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Bert Horn on New Math



 ********** Bert Horn on New Math ********** 

Dear Math Font enthousiasts,

     Berthold Horn has kindly answered some technical
and aesthetic questions I have posed concerning the new
TeX mathematics systems that have recently become
available: MathTimes and the Lucida New Math.

     Since I am sure most of you are as interested as I
in these important developments, I am posting a fairly
complete compte rendu below.  Basically I have just
suppressed ripples of confusion caused by one ambiguous
sentence in Berthold's first reply.

      Laurent Siebenmann


 *** math in Lucida bright ***

Dear Berthold,

     Quick question: Do you recommend Lucida bright for
heavy mathematics. I am interested but fear the math sys has
never been debugged.

  Cheers,

     Laurent Siebenmann

        <lcs@matups.matups.fr>

    

>From CompuServe.COM!71172.524 Fri Sep 24 17:08:43 1993
Date: 24 Sep 93 17:04:34 EDT
From: Louis Vosloo <71172.524@CompuServe.COM>
To: Laurent Siebenmann <laurent@math.toronto.edu>
Subject: LB + LNM

Dear Laurent:

Nice hearing from you again!

>    Quick question: Do you recommend Lucida Bright for heavy mathematics. 

Yes, I can recommend Lucida Bright + Lucida New Math for
heavy math.  The fonts and the TeX macro files have been
thoroughly tested. There are several text books that have
been done using LB + LNM, mostly with a lot of math.

>    I am interested but fear the math sys has never been debugged.

Oh, no, an enormous amount of work went into making sure
it works correctly. And as a straight replacement for CM
math it is easy to see that it should work, since the 0 -
127 range in LBMS is the same as in CMSY*, the 0 - 127
range in LBMO is the same as in CMMI*, and the 0 - 127
range in LBME is the same as in CMEX*.

[Berthold means to say that the glyphs are similarly named
and similarly encoded although quite *different* in details of
design.]

  (Its harder to convince oneself everything is OK with
MathTime, since in that font set there is *not* a complete
match with CM, which in fact does lead to some minor problems
--- not insurmountable, just distracting). The upper ranges
of the LBM fonts have additional glyphs, which cover the LaTeX
symbol font, the AMS math symbol fonts and more.

TeX macro files `lcdplain.tex' and `lcdlatex.tex' are
included for switching easily from CM to LB + LNM in both
plain TeX and LaTeX.  And the file `amssymlb.tex' defines
most of the AMS math symbols (without need for loading
AMS TeX).

There *are* things in the 75 CM fonts and 89 AMS fonts
that are missing in the 25 LB + LNM fonts, most notably
bold math, and a script font (but there is a calligraphic
font and a fraktur font).

So its mostly a matter of taste.  LucidaBright text fonts
have a larger x-height than CM, and less delicate
tendrils and swirls.  Lucida New Math fonts have math
relations and operators that are relatively small
compared to the variables, at least in comparison to CM,
which has relations and operators that are relatively
large when compared to the variables.

Cheers, Berthold Horn



  ** NEW MATH ***

Dear Berthold,

   I am pleased to hear that Lucida New Math has been well tuned.

   The divergence from CM is interesting.  I am all for the 
x-height increase and operator size changes.  

   Math Time seems *not* to have style variations according to
point size --- which seems natural because Times itself does
not. However the great use of math at small size (5 and 7 and
10 points versus 9 and 10 points for prose) makes me wonder
about the wisedom of this decision.

Where does Lucida stand on this matter?  And you?
How many Lucida New Math fonts in all --- not counting
Lucida Bright.

   I do use bold math for bold titles. What do you suggest
with Lucida? 

   A very high percentage of Adobe distributed roman fonts
cannot be directly used in math as math-roman parallel to
math-italic. I know this from bitter experience because the
French classically favor math-roman caps for math symbols over
math-italic caps --- an interesting stylistic tradition. In
contrast, Knuth tailored cmr to be acceptable as math-roman,
ie fam0 --- accepting some constraints on cmr. Thus he does
not have a cmmr, although conceptually I feel it is there but
coincident with cmr.

I wonder whether Biggelow & Holmes did the same for Lucida
Bright roman??  Or does Lucida New Math provide a special
math-roman (.tfm? shapes?)

...

    Larry S

PS.  With your permission I will post this exchange of views
on the math font list of Alan Jeffries.


  *** NEW MATH again ***

  Berthold!

   More quieries.

  How does Lucida New Math x-height compare with that of
BlueSky's CM/PS?  You are probably aware that BlueSky
increased the "true"="measured-on-output" x-height without
changing the metrics of CM.  And what do you think of using
the symbol font LBMS of Lucida New Math to replace that of
CM/PS? Reciprocally, what about using the bold math of CM/PS
as an additive to Lucida New Math?

