AI / 04

Institutional Gap: Logistic vs. Exponential

Why past institutions eventually caught up to technology, and why an exponential wave changes the gap.

The historical pattern: bounded gaps, finite catch-up

Past waves rose above institutional capacity and then plateaued. The AI wave is modeled with the same early rise but keeps climbing.

Institutional capacityPast technology wavesAI waveC: capability gapT: catch-up time
00.511.5200.350.71.051.4 Time Capability Institutional capacity rises linearly Past logistic technology wave 1 Past logistic technology wave 2 Exponential AI wave C: capability gap C T: catch-up time T Institutional capacity: Time 0, Capability 0Institutional capacity: Time 0.12, Capability 0.06Institutional capacity: Time 0.23, Capability 0.12Institutional capacity: Time 0.35, Capability 0.17Institutional capacity: Time 0.46, Capability 0.23Institutional capacity: Time 0.58, Capability 0.29Institutional capacity: Time 0.7, Capability 0.35Institutional capacity: Time 0.81, Capability 0.41Institutional capacity: Time 0.93, Capability 0.46Institutional capacity: Time 1.04, Capability 0.52Institutional capacity: Time 1.16, Capability 0.58Institutional capacity: Time 1.28, Capability 0.64Institutional capacity: Time 1.39, Capability 0.7Institutional capacity: Time 1.4, Capability 0.7 Past logistic wave 1: Time 0.02, Capability 0.02Past logistic wave 1: Time 0.13, Capability 0.17Past logistic wave 1: Time 0.25, Capability 0.18Past logistic wave 1: Time 0.36, Capability 0.18Past logistic wave 1: Time 0.48, Capability 0.18Past logistic wave 1: Time 0.59, Capability 0.18Past logistic wave 1: Time 0.7, Capability 0.18Past logistic wave 1: Time 0.82, Capability 0.18Past logistic wave 1: Time 0.93, Capability 0.18Past logistic wave 1: Time 1.05, Capability 0.18Past logistic wave 1: Time 1.16, Capability 0.18Past logistic wave 1: Time 1.27, Capability 0.18Past logistic wave 1: Time 1.39, Capability 0.18Past logistic wave 1: Time 1.4, Capability 0.18 Past logistic wave 2: Time 0.34, Capability 0.18Past logistic wave 2: Time 0.43, Capability 0.28Past logistic wave 2: Time 0.52, Capability 0.3Past logistic wave 2: Time 0.61, Capability 0.3Past logistic wave 2: Time 0.69, Capability 0.3Past logistic wave 2: Time 0.78, Capability 0.3Past logistic wave 2: Time 0.87, Capability 0.3Past logistic wave 2: Time 0.96, Capability 0.3Past logistic wave 2: Time 1.05, Capability 0.3Past logistic wave 2: Time 1.13, Capability 0.3Past logistic wave 2: Time 1.22, Capability 0.3Past logistic wave 2: Time 1.31, Capability 0.3Past logistic wave 2: Time 1.4, Capability 0.3Past logistic wave 2: Time 1.4, Capability 0.3 Exponential AI wave: Time 0.62, Capability 0.31Exponential AI wave: Time 0.65, Capability 0.32Exponential AI wave: Time 0.68, Capability 0.33Exponential AI wave: Time 0.71, Capability 0.35Exponential AI wave: Time 0.74, Capability 0.37Exponential AI wave: Time 0.77, Capability 0.41Exponential AI wave: Time 0.8, Capability 0.46Exponential AI wave: Time 0.83, Capability 0.54Exponential AI wave: Time 0.86, Capability 0.65Exponential AI wave: Time 0.89, Capability 0.8Exponential AI wave: Time 0.92, Capability 1.02Exponential AI wave: Time 0.95, Capability 1.34Exponential AI wave: Time 0.98, Capability 1.79Exponential AI wave: Time 1, Capability 2.16

Illustrative model. The C annotation marks a capability gap; T marks the catch-up time institutions would need if the curve stopped compounding.

Data: institutional-gap-model.csv

Description

This module restores the institutional-gap chart as its own research piece. It compares two bounded historical waves with an exponential AI wave that keeps widening before institutions can close the distance.

Methodology

The model uses a simple linear institutional-capacity line, two bounded logistic waves, and one exponential AI wave. It is a structural diagram, not an empirical forecast.

Data

All chart files for this module are local to this research folder.

Sources

Limitations

The chart is conceptual. It does not predict dates, regulatory capacity, or a specific AI ceiling; it shows why curve shape changes the burden placed on institutions.