Mark Boyden: Welcome, I'm Mark Boyden. I am the IT cowboy for Knowbility.
I wear a few other hats, too. We are a small but mighty non-profit in Austin, Texas.
You are welcome to be a digital ally. You are here…
For the equalize editor, a web app for Braille math document translation.
And I'm pretty excited to see this one today, too, myself.
A little bit about Knowbility.
This be a digital ally program is a monthly program with the goals of covering the basic skills and principles behind accessible digital design?
And to make digital content accessible to people with disabilities, which is effectively our overall mission.
And the audience is content creators of any skill level and those newer to accessibility, because those are the people that are interfacing
With the people who want the content.
Um, thank you for letting us be a part of your journey.
We always strive to have an inclusive and accessible space here at Be a Digital Ally and all our events and programs.
We ask that we all be kind, polite, and respectable of each other, and to ensure accessibility.
A little bit about Knowbility before we get started. We're an award-winning leader in digital accessibility. As I said, our mission is to create an inclusive digital world for people with disabilities.
Founded in 1999, about 26 years ago.
We are a 501c3 nonprofit based in Austin, Texas, and operate globally.
These are our primary community programs. The Accessibility Internet Rally, which is a hackathon I'll tell you about a little bit more in just a moment. AccessU, which is our upcoming digital accessibility conference.
And AccessWorks, which is a community program that brings
People with disabilities who want to do real-world testing for
payment, uh, we bring them together with those who need it.
Uh, we do K-12 digital accessibility, and this program, be a digital ally.
The Accessibility Internet Rally, it was our key program we started a little over 26 years ago, before Knowbility became a thing.
We bring together web developers with nonprofits, artists, and musicians.
They work together to develop a website along the way. We train the web developers how to build digital web media and technologies.
Tonight, weak accessibility program that ended a few weeks ago. The sites are being judged by our judges because it's a
fun, uh, competitive program.
The winners actually get tickets to our conference, and we have an awards ceremony coming up January 15th.
And if you're interested, you're welcome to join us for that program, either online or in person.
For more information, you can go to Knowbility.org slash air about this great program, but I recommend everybody tell everyone about it because it's great for nonprofits.
And artists and musicians who need websites, and it's great for the web developers, and the cost of entry is extremely minimal.
We also have a training conference coming up in May. Always an exciting time where we bring hundreds of people together to learn about digital accessibility. It's a hybrid event.
Where you can fully participate online or in person in our… in Austin, Texas at the St. Edwards University campus.
For more information on that, Knowbility.org slash AccessU.
We are in the… that time of year where we're doing an end of year fundraiser. We'd appreciate if you would support our work.
You and everybody like you are what keeps us going to be able to make this
work happen.
And we have improved technology access for millions with disabilities in our 25 years.
Our programs are free.
like this program, very low cost, like air, and provides scholarship opportunities like AccessU.
Tech equity relies on support of the whole community. You are part of that community. Please give to our year-end fundraiser at Knowbility.org slash donate, and together we'll create a more…
accessible digital world.
The other way that we bring in a little bit to cover what…
you and me and everybody else together can't, uh, help make it cover. We provide some services, so…
We work with corporations, government institutions, and anybody else that needs that assistance in accessibility testing and auditing, so we can audit your website and take a look at how that all works and what needs to be fixed, and help you
figure out how to get it fixed. We also work with teams and management to develop leadership and strategic consulting aspects.
We work with teams and build training programs, or bring in already pre-built programs.
Told you a little bit about Access Works, but the corporations, governments, and people who need this assistance are who come to us and look… looking for people.
Who can do real-world,
Testing by people with disabilities.
We also offer an accessibility help desk where you can buy blocks of time and contact us.
as needed to get assistance on any of your digital accessibility needs.
Later on the program, right afterwards, I'll ask you to give some feedback. I just want to remind you to stick around briefly so you can grab this QR code, or you can take it now. The URL is Knowbility.org slash badasurvey, B-A-Digital Ally Survey.
B-A-D-A.
Um, and you can stay connected with us. We have a monthly newsletter we put out, Knowbility.org slash subscribe. You can follow us on all the social medias.
And you can always email us at events at Knowbility.org.
Next month, in January, is Creating PDF forms. It will be led by Teenya Franklin, who is our Director of Community Programs and a PDF Accessibility Expert.
Now, a little bit about, uh, how we'll handle things in this program, and then we'll get started. You can ask your questions anytime in the Q&A, down along the bottom of your application screen, there are a bunch of buttons.
And there is a Q&A button.
You will also, if you'd like, you can ask in person. If you raise your hand, we will, um…
Sorry. If you raise your hand, and that is in the panel items or the menu at the bottom, it's under React, and then you'll find a raise hand label.
And if you do that, we'll find a place and recognize you to be able to unmute and ask your question in person. You can also type them in the chat.
Um, if that's the only place you can get to us with.
So at this point, I'd like to present to you the man who created this wonderful thing, and has
brought it forth,
to all of us, uh, so…
Sam, I'd like to turn it over to you. I introduce you to Sam Dooley. Take it away, sir.
Sam Dooley: Thank you so much, Mark, for the opportunity to present.
The Equalize Editor, let me make sure that I can…
share my screen here.
There. Not gonna be a whole lot of slides, but I did want to put up a title slide so everybody knows, yes, you're in the right place. I'm going to be talking about
The Equalize Editor, which is a web application for Braille math document translation.