  Does the B in the names LBMS, LBME, LBMS say Bright?  A
bit of history.  Lucida as text cum TeX math were "air-ware" in
1985-6.  What has in the interim?

  Both I and the math font list members know your standard blurb
on Lucida and I guess it will appear as an advert in the Aston
proceedings. Here I want more technical information.


   Larry


PS.     I hope the AmS math symbols are improved. Msam and msbm
seemed a bit tentative to me. 

 ...


>From CompuServe.COM!71172.524 Mon Sep 27 12:02:55 1993
Date: 27 Sep 93 11:45:51 EDT
From: Louis Vosloo <71172.524@CompuServe.COM>
To: Laurent Siebenmann <laurent@math.toronto.edu>
Subject: reply again

Dear Laurent:                                           1993/Sep/27

>  How does Lucida New Math x-height compare with that of BlueSky's CM/PS?  

The XHeight is substantially larger.  Note that this is
*independent* of any particular implementation or rasterization.
The CapHeight and Ascender are also larger (which is why we
recommend using 9.5pt for LBR text where one might use 10pt for
CMR), but not as much.

Here is CMR10:

        CapHeight 683.333
        XHeight 430.556
        Ascender 694.444
        Descender -194.444

Here is LBR:

        CapHeight 723
        XHeight 530
        Ascender 771
        Descender -193

>  You are probably aware that BlueSky increased the
> "true"="measured-on-output" x-height without changing the metrics of CM.

The BSR CM outlines are *perfectly* accurate --- they
correspond *exactly* to the METAFONT code (we did the hinting
work and conversion to Type 1 format).

What you are referring to is a difference in rasterization
between METAFONT and Adobe Type 1 at 300 dpi. The grid-fitting
in the two rasterizers work *very* differently.  And at that
*particular* resolution, it happens that the XHeight ends up
locked in one pixel higher in ATM than it does in METAFONT
output.

...

>  Does the B in the names LBMS, LBME, LBMS say Bright?  

Yes, when we started, we used these short files names (for TFM
files e.g.). Then another vendor used LBM for an inferior,
buggy, incomplete, non-TeX compatible set of math fonts in TT
format.  So we had to change the PS FontNames, but it was too
hard to change the short font file names at that point (since
these are what TeX uses).

> A bit of history.  Lucida as text cum TeX math were "air-ware"
in > 1985-6.  What has happened in the interim?

Not sure what that means?  The old Lucida (1987) and the old
LucidaMath (1990) from Adobe were rarely used because (i) the
bold fonts were generally considered too heavy (ii) they were
expensive (iii) TeX support was lacking (iv) there were no
previewers and printer drivers at that time that could properly
exploit them.  LucidaBright + LucidaNewMath benefitted from that
experience.

...

>    I hope the AmS math symbols are improved. 
>    Msam and msbm seemed a bit tentative to me.

I think the corresponding symbols in Lucida New Math look
better, but thats a matter of personal taste.  There has been a
lot of noise about in particular the AMS version of black board
bold (old and new).  Some in fact prefer the Adobe MathPi
interpretation of open-face (a.k.a. black-board bold).

Regards, Berthold.


  *** NEW MATHs again ***

Dear Berthold,

      I have partially checked your assertion that the
superiority of the Blue Sky CM/PS font series on 300dpi
PostScript printers is a rasterisation phenomenon and not at all
a matter of deformed outlines.  Indeed at very high resolutions
the measured

       x-height : capital height

converges to the same value for Blue Sky CM/PS and for metafont 
versions.  

      I recall however that the superiority of BlueSky's CM/PS
to BlueSky's or OzTeX's bitmapped CM is noticeable on many fonts
at moderate resolutions.  This suggests that PostScript Type1
hinting will usually produce better quality at 300dpi than
Metafont, even with the various grid-fitting parameters that
Knuth provides.

      For the record, I note the    x-height / capital height
ratios for cmr10, Times, Lucida Bright Roman are in sharply
increasing arithmetic progression:

cmr   .63  
Times   .68
Lucida Bright Roman   .73

In CM, in spite of the marked shape changes with *point size*,
this ratio is one thing that does not change to my knowledge
with *point size*.  (However it changes with style eg. for
cmcsc).

      A high value of this ratio (ie near 1) is helpful in math
fonts, because in $X^n$, $x^n$, it is distracting if the top of
n   falls below the top of  X  or if the base of  n  falls above
the top of x.

  -------------

LS>   Math Time seems *not* to have style variations according to point
LS>   size --- which seems natural because Times itself does not.
LS>   However the great use of math at small size (5 and 7 and 10
LS>   points versus 9 and 10 points for prose) makes me wonder about
LS>   the wisedom of this decision.
LS>   Where does LucidaBright / LucidaNewMath stand on this matter?  And you?

