Math and usability/accessibility

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  • Harlan Messinger

    Math and usability/accessibility

    I am reviewing a set of pages, some of which include in-line mathematical
    formulas represented as images. I am addressing the accessibility issues
    behind those images. (Conformance to Section 508 of the applicable US
    government regulations is required.) Ick--at least, I suppose, until MathML
    is generally supported.

    One approach would be to set the ALT attribute to be a linearized version of
    the equation. But this gets to be tough if there are multiple levels of
    fractions or exponents. For example, here is a linearized version of a
    normal probability density function:

    (1/σ√ (2π))e^(&min us;(x − μ)^2/(σ^2))

    ISSUE 1: Many formulas can't be linearized effectively, at least if they are
    to be kept in mathematical form.

    ISSUE 2: Can speech synthesizers even handle these? For example, if I use
    symbol ≓ and the user agent speaks Unicode, it's going to read "image
    of or approximately equal to" every time it sees this symbol. This seems
    overly burdensome for the user. Another strategy would be to spell
    everything out in words, as though I were reciting the expression:

    One over sigma times the root of 2 pi, times e to the power
    of the negative square of (quantity) x minus mu (close quantity)
    over the square of sigma.

    But then, in IE and Netscape 4.7, this would appear in a bubble and look
    awful.

    ISSUE 3: Is there yet a different set of considerations for users of Braille
    displays? Or are they comparable to those of users of speech synthesizers?

    ISSUE 4: So I wondered: what if I used both ALT and TITLE attributes on the
    same image? I could put a single blank space in the title and a linearized
    formula the alt. Or a single blank space in the title and a recitation in
    the alt. Or a linearized formula in the title and a recitation in the alt.

    I determined that when an <img> tag has alt text AND a non-trivial title, IE
    6 pops up the title; Netscape 4.7 pops up the alt text; and Netscape 7 and
    Mozilla pop up the title.

    When an <img> tag has alt text, and a title attribute consisting of a single
    space, IE 6 pops up a tiny, empty bubble; Netscape 4.7 pops up the alt text;
    and Netscape 7 and Mozilla don't pop up anything at all (which seems to be
    the best result of all).

    I'm wondering how any of this combinations will play out in:

    Text browsers, or graphical browsers with images turned off;

    Speech-synthesizing or Braille readers for mainstream browsers;

    Speech-synthesizing user agents;

    Braille-based user agents (are there any?)

    Are any of you familiar with these issues?

    --
    Harlan Messinger
    Remove the first dot from my e-mail address.
    Veuillez ôter le premier point de mon adresse de courriel.

  • Harlan Messinger

    #2
    Re: Math and usability/accessibility

    I assumed that having attribute="" in an HTML is the same as not having the
    attribute at all. But I decided to test my aforementioned scenario with

    alt="something" title=" "

    by changing it to

    alt="something" title=""

    with nothing at all in the title, to see what IE would do. What happens is
    that no pop-up appears! This is different from the case of

    alt="something"

    with no title, of course, because in that case the alt text pops up. Hmmm.

    Is it legal for an empty attribute to be treated differently from a missing
    one?

    Comment

    • jake

      #3
      Re: Math and usability/accessibility

      In message <br50hv$29evm5$ 1@ID-114100.news.uni-berlin.de>, Harlan
      Messinger <h.messinger@co mcast.net> writes[color=blue]
      >I am reviewing a set of pages, some of which include in-line mathematical
      >formulas represented as images. I am addressing the accessibility issues
      >behind those images. (Conformance to Section 508 of the applicable US
      >government regulations is required.) Ick--at least, I suppose, until MathML
      >is generally supported.
      >
      >One approach would be to set the ALT attribute to be a linearized version of
      >the equation. But this gets to be tough if there are multiple levels of
      >fractions or exponents. For example, here is a linearized version of a
      >normal probability density function:
      >
      > (1/&sigma;&#x221A; (2&pi;))e^(&min us;(x &minus; &mu;)^2/(&sigma;^2))
      >
      >ISSUE 1: Many formulas can't be linearized effectively, at least if they are
      >to be kept in mathematical form.
      >
      >ISSUE 2: Can speech synthesizers even handle these? For example, if I use
      >symbol &#x2253; and the user agent speaks Unicode, it's going to read "image
      >of or approximately equal to" every time it sees this symbol. This seems
      >overly burdensome for the user. Another strategy would be to spell
      >everything out in words, as though I were reciting the expression:
      >
      > One over sigma times the root of 2 pi, times e to the power
      > of the negative square of (quantity) x minus mu (close quantity)
      > over the square of sigma.
      >[/color]

