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Hierarchy, Symmetry and Scale in Mathematics and Bi-Logic in Psychoanalysis, with Consequences

Published online by Cambridge University Press:  14 April 2020

Fionn Murtagh
Fionn Murtagh*
Affiliation:
Centre of Mathematics and Data Science, School of Computing and Engineering, University of Huddersfield, UK. Email: [email protected]
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Abstract

Hierarchy has properties of symmetry and scale. All that is related to hierarchy provides important perspectives on many other domains. The primary focus here is on renowned psychoanalyst Ignacio Matte Blanco’s Bi-Logic. Bi-Logic relates to the two modes of being, respectively symmetry and asymmetry in thought and reasoning and brain processes, in unconscious and in conscious modes of being. Some further consequences and implications are noted. These include relevance and potential in social sciences; in qualitative as well as quantitative literary analysis, and content analytics of text, speech, visual recording, and so on; in security and forensics; and in the contemporary theme of research and development relating to Big Data analytics.

Type
Articles
Information
European Review , Volume 29 , Issue 2: Symmetry, Proportion and Seriality: The Semantics of Mirroring and Repetition in Science and the Arts , April 2021 , pp. 197 - 209
Copyright
© 2020 Academia Europaea

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References

Aylward, P (2012) Understanding Dunblane and Other Massacres: Forensic Studies of Homicide, Paedophilia, and Anorexia. London: Karnac Books.Google Scholar
Dijksterhuis, A and Nordgren, LF (2006) A theory of unconscious thought. Perspectives on Psychological Science 1, 95–109, https://doi.org/10.1111/j.1745-6916.2006.00007.x.CrossRefGoogle ScholarPubMed
Donoho, DL and Tanner, J (2005) Neighborliness of randomly projected simplices in high dimensions. Proceedings of the National Academy of Sciences 102, 9452–9457, https://doi.org/10.1073/pnas.0502258102.CrossRefGoogle ScholarPubMed
Hall, P, Marron, JS and Neeman, A (2005) Geometric representation of high dimensional, low sample size data. Journal of the Royal Statistical Society B 67, 427–444, https://doi.org/10.1111/j.1467-9868.2005.00510.x.CrossRefGoogle Scholar
Hausdorff, F (1934) Über Innere Abbildungen. Fundamenta Mathematicae 23, 279–291.CrossRefGoogle Scholar
Iurato, G, Khrennikov, A and Murtagh, F (2016) Formal foundations for the origins of human consciousness. p-Adic Numbers, Ultrametric Analysis and Applications 8, 249–279, https://doi.org/10.1134/S2070046616040014.CrossRefGoogle Scholar
Khrennikov, AY (2004) Information Dynamics in Cognitive, Psychological, Social and Anomalous Phenomena. Dordrecht: Kluwer.CrossRefGoogle Scholar
Krasner, M (1944) Nombres semi-réels et espaces ultramétriques. Comptes-Rendus de l’Académie des Sciences, Tome II, vol. 219, 433–435.Google Scholar
Lauro Grotto, R (2008) The unconscious as an ultrametric set. American Imago 64, 535–543, https://doi.org/10.1353/aim.2008.0009.CrossRefGoogle Scholar
Lauro Grotto, R (2014) Formal approaches in the age of mirror neurons: hints from computational psychoanalysis. IEEE 13th International Conference on Cognitive Informatics and Cognitive Computing. Published online 16 October 2014, https://doi.org/10.1109/ICCI-CC.2014.6921459.CrossRefGoogle Scholar
Lebaron, F (2015) L’espace social: statistique et analyse géométrique des données dans l’œuvre de Pierre Bourdieu. In Lebaron, F and Le Roux, B (eds), La Méthodologie de Pierre Bourdieu en Action: Espace Culturel, Espace Social et Analyse des Données. Paris: Dunod, pp. 43–58.CrossRefGoogle Scholar
Le Roux, B and Rouanet, H (2004) Geometric Data Analysis: From Correspondence Analysis to Structured Data Analysis. Dordrecht: Kluwer.Google Scholar