And… see if I can…
switch to my contact information. This will be around in the background, but I'll also bring it back up near the end of the talk. But now you've seen the entirety of my slides today, because the rest of the talk
today will be a demonstration of the Equalize Editor. So I'm going to switch to my web browser.
I happen to be using Google Chrome, but any other browser should be able to do. The URL that I'm using is lakepinesbrail.com.
slash EE. This is the…
website, where the Equalize Editor is hosted.
The Equalize Editor is a free, web-based application.
It allows Braille professionals to create, translate, remediate, and deliver braille-accessible, interactive documents using UEB-contracted text and Nemeth Braille math.
And we're gonna, as we'll see today, the user interface allows both sighted and braille users
equal access to the online math content, both in the authoring slash creation phase, and also in the consumption reading the document.
And being able to modify the document in interesting ways.
So, just by way of, uh, visual description to give people a little bit of context, the Equalize Editor contains
a large input area, which operates as a normal visual editor.
Outside of the input area, above the input area, and afterward in the tab order, there is a series of quick bar buttons.
For things like plus and minus and times and divide that have tooltips, both in text and in braille.
Now, if I get to the end of the quick bar, I get access to a set of sidebar panels.
That include expandable panels,
which contain even more operations, and we'll talk about those as we go through.
Before the…
Uh, input area in the tab order.
There's also a set of application menus, file menu, drive menu, edit menu, view menu, help menu, and we'll cover some of those as we go through the demo.
Also on the screen, below the input area,
is a visual panel that displays the braille equivalent of everything that's in the input area.
So if I want to create Braille using the equalize editor, I can just type in plain text.
the quick, round fox.
jumped over the lazy dog.
And as I type in plain text,
The Equalize Editor converts it to contracted UEB,
And displays it in the Braille panel, and echoes that
to any attached rail display that your screen reader is communicating with.
I could also switch to…
Home row key entry mode, and use the home row keys of the applic- of my computer keyboard.
to type Braille in a similar way. So I could type .6
T-H-E…
Uh, QK, real quick.
B-R-O-W…
in… and as I type each word…
The Equalize Editor will type whatever,
Royal, I type in and convert it into
Uncontracted text.
to put into the document, if I can type the braille today.
I'm typing the same letter over and over.
P… ED, and this is how you know that it's a real demo, is that you're going to get typos and stuff like that as I go along.
O-V-E-R.
And so on. The…
L-A-Z-Y
D-O-G.
And clearly, my braille typing is not nearly as fast as my QWERTY typing.
But the idea is that whether I'm typing as a sighted user, using a computer keyboard, or whether I'm typing in Braille using the Braille keyboard, I'm creating the same content here in text in both cases. So if I come up here to the File menu and say Alt-Shift-F,
V for view, S for source, what I see is that this document is represented in HTML. So I see an HTML paragraph,
For the text for the first line I typed in.
and an HTML paragraph for the second line that I typed in.
And they're exactly the same paragraph.
I can't tell at this point which one I typed in Braille, and which one I typed in as a sighted user.
I could do the same thing with math. I'm going to remove this second line, because I don't only need one of them.
But if I want to type Ctrl-Alt,
M, I can type visual math that then is going to be converted to Nimeth Braille on the fly. So if I type…
Why?
equals V…
underscore zero.
Close parenthesis, T.
plus 1 slash 2, close parenthesis, a…
T squared,
I get a simple equation that might just represent the vertical motion of that quick brown fox as he jumps over the lazy dog.
And as I type in that equation, it appears in Nemeth, here in this bottom panel, and therefore on the Braille display.
At the same time. Now, just like I can type in
Text using braille. I can also type in…
the math using Braille as well. If I switch back to home row key mode, I can say that I want a displayed equation by entering the begin Nemeth indicator,
And now I have a displayed math equation.
And I can type in Y…
Two braille cells for equals.
The subscript.
0.5 to return to baseline.
T plus…
open fraction.
1 slash 2…
5 to return to baseline again. I could also have typed the close fraction indicator at that point.
T, superscript to return to baseline.
And I've typed a math equation, both as a sighted user and as a Braille user.
And when I create these equations, whichever way that I create it,
Again, going back to
the document that's being produced,
In this case, the document that's being produced still has that paragraph that we created earlier, but now in the second paragraph,
We have a bit of markup.
That's encoded in MathML.
That's a very special kind of mathematical content math ML, that I'll explain in a moment.
But once again, regardless of which way I typed it in, I've got two paragraphs now that have the same markup in them.
And I can't tell whether I created them using
The cited user interface, or using Braille.
Now, I'm gonna go ahead and…
make it to where they only have one of these, I don't need two copies of this equation.
Now, going back to this…
source markup. If you've encountered
Content MathML before.
then that's going to be very unusual. If you encountered MathML at all, what you've probably encountered is something called Presentation MathML.
Which represents the way that form… that math symbols
are…
Written on a page.
So it's very good at creating a pretty picture of the math, but not very good at telling you what the math means.
Content MathML is an XML markup.
That's part of MathML that represents things like equals,
Plus… times…
subscript.
divide, power, and so on.
that tell you something about the formula that's being created.
And so, when you get done creating content in MathML using the equalize editor,
What you get is an unambiguous representation of the formula.
You can get that using… as a sighted user, timing it as a… treating it as a visual math editor.
Or, you can get it using Nemeth Braille.
