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".
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!
Even if the math of the arc length was correct (and you don't need to be a math professor to figure out it isn't) there's another logic misstep.
Implied in the caption is that the speed is the same at all heights (given that an increase in distance is implied as an increase in time.)
This is again obvious nonsense - speed is a function of thrust versus drag, and it's safe to say that both of those are affected by air density.
It becomes even less true once one gets to space. There height is a function of speed which means that to "catch up" something in front of you, you need to slow down.
I think the funny thing about this article is this numeric error (though not so egregious as the one that caused the article!):
> The mean radius of the earth is actually 3,459 miles or over 18 million feet.
That’s off by 500 miles; the correct figure is 3,959 miles. That makes it almost 21 million feet, and yields a ratio of about 1.0013378, even smaller than the quoted 1.0015.
“Bloomberg spent $500 million on ads. The U.S. population is 327 million. He could have given each American $1 million and still have money left over.”
seanhunter ·5 days ago
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".
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BalinKing ·5 days ago
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!
Show replies
bruce511 ·5 days ago
Implied in the caption is that the speed is the same at all heights (given that an increase in distance is implied as an increase in time.)
This is again obvious nonsense - speed is a function of thrust versus drag, and it's safe to say that both of those are affected by air density.
It becomes even less true once one gets to space. There height is a function of speed which means that to "catch up" something in front of you, you need to slow down.
Show replies
chrismorgan ·5 days ago
> The mean radius of the earth is actually 3,459 miles or over 18 million feet.
That’s off by 500 miles; the correct figure is 3,959 miles. That makes it almost 21 million feet, and yields a ratio of about 1.0013378, even smaller than the quoted 1.0015.
csours ·5 days ago
https://www.politifact.com/factchecks/2020/mar/06/msnbc/bad-...
“Bloomberg spent $500 million on ads. The U.S. population is 327 million. He could have given each American $1 million and still have money left over.”
https://www.youtube.com/watch?v=6egeUxIEQnM