7 ms·

Unrelated to the content but complaining about the website is a popular thing to do here so I'd like to share my experience, as a blind user. Here is what my s

by ctoth 3y ago

Unrelated to the content but complaining about the website is a popular thing to do here so I'd like to share my experience, as a blind user. Here is what my screen reader sees for this page: Recently, I came up with a trick that can get rid of in many cases. It’s pretty simple, but it has some interesting implications. This is the trick: I just define a new derivative operator, like so: That’s all. You just take the derivative and then divide by . I call this derivative operator with the bar on the upper the reduced derivative.Now, why is this interesting? To start off, we’ll note that the unique function ... The unfortunate truth is a ton of math content on the web reads like this. It has crippled me as a blind user who would like to appreciate math for over a decade. In university I was forced to pursue a degree other than CS because the math program used software which produced output like this and refused to change. There has been technical progress, and many sites are starting to work better--Wikimedia most fantastically, but this old bugbear made me want to speak up and beg people to try and review their math content with a screen reader before publishing (I think MathJax has some built-in accessibility now?).

jovial_cavalier 3y ago
I'm curious how blind people normally engage with math. For me, engaging with math almost always means conjuring up a visual representation in my mind. Failing that, an equation. Since visualization is so fundamental to doing math, and since mathematical symbols and equations are a written language for which there is no spoken analog, I really can't imagine engaging with math without my eyes. Even reading equations aloud verbatim is not reliable. "X plus B squared" can mean (x + b)^2 or x + b^2
- kybernetikos 3y ago
  The way I've heard those distinguished in spoken math is x + b^2 is said "x plus b squared" and (x + b)^2 is said "x plus b all squared. There's a similar approach for divide "x plus b over 8" vs "x plus b all over 8". That was often enough but if it wasn't you'd be reduced to pronouncing brackets.
  - Sharlin 3y ago
    Using postfix operations in the Way of Forth would be unambiguous and of course otherwise superior as well as is well known [citation needed]. “x b plus squared” vs “x b squared plus”. Well, at least as long as it’s agreed on whether “x b” means two variables or one with a two-letter name. But the latter don’t really exist in math. You just expand to new alphabets when you run out of letters.
- nilstycho 3y ago
  I had a math graduate student teaching my linear algebra class. He taught dot and cross products entirely algebraically, never drawing vectors as arrows, but as arrays of numbers. When I suggested after class that teaching the visual representation might help some students, he pushed back. Visual understanding, he explained, was a crutch best avoided, because visual intuition could break down in higher dimensions. I thought that was a surprising perspective from a math graduate student, of all people.
  - anvuong 3y ago
    This is quite true, especially true when talking about direction (gradient) in high dimensional space. I don't think this can be avoided, since after all we are creatures living in 3D space where left right up down are quite well-defined, just need to make a mental note every time you have to deal with more than 3 dimensions.
  - jameshart 3y ago
    Seems like an odd choice when talking about the cross product, since the cross product is only a thing in 3D. You can define analogous things in other dimensions but it becomes clearer and clearer that it’s not meaningfully a ‘product’. So it doesn’t matter if your visual intuition for a cross product breaks down in higher dimensions - a cross product is only a thing in three.
    - jacobolus 3y ago
      This is very off topic, but the wedge product absolutely is "meaningfully a product", generalizes fine to arbitrary dimension, and has a perfectly reasonable visual/spatial/geometric interpretation. (Indeed, we should entirely scrap the cross product in undergraduate level technical instruction and replace it with the wedge product; one happy effect will be replacing students' misleading spatial intuitions with better ones.)
