<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">22 mars 2023 kl. 08:53 skrev Asmus Freytag via Unicode <<a href="mailto:unicode@corp.unicode.org" class="">unicode@corp.unicode.org</a>>:</div></blockquote><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><br class=""></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>On 3/21/2023 9:36 PM, Kent Karlsson via Unicode wrote:<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>There is no law of nature (or of [c]omputing) that says that math expressions<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>must be non-plain text. Just because all of neqn/eqn, (La)TeX, MathML, OMML, and indeed<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>UnicodeMath are representations of math expressions that are *not* plain text does not<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>mean that math expressions must be expressed by a higher level protocol. I.e. it could<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>very well be a text level protocol (where the ”math controls” are not expressed as<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>printable text, but as control codes).<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>Using control sequences or codes for your markup does not make your content plain text.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>The fact remains that mathematical notation is fundamentally recursive when it comes to<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>super/subscript: it's not individual letters, but entire expressions that are super/subscripted<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>(and at least in theory, they cover the full range of mathematical expressions) and they are<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>recursive: they can contain nested super/subscripted expressions. Again, in theory, this recursion<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>is not limited, except that for reasons of practicality such recursion has to be realized in ways that <o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>the overall expression remains legible.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">True, but…<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>Therefore, if your goal is mathematical notation, you want an operator that super/subscripts an <o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>expression and not code points for single characters. The key takeaway is the natural scoping:<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>super/subscripting is applied on the level of a whole expression. That means that your markup<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>needs to be scoped and that definitely makes it rich text.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Two cases:<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><ol start="1" type="A" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoListParagraph" style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">Bidi algorithm. Whether based solely on characters’s bidi properties or also bidi controls are used, the bidi handling is intrinsically scoped. I think you still call that plain text. Further, in HTML the bidi control characters aren’t used, instead there are attributes to most tags that control the bidi handling. Even though markup is used, I think you still think of it as plain text… Indeed, a math expression is <i class="">more</i> plain text than a bidi text. From the appearance of the math expression you can derive the structure (ignoring “phantom” expressions, which I included only because MathML has that, and they seem to sometimes be practical; and some reservation for stretch, which only should have an effect on some symbols). On the other hand, for a bidi processed text, you <i class="">cannot</i> guarantee the recovery of the given structure from the displayed text, indeed I think that in general is impossible; not so plain…<o:p class=""></o:p></span></li></ol><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><ol start="2" type="A" style="margin-bottom: 0cm; margin-top: 0cm;" class=""><li class="MsoListParagraph" style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;"><span lang="EN-GB" class="">Combining characters. Before Unicode, ECMA-48 defined <b class="">CSI 1 SP _</b><i class=""><text></i><b class="">CSI 2 SP _</b> for “combining” the characters in<i class=""><text></i> to a single displayed character (for certain implementation defined values of <i class=""><text></i>). Unicode “replaced” (that is probably not what happened historically, but technically it can be seen that way) that by instead having combining characters. Without that invention, we would in hypothetical-HTML have a tag for doing such combinations (since HTML does not like C0/C1 control codes…). And… these combining characters do not work on a single character, but on the combining sequence (a “scope”) that precedes it; and they can indeed be seen as a special kind of control characters. You still consider these scoped controls to be plain text.<o:p class=""></o:p></span></li></ol><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">So that the controls have a “scope” that is more than a single character (as in both of the cases above) or are recursive (as in both of the cases above) does apparently not exclude a feature from being regarded as plain text. So I maintain that what is plain text or not is much in the eye of the beholder (regardless of internal representation), not only w.r.t. scopeness and recursiveness, but also possibility to correctly derive the structure of a text (which in general is impossible for bidi).<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>The existing single characters are (almost) all encoded for use in phonetic notation, which is not <o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>recursive and doesn't super/subscript entire expressions. Instead it uses super/subscripting to <o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" style="color: rgb(132, 60, 12);" class="">>indicate modification. Hence "modifier letters".<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="FR" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">True. And I have said nothing against that point. Indeed, I said that those characters do *not*<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">belong in a math expression, and should “stay” with (mostly) phonetic notation.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>Further, if some symbol/letter for some reason only ever occurred in superscript<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>position in math expressions, such examples would still be supporting evidence for<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>that symbol/letter. The closest practical example I can think of is the degree sign, which<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(68, 114, 196);" class="">>>in origin is a superscript 0.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>The degree sign is either the exception that proves the rule, or something else: a symbol<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>that occurs frequently in contexts that are not full mathematical expressions, as it is typical<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">True, but I was arguing against Peter Constable's postulation that something that (for whatever<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">reason) occurs only in a superscript position in a math expression <i class="">could not</i> have its encoding <o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">supported by an example where it occurred in a superscript position in a math expression.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">THAT postulation is false. (And the closest example I could think of was the degree sign; there<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">MAY be examples of yet unencoded characters that only occur in superscript position in math<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">expressions.)<span style="color: rgb(132, 60, 12);" class=""><o:p class=""></o:p></span></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>for unit symbols. When used with temperature, it's interesting to note that not all temperature<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>scales use it consistently. You don't see it with Fahrenheit very often, for example, reflecting<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>differences in traditional keyboard layouts.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Ok, let’s digress a bit… I do see that too, in news articles (in web apps) from USA and British news<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">companies and see also “C” when degrees Celsius is meant. But writing farad (F) or coulomb (C)<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">when referring to temperature is just horrible, and only embarrassing for the journalist who wrote<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">that. (Another related horror is “kph”, and there you cannot even blame keyboard layouts.)<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>Note that many unit symbols have one-off encodings that Unicode had to support via compatibility<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>characters or even canonical duplicates (think micro and Ohm vs. their Greek letter counterparts).<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>Without the need to support a transition from pre-existing character sets, these duplicates would<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>not exist. But they do<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Yes. (But not relevant to this discussion.)<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>and so does the degree sign.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">The degree sign is not a compatibility character. It “divorced” from superscript 0 looong before<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">computers…<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>Neither of them, however, form precedents for non-compatibility characters.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class="">Not sure what that sentence means, since the premise is skewed.<o:p class=""></o:p></span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" class=""> </span></div><div style="margin: 0cm; line-height: 15.546667098999023px; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-GB" style="color: rgb(132, 60, 12);" class="">>A./</span></div></div><br class=""></body></html>