The PlayMemorize Cognitive Index (PMCI)
Foundations, Telemetric Calibration, and Empirical Architecture of Revealed Cognitive Behavior
Abstract
Traditional psychometric assessments rely predominantly on self-reported surveys. These surveys are vulnerable to self-image distortions, aspirational biases, and social desirability effects. The PlayMemorize Cognitive Index (PMCI, also designated PMBI) introduces an empirical framework that derives cognitive temperaments from split-second gameplay telemetry. By measuring cognitive tempo (System 1 vs System 2 latency), domain search scope (specialist concentration vs polymathic breadth), error friction resilience (perseverant grind vs adaptive pivoting), and moral north star vectors (utilitarian welfare optimization vs Kantian duty constraints), PMCI establishes a 16-profile combinatorial taxonomy of revealed human cognitive architecture. This paper formalizes the theoretical foundations, attribution lineage, mathematical models, and scoring algorithms governing the engine.
1. The Stated Versus Revealed Divide
For nearly a century, psychometric evaluation has asked subjects to evaluate their own behavior. The fundamental flaw of self-reporting is that humans describe who they wish to be rather than how they behave under stress. When a respondent answers whether they are calm or methodical, they consult internal narratives rather than empirical event logs.
In economics, Paul Samuelson solved this dilemma in 1938 with Revealed Preference Theory. Samuelson established that an agent's true preferences are revealed solely by their concrete choices under constraints, not by stated claims. PMCI applies revealed preference to cognitive psychology: when a human plays a timed game, confronts an unforced error, chooses a domain, or arbitrates a moral dilemma, their digital telemetry provides authentic evidence of their mind architecture.
2. Intellectual Lineage and Academic Attribution
The PMCI architecture stands upon established cognitive, psychological, and philosophical literature. We cite and credit the primary intellectual pillars:
Paul Samuelson (1938)
Revealed Preference Theory
Provided the operational postulate that consumer and agent preferences cannot be measured by interview, but must be derived from observed actions in real choice environments.
Daniel Kahneman & Amos Tversky (1973, 1979, 2011)
Dual-Process Theory & Heuristics
Formalized the distinction between System 1 (fast, reflexive, intuitive heuristics) and System 2 (slow, deliberate, analytical verification). Directly informs the Thinking Tempo axis.
Angela Duckworth et al. (2007)
Grit & Post-Friction Persistence
Demonstrated that perseverance and sustained passion toward difficult goals operate independently of raw IQ. Directly informs the Error Resilience (Grinder vs Adaptive) axis.
Herbert A. Simon & Allen Newell (1958, 1972)
Bounded Rationality & Problem Spaces
Pioneered the analysis of cognitive search width versus depth. Defines our Cognitive Scope axis, contrasting deep domain concentration with lateral polymathic exploration.
Immanuel Kant (1785)
Deontological Categorical Imperative
Established that ethical actions are bound by categorical duties and inviolable moral maxims, rejecting utilitarian concessions that treat human individuals as mere means.
Jeremy Bentham & John Stuart Mill (1789, 1861)
Utilitarian Consequentialism
Formulated the principle of utility: actions are right in proportion as they promote net aggregate happiness and welfare, forming the consequentialist pole of our moral axis.
Robert Axelrod & Michael Tomasello (1984, 2016)
Evolution of Cooperation & Natural Morality
Demonstrated how repetitive game-theoretic dilemmas shape human cooperative instincts, mutual obligation, and normative evaluation in interactive environments.
Carl Jung, Katharine Briggs & Isabel Myers (1921, 1962)
Psychological Types & MBTI
Inspired the clean 4-letter combinatorial typology, allowing multi-axis behavioral signatures to be communicated in an intuitive, accessible cognitive language.
3. The Four Behavioral Axes
PMCI models cognition through four mathematically orthogonal axes:
Axis 1 · Thinking Tempo: Deliberate (D) vs Intuitive (I)
Measures decision latency per cognitive unit. Deliberate thinkers pause before action, deploying System 2 verification to eliminate unforced errors. Intuitive thinkers leverage System 1 pattern matching, favoring high velocity and fluid motor reflex.
Tempo_Ratio = (Sum(time_ms) / total_rounds) / 12000 ms Axis 2 · Cognitive Scope: Specialist (S) vs Polymath (P)
Evaluates gameplay concentration across domains (logic, memory, language, arithmetic, spatial). Specialists concentrate over 60 percent of rounds into one or two core games, achieving vertical domain mastery. Polymaths distribute effort across diverse games, optimizing lateral transfer and cross-domain pattern recognition.
