MyWiki:Reference desk/Archives/Science/2016 October 4

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October 4

Inches, Pounds, and 127

The inch is defined as exactly ⁠127/50⁠ cm, and the pound is ⁠127/280⁠ kg almost exactly, with an error of less than 47 ppm. Is there some logic to this, or is this merely coincidental ? — 82.79.181.106 (talk) 05:09, 4 October 2016 (UTC)

Coincidence. The kilogram, of course, was historically defined as the mass of 1,000 cm³ of water. But the exact size of the avoirdupois pound was set to a round 7,000 grains, and the inch and the grain were historically defined in relation to the size and mass of certain cereal grains; so there is no particular reason to expect their values to be related in a certain way. --69.159.61.230 (talk) 05:24, 4 October 2016 (UTC)

The articles about Inch, Metre (or meter American spelling), Pound and Kilogram give their historic origins. AllBestFaith (talk) 16:10, 4 October 2016 (UTC) The following discussion has been closed. Please do not modify it.

Given that the meter was originally defined as a fraction of a number of miles, it would make sense for inches and centimeters to have an exact ratio. The kilogram derives from cubic centimeters, while the pound was based on the grain, so you would not necessarily expect them to have an exact ratio. [Posted after edit conflict. I think we're saying the same thing.] ←Baseball Bugs ^{What's up, Doc?} carrots→ 05:27, 4 October 2016 (UTC)

Actually, as the article states, the inch was standardized to its current definition in 1959. Before that, there were various definitions which differed by a few ppm from each other. So the exactitude is due to the inch being defined from the meter, rather than the meter being defined from the mile. MChesterMC (talk) 08:19, 4 October 2016 (UTC)

@BB: Where is it stated that "the meter was originally defined as a fraction of a number of miles"? I can't find anything to support this. 65.74.20.82 (talk) 09:00, 4 October 2016 (UTC)

Yes, that's nonsense, the metre was originally defined as a fraction of the equator to pole distance. That distance was set at 10,000 km. SpinningSpark 12:38, 4 October 2016 (UTC)

You're right, 65.74.20.82 is speaking nonsense. He hasn't bothered to read the article, which says the meter was originally defined as "one ten-millionth of the length of a quadrant along the Earth's meridian; that is, the distance from the Equator to the North Pole." That qualifies as "a fraction of a number of miles." ←Baseball Bugs ^{What's up, Doc?} carrots→ 14:25, 4 October 2016 (UTC)

Of course it doesn't qualify as a fraction of a number of miles, the size of the Earth is not an exact number of miles. You could claim with equal justification (that is, none at all) that it is a fraction of a number of cubits, or a fraction of a number of parsecs. SpinningSpark 16:57, 4 October 2016 (UTC)

Well, who should I believe? You? Or the article on the origin of the meter? ←Baseball Bugs ^{What's up, Doc?} carrots→ 17:24, 4 October 2016 (UTC)

Here's how it works: 5,280 feet per mile. 63,360 inches per mile. About 6,215 miles along the meridian (24,860 divided by 4). That's about 393,700,000 inches along the meridian. Divide by 10 million, and you have 39.37 inches. And that's a meter. ←Baseball Bugs ^{What's up, Doc?} carrots→ 17:54, 4 October 2016 (UTC)

Bugs, you should probably step away from this. You are making some basic category errors, and missing the whole point of metrology and the efforts of standardization. The gracious thing to do would be to learn from your completely understandable mistake, not to double down on it as you seem to be doing. The meter was historically defined as a fraction of a specified distance. A mile is a unit of distance, but the distance from the pole to the equator has nothing to do with miles. We wouldn't say the meter was defined in terms of rods or astronomical units either, despite the fact that the distance from the pole to the equator can be measured in those units too. The whole point was to standardize a measure that could be based on a physical quantity, and not simply some other relatively arbitrary unit. The concepts of distance and units of measurement are ontologically distinct, and that is why it is simply incorrect to say that the meter is (or ever was) defined in terms of miles. It may be true that miles were used at the time to report the distance from pole to equator, but that's a different thing altogether -- the distance is the distance, independent of any unit. Hope that helps, SemanticMantis (talk) 19:05, 4 October 2016 (UTC)

I don't comprehend your logic. You can't say the meter is one ten-millionth of something that's not already defined otherwise. One then-millionth of X means nothing unless you already know how long X is in traditional units - be they inches, miles, cubits, or whatever. ←Baseball Bugs ^{What's up, Doc?} carrots→ 23:59, 4 October 2016 (UTC)

This is plainly untrue. Humans were simply unaware of the actual length of a terrestrial meridian. And when they did measure it, it turned out to be extremely close to a very round number of meters (forty million, to be exact). What you're saying would make sense only if the original definition of a mile would have been intended as a given fraction of a terrestrial meridian. But this was never the case historically. — 82.137.54.53 (talk) 15:18, 5 October 2016 (UTC)

Yeah, I know there's something you're missing, but I'm not sure how else to explain it. I'll try once more. It's like I held up a stick and said: this is how long a meter is. You don't need any other units, that's the entire point. This stick has the length it has, no matter what you want to call it or how you measure it. In fact, for a very long time, that's exactly how we defined the meter, see History_of_the_metre#International_prototype_metre. This is still how we define a kilogram: we hold up a very special lump of metal and say "a kilogram is this much mass". See Kilogram#International_prototype_kilogram for details. When we say the meter is 1/N of the length of the meridian from pole to equator, that's not any conceptually different from holding up a special stick and saying "this long". Since we can measure the length of that meridian in miles, that allows us to convert between meters and miles, but it's not part of the definition of a meter. SemanticMantis (talk) 14:57, 5 October 2016 (UTC)

Pound (mass) is the relevant article. According to it, the definition of the pound (in terms of the kilogram) was chosen to be divisible by seven, so that the grain, expressed in SI units, has the same number of significant figures as the pound. Tevildo (talk) 22:10, 4 October 2016 (UTC)