[Blindmath] The inline math problem affecting the proposal to use UEB text and Nemeth math

[Susan Jolly]

According BANA's September 5, 2012 report titled Concurrent Use of UEB and
Nemeth Code, the approach BANA plans to adopt will be to use UEB for
surrounding text and to use Nemeth code for actual math.  This approach is
technically feasible for displayed math where there would be some sort of
explicit or implied indicators for switching to Nemeth math and then back to
UEB text.

However, it seems to me that this approach could be problematic for dealing
with the large amount of embedded or inline math typically present in
technical material.  This issue is illustrated by the three paragraphs on
the third page of the introductory chapter of the book "Div, Grad, Curl, and
All That: An Informal Text on Vector Calculus." All of the math on this page
is inline or embedded; there is no displayed math. By the way, this book is
intended primarily for self-teaching.

The following is an edited version of the first paragraph where all of the
inline mathematical notation, with the exceptions of single-letter variables
and of numbers, has been replaced with "MATH" to show that the surrounding
text by itself is incomplete.

"A function of one variable, generally written MATH, is a rule which tells
us how to associate two numbers, x and y; given x, the function tells us how
to determine the associated value of y. Thus, for example, if MATH, then we
calculate y by squaring x and then subtracting 2. So, if MATH."

The second paragraph extends the discussion from functions of one variable
to functions of more than one variable and uses five inline math expressions
to show the differences between the two cases. The third paragraph states
that the "functions so far discussed are scalar functions" rather than
vector functions and uses nine inline math expressions to show the
differences in notation for vector functions of more than one variable. In
summary, taken together these three paragraphs have 17 separate inline math
expressions.

I suggest that BANA needs to give more thought to the impact of using UEB
surrounding text on the ease of reading and understanding inline Nemeth
math.

Sincerely,
Susan Jolly