Scope_Ratio = (Plays(Top1) + Plays(Top2)) / Total_Plays Axis 3 · Error Resilience (Grit): Grinder (G) vs Adaptive (A / P)
Analyzes behavior following a failed round or broken streak. Grinders demonstrate high tenacity, immediately restarting the exact mechanic and powering through difficulty until mastery. Adaptive thinkers pivot tactically: when encountering diminishing returns, they step back, rest, or recalibrate their strategy to preserve peak accuracy.
Grit_Score = Average_Streak * 12 + log2(Total_Rounds + 1) * 6 Axis 4 · Moral North Star: Utilitarian (U) vs Kantian (K)
Assesses moral arbitration vectors when confronted with ethical dilemmas. Utilitarians maximize net aggregate welfare, accepting calculated sacrifices when the arithmetic outcome saves more lives. Kantians uphold duty and categorical principles, refusing to actively harm an innocent regardless of numerical payoff.
Compass_Ratio = Utilitarian_Choices / (Utilitarian_Choices + Kantian_Choices) 4. The 16 Cognitive Archetypes Taxonomy
Combining the two poles of each axis produces 16 distinct mind architectures. The table below outlines the complete taxonomy:
| Code | Archetype Title | Nickname | Pillars |
|---|---|---|---|
| DSGU | The Methodical Master | Disciplined Craftsman | DDeliberateSSpecialistGGrinderUUtilitarian |
| DSGK | The Ethical Craftsman | Devoted Purist | DDeliberateSSpecialistGGrinderKKantian |
| DSPU | The Systematic Specialist | Pragmatic Analyst | DDeliberateSSpecialistPAdaptiveUUtilitarian |
| DSPK | The Rigorous Scholar | Classical Investigator | DDeliberateSSpecialistPAdaptiveKKantian |
| DPGU | The Strategic Polymath | Grand Synthesizer | DDeliberatePPolymathGGrinderUUtilitarian |
| DPGK | The Classical Philosopher | Renaissance Sage | DDeliberatePPolymathGGrinderKKantian |
| DPAU | The Holistic Strategist | Omni-Tactician | DDeliberatePPolymathAAdaptiveUUtilitarian |
| DPAK | The Contemplative Sage | Harmonic Thinker | DDeliberatePPolymathAAdaptiveKKantian |
| ISGU | The Laser Specialist | Focused Speedster | IIntuitiveSSpecialistGGrinderUUtilitarian |
| ISGK | The Dedicated Purist | Moral Champion | IIntuitiveSSpecialistGGrinderKKantian |
| ISPU | The Tactical Specialist | Agile Operative | IIntuitiveSSpecialistPAdaptiveUUtilitarian |
| ISPK | The Reflexive Artisan | Intuitive Craftsman | IIntuitiveSSpecialistPAdaptiveKKantian |
| IPGU | The Kinetic Problem-Solver | Omni-Dynamo | IIntuitivePPolymathGGrinderUUtilitarian |
| IPGK | The Principled Sprinter | Dynamic Idealist | IIntuitivePPolymathGGrinderKKantian |
| IPAU | The Agile Opportunist | Chameleon Mind | IIntuitivePPolymathAAdaptiveUUtilitarian |
| IPAK | The Intuitive Idealist | Free-Spirited Polymath | IIntuitivePPolymathAAdaptiveKKantian |
5. Mathematical Calibration and Typology Invariant
In formal typology notation, each dimension is assigned a categorical variable. To maintain unambiguous notation, the engine implements a structural invariant:
-
When Scope is Specialist (S), the adaptive resilience trait is designated P (Paced / Adaptive Specialist), yielding type codes
DSPU,DSPK,ISPU, andISPK. -
When Scope is Polymath (P), the adaptive resilience trait is designated A (Adaptive Polymath), yielding type codes
DPAU,DPAK,IPAU, andIPAK.
This invariant prevents typographical collisions between the Polymath scope (P) and Paced grit (P), ensuring every four-letter acronym maps bijectively to a single canonical profile.
6. Privacy and Telemetric Ethics
Unlike commercial psychometric systems that harvest personal data for advertising or recruitment profiling, the PlayMemorize Cognitive Index adheres to strict zero-tracking principles:
- Micro-telemetry (latencies, streaks, and dilemmas) is processed client-side or tied to anonymous session tokens.
- No third-party trackers, ad scripts, or data brokers are ever permitted on cognitive assessment endpoints.
- Public leaderboards display percentiles and skill rankings only, with strict anonymization of raw counts and identities.