      Put this in the 'alt' text and it should speak OK.
      [color=blue]
      >But then, in IE and Netscape 4.7, this would appear in a bubble and look
      >awful.
      >
      >ISSUE 3: Is there yet a different set of considerations for users of Braille
      >displays? Or are they comparable to those of users of speech synthesizers?
      >
      >ISSUE 4: So I wondered: what if I used both ALT and TITLE attributes on the
      >same image? I could put a single blank space in the title and a linearized
      >formula the alt. Or a single blank space in the title and a recitation in
      >the alt. Or a linearized formula in the title and a recitation in the alt.
      >
      >I determined that when an <img> tag has alt text AND a non-trivial title, IE
      >6 pops up the title; Netscape 4.7 pops up the alt text; and Netscape 7 and
      >Mozilla pop up the title.
      >
      >When an <img> tag has alt text, and a title attribute consisting of a single
      >space, IE 6 pops up a tiny, empty bubble; Netscape 4.7 pops up the alt text;
      >and Netscape 7 and Mozilla don't pop up anything at all (which seems to be
      >the best result of all).
      >
      >I'm wondering how any of this combinations will play out in:
      >
      > Text browsers, or graphical browsers with images turned off;
      >
      > Speech-synthesizing or Braille readers for mainstream browsers;
      >
      > Speech-synthesizing user agents;[/color]

      IBM's HPR will voice the ALT text.
      [color=blue]
      >
      > Braille-based user agents (are there any?)
      >
      >Are any of you familiar with these issues?
      >[/color]

      --
      Jake

      Comment

      • Andreas Prilop

        #4
        Re: Math and usability/accessibility

        "Harlan Messinger" <h.messinger@co mcast.net> wrote:
        [color=blue]
        > I am reviewing a set of pages, some of which include in-line mathematical
        > formulas represented as images.[/color]

        See http://www.unics.uni-hannover.de/nht...thematics.html
        and http://www.cs.tut.fi/~jkorpela/math/ how to do this in HTML
        without images.
        [color=blue]
        > (1/&sigma;&#x221A; (2&pi;))e^(&min us;(x &minus; &mu;)^2/(&sigma;^2))[/color]

        Make that
        1/√(2π) &#183;
        exp[−(x−μ)&#17 8;/σ&#178;] / σ

        --
        But thats what FP puts in to the page, so i asume thats correct
        Harry H. Arends in microsoft.publi c.frontpage.cli ent

        Comment

        • Stephen Poley

          #5
          Re: Math and usability/accessibility

          On Tue, 9 Dec 2003 12:28:28 -0500, "Harlan Messinger"
          <h.messinger@co mcast.net> wrote:
          [color=blue]
          >I assumed that having attribute="" in an HTML is the same as not having the
          >attribute at all. But I decided to test my aforementioned scenario with
          >
          > alt="something" title=" "
          >
          >by changing it to
          >
          > alt="something" title=""
          >
          >with nothing at all in the title, to see what IE would do. What happens is
          >that no pop-up appears! This is different from the case of
          >
          > alt="something"
          >
          >with no title, of course, because in that case the alt text pops up. Hmmm.
          >
          >Is it legal for an empty attribute to be treated differently from a missing
          >one?[/color]

          I think so. It is certainly regularly done with ALT attributes (with
          images off), where ALT="" causes no text to be displayed, while with a
          missing ALT, browsers typically display [IMG] or the file-name.

