The Sigmoids Won't Save You

2026-01-16 · Source: Astral Codex Ten · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Emerging Technologies & Innovation · Depth: Intermediate, medium

Summary

The common assertion that "all exponentials eventually become sigmoids" is often misapplied to predict the flattening of technological growth, particularly in AI capabilities. While it is true that no process can grow indefinitely, historical examples demonstrate that the point at which an exponential trend transitions to a sigmoid is frequently misjudged. The article highlights several "Sigmoid Misidentification" cases, including UN birthrate projections, solar power deployment forecasts by the World Energy Organization (WEO), and a 2026 Wharton paper on METR AI capabilities, all of which prematurely predicted a slowdown in exponential growth. These examples show that trends can continue exponentially for much longer than anticipated, often defying expert predictions based on perceived limits. The article suggests that without a deep understanding of the underlying process, Lindy's Law offers a default assumption for trend duration.

Key takeaway

For research scientists evaluating long-term AI capability projections, you should be wary of arguments that prematurely assume an exponential trend will soon become a sigmoid. If a model predicts a slowdown, ensure it provides a detailed, explicit explanation of the underlying dynamics or justifies its deviation from Lindy's Law. Your default expectation, absent specific evidence, should be that current exponential growth in AI could persist for a duration similar to its past trajectory.

Key insights

Exponential trends often persist longer than predicted, defying premature sigmoid curve assumptions.

Principles

• All exponentials eventually become sigmoids.
• Trends can continue exponentially longer than expected.

Method

When underlying process dynamics are unknown, apply Lindy's Law: a process will continue, on average, for as long as it has already continued.

In practice

• Critically evaluate claims of imminent trend flattening.
• Demand explicit models for predicted trend changes.

Topics

• Exponential Growth
• Sigmoid Curves
• AI Capability Forecasting
• Lindy's Law
• Trend Extrapolation

Best for: Research Scientist, AI Scientist, Director of AI/ML, Consultant

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Editorial summary, takeaway, and curation by AIssential. Original article published by Astral Codex Ten.