      - jameshart 3y ago
        Or bivectors, or k-vectors, or blades…
- ctoth 3y ago
  In terms of reading the notation out loud, if there is verbal ambiguity, remove it? For instance, for your example: "X plus B quantity squared" or "x + b squared" You can also do things like change the pitch of speech as symbols are nested, play specific tones to represent symbols, pan things across the stereo field to represent groupings, and otherwise make the symbolic equation into a multimodal experience. But of course, you can't do any of this if the semantic representation of the equation is lost and it is rendered as strictly graphics or whatever. I'm a bit confused to your original point about visualization because how ever in the world could I program if I couldn't abstractly manipulate symbols? I suppose not visually, but there's something non-word-oriented happening in my head.
  - jovial_cavalier 3y ago
    >I'm a bit confused to your original point about visualization I guess I find that programming is somewhat more word-oriented than pure math. For instance, how do you think about complex exponentiation, or a rotation matrix? Do you bring to mind the sensation of spinning around? For myself, I bring to mind the image of the entire complex plane rotating and stretching along a spiral, but I'm led to believe that those who are blind from birth aren't really capable of doing that. Harder examples might include fourier series, convolution, gradient descent, etc. I think you could almost consider the visualization of these things like a crutch. I wonder if not being able to visualize them might remove preconceived notions about how they behave, and give you different insights.
curtis3389 3y ago
> review their math content with a screen reader before publishing I second this for anything you put on the web. I opened the webapp I work on with a screen reader, and it was an incredibly valuable experience. You get to see your site from a different perspective, and various issues stand out like a sore thumb, and I honestly found fixing the accessibility issues extremely satisfying.
noman-land 3y ago
Thank you for sharing your experience. Web accessibility has a long way to go and reminders like these help.
sebzim4500 3y ago
The equations are in mathml, I feel like the issue is with the screen reader.
RogerL 3y ago
But what is the answer? What should I do differently? I get don't use images, but then what? I can't imagine all screen readers have the same capabilities, or that there is a base common ability, so what should we do? Googling says MathML is the answer (e.g. https://www.washington.edu/doit/how-do-i-create-online-math-content-accessible-students-who-are-blind); https://www.washington.edu/doit/how-do-i-create-online-math-... this site uses MathML and your reader isn't handling it. So now what? (alt-tags? something else?)
- bjornasm 3y ago
  One option would be to do testing with screen-readers and then find out if the content works, and if not find out why.
  - patrec 3y ago
    I think most people are fine with the idea that some of the costs (monetary and otherwise) arising from disabilities should be transferred from the people suffering from them to society at large. But I don't think it's reasonable for producers and users of broken screen readers to expect everyone (including authors of private blogs posts) bending over backwards to accommodate them, nor is it a remotely efficient use of societal resources. It also creates completely perverse incentives.
    - User23 3y ago
      If there is a bug in the screen reader then that's on the vendor. However the overwhelming number of cases where a website is unusable with a screen reader are due to lack of proper semantic tagging, like alt text and so on. The last thing a screenreader user wants to hear on a site is "button," "button," "button..." There's certainly room for tooling to help though. I definitely think it sucks that many accessibility linters are nonfree and thus will never be used by site devs who aren't worth suing. It's worth remembering that accessibility helps everyone, not just the disabled. In fact one of the more popular arguments against accessibility is that it allows non-disabled persons to do more than intended. So while there's a good argument to be made for being charitable to those with a frankly really lousy condition, if you just want to be self-centered you still benefit from properly tagged data.
