Gardner–Salinas braille codes

{{Short description|Tactile system for encoding mathematical and scientific notation}}

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.{{cite web |title=Index of Topics in Braille Section |url=http://dots.physics.orst.edu/gs_index.html |work=Oregon State University Science Access Project Braille topics. |access-date=2012-04-29 |url-status=dead |archive-url=https://web.archive.org/web/20120420124208/http://dots.physics.orst.edu/gs_index.html |archive-date=2012-04-20 }}

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|lc=y|2024}}.[https://www.brailleauthority.org/formats/2011manual-web/index.html]

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.{{Citation needed|date=September 2014}}

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 =

class="wikitable" style="text-align:center"
Symbol	0?	0?	1	2	3	4	5	6	7	8	9
Braille \| {{Braille Cell\|type=8\|136}} \|\| {{Braille Cell\|type=8\|346}} \|\| {{Braille Cell\|type=8\|16}} \|\| {{Braille Cell\|type=8\|126}} \|\| {{Braille Cell\|type=8\|146}} \|\| {{Braille Cell\|type=8\|1456}} \|\| {{Braille Cell\|type=8\|156}} \|\| {{Braille Cell\|type=8\|1246}} \|\| {{Braille Cell\|type=8\|12456}} \|\| {{Braille Cell\|type=8\|1256}} \|\| {{Braille Cell\|type=8\|246}}

class="wikitable" style="text-align:center"

Symbol

Braille

| {{Braille Cell|type=8|136}} || {{Braille Cell|type=8|346}} || {{Braille Cell|type=8|16}} || {{Braille Cell|type=8|126}} || {{Braille Cell|type=8|146}} || {{Braille Cell|type=8|1456}} || {{Braille Cell|type=8|156}} || {{Braille Cell|type=8|1246}} || {{Braille Cell|type=8|12456}} || {{Braille Cell|type=8|1256}} || {{Braille Cell|type=8|246}}

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
class="wikitable" style="text-align:center"
Braille \| {{Braille Cell\|type=8\|17}} \|\| {{Braille Cell\|type=8\|127}} \|\| {{Braille Cell\|type=8\|147}} \|\| {{Braille Cell\|type=8\|1457}} \|\| {{Braille Cell\|type=8\|157}} \|\| {{Braille Cell\|type=8\|1247}} \|\| {{Braille Cell\|type=8\|12457}} \|\| {{Braille Cell\|type=8\|1257}} \|\| {{Braille Cell\|type=8\|247}} \|\| {{Braille Cell\|type=8\|2457}} \|\| {{Braille Cell\|type=8\|137}} \|\| {{Braille Cell\|type=8\|1237}} \|\| {{Braille Cell\|type=8\|1347}}
Symbol	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
Braille \| {{Braille Cell\|type=8\|13457}} \|\| {{Braille Cell\|type=8\|1357}} \|\| {{Braille Cell\|type=8\|12347}} \|\| {{Braille Cell\|type=8\|123457}} \|\| {{Braille Cell\|type=8\|12357}} \|\| {{Braille Cell\|type=8\|2347}} \|\| {{Braille Cell\|type=8\|23457}} \|\| {{Braille Cell\|type=8\|1367}} \|\| {{Braille Cell\|type=8\|12367}} \|\| {{Braille Cell\|type=8\|24567}} \|\| {{Braille Cell\|type=8\|13467}} \|\| {{Braille Cell\|type=8\|134567}} \|\| {{Braille Cell\|type=8\|13567}}

