Review

Mathematical Models in Psychology for Stochastic Description of Human Feelings

Dohun Kwon 1 * , Jenna Saeyoon Choi 2
More Detail
International Journal of Social Sciences and Artistic Innovations, 4(4), 2024, 1, https://doi.org/10.35745/ijssai2024v04.04.0001
Published: 30 October 2024
OPEN ACCESS   242 Views   210 Downloads
Download Full Text (PDF)

ABSTRACT

We reviewed the application of mathematical analysis in psychology research, especially on human feelings. As mathematical analysis is widely used for modeling, it also has been applied to study human behavior. There are problems in applying mathematical analysis to psychology research due to the inherent subjectivity with multi-facets, intricacy, and dependence on context and memory of human feelings. Therefore, non-linear mathematical models and artificial intelligence engines are demanded to mimic human intuition for the better performance of models and, further, personalizing models accommodating individual differences. For this, adaptive learning methods need to be employed. Along with such technological considerations, diverse and reliable datasets are also mandatory to construct appropriate mathematical models. Human feelings are intricate and multifaceted, and cannot be easily expressed in mathematics. Therefore, it is necessary to develop mathematical analysis methods to understand and assess human feelings more precisely. With the development of computational technology and data-gathering techniques, existing problems can be solved, and data including sentiment analysis results and facial expressions with time-dependent components can be available. It is expected to have personalized models based on individual differences soon owing to the rapid development of mathematical analysis techniques. Such models to assess and predict human feelings can be used for diverse applications including psychology, marketing, education, and others.
Keywords: Mathematical Analysis, Modeling, Human Feelings, Emotions, Quantitive Assessment, Artificial Intelligence, Non-linear Model

CITATION (APA)

Kwon, D., & Choi, J. S. (2024). Mathematical Models in Psychology for Stochastic Description of Human Feelings. International Journal of Social Sciences and Artistic Innovations, 4(4), 1. https://doi.org/10.35745/ijssai2024v04.04.0001

