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| 182.8 Meters |
 Title text: They rounded down to 182.8 instead of rounding up to 182.9 because 182.9 might make the statement incorrect. |
Explanation
This is a comic in the My Hobby series — the hobby here being reverse-engineering original units from oddly specific measurements in another unit. Unlike many of the My Hobby comics, where Cueball's hobby is something eccentric, prankish or dangerous, in this situation he uses his hobby simply to understand the origin of someone else's unusual phrasing.
When presenting measurements where perfect accuracy is not required, such as in casual conversation or when giving simple presentations to the public, speakers will often use approximations, such as rounding to the nearest whole number, or the nearest ten, or using only the most significant digit. When translating these approximations into other measurement systems, however, people will often treat them as precise, and use the standard conversion formulae to get an exact value. This leads to examples of false precision, where the presentation of a measurement implies more information than is actually contained in it. In this case, a fathom is a unit of measurement used to measure how deep water is. One fathom is equal to six feet, or 1.8288 metres. The depth of the bay has been measured as being greater than 100 fathoms, and someone has converted that (via the value 182.88) to 182.8 meters.
In most cases, 182.88 would round to 182.9. As the title text explains, in this case they rounded down in order to prevent a possibly incorrect statement. This is a comical attempt at mitigating the false precision; it retains the overly-precise initial statement (of unknown precision or accuracy, having just one obviously significant figure) was too approximate to imply. It suggests that they were worried that the maximum depth may be between 182.88 meters and 182.9 meters — a margin of just 2 centimeters, which is beyond the accuracy/precision with which anyone is likely to be measuring such things. Moreover, in most areas of seawater it would be within the daily variance due to tidal activity (requiring reference to a specific choice of tidal datum), and the seabed is typically a dynamic environment in which the depth profile could be changing by this much over very short periods through the redistribution of sediment from both tides and weather-induced events. A more reasonable attempt to translate 'the bay is more than 100 fathoms deep' might be "the bay is more than 180 meters deep"; this stays close to the initial measurement while rounding to the nearest ten, to convey that the measure is approximate.
Assuming that the original "100 fathoms" was itself a rounding of the measurement (or even just a vague 'best estimate') to the nearest ten (i.e. above 95 fathoms but no higher than 105 fathoms), the precisely converted limits would have been 18.288 meters apart, which might have been better converted to a ±10 meter 'tolerance'; slightly more 'flexible' than the original assumption, but at no risk of being incorrectly exact about an inherently inexact fact. Although even that may be wrong, if the rounding to 100 was instead to the nearest twenty or even one hundred fathoms. The value could have been rounded to just a single figure of accuracy, and without further information it is impossible to rule that out; it was in order to avoid this very misunderstanding that one of the first accurate measurements of Mount Everest was subtly adjusted to not appear to be an approximate value.
False precision may also sometimes be used in product labelling to present things as "more than a" precise number, to make the product sound more enticing, cheap or worthwhile (for example, saying "now with more than 28.4% more water", when the product only has 28.5% more water). That also relates to the confusion between "five times more than" and "five times as much as", which some people use synonymously creating a potential off-by-one error.
Randall has previously used conversion between measurement systems as main subject of his comics, including using the overly exact conversion and re-rounding of values, which also involved fathoms.
Transcript
- [Hairbun stands at a podium to the left, gesturing toward a sign, with an oval (likely representing the bay) and some illegible text on it. Four visitors stand nearby observing: Ponytail, Cueball, Megan, and White Hat (in that order). Cueball has a thought bubble.]
- Hairbun: In some places, the bay is more than 182.8 meters deep.
- Cueball: (thinking) "More than"? Why would they use that for such a precise...
- Cueball: (thinking) ...Aha! 100 fathoms!
- [Caption below the panel:]
- My Hobby: Reverse-engineering original units
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