Talk:International System of Quantities

ISQ is more limited than ISO 80000
I'll repeat here some concerns I raised when this material was at International System of Units and still have now that we've moved the material here, restoring and expanding this article. The earlier discussion among myself, and  is at Talk:International System of Units/Archives/05/2015.

I fear 's assessment of the primary sources has inherent errors in the sections International System of Quantities and International System of Quantities.
 * The ISQ does not define units. The ISO 80000 series does, but it makes a clear distinction in the introduction, e.g.
 * The ISQ does not comprise all of the extensive lists of quantities in the ISO 80000 series, which as mentioned in the above quote includes additional quantities. That introduction also states
 * and as the SI brochure as amended by the 2014 supplement says
 * Far from describing the entire contents of that series as the ISQ, it's explicitly restrictive.

I think this means we have to edit the article, either to make it clear that some of the quantities and all of the units mentioned are not part of ISQ, or to simply remove them as out of scope. I'm tending to the latter, especially given that we have an article on ISO 80000 already. What do others think? NebY (talk) 14:29, 17 May 2015 (UTC)
 * I'm not sure. An extract from ISO 80000-1:2009 reads (my emphasis) "The system of quantities, including the relations among them the quantities used as the basis of the units of the SI, is named the International System of Quantities, denoted “ISQ”, in all languages. This name was not used in ISO 31, from which the present harmonized series has evolved. However, ISQ does appear in ISO/IEC Guide 99:2007 and in the SI Brochure [8], Edition 8:2006. In both cases, this was to ensure consistency with the new Quantities and units series that was under preparation at the time they were published; it had already been announced that the new term would be used. It should be realized, however, that ISQ is simply a convenient notation to assign to the essentially infinite and continually evolving and expanding system of quantities and equations on which all of modern science and technology rests. ISQ is a shorthand notation for the “system of quantities on which the SI is based”, which was the phrase used for this system in ISO 31." The author(s) of these words surely intended the scope of the ISQ to cover all of ISO/IEC 80000, and possibly beyond. Dondervogel 2 (talk) 22:59, 22 May 2015 (UTC)
 * Possibly significant here is the potential distinction between quantities and units. So, if these are considered to be mutually exclusive, the ISQ might comprise all of the quantities mentioned in ISO 80000 (and possibly all of the equations relating them), but none of the units.  As such, ISO/IEC 80000 might specify many units not in the SI, but that does not necessarily make them part of what has been labelled the ISQ. We might need to find a new term for the units defined by ISO/IEC 80000. —Quondum 00:30, 23 May 2015 (UTC)
 * I think Quondum is right. Entry 3.6 of ISO 80000-1:2009 reads
 * 3.6
 * International System of Quantities
 * ISQ
 * system of quantities based on the seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity
 * NOTE 1 This system of quantities is published in the ISO 80000 and IEC 80000 series Quantities and units, Parts 3 to 14.
 * NOTE 2 The International System of Units (SI) (see item 3.16) is based on the ISQ.
 * NOTE 3 Adapted from ISO/IEC Guide 99:2007, definition 1.6, in which Note 1 is different."
 * This gives me the impression that the units defined by ISO 80000 are not part of the ISQ. Dondervogel 2 (talk) 15:50, 23 May 2015 (UTC)


 * I think we have consensus! On the quantities, Dondervogel 2 has highlighted text which makes it clear that ISQ now goes far beyond providing quantities for SI's units, completely allaying my concerns. On the units, we've all concluded - from a variety of perspectives and sources - that the ISQ doesn't include units. I'll remove that section now. I'll also try a small edit to the first paragraph to convey a little more of what Dondervogel 2's shown here. I hope that's all acceptable. NebY (talk) 16:57, 23 May 2015 (UTC)
 * Sounds good to me. I have moved the section on units to ISO/IEC 80000. Dondervogel 2 (talk) 17:12, 23 May 2015 (UTC)

Symbolic Representation of Base Quantities
Under the Base Quantities section, it says, "The conventional symbolic representation of the dimension of a base quantity is a single upper-case letter in roman (upright) sans-serif type."