 BH>      There is only one design size of each font.  It would,
 BH> of course, be possible to make other sizes (as in the CM
 BH> fonts in Type 1 format), but its hard to justify the
 BH> enormous amount of work for the small improvement possible.
 BH> Keep in mind that the market for these fonts is under
 BH> 1/1000-th (!) of the market for the MicroSoft TrueType
 BH> font pack for Windows, and that just the *hinting* for a
 BH> commercial grade font may take from a few man days to a few
 BH> man weeks depending on tools available, complexity of the
 BH> font and how good a job one wants to do.  Eventually tools
 BH> for Making Multiple Masters may improve, but one still has
 BH> to design the `master fonts' at the corners of the
 BH> parameter hyper-cube.
 BH> 
 BH> Despite this, math looks good.  One thing one should *not*
 BH> do, however, is use the CM scheme of 10pt for text size,
 BH> 7pt for subscripts, 5pt for subsubscript.  That set of
 BH> sizes works *only* if the smaller sizes are extended, i.e.
 BH> proportionatly much wider than the larger sizes (when
 BH> scaled to the same x-height).  Instead use something like
 BH> 9.5pt, 6.9pt and 5.2pt for LucidaNewMath (For MathTime use
 BH> 10pt, 7.6pt and 6.0pt).

    I have recently run tests with MathTime on an algebraic
topology monograph containing many sub- and super-scripts of
both first and second order. (Third order scripts are forbidden
and relatively easy to eliminate in practice.)  The 10pt, 7pt,
and 5pt script sizing that has been preprogammed by M. Spivak
produced disastrous results with 10-point type. Although I have
not verified, I feel the results would also be disastrous at
resolutions higher than 300dpi, and even at infinite resolution
for people with not-quite-perfect vision. The 10pt, 7.6pt and
6.0pt was I my opinion much better, approaching the readability
of the CM scheme of Knuth using 10pt, 7pt, and 5pt.

     Incidentally, I feel that the distribution of Spivak's
macros using 10,7,5  will cause a a lot of damage to readability
of math in the near future unless warning is sounded and the
distributions are soon revised.

    To get a scheme in which I was happy about the readability
of the second order subscripts, I had to make them about 6.5pt!!

    Then there was then a problem that in $x_N$, the N  is about
as big as the x.  This problem is admittedly less severe for
Lucida Bright because of the proportionally greater x-height.

    In conclusion, in spite of the difficulties involved, I
conclude that shape variation for script and scriptscript is a
goal that should be kept prominently in view for math font
systems. I suspect the CM system will not be distinctly
surpassed without it.

 -----------

 BH> Maybe wait for an `expert font pack' ?

Interesting; do explain!

 -----------

 BH> In fact, CMR does *not* work well as a math roman font,
 BH> since it has to work as a text font.  A math font has to do
 BH> weird and wonderful things. For example, in a math fonts,
 BH> character widths are *not* character widths, but where to
 BH> put the subscript, italic corrections are *not* italic
 BH> corrections, but where to put the superscript, kern pairs
 BH> are *not* kern pairs, but where to put the accent, etc.
 BH> So, for a start with cmr as a math roman font, subscripts
 BH> and superscript of necessity have to be directly above one
 BH> another, which for some letters means there is too much
 BH> space between sub/superscripts and the letter. At the
 BH> minimum, one has to create a new font with altered
 BH> character widths and side-bearings, and added bogus kern
 BH> pairs for accent positioning.

Basically I agree.  Nevertheless I still conjecture that Don
Knuth constrained cmr to be a reasonable good Math Roman.  No
one did this for Times Roman. With Adobe fonts there is a
tendancy, very evident with Baskerville, to anticipate kerns.
For example the T does not have its full width but rather
anticipates a kern with a following lowercase.  Conflict with
the superscript in $\fam0 T^n$ results. The same problems seem
present with Times although I have not observed outright
collisions; just very uneven and incoherent spacing.  Thus as
matters stand the MathTime fonts cannot be used for classical
French math typography. And in the Anglo-German tradition one
has to treat what rare Math Roman there is with extreme care,
say by forming operator symbols with special spacing. Perhaps
the mere use of an altered .tfm could sort things out pretty
well in the case of Times!?

LS> I wonder whether Bigelow & Holmes did the same 
LS> [as Knuth did for cmr] for Lucida
LS> Bright roman??  Or does Lucida New Math provide a special
LS> math-roman (.tfm? shapes?)

 BH> Maybe wait for LNM-Roman ?

Sounds like a fine idea!  

    Best wishes.

       Laurent Siebenmann

        <lcs@matups.matups.fr>