And again, in either case, the formula that's created
is displayed visually for the sight to the user.
And it's also displayed in braille for the Braille user.
And either method creates ContentMathML in HTML context.
So the equalize editor allows visual users to create Braille documents, and Braille users to create visual documents using an accessible authoring process.
It creates really accessible, interactive documents so a sighted teacher can create accessible documents without using braille.
The Abrail student can read.
And a braille student can create visual documents using only Braille.
that a sighted teacher can read.
Now, if I wanted to continue this example a little bit, I could…
turned back into, uh, QWERTY entry mode, so I can type this a little faster.
And I could say, well, in this equation, I want to explain it a little bit. I can say…
Ctrl-M, V sub 0.
Ctrl-M to exit math mode is the initial velocity.
If I could type today, if I could spell.
A is the…
Acceleration of gravity.
And… Well, what does the gravity? Let's see, if I remember right, that's minus 9.2
8 meters…
per second.
squared.
End of math, comma,
Comma.
And… T…
is the elapsed time.
So now I've got a little, uh, mini-lesson that I could entitle,
a basic…
equation of motion.
I could say CTRL-Alt-1,
To turn this first line into an H1 title.
And then when I look at the source file for this document, I've got my header,
I have my paragraph that has only text in it.
I have the paragraph that includes only math in it.
Then I have another paragraph that contains both text and math interleaved.
represented in HTML, plus content MathML.
This is great. So now I can…
save this file, I'm going to save this.
As source. I'm gonna call this
FoxMotion.equationEditor.
Because it will save the content markup and HTML markup needed to represent the document.
And load it back in.
Then I could take this document, I'm gonna go ahead and replace the version that's there.
And share it.
with someone else. They can also run this…
this program.
Just log into the website, I could go File,
Open, navigate to that file, and open it, and now I've got this file loaded back in.
And so, now the student can read this document,
Either as a sighted student or as a Braille student.
And understand what happens when the quick brown fox jumps over the lazy dog.
Now, if I'm an instructor and I want to make a little bit of a quiz out of it, I could come in here and say, well, maybe I want to remove some of this.
see if I can make this work.
And I'm going to use an omission symbol.
to fill in.
these words.
That V0 is… well, I don't remember what ZV0 is anymore.
I don't remember what A is.
I don't remember what T is.
And so that's going to be kind of a mini-quiz.
For the students, where that if I distribute this document,
Let's save that as…
The quiz?
to replace it. And when the student loads that in,
They have the opportunity to navigate here to these emission symbols, and for the villain, let's see, what was V0?
It was the acceleration.
Gravity?
No, it wasn't.
See, I've already got my own quiz wrong. That's why you know this is a real demo. V0 is the initial velocity.
A is the acceleration.
of gravity.
And T is the elapsed time.
And so, you can imagine giving a quiz to a student,
who reads Braille, not having typed…
A single braille cell.
Send the quiz to the student,
And have them return it to you.
in real time, or near real time.
It's kind of hard to give a pop quiz if it takes a week
to prepare the pop quiz,
out of line, the student will see it coming.
So, cited teacher can share this simple quiz with a Braille student or a sighted student without having to code the Braille themselves.
And now the Equalize Editor then creates Braille-accessible documents from visual or braille mathematation,
Using keyboard input, and produces print and braille output presentations that are accessible to either audience.
It also provides editing tools to allow you to remediate common class… classes of visual math tool limitations.
And do all the kinds of interactions that you would hope to do with a visual math editor.
But you can control it all within Braille.
Now, the equalize editor can save output files that contain lots of different markup formats. We've already seen…
the source markup used by the equalize editor as HTML, plus ContentMathML.
You can also look at…
the HTML markup,
produced by the Equalize Editor, which includes HTML,
Plus, MathML.
That is…
ready for display inside a web browser.
or we're inside a web browser. Why don't I just take and…
preview that HTML.
And now I've got a dynamic web page that is the basic equation of motion that we just typed in.
And not only that, I can tab to the math,
And… get…
all the MathJacks support that I might want from the webpage that I just created dynamically.
And you didn't have to use any of the math markup to be able to make that happen.
Now, if I can create that kind of a web page, I could also
print it as HTML.
Where, by just invoking the print dialogue from the browser.
So it says, here's my document, and I can either save it as PDF,
Or if I happen to be connected to the right network, I might be able to connect to my printer that's at my house, and I can go ahead and print that off.
exactly the way that MathJacks will
display it.
In addition, you can also produce
BRF files. So,
If you're look… if you're watching…
The output here from a basic equation of motion
And you see that this is…
computer braille, and if you can read this computer braille, my condolences to you.
It's a little bit tough to read, but there's an act to it. Certain
Uh, symbols.
are mapped to Braille patterns, and you can learn to recognize that the open curly brace is the OW contraction, and so on.
And this is the same BRF notation that you could then
send to a Braille embosser.
So, if your technology is aligned correctly, and
You've done all the right connections, and so forth, you can say print…
PRF, and if you have a braille embosser on the list of your printers,
then you could send this BRF file directly to your printer.
In most cases, what you'll want to do is take the BRF file, save it to a file,
And loaded inside another program like Duxbury, that's more familiar with how to communicate to your embosser.
You can also, uh, preview.
a BRL file,
Which uses a Simbraille font to display the actual Braille contents.
