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Math and usability/accessibility

P: n/a
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^(−(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.

Jul 20 '05 #1
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17 Replies


P: n/a
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?

Jul 20 '05 #2

P: n/a
In message <br*************@ID-114100.news.uni-berlin.de>, Harlan
Messinger <h.*********@comcast.net> writes
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^(&minus;(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.

Put this in the 'alt' text and it should speak OK.
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;
IBM's HPR will voice the ALT text.

Braille-based user agents (are there any?)

Are any of you familiar with these issues?


--
Jake
Jul 20 '05 #3

P: n/a
"Harlan Messinger" <h.*********@comcast.net> wrote:
I am reviewing a set of pages, some of which include in-line mathematical
formulas represented as images.
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.
(1/&sigma;&#x221A;(2&pi;))e^(&minus;(x &minus; &mu;)^2/(&sigma;^2))


Make that
1/√(2π) ·
exp[−(x−μ)²/σ²] / σ

--
But thats what FP puts in to the page, so i asume thats correct
Harry H. Arends in microsoft.public.frontpage.client
Jul 20 '05 #4

P: n/a
On Tue, 9 Dec 2003 12:28:28 -0500, "Harlan Messinger"
<h.*********@comcast.net> wrote:
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?


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

http://www.xs4all.nl/~sbpoley/webmatters/
Jul 20 '05 #5

P: n/a

"Andreas Prilop" <nh******@rrzn-user.uni-hannover.de> wrote in message
news:091220032012228382%nh******@rrzn-user.uni-hannover.de...
"Harlan Messinger" <h.*********@comcast.net> wrote:
I am reviewing a set of pages, some of which include in-line mathematical formulas represented as images.


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.
(1/&sigma;&#x221A;(2&pi;))e^(&minus;(x &minus; &mu;)^2/(&sigma;^2))


Make that
1/√(2π) ·
exp[−(x−μ)²/σ²] / σ


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?

Jul 20 '05 #6

P: n/a
"Harlan Messinger" <h.*********@comcast.net> wrote:
What's wrong with using entity codes for Greek letters?


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

Jul 20 '05 #7

P: n/a
"Harlan Messinger" <h.*********@comcast.net> wrote:
I assumed that having attribute="" in an HTML is the same as not
having the attribute at all.
It isn't - especially not for attributes that have default values.
Is it legal for an empty attribute to be treated differently from a
missing one?


Yes.

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

Jul 20 '05 #8

P: n/a
"Harlan Messinger" <h.*********@comcast.net> wrote:
ISSUE 1: Many formulas can't be linearized effectively, at least if
they are to be kept in mathematical form.
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.
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.
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.
But then, in IE and Netscape 4.7, this would appear in a bubble and
look awful.
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).
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?


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

Jul 20 '05 #9

P: n/a

"Jukka K. Korpela" <jk******@cs.tut.fi> wrote in message
news:Xn*****************************@193.229.0.31. ..
"Harlan Messinger" <h.*********@comcast.net> wrote:
What's wrong with using entity codes for Greek letters?


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.


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

Jul 20 '05 #10

P: n/a

"Jukka K. Korpela" <jk******@cs.tut.fi> wrote in message
news:Xn****************************@193.229.0.31.. .
"Harlan Messinger" <h.*********@comcast.net> wrote:
ISSUE 1: Many formulas can't be linearized effectively, at least if
they are to be kept in mathematical form.
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.
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.


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


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 "approximately equal to".)

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


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.
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?


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.


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?

Jul 20 '05 #11

P: n/a

On Wed, 10 Dec 2003, Harlan Messinger wrote:
"Jukka K. Korpela" <jk******@cs.tut.fi> wrote
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).
Well, it's worth worrying about when it (IE) is the browser the
majority of our audience uses,


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.
If this were only a problem in Netscape 4.*,
As Jukka said, it _is_ a problem specifically with NN4.*
I wouldn't worry about it.


Hmmm.

Jul 20 '05 #12

P: n/a
On Tue, 9 Dec 2003, Harlan Messinger wrote:
Make that
1/√(2π) ·
exp[−(x−μ)²/σ²] / σ
I think that's the end of my career writing HTML in a text editor!


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".
What's wrong with using entity codes for Greek letters?


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

Jul 20 '05 #13

P: n/a
On Wed, 10 Dec 2003, Harlan Messinger wrote:
I am *so* ready to stop supporting Netscape 4.*.


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

View my page
http://www.unics.uni-hannover.de/nht...thematics.html
with Netscape 4.0!

