[Blindmath] Some examples of mathematics speech text

[Michael Whapples]

Hello,
I agree with John on the idea that may be for single elements ends don't 
need marking, like how LaTeX doesn't require the braces. If speaking an 
equation under such a condition I probably would leave a slight pause 
just after the element to indicate this.

Now to something I was going to mention when you were asking about the 
speaking of an equation, however this probably only works in the actual 
spoken form rather than the written down "what should be spoken". 
Consider how prosody might be used. Here is an example (I am only using 
pauses but speed may be good as well):
1 over x <pause> plus 2 x squared
or,
1 over x plus 2 <pause> x squared
or,
1 over x plus 2 x <pause> squared
Probably for the above brackets may make things clearer but hopefully it 
shows how pauses could be used to make things clearer.

If using a text to speech synthesiser the above can be done using SSML 
which can be passed to the synthesiser (espeak is one which accepts 
SSML, there are others). As part of the MSOR work I did I did implement 
this.

This idea can be broadened to use more than just speech, possibly 
positional audio (eg. bracket being said from the left could indicate 
open bracket saving on a word, similar for fractions, etc). Also how 
about speeding these key words up very fast and/or shortening them where 
it seems sensible (eg. saying frac instead of fraction)?

Instead of continuing with this I will point you to some research which 
I saw last year at the International Conference for Computers Helping 
People with Special Needs (ICCHP), you should have access to it through 
the Open University library system, its on Springer. The paper is called:
"Spoken MathematicsUusingPprosody: Earcons and Spearcons"and I believe 
is by D. Fitzpatrick and E. Bates, published as part of the ICCHP 2010 
proceedings.

I have to say I was very impressed with the idea and think it has great 
potential. Sometimes I think these formal spoken systems seem so clunky.

Michael Whapples

On -10/01/37 20:59, John Gardner wrote:
> Hello Jonathan, I like your philosophy of writing equations.  I can suggest
> two big improvements.  One is to compact the vocabulary so that you write
> things like end fraction as EndFraction.  This helps a lot when one is
> stepping through the equation with CTRL right-arrow and is fine for audio
> recordings too.  For text that is to be read by a screen reader, adopt an
> extension of the Latex rule that drops braces for single character sub and
> superscripts.  I do not require the equivalent of braces when sub or
> superscripts are written as a single string.
> Let me illustrate. First your examples.
>
> Sum of two fractions: fraction 2 over 3 end fraction minus fraction 1 over 6
> end fraction
> I would write: fraction 2 over 3 EndFraction minus fraction 1 over 6
> EndFraction.
> This reads a bit easier/faster when CTRL right-arrowing through, and it
> helps even more when there are lots of end things.  Screen reader defaults
> pronounce "split" words like EndFraction as end fraction and not
> endfraction.
>
> Number to negative fractional power: 125 sup minus fraction 1 over 3 end
> fraction end sup
> I would write: 125 super -fraction 1 over 3 EndFraction
> The superscript is written as a continuous string so doesn't require an
> EndSuperscript.
>
> Numerator of quadratic formula. minus b plus or minus square root of b
> squared minus 4 a c end root
> I would write: -b PlusMinus SquareRoot b squared -4ac EndRoot
> This reads fine except that the -4ac says negative 4 ack with my screen
> reader, but in stepping through I stop at this term and arrow through to
> hear it say dash 4 a c.  Not good for an audio recording, but fine for me.
>
> Gravitational attraction. cap G fraction m sub 1 m sub 2 over r squared end
> fraction
> I would write: F sub G = G fraction m sub 1 m sub 2 over r squared
> EndFraction
> I find Cap G to be annoying, and the case of characters is usually clear
> from context.  It's easy enough for me to arrow to the G and hear that it is
> a capital.  There are others who really want to hear that cap, so you need
> to give users the ability to control how such things are spoken.
>
> Concentration of a solution: 10 sup -3 end sup micro grammes per millilitre
> I would write: 10 super -3 micro grammes per milliliter
> Don't need the EndSuper because the -3 is written as a single string.  By
> the way, it's often hard to tell the difference between sup and sub, so I
> write super and sub.
>
> A few more examples might be instructive.  The full quadratic equation
> solution:
> x = Fraction -b PlusMinus SquareRoot b Squared -4ac EndRoot over 2a
> EndFraction.
>
> Let me give an example of some difficult notation that gets really messy
> normally.  A common notation in nuclear physics uses an element symbol with
> both left and right subscripts and superscripts. For example I once used the
> 111-indium metastable isotope whose full notation  can be written in Latex
> as
> _{49}^{111}In_{62}^{m*}
> [Note that the sub and superscript order is not important - the superscript
> can be first and the subscript second.]  I would write this expression as:
> LeftSubscript 49 LeftSuperscript 111 In subscript 62 superscript m*
> which is spoken perfectly except for the In, which would need to be stepped
> through to hear that it is I n.  [Yes I know this is not quite correct, the
> In should be expressed in roman font]  For comparison, my MathPlayer speaks
> this expression as:
>   sub 49 also super 111,  cap i, sub-superscripted n sub 62 super m  times,
> end sub-superscripted
> This and the Latex expression are, I claim, a whole lot harder to understand
> than my compact notation.  By the way, the MathPlayer expression is wrong,
> because it somehow makes the "n" In "In" a subscript.  I've asked Neil to
> check this out to find out whether the mistake is mine or MathPlayer's.
>
> What about more complicated sub and superscripts that need an EndSub or
> EndSuperscript?  For illustration I distinguish the two cases:
> x^n_i and x^{n_i}
> respectively as
> x superscript n sub i
> and x LongSuperscript n sub i EndSuperscript
>
> Okay, that's my opinion.  By the way, Roopakshi mentioned Aster.  It uses
> prefix notation.  Prefix notation is used in Content MathML and to some
> extent in Presentation MathML.  For example, the (infix) expression x sub I
> is, in prefix notation something like sub x i.  Good for computers, and TV
> Raman would argue that you and I should use prefix notation too.  As I said,
> there is no single "right" way to express math verbally.
>
> I look forward to some interesting commentary.
>
> John
>
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