The Pivotal Role of Control in the Connection between Mathematics and Trauma

Collabortion between:  Kelly Clark Lewis and Nikki Dunn.                            Both are Mathematicians living with PTSD. 

One a teacher. One a student.     One a researcher. One a veteran.   

Mathematics is a universal truth. It is logic separate from reason. 

A peaceful, calm world separate from chaos. Transitioning from one pure, objective statement to another creating a symmetrical story between the two disconnected objects. When ensembled effectively, the black and white, discreteness of the analytical argument transforms into a beautiful, aesthetic journey through finite nature. Like a dancer gracefully floats with deliberate movements across the stage drawing the viewer into the performance, mathematics also has rhythm. A similar dichotomy is found in music as notes triumphantly becomes a harmonious melody. The slow crescendo the listener journeys with the musician is where the most significant impact is made. Not the climax or the peak. Rather, the pivotal moment right before as the performer changes direction and magnitude from what is known to what is unknown. From chaotic to controlled and purposeful, the most impactful experiences evoke emotions.

Without a gradual slope, there is too much of a disconnected leap. Continuity allows for a logistical connection from the familiar and meaningful to the misunderstood and unappreciated. There are times, however, when there is a lack of coherence. Whether in music, dance, mathematics, or the human experience, detaching from what logistically belongs and disordering the accepted pattern causes a stressful event. In other words, trauma. By disrupting that which is structured and that which is being regulated, control is no longer the center of activity. Traumatic stress can have a variety of long-lasting impacts, particularly relational trauma, when there exists a continuous and ongoing pattern of adverse experiences (Felitti et all, 1998; Hannah Goldstein, 2016; Walker, 2017).

Like a service dog guarding its owner as medical care is administered to a wound, trauma protects the self from accessing the event and trauma controls how the injured emotions are perceived.

Both the emotional experiences associated with trauma and the analytical foundations of mathematics intersect in the need to feel in control.

BRAIN HARDWIRED FOR PATTERN

Mathematics is the medium through which everything – human interaction, nature, philosophy, art, music, science, technology, and human development – can be derived, discovered, and discerned. Logic does not require that we “discover” or “create” it since it exists outside of the meaning we assign to it. Another systematic classification would have formed had the current mathematical system not been adopted. It is how the brain is designed.     

As a pattern recognition machine, we are hardwired with the primitive need to ensure survival. This instinctive dominance is dependent upon observing the environment, making predictions, and learning to adapt as necessary (Maslow, 1943). As we evolved throughout history, our more advanced, intellectual brain influenced mathematics into a hierarchical system for organizing complex concepts and abstract structures. Assigning a conceptual framework of the information and patterns into a familiar pattern and meaningful method creates an understandable and explainable concreteness for our perceptions and experiences. Math is a way to organize individual elements into sequences, sequences into patterns, and patterns into a system of logic. At its foundation, math is a way to order. 

CONTROL, FREEDOM AND FEAR

Humans have an innate tendency to see patterns due to our need for control (Huettel, S., Mack, P., & McCarthy G., 2002). More control and power are desired because it provides a way for an individual to have more freedom and autonomy (Lammers, Stoker, Rink, et all, 2016). Being able to spot and analyze patterns quickly and accurately aids in evolutionary survival, in reproduction, in safety and security, and in learning (Maslow, 1943; Carretie, Hinojosa, Mercado, & Tapia, 2005; Skinner, 1950)  

At the opposite end of the spectrum, is fear. Freud’s “Structural Theory of Personality”, Pavlov’s “Classical Conditioning”, Watson’s “Behaviorism”, Skinner’s “Operant Conditioning”, and Maslow’s “Hierarchy of Human Needs in Motivating Behavior” all contain aspects of fear and how it relates to “needs”, “desires”, and “motivations” of the behavior of individuals, animals, and groups. By self-protecting and avoiding psychological stress, there is an increase in homeostasis and an increase of survival and reproduction (Taormina & Gao, 2013; Walker, 2013).

EMOTIONAL ATTACHMENT AND TRAUMA

One of the main ways to increase survival, safety, and security is by being in community and forming an attachment with others and with other groups (Ainsworth, 1973, 1989). Not only is there an evolutionary foundation for belonging, as there is for homeostasis, but being deprived of interpersonal attachments, for which love is the fulcrum, can have sustained negative consequences (McLeod, 2017). Attachment theory states that animals are born into vulnerable, fragile states isolated from others and dependent upon them for survival. Therefore, it is vital to embrace this physical and emotional vulnerability by developing healthy relationships (Ainsworth, 1973, 1989; Bowlby, 1969).  

In 1998, the first Adverse Childhood Experiences (ACE) research study concluded that extreme childhood trauma, such as abuse, domestic violence, abandonment, and neglect, is the most significant risk factor for an increase in future mental and physical illnesses and injuries as well as a reduction in life expectancy (Felitti et all, 1998). Trauma-inducing experiences have the common denominator of fear.  A consistent and persuasive pattern of coercion and control are used as methods to ensure compliance out of fear (Hannah & Goldstein, 2016).  

