Translating math to english. . .

Factual Questions
1

Does anyone know of any guidelines for translating mathematical expressions to english language?

Our company has to make our website “compatible” for the sight-impaired, dig?

And, apparently there are some sort of text-reader programs out there.

But, we need to get expressions like



f = [(a-b)/c)]*d

translated. (and more complicated expressions, but I’ll use that as an example)

So, I’m coming up with “f equals the product of d and the quotient of the quantity a minus b and c”.

or

“f equals quantity a minus b over c times d”

Notice I can’t say “f equals d times a minus b over c” which I could probably convey to you conversationally.

And,I can’t go reducing formulas in my head

“f equals the quanitty a times d over c minus the quantity b times d over c”.

Basically, I’m looking for a general set of rules for doing this. I can translate the stuff so that it is technically correct, but it’s a sonofabitch finding a clear way, and I’m wondering if there are standards.

I did not get any sort of standards with the assignment.

Also, is this term “the quantity” archaic to you?

If I was really trying to get you to write what I was saying, I’d probably say,

“f equals open square bracket open paren a minus b close paren over c close square bracket times d”.

You see why this is getting a little crazy, right?

2

“Translating” a long, complex expression is a losing proposition. Unless you have to squeeze it through some sort of filter that scrapes off everything that’s not words, it’s easier to keep things in algebraic form. Even people comfortable with math are going to see your “translated” wordy expresions and find them damned near incomprehensible.
It, for some reason, you DO have to turn these expressions into words, it’s probably better to break up complex expressions into small, manageable units, and express each of those in “English”, and combine them. It’s easier to define, say, Alpha and Beta, then say that the result “Gamma is the square root of the sum of the squares of Alpha and Beta” that to try to do the entire expression in one shot.

Anyone having to work with this will thank you.

3

This way lies madness.

For this example, the best I can think of is this:

“f equals the quotient d over c, times the sum a minus b”

The idea being to group expressions into words like “quotient” and “sum.” I don’t see how you can avoid rearranging the terms. Even so, it’s a bit ambiguous. The comma is ungrammatical, but it might cause the speaking software to pause, separating the terms a little.

4

I think this is the only reasonable approach. A bunch of short equations is much easier than one really big one.

5

You are going to have separate sight-impaired and sighted versions, right? I’m all for access, but if you only present the wordified version then, well, it would not be pleasant.

You really ought to get a copy of the most likely speaking software so you can tell what it’s going to do with your site. Macs have text-to-speech built in, but I can’t get mine working just now. (Probably a preference thing.)

6

Google “508 compliance”. We have to.

As to the suggestion of breaking everything down into “alpha over beta where alpha equals gamma minus delta where gamma equals average yearly rate etc.”

is probably the way to go, and the way we’re conceiving it, since we tend to program that way. However, I haven’t heard, yet, whether the translations are supposed to be “verbatim” to what’s on the page, or something that is more translatable to a mathematician following along.

But, the documents will remain in original mathematical form AND have to be translated as I describe. The user who would actually hear such a translation and follow along? Inconceivable that this person exists.

7

This is not intended to be a commercial for the company, but if you contact the engineers at Freedom Scientific (formerly French Scientific :D), they might be able to point you in the right direction. Try googling keywords, Freedom Scientific, JAWS, contact us.

8

I think you’re reading more into this than is necessary. Section 508 does NOT require that everything be translated into english words. The screen readers for blind people can read numbers and symbols, after all. And blind engineers are used to hearing an equation read with symbols, and translating that inside their head into a mental model.

My niece, who is blind and works for the Federal governmen in evaluating websites for compliance, refers to tactics like you are asking about as combative compliance. Designers deliberately make their ‘compatible’ versions of the website confusing, complicated and unmaintainable, because they are opposed to the whole idea of accessibility. (Or just offended that anyone might critique their wonderful design!)