          --
          Stephen Poley


          Comment

          • Harlan Messinger

            #6
            Re: Math and usability/accessibility


            "Andreas Prilop" <nhtcapri@rrz n-user.uni-hannover.de> wrote in message
            news:0912200320 12228382%nhtcap ri@rrzn-user.uni-hannover.de...[color=blue]
            > "Harlan Messinger" <h.messinger@co mcast.net> wrote:
            >[color=green]
            > > I am reviewing a set of pages, some of which include in-line[/color][/color]
            mathematical[color=blue][color=green]
            > > formulas represented as images.[/color]
            >
            > See http://www.unics.uni-hannover.de/nht...thematics.html
            > and http://www.cs.tut.fi/~jkorpela/math/ how to do this in HTML
            > without images.
            >[color=green]
            > > (1/&sigma;&#x221A; (2&pi;))e^(&min us;(x &minus; &mu;)^2/(&sigma;^2))[/color]
            >
            > Make that
            > 1/√(2π) &#183;
            > exp[−(x−μ)&#17 8;/σ&#178;] / σ[/color]

            I think that's the end of my career writing HTML in a text editor! What's
            wrong with using entity codes for Greek letters?

            Comment

            • Jukka K. Korpela

              #7
              Re: Math and usability/accessibility

              "Harlan Messinger" <h.messinger@co mcast.net> wrote:
              [color=blue]
              > What's wrong with using entity codes for Greek letters?[/color]

              They are less widely supported than the (numeric) character references.
              It's not a big issue any more, though - it's basically Netscape 4 that
              doesn't implement the entities.

              --
              Yucca, http://www.cs.tut.fi/~jkorpela/
              Pages about Web authoring: http://www.cs.tut.fi/~jkorpela/www.html

              Comment

              • Jukka K. Korpela

                #8
                Re: Math and usability/accessibility

                "Harlan Messinger" <h.messinger@co mcast.net> wrote:
                [color=blue]
                > I assumed that having attribute="" in an HTML is the same as not
                > having the attribute at all.[/color]

                It isn't - especially not for attributes that have default values.
                [color=blue]
                > Is it legal for an empty attribute to be treated differently from a
                > missing one?[/color]

                Yes.

                --
                Yucca, http://www.cs.tut.fi/~jkorpela/
                Pages about Web authoring: http://www.cs.tut.fi/~jkorpela/www.html

                Comment

                • Jukka K. Korpela

                  #9
                  Re: Math and usability/accessibility

                  "Harlan Messinger" <h.messinger@co mcast.net> wrote:
                  [color=blue]
                  > ISSUE 1: Many formulas can't be linearized effectively, at least if
                  > they are to be kept in mathematical form.[/color]

                  That's correct. Complicated mathematical formulas have inherent
                  accessibility problem, since they _are_ the conventional "native
                  language" of mathematics and they use, by design, two-dimensional
                  notations too, and utilize a large set of characters.
                  [color=blue]
                  > ISSUE 2: Can speech synthesizers even handle these? For example, if
                  > I use symbol &#x2253; and the user agent speaks Unicode, it's going
                  > to read "image of or approximately equal to" every time it sees
                  > this symbol.[/color]

                  It hopefully won't say "image of" unless you write that. It's supposed
                  to read the alternative content you specify.

                  But I'm afraid speech synthesizers have relatively limited
                  understanding of special characters. Here we have a problem similar to
                  that of lack of font support in the visual presentation, just worse.
                  [color=blue]
                  > But then, in IE and Netscape 4.7, this would appear in a bubble and
                  > look awful.[/color]

                  It's to be consider a browser oddity (or bug) if they show the alt
                  attribute value when the image _is_ displayed. It's not worth worrying
                  about, but you can set title="" if you like (though Netscape 4 will
                  ignore it).
                  [color=blue]
                  > ISSUE 3: Is there yet a different set of considerations for users
                  > of Braille displays? Or are they comparable to those of users of
                  > speech synthesizers?[/color]

                  I only know that there are different Braille displays, with different
                  character repertoires.

