TY - JOUR

T1 - Mathematical self-determination theory II

T2 - Affine space representation

AU - Ünlü, Ali

N1 - Publisher Copyright:
© 2023 Elsevier Inc.

PY - 2023/9

Y1 - 2023/9

N2 - Self-determination theory is a well-established theory of motivation. This theory provides for fundamental concepts related to human motivation, including self-determination. The mathematization of this theory has been envisaged in a series of two papers by the author. The first paper entitled “Mathematical self-determination theory I: Real representation” addressed the representation of the theory in reals. This second paper is in continuation of it. The representation of the first part allows to abstract the results in more general mathematical structures, namely, affine spaces. The simpler real representation is reobtained as a special instance. We take convexity as the pivotal starting point to generalize the whole exposition and represent self-determination theory in abstract affine spaces. This includes the affine space analogs of the notions of internal locus, external locus, and impersonal locus, of regulated and graded motivation, and self-determination. We also introduce polar coordinates in Euclidean affine motivation spaces to study self-determination on radial and angular line segments. We prove the distributivity of the lattice of general self-determination in the affine space formulation. The representation in an affine space is free in the choice of primitives. However, the different representations, in reals or affine, are shown to be unique up to canonical isomorphism. The aim of this paper is to extend on the results obtained in the first paper, thereby to further lay the mathematical foundations of self-determination motivation theory.

AB - Self-determination theory is a well-established theory of motivation. This theory provides for fundamental concepts related to human motivation, including self-determination. The mathematization of this theory has been envisaged in a series of two papers by the author. The first paper entitled “Mathematical self-determination theory I: Real representation” addressed the representation of the theory in reals. This second paper is in continuation of it. The representation of the first part allows to abstract the results in more general mathematical structures, namely, affine spaces. The simpler real representation is reobtained as a special instance. We take convexity as the pivotal starting point to generalize the whole exposition and represent self-determination theory in abstract affine spaces. This includes the affine space analogs of the notions of internal locus, external locus, and impersonal locus, of regulated and graded motivation, and self-determination. We also introduce polar coordinates in Euclidean affine motivation spaces to study self-determination on radial and angular line segments. We prove the distributivity of the lattice of general self-determination in the affine space formulation. The representation in an affine space is free in the choice of primitives. However, the different representations, in reals or affine, are shown to be unique up to canonical isomorphism. The aim of this paper is to extend on the results obtained in the first paper, thereby to further lay the mathematical foundations of self-determination motivation theory.

KW - Affine space

KW - Amotivation

KW - Convexity

KW - Motivation

KW - Polar coordinate

KW - Self-determination theory

UR - http://www.scopus.com/inward/record.url?scp=85164458939&partnerID=8YFLogxK

U2 - 10.1016/j.jmp.2023.102793

DO - 10.1016/j.jmp.2023.102793

M3 - Article

AN - SCOPUS:85164458939

SN - 0022-2496

VL - 116

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

M1 - 102793

ER -