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    Re: Unwarranted levels of precision
    From: Frank Reed
    Date: 2017 Dec 28, 09:54 -0800

    Here's one.Today at newsweek.com there's a story about a meteoroid that will be passing the Earth today. The object is referred to as an asteroid, which is an interesting example of a scale precision issue in our non-mathematical astronomical language. Closer to the numerical precision issue being discussed, the story says that the object "is believed to measure between 22.6 and 49 feet in diameter". Really?? 22.6 is the lower limit?! The author of the little newsweek.com story then attributes these numbers to another site (which is odd). That other site says that the "asteroid" has "an estimated diameter of 6.9 to 15 m (22.6 to 49 feet)." So... how did we get here?? Listing the lower limit of the size range to the nearest tenth of a foot was funny, sure, but the number from which it is derived has a precision of a tenth of a meter. Both of these are a bit absurd when the uncertainty, even as listed, is roughy a factor of two.

    On a general level, conversions from meters to feet are often problematic, in part because the conversion factor, approximately 3.3 is very close to half an order of magnitude. An "order of magnitude" is usually counted as a factor of ten. Given that definition, half an order of magnitude is equal to the square root of ten, which is about 3.16. This can lead to "creeping significant digits". If I estimate that an asteroid is roughly 100 meters across, and I convert that to feet, I get about 330. But if the size in meters is only an order of magnitude estimate, then what should we "properly" list for the converted size in feet? Should it be 300 feet? That's an improvement, yes, but the original estimate in meters is strictly an order of magnitude, implying that the lower limit could be three times smaller and the upper limit three times larger. I know, I know, just ignore feet and go SI all the way... But that doesn't work if you're writing for "certain audiences". 

    By the way, there are plenty of examples like this in USCG licensing exams. I saw a problem recently that reported the observer's height of eye for a celestial problem as 41.3 feet. Licensing exams are dangerous, frequently absurd things in every profession, of course.

    Frank Reed

       
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