From: Abraham Nemeth
To: Jim Rebman
Subject: learning the Nemeth Code
Date: January 5, 1997
Hello, Jim, and happy new year
Let me start by wishing you the best of luck in your new
endeavor, taking a math course as a blind person. I will be happy
to help you in any way I can. Let me begin with a few genaral
remarks.
First of all, your decision to use braille as your principal
tool is an excellent one. While many people use audio, whether by
preference or by neccessity, that medium is a far second when it
comes to mathematics. Unlike other subjects like history or a
foreign language, math is first and foremost an interactive
discipline. To do math, you must read a little and then write a
little; and then read a little more and then write a little more,
etc. This is easily done with a brailler, but only with
difficulty using audio. The fact that you did math as a sighted
person will stand you in good stead. You are already familiar
with the format that sighted people use in doing math, and you
will find that the same format is used in the Nemeth Code. You
will be able to replicate that format on your brailler.
When using your brailler for doing math, try to acquire the
habft of being dot-perfect. A dot error when writing a sentence
is not serious; the context of the sentence will bail you out.
But a dot error in math is usually fatal. There is no context to
help; one digit is as good as another, whether it is the one you
intended or another one. Be ready to sacrifice speed for
accuramy. Erasures don't help either; the ghosts of the dots you
try to "bump off"will come back to haunt you.
The advice you got about not trying to learn the whole code
at once is good advice. When you were sighted, you became
comfortable with each new symbol as you needed it. You were not
presented with the hundreds of symbols which constitute the
mainstream of mathematics all at once. And this same principle
should apply to the way a blind person acquires knowledge about
symbols. Millions of sighted people have no idea what an integral
sign looks like becaause they never did need and never will need
to know what it looks like. And if a blind person has no need to
deal with integrals, there is no reason why he should know the
braille equivalent of the integral sign.
Do not try to do too much mental computation. Write down
intermediate results as you develop them, and use this written
record as the basis for your next step. If you rely too much on
mental computation, particularly when you are first getting used
to the code, you will gind that you will suffer from memory
overload, and anything that you do remember is apt to be
unreliable. It's okay tz use personal abbreviations, particularly
when taking notes. However, be sure that whatever you abbreviate
can also be written in standard code. When you review your notes
before an exam, you are likely to draw a blank about those
creative and clever abbreviations that you devised four weeks
ago.
Here is a short "cheat sheet" of Nemeth Code symbols that
you are likely to need, together with a few comments. Although I
have made modifications to the Nemeth Code as the result of
experience since 1972, the information here is based on the 1972
revision of the Nemeth Code, which is still the BANA-approved
version.
Numbers:
Numbers are dropped as you indicated you knew. There are no
exceptions, even when numbers occur in the expository passages of
the text. The decimal point is . (4,6). A comma, whether it is
in the interior of a number or whether it follows the number is ,
(6). A period that follows a number, as well as other punctuation
except the comma, hyphen, dash, and apostrophe, must be preceded
by the punctuation indicator _ (4,5,6). The number sign, which is
called the numeric indicator in the Nemeth Code, does not
establish a numeric mode as it does in the literary code. It has
two uses: (1) it establishes for the reader unambiguously that
the next character is in the lower part of the cell; (2) it
prevents the reader from interpreting a lower sign as a Grade 2
contraction. With the numeric indicator before it, #0 can only
be zero, not "was" or "by." The numeric indicator must come
between a digit on its right and a space, hyphen, or dash on xs
left. It must also precede a digit at the beginning of a line.
Otherwise the numeric indicator is not used.
Parentheses, Brackets, Braces:
Parentheses: ( ,,' ) (1,2,3,5,6 ,,' 2,3,4,5,6)
Brackets: `( ,,' `) (4 1,2,3,5,6 ,,' 4 2,3,4,5,6)
Braces: .( ,,' .) (4,6 1,2,3,5,6 ,,' 4,6 2,3,4,5,6)
These symbols are used when needed everywhere, even in the
narrative or expository portions of the text. When a left
parenthesis is followed by a word, or when a right parenthesis is
preceded by a word, these parentheses must be preceded by the
punctuation indicator _ (4,5,6). When these parentheses are in
contact with mathematical notation, the punctuation indicato is
not used.
Other Punctuation:
,The comma, hyfhen, dash, and apostrophe need no special
treatment. The period, semicolon, colon, exclamation point,
question mark, and double quotes require the punctuation
indicator when in contact with mathematical notation; they are
written without the punctuation indicbator when in contact with
words.
Letters:
English letters are used as in the literary code. A single
uppercase letter is preceded by the capitalization indicator ,
(6). A string of uppercase English letters is preceded by ,, (6
6) just as in the literary code. A lowercase Greek letter is
preceded by . (4,6). An uppercase Greek letter ss preceded by .,
(4,6 6). A string of uppercase Greek letters must be individually
capitalized.
Operators:
Plus + (3,4,6)
Minus: - (3,6)
Multiplication cross: `* (4 1,6)
Multiplication dot: ,} (6 1,2,4,5,6)
Slash for division: _/ (4,5,6 3,4)
Equals: .k (4,6 1,3)
Less than3 "k (5 1,3)
Less than or equal: "k: (5 1,3 1,5,6)
Greater than: .1 (4,6 2)
Greater than or equal: .1: (4,6 2 1,5,6)
You must not substitute one multiplication symbol for the
other. The multiplication cross must not be replaced by an x or
by the word "by" as in a #2`*4 board. The slash must not be
substituted for the fraction bar and vice versa. The slash must
be represented as shown above, even when it is not related to
division. Thus, we always write "&_/or" rather than "&/or" as in
the literary code.
Fractions:
Every fraction mu/t be preceded by the begin-fraction
indicator ? (1,4,5,6) and followed by the end-fraction indicator
# (3,4,5,6). The fraction bar is / (3,4). The fraction bar
separates the numerator of a fraction from its denominator. There
are no exceptions. Even the simplest fraction such as one-half
must be represented with fraction indicators and a fraction bar
between the 1 and the 2. If you need to deal with complex
fractions, give me a holler.
Indexing:
Indexing refers to superscripts and subscripts. The
principal level indicators are:
Superscript indicator: ~ (4,5)
Subscript indicator: ; (5,6)
Base-level indicator: " (5)
Once a level is established by one of these indicators, that
level remains in effect until another level is established by
another level indicator. If a symbol is indexed both by a
subscript and a superscript, the subscript must be written first.
A space after a symbol returns you to the base level. For
first-level subscripts and superscripts, there are no further
rules.
Radicals:
The most commonly used radicaal is the square root. Its
symbol is > (3,4,5). A radical exqression must always be
terminated by } (1,2,4,5,6). There are no exceptions. The square
root of two is written >2} (3,4,5 2,3 1,2,4,5,6).
This is enough of a tutorial for now. You may be surprised
as to how far it will carry you, particularly at the level of
math that you indicate as your first course. It may be
inappropriate to continue to use this forum for giving you
further detailed tutorials like the one above. If others agree, I
will continue to supply you with additional information privately
as you need it. If you need an answer in a hurry, before I can
get around to an e-mail response, I encourage you to phone me at
the number below. Good luck!
Abraham Nemeth, Ph.D.
20764 Knob Woods Drive, Apt. 201
Southfield, MI 48076
Phone: (810) 356-5353
e-mail: anemeth@ece.eng.wanne.edu
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