How Our Brain Mirrors the Taylor Series: From Perception to Understanding

The article uses the mathematical concept of Taylor series as a metaphor for human cognition, describing how initial perception, detailed analysis, and pattern recognition progressively refine our understanding of the world, while also reflecting on the historical origins of the series and its philosophical implications.

Taylor seriescognitive scienceknowledge acquisition

0 likes · 5 min read

How Our Brain Mirrors the Taylor Series: From Perception to Understanding

Liangxu Linux

Jul 25, 2024 · Fundamentals

Uncovering a 55‑Year‑Old Bug in the Original Lunar Lander Game

A retired software engineer revisits the 1969 text‑based Lunar Lander game, exposing a decades‑old mathematical error that causes the simulation to misjudge soft landings, and explains the physics, numerical approximations, and optimal burn strategies behind the classic program.

Lunar LanderNumerical MethodsRetro Gaming

0 likes · 11 min read

Uncovering a 55‑Year‑Old Bug in the Original Lunar Lander Game

Model Perspective

Oct 3, 2023 · Fundamentals

Infinite Series Explained: Concepts, Convergence Tests, Real-World Uses

This article introduces infinite series, outlines common types such as arithmetic, geometric, harmonic, p‑series, Taylor, and Fourier series, explains key convergence tests, and demonstrates practical applications in physics, engineering, economics, and mathematical modeling.

ApplicationsFourier SeriesTaylor series

0 likes · 8 min read

Infinite Series Explained: Concepts, Convergence Tests, Real-World Uses

Model Perspective

Jun 5, 2022 · Fundamentals

How to Numerically Solve Differential Equations: Methods & Examples

This article explains why numerical solutions are needed for differential equations, introduces the initial value problem for first‑order ODEs, and details three common discretization techniques—forward difference, numerical integration, and first‑order Taylor expansion—highlighting their formulation and error considerations.

Taylor seriesdifferential equationsinitial value problem

0 likes · 4 min read

How to Numerically Solve Differential Equations: Methods & Examples