As it is stored in the brain, the traumatic event and the emotional aspects related to the event no longer have healthy/normal neural connections. Instead, they exist in isolation and are activated by experiences associated with the previous stressful event (SAMHSA, 2014). Since there is no control or power over the hyperarousal and hypervigilance state, the fear-based responses, known as the 4F’s, are the main reactions when homeostasis is disrupted or threatened:  

• Flight: Attacking and narcissistic defenses
• Flight: Fleeing, obsessive, and compulsive defenses
• Freeze: Numbing and dissociating defenses
• Fawn: Complying and codependence defenses   

    (Bernard, 1932; Cannon, 1915; Walker, 2013).        

NEUROBIOLOGICAL CORRELATION OF TRAUMA AND LOGIC

Like an airplane flying in a holding pattern, the physiological reactions and the psychological components delay the individual’s ability to connect their dysregulation of emotions and behaviors to the original traumatic event and the pain and fear associated with it (SAMHSA, 2014). By staying in a “loop of safety”, the individual remains in homeostasis, avoiding exposure of their fundamental needs for interpersonal connection, belonging, and love (Walker, 2013). Early adverse childhood experiences create unresolved past trauma from the reinforced pattern of not being able to exist in a calm, undefended state. In essence, the 4 F’s protect the vulnerable child from fear (and the fragile animal from danger) by creating a false, unhealthy sense of attachment in an effort to protect against further abandonment and disconnection as well as by unconsciously believing safety can be created by controlling the unstable environment with their behavior (Walker, 2013). This reinforced pattern of encountering fear, when sharing vulnerability, is learned by the child/animal and imprinted upon the brain. There is no continuity. 

Instead, turbulence exists between the understood and the chaotic.

LEFT AND RIGHT BRAINED CORRELATION OF TRAUMA AND LOGIC

Research has shown that the amygdala, the hippocampus and hypothalamus, the prefrontal cortex, and the anterior cingulate cortex are the critical brain regions for fear (and other emotional responses) and where the brain processes patterns and learns logic (Bernard, 1932; Cannon, 1915; Frenois et all, 2007; Konovalov and Krajbich, 2018; SAMHSA, 2014; Toyoda et all, 2011). Each of these brain regions are located in both the left and right hemispheres. The left hippocampus is associated with an egocentric, pattern representation and recognition, while the right hippocampus is more allocentric (Shipton et all, 2014). The hippocampus is also where the “right” and “left” brain characteristics are mainly found. When a person is left-handed, they are more right-brain dominant and tend to be stronger in visual-spatial information and with a holistic-based perception. The left-brain dominant person, who is right-handed, tends to gravitate more towards sequential-spatial information and has a deductive perception. The individual brain regions do not behave in a disconnected manner. Like the left and right hippocampus, the left and right amygdala also complement each other. Both the left and right amygdala were equally linked with “Harm Avoidance”, even though the right amygdala is believed to involve the detection of an emotional stimulus and the left amygdala is believed to involve the evaluation of that stimulus (Baeken et all, 2014). This interdependence of the regions and the connectivity between the two lateralizations demonstrate the complexity and coherence of the brain (Prado, Chadha, & Booth, 2011). 

“Give me a lever long enough and a fulcrum on which to place it,

and I shall move the world.”

- Greek Mathematician, Archimedes

Much like mathematics, our brain does not operate in a black and white, disassociated forum. Our egotistical need to create a logical system, based on deductive reasoning and on inferential processes, highlights the attachment between systems. Continuity allows for a connection to exist between the chaotic to controlled. Having coherence provides control between what is unknown and known; what is misunderstood and unappreciated to the familiar and meaningful. Remaining in a holding pattern or pivoting to quickly to change direction and magnitude, disrupts safety and causes stress. Avoiding harm and fear is avoided once traumatic stress has occurred. When there exists a continuous pattern of adverse experiences, trauma steps in to protect the self from accessing the memory of the event and controls how the injured emotions are perceived, much like a dog guards its injured owner. At the intersection of interpersonal trauma and analytical mathematics, is the desire, motivation, and need to feel in control. Power and control ensure that there is an increase in homeostasis, survival, and reproduction. In other words, when there is a decrease in fear then there is an increase in freedom.  

   The listener and participant of a musical piece both experience the gentle slow rise of the movement and the conductor has the power to determine the tempo of that musical movement. However, it is only within logic, that the viewer, the artist, the director, and the composer exist all as one. The freedom awarded to the composer can only be given to one person. The other roles can be filled by anyone at any time; their ability to control the environment is a mere illusion.   

For, it is actually the position of mathematician, with its (egotistical) universal truth, that can leverage the world and control the symphony.   

#Change always starts with a #conversation . Most people, however, are too #comfortable with the illusion they are in #control that they do not make a #connection with #chaos . #Mathematicians know chaos is merely a #different kind of #pattern . One that can be logically explained, if there is enough #commitment to #comprehension.

