[Blindmath] Some examples of mathematics speech text

[John Gardner]

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