Very Wrong Math

192 点作者 breadbox5 个月前

23 条评论

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".

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BalinKing5 个月前

Related Wikipedia article: <a href="https://en.wikipedia.org/wiki/String_girdling_Earth#Implications" rel="nofollow">https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat...</a>.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!

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bruce5115 个月前

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.

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chrismorgan5 个月前

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.

csours5 个月前

Reminds me of this classic:<a href="https://www.politifact.com/factchecks/2020/mar/06/msnbc/bad-math-msnbc-bloombergs-ad-spending-wasnt-enough/" rel="nofollow">https://www.politifact.com/factchecks/2020/mar/06/msnbc/bad-...</a>“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.”<a href="https://www.youtube.com/watch?v=6egeUxIEQnM" rel="nofollow">https://www.youtube.com/watch?v=6egeUxIEQnM</a>

n4r95 个月前

Don't know if anyone mentioned this yet, but presumably the flight path does not follow a normal vector to gain height, but generally something more diagonal in the direction of travel.

prmph5 个月前

One question I've always had with this: How does the rotation of the earth affect an airplane's flight time, if any? And how does this change with altitude?

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lynguist5 个月前

I would do it like this:Approximate Earth as a flat line. (The 5000ft path is close enough that it is also represented by the flat line. This is the 5000ft path.)Then make the 33000ft path which is a slightly looser line on top of this line.This new path is not 4 times longer. Just a little bit raised, because 33000 ft is “nothing” compared to Earth. (To become 4x longer we would go deep into outer space and back.)

syntex5 个月前

just 2piR and then extra h change the result very little fraction. How is that counter-intuitive :)

simplicio5 个月前

Seems intuitively obvious. On a flat Earth the two distances would be the same, and while the Earth isn't flat, its close enough to approximate a flat surface for most purposes, so you'd expect the differences in the two arcs to be ~0

pessimizer5 个月前

Does "Remember the high you go the further it'll have to travel" really need to be debunked? Did the "design and construction firm" spell "drill" with one "l"?

jodrellblank5 个月前

Earth in the picture is scaled to roughly 300,000 feet per pixel; Earth's surface and both flying altitudes would be the same pixel if drawn to scale.(~42M feet diameter shown in ~134 pixels).

tenthirtyam5 个月前

xkcd what-if has a great picture of what a typical orbital flight is really like: <a href="https://what-if.xkcd.com/58/" rel="nofollow">https://what-if.xkcd.com/58/</a>tl;dr: Our atmosphere is surprisingly thin.

kubb5 个月前

Curious, does the air being thinner affect flight time?

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wittjeff5 个月前

"the high you go" reinforces my initial assumption that this is self-filtering clickbait.

1970-01-015 个月前

All models are wrong, but some are useful. ⇒ Some models are wrong and useless.

svilen_dobrev5 个月前

Charles Petzold.. His c++ book stood on the shelf behind me. 30y ago. heh :)

quantified5 个月前

Holy crap is one drop of stupid consuming a lot of mental energy. This is after the drop of stupid that was Terence Howard's "1 x 1 = 2" physics rant fell on everyone's head. Individual drops quickening into rain would drown us all, apparently. Do serious people like Charles Petzold (here) and in other venues address this stupid out of fear that the stupid spreads, or because they just can't stand someone being wrong somewhere like a cognitive itch that must be scratched? If one troll flooded the zone with 30 of these over a month, mayhem would ensue. Absent knowing the true origin for this diagram, we don't even know if was stupid or malicious.

teo_zero5 个月前

And of course pi = 22/7! ;)

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nejsjsjsbsb5 个月前

Are we talking spacetime?

fargle5 个月前

i've seen that exact image posted semi-regularly on various reddit and facebook groups. (it's one of 500 things i hate about those sites. but for some communities that's where the information lives, that's where marketplace lives, etc., so i'm stuck with it)these kind of things are intentionally wrong "puzzles" that are designed to get hundreds of people mad and post rebuttals to "drive engagement" or whatever. the pictures of a wheel with sledgehammers and chains and jacks with lugnuts plainly still in place and a post "how can i get this off it's stuck and i've tried everything". sigh... it's just another form of trolling.sure enough, notice the sibling comments here. how many nice people took the time to patiently explain the fallacy(ies) for the 1000th time. then the pedants who correct the grammar/math/etc. in the 98% correct explanations. then the "true believers"/trolls who don't get it and argue back. and so on.<a href="https://xkcd.com/386/" rel="nofollow">https://xkcd.com/386/</a>

juresotosek5 个月前

haha crazy

mppm5 个月前

xkcd.com/386