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Re: Math Arrows and Harpoons

i said, commenting on taco's arrows font,
    the arrows in 120, 121 and 123 should definitely have the arrowheads
    pointing up at an angle, rather than horizontal.  the shape of the
    wavy stem is more-or-less that of a similar sign (or its mirror
    image).

hans aberg responded 
    I foind this comment strange: As far as I am concerned, these correspond to
    the LaTeX \leads to. For leads to, the arrow head-head should point as
    normal. It  consists of a part which is like a \sim followed by a short
    staright, horizontal part, to which the otherwise normal arrow-head is
    attached.

      When drawn by hand, it it may happen the arrowhead becomes bent, but that
    is not how it should be. This applies to the math I know; physicists may
    have invented their own version.

more from me:
     this is how they appear in both the unicode manual and the
    afii glyph register; in the latter, the rightwards version has a
    subsidiary meaning/description "functional relationship", which i
    think may have come from the iso tech report 9573-13, which has a bit
    of a physics orientation.

more from hans:
    The Unicode just provides a suggestion for a possible rendering, not a norm
    on how it actually should be drawn.

that's why i included the afii reference.  that is a standard glyph
image, not just a suggestion.

i've also come upon the glyph (afii 042/070 = 2238) rightwavyarrow
over dash (the dash is the same length as the arrow) with the glyph
description "isomorphism mapping".  i don't know the source of this
glyph, but the arrow definitely has the head pointing up to the right
at very nearly a 46\degree angle.  this one is not in the stix table,
by the way; i suppose someday i should thoroughly examine the afii
glyph register to see what i missed.  (i was a charter member of afii,
and secretary of the organization for a number of years, and have a
copy of every registry-related document that was ever issued publicly.
most of this is only on paper, and because of the nature of the
registration process -- first in, first posted --, grubbing through
these papers is a beast of a job.)
    
i said,
    the arrow in 122, in both the unicode manual and afii glyph register,
    has an "up" wave in the middle; taco's has a "down" wave.  again, i
    think this may have come from iso tr 9573-13.

hans replied,
    On such issues I think that one is left one ones own: I think that a
    mathematician could be able to distinguish between up/down wave in the
    middle, or using a \sim wave (two waves instead of three, up/down followed
    by down/up), and use them side-by-side as different symbols. If so, they
    should have different symbols. If one is judging the variations to be
    indistinguishable, it probably makes no difference which one is choosing,
    only that it is the one that looks the best.

if a composite symbol is to be taken with a single meaning, then for
unicode it requires a single code.  granted, there are some exceptions
that were grandfathered in, but the rule now is as i've stated it.  (i
was a member of the group, composed of representatives from the standards
working groups x3v1 and x3l2, that drafted the white paper on what is
a character and what is a glyph, relevant to unicode/iso 10646 and the
iso standard glyph registration process for which afii is registrar.)

me:
    hans aberg commented on the fishtails in an earlier message, saying
    that he doubted that these are used by themselves, as opposed to being
    part of some composite.  i've never seen (and am desparately looking
    for) published examples, but from the unicode, afii, and iso tr 9573-13
    evidence, believe that they are indeed individual symbols.

hans:    
      The problem is that Unicode just collects graphics, labels them symbols,
    without one knowing what the intended use should be. If there were two
    fonts, one for symbols, and for arrows described in components (head, tail,
    stem), then these problems could be resolved: One variation in each font,
    perhaps.

in this case, not so, if i am to believe my contacts in the iso coding
working group and the unicode technical committee.  unicode will not
assign a code to something unless it has a clear meaning.  what they
choose to call it in their published manual is something else again;
that may well be descriptive of the shape rather than giving the actual
meaning.

me:
    another naming overlap: 087 and 111 are both named Mapsto.  since
    the initial cap on most other arrows denotes a doubling of the stem,
    i think that 111 should keep this name, and 087 should be renamed to
    twoheadmapsto following the model of 015, twoheadrightarrow.

hans:
    There is a conflict in naming these arrows: Should one name them after a
    mathematical intended use (like "maps to") or by its redering. It is
    probably wise to not mix the two. Suppose one only uses naming by
    rendering: Then the original "maps to" |-    might be named
    "rightheadleftvertical", and |=    could be named
    "rightheaddoublestemleftvertical", or something.

here i agree.  i'm not a mathematician, do not know what many of these
symbols mean.  i'm counting on guidance from people who *do* know the
territory, but it has been a struggle to obtain this.  if someone can
provide a published reference from an established publisher, especially
one in which the symbols in question are defined in context (i'm
yearning for an advanced, possibly encyclopedic, expository source
with a detailed section on notation), i'll quite happily make changes
to any names that haven't been long established.  i'm hoping for the
possibility of deriving somewhat shorter names than hans has used here
though ...
							-- bb