Using Braille to Memorize Mathematical Formulas

Continuing the discussion from Learn Braille In No Time Using Your Binary System:

There have been quite a few times that people here have asked for ways to memorize mathematical formulas and things of that nature. Just like in the post linked above, you can use braille for that as well.

Quick recap: If you have a 00-99 image system, you can create a binary system, and that in turn let’s you encode braille cells. So all of this can be done using your existing system. Click the link above to see how to link your existing system to a braille cell.

This Braille Code for Mathematics and Science Notation has been prepared to provide a system of symbols which will allow technical literature to be presented and read in braille. The Code is intended to convey as accurate an impression as is possible to the braille reader of the corresponding printed text, and this is one of its principal features. When the braille reader has a clear conception of the corresponding printed text, the area of communication between himself and his teacher, his colleagues, his associates, and the world at large is greatly broadened.

A word of caution though… Nemeth is not a worldwide standard and if you want to also be able to read braille resources in your language / region, you might want to have a look here first:

3 Likes

A lot of good values here! Thank you.

Thanks @Erol!

Just had some time and decided to draw up a quick example for people that don’t follows links and this way it’s a bit more obvious in the post itself as well. (I’m using French braille instead of Nemeth by the way.)

5^2 \sqrt{3}\neq5^{2\sqrt{3}}

⠱⠈⠣⠜⠩⠨⠶⠱⠈⠰⠣⠜⠩⠆

16, 01, 34
43, 15, 05
66, 16, 01
06, 34, 43
15, 60

For those of you that don’t have a binary system yet but images for 00…99, here’s how you read the binary as decimal:

① ①
② ②
④ ④

Two columns make a cell and if a dot is raised for that column you add it, so you’ll alway have a value between 0 and 7 in each of the two cells. In the end you can encode the above math expression using your existing PAO system with just 5 locations. Best of all, there is absolutely no ambiguity!

2 Likes

Wow, this is a really innovative technique! How did you come up with the idea of learning braille using binary numbers?

Intuition, that’s just what it looked like to me from the get-go. If I had to analyze it, I’d probably blame ASCII and chmod commands (maybe)…

…if you have a look at the ASCII table and look at the difference between a:A, b:B, c:C, etc. you’ll find that the uppercase and lowercase version of the same letter always differ by the same bit in binary. Something similar happens in braille after the first 10 characters.

\begin{array}{rr|r|r|r} &{\color{green}{①}}\ {\color{gray}{①}} &{\color{green}{①}}\ {\color{gray}{①}} &{\color{green}{①}}\ {\color{gray}{①}} \\ &{\color{gray}{②}}\ {\color{gray}{②}} &{\color{gray}{②}}\ {\color{gray}{②}} &{\color{gray}{②}}\ {\color{gray}{②}} \\ &{\color{gray}{④}}\ {\color{gray}{④}} &{\color{red}{④}}\ {\color{gray}{④}} &{\color{red}{④\ ④}} \\ \hline &A &K &U \end{array}
\begin{array}{rr|r|r|r} &{\color{green}{①}}\ {\color{gray}{①}} &{\color{green}{①}}\ {\color{gray}{①}} &{\color{green}{①}}\ {\color{gray}{①}} \\ &{\color{green}{②}}\ {\color{gray}{②}} &{\color{green}{②}}\ {\color{gray}{②}} &{\color{green}{②}}\ {\color{gray}{②}} \\ &{\color{gray}{④}}\ {\color{gray}{④}} &{\color{red}{④}}\ {\color{gray}{④}} &{\color{red}{④\ ④}} \\ \hline &B &L &V \end{array}

Much in the same way, K and U are just modified versions of A. Same is true for L and V with respect to B, and so on for the rest of the first 10 characters.

More generally, four bits make a word and 2 words make a byte… there is an extended braille cell that is two columns and four rows, so it matches the pattern of a byte exactly: two columns of four bits each.

① ①
② ②
④ ④
⑧ ⑧

I guess that is where my brain then decided that the common octal binary system that most of us use in competitions matches the 6-dot braille cell… only difference is that you read it top-to-bottom instead of left-to-right.

Lastly the naming convention of the cells reminded me a lot of chmod commands. For example, B is called dots-1-2 because that’s the raised dots. A is just called dots-1 and you end up with variable length for the names. Same is true for chmod commands when you use +r, +rw, -wx notation. There is another notation though that assigns binary values to read, write and execute permissions and you can simply write chmod 777, etc.

So I guess a combination of all the above made it jump out at me.

2 Likes

Very cool, if I do this I can learn about Braille and a technique for memorising formulae, two birds one stone:)

Go for it… let us know how it’s working for you.