In a visual form, so that if you're a sighted user and you want to
copy edit the Braille that's being produced. You can look through this before you
Imagine sending it to your embosser.
So with all these different file formats, the Equalize Editor
rail workflow supports the standard braille formats that can be used by other well-known
rail tools and devices, so that you can get
The document that you want to create,
into the Braille format that you need, and deliver it to the location where you need it to deliver it to.
So far, we've taken a look at the use of the equalize editor with the file system. You've seen me use File Open, File Save.
which writes to your local machine.
You can also interact with Google Drive.
So if I say drive open instead of file open,
Google will authenticate me as what user I want to use, and then it will connect me to
folder picker.
Where I can navigate to whatever file that I want to open. I'm going to go back and…
open a copy of Foxmotion.exe,
As I saved it over to Google Drive, and that this is a convenient way to distribute to other Google Drive users. So this file is now on Google Drive. I could now save it on Google Drive.
And…
I want to select a folder to save into.
And once I select that folder…
There, I want to select the folder. It will ask me for a name of the file, and then I can save it off into that file.
I want to cancel out of that.
In addition,
The equalize editor can be integrated into the Google Drive user interface, so if I say, help
samples, it will bring up the Google Drive user interface using my user.
And I've created… I have my Google Drive folder that has some files that I created for the purpose of this demo.
And I can come in here and select one of them.
And say that I want to open that with the accessible equation editor.
And it will open that document in a new window.
So in addition to being able to use
file system, you can also use
Uh, Google Drive to get to…
these files and to share them with others.
All right.
Unwinding some of that.
So that you can add the equalize editor as an app to Google Drive so that it will allow you to open these files from the Google Drive user interface. Alternatively, you can use
equalize editor drive menu to open and save files contained in your Google Drive space.
And using the equalize editor with Google Drive provides a convenient, shared workflow between cited teachers
And real students.
I'm fully aware that Google Drive itself
is not the most accessible user interface.
But with better integration for these kinds of tools, we can
mitigate that somewhat.
Alright, any questions so far before I move on to the next…
portion of the demo.
Mark Boyden: Uh, the… so, Nancy asks…
Can a screen reader use it with any OS and screen reader? How is a screen reader user's location indicated?
Sam Dooley: How is the screen reader's location indicated? Well,
The equalize editor works inside of a web page as an application,
And so there are special ways that the screen reader interacts with
forms and other controls and applications within a web page.
And I wish I could say that I…
can predict what exactly a screen reader is going to do at any one particular time with those, but if you're familiar with
Forms mode in a screen reader. That's the kind of technology that will happen.
And as often as possible, the Equalize editor will be in control of
the location that is displayed on the Braille display.
And this is true both using
different browsers, Chrome, IE,
Um, Firefox…
Um, on Mac, Safari,
And on Chromebooks,
Google Chrome, of course.
All of these browsers have ways of interacting with applications running inside of a web page, and the equalize editor will take advantage of
those facilities to do that.
completely answer your question, but hopefully it gives you a little bit of an introduction to the kinds of things that we're going to be able to do.
Other questions?
Mark Boyden: The, uh, the other question, which you may be covering here in a little bit, is can you take plain text math from some other source and paste it here?
Sam Dooley: That is absolutely a great question. I'm so glad you asked that. I'm sorry that I somehow gave you a copy of the notes that I'm using so that you can see what I'm going to do next.
But let me make a transition now, and talk about
Uh, math that can be retrieved from other programs.
So, I'm going to start with Microsoft Word.
So, if you're familiar with Microsoft Word,
Here's a document that I created using Microsoft Word, just by looking at Microsoft's
insert equation.
drop-down box, which contains a list of about 9 or so sample equations that can be created using Microsofts.
Equation Editor. It's got the area of a circle, binomial theorem, expansion of a sum, Fourier series,
Pythagorean theorem, quadratic formula, Taylor expansion,
And a couple of trig identities now at the end.
And you can select any one of these and have it be inserted into a Microsoft Word document.
Or you can use the Microsoft Word equation editor to create these yourself.
Now, I'm not truly a user-level expert on Microsoft Word's Equation Editor.
But there are a couple of things that I can do with it.
So, if, for example, I select this first equation, the area of a circle, A equals pi r squared,
and copy it to the clipboard using CTRL-C,
And what that does is copies
You remember we talked about presentation math ML before? It copies the Presentation MathML that Word produces,
to the clipboard. And so I could type
Windows V and look at
this first piece of markup,
for that equation. Oh, and it looks like I added another copy, which I did not intend to do.
go back to that. You can see that it begins with angle bracket math equals, and this is the same presentation math up… mathML that we were talking about before.
But the equalize editor doesn't rely on presentation MathML, it needs the Content MathML. Well, let's see what we can do with it.
I'm going to copy that equation to the clipboard, I already did that.
back to the equalize editor, I'm going to type Ctrl-V.
And sure enough, the equalize editor is able to take the presentation MathML that was on the clipboard,
con… it was able to convert it
From Presentation MathML into content math ML, and
render that equation,
In Content MathML, A equals pi R squared.
And in Nemeth Braille.
And… I didn't have to type any Braille, I just had to copy and paste.
I don't know if… I know that Word…
probably doesn't have a whole lot of knowledge of Nemeth Braille. If you put it with a screen reader, it probably has more, and I know that there are add-ons to Microsoft Word that help it
work with Duxbury and so forth, but to me, it's much more convenient just to be able to copy and paste.
