History of blackboard bold?

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Robin Houston

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Oct 5, 2003, 12:05:56 PM10/5/03
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I'm trying to trace the use of blackboard bold
symbols (Z, N, Q, R, ...) in printed mathematics.
There are two distinct sets of letterforms in
common use: one mimics the way that these letters
are often written, as seen in Adobe's Mathematical
Pi, for instance:
http://www.myfonts.com/fonts/linotype/universal-mathematical-pi/mathematical-pi-6/testdrive.html?s=N+Q+R+Z+C&p=72

and the other just uses traditional inline letters:
http://www.myfonts.com/fonts/mathtype/euclid-math-two/euclid-math-two/testdrive.html?s=N+Q+R+Z+C&p=72

(Note: this mysterious "Euclid" is simply a
copy of the Computer Modern and AMS fonts.)

These symbols often seem to be associated with the
name Bourbaki. However the original Éléments de
Mathematique -- at least Livre II from 1958 -- uses
ordinary boldface for N, Z, Q.

Does anyone have any information about when and where
these symbols were first used in print, and which
style was first printed? I do know that the AMS has
used the inline style since the early seventies.

Thanks for any help or ideas!

Robin

Lee Rudolph

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Oct 5, 2003, 3:08:30 PM10/5/03
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Robin Houston <ro...@remove-this-bit.kitsite.com> writes:

>I'm trying to trace the use of blackboard bold
>symbols (Z, N, Q, R, ...) in printed mathematics.

...


>Does anyone have any information about when and where
>these symbols were first used in print, and which
>style was first printed?

[After writing all the following blather, I noticed
that the only part which is truly responsive to the
question asked is "something not completely unlike
your first set of examples appeared from Prentice-Hall
in 1965, and I find no earlier instances in my home
library". Read the rest at your peril.]

It is my impression that such symbols were first used
in polycopied/mimeographed notes, and similar materials
prepared on typewriters. Although (as I recently mentioned
in another thread in c.t.t) there was at least one office
typewriter (an Olympia) for sale by the mid 1960s with a
built-in "poor man's bold" doublestrike function, for a
long time--until the era of Typ-It insertible type bars,
and not too much later the IBM Executive and Selectric
lines of typewriters--about the best that could easily
be done to fake "bold" was to overstrike an uppercase I
(or a single quote) on your R or C. Given a Selectric,
one had the further option of doublestriking your R, C,
Z, Q, or N with a slight offset (this involved manual
intervention with the device that carried the "golf-ball"
type element, and was very hard to do consistently).

The typed notes prepared by typists in the Princeton
mathematics department sometime in the late 1950s,
and published by D. Van Nostrand Company in 1959 as
"Advanced Calculus" by Nickerson, Spencer, and Steenrod,
show no effort to fake bold in any way; Typ-It (or its
equivalent) has been used for various symbols like
\union and \in. The typed notes from the same source,
prepared in 1961 and published in 1962 by Princeton
University Press as "Lectures on Modular Forms"
(Annals of Mathematics Study 48) by Gunning is also
devoid of boldfakery, and has assorted Type-It symbols.

By 1966, however, Gunning (in "Lectures on Riemann Surfaces",
PUP Princeton Mathematical Notes) uses doublestruck C and R;
the typewriter is almost surely a Selectric (and thus, for
instance, script letters--which were typed with Typ-It in
"Lectures on Modular Form"--have been written in by hand).
Gunning very much liked the use of "blackboard bold"
(I believe it was from him that I learned to use it,
at just around that time); his 1965 textbook (with Rossi),
"Analytic Functions of Several Complex Variables", in
the Prentice-Hall Series in Modern Analysis, produced from
notes written in 1960-1962, is typeset with a *realllly*
*ugly* \mathbb{C} (it must be seen to be believed), more
in the "Mathematical Pi" than the "Euclid Math Two" style.

Going back to typescript notes: Serre's 1964 lectures at
Harvard, "Lie Algebras and Lie Groups", printed from (surely
author-supplied, camera-ready) typescript by W. A. Benjamin,
Inc., in 1965, uses a double-underline (handwritten) beneath
C and Z to denote the complex numbers and the integers,
respectively; Narasimhan's 1966 "Introduction to the Theory
of Analytic Spaces", printed from (author-supplied, camera-
ready) typescript as Springer LNM 25, looks like Selectric
Courier to me, and has all Fraktur and script characters
written in by hand, *but* has somehow arranged to have very
elegant typewritten versions of \mathbb{C} and \mathbb{R},
I have no idea how. Karoubi's thesis (University of Paris,
1967) is typewritten with no distinction for C, R, etc.,
at all (though when C stands for some category, it has a
handwritten x beneath it--very odd). Mumford's original
"Red Book" ("Introduction to Algebraic Geometry--Preliminary
version of first 3 Chapters"), which is undated and has no
publisher noted anyway (I assume it was printed by Harvard
in or about 1969) uses a mixture of over- and doublestriking
for \mathbb: doublestruck A (for "affine space"), P overstruck
with I (for "projective space").

Of all these, the authors closest to Bourbaki (Serre and
Karoubi) have, if anything, the type that's furthest from
blackboard bold.

Lee Rudolph

G. A. Edgar

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Oct 5, 2003, 3:16:07 PM10/5/03
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In article <3F804164...@remove-this-bit.kitsite.com>, Robin
Houston <ro...@remove-this-bit.kitsite.com> wrote:

Compare the old AMS TeX font msym to the more recent font msbm.
The old msym is like the Mathematical Pi quoted, while the new msbm is
like the Eudlid Math 2.

