Very Wrong Math
charlespetzold.com

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7 hours ago

17 comments

seanhunter ・ 30 minutes ago

I have seen a very similar (incorrect) argument used to justify the idea of a flat earth. A builder on youtube made the argument (with a similar out of scale drawing of the earth) that if he drops a plumb bob and makes a right angle so he has a straight horizontal line and then goes across that line for a bit and drops another plumb bob, the two lines he has dropped are parallel, "proving" that the surface of the earth must be parallel to the horizontal line and therefore flat and not curved. If the earth's surface was actually curved he argued then the two lines he has dropped should tilt slightly inward towards each other. Which of course they do. The earth is just much much much bigger than in the diagram so the effect is within the margin of error for the measurement he was taking.

As a meta point, our intuition often fails us hilariously when we are dealing with stuff that is out of the scale we have commonly seen in our lives. We joke about LLMs hallucinating but I'm not convinced we are so superior when we are outside our personal "training data".

BalinKing ・ 4 hours ago

Related Wikipedia article: https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat....

The takeaway is that the extra length of the arc is likely much smaller than one would intuitively expect. The problem is usually framed like so: If you wrapped a rope around the earth, how much more rope would you need to add so that it would be 1 meter above the ground at all points? The answer is only 2π meters!

  • kurthr ・ 3 hours ago

    The only issue I see with this is that as a classic physics trope, we've approximated the earth as a sphere.

    If, instead we approximate it as a fractal... then the distance is infinite, or at least highly dependent on the thickness of the rope!

    The error in the original is assuming that the radius is proportional to the height above the earth (Earthradius=0?).

    • seanhunter ・ 38 minutes ago

      We actually model the earth as a very large spherical cow. This is approximately the same for most purposes but ends up being more convenient.

      P.S. Not a physicist, but my child is studying maths and physics at Uni at present, so I have it on good authority that this is still going on. They told me in their first week one of their classes had a worked example where the lecturer used the phrase "Assume the penguin's beak is a cone".

    • Dylan16807 ・ 3 hours ago

      > infinite, or at least highly dependent on the thickness of the rope

      The latter. But that's only if it's not somewhat taut. Some tension brings it closer to a circle and makes the actual thickness pretty unimportant.

      But I like the idea overall. It means that lifting up the string makes it smoother and it actually needs less length. How's that for being unintuitive?

      • kurthr ・ 3 hours ago

        Exactly, if you're only 1cm off the surface you follow every nook and cranny. If you're 10km off the surface only Everest is a blip.

teo_zero ・ 8 minutes ago

And of course pi = 22/7! ;)

kubb ・ an hour ago

Curious, does the air being thinner affect flight time?

  • aja12 ・ 26 minutes ago

    From what I've learned reading AdmiralCloudberg's plane crashes analysis [1]: altitude heavily matters in fuel consumption. Jet planes use a lot less fuel at a higher altitude, up to the point that a plane on the verge of running out of fuel at a medium altitude might manage to squeeze in 50 or 100 more miles of flight by climbing 5000 feet, even accounting for the increased fuel consumption during climb. I guess that correlates with speed as well. Turbofan engines, on the other hand, are more fuel efficient than jet engines at lower altitudes, hence they remain common for interstate transit. The difference seems to be directly caused by the effect of air "thickness" on the engines.

    [1] https://admiralcloudberg.medium.com/

  • jhanschoo ・ 31 minutes ago

    There's no straightforward answer because there are many factors that affect flight time and fuel economy, including the aerodynamics of the plane and the engine technology. I hazard a guess that for commercial airplanes these are chosen primarily for reasons of fuel economy per seat and then that determines the model's designated cruising altitude.

    For a particular model, flying above the model's cruising altitude should lead to lower fuel efficiency.

  • Waterluvian ・ an hour ago

    I think in a way that’s why planes fly so much further up than you’d think they’d need to. They want more consistent and minimal atmospheric conditions. Less air means less energy means less turbulence, I think?

    If you’re talking about friction… oooh that’s an interesting one. Intuitively yes. But is it also negligible?