So I could continue on here, I could take…
This, uh, binomial expansion.
Copy, paste, and I got a summation there. I've got an infinite series.
for 1 plus X to the n…
Oh, yes, and here's my Fourier series.
That has both square root… or sorry, summations, cosines, and sines, and a lot of parentheses and other expressions.
Good old Pythagoras shows up and gives us a very simple equation.
And for each of these equations, I'm taking the presentation markup,
that Microsoft Word is producing.
And converting it to content markup, and thereby to Nemeth Braille.
Some of these tough ones down here include…
interesting operator precedences involving trigonometric functions.
So, something that we often look by… look past very quickly is that 2 times sine times 1 half times alpha plus minus beta.
Sign of the 1 half times the alpha plus beta is inside the sign, but then you want to multiply it times cosine, which is outside.
the sign. And so, interpreting that operator precedence can be a little tricky.
But again, all of these are now represented in Content MathML.
Now, if I wanted to take a deep dive on one of these, copy it.
Get rid of the rest of them, paste it back in, and we could take a quicker look that this equation
is parenthesis 1 plus X to the N.
equals 1 plus…
open fraction N times X over 1 factorial, closed fraction plus
Open fraction, N…
parenthesis and minus 1, close parenthesis,
times X squared,
over 2 factorial and fraction.
Plus… dot dot dot.
And the dot dot dot then gets represented as a symbol in the equation.
So, it would take me longer to…
copy, edit, and take a look at the map at the Nemeth markup that's being created, the Nemeth Braille that's being created, than it does to just copy and paste it.
Now, Microsoft does me dirty. If I want to select everything in the equa- in the document, I can do that, and copy everything.
But then when I paste it into the equalize editor,
Microsoft doesn't give me the nice presentation mathML that I was using just a minute ago. It gives me a plain text representation for the math,
Because it thinks that that plain text needs to be embedded in a larger context. Well, no matter, I can come in here and select each one of these equations,
Type Ctrl-M, and convert…
Each of these pieces of text.
one line at a time into the Content MathML
And the Nemus Braille that I want.
Just to give you a sense that…
Not much in the way of smoke and mirrors going on here.
It's just trying to deal with…
whatever it is that Microsoft Word wants to do, as far as its math markup.
But the idea is that if you've got math markup,
in Microsoft Word as Presentation MathML.
You can copy and paste it into the equalize editor.
as Content MathML.
I got a lot of things in the chat window. I should probably stop for a moment, Mark, and see if there are any questions that need to be, uh,
into the discussion here.
Mark Boyden: The basic, uh…
Uh, wording that's happening in the chat right now is,
Wow.
Sam Dooley: Thank you for that. I appreciate that. Uh…
Any of you that are familiar with MathML, you might recognize that it's very easy to convert from content MathML, which represents the formulas, into Presentation MathML that represents pretty pictures. And the Equalize Editor's been able to do that for some time.
But it's only recently that we've been able to add the capability of being able to
interpret the presentation markup, and produce content markup.
Now, this presentation markup to content markup facility can be used not just with Microsoft Word,
but also with other tools as well. Let me clear this document. And…
I want to switch over to another program that many people might be familiar with called MathPix.
So let me see if I can…
get to my math picks here. I'm going to have to…
There we go.
So I'm going to log into my MathPix account.
And take a look at a particular MathPix SNP.
A MathPix SNP is just a…
Capture of an image that's been loaded into MathPix.
Which can then be…
converted into math markup.
The type of math markup that MathPix produces is it does an OCR on an image, like a PDF,
And it will produce ASCII math,
It will produce LaTeX, where appropriate.
And so we're dealing with the same kind of presentational forms that we see coming out of Microsoft Word.
Now, you know that you're a geek,
a math geek,
If I take a look at my SNPs here, let me go find the… ah, yes.
When your adult daughter sends you a math
image, which is a limerick.
By a text message.
So, my math geek daughter, who is actually a music teacher, not a math geek,
Send me this and thought it was funny.
The image looks like this.
It says, a limerick. The limerick is…
Open fraction, 12 plus 144 plus 20 plus 3 times the square root of 4.
All over 7 in the denominator, closed fraction.
Plus 5 times 11.
equals 9 squared plus 0.
wait a minute, that's not a limerick, that's a math formula.
Doesn't look like a limerick to you? We'll try this.
A dozen, a gross, and a score.
plus 3 times the square root of 4,
Divided by 7 plus 5 times 11 is 9 squared and not a bit more.
Now, this image I found to be very funny, because the math actually works, and it actually
matches the Ryman meter of a limerick, if you read it through.
But for the purpose of this talk,
What we want to focus on is the fact that this is an image.
And so, MathPix has to do OCR to recognize the text and the math,
And to produce something that you can then export to other programs.
Now, if I were to hit the Edit Snip button, it will show me what markup it creates, and it looks a lot like plain text with a little bit of
LaTec inside of it, if you're familiar with LaTeX, LaTeX is almost a programming language that lets you describe what math looks like.
It's another one of these languages that's good for…
producing pretty math pictures.
But I can copy
this markup.
switch over to the Equalize Editor,
and paste it into the equalize editor, and I get both the text
the math formula.
And the lyric.
And… sadly, the equalize editor doesn't know anything about the proper rhyme and meter scheme of a limerick, but you can read it through and
Uh, and decide whether or not it makes sense to you from that perspective.
