How I Learned to Become Nonlinear: The Prequel

ABSTRACT

Late adolescent development can be described in terms of a nonlinear dynamic complex system including processes of emergence, that develop at the edge of chaos, and the shaping of development by the adolescent’s engagement in a variety of social and educational systems. Autobiographical material from the author’s late adolescence is used to illustrate these processes as they occurred in the author’s late adolescent and early adult development.

KEYWORDS:

• Adolescent development
• nonlinear dynamic systems
• adolescent psychoanalysis
• complex systems
• edge of chaos

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Please ignore this footnote, in which more precise meanings are given to some of the technical terms mentioned in this paper, until or unless you find it useful. A system is a collection of elements along with the connections of those elements. A dynamic system is a system that changes over time. A linear dynamic system is one that can be adequately described by linear equations (see the text below). A nonlinear system is one that cannot be so described. Attractors are patterns that endure for some period of time. The actual trajectory of the system tends toward attractors. Chaos refers to states of systems in which minimal perturbations of the system result in radical changes in the system’s course. The edge of chaos (also referred to as complexity) refers to a state of a system that is neither stable nor chaotic but sufficiently disorganized that changes in condition may move the system toward significantly different paths.

2. As a clinician I have been struck with how common experiences like this are for fortunate late adolescents. Experiences in which a whole new world opens before them and seems to rapidly pull them to a new life course. An example – a college student goes to a museum to fulfill a course requirement and realizes suddenly that “being an artist” is what she “must” do with her life, and actually shifts to a new life course.

3. The relationship between mathematics, its applications to science, and particularly highly theoretical sciences that resemble mathematical thinking, is complex, and may in fact, as Wigner observed, result not so much from the intrinsically mathematical nature of physical reality as the imposition of available mathematics on thinking about physical reality (Wigner 1960). The mathematics available at any given moment in history determines what can be studied mathematically with the result that while it may appear that the mathematics almost magically encompasses reality, in fact what has happened is that the vision of reality has been limited to what mathematics can encompass. Many of the developments associated with nonlinear dynamic systems theory have resulted from the availability of mathematics that point to the possibilities of complex systems which then lead those familiar with the mathematical ideas to observe them in the world. It was, for example, only after the mathematical idea of fractals was well developed that people started to see fractals everywhere (Barnsley 1988; Galatzer-Levy 2019).

This is nowhere better demonstrated than in the field that has become nonlinear dynamic systems theory in which the availability of nonlinear mathematics led to the recognition of the nonlinearity of complex systems.

Additional information

Notes on contributors

Robert M. Galatzer-Levy

Robert M. Galatzer-Levy, MS, MD, is a psychoanalyst and psychiatrist who works with people from birth to old age and across diverse populations. He is a Clinical Professor of Psychiatry and Behavioral Neuroscience at the University of Chicago and a Faculty Member (Training, Supervising and Child and Adolescent Supervising Analyst) at the Chicago Psychoanalytic Institute.