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
class="wikitable" style="text-align:center"
Braille \| {{Braille Cell\|type=8\|18}} \|\| {{Braille Cell\|type=8\|128}} \|\| {{Braille Cell\|type=8\|12458}} \|\| {{Braille Cell\|type=8\|1458}} \|\| {{Braille Cell\|type=8\|158}} \|\| {{Braille Cell\|type=8\|13568}} \|\| {{Braille Cell\|type=8\|1568}} \|\| {{Braille Cell\|type=8\|14568}} \|\| {{Braille Cell\|type=8\|248}} \|\| {{Braille Cell\|type=8\|138}} \|\| {{Braille Cell\|type=8\|1238}} \|\| {{Braille Cell\|type=8\|1348}}
Symbol	ν	ξ	ο	π	ρ	σ	τ	υ	φ	χ	ψ	ω
Braille \| {{Braille Cell\|type=8\|13458}} \|\| {{Braille Cell\|type=8\|13468}} \|\| {{Braille Cell\|type=8\|1358}} \|\| {{Braille Cell\|type=8\|12348}} \|\| {{Braille Cell\|type=8\|12358}} \|\| {{Braille Cell\|type=8\|2348}} \|\| {{Braille Cell\|type=8\|23458}} \|\| {{Braille Cell\|type=8\|1368}} \|\| {{Braille Cell\|type=8\|1248}} \|\| {{Braille Cell\|type=8\|123468}} \|\| {{Braille Cell\|type=8\|134568}} \|\| {{Braille Cell\|type=8\|24568}}
Symbol	Γ	Δ	Θ	Λ	Ξ	Π	Σ	Υ	Φ	Ψ	Ω
Braille \| {{Braille Cell\|type=8\|124578}} \|\| {{Braille Cell\|type=8\|14578}} \|\| {{Braille Cell\|type=8\|145678}} \|\| {{Braille Cell\|type=8\|12378}} \|\| {{Braille Cell\|type=8\|134678}} \|\| {{Braille Cell\|type=8\|123478}} \|\| {{Braille Cell\|type=8\|23478}} \|\| {{Braille Cell\|type=8\|13678}} \|\| {{Braille Cell\|type=8\|12478}} \|\| {{Braille Cell\|type=8\|1345678}} \|\| {{Braille Cell\|type=8\|245678}}

= Characters differing from English Braille =

class="wikitable" style="text-align:center"
rowspan=2\| Symbol	colspan=2\| Parentheses	colspan=2\| Brackets	colspan=2\| single quote
open	close	open	close	open	close	?
Braille \| {{Braille Cell\|type=8\|238}} \|\| {{Braille Cell\|type=8\|457}} \|\| {{Braille Cell\|type=8\|23678}} \|\| {{Braille Cell\|type=8\|35678}} \|\| {{Braille Cell\|type=8\|378}} \|\| {{Braille Cell\|type=8\|3}} \|\| {{Braille Cell\|type=8\|2356}}

class="wikitable" style="text-align:center"

rowspan=2| Symbol

colspan=2| Parentheses

colspan=2| Brackets

colspan=2| single quote

open

Braille

| {{Braille Cell|type=8|238}} || {{Braille Cell|type=8|457}} || {{Braille Cell|type=8|23678}} || {{Braille Cell|type=8|35678}} || {{Braille Cell|type=8|378}} || {{Braille Cell|type=8|3}} || {{Braille Cell|type=8|2356}}

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

= ASCII symbols and mathematical operators =

Symbol	"	$	&	@	\	^	_	`	{	}	~
class="wikitable" style="text-align:center"
Braille \| {{Braille Cell\|type=8\|2578}} \|\| {{Braille Cell\|type=8\|34567}} \|\| {{Braille Cell\|type=8\|12346}} \|\| {{Braille Cell\|type=8\|348}} \|\| {{Braille Cell\|type=8\|1678}} \|\| {{Braille Cell\|type=8\|57}} \|\| {{Braille Cell\|type=8\|28}} \|\| {{Braille Cell\|type=8\|378}} \|\| {{Braille Cell\|type=8\|1235678}} \|\| {{Braille Cell\|type=8\|2345678}} \|\| {{Braille Cell\|type=8\|678}}
Symbol	#	%	*	+	/	<	=	>	×	·	÷
Braille \| {{Braille Cell\|type=8\|3456}} \|\| {{Braille Cell\|type=8\|2346}} \|\| {{Braille Cell\|type=8\|3458}} \|\| {{Braille Cell\|type=8\|257}} \|\| {{Braille Cell\|type=8\|3478}} \|\| {{Braille Cell\|type=8\|358}} \|\| {{Braille Cell\|type=8\|235678}} \|\| {{Braille Cell\|type=8\|267}} \|\| {{Braille Cell\|type=8\|278}} \|\| {{Braille Cell\|type=8\|258}} \|\| {{Braille Cell\|type=8\|578}}