Does it actually have to be sans-serif? Considering the heavy usage of serif fonts in official documentation of most organisations (the default "professional" font style in businesses, nonprofits, etc. is most often Times New Roman), I find it somewhat difficult to believe that serif font styles would not be allowed under at the *very* least most circumstances.

– SarahTehCat (talk) 21:09, 30 May 2015 (UTC)


 * I don't see "sans-serif" anywhere - just "roman (upright)". The precise words from ISO 80000-1:2009 are "The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) type. The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity."   Dondervogel 2 (talk) 22:00, 30 May 2015 (UTC)


 * This statement was obtained directly from note 2 on p. 5 of this reference:  I realize that this document is not part of the standard, so one wonders where BIPM got this from.  —Quondum 22:42, 30 May 2015 (UTC)

Here's a screenshot. It's very clearly there. Base Quantities > 2nd paragraph, 2nd sentence.  – SarahTehCat (talk) 17:36, 3 June 2015 (UTC)


 * Yeah, I see what you're talking about in the article. The question is whether we should simply ignore the BIPM/JCGM's take on it.  The sources do not seem to agree on this, and I do not have access to the standard for a more complete reading. , what is your take on this?  —Quondum 18:30, 3 June 2015 (UTC)
 * Why not just cite both sources and include a factual statement to the effect that the secondary source requires sans-serif while the primary one does not? Dondervogel 2 (talk) 01:22, 4 June 2015 (UTC)
 * Good idea. Done. —Quondum 01:55, 4 June 2015 (UTC)

Agreed. Good idea, Dondervogel 2 – SarahTehCat (talk) 17:11, 4 June 2015 (UTC)

Logarithmic quantities and levels
Logarithmic quantities and levels are defined in ISO 80000-3:2007 § 0.5 in reasonably pleasing detail. Indispensable to the definition of a level as defined in the ISQ is the definition of a 'field quantity' and a 'power quantity' (this is IMO unfortunate historical baggage, but c'est la vie). The article is currently inaccurate, since it does not capture this distinction, which conditionally selects the applicable formula. To quote, "a field quantity is defined as a quantity whose square is proportional to power when it acts on a linear system", and further, "Meaningful measures of power quantities generally require time averaging to form a mean-square value that is proportional to power. Corresponding field quantities may then be obtained as the root-mean-square value."

This hobbled definition is stopping me from simply rewriting this. (What could have become a beautiful system has hung onto some utter abominations.) But maybe I'll get to rewording the section, since ISO 80000:3 does a sterling job of retrospective description in this case, within the historical constraints. —Quondum 17:00, 23 December 2017 (UTC)


 * A word of warning: Don't forget that "field quantity" is deprecated by ISO 80000-1:2009, making the ISQ internally inconsistent in this regard. See ISO 18405 for details. Dondervogel 2 (talk) 20:51, 23 December 2017 (UTC)

Challenge to "ISO defines ISQ"
I wish to challenge the statement
 * "The ISQ is defined in the international standard ISO/IEC 80000, and was finalised in 2009 with the publication of ISO 80000-1."

