Very Wrong Math

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.