The General Theory of Stupidity

Abstract

This paper presents a formal mathematical model of the integral "Stupidity" index ($G$) — a metric evaluating the probability of irrational behavior (cognitive failure) of an agent under information load. Unlike traditional theories linking rationality to general intelligence ($g$-factor), stupidity here is defined as an architectural vulnerability arising from the imbalance between environmental complexity and attention control mechanisms. The model introduces three fundamental components: (1) separation of cognitive biases into stochastic errors ($B_{err}$) and motivated beliefs ($B_{mot}$), resistant to intelligence; (2) an exponential penalty function for digital overload ($D_{eff}$); and (3) an attention control factor ($A$) as the key regulator of rationality in the information economy. Simulation modeling on synthetic agents demonstrates the model's ability to identify "smart stupidity" scenarios that remain invisible to linear $IQ$ metrics.

Keywords: G-factor, cognitive security, attention economy, motivated reasoning, digital psychometrics.

1. Introduction

1.1. The Problem of Rationality in Conditions of Information Asymmetry

Traditional psychometric paradigms relying on the concept of general intelligence ($g$-factor, Spearman, 1904) were developed for the static information environment of the industrial era. However, in the 21st century, cognitive agents operate under conditions of radical uncertainty and "information storm". According to the "Evolutionary Mismatch" hypothesis, human neurobiological architecture, adapted for small social groups (Dunbar's number), proves incapable of efficiently filtering the exponentially growing stream of digital stimuli.

Modern cognitive science data (Stanovich, 2009) introduces the concept of dysrationalia — the inability to think and act rationally despite often high intelligence. Empirical studies (Kahan, 2013) confirm that high $IQ$ not only fails to protect against cognitive biases (bias blind spot) but also, paradoxically, enhances the capacity for motivated reasoning, allowing the agent to find complex justifications for irrational claims. Thus, in the modern environment, the deficit is not in the brain's computational power ($IQ$), but in the resource of cognitive control and attention.

1.2. Defining Stupidity: A Cybernetic Approach

In this work, "Stupidity" ($G$) is postulated not as a characteristic of intelligence (lack of mind), but as a measure of functional cognitive vulnerability. It is a state of maladaptation where an agent loses decision-making agency under the influence of external factors.

Formally, $G$ is defined as a function of the imbalance between environmental complexity and the system's regulatory capabilities:

Stupidity ($G$) is a system failure [of control architecture] arising when demands for signal filtering ($D$) and social conformity ($S$) exceed the available resource of attention control ($A$) and epistemic vigilance ($C$), leading to systematic adoption of decisions contrary to the agent's long-term interests.

This definition shifts the problem from the plane of individual psychology to the plane of cybernetics and Control Theory.

2. Methodology and Axiomatics

The model is based on a synthesis of Bounded Rationality theory, Cognitive Load Theory, and second-order cybernetics.

2.1. Axiomatics of Cognitive Failure

The $G$ model is based on three formal axioms:

Axiom 1 (Resource Limitation). An agent's cognitive system has finite throughput capacity $\mathbb{C}_{max}$. Any excess of input signal $D(t) > \mathbb{C}_{max}$ leads to non-linear degradation of decision quality.

Axiom 2 (Primacy of Motivation). In the absence of an external regulator (critical thinking), high intelligence ($I$) minimizes not prediction error but cognitive dissonance, directing computational power to protect beliefs ($B_{mot}$).

Axiom 3 (Environmental Entropy). An agent's rationality is inversely proportional to environmental entropy ($D$) and social pressure ($S$).

2.2. Operationalization of Variables

Table 1 presents the model variables, their theoretical meaning, and measurement tools. All metrics are normalized in the range $[0, 1]$.

Table 1. Variables of Model $G$

2.3. Mathematical Specification (G-Formula)

The final function $G(X)$ represents the sum of weighted vulnerability components:

where $\gamma = 0.5$ (pressure permeability coefficient).

Component (1): Internal Vulnerability

Here Axiom 2 is formalized. The term $B_{err}/I$ reflects the classical view: "a smart person makes fewer mistakes". The term $B_{mot}$ is introduced additively, postulating that ideological engagement is orthogonal to intelligence ($\partial B_{mot} / \partial I \approx 0$).

Component (2): Environmental Load

Reflects Axioms 1 and 3. Effective noise $D_{eff}$ is modeled as:

Where $D_{thresh}=0.7$ is the phase transition point ("cognitive collapse"). The only divisor here is $A$ (Attention), since when the channel is overloaded, other competencies (EQ, CQ) cannot be engaged.

Component (3): Social Context

Group pressure ($S$) can be reduced through cultural competence ($1-C$) and emotional stability ($E$).