I think we have the conceptualization of the ISQ entirely back-to-front. ISO 80000 does not define the ISQ, but rather an interpretation of parts of it. The SI is based on the ISQ, which is in some sense informal, but ISO has no authority over the SI. We need to completely separate the concepts of ISQ and ISO 80000. —Quondum 18:20, 29 February 2020 (UTC)
 * I'm not sure where the ISQ concept originated in ISO or BIPM, but I don't think ISQ and ISO 80000 are easily separated. Perhaps this extract (from ISO 80000-1:2009) helps:
 * "The system of quantities, including the relations among them the quantities used as the basis of the units of the SI, is named the International System of Quantities, denoted “ISQ”, in all languages. This name was not used in ISO 31, from which the present harmonized series has evolved. However, ISQ does appear in ISO/IEC Guide 99:2007 and in the SI Brochure [8], Edition 8:2006. In both cases, this was to ensure consistency with the new Quantities and units series that was under preparation at the time they were published; it had already been announced that the new term would be used. It should be realized, however, that ISQ is simply a convenient notation to assign to the essentially infinite and continually evolving and expanding system of quantities and equations on which all of modern science and technology rests. ISQ is a shorthand notation for the “system of quantities on which the SI is based”, which was the phrase used for this system in ISO 31."
 * Dondervogel 2 (talk) 18:50, 29 February 2020 (UTC)
 * Yes, I am basing my argument on that, as well as other descriptions and passages, including in the SI brochure. You will notice that the above passage is describing the ISQ, not the ISO standard, and makes it clear that the ISO standard could not possibly define the ISQ.  The SI Brochure refers to an unspecified system of quantities ("The system of quantities underlying the SI and the equations relating them are based on the present description of nature and are familiar to all scientists, technologists and engineers."), though other references make it evident that this is the ISQ.  The SI Brochure's references to ISO standards are purely informative.  So a statement to the effect that that "The system of quantities that the SI is based (namely the ISQ) is that which is defined by the ISO standard" would be completely false.  We need to think of the ISQ as some nebulous but consistent system of quantities independent of ISO standards, and that ISO has (independently of the reliance that the SI places on the ISQ) attempted to describe aspects of this system in such a way that engineers can work with it, such as by assigning symbols and names to quantities.  —Quondum 20:29, 29 February 2020 (UTC)
 * I certainly agree with "nebulous". I do think that ISO is the first international organization to formalize the ISQ though. And judging from the quoted passage they claim their first attempt to do so was in the 1990s (or earlier). Dondervogel 2 (talk) 20:43, 29 February 2020 (UTC)
 * I think this affects how we treat the two things. The wording we use suggests that the ISQ is brought into being ("defined") by the ISO standard.  To describe ISO as formalizing the system is far better.  For example, SI defines the metre as something within its jurisdiction, and can change that definition (as it did).  ISO, in contrast, has no jurisdiction over the ISQ, even though it formalizes parts of it.  We need to use wording that supports the correct intuition, and we could start by using words such as "formalize" in place of "define".  The existing wording can be read as that the definition of the ISQ was finalized with the completion of the ISO standard, whereas the ISO standard does not really have an impact on the ISQ.  —Quondum 21:00, 29 February 2020 (UTC)
 * You have good instincts for the big picture. Go for it. We can quibble about detail later. Dondervogel 2 (talk) 21:22, 29 February 2020 (UTC)
 * I have rewritten the lead. The body of the article will naturally have to be rewritten essentially in its entirety, because it is about SI and ISO 80000, not the ISQ.  For example, there is no set of "base quantities" in the ISQ.  —Quondum 01:11, 1 March 2020 (UTC)
 * I like the new lede. I added mention of the IEC, and the fact that ISO and IEC work together on this project. Dondervogel 2 (talk) 07:10, 1 March 2020 (UTC)

essentially follows on from the discussion above. The claim of a lack of formal basis may be considered to be overly strong, but the gist is that citations show that the ISQ is not the same thing as and is only partly formalized in ISO 80000: the ISQ is inherently incompletely defined, it is not circumscribed, is continually evolving, and is essentially defined as what is generally accepted as opposed to what is fully defined by a formal definition. ISO 80000 can be seen as a formalization of parts of the ISQ, but I do not think one can call it a "formal basis for the ISQ". Some quotations:
 * SI Brochure 8: The system of quantities, including the equations relating the quantities, to be used with the SI, is in fact just the quantities and equations of physics that are familiar to all scientists, technologists, and engineers. They are listed in many textbooks and in many references, but any such list can only be a selection of the possible quantities and equations, which is without limit.
 * ISO 80000-1:2009 §0.1: The quantities and the relations among them are essentially infinite in number and are continually evolving as new fields of science and technology are developed. Thus, it is not possible to list all these quantities and relations in this International Standard; instead, a selection of the more commonly used quantities and the relations among them is presented. ... The system of quantities, including the relations among them the quantities used as the basis of the units of the SI, is named the International System of Quantities, denoted “ISQ”, in all languages. ... It should be realized, however, that ISQ is simply a convenient notation to assign to the essentially infinite and continually evolving and expanding system of quantities and equations on which all of modern science and technology rests. ISQ is a shorthand notation for the “system of quantities on which the SI is based”, ...
 * ISO 80000-1:2009 §3.6: International System of Quantities (ISQ) – system of quantities based on the seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity
 * SI Brochure 9: The system of quantities underlying the SI and the equations relating them are based on the present description of nature and are familiar to all scientists, technologists and engineers.

(It may be noted that ISO 80000-1:2009 is self-contradictory in this respect: the two quoted extracts above are mutually inconsistent (if one takes §3.6 to be circumscribing rather than descriptive of a minimal inclusion) .) One could say that the system of base and derived quantities in the ISQ is formalized by ISO 80000. We could revise the statement "The ISQ does not have a formal basis" to read something more directly derivable from the sources, such as "The ISQ is not a formal or fully defined system." —Quondum 13:23, 2 August 2020 (UTC)
 * So on this basis let's just say it's incomplete. I don't see it as informal. Dondervogel 2 (talk) 13:45, 2 August 2020 (UTC)
 * Fair enough. Whether it is informal, in this context, is interpretive.  I see it as having a formalized aspect, with a lot more that resists such categorization.  Perhaps "The ISQ is not a fully defined system", or something similar?  The important point to convey is that SI and ISO 80000 do not fully define the ISQ.  —Quondum 14:01, 2 August 2020 (UTC)
 * I prefer to say "The ISQ is an incompletely defined system" because stating that it is not fully defined implies that it could be. In fact the system will remain incompletely defined for as long as it exists because the system is infinite. Dondervogel 2 (talk) 14:39, 2 August 2020 (UTC)
 * That works for me. The subtleties of phrasing in English!  I suppose the SI Brochure 8 quote above is the best reference for that (they went all minimalist in some ways in SI Brochure 9).  Once ISO/CD 80000-1 is published, maybe it will be citable too.  —Quondum 14:59, 2 August 2020 (UTC)

Non-Conformance with Dictionary 101
This article repeatedly uses the word being defined within the definition. For example in Paragraph 1 Line 1, "The Interntional System of Quantities (ISQ) is a system of quantities..." Again under the heading Base Quantity: "A base quantity is a physical quantity..." This is like saying an apple is defined as an apple. Not informative. Not helpful to young readers. Poor grammar, and run-on sentences at several locations lead to significant confusion for an experienced reader to understand the main point in the article, which is believed to be a presentation of the organizational hierarchy described among different organizations, I think! The net result is a confusing article with no premise and no conclusion, sorry. — Preceding unsigned comment added by Kprainville (talk • contribs) 13:21, 6 May 2021 (UTC)


 * Well, the article does link to both Quantity and Physical quantity as a good hyperlinked encyclopedia should, but it does rather rush into talking about the bureaucracy behind the documentation. A little reorganisation that started with more about what a system of quantities is, perhaps bringing forward some of the material under Base Quantities, and linked to Physical quantity before the more abstruse Quantity (if at all), could be much more accessible and not give the impression that the ISQ is an organizational hierarchy among different organizations! Even so, I fear the very idea of a system of quantities will remain inherently more abstruse than, say, a system of units or the physical constants. NebY (talk)


 * The definitions are not circular in the manner being suggested. For example, defining a "green apple" as "an apple that is not ripe" assumes that the concept "apple" is already defined, and is only defining a subcategory of that concept called "green apples".  The comment about style is good though: this type of phrasing can be confusing, and can be improved for greater accessibility.  —Quondum 21:26, 6 May 2021 (UTC)