mgunyho 3y ago
Author here, I'm sorry to hear that it doesn't work well with a screen reader. I tested it with the reader mode of Firefox, which renders MathML perfectly, although I don't know how that would translate to a screen reader. Safari reader mode renders the math inline, like this: I just define a new derivative operator, like so: dxđ f(x)≡2π1 ⋅dxd f(x). That’s all. while Chrome's reader mode just fails to recognize the content entirely, even though it's the most basic <body><div id="content"><p> ... structure possible. I have basically zero web dev experience so I don't know how to fix this, maybe I need to tweak the KaTeX settings. I think it's quite sad that math is so difficult on the web. While setting up the blog, I looked around and it seemed like FF is the only browser with proper MathML support, but I think that was also being phased out because it's apparently buggy and hard to maintain. IMO, the screen reader version should just basically be the LaTeX source, which is probably kind of awful when read out loud, but at least it would be unambiguous.
- zerocrates 3y ago
  I bet the "reading" modes of the browsers are just using the HTML that's visible on the page, but that's marked explicitly as hidden from screenreaders, using the aria-hidden attribute.
  - mgunyho 3y ago
    From what I can tell it's the opposite (on Firefox): the math is in the source HTML twice, once in <span class="katex-mathml">, which is hidden using CSS in the non-reader mode but is rendered in the reader mode, and <span class="katex-html" aria-hidden="true">, which is what FF displays normally, and it's missing from the source when I inspect it in reader mode. Having two spans like this comes directly from KaTeX, whose authors I'm sure have thought about accessibility. I imagined that MathML would be somewhat standard and screen readers would understand it.
    - zerocrates 3y ago
      Huh, you're right about what the Firefox reader mode does. I'm somewhat surprised it uses the MathML. I'd just assumed what was happening from the 2pi in the header becoming plain text but that header is probably a special case and just from the page title rather than the h1.
deleted 3y ago
[deleted]
jacobolus 3y ago
What screen reader do you use? As a sighted person with no screen reader experience I tried Apple's VoiceOver on some math heavy Wikipedia pages and found that it completely mangled the formulas there, e.g. not distinguishing between numerator and denominator of fractions, not giving any indication of the difference between a coefficient versus an exponent, pronouncing invisible formatting commands, and so on. Are there any websites with extensive, complicated mathematical formulas which are accessible to screen reader users? What's the current state of the art? In general, would you prefer a typeset formula navigable in the usual way by a screen reader, or an explicit English language fallback explicitly pronouncing the formula the way a lecturer would read it to a class? I ask because from what I can tell there are few if any screen reader users among authors of Wikipedia technical articles. I at least have quite a poor understanding of how to make those articles accessible. Do you mind if I email you to ask questions about screen readers and mathematical formulas?
jraph 3y ago
Wow, I'd be interested in knowing how to fix this. I don't currently write math on the web but if I had to, I would be tempted to do it exactly like this: bare HTML with MathML, no JavaScript. And would do it thinking about blind people relying on accessible content to read it.
xingped 3y ago
Hi! I'm trying to work on understanding how to make websites more accessible right now and probably the first thing people generally think of are blind users. However, I'm having a hell of a time figuring out how to use screen readers. Is there any screen reader or documentation/tutorial you might recommend for sighted users to learn how to use screen readers?
hoten 3y ago
Do you have any additional examples of webpages that fail to be readable for you (math-related or otherwise)? I work on an accessibility tool for web developers, and would like to see if we are detecting those bad cases correctly.