3. Results (Experimental Data)

To validate the model, large-scale numerical experiments were conducted (Monte Carlo Method, $N=10,000$ synthetic agents) along with sensitivity analysis.

3.1. Statistical Analysis of G Distribution

When generating a population with a normal IQ distribution ($100 \pm 15$) and beta-distribution of environmental parameters ($D, S$), the average stupidity index value was $G_{mean} = 1.28$ ($\sigma=0.45$).

Fig. 1: Distribution of Stupidity Index ($G$) from Monte Carlo simulation ($N=10,000$).

• Observation: 73% of the population falls into the "Critical Risk" zone ($G > 1.0$). This confirms the hypothesis that the modern digital environment is toxic by default for unadapted cognitive apparatus ("The Default Mode is Failure").
• Distribution: The G histogram has a "heavy right tail", indicating the risk of extreme cognitive failures.

3.2. Phase Transition: Stupidity Singularity

Heat map analysis ($D$ vs $A$, see Fig. 2) revealed a clear phase transition.

Fig. 2: Heatmap of digital noise ($D$) versus attention control ($A$), demonstrating the phase transition to stupidity singularity.

• At $D < 0.7$, the system behaves linearly.
• At $D > 0.7$ and $A < 0.5$, exponential growth of $G$ is observed, designated as "Stupidity Singularity" ($G \to \infty$). In this zone, the agent completely loses agency.

3.3. Sensitivity Analysis

Analysis of the model's robustness to weight changes ($\alpha_i \pm 10\%$) showed:

• The greatest sensitivity is observed to the weight $\alpha_2$ (Environment): a 10% change causes a 5.6% shift in $G$.
• Sensitivity to $\alpha_1$ (Cognition) is 3.4%.
• This confirms that in model v0.3, the environmental factor dominates over individual intelligence.

3.4. Case Studies (Scenario Analysis)

The model was tested on four archetypal profiles to verify reaction validity:

1. "Smart Fanatic"
   • Profile: $IQ=150, B_{mot}=0.8$ (ideologue), $D=0.5$.
   • $G = 0.65$. The model shows that intelligence does not save from motivated bias. The subject is rational in work but dysfunctional in matters of faith.
2. "Digital Addict"
   • Profile: $D=0.95$ (info-noise), $A=0.3$ (lost focus).
   • $G \approx 1.25$ (Singularity Zone). Complete loss of control. This demonstrates the dominance of factor $A$ in the equation.
3. "Bureaucrat"
   • Profile: High social pressure ($S=0.9$), low critical thinking ($C=20$), low noise ($D=0.3$).
   • $G = 0.95$. Even in a calm digital environment, conformity ($S$) combined with a lack of criticism ($C$) leads to a borderline state ("collective stupidity").
4. "Resilient Operator"
   • Profile: Critical noise ($D=0.95$), but extreme concentration ($A=0.9$) and self-control ($R=0.9$).
   • $G = 0.78$. The subject maintains rationality on the edge, avoiding singularity thanks to high attention resources. This proves the possibility of adaptation to modern conditions.

3.5. Cross-validation on Empirical Distributions (Big Five)

To assess the ecological validity of the model, testing was conducted on a sample of real profiles ($N=15,000$) obtained from the open dataset Open Psychometrics Big Five.

Proxy Variable Methodology

Since direct measurements of $A$ (Attention) and $G$ are absent in historical data, a procedure for mapping latent traits was applied:

• Attention ($A$) is approximated through the Conscientiousness factor, responsible for self-control and goal-setting.
• Emotional Regulation ($E$) is approximated as the inverse of Neuroticism.
• Bias ($B_{mot}$) is approximated as the inverse of Openness (dogmatism).

Stress Test Results

The population was placed in a simulated environment with modern metropolis parameters ($D=0.8$, $S=0.6$). Results demonstrate fundamental maladaptation of the average phenotype:

1. Mean Value: $\mu_G = 1.27$ ($\sigma = 0.83$).
2. Failure Rate: 95.1% of the sample exceeded the cognitive collapse threshold ($G > 1.0$).

Conclusion: Confirmation of the Structural Nature of Stupidity

This experiment empirically confirms Axiom 3 (Environmental Entropy) and the dominant role of the environmental term ($\alpha_2$) in equation $G$.

The fact that 95% of the "normal" population falls into the cognitive collapse zone ($G > 1.0$) proves that "Stupidity" within our theory is not a deviation of intelligence, but a deterministic system state arising when digital load ($D$) exceeds biological attention limits ($A$). Thus, the model validates the thesis that in the 21st century, rationality is impossible without artificially reducing $D$ or training $A$.

4. Discussion

Simulation results allow for a detailed review of fundamental approaches to assessing human capital and designing information systems.