                  There's not much you can do about it. When you are presenting
                  complicated mathematics, you just have to use mathematical symbols.
                  Authors cannot be expected to do everything; user agents, too, must
                  evolve so that they can cope with special characters, somehow.

                  --
                  Yucca, http://www.cs.tut.fi/~jkorpela/
                  Pages about Web authoring: http://www.cs.tut.fi/~jkorpela/www.html

                  Comment

                  • Harlan Messinger

                    #10
                    Re: Math and usability/accessibility


                    "Jukka K. Korpela" <jkorpela@cs.tu t.fi> wrote in message
                    news:Xns944D153 F1887Djkorpelac stutfi@193.229. 0.31...[color=blue]
                    > "Harlan Messinger" <h.messinger@co mcast.net> wrote:
                    >[color=green]
                    > > What's wrong with using entity codes for Greek letters?[/color]
                    >
                    > They are less widely supported than the (numeric) character references.
                    > It's not a big issue any more, though - it's basically Netscape 4 that
                    > doesn't implement the entities.[/color]

                    I am *so* ready to stop supporting Netscape 4.*.

                    Comment

                    • Harlan Messinger

                      #11
                      Re: Math and usability/accessibility


                      "Jukka K. Korpela" <jkorpela@cs.tu t.fi> wrote in message
                      news:Xns944D175 0F1D8jkorpelacs tutfi@193.229.0 .31...[color=blue]
                      > "Harlan Messinger" <h.messinger@co mcast.net> wrote:
                      >[color=green]
                      > > ISSUE 1: Many formulas can't be linearized effectively, at least if
                      > > they are to be kept in mathematical form.[/color]
                      >
                      > That's correct. Complicated mathematical formulas have inherent
                      > accessibility problem, since they _are_ the conventional "native
                      > language" of mathematics and they use, by design, two-dimensional
                      > notations too, and utilize a large set of characters.
                      >[color=green]
                      > > ISSUE 2: Can speech synthesizers even handle these? For example, if
                      > > I use symbol &#x2253; and the user agent speaks Unicode, it's going
                      > > to read "image of or approximately equal to" every time it sees
                      > > this symbol.[/color]
                      >
                      > It hopefully won't say "image of" unless you write that. It's supposed
                      > to read the alternative content you specify.[/color]

                      I see that this particular example is confusing, especially in light of our
                      earlier conversation on image tags. There was no connection between the
                      occurrence of the word "image" and the fact that I'm talking about an
                      equation being implemented as an image. My premise is that if a speech
                      synthesizer does render every Unicode character, it will likely use the
                      description of each character as provided in the Unicode code charts. For
                      the symbol I chose as an example, this description is "Image of or
                      approximately equal to". (In other words, the symbol is used in at least a
                      couple of contexts, in which one of which it is read as "image of", and in
                      another of which it is read as "approximat ely equal to".)
                      [color=blue]
                      >
                      > But I'm afraid speech synthesizers have relatively limited
                      > understanding of special characters. Here we have a problem similar to
                      > that of lack of font support in the visual presentation, just worse.
                      >[color=green]
                      > > But then, in IE and Netscape 4.7, this would appear in a bubble and
                      > > look awful.[/color]
                      >
                      > It's to be consider a browser oddity (or bug) if they show the alt
                      > attribute value when the image _is_ displayed. It's not worth worrying
                      > about, but you can set title="" if you like (though Netscape 4 will
                      > ignore it).[/color]

