Very Wrong Math
A viral graphic claiming that higher‑altitude flights must be vastly longer than low‑altitude ones prompts a teardown of its flawed geometry and unrealistic scaling. Commenters use classic thought experiments like the “rope around the Earth” and flat‑Earth misconceptions to show how human intuition breaks down at planetary scales, why simplifying models (spherical Earth, ideal shapes) are necessary yet easily misapplied, and how real factors like air density, jet streams, and orbital mechanics actually affect travel. Many also note that such deliberately wrong puzzles thrive online as engagement bait precisely because they invite endless corrections and pedantic debate.
String-around-Earth and math intuition
- Several comments reference the classic “rope around the Earth” puzzle: raising a rope 1 m everywhere only requires an extra length of 2π m, independent of Earth’s size.
- People note how counterintuitive this is and tie it to dimensional analysis as a key tool for checking such reasoning.
- The original viral image’s math is called “obviously wrong”; even if fixed, its logic assuming equal speeds at different altitudes would still be flawed.
Approximations and modeling
- Multiple comments stress using simple models (sphere, flat line) for intuition, then correcting if necessary.
- Jokes and examples include “spherical cows,” “penguin beak is a cone,” and the idea that going slightly higher doesn’t multiply path length because altitudes are tiny relative to Earth’s radius.
- A side note points out a numerical error in the blog’s Earth radius that slightly changes the final ratio.
Flight altitude, drag, and fuel
- Thinner air at higher altitude reduces drag but also reduces available thrust; overall it’s usually more efficient and smoother higher up.
- Jetstream winds (partly due to rotation/Coriolis) strongly affect flight times; airlines plan routes and altitudes to exploit or avoid them.
- Discussion touches on engine types and how fuel efficiency depends on altitude and design, with some confusion and correction about turbofan vs turboprop.
Earth’s curvature and flat-earth arguments
- A common flat-earth “plumb bob” argument is dissected as a scale error: curvature is small but measurable (e.g., bridges, ships over the horizon, sunset height experiment).
- Thought experiments explore what gravity would look like on a disk-shaped Earth, showing it would produce non-parallel plumb lines and odd “endless mountainside” effects.
- Flat-earth alternatives to gravity (upward acceleration, “things just go down,” theological occasionalism) are discussed as internally inconsistent but rhetorically resilient.
Orbital mechanics vs aircraft
- In orbit, “forward is up, up is back, back is down, and down is forward”: speeding up raises your orbit and can move you farther behind a target; catching up often requires slowing down.
- This contrasts with aircraft, which can apply continuous lift and thrust to maintain altitude while changing speed.
Earth’s rotation and flight times
- Consensus: rotation itself doesn’t directly change flight time because the atmosphere largely co-rotates with the surface.
- Indirect effects via winds and jetstreams are significant; exotic effects like frame-dragging are acknowledged but considered negligible for aviation.
Meta: online wrongness and human intuition
- Several comments see the viral graphic (and similar “puzzles”) as deliberate engagement bait.
- Others compare human intuition outside familiar scales to LLM “hallucinations,” noting both can produce confident but wrong answers.