4.1. The "Heavy Tail" Phenomenon: Stupidity as Norm

Unlike the normal distribution of $IQ$, the distribution of $G$ has a pronounced right-sided asymmetry (heavy tail). The empirical mean $\mu_G \approx 1.28$ indicates that the state of cognitive failure is the statistical norm in the current technological environment ($D > 0.7$).

• 0.0 – 0.3 (Rationality Zone): Achievable only for agents with extreme Attention indicators ($A > 0.9$) or in a sterile environment ($D < 0.3$).
• 0.3 – 1.0 (Risk Zone): The working zone of most people. Characterized by periodic loss of agency under the influence of social triggers.
• > 1.0 (Singularity): A state identified in 95% of the Big Five sample. Characterized by complete degradation of critical thinking.

4.2. The "Smart Stupidity" Paradox

The model resolves the contradiction noted by Stanovich (2009): why do smart people believe in irrational concepts?

Simulation results (Scenario 3.4.1) show that the component $B_{mot}$ (motivated reasoning) is orthogonal to intelligence. Moreover, high $IQ$ can serve as a tool for generating more complex arguments in defense of erroneous beliefs (rationalization effect), making the "smart fanatic" a more dangerous agent ($G \approx 0.65$, but with high influence) than a simple ignoramus.

4.3. Attention Economy and the $G^*$ Imperative

The revealed phase transition at $D > 0.7$ questions the effectiveness of traditional education methods. If the attention channel is noisy, increasing $I$ (education) or $C$ (culture) does not reduce $G$, as the denominator $A$ tends to zero.

Practical Recommendation:

To minimize stupidity ($G^* = \min G$), organizations and states must shift focus from "pumping knowledge" to "attention hygiene":

1. HR Policy: Introduction of the ACS (Attention Control Scale) metric as a stronger predictor of efficiency than WAIS ($IQ$).
2. Process Design: Forced limitation of digital noise ($D$) in work protocols.

4.4. Study Limitations

The model relies on calibrated weights $\alpha$, which require refinement in field experiments. Validation on Big Five is indirect, as it uses proxy variables. Nevertheless, the qualitative picture (dominance of environment over personality) remains stable in all sensitivity tests.

5. Conclusion: The Imperative of Cognitive Ecology

This work formalizes and empirically confirms the "$G$" theory — a model of functional stupidity as a system failure. The study shows that under conditions of high entropy ($D > 0.7$), traditional predictors of rationality ($IQ$) lose predictive power, giving way to regulatory mechanisms ($A$).

5.1. Applied Significance: Multifactor Approach

Model $G$ demonstrates that sustainable rationality is impossible through optimizing only one parameter. Solutions must be comprehensive, considering all variables of the equation:

1. Education ($I + A + C$)

Problem: The traditional model, focused exclusively on knowledge transfer ($I$), is necessary but insufficient under overload conditions.

• Solution: The educational standard must include three equal components:
  • Fundamental Knowledge ($I$) to reduce errors ($B_{err}$).
  • Attention Hygiene ($A$) for protection against overload ($D$).
  • Critical Thinking ($C$) for deconstructing social narratives ($S$).

2. Corporate Governance ($I + E + D$)

High employee intelligence ($I$) is nullified by a toxic environment ($D$) and low emotional intelligence ($E$).

• Solution:
  • Introduction of Attention Control Scale in hiring (balance $I/A$).
  • Reduction of digital noise ($D$) through "quiet hours" regulations and asynchronous communication.
  • Emotional regulation training ($E$) to reduce vulnerability to group pressure.

3. Public Policy ($D + S$)

The main risk to society is created by the uncontrolled growth of digital entropy ($D$) and manipulative social pressure ($S$).

• Solution:
  • Qualification of algorithmic amplification of bias ($B_{mot}$) as a risk factor.
  • Introduction of "Cognitive Security" standards limiting the density of information flow in public services.

5.2. Final Synthesis

Modern civilization is at a bifurcation point. If the external environment continues to become more complex ($D \uparrow$) without compensatory growth in attention management technologies ($A \uparrow$), society is doomed to "Stupidity Singularity" — a state where collective decisions become statistically worse than random ones. Theory $G$ provides a precise mathematical language for diagnosing and preventing this scenario.

Data Availability

Validation code (Validation_Study.py), implementation details (Calc_G_Implementation.py), and synthetic datasets used in this study are available in the project repository: https://github.com/bricsin4u/stupidity-theory-research-data.

References

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2. Stanovich, K. E. (2009). What Intelligence Tests Miss: The Psychology of Rational Thought. Yale University Press.
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4. Sweller, J. (2011). Cognitive load theory. Psychology of Learning and Motivation.
5. Wu, T. (2016). The Attention Merchants: The Epic Scramble to Get Inside Our Heads. Knopf.
6. Kahneman, D. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux.