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<p class="MsoNormal"><span lang="EN-US">Dear Semantics group,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I have to report some contradictions in the VOUnit v1.1 recommendation regarding the unit string used for unitless quantities.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Here below I quote the related sentences, I then comment on them, ask the fundamental question, and attempt my own way out of those contradictions using the VOTable standard to resolve the issue.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Whatever the answer to my question, it is clear that we need an ERRATA.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">-----------------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><b>1 Introduction (informative)<o:p></o:p></b></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b>1.5 VOUnits syntax summary<o:p></o:p></b></p>
<ul type="disc">
<li class="MsoNormal" style="color:black;mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1 level1 lfo1;background:white">
<span style="font-size:11.0pt">The string `</span><span class="small"><span style="font-size:11.0pt;color:#7F4C00">1</span></span><span style="font-size:11.0pt">' may be used to represent a dimensionless quantity (Sect. <a href="https://ivoa.net/documents/VOUnits/20231215/REC-VOUnits-1.1.html#sec:parsing-components"><span style="color:#547FAA">2.2</span></a>).</span><o:p></o:p></li></ul>
<p class="MsoNormal"><b>2 The VOUnits syntax (normative)<o:p></o:p></b></p>
<p class="MsoNormal"><b><span lang="EN-US"><o:p> </o:p></span></b></p>
<p class="MsoNormal"><b>2.2 Parsing unit strings - overview<o:p></o:p></b></p>
<p class="MsoNormal"><span style="font-size:11.0pt;color:black;background:white">In each of the grammars here, the empty string is <i>not</i> a valid units string - in particular, it is not taken to indicate a dimensionless quantity. If a particular context
wishes to interpret such a string as indicating a dimensionless quantity, or perhaps instead indicating `units unknown', then it should handle that case separately. The VOUnits syntax, though it also deems the empty string to be invalid, recognises the string 1 as
positively indicating a dimensionless quantity.</span><span lang="EN-US" style="font-size:11.0pt;color:black;background:white"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:13.5pt;font-family:"Arial",sans-serif;color:black;background:white"><o:p> </o:p></span></p>
<p class="MsoNormal"><b>2.8 Other symbols, and other remarks<o:p></o:p></b></p>
<p class="MsoNormal">If there is no unit associated with a quantity (for example a quantity that is a character string, or unitless), data providers <b>should</b> indicate this with an empty string rather than blanks or dashes.<span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b>C.4 The VOUnits grammar (normative)<o:p></o:p></b></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal">input: complete_expression<o:p></o:p></p>
<p class="MsoNormal"> | scalefactor complete_expression<o:p></o:p></p>
<p class="MsoNormal"> | LIT1<span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal">scalefactor: LIT10 power numeric_power<o:p></o:p></p>
<p class="MsoNormal"> | LIT10<o:p></o:p></p>
<p class="MsoNormal"> | LIT1<o:p></o:p></p>
<p class="MsoNormal"> | VOUFLOAT<o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">-----------------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US"><o:p> </o:p></span></b></p>
<p class="MsoNormal"><b><span lang="EN-US">Comments<o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">It is that LIT1 in §C.4 what allows the value 1 to describe a dimensionless unit.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Main issue: the above sections contradict each other multiple times:<o:p></o:p></span></p>
<ul style="margin-top:0cm" type="disc">
<li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo2"><span lang="EN-US">Valid unit string for a dimensionless quantity is either:<o:p></o:p></span></li><ul style="margin-top:0cm" type="circle">
<li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level2 lfo2"><span lang="EN-US">1 according to §1.5, §2.2, and §C.4<o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level2 lfo2"><span lang="EN-US"> (an empty string) according to §2.8<o:p></o:p></span></li></ul>
<li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo2"><span lang="EN-US">But an empty string is invalid according to §2.2<o:p></o:p></span></li></ul>
<p class="MsoNormal"><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">§2.2 states that the empty string is not a valid unit string according to the grammars presented in the document. That is true, but what the document does not say is where the FITS grammar was taken from.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Nowhere in the FITS standard it is stated that an empty string is invalid (unless Im wrong of course).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The FITS standard does not allow 1 as a valid unit string (10**0 is allowed but thats a different string).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US">Question</span></b><span lang="EN-US">: shall 1 or an empty string be used to represent the unit of a dimensionless quantity?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US">Answer</span></b><span lang="EN-US">:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The answer is simple noting that the string 1 would break the round-trip FITS-VOTABLE-FITS principle that we have always used and stated in the last paragraph of section 2.9 of the VOTable standard (v1.5).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Because of that, and because the FITS standard allows an empty string,
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">it seems to me that the VOUnit statement of §2.8 (<b>empty string</b>) is the only one viable.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I understand that there will be some debates about this, but at least on one thing we will agree:
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">we need to amend the VOUnit document with an ERRATA to remove the contradictions.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Cheers, seasonal greetings to you all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Alberto<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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