Logistic vs. Exponential Growth | The American Fabric

Logistic vs. exponential technology curves

A stylized comparison of bounded adoption and compounding capability.

LogisticExponential

Illustrative model only, built to show curve shape rather than forecast a specific date or capability level.

Description

This module keeps the curve-shape argument together: logistic saturation, exponential divergence, and institutional lag.

The curve comparison is illustrative. It matches the early shape of a logistic curve before allowing the exponential path to keep compounding.

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

Verhulst logistic model The standard bounded-growth curve used for the logistic series.
Rogers, Diffusion of Innovations Technology-adoption S-curve framing.
Kaplan et al. 2020, Scaling Laws for Neural Language Models AI scaling-law literature behind the exponential-capability framing.
Sevilla et al. 2022, Compute Trends Across Three Eras of Machine Learning Evidence for rapid post-2012 training-compute growth.

The chart is not a forecast. It is a structural model for why uncertainty about curve shape changes the cost of waiting.