= Text symbols =

class="wikitable" style="text-align:center"
Symbol	•	©	†	‡	£
Braille \| {{Braille Cell\|type=8\|123568}} \|\| {{Braille Cell\|type=8\|148}} \|\| {{Braille Cell\|type=8\|124568}} \|\| {{Braille Cell\|type=8\|1234568}} \|\| {{Braille Cell\|type=8\|34568}}

class="wikitable" style="text-align:center"

Symbol

•

†

‡

Braille

| {{Braille Cell|type=8|123568}} || {{Braille Cell|type=8|148}} || {{Braille Cell|type=8|124568}} || {{Braille Cell|type=8|1234568}} || {{Braille Cell|type=8|34568}}

= Math and science symbols =

class="wikitable" style="text-align:center"
Symbol	≈	≅	≡	∝	{{pipe}}x{{pipe}} (abs. value)	∞	∫	line ∫	closed ∫
Braille \| {{Braille Cell\|type=8\|23567}} \|\| {{Braille Cell\|type=8\|23568}} \|\| {{Braille Cell\|type=8\|12345678}} \|\| {{Braille Cell\|type=8\|3678}} \|\| {{Braille Cell\|type=8\|12568}}...{{Braille Cell\|type=8\|12568}} \|\| {{Braille Cell\|type=8\|1258}} \|\| {{Braille Cell\|type=8\|234678}} \|\| {{Braille Cell\|type=8\|23467}} \|\| {{Braille Cell\|type=8\|23468}}

class="wikitable" style="text-align:center"

Symbol

≈

≅

≡

∝

{{pipe}}x{{pipe}} (abs. value)

∞

∫

line ∫

closed ∫

Braille

| {{Braille Cell|type=8|23567}} || {{Braille Cell|type=8|23568}} || {{Braille Cell|type=8|12345678}} || {{Braille Cell|type=8|3678}} || {{Braille Cell|type=8|12568}}...{{Braille Cell|type=8|12568}} || {{Braille Cell|type=8|1258}} || {{Braille Cell|type=8|234678}} || {{Braille Cell|type=8|23467}} || {{Braille Cell|type=8|23468}}

class="wikitable" style="text-align:center"
Symbol	〈	〉	∇	∂	...	→	←	○	ℵ	∈	⇌
Braille \| {{Braille Cell\|type=8\|24678}} \|\| {{Braille Cell\|type=8\|13578}} \|\| {{Braille Cell\|type=8\|14678}} \|\| {{Braille Cell\|type=8\|1468}} \|\| {{Braille Cell\|type=8\|368}} \|\| {{Braille Cell\|type=8\|2367}} \|\| {{Braille Cell\|type=8\|3568}} \|\| {{Braille Cell\|type=8\|2458}} \|\| {{Braille Cell\|type=8\|15678}} \|\| {{Braille Cell\|type=8\|1578}} \|\| {{Braille Cell\|type=8\|234567}}

class="wikitable" style="text-align:center"

Symbol

〈

〉

∇

∂

...

→

←

○

ℵ

∈

⇌

Braille

| {{Braille Cell|type=8|24678}} || {{Braille Cell|type=8|13578}} || {{Braille Cell|type=8|14678}} || {{Braille Cell|type=8|1468}} || {{Braille Cell|type=8|368}} || {{Braille Cell|type=8|2367}} || {{Braille Cell|type=8|3568}} || {{Braille Cell|type=8|2458}} || {{Braille Cell|type=8|15678}} || {{Braille Cell|type=8|1578}} || {{Braille Cell|type=8|234567}}

= Markup =

class="wikitable" style="text-align:center"
Symbol	Superscript	Subscript	Left-superscript	Left-subscript	Begin fraction	Denominator	End fraction	Over *
Braille \| {{Braille cell\|type=8\|35}} \|\| {{Braille cell\|type=8\|26}} \|\| {{Braille cell\|type=8\|3578}} \|\| {{Braille cell\|type=8\|2678}} \|\| {{Braille cell\|type=8\|12356}} \|\| {{Braille cell\|type=8\|34}} \|\| {{Braille cell\|type=8\|23456}} \|\| {{Braille cell\|type=8\|345}}

class="wikitable" style="text-align:center"

