Longest Straight Line Paths on Water or Land on the Earth (2018)

Three years before this paper hit arXiv, some guy on Reddit claimed a "straight line" from Pakistan to Russia's Kamchatka Peninsula was the longest overland path on Earth. The internet ate it up. Then a pair of researchers actually sat down, ran the calculus, and said: nah, that's not even close. The real winner is a great-circle arc cutting through 13 countries from Liberia's coast to the eastern tip of China. That's the thing about half-baked viral math — it always loses to someone who actually does the homework. The beauty of this problem is that it's a beautifully constrained optimization with a nasty boundary condition: you want the longest geodesic on a sphere that never dips below 0 altitude. The paper essentially turns the entire Earth's topography into an obstacle course, then sweeps great circles until a path threads the needle. It's a perfect example of applied computational geometry — the kind of thing that only becomes tractable with decent discretization and a whole lot of compute. And unlike most fancy math papers, the code and data are, in the spirit of open science, available for anyone to poke at. Why does this matter beyond idle trivia? Because it's a litmus test for how we communicate geographic truth in a world of map projections and TikTok geography memes. Any flat map makes straight lines look bentفقود. This paper is a quiet reminder that "straight" on a globe means something fundamentally different than what your brain assumes when staring at a Mercator projection. It's also a gentle middle finger to the "is this the longest X?" content farm genre — a rigorous answer squatting on the same turf as the clickbait. The Hacker News thread (https://news.ycombinator.com/item?id=49496782) is predictably full of people arguing about whether the algorithm handled coastlines correctly and whether a straight line through a tunnel under a mountain "counts." Four comments, 20 points — modest by HN standards, which is fitting. This isn't shiny or trendy. It's just math doing what math does best: converting a fun question into a precise, reproducible answer. In a world drowning in AI slop, that's a virtue worth defending. Source: https://arxiv.org/abs/1804.07389