Gardner–Salinas braille codes

The Gardner–Salinas braille codes are a proposed method of encoding mathematical and scientific notation linearly using braille cells for tactile reading by the visually impaired. The most common form of Gardner–Salinas braille is the 8-cell variety, commonly called GS8. There is also a corresponding 6-cell form called GS6.

The codes were developed as a replacement for Nemeth Braille by John A. Gardner, a physicist at Oregon State University, and Norberto Salinas, an Argentinian mathematician. However, 15 years later Nemeth code was still the standard, with no further change As of 2024.

The Gardner–Salinas braille codes are an example of a compact human-readable markup language. The syntax is based on the LaTeX system for scientific typesetting.

See also: Braille and Braille music

Table of Gardner–Salinas 8-dot (GS8) braille

The set of lower-case letters, the period, comma, semicolon, colon, exclamation mark, apostrophe, and opening and closing double quotes are the same as in Grade-2 English Braille.

Digits

Symbol	0?	0?	1	2	3	4	5	6	7	8	9
Braille

Apart from 0, this is the same as the Antoine notation used in French and Luxembourgish Braille. Sources disagree on 0. Both claimed forms are presented above. The second is the ISO form. Note however that ISO is concerned only with a one-to-one assignment between 8-dot braille and ASCII, and so has no particular connection to Gardner–Salinas braille.

Upper-case letters

GS8 upper-case letters are indicated by the same cell as standard English braille (and GS8) lower-case letters, with dot #7 added.

Symbol	A	B	C	D	E	F	G	H	I	J	K	L	M
Braille
Symbol	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
Braille

Compare Luxembourgish Braille.

Greek letters

Dot 8 is added to the letter forms of International Greek Braille to derive Greek letters:

Symbol	α	β	γ	δ	ε	ζ	η	θ	ι	κ	λ	μ
Braille
Symbol	ν	ξ	ο	π	ρ	σ	τ	υ	φ	χ	ψ	ω
Braille
Symbol	Γ	Δ	Θ	Λ	Ξ	Π	Σ	Υ	Φ	Ψ	Ω
Braille

Characters differing from English Braille

Symbol	Parentheses		Brackets		single quote
	open	close	open	close	open	close	?
Braille

The single quotation marks are the ASCII back tick ` and apostrophe '.

ASCII symbols and mathematical operators

Symbol	"	$	&	@	\	^	_	`	{	}	~
Braille
Symbol	#	%	*	+	/	<	=	>	×	·	÷
Braille

Text symbols

Symbol	•	©	†	‡	£
Braille

Math and science symbols

Symbol	≈	≅	≡	∝	|x| (abs. value)	∞	∫	line ∫	closed ∫
Braille					...

Symbol	〈	〉	∇	∂	...	→	←	○	ℵ	∈	⇌
Braille

Markup

Symbol	Superscript	Subscript	Left-superscript	Left-subscript	Begin fraction	Denominator	End fraction	Over *
Braille

* Encodes the fraction-slash for the single adjacent digits/letters as numerator and denominator.

Symbol	√	complex radicand *		displayed equation **		math expressions **		hyperlink **
		Open	Close	Open	Close	Open	Close	Open	Close
Braille

* Used for any > 1 digit radicand.

** Used for markup to represent inkprint text.

Symbol	Array
	Begin	End	End element	End line	vert. stack	horiz. combo	superposition
Braille

Symbol	Misc. Symbol *				Modifiers
	Begin	End	Quantity	Markup indicator	Inverted	Stroke/Not	Variant	Large
Braille

Typeface indicators

Symbol	Script	Bold	Italic	Underline	Definable font 1	Fractur	Roman	Underline
Braille

The difference between the two underline markers is not explained.

Shape symbols

Symbol	⊥	∥	∠	Open Square	⊿
Braille

Set theory

Symbol	∪	∩	⊂	⊃
Braille

References

• Blind physicist creates better Braille — a CNN news item, November 9, 1995
• The world of blind mathematicians — article in Notices of the AMS, November 2002