RE: Mathematics as Images

Once again acknowledging that Algebra 12 in the ‘80s is the limit of my experience, I believe the start of this discussion was to do with author responsibility when creating math notation. To that end, it seems like there may be value in adding a Sufficient technique for Images of Text for using appropriate technology for creating math symbols as text and not images.  That short-circuits the need to tackle this in Reflow. But what that appropriate technology would be seems to point back to user agent shortcomings.

The quote in this article<https://www.purplemath.com/modules/mathtext.htm>, which has nothing to do with accessibility, identifies part of this challenge:

“But when you go to e-mail your instructor with a question, or post your question to a math tutoring forum, you can end up with a mess or with something that totally doesn't mean what you meant to say.”

That document’s “typed-text-only” approach seems like an attempt to bypass some of the technology challenges using common type characters.

Then there’s this ascii math approach http://asciimath.org/, which includes alts for the symbols, etc.

At the least, an Images of Text sufficient technique using MATHML would help guide folks to what I’m assuming is the preferred approach. Is there a reason writing that technique isn’t being prioritized?

Speaking of MATHML, I see the nobreak, badbreak and goodbreak attributes, which takes me back to my prior question “Is it scalable to have every author specifying breaks?” Hopefully someone with the background to write a MATHML technique could also address that, to some degree.

Great to see you active again, Wayne!
Mike



From: Wayne Dick <wayneedick@gmail.com>
Date: Sunday, July 23, 2023 at 5:48 PM
To: Patrick H. Lauke <redux@splintered.co.uk>, W3C WAI ig <w3c-wai-ig@w3.org>
Subject: [EXTERNAL] Re: Mathematics as Images
Dear W3C Friends, I think that I should patiently explain the problem of representing mathematical notation as an image rather than text. Also, why this relates to SC. 1. 410. Issues with Notation as Image. The attached files give two images
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Dear W3C Friends,
I think that I should patiently explain the problem of representing mathematical notation as an image rather than text. Also, why this relates to SC.1.410.

Issues with  Notation as Image.
The attached files give two images of a text page from the  Vital Source bookshelf. Image_1 is the print part of a screen capture for page xx from Projective Geometry by yy. The second image is of the same page with a vertical midline and a square enclosing an image of mathematics text. As is plane this image cannot enlarge to 400% without running off the page. This is because it occupies more than half of the page width at 100%.
Now as stated 1.4.10 would allow this because the notation in the box is an image and exempted from reflow. The problem is that authors put formulas in a format so that they appear on one screen so that readers understand relations between objects at a single glance.
In this example the author wants the reader to appreciate the equality of the function beta applied to four cyclic permutations of the parameters. It is clear that the author intends for readers to equate all for expressions in the same statement. Thus, to meet the author’s intension this formula should  appear on one screen when presented. This is not satisfied by an image that cannot fit on a screen. If, however, the image was split into four pieces and allowed to reflow the entire sequence would appear on one screen, and the visually impaired reader could have the learning experience intended by the author. For those of you that do not read at 400%, you should note that more than for lines fit on a page at 400% of say 12 point.

Notation is Text
The images of mathematics that we read  in books and web pages are constructed from markup languages like LaTeX or MathML. These expressions consist of markup element symbols and characters from a few special alphabets. All the characters are represented as single characters in Unicode. For example, the integral symbol is U+222B. As such they can be enlarged as characters, converted to braille, and read out loud. They can be parsed like  any other computer language.
Also, mathematical notation can be spoken. This is important. The main contribution of algebra was to integrate mathematical computations into written language. Before algebra people used to write out all their calculations in language. Galileo wrote  out some of his theories as plays.
Images cannot be parsed into language. Once a markup language is converted to an image its linguistic properties are lost to media players. Even SVG can only give geometric descriptions of character curves. It does not hold  the semantic information of characters.
The fact that notation is text means that its linguistic structure can be exploited to identify break points in lines when we need to convert paragraphs into lines (reflow).

I do hope this begins to explain the problems with using images to represent mathematics and the need for reflow.

Most of you do not know  what it is like to read mathematics with low vision. It is hard to imagine. I know enlargement tricks most of you have never imagined. I need to. I use browser zoom, screen magnifiers, CSS, Word, LaTeX, Jupyter and even some tricks with PDF.

Best, Wayne



On Thu, Jul 20, 2023 at 3:52 PM Patrick H. Lauke <redux@splintered.co.uk<mailto:redux@splintered.co.uk>> wrote:
On 20/07/2023 23:35, Steve Green wrote:
[...]

> Based on those definitions, I would say there is a very strong case that formulae are text and that images of formulae violate SC 1.4.5 Images of Text.

Note though the start of 1.4.5 "If the technologies being used can
achieve the visual presentation". As said, while MathML has been getting
better, with support coming directly into browsers (rather than
requiring some plugin solution), I'm not sure it's as pervasively
supported yet to be able to fail formulae presented as images.

Also - and I'll admit I'm not too hot on MathML ... are there actually
defined rules for how MathML itself is supposed to reflow, at a
technical level?

P
--
Patrick H. Lauke

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