Talk:Gram per cubic centimetre

nonsense definition
The lead currently contains the nonsensical definition of g/cm^3 as "mass in grams divided by volume in cubic centimetres". If I were to take a lump of water and divide its mass in grams by its volume in cubic centimetres, the answer I would get is a number, approximately equal to 1. If I were to do the same with a lump of air I would get another number, about 800 times smaller, because the density of water is about 800 times that of air. In neither case is the result equal to 1 g/cm^3, and it is certainly not the DEFINITION of g/cm^3. How can we correct such nonsense? Dondervogel 2 (talk) 09:39, 27 October 2023 (UTC)
 * See SI Brochure 9, 2.3.4 (NIST SP330 2019 2.3.4), unchanged from SI Brochure 8 1.4, "Derived units are defined as products of powers of the base units." NebY (talk) 10:07, 27 October 2023 (UTC)
 * The BIPM brochure is (unsurprisingly) correct. What it means is that 1 kg/m^3 is the product of 1 kg and (1 m)^-3. Similarly, it means that 1 g/cm^3 is the product of 1 g and (1 cm)^-3. If you don't understand the difference between the BIPM definition and the nonsense stated in the lead, I suggest you refrain from editing articles about units. Dondervogel 2 (talk) 10:43, 27 October 2023 (UTC)
 * Good grief. NebY (talk) 12:07, 27 October 2023 (UTC)
 * I think "divided by" should rather be "per". Gawaon (talk) 14:26, 27 October 2023 (UTC)
 * Dondervogel 2, doesn't this qualm rely on a pretty narrow, naïve concept of 'division' as a physical process, rather than mathematically equivalent to multiplying by an inverse? — Remsense  聊  14:55, 27 October 2023 (UTC)
 * I think I understand the point that @Dondervogel 2 is making; I'll see if I can make it more clear. "Mass in grams divided by volume in cubic centimetres" would be written mathematically as (m/g)/(V/cm3). m/g is dimensionless, because g cancels the inherent unit in m. The same applies to V/cm3, so the whole expression (m/g)/(V/cm3) is a dimensionless number, and this is not a valid definition of the unit g/cm3. Indefatigable (talk) 16:18, 27 October 2023 (UTC)
 * Dondervogel is technically correct. The unit is a unit of density; the text in question gives not a definition of the unit, but rather a units-specific definition of density.  That said, the meaning is reasonably clear, and I'm not sure how to address the objection without making the text unreadable.  DV, can you propose an alternative? --Trovatore (talk) 16:59, 27 October 2023 (UTC)
 * My proposal is to revert this edit Dondervogel 2 (talk) 18:16, 27 October 2023 (UTC)
 * Oh, I see. I agree your version is more correct, but it may be harder to follow for readers who don't grok dimensional analysis.  We could do something like "... a unit of density in the cgs system, whereby an object with a mass of m grams and a volume of V cubic centimetres (sic) has an average density of m/V g/cm3.  Wordy but correct and understandable. --Trovatore (talk) 18:29, 27 October 2023 (UTC)
 * Too wordy, in my view. When in doubt, better leave it as is. Gawaon (talk) 18:57, 27 October 2023 (UTC)
 * Factual accuracy is not a matter of opinion. The present definition is demonstrably incorrect and has to go. Whether it is replaced by Trovatore's proposal or mine (which are both correct) is a matter of taste/opinion. Dondervogel 2 (talk) 19:01, 27 October 2023 (UTC)
 * Indefatigable, Thank you, I understand the issue now. — Remsense  聊  17:02, 27 October 2023 (UTC)
 * How is "mass in grams" unitless? Somebody's mass in grams may be 85,000 grams, while their mass in kilograms would be 85 kg, or in pounds 187 pounds. Neither of these expressions is unitless, they just use different units. Gawaon (talk) 19:01, 27 October 2023 (UTC)
 * If someone's mass is 85 kg, their mass in grams is 85000, a dimensionless number. Dondervogel 2 (talk) 19:03, 27 October 2023 (UTC)
 * In a certain mathematical understanding, yes. But we're dealing with language here, not with math. In English, one can use "in" to express a preference for the unit to be used, and that doesn't make the unit go away. Gawaon (talk) 19:18, 27 October 2023 (UTC)
 * The semantics of that seem a bit muddled, but even if we ignore that point, the problem remains that the current text claims to define a unit, but instead defines density as measured in that unit. I think that's too sloppy.  Wordy is better than sloppy. --Trovatore (talk) 19:35, 27 October 2023 (UTC)
 * OK, then what about something along the lines of "defined as grams (measuring mass) divided by cubic centimetres (measuring volume)"? (I see that's getting quite close to what already had.) Gawaon (talk) 19:54, 27 October 2023 (UTC)
 * That could work. --Trovatore (talk) 22:17, 27 October 2023 (UTC)
 * Gawaon's proposal is vague (it does not address the questions of how many grams or how many cubic centimetres), but has the benefit of being not wrong. It would be better than what we have now, which is simply incorrect. Dondervogel 2 (talk) 08:45, 28 October 2023 (UTC)

This seems like an argument over an excessively fussy, small detail. I vote for clarity over rigorous fussy, fussy accuracy any day. Accuracy on a subtle technical point that almost nobody will understand or appreciate does not outweigh clarity for the casual reader who just wants to know what the heck "grams per cubic metre" is. If you can find a way to accommodate both needs, great, but if not keep it clear even at the expense of rigorous accuracy.--Srleffler (talk) 17:23, 29 October 2023 (UTC)


 * There's nothing fussy about it. In its present form, the article prescribes how to calculate the density of an object, which is a variable. What is needed is a definition of a unit of density, which is a constant. A variable density can never be equal to a constant unit. Dondervogel 2 (talk) 17:28, 29 October 2023 (UTC)
 * I don't believe there exists any reader whose understanding of the topic would be in any way impaired by the present wording. --Srleffler (talk) 01:56, 30 October 2023 (UTC)

Dondervogel, I rephrased the definition in a way that might suit both of us. What do you think?--Srleffler (talk) 02:04, 30 October 2023 (UTC)
 * I won't speak for DV but it works for me. --Trovatore (talk) 05:00, 30 October 2023 (UTC)
 * That works for me too. This is exactly what I have been arguing for, just with more words. If we all agree on this solution at g/cm^3, it needs to be applied also at kg/m^3 Dondervogel 2 (talk) 06:36, 30 October 2023 (UTC)