But again, the idea is that the equalize editor can be used in connection with OCR tools, like MathPix,
convert PDF files into interactive, rail-accessible forms.
So, we've taken a look at different features of the Equalize Editor. It supports FileIO, clipboard, cut and paste, document export to HTML, PDF, and BRF formats. It supports input from HTML, MathML, ASCII math,
Markdown, LaTeX formats,
And cut and paste from programs like Microsoft Word and MathPix and the OCR output that MathPix can produce.
And all of these features, taken together,
position the equalize editor as a tool that can help math document remediation.
in a lot of different contexts.
It is not a one-size-fits-all solution.
Because there is no way that
one application can predict
Where you're getting your math documents from, or how they're being produced, or what formats.
And can predict what type of format you need to convert it to.
You've got a low vision user, and you need an interactive document that you can then scale.
The font size. Maybe you have…
a dyslexic student that needs to feed this
Uh, markup into other software that helps them
deal with the print limitations that they may have.
So all of these things can be done, because…
The equalize editor will produce
these documents using standard markup formats.
Alright, so now, I've got a little bit of time left, and so what I'm hoping to do now is drop into a series…
A part of the talk where we can talk about questions a little bit more actively, and where I can show a little bit more deeply some of the capabilities of the Equalize Editor.
Marker, are there any questions that I should…
handle before I deep into… before I drop into a couple more examples.
Not at this point, sir.
All right, so…
We've talked a lot about Nimeth Math, we've talked a lot about contracted UEB, we've talked a lot about
Entering Braille, and so forth.
But I want to dive a little bit deeper.
The Equalize Editor supports Nimeth output and input translations,
For over 2,200 mathematical symbols. If I go to the Help,
to the settings, open up all of the symbol palettes that are available,
get… some…
these windows out of the way, alright.
And everything from…
arithmetic, free algebra, algebra, geometry, trigonometry, uh…
Calculus. Chemistry.
Units of measurement, math alphabetic symbols,
Greek, Hebrew, Cyrillic…
Bold, italic, bold italic font variations.
These are all the symbols that are supported by the Equalize editor, both for rail input,
and Braille output.
You may recognize some of these forms don't have standard Nemeth Braille…
Uh, corresponding…
Uh, braille sequences defined. So, in some cases, we've had to make some conservative extensions.
Um, I doubt that you will…
You might be able to find, uh, Greek sans-serif, bold italic,
fonts…
in Unicode.
Not sure if…
Nemeth Braille actually gives me a correspondence for that, but you could get it by doing Greek is .46,
bold is .456.
Uh, I just happened to type a…
partial symbol, which is a variant.
Delta, so that would be a…
dot 4, .
4-6 for D. So that's basically…
Greek, bold, variant.
D is used for
Old italic, partial. And repeat that for
like I say, 2200
symbols that are supported.
So these symbols can be entered either by navigating
these pallets, which… these pallets are searchable by sighted users, simply by virtue of the fact I can type in here and
Use the browser search mechanism. If I want to search for, uh…
elements, and I can find my chemical elements.
pallet, which has all the chemical element symbol on it.
Um, sadly, there seems like that there are a whole lot more chemical elements on the periodic table
than when I took chemistry, but that's neither here nor there.
But we can actually insert these into a document
to start building formulas that
that could be used to represent chemical equations and reactions.
Well, I haven't been able to do yet is find an equally accessible way of searching these pallets.
or a rail user.
we'll still work on that.
All right. Couple of examples, since we mentioned chemistry.
We support both chemical element symbols and SI units, so that you can type in, for example,
kilometers as a unit symbol, so if I type in KM,
It will recognize that as a kilometer and represent that in Nemeth Braille as
shape you for a unit?
K, M, and shape.
And then a Braille user could recognize this as an SI unit.
You may… maybe you… maybe you haven't thought about this problem, but can anybody tell me…
An SI unit
whose symbol is the same as a chemical element symbol.
Mark, you're gonna have to tell me if anybody is raising their hand here.
Or did I stump the audience?
Mark Boyden: Well, if you've stumped me.
Sam Dooley: All right, well, we'll give it away by opening a file that I created to show these off.
see if I can go grab it.
Uh…
There are… I found exactly 4…
Chemical element symbols that are also SI units.
So, capital MG is both magnesium
And Megagram?
PM, I think, is Polonium. I may not be pronouncing that right, but it's also Petometers.
TM is terra meters, and I think tellurium or something like that? I don't even know all of some of these. Like I said, these were…
I don't think these were on the periodic table when I took chemistry. I think they added a few of them and snuck them in there. And PA is for pascals, and I think…
uh… protactinium.
is that one. So how do we distinguish these? Well, in Braille, it's easy enough. We can just invent
codes to say that if I want a chemical,
unit symbol, I can type shape
you for units, and then shape X,
or chemistry.
If I want to do this in content math ML,
Oh, nope, nope, nope. Cancel.
File, view, source,
I can use UnitMg for a…
the SI unit, and CH…
MG for the chemical element.
And keep them apart that way, so that I can produce the appropriate braille.
If I take a look at the presentation markup,
Presentation markup is almost exactly the same.
They both use the symbol MG.
One of them is marked as being
sourced from a unit, and one from a chemical element.
And so this approach allows me to take this document, and I can even save out the presentation markup.
which no longer contains the
chem… the content markup,
And I can read it back in and preserve the semantics of what was created, whether it was a chemical element,
or an SI unit.
