordings with more frequent ones. Without measurements, it has been unclear how effectively DLP has been used in the reconstruction of texts, and how effectively it could be used. We analyze a case history of acknowledged editorial excellence that mimics an experiment: the reconstruction of Lucretius's <em>De Rerum Natura</em>, beginning with Lachmann's landmark 1850 edition based on the two oldest manuscripts then known. Treating words as characters in a code, and taking the occurrence frequencies of words from a current, more broadly based edition, we calculate the difference in entropy information between Lachmann's 756 pairs of grammatically acceptable alternatives. His choices average 0.26±0.20 bits higher in entropy information (95% confidence interval, <em>P</em> = 0.005), as against the single bit that determines the outcome of a coin toss, and the average 2.16±0.10 bits (95%) of (predominantly meaningless) entropy information if the rarer word had always been chosen. As a channel width, 0.26±0.20 bits/word corresponds to a 0.790.79<sup>+0.09</sup><sub>−0.15</sub> likelihood of the rarer word being the one accepted in the reference edition, which is consistent with the observed 547/756 = 0.72±0.03 (95%). Statistically informed application of DLP can recover substantial amounts of semantically meaningful entropy information from noise; hence the extension <em>copiosior informatione lectio potior</em>, “the reading richer in information [is] preferable.” New applications of information theory promise continued refinement in the reconstruction of culturally fundamental texts.</p></div>", "links"=>[], "tags"=>["mathematical", "entropy", "refining", "anticipation"], "article_id"=>145027, "categories"=>["Evolutionary Biology", "Mathematics", "Physics", "Cancer"], "users"=>["John L. Cisne", "Robert M. Ziomkowski", "Steven J. Schwager"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008661", "stats"=>{"downloads"=>6, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Mathematical_Philology_Entropy_Information_in_Refining_Classical_Texts_Reconstruction_and_Early_Philologists_Anticipation_of_Information_Theory/145027", "title"=>"Mathematical Philology: Entropy Information in Refining Classical Texts' Reconstruction, and Early Philologists' Anticipation of Information Theory", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-01-13 01:23:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/867501"], "description"=>"<p>The mean value 〈Δ<i>I</i>〉 = +0.257±0.196 bits/word (95% confidence interval; <i>P</i>–value = 0.005, one-sided) corresponds to a 0.79<sup>+0.09</sup><sub>−0.15</sub> likelihood of the rarer word being the better choice, showing the value of the <i>difficilior lectio potior</i> principle (DLP) that “the less probable reading is preferable” in choosing between otherwise acceptable alternatives in reconstructing a text from variously miscopied manuscripts. The Renaissance and earlier philologists who framed DLP evidently had a prescient understanding of information as a probabilistic phenomenon.</p>", "links"=>[], "tags"=>["entropy", "756", "pairs", "words", "manuscripts", "lachmann", "reconstruction", "rerum", "gaussian", "fitted"], "article_id"=>537948, "categories"=>["Evolutionary Biology", "Mathematics", "Physics", "Cancer"], "users"=>["John L. Cisne", "Robert M. Ziomkowski", "Steven J. Schwager"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0008661.g001", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_difference_I_in_entropy_information_between_756_pairs_of_otherwise_acceptable_alternative_words_in_the_two_manuscripts_on_which_Lachmann_based_his_reconstruction_of_Lucretius_s_De_Rerum_Natura_On_the_Nature_of_Things_60_BCE_1_and_a_Gaussian_curve_fit/537948", "title"=>"The difference Δ<i>I</i> in entropy information between 756 pairs of otherwise acceptable alternative words in the two manuscripts on which Lachmann based his reconstruction of Lucretius's <i>De Rerum Natura</i> (<i>On the Nature of Things</i>, ∼60 BCE) [1], and a Gaussian curve fitted to the data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-01-13 02:12:28"}

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Relative Metric

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