Re: [EXTERNAL] Re: Thoughts on mrow default intent

Hi Murray,

It is good that I had 7 meanings for |·| in my previous message, so
that the "norm" one doesn't detract too much from the general point
:-) But to clarify, I am also myself most acquainted with the ‖
(U+2016) notation for norm, I think in modern texts it is almost
ubiquitous. That is not a numeric measurement however, just a general
feeling from my own readings.

And that was the crux of my question - which notational constructs and
*why* make the cut to be "default-worthy" in the spec?

As to more outdated (deprecated?) uses of |·| which denote norms, here
is some evidence:
- The encyclopedic resource I picked this up from was MathWorld:
https://mathworld.wolfram.com/VectorNorm.html
https://mathworld.wolfram.com/L2-Norm.html

- I now see that wikipedia also gives an example:
"For the length of a vector in Euclidean space (which is an example of
a norm, as explained below), the notation |v| with single vertical
lines is also widespread. "
https://en.wikipedia.org/wiki/Norm_(mathematics)#Notation

- the confusion has been discussed on math.stackexchange:
https://math.stackexchange.com/questions/2486271/is-there-a-difference-between-one-or-two-lines-depicting-the-norm

- and some course notes reachable online seem to still linger with the
single vertical line use:
https://www2.math.upenn.edu/~ryrogers/HW1-solutions.pdf

So while I agree with recommending ‖ (U+2016) to write norms in new
documents, I can't agree that defaulting existing |·| is "easily"
absolute value. The good news is that at least "norm" isn't in the K12
set, I vaguely remember it is college-level math.

---
@all:

I have to say I am puzzled with "computation" becoming the foreground
topic of the current email thread about "mrow defaults". That is a
long discussion in its own right, but it is one not present in the
current charter - which focuses on "accessibility" and "search". I
currently hold an opinion that we need a modern revamp of Content
MathML sooner or later, and before that time comes I'll try to skirt
away from the entire computability topic. I quite enjoy that the
current 'intent' attributes enable (and were meant to enable) partial
annotation. But that means there is no guarantee for a complete
content tree at the end of an annotation pass. And respectively - in
my mind - no general expectation of "computable" expressions, just
"accessible" ones. Weaker outcome in a way, but a lot easier to
produce by authors.

Deyan


On Wed, Dec 16, 2020 at 6:43 PM Murray Sargent
<murrays@exchange.microsoft.com> wrote:
>
> Deyan wrote:
>
>
>
> 5. Question: did you think of |a| as defaulting to "absolute value"? If so, why that operation? It could be any of "absolute-value", "cardinality", "norm", "seminorm", "determinant", "hyperdeterminant", "order-of-group", to borrow from our Level lists. I can imagine that absolute value is the one taught earliest, but I do remember Bulgarians and Romanians learn the determinant syntax in the last grades of highschool. A quick search on Khan academy suggests this is taught in "precalculus", which may be encountered in the last years of K12 also in the US. So we get two meanings for the |a| notation already in K12 math.
>
>
>
> In my math speech implementation (used in Word, PowerPoint, OneNote,…), I default to “absolute value” for |…| unless the … is a matrix because norm is denoted with ‖ (U+2016), not |. It’s true that I don’t have a way to force “cardinality” and “order of group” and it’d be great to have such a convention. But for defaults, it’s easy to decide when to say “absolute value” and when to say “determinant” (in whatever natural language).
>
>
>
> Thanks,
>
> Murray

Received on Thursday, 17 December 2020 01:54:18 UTC