Math Reference, Accessibility

Math Reference Project
Accessibility

There are very few people in the world who can convey high level mathematics to a blind student, in a text based format.  Everything must be explained in words, and some of the proofs even change slightly.  Let me show you what I mean.

Assume a proof involves trig substitution.  In fact there may be an entire jacobian filled with sines and cosines.  A sighted person would simply write it all out, because he assimilates the compound expression sin(θ) at a glance, and treats it as a single entity.  The blind user cannot do this.  He must hear the words (synthesizer) or feel the dots (braille):

sine left parent theta right paren

By the time he has heard all those words and compressed it into a single entity, the context is lost.  A proof written for the blind might begin like this.

For notational convenience, let s = sin(θ) and let c = cos(θ).  Remember that s^2+c^2 = 1.  We will use this identity below.

Using concise notation almost puts the blind user on an equal footing, relative to his sighted peers, especially if the same notation is used consistently throughout the website.

But if you are a blind user, these notational tricks are the least of your worries.  You want to find a math site that you can read, period!  This is the only one.  To be fair, some pages of MathPages.com can be deciphered with a text-based browser, but you're going to have to work at it.  Most of those pages employ "ascii art".  The equation 1/2 + 1/3 = 5/6 might be written like this. 

 1     1     5 
--- + --- = ---
 2     3     6

A synthesizer would read this as:

1 1 5 - - - + - - - = - - - 2 3 6

Other websites are entirely inaccessible, because the equations are presented as gif images.  They look just like the equations in your textbook, spread out in two dimensions, but they remain hidden from the blind user, like a trove locked away in a sealed vault.

How do I know so much about this subject?  I am totally blind, and have been so since age ten.  I also have advanced degrees in math and computer science.  This puts me in a unique position.  I understand most of the material at the college level, I can explain it to blind users, and I can write html.  So I am gradually bringing ten years of notes on-line.  And it will probably take me ten more years to complete this project.

The Impossible Conpromise

How many blind student study graduate level math, and how many of those are going to find this website?  Am I really willing to do all this work for 100 people?  Perhaps, but with some tweaking here and there, the same website can benefit everyone.  Thus the impossible compromise is born.  I am trying to write these pages in a format that is accessible to blind and sighted users alike.  This is a challenge indeed!

The sighted user won't tolerate inline equations, such as x squared plus y squared equals z squared; he simply can't learn math that way.  On the other hand, a blind person can't assimilate a two dimensional equation, with subscripts and superscripts.  Or can he?

Remember that html is not a bitmap image.  It has codes that indicate subscripts and superscripts.  These codes tell the browser to display the 2 above or below the line, and in a smaller font.  A specialized browser could intercept these codes and render x<sup>2</sup> as x^2, which is standard in-line notation for x squared.  The speech adapter can then read x^2 as x squared, which sounds natural to the user.  This is the compromise I have made.  Equations employ subscripts and superscripts via html tags, and the pages are still accessible to the blind, if you use the right browser.

Where can you find a browser that renders superscripts, subscripts, Greek letters, and mathematical symbols in-line, using English words?  You can find it here.  I wrote this browser several years ago, before the MathReference project was born.  I believe strongly in text based interfaces, and at that time lynx was the only game in town.  Yet even lynx was not written for blind people.  Its interface is satisfactory for a sighted user running a character terminal, but it is very awkward for a blind user.  So I wrote edbrowse in my spare time.  This is a C program that runs on most Unix machines.  (It can probably be ported to Windows; I just haven't done it.)  It presents the web pages in text format, line by line, like /bin/ed.  And the latest version is compatible with MathReference.com.  It converts x<sup>2</sup> to x^2, x<sub>5</sub> to x[5], &#952; (unicode) to theta, &#8747; to integral, and so on.  The edbrowse editor is designed to read these pages, and conversely, these pages are written in a consistent format, following certain html guidelines, so that edbrowse will read them properly.  The browser and website work together as one.  The blind user can use another browser and still understand the material, but the experience will be suboptimal.

Pictures

Unfortunately the sighted user is at a disadvantage, because there are few pictures on the site.  For most people, learning math without a picture or diagram is difficult.  I have no qualms about adding images to this website, as long as somebody else creates them.  This is something I simply cannot do myself.  If you can help create gif images, please drop me a line.

Most of the pictures on this site were developed by Stewart Wilcox, a tireless, unpaid volunteer from Harvard University.  My sincere thanks to Stewart, and to others who have contributed to this effort.

Summary

This website presents college level mathematics to blind and sighted users alike.  These two goals are almost antithetic, but I'm doing my best.  If you have any suggestions on presentation, that would make the site more accessible to either group, without making it less accessible to the other, I'd love to hear from you.  I am open to all ideas.

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