Symbol

Superscript

Subscript

Left-superscript

Left-subscript

Begin fraction

Denominator

End fraction

Over *

Braille

| {{Braille cell|type=8|35}} || {{Braille cell|type=8|26}} || {{Braille cell|type=8|3578}} || {{Braille cell|type=8|2678}} || {{Braille cell|type=8|12356}} || {{Braille cell|type=8|34}} || {{Braille cell|type=8|23456}} || {{Braille cell|type=8|345}}

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

class="wikitable" style="text-align:center" ! rowspan=2 scope="row" \| Symbol ! rowspan=2 scope="col" \| {{abbr\|√\|square root symbol}} ! colspan=2 scope="col" \| complex radicand * ! colspan=2 scope="col" \| displayed equation ! colspan=2 scope="col" \| math expressions ! colspan=2 scope="col" \| hyperlink **
scope="col" \| Open ! scope="col" \| Close ! scope="col" \| Open ! scope="col" \| Close ! scope="col" \| Open ! scope="col" \| Close ! scope="col" \| Open ! scope="col" \| Close
Braille \| {{Braille cell\|type=8\|2468}} \|\| {{Braille cell\|type=8\|2378}} \|\| {{Braille cell\|type=8\|5678}} \|\| {{Braille cell\|type=8\|123678}} \|\| {{Braille cell\|type=8\|345678}} \|\| {{Braille cell\|type=8\|23578}} \|\| {{Braille cell\|type=8\|25678}} \|\| {{Braille cell\|type=8\|2357}} \|\| {{Braille cell\|type=8\|2568}}

class="wikitable" style="text-align:center"

! rowspan=2 scope="row" | Symbol

! rowspan=2 scope="col" | {{abbr|√|square root symbol}}

! colspan=2 scope="col" | complex radicand *

! colspan=2 scope="col" | displayed equation **

! colspan=2 scope="col" | math expressions **

! colspan=2 scope="col" | hyperlink **

scope="col" | Open

! scope="col" | Close

! scope="col" | Open

! scope="col" | Close

! scope="col" | Open

! scope="col" | Close

! scope="col" | Open

! scope="col" | Close

Braille

| {{Braille cell|type=8|2468}} || {{Braille cell|type=8|2378}} || {{Braille cell|type=8|5678}} || {{Braille cell|type=8|123678}} || {{Braille cell|type=8|345678}} || {{Braille cell|type=8|23578}} || {{Braille cell|type=8|25678}} || {{Braille cell|type=8|2357}} || {{Braille cell|type=8|2568}}

* Used for any > 1 digit radicand.

** Used for markup to represent inkprint text.

class="wikitable" style="text-align:center"
rowspan=2\| Symbol	colspan=4\| Array
Begin	End	End element	End line	vert. stack	horiz. combo	superposition
Braille \| {{Braille cell\|type=8\|38}} \|\| {{Braille cell\|type=8\|67}} \|\| {{Braille cell\|type=8\|27}} \|\| {{Braille cell\|type=8\|237}} \|\| {{Braille cell\|type=8\|3467}} \|\| {{Braille cell\|type=8\|34678}} \|\| {{Braille cell\|type=8\|3468}}

class="wikitable" style="text-align:center"

rowspan=2| Symbol

colspan=4| Array

Begin

End

End element

End line

vert. stack

horiz. combo

superposition

Braille

| {{Braille cell|type=8|38}} || {{Braille cell|type=8|67}} || {{Braille cell|type=8|27}} || {{Braille cell|type=8|237}} || {{Braille cell|type=8|3467}} || {{Braille cell|type=8|34678}} || {{Braille cell|type=8|3468}}

