The Monad: A Formal Model of the Learning Process
Keywords:
monad, Euler’s number, auto-similarity, Taylor series, decay orderAbstract
Objectives: This paper aims to apply categorical math notions and functional programming in the cognitive field of study. Prior Work: I am using a monad, an endofunctor in the category of monoids, to represent the process of learning. Approach: For this purpose, I have used financial math modeling and Taylor series. Results: The model obtained combines compound interest rate with structural correctors and tail-decaying order terms. Implications: This paper is important for employing methods from different fields of study (finance, math, functional programming) to develop a versatile model for the learning process. Value: This paper is original for applying natural growing metrics and the auto-similarity concept in cognitive sciences.
References
Boyd, J. P. (1999). The asymptotic Taylor series and its remainder decay. Applied Mathematics and Computation, 105(1), 79–94.
Heidegger, M. (1967). Sein und Zeit [Being and Time]. Niemeyer.
Koellner, P. (2018). On the Question of Whether the Mind Can Be Mechanized, II: Penrose’s New Argument / On Whether the Mind Can Be Mechanized. The Journal of Philosophy, 115(9), 453–484.
Mandelbrot, B. (1982). Self‑similarity and fractional dimension. Proceedings of the National Academy of Sciences, 79(10), 4054–4060.
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