Unified English Braille (UEB) is a complete code that is used for both literary (non-technical) and STEM (technical) materials in English-speaking countries. It was developed by the International Council on English Braille (ICEB). The general principle of UEB is that each print symbol has one and only one braille equivalent by using the same physical symbol regardless of context (literary or technical).
What is a Braille Cell?
A braille cell is a systematic arrangement of raised dots. Each braille cell consists of six raised dots arranged in two parallel columns each having three dots in each column. The dot positions are identified by numbers from one to six, much like the number six on a dice.⠿
6-Dot Braille Cell
The top dot in the left column is known as dot 1. Below dot 1 is dot 2 and dot 3 respectively. Dot 4 is found at the top of the right column with dots 5 and dot 6 below it.
How does braille work?
In Unified English Braille (UEB, braille signs are used to represent both literacy (non-technical) and STEM (technical) materials that can denote letters of the alphabet, numbers, punctuation, part of a word, or even a whole word. These tactile signs are made up of raised dots arranged in a 3×2 matrix, known as a 6-dot cell, that blind people can read through touch. There are sixty-four possible combinations for a 6-dot braille cell. To overcome this limitation some signs will have more than one braille cell, or one braille cell will represent more than one character.
For instance, a braille sign that represents the individual letters of the print alphabet occupy only one cell, such as the letter f, which is formed with dots 12 and 4. Another example would be the strong wordsign "and" where the three characters are represented as one cell and formed with dots 123 and 46. This is known as contracted braille.
In most cases though a sign will occupy two or more cells. A good example would be an asterisk (*) which is formed with two cells, a prefix, and a root. In UEB a prefix is a braille character that has only right-hand dots. The root is any of the fifty-six braille characters that are not a prefix. In the case of an asterisks, it has a dot 5 prefix and a root with dots 3 and 5.
An empty cell, consisting of no dots, that denotes a blank space which is left between words and between the end of one sentence and the beginning of the next.
Mathematical Notation
In this blog I will focus primarily on UEB for technical material that contains braille symbols for every possible kind of mathematical and scientific notation, even the most complex. All the technical braille signs will be accompanied with the equivalent print notation so that both sighted and blind academics can follow along. I will begin at a very basic level and gradually build up to more complex mathematical functions.
I assume that you have prior knowledge of UEB literary braille (non-technical), at the very least the fundamentals, as it is integral to the STEM (technical) materials that will be covered in this long series that will connect the dots of Unified English Braille to the print equivalent of mathematical notation.
Introducing Numbers
The number system 1-9 and 0 are represented in UEB by the numeric indicator followed by the letters a–i and j. The numeric indicator must be used before each number to prevent confusion with the corresponding letter.
Numeric Indicator ⠼ dots 3 and 456
The numeric indicator turns on numeric mode. Below are the ten digits 1-9 and 0 which are formed with the letters a-i and j, preceded by the numeric indicator.
Ten Digits
⠼⠁ dots 3 and 456, dot 1
⠼⠃ dots 3 and 456, dots 12
⠼⠉ dots 3 and 456, dots 1 and 4
⠼⠙ dots 3 and 456, dots 1 and 45
⠼⠑ dots 3 and 456, dots 1 and 5
⠼⠋ dots 3 and 456, dots 12 and 4
⠼⠛ dots 3 and 456, dots 12 and 45
⠼⠓ dots 3 and 456, dots 12 and 5
⠼⠊ dots 3 and 456, dots 2 and 4
⠼⠚ dots 3 and 456, dots 2 and 45
For Example:
Below are some basic examples of how to write numbers in units, tens, hundreds, and thousands in UEB mathematics.
2 ⠼⠃
20 ⠼⠃⠚
200 ⠼⠃⠚⠚
2022 ⠼⠃⠚⠃⠃