# Braille: Letters that rotate and change in space, the symmetries of the system

Giuseppe Di Grande Updated the 04/22/2021 08:00**Braille** uses a series of raised or lowered dots to represent letters, numbers, and symbols. The dots have a specific arrangement within a surface called a cell. The dots in classical **Braille** are arranged within a grid of two by three dots. The sets of dots that make up some letters have a spatial configuration that sometimes leads to confusion, due to the rotation or symmetry of their configuration.

## - ⠑ ⠊ -

The vowels "E" and "I" are a classic example of mirror vowels that those who began to write and read in **Braille** had to deal with. The vowel "E" is reproduced using dots 1-5. The spatial arrangement of these dots is exactly mirrored to the dots of the vowel "I", which is reproduced using dots 2-4. To solve once and for all the doubt, we can keep in mind that if on the left there is the highest point, that is the point 1, the vowel is "E"; while if the cell on the left has the middle point, that is the point 2, it means that the vowel is "I". In a certain way there is an order between the two vowels also in **Braille**, where the point 1 of "E" precedes the point 2 of "I".

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A similar specularity we have with the consonants "R" and "W". The "R" has the dots 1-2-3-5; while the "W" has the dots 2-4-5-6, exactly mirroring the "R". We can keep in mind a rule also in this case, remembering that if on the left we find all the raised points 1-2-3 we are in presence of an "R"; while if all the raised points we have on the right 4-5-6 we have under the finger a "W".

## - ⠝ ⠵ -

Let us now examine the rotation we find between two consonants, the "N" and the "Z". The "N" is represented with the dots 1-3-4-5, while the "Z" with the dots 1-3-5-6. We are in the presence of a perfect vertical specularity that sends the brain of the beginner reader into a tizzy. We can simply say that the right dots slide down one position, but it is more correct to invert vertically the letter to go from one to the other. To derive a rule from the spatial position of the dots of the two consonants, we can say that: if the upper part is full, that is with the dots 1-4 raised, we are in presence of an "N"; vice versa, if the dots of the lower part are raised, that is the dots 3-6, we are in presence of a "Z".

In this article we are only analyzing the confusion induced by the rotation or symmetry of some letters. If we were to consider numbers, punctuation and symbols, the problem would be extended and we would have to consider also the confusion induced by the position of the dots.

## - ⠙ ⠋ ⠓ ⠚ -

Let's look at two other pairs of letters, which when taken all four together become the biggest doubt of anyone learning to read **Braille**. We are talking about the pair "D" and "F" and the pair "H" and "J". Among other things, these four letters are part of the first series, that is, the first ten letters of the alphabet, also used to represent numbers. These letters present a horizontal symmetry, similar to that seen for the vowels "E" and "I" and for the consonants "R" and "W".

The letter "D" is represented by the dots 1-4-5; while the letter "F" is given by the dots 1-2-4. The two letters are perfectly mirrored. The rule we have to keep in mind is similar to that of "E" and "I", which by the way are vowels that share two thirds of the points of these letters. If we have raised points 1-5 (of course there is also point 4), we are in the presence of "D" (similar to "E"); if instead we have raised points 2-4, we are in the presence of "F" (which shares points with "I", apart from point 1).

A similar case we have between "H" and "J". The "H" uses the points 1-2-5, while the "J" uses the points 2-4-5: they are exactly specular. We can surely keep in mind that if we touch the dots 1-2 we have under our finger the "H", while if the dots are moved to the right on 4-5 we have the "J".

However, these four letters have a particular position, because the person new to **Braille** is likely to confuse them. Not only are the "D-F" and "H-J" pairs mirrored, but so are the "D-H" and "F-J" pairs, but vertically. If we start with "D" and begin to rotate the **Braille** form of the letter in space, we get the sequence of letters "D-F-H-J" clockwise, and "D-J-H-F" counterclockwise; and that is also the charm of **Braille**.

We have played a little with **Braille**, with the symmetries, with the position, the spaces, the specularity of the dots that make this system of reading and writing a useful and fascinating means for all the blind of the world, and not only.

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