I’m not saying that this is why you (or your bosses) are doing this, but you might ask for some clarification on this: what makes them think that converting equations into english words is required by section 508?

9

Honestly, we’re not sure what is required. But, I’m not being combative about it. I came here asking in good faith about whether there are standards for doing this.

However, here’s the result of some of the research this has made me do. . .

Basically, I see the main idea as this, “Section 508 also requires that individuals with disabilities, who are members of the public seeking information or services from a Federal agency, have access to and use of information and data that is comparable to that provided to the public who are not individuals with disabilities, unless an undue burden would be imposed on the agency.”

OK, sounds fair.

And, from the 508 page. . .

Hmmmm. . . .

non-text element – any element that is not presented in electronically readable text and that conveys meaning that is required for comprehension of content or to facilitate navigation. (e.g., an image, image of text, graphic, audio clip, or other element).

::Trunk keeps digging::

HOWEVER. . .I’ve checked the HTML and it looks like the equations are an image, not from a Math Mark Up Language.

HOWEVER 2: it also looks like someone wrote some kind of MathML (I don’t know MATHML, but I know LaTeX, so I figure it’s a similar idea).

The upshot of all of this: I’m where I need to be for the time being.

Thanks all.

10

Since nobody else has answered this yet, I’d say “No, it’s not archaic.” The way I’d pronounce something like (x + y)[sup]2[/sup] is “the quantity x plus y squared” or “x plus y, the quantity squared” (or, if I’m feeling literal, "x plus y in parentheses, squared).

(As a math teacher, I do a lot of pronouncing of mathematical expressions. I try to say out loud everything I write on the board. It’s a habit I got into my very first semester as a teaching assistant, when I had a blind student in my Calculus section. And I try (which is not to say I always succeed) to say things in such a way that, hopefully, my listeners would be able to write down the correct formula just from hearing me say it.)
Edited To Add a quote from one of my math profs: “It’s dangerous to ask old-fashioned people if something’s old-fashioned.”

11

Are there few enough expressions that you can do them individually, or are you looking for some kind of universal algorithm?

I’d pronounce the equation in the OP as, “A minus B, all divided by C and then multiplied by D”, in order to keep the form of the equation consistent.

I use “quantity” all the time, usually when talking about squares, cubes, and roots.

12

I had a blind professor teaching graduate physics electromagnetics. As he wrote, he also said everything, since the legibility wasn’t that great. Your example

f = [(a-b)/c)]*d

would be something like

“f equals left bracket left paren a minus b right paren slash c right bracket times d”

This is unambiguous, and you can even see how you could write a simple translator to automate it.

13

I don’t understand why you wouldn’t just transcribe it like so:

“f equals open bracket open paren a minus b close paren divided by c close paren close bracket times d.”

What would be wrong with this?

-FrL-

14

The extra “close paren”? :stuck_out_tongue:

15

Wouldn’t the text reader read “[” as “open bracket” anyway?

16

Oops, I see you already made the same suggestion.

But I think you’re missing a paren…

-FrL-

17

Hey, you’re right. <Shakes fist at Trunk>

18

This is off-topic, since it doesn’t involve accessibility, but if you’re doing math take a look at this: a way to do math in webpages without using images*

full disclosure: not affiliated in any way

19

See, that seems fine to me if you were describing it to me.

But, I don’t know if that’s the best way to describe it to a blind person. Does that person get “open bracket” “open paren”? It might be. I just don’t know.

Or, would they rather hear “f equals the product of d and the quotient of the quantity a minus b and c” which describes what is going on without the text symbols of “bracket” and “paren” at all.

See, I don’t know WHAT the text reader does. But, I do know that if an expression is inserted into a web page as a gif, that it doesn’t read that.

Thanks for all of the suggestions. I’m meeting on this again today.

20

“quantity a minus b” = “difference of a and b”

it would be pretty unambiguous if you did the whole thing that way, you’d be converting from infix notation to prefix notation.