The article explains how our habitual reliance on linear thinking produces systematic prediction errors across domains such as sports, learning, finance, biology, epidemiology, and urban growth, and it offers concrete non‑linear examples and strategies for adopting more accurate, system‑level models.
In this extensive interview, Ray Kurzweil discusses his predictions for artificial general intelligence by 2029, the exponential growth of computing power, the impact of AI on medicine, security, brain‑computer interfaces, longevity, and the societal transformation expected around the 2045 singularity.
The article argues that while AI can quickly generate seemingly correct answers for students, bypassing the slow, cumulative learning process undermines deep understanding and long‑term growth, much like the early stage of an exponential function.
This article explores why returns in business, knowledge, and influence often grow faster than linearly, attributing the phenomenon to exponential growth, threshold effects, and network dynamics, and offers practical strategies for identifying and leveraging such superlinear opportunities.
This article explains the classic exponential growth model derived from Malthusian assumptions and then introduces the logistic (stagnation) model, showing how resource limits modify growth dynamics and presenting the differential equations and their solutions for both cases.
This article explains the classic exponential growth model derived from Malthus’s assumptions and then introduces the logistic (or Verhulst) model, showing how resource limits create a carrying capacity that slows growth, with step-by-step derivations using separation of variables.
