Bagua: An Ancient Structural Framework for Classification and Analysis with Analogies to the Modern 2×2 Contingency Table
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901315244785664 |
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| author | Müller, Ying Müller, Uwe |
| author_facet | Müller, Ying Müller, Uwe |
| contents | <p class="MsoNormal"><a name="_Toc226899587"></a><span>This study systematically examines the structure of the Bagua from the I Ching (hereafter “Bagua”) from a data-analytical perspective. It is shown that the millennia-old Bagua can be understood as a method of data analysis that structurally corresponds to the 2×2 contingency table, yet existed several thousand years before the development of percentage calculation.</span></p> <p class="MsoNormal"><span><span>Over the course of historical development, however, interpretations—among them those influenced by Confucius—came to dominate and interpreted the Bagua primarily from a philosophical or symbolic perspective. In this process, a possible analytical approach was lost over centuries, so that in contemporary perception the Bagua is often understood only as a mystical element. In the present work, the Bagua is interpreted by us as a combinatorial structure consisting of three binary levels and is reanalyzed with regard to its structural as well as data-related relationships.</span></span></p> <p class="MsoNormal"><span><span>It is further shown that although the Bagua formally exhibits binary characteristics, as already described by Leibniz, its structure is better understood as a system based on complement relations and not as a simple binary encoding. In this respect, it shows a greater proximity to the fundamental concepts of set theory developed in 19th-century Europe, although the origins of the Bagua date back several thousand years.</span></span></p> <p class="MsoNormal"><span><span>On the basis of a structured analysis of a concrete example (the “Steve problem” formulated by Kahneman), as well as in comparison with the 2×2 contingency table, it is further shown that the Bagua is capable of representing symmetric relationships and direct comparisons within the same level, whereas the 2×2 contingency table is particularly suited to representing conditional dependencies between variables and proportional relationships. Both forms of representation therefore fulfill different but complementary functions.</span></span></p> <p class="MsoNormal"><span><span>Building on this, it is proposed that the Bagua can be understood as an early instrument of data classification and analysis whose functioning does not depend on percentage calculation. Furthermore, in connection with the structural analysis of He Tu and Luo Shu, the possibility is discussed that point-based markings can be interpreted as a means of data representation.</span></span></p> <p class="MsoNormal"><span><span>In summary, a structural approach to understanding the Bagua is proposed, which considers it as a potential framework for the representation and analysis of data. This perspective contributes to making the internal relationships of traditional diagrammatic forms visible and at the same time provides a new interpretative framework together with a directly applicable analytical approach.</span></span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19684490 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Bagua: An Ancient Structural Framework for Classification and Analysis with Analogies to the Modern 2×2 Contingency Table Müller, Ying Müller, Uwe Bagua I Ching Yijing Data classification Contingency table Probability theory Information structure History of mathematics Binary systems Ancient Chinese science Complementary structure <p class="MsoNormal"><a name="_Toc226899587"></a><span>This study systematically examines the structure of the Bagua from the I Ching (hereafter “Bagua”) from a data-analytical perspective. It is shown that the millennia-old Bagua can be understood as a method of data analysis that structurally corresponds to the 2×2 contingency table, yet existed several thousand years before the development of percentage calculation.</span></p> <p class="MsoNormal"><span><span>Over the course of historical development, however, interpretations—among them those influenced by Confucius—came to dominate and interpreted the Bagua primarily from a philosophical or symbolic perspective. In this process, a possible analytical approach was lost over centuries, so that in contemporary perception the Bagua is often understood only as a mystical element. In the present work, the Bagua is interpreted by us as a combinatorial structure consisting of three binary levels and is reanalyzed with regard to its structural as well as data-related relationships.</span></span></p> <p class="MsoNormal"><span><span>It is further shown that although the Bagua formally exhibits binary characteristics, as already described by Leibniz, its structure is better understood as a system based on complement relations and not as a simple binary encoding. In this respect, it shows a greater proximity to the fundamental concepts of set theory developed in 19th-century Europe, although the origins of the Bagua date back several thousand years.</span></span></p> <p class="MsoNormal"><span><span>On the basis of a structured analysis of a concrete example (the “Steve problem” formulated by Kahneman), as well as in comparison with the 2×2 contingency table, it is further shown that the Bagua is capable of representing symmetric relationships and direct comparisons within the same level, whereas the 2×2 contingency table is particularly suited to representing conditional dependencies between variables and proportional relationships. Both forms of representation therefore fulfill different but complementary functions.</span></span></p> <p class="MsoNormal"><span><span>Building on this, it is proposed that the Bagua can be understood as an early instrument of data classification and analysis whose functioning does not depend on percentage calculation. Furthermore, in connection with the structural analysis of He Tu and Luo Shu, the possibility is discussed that point-based markings can be interpreted as a means of data representation.</span></span></p> <p class="MsoNormal"><span><span>In summary, a structural approach to understanding the Bagua is proposed, which considers it as a potential framework for the representation and analysis of data. This perspective contributes to making the internal relationships of traditional diagrammatic forms visible and at the same time provides a new interpretative framework together with a directly applicable analytical approach.</span></span></p> |
| title | Bagua: An Ancient Structural Framework for Classification and Analysis with Analogies to the Modern 2×2 Contingency Table |
| topic | Bagua I Ching Yijing Data classification Contingency table Probability theory Information structure History of mathematics Binary systems Ancient Chinese science Complementary structure |
| url | https://doi.org/10.5281/zenodo.19684490 |