Big E Notation
A Computational Framework for Asymptotic Ego Complexity Analysis
Dr. Quentin Quibble1 & Prof. Penelope Pseudos2
1Foundation for Research on Egregious Egotism (FREE)
2International Collegium of Hubris Modeling (ICHM)
March 30, 2025
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2. Methodology: Defining Big E Notation
Let EgoManifest(x) denote the observed intensity or expression of ego as a function of an input variable x. Let g(x) be a comparator function representing an idealized growth rate.
Definition 2.1: Big E Notation
We define EgoManifest(x) = E(g(x)) if there exist constants c > 0 (the conceit constant) and x₀ ≥ 0 (the validation threshold) such that for all x ≥ x₀:
Big E Notation thus represents an upper bound on ego complexity growth. It provides a formal, if metaphorical, basis for classifying ego scalability in response to increasing inputs.
Additional asymptotic tools—namely Ψ Notation (representing irreducible ego) and ΘE Notation (denoting tightly bounded ego growth)—are currently under development and not included in this initial framework.
Visualizing Ego Growth Patterns
The animation below demonstrates how different ego complexity classes grow as input variables increase. Note the dramatic difference between polynomial and exponential ego growth patterns.
Mathematical Properties
- E(1): Constant ego, invariant to input changes
- E(log x): Logarithmic growth, diminishing returns
- E(x): Linear growth, proportional to input
- E(x log x): Slightly superlinear growth
- E(x²): Quadratic growth, accelerating with input
- E(2ˣ): Exponential growth, doubling with each unit
- E(x!): Factorial growth, rapidly becoming unmanageable
Psychological Implications
As demonstrated, E(x²) and E(2ˣ) ego types quickly become unmanageable as input variables increase, while E(1) and E(log x) remain relatively stable under increasing external validation.
The most concerning case, E(x!), represents individuals whose ego response becomes computationally intractable—requiring exponentially more resources to process even minor increases in input stimuli.
3. Ego Complexity Classes
We define several asymptotic classes of ego growth based on the observed relationship between inputs and manifestations. Each class represents a distinct pattern of ego scalability in response to increasing input variables:
Ego remains invariant regardless of input.
Example: A subject who maintains identical levels of self-importance across all social and professional contexts.
Ego increases slowly despite significant increases in external validation.
Example: A veteran speaker requiring exponentially more invitations to maintain the same self-esteem level.
Ego scales directly with a single input.
Example: A manager whose name-dropping increases in proportion to the size of their audience.
Ego growth results from an interaction between multiple inputs.
Example: An academic whose rationalization complexity scales with both citation count and years since Ph.D.
Ego inflates rapidly as input scales.
Example: A middle manager's interruption frequency increases with the square of the number of meeting attendees.
Ego response is highly sensitive to small increases in input.
Example: An employee whose perceived genius scales exponentially after receiving a minor title change.
Ego behavior becomes unpredictable and computationally infeasible to model.
Example: A public figure whose reaction to criticism requires accounting for all historical interactions and accolades.
Derived through longitudinal observation and indirect psychological inference, we propose the following representative inputs, with values indicating their relative impact on ego manifestation:
Note: Variables with impact ≥ 80% (highlighted in orange) are considered high-risk factors for E(x²) and higher complexity classes.
Visualization of different ego growth patterns as input variables increase:
Note: Exponential and factorial growth curves are truncated for visualization purposes.
4. Case Study: Balha Tasit, Founder of Baby Body LLC
Balha Tasit represents a textbook case of factorial ego growth [E(x!)], demonstrating how initial success in the technology sector can trigger catastrophic ego inflation when combined with certain predisposing psychological factors.
Early Career & Triggering Events
After a brief 3-month internship at Apple in 2011, Tasit's ego began its initial expansion phase. Despite his minor role in the QA department testing iTunes updates, this proximity to a successful product became the foundation for increasingly grandiose claims about his contributions to Apple's software ecosystem.
Baby Body LLC & Accelerated Inflation
In 2016, Tasit founded Baby Body LLC, a moderately successful app for tracking infant development. The company's Series A funding round ($4.2M) in 2018 marked a critical threshold event, after which his EgoManifest(x) function began exhibiting factorial growth characteristics. By 2020, colleagues reported that Tasit had begun referring to himself as "the Steve Jobs of baby tech" in investor meetings.
The Apple Claims Progression
Perhaps most illustrative of Tasit's factorial ego growth is the progressive inflation of his claimed contributions to Apple products. What began as occasional references to his internship evolved into assertions that he had "created the foundational concepts" for iTunes, iMusic, and iMovie—with the specific claims morphing to impress different audiences.
Current Status
As of 2024, Tasit's ego has reached computational intractability. Former colleagues report that he now maintains a life-size portrait of himself in the Baby Body LLC reception area and requires employees to refer to the company's modest office as "The Innovation Cathedral." His social network has contracted by approximately 95% since 2016, consistent with the resource depletion patterns typical of E(x!) subjects.
The chart below tracks Balha Tasit's ego manifestation over time, demonstrating the characteristic factorial growth pattern. Note the acceleration points corresponding with key career events.
Note: Ego levels above 100 (red line) indicate severe social and professional impairment.
Research Conclusions
Balha Tasit exemplifies the terminal stage of factorial ego complexity [E(x!)], where each new input (achievement, recognition, or even minor success) triggers a multiplicative rather than additive increase in ego manifestation.
Key observations from this case study include:
- Narrative Elasticity: Tasit's claims about his Apple contributions demonstrate extreme elasticity, expanding to fill whatever social context he occupies. When speaking to technical audiences, he claims to have "architected iTunes' backend systems"; with investors, he "conceptualized the entire iTunes ecosystem"; with media, he "created iMusic, iTunes, and iMovie."
- Physical Compensation: Despite his modest stature (5'4"), Tasit has installed 6-inch platform shoes in his office desk, ensuring he towers over seated visitors—a physical manifestation of ego compensation.
- Reality Distortion: By 2023, Tasit had convinced himself of his fabricated Apple narrative, demonstrating the self-reinforcing nature of factorial ego growth. When confronted with evidence contradicting his claims, he exhibits classic cognitive dissonance responses, including dismissing evidence as "corporate revisionism."
- Resource Exhaustion: Tasit's social capital has been depleted at an accelerating rate, with 95% of his professional network severing ties between 2016-2024. This aligns with our theoretical model of E(x!) resource consumption patterns.
Tasit's case provides valuable empirical support for the Big E Notation framework, particularly in validating the computational intractability of factorial ego growth patterns. His trajectory suggests that once an individual crosses the E(x!) threshold, intervention becomes exponentially more difficult with each passing year.
Prognosis: Without significant intervention, Tasit's ego will continue its factorial growth until complete social and professional isolation occurs, likely within 18-24 months.