Jul 20 '05 #14

P: n/a
On Tue, 9 Dec 2003, I wrote:
Make that
1/√(2π) ·
exp[−(x−μ)²/σ²] / σ


Correction:

1/√(2π) ·
exp[−(x−μ)²/2σ²] / σ
^
And see
http://www.unics.uni-hannover.de/nht...emp/gauss.html
which displays well even in Netscape 4.x.

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

Jul 20 '05 #15

P: n/a
On Wed, 10 Dec 2003, Andreas Prilop wrote:
BTW:
<http://google.com/search?ie=ISO-8859-7&oe=UTF-8&q=%22exp+x+%EC+2%22>


WTF? Three of the top 4 hits were in Japanese. Does this tell us
something?

Jul 20 '05 #16

P: n/a
"Harlan Messinger" <h.*********@comcast.net> wrote:
> 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.
It hopefully won't say "image of" unless you write that. It's supposed
to read the alternative content you specify.


I see that this particular example is confusing, especially in light of
our earlier conversation on image tags.


I'm sorry, I had thought you meant the use of an image representing the
character. And I didn't even check that the Unicode name of &#x2253; is
really "image of or approximately equal to" (and I still have no idea of what
it means).
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.
It's natural to assume that if it recognizes the character, then the simplest
mode of support is to read the name of the character.*) This is by no means
required, and it's usually not the best way - just as we don't want a speech
browser to say FULL STOP when it encounters a full stop (period, "."). But
the more specialized and rare a character is, the more probable it is that
reading the name is the best we can reasonably expect.
*) Well, it's even simpler to read the code number of the character, saying
something like "Unicode character two two five three hex" or something like
that. It would in a sense convey the information and be in that sense better
than saying nothing, or just beeping, but very few people would be able to
make use of the information.
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 "approximately equal to".)
I see. In that case, it would appear to be adequate to use "Alan's device":
<span title="image of">&#x2253;</span>
or
<span title="approximately equal to">&#x2253;</span>
respectively, perhaps with some modification to the wording as required by
context (e.g. "is approximately equal to" or "approximately equals"). Whether
speech browsers would make use of it is debatable, but they _could_ at least
give the user optional access to the advisory title - analogously with how
graphic browsers show the advisory title as a tooltip on mouseover. And this
visual effect could be useful to people who have no difficulty in seeing the
character but do not understand what it means.
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.)


The EU has no accessibility regulations, just recommendations - which have
been issued at a high political level, by the European Commission and the
European Parliament, specifically declaring it to be important to achieve WAI
Priority level 2 (AA compliance). But it seems that the recommendations are
easily ignored when there are no _requirements_. - Some European countries
(not Finland) have accessibility legislation at the national level, and there
has been some talks on creating some at the EU level, but I don't think there
will be much progress.

In a sense, recommendations can be stricter than regulations. When you just
recommend something, you can ask for the impossible. But if you wish to
enforce something by the law, you can't.

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

Jul 20 '05 #17

P: n/a

"Jukka K. Korpela" <jk******@cs.tut.fi> wrote in message
news:Xn*****************************@193.229.0.31. ..
"Harlan Messinger" <h.*********@comcast.net> wrote:
> 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.

It hopefully won't say "image of" unless you write that. It's supposed
to read the alternative content you specify.
I see that this particular example is confusing, especially in light of
our earlier conversation on image tags.


I'm sorry, I had thought you meant the use of an image representing the
character. And I didn't even check that the Unicode name of &#x2253; is
really "image of or approximately equal to" (and I still have no idea of

what it means).
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.
It's natural to assume that if it recognizes the character, then the

simplest mode of support is to read the name of the character.*) This is by no means required, and it's usually not the best way - just as we don't want a speech browser to say FULL STOP when it encounters a full stop (period, "."). But
the more specialized and rare a character is, the more probable it is that
reading the name is the best we can reasonably expect.
*) Well, it's even simpler to read the code number of the character, saying something like "Unicode character two two five three hex" or something like that. It would in a sense convey the information and be in that sense better than saying nothing, or just beeping, but very few people would be able to
make use of the information.
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 "approximately equal to".)
I see. In that case, it would appear to be adequate to use "Alan's

device": <span title="image of">&#x2253;</span>
or
<span title="approximately equal to">&#x2253;</span>
respectively, perhaps with some modification to the wording as required by
context (e.g. "is approximately equal to" or "approximately equals"). Whether speech browsers would make use of it is debatable, but they _could_ at least give the user optional access to the advisory title - analogously with how
graphic browsers show the advisory title as a tooltip on mouseover. And this visual effect could be useful to people who have no difficulty in seeing the character but do not understand what it means.


Ah. Very good. Thanks.
Jul 20 '05 #18

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