That’s a stretch, no? Mathematical notation is textual in the same way that, say, a flow diagram, an org chart or the structural formula for a chemical compound are textual. That is, there are textual glyphs in the visual representation, but the positioning and the other symbols are important to the meaning as well.
Can you type a mathematical equation on a keyboard, represent it unambiguously in a standardised character set, put it under version control, diff it, merge your edits with those of a colleague, still have something you can display reliably at the end, and then go back a decade later and search your archive for a specific equation? Not with any tool set I’ve ever seen. It’s still difficult enough just representing non-trivial mathematics on a web page so that everyone can read it.
Speech isn't.
No, but one of the advantages of textual representations that has been offered in this discussion is that textual formats can be used as inputs to screen readers and the like for improved accessibility. So again, I think this points to the inadequacy of purely textual notations as a way of representing complex information.
> That is, there are textual glyphs in the visual representation, but the positioning and the other symbols are important to the meaning as well.
The positioning of symbols is important in plaintext too! There is a distinction between the space separating words, versus the space separating paragraphs.
Similarly, all those non-letter symbols are important to the meaning. (Like the parentheses indicating that this is a side comment.)
I'm not sure I understand your argument here -- do you think mathematics would be text if it didn't have superscripts and subscripts?
To some extent you seem to be arguing that because tools for working with mathematical text are currently woefully in adequate, mathematics is not text. But this view seems backwards to me -- surely other languages that are not based on the latin character set had proper tooling developed later?
I'm not sure I understand your argument here -- do you think mathematics would be text if it didn't have superscripts and subscripts?
The context for this discussion is how text formats offer various advantages, as cited in the original article. The kind of mathematical notation we’re talking about does not offer many of those advantages, so it isn’t text in the sense that the original article was using the term.
(One could certainly debate whether or not notations like mathematics are “text” by some broader definition, but that doesn’t seem to advance this particular discussion.)
To some extent you seem to be arguing that because tools for working with mathematical text are currently woefully in adequate, mathematics is not text.
In the sense of the original article, yes, I suppose I am.
However, I think the important point is that we have a useful notation that doesn’t enjoy the benefits of plain text because of the lack of good tooling. The words we use to classify that notation don’t matter much.
Mathematical notation is text.
That’s a stretch, no? Mathematical notation is textual in the same way that, say, a flow diagram, an org chart or the structural formula for a chemical compound are textual. That is, there are textual glyphs in the visual representation, but the positioning and the other symbols are important to the meaning as well.
Can you type a mathematical equation on a keyboard, represent it unambiguously in a standardised character set, put it under version control, diff it, merge your edits with those of a colleague, still have something you can display reliably at the end, and then go back a decade later and search your archive for a specific equation? Not with any tool set I’ve ever seen. It’s still difficult enough just representing non-trivial mathematics on a web page so that everyone can read it.
Speech isn't.
No, but one of the advantages of textual representations that has been offered in this discussion is that textual formats can be used as inputs to screen readers and the like for improved accessibility. So again, I think this points to the inadequacy of purely textual notations as a way of representing complex information.
> That's a stretch, no?
No.
> That is, there are textual glyphs in the visual representation, but the positioning and the other symbols are important to the meaning as well.
The positioning of symbols is important in plaintext too! There is a distinction between the space separating words, versus the space separating paragraphs.
Similarly, all those non-letter symbols are important to the meaning. (Like the parentheses indicating that this is a side comment.)
I'm not sure I understand your argument here -- do you think mathematics would be text if it didn't have superscripts and subscripts?
To some extent you seem to be arguing that because tools for working with mathematical text are currently woefully in adequate, mathematics is not text. But this view seems backwards to me -- surely other languages that are not based on the latin character set had proper tooling developed later?
I'm not sure I understand your argument here -- do you think mathematics would be text if it didn't have superscripts and subscripts?
The context for this discussion is how text formats offer various advantages, as cited in the original article. The kind of mathematical notation we’re talking about does not offer many of those advantages, so it isn’t text in the sense that the original article was using the term.
(One could certainly debate whether or not notations like mathematics are “text” by some broader definition, but that doesn’t seem to advance this particular discussion.)
To some extent you seem to be arguing that because tools for working with mathematical text are currently woefully in adequate, mathematics is not text.
In the sense of the original article, yes, I suppose I am.
However, I think the important point is that we have a useful notation that doesn’t enjoy the benefits of plain text because of the lack of good tooling. The words we use to classify that notation don’t matter much.