Lerman, IC (1981) Classification et Analyse Ordinale des Données. Paris: Dunod.Google Scholar
Matte Blanco, I (1975) The Unconscious as Infinite Sets: An Essay in Bi-Logic. London: Karnac Books.Google Scholar
Murtagh, F (2004) On ultrametricity, data coding, and computation. Journal of Classification 21, 167–184, https://doi.org/10.1007/s00357-004-0015-y.CrossRefGoogle Scholar
Murtagh, F (2005) Identifying the ultrametricity of time series. The European Physical Journal B 43, 573–579, https://doi.org/10.1140/epjb/e2005-00092-8.CrossRefGoogle Scholar
Murtagh, F (2009a) Symmetry in data mining and analysis: a unifying view based on hierarchy. Proceedings of Steklov Institute of Mathematics 265, 177–198, https://doi.org/10.1134/S0081543809020175.CrossRefGoogle Scholar
Murtagh, F (2009b) The remarkable simplicity of very high dimensional data: application to model-based clustering. Journal of Classification 26, 249–277, https://doi.org/10.1007/s00357-009-9037-9.CrossRefGoogle Scholar
Murtagh, F (2012a) Ultrametric model of mind, I: review. p-Adic Numbers, Ultrametric Analysis and Applications 4, 193–206, https://doi.org/10.1134/S2070046612030041.CrossRefGoogle Scholar
Murtagh, F (2012b) Ultrametric model of mind, II: application to text content analysis. p-Adic Numbers, Ultrametric Analysis and Applications 4, 207–221, https://doi.org/10.1134/S2070046612030053.CrossRefGoogle Scholar
Murtagh, F (2014a) Mathematical representations of Matte Blanco’s bi-logic, based on metric space and ultrametric or hierarchical topology: towards practical application. Language and Psychoanalysis 3, 40–63, http://dx.doi.org/10.7565/landp.2014.008.CrossRefGoogle Scholar
Murtagh, F (2014b) Pattern recognition of subconscious underpinnings of cognition using ultrametric topological mapping of thinking and memory. International Journal of Cognitive Informatics and Natural Intelligence (IJCINI) 8, 1–16, https://doi.org/10.4018/ijcini.2014100101.CrossRefGoogle Scholar
Murtagh, F (2017) Data Science Foundations: Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics. Boca Raton, FL: Chapman and Hall/CRC.CrossRefGoogle Scholar
Murtagh, F and Ganz, A (2015) Pattern recognition in narrative: tracking emotional expression in context. Journal of Data Mining and Digital Humanities. Published online 26 May 2015, https://arxiv.org/abs/1405.3539.Google Scholar
Murtagh, F and Iurato, G (2016) Human behaviour, benign or malevolent: understanding the human psyche, performing therapy, based on affective mentalization and Matte-Blanco’s bi-logic. Journal of Translational Medicine. Published online December 2016, https://doi.org/10.21037/atm.2016.12.37.CrossRefGoogle Scholar
Rammal, R, Toulouse, G and Virasoro, MA (1986) Ultrametricity for physicists. Reviews of Modern Physics 58, 765–788, https://doi.org/10.1103/RevModPhys.58.765.CrossRefGoogle Scholar
Simon, HA (1996) The Sciences of the Artificial, 3rd edn. Cambridge, MA; London: MIT Press.Google Scholar
Stakhov, AP (2009) The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science. Singapore: World Scientific.CrossRefGoogle Scholar
Starck, JL, Murtagh, F and Bijaoui, A (1998) Image Processing and Data Analysis: The Multiscale Approach. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Starck, JL, Murtagh, F and Fadili, J (2016) Sparse Image and Signal Processing: Wavelets and Related Geometric Multiscale Analysis, 2nd edn. Cambridge: Cambridge University Press.Google Scholar
Volovich, IV (2010) Number theory as the ultimate physical theory. p-Adic Numbers, Ultrametric Analysis and Applications 2, 77–87, https://doi.org/10.1134/S2070046610010061.CrossRefGoogle Scholar
Weyl, H (1952) Symmetry. Princeton: Princeton University Press.CrossRefGoogle Scholar