The Difference between Zero and Infinity is Only 1. 1 Connection.

0 ---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- 1

WORKS CITED

Ainsworth, M. D. S., & Bell, S. M. (1970). Attachment, exploration, and separation: Illustrated by the behavior of one-year-olds in a strange situation. Child Development, 41, 49-67.

Ainsworth, M. D. S. (1973). The development of infant-mother attachment. In B. Cardwell & H. Ricciuti (Eds.), Review of child development research (Vol. 3, pp. 1-94) Chicago: University of Chicago Press.

Bowlby, J. (1958). The nature of the child's tie to his mother. International Journal of Psychoanalysis, 39, 350-371.

Bowlby J. (1969). Attachment. Attachment and loss: Vol. 1. Loss. New York: Basic Books.

Baeken, C., Marinazzo, D., Schuerbeek., P., et all. (2014). Left and Right Amygdala - Mediofrontal Cortical Functional Connectivity is Differentially Modulated by Harm Avoidance. PLOS. 9 (4). e95740. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3997418/ 

Carretie, L., Hinojosa, J., Mercado, F., & Tapia, M. (2005). Cortical response to subjectively unconscious danger. NeuroImage, 24, 615–623

Felitti, V. J., Anda, R. F., Nordenberg, D., Williamson, D. F., Spitz, A. M., Edwards, V., Koss, M. P., & Marks, J. S. (1998). Relationship of childhood abuse and household dysfunction to many of the leading causes of death in adults: The Adverse Childhood Experiences (ACE) Study. American Journal of Preventive Medicine, 14(4), 245–258. https://doi.org/10.1016/S0749-3797(98)00017-8

Frenois, F., Moreau, M., O’Connor, J., et all (2007). Lipopolysaccharide induces delayed FOSB/DeltaFosB immunostaining within the mouse extended amygdala, hippocampus and hypothalamus, that parallel the expression of depressive-life behavior. Psychoneuroendocrinology. 32 (5). 516-531. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1978247/

Hannah, M. & Goldstein, B. (2016). Domestic Violence, Abuse, and Child Custody. Legal Strategies and Policy Issues. II. https://www.civicresearchinstitute.com/toc/DVAC2_TOC.pdf

Huettel, S., Mack P., & McCarthy, G. (2002). Percieving patterns in random series: dynamic processing of sequence in prefrontal cortex. Nat. Neurosci. (5). 485-490.

Konovalov, A. & Krajbich, I. (2018). Neurocomputational Dynamics of Sequence Learning. Neuron. DOI:https://doi.org/10.1016/j.neuron.2018.05.013 

Lammers, J. Stoker, J., & Rink, F. (2016). To Have Control Over or to Be Free From Others? The Desire for Power Reflects a Need for Autonomy. Personality and Social Psychology. 

McLeod, S. A. (2017). Attachment theory. Simply Psychology. https://www.simplypsychology.org/attachment.html

Maslow, A. H. (1943). A theory of human motivation. Psychological Review, 50, 370–396.

Monti, M. & Osherson, D. (2011). Logic, Language, and the Brain. Brain Research. https://www.princeton.edu/~osherson/papers/LLBrain.pdf 

    Prado, J., Chadha, A., & Booth, J. (2011). The Brain Network for Deductive Reasoning: A Quantitative Meta-analysis of 28 Neuroimaging Studies. Neuroscience. 23(11); 3483-3497. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3188687/

Prior, V., & Glaser, D. (2006). Understanding attachment and attachment disorders: Theory, evidence and practice. Jessica Kingsley Publishers.

Schaffer, H. R., & Emerson, P. E. (1964). The development of social attachments in infancy. Monographs of the Society for Research in Child Development, 1-77.

Shermer, M. (2008). Patternicity. Scientific American, December. Online. https://www.cell.com/neuron/fulltext/S0896-6273(18)30385-4?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0896627318303854%3Fshowall%3Dtrue

Shipton, A., El-Gaby, M., Apergis-Schoute, J., et all. (2014). Left-right Dissociation of Hippocampal Memory Processes in Mice. PNAS. 111 (42) 15238-15243. https://www.pnas.org/content/111/42/15238

Substance Abuse and Mental Health Services Administration (SAMHSA). (2014). Trauma-Informed Care in Behavioral Health Services. 57. https://www.ncbi.nlm.nih.gov/books/NBK207191/ 

Taormina, R., & Gao, J. (2013). Maslow and the Motivation Hierarchy: Measuring Satisfaction of the Needs. The American Journal of Psychology. DOI: 10.5406/amerjpsyc.126.2.0155 

Toyoda, H., Li, X., Wu, L., et all (2011). Interplay of Amygdala and Cingulate Plasticity in Emotional Fear. Neural Plasticity. 2011 (9). 813749. https://www.hindawi.com/journals/np/2011/813749/ 

 Walker, P. (2013). Complex PTSD: From Surviving to Thriving: A Guide and Map for Recovering from Childhood Trauma.