                      Well, it's worth worrying about when it (IE) is the browser the majority of
                      our audience uses, whether it complies with standards or not. If this were
                      only a problem in Netscape 4.*, I wouldn't worry about it.
                      [color=blue]
                      >[color=green]
                      > > ISSUE 3: Is there yet a different set of considerations for users
                      > > of Braille displays? Or are they comparable to those of users of
                      > > speech synthesizers?[/color]
                      >
                      > I only know that there are different Braille displays, with different
                      > character repertoires.
                      >
                      > There's not much you can do about it. When you are presenting
                      > complicated mathematics, you just have to use mathematical symbols.
                      > Authors cannot be expected to do everything; user agents, too, must
                      > evolve so that they can cope with special characters, somehow.
                      >[/color]

                      As a practical matter, I agree. I'm interested, though, in how far beyond
                      the practical the regulations expect us to go! (Does Finland have similar
                      regulations? I believe the EU does.)

                      By the way, do you prefer to be associated with the succulent plant found in
                      western parts of North America, or with the tuber also known as cassava or
                      manioc?

                      Comment

                      • Alan J. Flavell

                        #12
                        Re: Math and usability/accessibility


                        On Wed, 10 Dec 2003, Harlan Messinger wrote:
                        [color=blue]
                        > "Jukka K. Korpela" <jkorpela@cs.tu t.fi> wrote
                        >[color=green]
                        > > It's to be consider a browser oddity (or bug) if they show the alt
                        > > attribute value when the image _is_ displayed. It's not worth worrying
                        > > about, but you can set title="" if you like (though Netscape 4 will
                        > > ignore it).[/color]
                        >
                        > Well, it's worth worrying about when it (IE) is the browser the
                        > majority of our audience uses,[/color]

                        I don't see any need to "worry" - just follow the above advice. IE
                        has, as of several versions already, given priority to the title=".."
                        attribute for this purpose.
                        [color=blue]
                        > If this were only a problem in Netscape 4.*,[/color]

                        As Jukka said, it _is_ a problem specifically with NN4.*
                        [color=blue]
                        > I wouldn't worry about it.[/color]

                        Hmmm.

                        Comment

                        • Andreas Prilop

                          #13
                          Re: Math and usability/accessibility

                          On Tue, 9 Dec 2003, Harlan Messinger wrote:
                          [color=blue][color=green]
                          >> Make that
                          >> 1/√(2π) &#183;
                          >> exp[−(x−μ)&#17 8;/σ&#178;] / σ[/color]
                          >
                          > I think that's the end of my career writing HTML in a text editor![/color]

                          Feel free to use a Unicode-savvy editor and write your text in UTF-8.
                          You don't have to stick with numeric character references.

                          My point was also to write "exp(x)" instead of "e^x".
                          [color=blue]
                          > What's wrong with using entity codes for Greek letters?[/color]

                          Netscape 4.x will display both UTF-8-encoded text and &#number;
                          expressions, but fails to display most non-Latin-1 entities
                          like &alpha; .

                          Comment

                          • Andreas Prilop

                            #14
                            Re: Math and usability/accessibility

                            On Wed, 10 Dec 2003, Harlan Messinger wrote:
                            [color=blue]
                            > I am *so* ready to stop supporting Netscape 4.*.[/color]

                            Why should you do this when you can easily write text
                            that is suitable for Netscape 4.x, too?

                            View my page

                            with Netscape 4.0!

                            Comment

                            • Andreas Prilop

                              #15
                              Re: Math and usability/accessibility

                              On Tue, 9 Dec 2003, I wrote:
                              [color=blue]
                              > Make that
                              > 1/√(2π) &#183;
                              > exp[−(x−μ)&#17 8;/σ&#178;] / σ[/color]

                              Correction:

                              1/√(2π) &#183;
                              exp[−(x−μ)&#17 8;/2σ&#178;] / σ
                              ^
                              And see

                              which displays well even in Netscape 4.x.

                              BTW:
                              <http://google.com/search?ie=ISO-8859-7&oe=UTF-8&q=%22exp+x+%E C+2%22>

                              Comment

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