class="wikitable" style="text-align:center"
rowspan=2\| Symbol	colspan=2\| Misc. Symbol *			colspan=4\| Modifiers
Begin	End	Quantity	Markup indicator	Inverted	Stroke/Not	Variant	Large
Braille \| {{Braille cell\|type=8\|37}} \|\| {{Braille cell\|type=8\|7}} \|\| {{Braille cell\|type=8\|123456}} \|\| {{Braille cell\|type=8\|367}} \|\| {{Braille cell\|type=8\|78}} \|\| {{Braille cell\|type=8\|347}} \|\| {{Braille cell\|type=8\|168}} \|\| {{Braille cell\|type=8\|1234567}}

class="wikitable" style="text-align:center"

rowspan=2| Symbol

colspan=2| Misc. Symbol *

colspan=4| Modifiers

Begin

End

Quantity

Markup indicator

Inverted

Stroke/Not

Variant

Large

Braille

| {{Braille cell|type=8|37}} || {{Braille cell|type=8|7}} || {{Braille cell|type=8|123456}} || {{Braille cell|type=8|367}} || {{Braille cell|type=8|78}} || {{Braille cell|type=8|347}} || {{Braille cell|type=8|168}} || {{Braille cell|type=8|1234567}}

= Typeface indicators =

class="wikitable" style="text-align:center"
Symbol	Script	Bold	Italic	Underline	Definable font 1	Fractur	Roman	Underline
Braille \| {{Braille Cell\|type=8\|48}} \|\| {{Braille Cell\|type=8\|458}} \|\| {{Braille Cell\|type=8\|468}} \|\| {{Braille Cell\|type=8\|4568}} \|\| {{Braille Cell\|type=8\|478}} \|\| {{Braille Cell\|type=8\|4578}} \|\| {{Braille Cell\|type=8\|4678}} \|\| {{Braille Cell\|type=8\|45678}}

class="wikitable" style="text-align:center"

Symbol

Script

Bold

Italic

Underline

Definable font 1

Fractur

Roman

Underline

Braille

| {{Braille Cell|type=8|48}} || {{Braille Cell|type=8|458}} || {{Braille Cell|type=8|468}} || {{Braille Cell|type=8|4568}} || {{Braille Cell|type=8|478}} || {{Braille Cell|type=8|4578}} || {{Braille Cell|type=8|4678}} || {{Braille Cell|type=8|45678}}

The difference between the two underline markers is not explained.

= Shape symbols =

class="wikitable" style="text-align:center"
Symbol	⊥	∥	∠	Open Square	⊿
Braille \| {{Braille Cell\|type=8\|8\|2378}} \|\| {{Braille Cell\|type=8\|568\|237}} \|\| {{Braille Cell\|type=8\|8\|3578}} \|\| {{Braille Cell\|type=8\|568\|25678}} \|\| {{Braille Cell\|type=8\|568\|378}}

class="wikitable" style="text-align:center"

Symbol

⊥

∥

∠

Open Square

⊿

Braille

| {{Braille Cell|type=8|8|2378}} || {{Braille Cell|type=8|568|237}} || {{Braille Cell|type=8|8|3578}} || {{Braille Cell|type=8|568|25678}} || {{Braille Cell|type=8|568|378}}

= Set theory =

class="wikitable" style="text-align:center"
Symbol	∪	∩	⊂	⊃
Braille \| {{Braille Cell\|type=8\|568\|5678}} \|\| {{Braille Cell\|type=8\|568\|2568}} \|\| {{Braille Cell\|type=8\|568\|2578}} \|\| {{Braille Cell\|type=8\|58\|25678}}

class="wikitable" style="text-align:center"

Symbol

∪

∩

⊂

⊃

Braille

| {{Braille Cell|type=8|568|5678}} || {{Braille Cell|type=8|568|2568}} || {{Braille Cell|type=8|568|2578}} || {{Braille Cell|type=8|58|25678}}

References

[https://web.archive.org/web/20060615173923/http://www-cgi.cnn.com/TECH/9511/new_braille/index.html Blind physicist creates better Braille] — a CNN news item, November 9, 1995
[https://www.ams.org/notices/200210/comm-morin.pdf The world of blind mathematicians] — article in Notices of the AMS, November 2002

Category:Braille symbols

Category:8-dot braille scripts

Category:Mathematical notation