REFERENCES

  1. Ambrosio, Benjamin. (2020). Beyond The Brain: Towards a Mathematical Modeling of Emotions. Available online: http://dx.doi.org/10.21203/rs.3.rs-70516/v1 (accessed on July 15, 2024)
  2. Barrett, L. Feldman and Russek, James. A (1999). The Structure of Current Affect: Controversies and Emerging Consensus. Current Directions in Psychological Science, 8(1), 10–14. https://doi.org/10.1111/1467-8721.00003.
  3. Batcheelder, H. William. (2015). Mathematical Psychology: History. International Encyclopedia of the Social & Behavioral Sciences (Second Edition), 1, 5, 808–815. https://doi.org/10.1016/B978-0-08-097086-8.43059-X.
  4. Damasio, R. Antonio. (2022). The Science of Emotion. Available online: https://www.loc.gov/loc/brain/emotion/Damasio.html. (accessed on July 25, 2024)
  5. Anmol. (2020). A Review on Mathematical Patterns In Psychological Analysis: A New Perspective. Journal of Mathematical Problems, Equations and Statistics, 1, 67–70. https://www.mathematicaljournal.com/article/105/4-2-5-511.pdf.
  6. Bakdash, Z. Jonathan, & Marusich R. (2017). Current Practices in Data Analysis Procedures in Psychology: What Has Changed? Frontiers in Psychology, 8, 13, 00456. https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.00456/full.
  7. Betterhelp. (2024). Feelings Vs. Emotions: Is There a Difference? Available online: https://www.betterhelp.com/advice/general/feelings-vs-emotions-is-there-a-difference-between-them/ (accessed on July 15, 2024).
  8. Bieleke, Malik, Goetz, Thomas, Yanagida, Takuya, Botes, Elouise, Frenzel, C. Anne, & Pekrun, Reinhard (2023). Measuring Emotions In Mathematics: The Achievement Emotions Questionnaire—Mathematics (AEQ-M). ZDM Mathematics Education, 55, 269–284. https://doi.org/10.1007/s11858-022-01425-8.
  9. Blanca, J. Maria, Alarcón, Rafael, & Bono, Roser. (2018). & Marusich R. (2017). Repeated Measures Correlation. Frontiers in Psychology, 8, 456. https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.00456/full.
  10. Brody, C. Dorje. (2022). The Mathematics of Human Behavior: How a New Model Can Spot Liars and Counter Disinformation. Available online: https://phys.org/news/2022-06-mathematics-human-behavior-liars-counter.html (accessed on July 15, 2024)
  11. Carbonaro, Bruna, & Giordano, Concetta (2005). A Second Step Towards a Stochastic Mathematical Description of Human Feelings, Mathematical and Computer Modelling, 41, 587–614. https://doi.org/10.1016/j.mcm.2003.05.021.
  12. Cavagnaro, R. Daniel, Myung, I. Jay, & Pitt, A. Mark. (2013). Mathematical Modeling (Little D. Todd Ed.) In The Oxford Handbook of Quantitative Methods in Psychology. Oxford UK: Oxford Library of Psychology. https://doi.org/10.1093/oxfordhb/9780199934874.013.0021.
  13. Conocimiento, al Ventana. (2020). Biomathematics: the numerical secrets of biology. Available online: https://www.bbvaopenmind.com/en/science/mathematics/biomathematics-the-numerical-secrets-of-biology/ (accessed on July 15, 2024).
  14. Cooper, Harris, Coutanche, N. Marc, McMullen, M. Linda, Panter, A. T., Rindskopf, David, & Sher, J. Kenneth. (2023). APA Handbook Of Research Methods In Psychology: Data Analysis And Research Publication (2nd Ed.). Washington D.C., USA: American Psychological Association. https://doi.org/10.1037/0000320-000.
  15. Earl, Richard. (2023). Mathematical Analysis: A Very Short Introduction. (Online Ed.) Oxford, UK: Oxford Academic. https://doi.org/10.1093/actrade/9780198868910.001.0001.
  16. Edelsbrunner, A. Peter, & Dablander, Fabian. (2019). The Psychometric Modeling of Scientific Reasoning: a Review and Recommendations for Future Avenues. Educational Psychology Review 31, 1–34. https://doi.org/10.1007/s10648-018-9455-5.
  17. Foster, Henry. (2024). The Role of Math in Psychology: A Closer Look. Psychological Research and Methodology. Available online: https://listen-hard.com/psychological-research-and-methodology/math-psychology/ (accessed on July 15, 2024).
  18. Foster, Jamie. (2023). The Integral Role Of Mathematics In Scientific Progress. Available online: https://www.jamiefosterscience.com/why-is-mathematics-important-to-science/ (accessed on July 15, 2024).
  19. Hewitt, Edwin and Stromberg, Karl. (1965). Preface. (Hewitt, Edwin and Stromberg, Karl Ed.) In Real and Abstract Analysis: A Modern Treatment of The Theory of Functions of A Real Variable. Berlin, Germany: Springer-Verlag.
  20. Westin, Jack. (2024). The Role of Biological Processes in Perceivin Emotion. Available online: https://jackwestin.com/resources/mcat-content/emotion/the-role-of-biological-processes-in-perceiving-emotion (accessed on July 15, 2024).
  21. Kaiser, Caspar, & Oswald, J. Andrew. (2022). The Scientific Value Of Numerical Measures Of Human Feelings. Economic Sciences, 119, e2210412119. https://doi.org/10.1073/pnas.2210412119.
  22. Mittelstadt, Brent Daniel, Allo, Patrick, & Floridi Luciano. (2016). The Ethics of Algorithms: Mapping the Debate. Big Data & Society, 3(2), 1c–21. https://doi.org/10.1177/2053951716679679.
  23. Ohue, Masahito, Sasayama, Kotoyu, & Takata, Masami (2024). Mathematical Modeling and Problem Solving: From Fundamentals To Applications. Journal of Supercomputing 80, 14116–14119. https://doi.org/10.1007/s11227-024-06007-x.
  24. Oxford Languages (2024). Psychology. Available online: https://thinkpsych.com/blogs/posts/what-is-the-difference-between-feelings-and-emotions (accessed on July 15, 2024).
  25. Pérez-Escobar, José Antonio. (2023). A New Role Of Mathematics In Science: Measurement Normativity. Measurement, 223, 113631. https://doi.org/10.1016/j.measurement.2023.113631.
  26. Pollak, D. Seth, Camras, A. Linda, & Cole, M. Pamela. (2019). Progress in Understanding the Emergence Of Human Emotion. Developmental Psychology, 55, 1801–1811. https://doi.org/10.1037/dev0000789.
  27. Richardson, C. Frank, & Suinn, M. Richard. (1972). The Mathematics Anxiety Rating Scale: Psychometric data. Journal of Counseling Psychology, 19, 551–554. https://doi.org/10.1037/h0033456.
  28. Ryser, Valérie-Anne. (2023). Measuring Psychological Constructs. FORS Guide 22. Available online: https://forscenter.ch/wp-content/uploads/2023/05/fg_measuringpsychologicalconstructs2023_final.pdf (accessed on July 15, 2024).
  29. Sanderson, Katharine. (2023). Ai Science Search Engines Are Exploding in Number — Are They Any Good? Nature News. Available online: https://www.nature.com/articles/d41586-023-01273-w (accessed on July 15, 2024).
  30. Science Daily (2024). New Model Allows a Computer to Understand Human Emotions. Available online: https://www.sciencedaily.com/releases/2024/06/240604132136.htm (accessed on July 15, 2024).
  31. Sufyan S. Nabil, Fadhel, H. Fahmi, Alkhathami S. Saleh, & Mukhadi Y.A. Jurban. (2024). Artificial Intelligence and Social Intelligence: Preliminary Comparison Study between AI Models and Psychologists. Frontiers in Psychology, 15, 1353022. https://doi.org/10.3389/fpsyg.2024.1353022.
  32. ThinkPsych. (2022). What Is the Difference Between Feelings and Emotions? Available online: https://thinkpsych.com/blogs/posts/what-is-the-difference-between-feelings-and-emotions. (accessed on July 15, 2024).
  33. University of Jyväskylä (2024). Model Uses Mathematical Psychology To Help Computers Understand Human Emotions. Available online: https://techxplore.com/news/2024-06-mathematical-psychology-human-emotions.html. (accessed on July 15, 2024).
  34. Veenman, Myrthe., Stefan, M. Angelika, & Haaf, M. Julia. (2023). Bayesian Hierarchical Modeling: An Introduction and Reassessment. Behavioral Research, 56, 4600–4631. https://doi.org/10.3758/s13428-023-02204-3.
  35. Zhang, E. Jiayi, Hilpert, Bernhard, Broekens, Joost, & Jokinen P.P. and Jussi. (2024). Simulating Emotions With an Integrated Computational Model of Appraisal and Reinforcement Learning. Proceedings of the CHI Conference on Human Factors in Computing Systems, 1–23. https://doi.org/10.1145/3613904.3641908.