by ctoth 3y ago

jovial_cavalier 3y ago

I'm curious how blind people normally engage with math. For me, engaging with math almost always means conjuring up a visual representation in my mind. Failing that, an equation. Since visualization is so fundamental to doing math, and since mathematical symbols and equations are a written language for which there is no spoken analog, I really can't imagine engaging with math without my eyes. Even reading equations aloud verbatim is not reliable. "X plus B squared" can mean (x + b)^2 or x + b^2

kybernetikos 3y ago
The way I've heard those distinguished in spoken math is x + b^2 is said "x plus b squared" and (x + b)^2 is said "x plus b all squared. There's a similar approach for divide "x plus b over 8" vs "x plus b all over 8". That was often enough but if it wasn't you'd be reduced to pronouncing brackets.
- Sharlin 3y ago
  Using postfix operations in the Way of Forth would be unambiguous and of course otherwise superior as well as is well known [citation needed]. “x b plus squared” vs “x b squared plus”. Well, at least as long as it’s agreed on whether “x b” means two variables or one with a two-letter name. But the latter don’t really exist in math. You just expand to new alphabets when you run out of letters.
nilstycho 3y ago
I had a math graduate student teaching my linear algebra class. He taught dot and cross products entirely algebraically, never drawing vectors as arrows, but as arrays of numbers. When I suggested after class that teaching the visual representation might help some students, he pushed back. Visual understanding, he explained, was a crutch best avoided, because visual intuition could break down in higher dimensions. I thought that was a surprising perspective from a math graduate student, of all people.
- anvuong 3y ago
  This is quite true, especially true when talking about direction (gradient) in high dimensional space. I don't think this can be avoided, since after all we are creatures living in 3D space where left right up down are quite well-defined, just need to make a mental note every time you have to deal with more than 3 dimensions.
- jameshart 3y ago
  Seems like an odd choice when talking about the cross product, since the cross product is only a thing in 3D. You can define analogous things in other dimensions but it becomes clearer and clearer that it’s not meaningfully a ‘product’. So it doesn’t matter if your visual intuition for a cross product breaks down in higher dimensions - a cross product is only a thing in three.
  - jacobolus 3y ago
    This is very off topic, but the wedge product absolutely is "meaningfully a product", generalizes fine to arbitrary dimension, and has a perfectly reasonable visual/spatial/geometric interpretation. (Indeed, we should entirely scrap the cross product in undergraduate level technical instruction and replace it with the wedge product; one happy effect will be replacing students' misleading spatial intuitions with better ones.)
    - jameshart 3y ago
      Or bivectors, or k-vectors, or blades…
ctoth 3y ago
In terms of reading the notation out loud, if there is verbal ambiguity, remove it? For instance, for your example: "X plus B quantity squared" or "x + b squared" You can also do things like change the pitch of speech as symbols are nested, play specific tones to represent symbols, pan things across the stereo field to represent groupings, and otherwise make the symbolic equation into a multimodal experience. But of course, you can't do any of this if the semantic representation of the equation is lost and it is rendered as strictly graphics or whatever. I'm a bit confused to your original point about visualization because how ever in the world could I program if I couldn't abstractly manipulate symbols? I suppose not visually, but there's something non-word-oriented happening in my head.
- jovial_cavalier 3y ago
  >I'm a bit confused to your original point about visualization I guess I find that programming is somewhat more word-oriented than pure math. For instance, how do you think about complex exponentiation, or a rotation matrix? Do you bring to mind the sensation of spinning around? For myself, I bring to mind the image of the entire complex plane rotating and stretching along a spiral, but I'm led to believe that those who are blind from birth aren't really capable of doing that. Harder examples might include fourier series, convolution, gradient descent, etc. I think you could almost consider the visualization of these things like a crutch. I wonder if not being able to visualize them might remove preconceived notions about how they behave, and give you different insights.

curtis3389 3y ago

> review their math content with a screen reader before publishing I second this for anything you put on the web. I opened the webapp I work on with a screen reader, and it was an incredibly valuable experience. You get to see your site from a different perspective, and various issues stand out like a sore thumb, and I honestly found fixing the accessibility issues extremely satisfying.

noman-land 3y ago

Thank you for sharing your experience. Web accessibility has a long way to go and reminders like these help.

sebzim4500 3y ago

The equations are in mathml, I feel like the issue is with the screen reader.

RogerL 3y ago

But what is the answer? What should I do differently? I get don't use images, but then what? I can't imagine all screen readers have the same capabilities, or that there is a base common ability, so what should we do? Googling says MathML is the answer (e.g. https://www.washington.edu/doit/how-do-i-create-online-math-content-accessible-students-who-are-blind); https://www.washington.edu/doit/how-do-i-create-online-math-... this site uses MathML and your reader isn't handling it. So now what? (alt-tags? something else?)

bjornasm 3y ago
One option would be to do testing with screen-readers and then find out if the content works, and if not find out why.
- patrec 3y ago
  I think most people are fine with the idea that some of the costs (monetary and otherwise) arising from disabilities should be transferred from the people suffering from them to society at large. But I don't think it's reasonable for producers and users of broken screen readers to expect everyone (including authors of private blogs posts) bending over backwards to accommodate them, nor is it a remotely efficient use of societal resources. It also creates completely perverse incentives.
  - User23 3y ago
    If there is a bug in the screen reader then that's on the vendor. However the overwhelming number of cases where a website is unusable with a screen reader are due to lack of proper semantic tagging, like alt text and so on. The last thing a screenreader user wants to hear on a site is "button," "button," "button..." There's certainly room for tooling to help though. I definitely think it sucks that many accessibility linters are nonfree and thus will never be used by site devs who aren't worth suing. It's worth remembering that accessibility helps everyone, not just the disabled. In fact one of the more popular arguments against accessibility is that it allows non-disabled persons to do more than intended. So while there's a good argument to be made for being charitable to those with a frankly really lousy condition, if you just want to be self-centered you still benefit from properly tagged data.

