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

Tue Jun 29 11:39:05 UTC 2010

Hi Christine,

I'm happy to add that I'd be especially glad to hear from a
blind psychologist how spoken language comprehension works.
But, am I entirely wrong to say that you/we do not have a handle
on this yet?  I have read Davies' 2003 work on how the processing
hierarchy is similar to that in vision; but is that the only
handle? I did not quote, but had in mind, Tanenhaus on visual
and linguistic integration in what I did say. [Both papers, I
think widely and freely available ...]

Way off list, though.  And back to it.  If you write on a
persons back (game I play with students in explaining how
computer graphics works ...) the person can "read" it. Like
my Braille, it takes time and repetition, but it works.
"What gives" I ask?  I then describe an imaginery orange
in my hand which I pluck from my shoulder and show to
the students.  I say that from now on whenever I do this
you'll know that this is how you should imagine a luscious
orange (this is learning, I say).  Later, I use the motion to
indicate the colour, again I ask "what gives?".
Is it just pattern, I ask? a pattern that is free of tactile,
auditory, visual implications when converted to "the pattern"
form?  If yes, do I need vision to see a picture, or to feel
the sphericity of orange or to hear the sound of colour?  Do
I just need to learn the language of pattern - indeed any
language will do? And how does that work?

Reading Lakoff on metaphor helps fix maths as pattern in
this sense. But, what are the determinants - well I've said
it before, sequence, and 2D spatial layout.  The latter, hard
to grasp and prone to error in representation - but do read
what Wulfram says on this.  The former, depends on who does
the serialisation, and the number of symbols read at a time,
the "words" used, if you will.  However, this does not touch
the key issue - "understanding" the maths.  Here, again,
it's the notion of metaphor, analogy, and mapping that
Lakoff outline, I suspect, that are important.  OK I cheated
and extended what they said to suggest it was intrinsic; and
to hint that slugs knew all about infinity (a bit like white
mice knowing what 42 means I suppose?) but I did put some
smile symbolism in the post intentionally ...

Maths is fun personified - no science there at all, just
pure artifice (the reason for us sapiens). It's knowing how
to do things, to understand bits of the patterns that are
somehow intrinsic. And, the delight in being able to blather
on about it ... whoops, my slip is showing, sorry.

Kind regards, smile a lot - Bernard Diaz.

Christine Szostak wrote:
>> Now, I WOULD ask a blind person how to do moths.  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.
> 
>   Hey hey, those are fighting words to a blind psychologist (ok psychology
> graduate student) who studies spoken language comprehension (e.g.,
> understanding) <smile>. Sorry, I just had to throw this in since I am in the
> middle of reading a paper all about how humans understand spoken words:).
> 
>   I actually really enjoyed your comments below especially in the
> picture/word comparisons.
> Many thanks and have a wonderful Monday everyone!
> Christine
> 
> 
> ----- Original Message -----
> From: "Bernard M Diaz" <b.m.diaz at liverpool.ac.uk>
> To: "Blind Math list for those interested in mathematics"
> <blindmath at nfbnet.org>
> Cc: <jtenenbg at uw.edu>
> Sent: Monday, June 28, 2010 10:03 AM
> Subject: Re: [Blindmath] A Blog Post on Pronunciation Guides for
> Mathematical Notation, Expressions, and Greek Letters
> 
> 
>> 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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