MBTI model

The Myers-Briggs Type Indicator (MBTI) is a personality assessment tool designed to identify a person’s personality type, strengths, and preferences. Developed by Isabel Briggs Myers and her mother Katharine Briggs in the mid-20th century, the MBTI is based on the psychological theories of Carl Jung.

The assessment categorizes personalities into 16 distinct types based on four dichotomies:

1. Extraversion (E) vs. Introversion (I): Describes where individuals prefer to focus their attention and get their energy—from external objects, people, and activities (E) or their inner world of ideas and experiences (I).
2. Sensing (S) vs. Intuition (N): Relates to how individuals prefer to perceive information, concretely through the five senses (S) or abstractly using patterns and impressions (N).
3. Thinking (T) vs. Feeling (F): Involves decision-making preferences, whether through logical analysis (T) or guided by personal values and concerns about others (F).
4. Judging (J) vs. Perceiving (P): Indicates whether a person interacts with the external world by planning and controlling (J) or staying open to new information and options (P).

Each personality type is represented by a four-letter code combining one preference from each dichotomy. For example, INTJ stands for Introversion, Intuition, Thinking, Judging.

One can find the MBTI type test in this website. I’m an INTJ. My favorite INTJs are Riemann, Hilbert, Rusell, Bertrand Russell, Beethoven, Brahms, Sviatoslav Richter, Nikola Tesla, Elon Musk.

In the proposed model for understanding the MBTI through a mathematical framework, the traditional discrete classification of personality into 16 types is expanded into a more fluid and dynamic system. Traditionally, MBTI assigns a person one of two options in four categories, resulting in a fixed type such as INFP or ESTJ. However, the limitations of this model in capturing the nuance and variability of human personality suggest the need for a more sophisticated approach.

Instead of viewing personality traits as binary, the new model proposes using a continuum from 0 to 1 for each of the four axes—Extraversion-Introversion, Sensing-Intuition, Thinking-Feeling, Judging-Perceiving. This approach positions an individual’s personality within a 4-dimensional hypercube, where each point in this hypercube represents a unique blend of these traits at varying intensities. This allows for a more precise characterization of personality that acknowledges the spectrum nature of these traits rather than strict dichotomies.

To capture the dynamic nature of personality—which can evolve over time or in response to different environments—the model advances the idea of transforming the hypercube into a 4-dimensional manifold with curvature. This manifold is not merely a static space but one that can exhibit complex geometric properties such as curvature, which metaphorically represents the psychological propensities and vulnerabilities of different personality configurations. For instance, certain regions of this manifold might be akin to valleys, representing personality states towards which an individual might naturally gravitate under typical conditions, or peaks representing less stable, harder-to-maintain states.

The mathematical concept of dynamical systems is then applied to this manifold to model the trajectories of personality over time. This approach uses differential equations to describe how an individual’s personality point moves within this manifold, influenced by internal predispositions and external circumstances. The introduction of curvature into the manifold allows for the modeling of phenomena such as stable and unstable nodes—personality types that might serve as attractors or repellents under specific psychological or environmental conditions.

To further enhance the model’s realism and predictive power, stochastic elements could be introduced through stochastic differential equations. These equations account for the randomness and unpredictability of human behavior and external influences, providing a way to simulate how real-world variability might affect personality trajectories.

Overall, this mathematical modeling of MBTI offers a profound expansion of our understanding of personality, providing a tool that not only describes who we are but also predicts how we might change over time. It bridges the gap between rigid typological systems and the fluid reality of human psychology, offering a nuanced, scientifically grounded framework for exploring the complexities of human behavior.