So, this kind of approach allows me to disambiguate
lots of different mathematical formulas.
that might otherwise be…
difficult to distinguish. If you've ever tried to…
translate a piece of math into braille?
And you didn't know what math you were translating?
And so you didn't know what braille to use.
This is a way of approaching those kind of ambiguities.
All right.
Any other questions so far? I'll see if I can grab one more, two more examples while we've got time.
Mark Boyden: This is, uh, sort of a question, um…
Sam Dooley: Yes.
Mark Boyden: Well, Aunt Nancy says, not playing with this yet as a screen reader user.
I'm guessing that if a colleague typed a worksheet into this, the beginning and beneath indicators would show,
As long as they were in math mode when typing.
Correct?
Sam Dooley: Correct. So if I type in math mode, I can type an equation like AX squared,
plus B… plus BX, if I could type the plus, plus BX plus C equals 0 as a sighted person,
And it includes the open Nemeth and closed Nemeth indicators
around the Nemeth formula when it does, whether it's in displayed mode or in inline mode.
Does that answer the question?
Awesome.
Alright. Couple of other quick things, just in terms of rail entry. I use what's called QWERTY Entry Mode.
For the most part, where I'm acting as a QWERTY computer user, and the…
Equalize Editor acts as you would expect, a math
As we were for a visual user interface to act. I can also use home row key mode.
to simulate a braille display on my
There's a third mode called Rail Entry Mode, where the Equalize Editor is now set up to expect
Uh, computer braille, the way that it would be sent from a Braille display when it's configured to do so.
So, the equalize editor assumes if you've got a Braille display, you set it up to send computer braille, and then if I type
The letter B. That's gonna be…
provide me .12, I hit a space, and it will expand it to the word BUT.
And similarly with other single-letter contractions, you cannot quite have
It just as you will like.
And each time that I'm typing in
computer braille, I can simulate that on my computer keyboard, of course, but I can also get it directly from the Braille keyboard.
And as you type each word in succession from the Braille keyboard, it will expand the contracted form into the uncontracted form at each word boundary.
So if I type B followed by a hyphen, it says, aha, I must be at the end of the word. Expand that to the word but.
Uh, if I also type, uh, let's see, it's quote dash, I think.
Nope. Uh, become a dash is the longer… a little bit longer dash,
double quote, comma, dash, for a M-dash.
And so there's all sorts of knowledge in the editor for handling UEB contractions, for things like hyphens.
For things like, uh, numeric fractions, I could type number sign,
Uh… A slash…
B, and that gives me the fraction 1 half, which is a single Unicode character. I could do slash
1 slash 4, same… whoops.
If I could type it right, slash A slash
D gives me 1 fourth, but if I type number sign
A slash J, which is the fraction 1 over 0. There's not a Unicode character for that, so the equalize editor will leave it as multiple characters.
I could do the same thing, uh, in the UAB.
tech support for things like accent marks. Let's see if I can remember some of my accent marks.
And type some of those in.
If I type in the sequence,
tilde star A in computer braille.
You would do that using your…
Uh, rail display using dots,
5… dots 45 dots 16.1.
That gives me an A with a grave accent.
And so on, I could type in
An A with an acute accent.
type in… whoops, I don't want caps lock on.
Okay. I could type in…
tilde at sign A for circumflex, so the close paren A for a tilde.
Uh, till the DA for a dotted A.
Umlaut underneath. I could even type.
Asidya under a sea.
Or since I had recently lived in Albuquerque, sometimes I like to put the Cedilla underneath the letter K.
giving me a quesadilla.
I know I heard at least one person say they were from Los Angeles. I know they know about quesadillas out there, so I had to make sure that I could copy and paste and make sure that I could bring enough for everybody.
So, there's your dad joke for the day.
Also, quotation marks,
I could type single quote, a quote.
I can type, uh, 8…
a zero for the straight double quote.
tilde 8A, tilde 0 for the curly double quotes.
comma 8A, comma 0.
For the curly single quotes, and so on.
So the equalize editor interprets each key…
As the computer braille code for a braille symbol, and then interprets the braille symbol,
According to the rules of contracted UEB for literary text, or the rules for Nemeth Braille.
If they're typing math.
Alright, one final thing that I wanted to be able to show. We talked a little bit about this, but I didn't get a chance to show it yet.
I'm going to…
create a new document here, and I'm going to load a file.
With some examples of…
Let's see… I want to be…
I want to load a couple of examples of LaTeX Markup.
You may be familiar with LaTeX Markup as another way of representing presentational forms for mathematics.
It has a lot of backslashes and control sequences and curly braces.
So this is the formula that would represent the solution to the quadratic equation.
I can type that into the equalize editor, and type Ctrl-M to convert it to ContentMathML.
Using the same type of features that we were talking about before. We can say e to the i pi is negative 1.
Oh, and here's an interesting chemistry formula that shows off some of the other chemical symbols we were looking at earlier.
Uh, transfinite Cardinals using the letter Alla from the Hebrew alphabet.
a definite integral with its solution.
So, clearly, I could stay here all day long with these kinds of examples. I would love to be able to share everything
editor could possibly do. I'm happy to stay around later and answer.
questions as we close… bring the media… the meeting to a close.
But I wanted to be able to emphasize that the Equalize Editor is a free web-based application.
