g∫dt

CHC Psychometric Investment & Senescence Lab

Empirical simulation of Gf(t) hardware decay vs. Gc(t) structural compounding

Inspecting Chronological Age: {{ inspectAge }} yrs
12y 80y
Realized Gf(t) {{ formatPercentile(currentSnapshot.gfRealized) }}
{{ currentSnapshot.gfRealized.toFixed(1) }} (-{{ currentSnapshot.bioPenalty.toFixed(1) }} bio)

Genetic ceiling at {{ inspectAge }}: {{ currentSnapshot.gfCeiling.toFixed(1) }}

Crystallized Gc(t) {{ formatPercentile(currentSnapshot.gc) }}
{{ currentSnapshot.gc.toFixed(1) }} {{ currentSnapshot.deltaGc >= 0 ? '+' : '' }}{{ currentSnapshot.deltaGc.toFixed(2) }}/yr

Compounded mental models & heuristics

Effective Output {{ formatPercentile(currentSnapshot.effectiveOutput) }}
{{ currentSnapshot.effectiveOutput.toFixed(1) }} IQ-Eq

Real-world complex problem-solving yield

Working Memory
{{ currentSnapshot.wmChunks.toFixed(1) }} slots × {{ currentSnapshot.chunkComplexity.toFixed(1) }}x

Hardware slots × Schema abstraction depth

Lifespan Psychometric Trajectory (Age 12 → 80)

Click or drag anywhere on the graph to scrub chronological age and inspect differential rates

Genetic Gf Ceiling Realized Gf(t) Crystallized Gc(t) Effective Output App Game Score (Fake IQ) Ghost ({{ ghostProfile.label }})
{{ iqTick }} {{ ageTick }}y POPULATION MEAN (100 IQ)
Differential Rates at t={{ inspectAge }}: dGf/dt = {{ currentSnapshot.deltaGf >= 0 ? '+' : '' }}{{ currentSnapshot.deltaGf.toFixed(2) }}/yr | dGc/dt = {{ currentSnapshot.deltaGc >= 0 ? '+' : '' }}{{ currentSnapshot.deltaGc.toFixed(2) }}/yr
Peak Output Age: {{ lifecycleSummary.peakOutputAge }} yrs ({{ lifecycleSummary.peakOutputVal.toFixed(1) }}) | Wasted Genetic Potential: {{ lifecycleSummary.wastedPotentialPct.toFixed(0) }}%
Unvarnished Psychometric Audit Archetype: {{ currentPresetObj.name }}

{{ dynamicAudit.headline }}

{{ currentPresetObj.brutalConclusion }}

{{ diag.type === 'critical' ? '[!]' : diag.type === 'warning' ? '[~]' : '[✓]' }}
{{ diag.title }}: {{ diag.body }}

Governing Differential Equations

// 1. Realized Fluid Hardware
Gf(t) = Gf,gen(t) - Δsleep - Δmetabolic
// 2. Cattell Investment Integral
dGc/dt = κ·[Gf(t)^α · E · M] - μ·Gc(t)
// 3. Effective Real-World Yield
Y(t) = (wfGf + wcGc) · (1 + λtool·Φ(Gc)) - Ψbias
Bottleneck Attribution (Age {{ inspectAge }})
Raw Hardware Ceiling (Gf0 + Age) {{ bottleneckBreakdown.hardwareShare }}%
Schema Compounding (E × M) {{ bottleneckBreakdown.investmentShare }}%
Self-Inflicted Bio Drag (Sleep/VO₂) {{ bottleneckBreakdown.bioDragShare }}%
Twin Study Note: Plomin et al. demonstrate that h² of g rises from ~40% in childhood to ~80% in adulthood via active gene-environment correlation (rGE).
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How to Use This Lab & Symbol Glossary

Decoding the Cattell–Horn–Carroll (CHC) differential equations and telemetry

Quick 3-Step Experiment Workflow

  1. Pick an Archetype Preset: Use the top dropdown to load a realistic cognitive profile (e.g., "1. The Coasting Former Gifted Kid").
  2. Pin a Baseline Ghost: Click "Pin Baseline Ghost" in the header to freeze that curve in purple on the chart, then switch to "2. The Disciplined 112-IQ Compounder" to see the exact age where disciplined schema building overtakes raw uninvested talent.
  3. Scrub Chronological Age: Drag horizontally across the graph (or use the age slider) to inspect how fluid decay and crystallized compounding trade off from age 12 to 80.

Complete Mathematical & Psychometric Symbol Glossary

Gf(t) & Gf0 — Fluid Intelligence

Raw biological compute power: working memory capacity, abstract pattern speed, and novel reasoning. Peaks around age 22–24 (Gf0) and declines monotonically due to prefrontal senescence.

Gc(t) — Crystallized Intelligence

Accumulated mental models, domain abstractions, vocabulary, and compressed problem-solving heuristics. Built by investing Gf over time; can compound into your 60s.

h² ≈ 0.75 — Narrow-Sense Heritability

Proportion of population variance in adult general intelligence (g) attributable to additive genetic variance in twin and polygenic studies.

δ (Delta) — Prefrontal Senescence Slope

Speed of biological brain aging after age 24 (white-matter demyelination & synaptic pruning). Accelerated by vascular disease; slowed by aerobic Zone-2/VO₂ max fitness.

E & M — Epistemic Rigor & Practice

In Cattell's integral ∫ Gf·E·M dt, E is the structural depth of what you study (math/logic vs. trivia), and M is deliberate practice strain.

μ (Mu) — Entropy / Dogma Ossification

Rate at which your acquired Gc becomes obsolete or rigidified by ideological dogma. High if you memorize fleeting tool syntax; low if you master first principles.

Cowan's K — Working Memory Slots

Nelson Cowan's constant (~4 ± 1 chunks in an average adult). You cannot add more hardware slots, but high Gc packs exponentially more meaning into each slot.

dGf/dt & dGc/dt — Yearly Velocity

Instantaneous rate of change (in IQ points per year) at the inspected age. Notice the yellow circle on the chart where Gc crosses above Gf.

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