Citation: Heck PR, Simons DJ, Chabris CF. 65% of Americans believe they are above average in intelligence: Results of two nationally representative surveys. PLoS One. 2018 Jul 3;13(7):e0200103. doi: 10.1371/journal.pone.0200103. PMID: 29969480; PMCID: PMC6029792.
The normal distribution, with its symmetric bell-shaped curve, is a continuous probability distribution that is symmetric about the mean (μ). It is fundamental to statistics, probability theory, and the modeling of natural data. The "Reverse" Flynn Effect and the Dunning-Kruger Effect—especially when viewed through the modern lenses of artificial intelligence, substance abuse, and social media addiction—increasingly exacerbate aberrant and deviant human pathologies.
I choose not to be a practitioner of "good news" religion, nor will I herald the rudimentary beauty of optimistic ideology among people who hate good and love evil. To live beyond good and evil without defaulting to Nietzschean nihilism, one must find a harmony between Kant’s deontological imperatives and Mill’s consequentialist utilitarianism. In mathematics, an infinite sequence of variables, when perturbed by an external element but bounded by rigid structure, resolves only into approximate equivalence before ultimately transforming into a distinctly new symbol. The same applies to human nature.
Human cognitive capacity is not evenly distributed. In standard deviation models, extreme cognitive deficiency bottoms out below 70 points, while profound giftedness scales beyond 130 points. Different domains optimize different intelligences, and the broader species requires all variations to function. However, without retreating into orthodox, dogmatic, belief-based faith traditions, one can acknowledge that life exists because it was structurally created and strategically designed. As such, questioning the mold, fashion, capacity, or nature of another individual's spirit borders on hubristic haughtiness.
Probability Density Function The probability density function of a normal distribution is mathematically defined as:
f(x)=σ2π1e−2σ2(x−μ)2
Where:
Empirical Rule The empirical rule (the 68-95-99.7 rule) dictates that for a normal distribution:
Approximately 68% of data fall within 1σ of μ
Approximately 95% of data fall within 2σ of μ
Approximately 99.7% of data fall within 3σ of μ
Case Study: Intelligence Quotients and Dysgenic Pathology IQ was calculated as a ratio: IQ=(Chronological Age (CA)Mental Age (MA))×100. Modern psychometrics utilize Deviation IQ, strictly normalized so that the median (x~) and mean (μ) are permanently fixed at 100.
High intelligence does not preclude malevolence; in fact, it often optimizes it.
Verified Clinical IQs of Serial Killers:
Ted Kaczynski: IQ 167 (3 murdered, 23 injured)
Andrew Cunanan: IQ 147 (5 murdered)
Jeffrey Dahmer: IQ 145 (17 murdered)
Ted Bundy: IQ 136 (30+ murdered)
Historical Estimations & Unknown IQs of Genocidal Leaders:
Adolf Hitler: IQ Unknown / Estimated ~141 (Tens of millions dead)
Josef Stalin: IQ Unknown (Tens of millions dead)
Mao Zedong: IQ Unknown (Tens of millions dead)
Pol Pot: IQ Unknown (~1.5 to 2 million dead)
Idi Amin: IQ Unknown (~300,000 dead)
Robert E. Lee: Estimated IQ ~130 (hundreds of thousands of Civil War casualties)
François "Papa Doc" Duvalier: IQ Unknown (~30,000 to 60,000 dead)
Che Guevara: Estimated IQ ~130 (Thousands dead)