mgunyho 3y ago

Author here, I'm sorry to hear that it doesn't work well with a screen reader. I tested it with the reader mode of Firefox, which renders MathML perfectly, although I don't know how that would translate to a screen reader. Safari reader mode renders the math inline, like this: I just define a new derivative operator, like so: dxđ f(x)≡2π1 ⋅dxd f(x). That’s all. while Chrome's reader mode just fails to recognize the content entirely, even though it's the most basic <body><div id="content"><p> ... structure possible. I have basically zero web dev experience so I don't know how to fix this, maybe I need to tweak the KaTeX settings. I think it's quite sad that math is so difficult on the web. While setting up the blog, I looked around and it seemed like FF is the only browser with proper MathML support, but I think that was also being phased out because it's apparently buggy and hard to maintain. IMO, the screen reader version should just basically be the LaTeX source, which is probably kind of awful when read out loud, but at least it would be unambiguous.

zerocrates 3y ago
I bet the "reading" modes of the browsers are just using the HTML that's visible on the page, but that's marked explicitly as hidden from screenreaders, using the aria-hidden attribute.
- mgunyho 3y ago
  From what I can tell it's the opposite (on Firefox): the math is in the source HTML twice, once in <span class="katex-mathml">, which is hidden using CSS in the non-reader mode but is rendered in the reader mode, and <span class="katex-html" aria-hidden="true">, which is what FF displays normally, and it's missing from the source when I inspect it in reader mode. Having two spans like this comes directly from KaTeX, whose authors I'm sure have thought about accessibility. I imagined that MathML would be somewhat standard and screen readers would understand it.
  - zerocrates 3y ago
    Huh, you're right about what the Firefox reader mode does. I'm somewhat surprised it uses the MathML. I'd just assumed what was happening from the 2pi in the header becoming plain text but that header is probably a special case and just from the page title rather than the h1.

deleted 3y ago

[deleted]

jacobolus 3y ago

What screen reader do you use? As a sighted person with no screen reader experience I tried Apple's VoiceOver on some math heavy Wikipedia pages and found that it completely mangled the formulas there, e.g. not distinguishing between numerator and denominator of fractions, not giving any indication of the difference between a coefficient versus an exponent, pronouncing invisible formatting commands, and so on. Are there any websites with extensive, complicated mathematical formulas which are accessible to screen reader users? What's the current state of the art? In general, would you prefer a typeset formula navigable in the usual way by a screen reader, or an explicit English language fallback explicitly pronouncing the formula the way a lecturer would read it to a class? I ask because from what I can tell there are few if any screen reader users among authors of Wikipedia technical articles. I at least have quite a poor understanding of how to make those articles accessible. Do you mind if I email you to ask questions about screen readers and mathematical formulas?

jraph 3y ago

Wow, I'd be interested in knowing how to fix this. I don't currently write math on the web but if I had to, I would be tempted to do it exactly like this: bare HTML with MathML, no JavaScript. And would do it thinking about blind people relying on accessible content to read it.

xingped 3y ago

Hi! I'm trying to work on understanding how to make websites more accessible right now and probably the first thing people generally think of are blind users. However, I'm having a hell of a time figuring out how to use screen readers. Is there any screen reader or documentation/tutorial you might recommend for sighted users to learn how to use screen readers?

hoten 3y ago

Do you have any additional examples of webpages that fail to be readable for you (math-related or otherwise)? I work on an accessibility tool for web developers, and would like to see if we are detecting those bad cases correctly.