 * I have tried to encapsulate a definition of the ISQ in the first paragraph while making it short. It is a tricky idea to put across, so specific suggestions would be helpful.  —Quondum 22:04, 6 May 2021 (UTC)
 * That reads much better. I've tried to copy-edit it some more, almost accidentally making it more concise as I realised that: the ISQ is not the name of something, it is something; the quantities ae used in physics and science in general but not in nature, which is not a science; that equations are not relationships, they are a means of describing relationships; the ISQ is not a comprehensive listing of all science's equations; that it's questionable to say "the name is used ... in particular with reference to a system that is consistent with the SI", as if the GCPM may use it differently from the ISO to describe a subset of the ISQ described by the ISO. I've also tried to give examples early on to help readers who chance on this article unprepared.
 * The article was dwelling at length on the documentation of the system before returning to describing the actual system, but that turns out to be easily resolved by following MOS:INTRO, giving the documentation its own section and keeping a brief summary in the lead.
 * There seems to be a typo in the quote in the first reference, " including the relations among them the quantities used", but that's down to the ISO's editors, who seem to have been nodding. They started that clause well by using italics and quotation marks and then forgot to continue. NebY (talk) 07:44, 8 May 2021 (UTC)


 * I like it. The name "International System of Quantities" is a bit of a misnomer, since it suggests that it is something arrived at through agreement between political entities.  At root, it is is no more "international" than is "modern physics" or "modern science", and simply reflects understanding of some specifics of those disciplines.  This article has been through an arc from "that which is defined by ISO/IEC 80000" to "a semi-nebulous system of quantities that is consistent with SI and modern physics, but with some identifiable parts".  That is, the article initially portrayed ISO 80000 as being central but changed its role to being secondary, which is as it should be.
 * An interesting point might be whether "angle" in the ISQ is necessarily as defined by SI (there is debate about how it should be defined, akin to the split between CGS and SI). I would suggest that the ISQ has a dimensional quantity that we intuitively call angle, but is not the quantity that SI defines as angle.  In a sense, this is a question about whether the ISQ has an apparent independent existence in the same way that mathematics has, or whether the arbitrary choices (what words to attach to quantities, what quantities to label as base quantities, the number of base quantities, etc.) are really part of the ISQ, or just labels attached to quantities in the ISQ by SI.
 * Hopefully, the weird quote you mention will be fixed when they publish the revised ISO/IEC 80000-1, which has been expected for some time. But don't hold your breath.  —Quondum 13:31, 8 May 2021 (UTC)


 * Oh good! Yes, as a project the ISQ does seem to be riding on the coattails of the SI, and I'm still not clear what the demand for it was, or the perceived need. I'm rather reminded of the awesome ISO standards which are multilingual glossaries of terms used when producing ISO standards. I didn't know about the debate around "angle" but I'm curious now - thank you. I'm rather leary of seeing the ISQ as so independent, but in an ill-formed, gut reaction way, so I'm gald you're keeping track of it. And yes, I used to try to keep track of certain ISO revision processes and would reassure colleagues that nothing was going to happen yet. :) NebY (talk) 11:43, 9 May 2021 (UTC)


 * I wouldn't describe it as "riding on the coattails of the SI", but instead as "being a belated foundation to prop up the otherwise ill-defined SI". A system of quantities and their relationships (but not the conventions of how we label things) are foundational to any unit system, but because of how our intuition works, we do not realize that there is a huge amount of presumption that we have failed to formalize.  Symptoms appear in various confusions, such as the apparent CGS–SI incompatibility, the confusing "2$\pi$ rad/s is the same as 1 Hz" while being clearly unequal as quantities (2π s−1 ≠ 1 s−1), and indeed that we usually fail to distinguish unit systems from their underlying system of quantities.  Starting with a system of quantities, all of this can be readily reconciled.  I think the CIPM came to this realization long after units were standardized, and started constructing the foundation to make SI units well-defined, and the "ISQ" is the fledgling attempt to provide a more formal framework in which to talk about this, with the goal of the SI attaining a greater logical legitimacy.
 * On angle, if you're interested you might want to look for publications related to the topic in Metrologia and elsewhere by Mills, Mohr, Taylor, Phillips, Quincey, etc. —Quondum 14:49, 9 May 2021 (UTC)


