[Blindmath] A Blog Post on Pronunciation Guides for Mathematical Notation, Expressions, and Greek Letters

[Bernard M Diaz]

Hi all,

With regard to the link below, it leads to good stuff, but
I'd caution care in looking too much at the stuff generated
by the sighted, me included :-)

The key trick with mathematics is "understanding" and this is
not aided by bandying Fred Barnard's fallacious myth (used in
two links pointed at from the link below) that "a picture is
worth a thousand words" - just ask a sighted teacher trying
to teach blind students :-)
And what is meant by "picture", "worth", and "thousand" anyway?
After all, we 'know' that a "word" is at least one million bits!
Barnard, wiki tells us, was in advertising ink, mmm need I
use a 1000 bits to 'say' more?
The really good notion to stick to is that "radio has better
pictures than cinema" - and I have no idea who said that?

Now, I WOULD ask a blind person how to do maths.  They usually
know, because they appreciate that it is the "understanding"
that is key.  And sadly, the psychologists do not have their
handles on this yet, I believe.
[This list is a shining/roaring example of what I say/write ...]

What is it that they "understand".  Well the difficulties in
transcribing "my idea" into "your idea". "My idea" of linking
two things is to draw a line; "your idea" might be to tie a
piece of string to two chairs. The idea, the notion of "linkage"
here is key - was it helped by my drawing? would it be more
helped with your knotting?

They key to "the understanding", it is my belief, is to
appreciate that the chimpanzee's brain can do it!  It may
be that the slug's brain can do it too - here the psychologists
and zoologists are currently silent, I believe. IF & that is a
big if :-) IF this is true, then we can all do it - why do I
say this, well because you've taken the time to read this far,
and you've had the 'English' "voiced" to you by something - was
it your brain?  It's just a matter of evolving to appreciate
that we can. And, what is it that we need to evolve? - well
the "language", the jargon, the notation, 'call' it what you
will - "the voice and pictures in your head".

And what is that "language" etc ... we'll stick with the
term "notation" for the moment. It's the sequential making
of sound (we'll call it "voicing", N.B., not "reading"), and
the appreciation that there is a secondary process, the "reading"
of the meaning.  How was it transferred?  I'm not absolutely
sure, but reading the well good mathematics book by a pair of
psycholgists (I think they are anyway), I believe it is by
the process of "analogy" or "mapping", from the voicing and
reading of "your" idea into some (possibly intrinsic) "my" idea.
Thus, they suggest, we "intrinsically" appreciate the notion
of "infinity". We map the symbol we read (Cantor's Hebrew
'aleph' perhaps ...) into that intrinsic idea, and away we
go.  We now have a picture (whoops) 'symbol', a notion, or
notation, for what "he" meant, which "we" can now use ... it
has been mapped to what we already knew, but didn't know (as
it we re).  The search now becomes finding what else we knew
we don't know [read this several times - it's a mathematical
code ... :-) ...].
The book is "Where mathematics comes from" by Lakoff and Nunez
and I'm indebted to Josh Tenenberg, Co-Editor-in-Chief, ACM TOCE
for pointing me at this excellent text, a must read (I believe)
for all those interested in maths (and computing) pedagogy
along with Lancelot Hogben's "Mathematics for the Million".
[I'm not sure if either of these is in Braille and/or available
as a speaking book? ... but they should be!]

Where does this get us? I hope to the practical bit. Take care
to understand how you serialise (order into linear or sequential
form) voiced single symbols.  Thus, 'voice' "script-greek lower
delta squared" but appreciate that it is 'read' "second derivative"
or whatever - look to the multitude of "readings", in the examples
with this post/links to appreciate this.  Do not confuse reading
the 2D layout, with how it is voiced - on one side; and how to
read it, and what it may mean, on the other.  Appreciate, that
voicing the 2D layout is not tantamount to the transcription
of knowledge, nor is it a code, the learning of which is going
to help (Nemeth Braille is wonderful, belive me, I can see it,
and know it produces wonderful pictures!) nor so is Knuth's
Latex with its cryptic parentheses, visual "piles" and "overs"
that produces equally impressive text and expression pictures!
[And by the way, "piles", and "overs" come, I believe, from
heraldry, where a Norman "voice" (blazon) is used to describe
an unique "picture" - shield or archievement; and it has been
argued, constitutes the oldest "computer" 'language']

And once you have it, you have the mapping from him to you;
take it and pass it to all - or as many as will listen.
Lead, and remember, this is one subject where the blind do
lead; you have a streets advantage, you know what it means,
and more (I believe) can pass it on more successfully because
hopefully, you understand how your understanding evolved!!

OK I'll say it again, "the radio produces better pictures
than the cinema does", doesn't it?  Does it not depend on the
tone of voice (I've in my head the wonderful voice of middle
America what's his name, "W.O.B. Gone"?); or the content of
the bits - which any computer can understand?

Kind regards, and apologies for trespassing on your time - Bernard Diaz

cc Josh Tenenberg with belated thanks for the recommendation.

Roopakshi Pathania wrote:
> 
> Actually I was going through the blog looking for R and LaTeX based
> posts when I found this. Thought this would be of interest to
> someone.
> 
>> From the blog:
> 
> When doing research in psychology you are sometimes required to study
> new statistical or mathematical techniques on your own. However,
> mathematical books rarely tell you how to pronounce the mathematical
> symbols. And even if you know how to pronounce the symbols in
> isolation, this does not guaranty that you can pronounce a
> mathematical expression made up of multiple symbols. Being able to
> read mathematical notation is a basic first step in aiding memory and
> conceptual understanding. The following links provide resources on
> reading mathematical symbols and provide a good reference if you
> encounter symbols and expressions with which you are not familiar.
> 
> http://jeromyanglim.blogspot.com/2009/05/pronunciation-guides-for-mathematical.html
> 
> 
> 
> 
> 
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