From: Asmus Freytag (asmusf@ix.netcom.com)
Date: Tue Oct 12 2010 - 19:48:24 CDT
Ken,
some comments, and a few suggestions near the end.
On 10/12/2010 4:56 PM, Kenneth Whistler wrote:
> Karl Williamson asked:
>
>> The Unicode standard only gives numeric values to rational numbers. Is
>> the reason for this merely because of the difficulty of representing
>> irrational ones?
> No. Primarily it is because the Unicode Standard is a *character*
> encoding standard, and not a standard for numeric values for
> various mathematical constants that some characters might be
> used to represent.
Correct.
>
>
> I consider "EULER CONSTANT" an unfortunate misnomer from the
> very, very early days of the Unicode Standard. If we had it to
> do over, particularly given the later addition of all the
> styled mathematical alphanumerics, I would have favored:
>
> 2107 [insert stylename here] CAPITAL E
> = Euler constant
>
> Or something similar -- just to make the point clearer.
Actually, what you advocate here is what I consider the mistake that was
made with the WEIERSTRASS ELLIPTIC FUNCTION. The problem is that the
Letterlike Symbols were conflated with "styled letters used as symbols".
They are not at all the same category. The Planck constant is a "styled
letter used as symbol", and is correctly unified with the italic h, but
the planck constant / (2 * pi), or h-bar is not a styled letter but a
symbol derived from a styled letter - a true letterlike symbol.
2107 and 2118 are one-off designs, not part of complete sets, same as 210F.
Because these characters came from not-well-understood legacy
collections, and because the "styled letters used as symbols" were
initially deemed inadmissible to Unicode as complete sets these
distinctions weren't clear at the time.
>> NamesList.txt
>> says that U+03C0, GREEK SMALL LETTER PI is used for the ratio of a
>> circle's circumference to its diameter, but it has other uses as well,
>> and does not have the Math property.
> Having the Math property basically has nothing to do with whether
> a character is assigned a Numeric_Value or not.
Correct.
>> The various Math PI's don't seem
>> that they necessarily mean this value either. Things like the two
>> characters that have "Planck's constant" in their names, even if the
>> code points always meant that, have different values in different
>> measurement systems, so couldn't be said to refer to particular numbers.
>>
>> I'm curious if any thought was given to this, and what code points I'm
>> missing in my analysis.
> U+1D452 MATHEMATICAL ITALIC SMALL E (or merely U+0065 LATIN
> SMALL LETTER E), also used for Euler's number. See also U+2147.
Now you are confusing Euler's constant - also depicted with U+03B3 GREEK
SMALL LETTER GAMMA, with the natural exponent. That kind of confusion is
really not helpful and is what drives people like Karl to ask for
numeric property values in the first place - to unambiguously define
what these symbols were encoded for.
The proper place to document that, without introducing a formal
property, is with additional nameslist annotation for a few characters.
I suggest that you add the correct value for Euler's constant as a
comment and cross reference that character it to 03B3
0.57721 56649 01532 86060 65120 90082 40243 10421 59335 93992
should be approximate enough...?
At the same time you could add a comment e ≈ 2.718 for 212F - Again, not
to document the value, but to make clear, beyond the character name,
what constant the alias for 212F denotes.
> For that matter, why stop with irrationals? There is
> also U+1D456 MATHEMATICAL ITALIC SMALL I (or merely U+0069 LATIN
> SMALL LETTER I), used for the imaginary number, square root
> of -1. See also U+2148 and U+2149.
>
> Basically, there is no end to how mathematicians may end up
> assigning odder and more exotic kinds of "numbers" to various
> symbols available in the standard. And I think how they do
> so and exactly what those values mean is basically out of
> scope of the Unicode Standard.
>
Correct - it's not Unicode's role to make the assignment, but common
usage can and should be documented informally - that's no different to
documenting modifier letters with detailed linguistic usage.
A./
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