 * Thank you for that - a welcome overview to counter my narrow cycnicism. In fact, something like that would make a great addition to the article! Meanwhile I'll follow your leads to articles about angle, though perhaps not this week. Thanks again. NebY (talk) 16:15, 9 May 2021 (UTC)
 * Wow! I've just read the revised lead. You two have done a great job in clarifying. I concur with on the relationship between SI and ISQ. In addition to angle, the "system" is also wrestling with the definitions of logarithmic quantities and their units. Two new standards (parts 15 and 17) under development by IEC should shed light on a host of issues, including the relationship between decibel and neper. I wonder if the same standard(s) will also clarify the relationship between bit and nat but perhaps that is too much to hope for. Dondervogel 2 (talk) 00:07, 10 May 2021 (UTC)

Dondervogel, I tend to make some inferences from the changes that I have seen. A significant observation is that SI and ISO have omitted almost all mention of logarithmic quantities, as though they belatedly realized that including half-baked stuff attempting to turn the historical mishmash into a standard is worse than no standard. To produce a consistent set of definitions requires actually ditching the inconsistencies, which is not easy. The SI saw some debate around historical baggage around angle, which in the end had no effect: the status quo remained. In contrast, I haven't noticed any significant debate about the tougher area of level and its units, and suddenly materializing something untested by robust debate is a recipe for disaster. My bet is that we will not get anything but a very trimmed version of what we had before, or that it will simply not materialize for many years to come. What is unclear about the relationship between the shannon (aka bit) and the nat? —Quondum 13:59, 10 May 2021 (UTC)
 * Units of level: My understanding is that IEC 80000-15, currently under development, is to include new definitions of the bel, decibel and neper. The work of Mills and Morfey 2005 is relevant.
 * Units of information: I agree that if one defines the bit as one shannon, conversion to the nat or hartley becomes trivial. I see that shannon (unit) asserts that 1 bit = 1 shannon but I find this questionable. For example, I don't think IEC 80000-13 defines the bit in this way, though I confess I'm not sure. I'll check and get back to you.
 * Dondervogel 2 (talk) 14:27, 10 May 2021 (UTC)
 * I scoured IEC 80000-13 for a definition of bit, but did not find one. The standard defines the hartley, shannon and nat as units of information, whereas the bit is used as a unit of storage capacity. Nowhere in the standard is it suggested that the bit and shannon are related, less still equal. Dondervogel 2 (talk) 14:48, 10 May 2021 (UTC)
 * Thanks for the link to that paper. I will go through it.  On the "shannon = bit", I think that is .  Note the mention of IEEE Std 260.1-2004 in shannon (unit), which suggests that use of the term "bit" to represent a unit of information may have reached a level of formality, though this was withdrawn recently: on 2021-03-25.  Combined with what you say about IEC 80000-13, I think an edit is in order to remove the "equality".  —Quondum 15:12, 10 May 2021 (UTC)
 * Hmm. That paper completely overlooks two aspects of confusion and resolution, namely the factor-of-2 problem and the independent-base-quantity approach.  I'm used to Mills showing more insight in an analysis of quantities and their units, though that paper was was a while ago, well before the currently available ISO/IEC 80000 standards and Mills's more recent publications.  I'll stay with my position of "not enough seems to be happening; don't hope for anything helpful".  Of course, I must make the disclaimer that I don't know what is actually happening.  —Quondum 20:15, 10 May 2021 (UTC)

Draft VIM4 accessible
I see that a draft of VIM4 is accessible here:. I see that time has moved to the top of the table. Some wording has been tweaked. —Quondum 16:51, 12 May 2021 (UTC)