That allows Braille professionals to create,
Translate, remediate, and deliver
rail-accessible, interactive documents using UEB
contracted text, and Nemeth Braille math.
And the user interface allows both.
sighted, and Braille users
Equal access to that online interactive math content.
So, I promised that I would make it possible for you to
C… contact information. Again, my name is Sam Dooley. My company is Lake Pines Braille.
And the equalize editor can be accessed at lakepinesbraille.com slash EE.
My email address is fam at lakepinesbrail.com, and I am… I would be…
Happy to receive emails from anybody who's on this call. If you have additional questions, comments,
Suggestions. There's also a collection of
Uh, YouTube videos on how to use the Equalize Editor on the YouTube channel Equalize Editor.
And I'd be happy to have you subscribe to that channel.
View the videos, and any suggestions for additional videos you'd like to see, I'm happy to receive those as well.
Thank you so much.
Jan McSorley: Okay, Sam, this is Jan.
I know that, uh, you mentioned it, but could you take just a second and show them the contractions, how you can turn those on and off?
Sam Dooley: Yes, I can. I knew that's where you would be headed. Thank you, Jan.
Jan McSorley: Yeah, you knew that's where I was going, yes, because…
Sam Dooley: Yes, I did. Uh…
Jan McSorley: Guys, I think this is great for kids who've been adventitiously blinded and are…
Maybe late Braille learners, um, in terms of being able to give them content
Sam Dooley: So what I can do is I can drop in here to the options page, like Jan mentioned, and I can turn off all Brio contractions.
I can say, now I can work with the equalize editor as if no contractions existed. So if I type the
Quick brown box.
then everything is in uncontracted braille. The word the spelled out, quick is spelled out, the OW contraction is not used. But now, if I go back to the settings page and drop into the rules, let's see. V is a strong contraction, if I remember correctly.
Uh, QK is a short form.
Let's just do those two and see what we get.
Well, we got the contraction for the word the, good.
We got the contraction for the word quick,
And we did not use the contraction
for the OW contraction in the middle of the word brown.
And that's exactly what we requested, under the assumption that those were the contractions that we were familiar with.
and able to use. And so, as the student would typically progress through this, you'd say, oh, let's just turn on these first few that I've learned so far.
And then I can interact with the program. Well, maybe I'm learning the next set of contractions that I want to be able to learn.
that only has the contractions that they have learned and or are in the process of learning.
So, Jen, thank you for reminding me of that.
Can you… can you tell them again where to get to that?
Just one more time.
Help. Settings.
then under Braille Rules,
You're welcome.
Mark Boyden: Yes, indeed, Sam. Thank you so much. This is, uh, as people have been saying in the chat, this is a game changer. It's just wow.
Uh, Nancy… I'm sorry, Norma was asking about a blind student wanting to take engineering classes, and if this would be helpful.
Which I can't imagine it not be, but what have you got to say about that?
Sam Dooley: What I have to say about that is that the engineering classes will stress the level of math that gets used more than any other classes, I think, will.
But there is support.
As we showed just a little bit ago.
Let me get back to that.
And on the series,
palette for things like summations,
products, integrals,
Uh, multiple integrals, even…
Uh, circle integrals and other large operators that are used in such engineering courses.
Many of the things that are on these pallets are motivated by corresponding operators.
or characters,
that are defined by the Unicode standard. So again, these will use standard Unicode concepts.
standard MathML concepts to communicate these math formulas.
So, yes, I believe it would be helpful, but as with all of this, I would…
Uh, caution that…
Again, since math has such a large learning curve,
The learning curve for finding the symbols
to be used, how to encode them in Nemeth, and how to
Uh, enter them in Nemeth, how to read them in Nemeth,
And so on. It's going to be a little bit of a learning curve, so I'm happy to help out if you've got a particular student in mind looking for particular symbols, and making sure that those are going to work for you in a way that would be successful.
Mark Boyden: Thanks again, Sam. We're essentially out of time, but while I share the feedback code here, one of the questions was, I am so curious about your development process.
Sam Dooley: Haha! Good question. So am I. Uh, no, I'm teasing.
The development process for this software is that it initially started as a project at IBM Research,
to provide a visual,
Math Editor that could be used in interactive
Student experiences in web pages.
and about the Netscape 3.
time frame. So this was mid-90s.
Where some of this was originally being developed.
as it, uh, developed over time,
I was introduced to my first
Royal Student, and to my first Braille professional.
Um, I think Susan may still be on the call, Susan Osterhaus, uh, was a wonderful resource.
for teaching me where to find resources about the Nemeth Code,
And how the technology that I already had in place
for handling
Both content and presentation MathML,
could be adapted to treat Nemeth
rail, as first a presentation,
Output language, and also as an input language, where each Braille symbol
works the same way that keys on the keyboard do.
So, that's a quick view into the development process. This is all written in JavaScript.
And… it is not open source, but it is a free application.
that you can log in and use it.
on the website address that we gave you.
Mark Boyden: Alrighty, folks.
Sam Dooley: Anything else I can answer?
Mark Boyden: I'll bet there is, but uh… so far, nobody has put anything in, so we'll call it a day. Thank you again, Sam, so much for being here, and you guys have the contact info, we'll include that as well.
When we send out the recording information and other accompanying materials.
Y'all have a good evening and a happy holiday, however you celebrate.
Sam Dooley: Thank you, everyone, for coming and attending.