Of course "new" is a relative term, and msbm has indeed been around for
a long time. But in the TeXBook (at least the first edition) in the
index under "blackboard bold" you will see a letter R in the old msym
style.

Of course this way of writing was devised for writing by hand (on a
blackboard, for example); and then adapted for use by a typewriter
(those ancient machines used before personal computers for producing
documents in a home or office environment). Produce the blackboard
bold R by typing an I and an R close together.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

Robin Houston

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Oct 5, 2003, 5:30:40 PM10/5/03
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G. A. Edgar wrote:
> Compare the old AMS TeX font msym to the more recent font msbm.
> The old msym is like the Mathematical Pi quoted, while the new msbm is
> like the Eudlid Math 2.

This contradicts Barbara Beeton's claim in
http://groups.google.com/groups?selm=786755680....@MATH.AMS.ORG
I quote:
> i assure you that the doubled strokes in msym, in the sti openface
> font, and in msym are all in exactly the same places -- i checked
> all three from contemporaneous source documents before replying.
> i will be happy to produce the evidence, which is part of my
> permanent library.

Is there any reliable way to check for sure? I have access to
libraries, it's just knowing what to look for... Are there
any journals that indisputably used msym during some period?

Thanks everyone who's replied, I hope we can get to the bottom
of this one!

Robin

G. A. Edgar

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Oct 5, 2003, 7:47:47 PM10/5/03
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In article <3F808D80...@remove-this-bit.kitsite.com>, Robin
Houston <ro...@remove-this-bit.kitsite.com> wrote:

OK, here are the two AMS fonts:

<http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>

Don't you agree that msym looks like Mathematical Pi? (The little
swish on the Q is maybe different.) And msbm is the same as Euclid
Math 2.

Robin Fairbairns

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Oct 6, 2003, 3:39:06 AM10/6/03
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"G. A. Edgar" <ydp4f...@sneakemail.com> writes:
>OK, here are the two AMS fonts:
>
><http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>
>
>Don't you agree that msym looks like Mathematical Pi? (The little
>swish on the Q is maybe different.) And msbm is the same as Euclid
>Math 2.

you're right, of course. i remember thinking that msbm was a great
improvement, at the time it was released, but over the years there
have been people hankering after the shapes of msym. looking at them
side by side again, after all this time, i realise i was right (for my
value of "better") and they were wrong ;-)
--
Robin (the partially spineless) Fairbairns, Cambridge

Robin Houston

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Oct 6, 2003, 4:32:28 AM10/6/03
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G. A. Edgar wrote:
> OK, here are the two AMS fonts:
>
> <http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>

Very useful, thanks! I see now that I have misinterpreted
Barbara's remark: she was talking only about the _location_
of the doubled strokes, which is indees the same as in msbm.
(This is different from Alan Jeffrey's bbold font, for
example, which seems to be what's shown in
http://www.w3.org/TR/MathML2/double-struck.html)

> Don't you agree that msym looks like Mathematical Pi?

Yes, absolutely. So perhaps msbm was indeed the first
use of the "inline" style for blackboard bold. That would
be surprising, since inline fonts certainly predate
blackboard bold: for example
http://www.myfonts.com/fonts/linotype/cloister-open-face/cloister-open-face/testdrive.html?s=N+Q+R+Z+C&p=72
is a font designed in 1929.
One would expect printers to use the fonts they had already
available, where possible.

Robin

gowan

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Oct 6, 2003, 10:25:50 AM10/6/03
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"G. A. Edgar" <ydp4f...@sneakemail.com> wrote in message news:<051020031516078853%ydp4f...@sneakemail.com>...

> Of course this way of writing was devised for writing by hand (on a
> blackboard, for example); and then adapted for use by a typewriter
> (those ancient machines used before personal computers for producing
> documents in a home or office environment). Produce the blackboard
> bold R by typing an I and an R close together.

I agree this style must have originated as a way to produce "bold"
letters by hand on paper or blackboard. As an attempt to narrow the
date of origin I recall not seeing this as an undergraduate at a
mathematically sophisticated school in the early 1960's but
encountering it as a graduate student in the mid-60's. But I imagine
something like this was used in Europe or Germany, especially, before
that.

Lee Rudolph

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Oct 6, 2003, 10:47:00 AM10/6/03
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Yesterday I wrote:

>By 1966, however, Gunning (in "Lectures on Riemann Surfaces",
>PUP Princeton Mathematical Notes) uses doublestruck C and R;

...


>(I believe it was from him that I learned to use it,
>at just around that time);

and so on. Since writing that, I have exchanged e-mail with
Professor Gunning. Like others, he has heard that the notation
goes back to Bourbaki--more specifically, he says he picked it
up in the Kodaira-Spencer seminars (at Princeton, early 1960s),
and that someone there (whose name he can't recall) attributed
it to Bourbaki. He confirms that it was in the early 1960s
that he himself was converted to the notation, and started
passing it on to students; and he says (I paraphrase, since
I didn't ask permission to quote) that Addison-Wesley didn't
give him and Rossi any trouble about using blackboard bold
for the complex numbers (but that he and Rossi *did* have
trouble convincing A-W to allow non-bold vectors and yet
bold germs). He has also promised to ask other veterans
of the K-S seminar for their memories, which I will pass
on as they arrive. (I think I will not act on his implicit
suggestion that one might ask Serre; but if anyone else has
the chutzpah to do so, I don't doubt something useful might
be learned from the experiment.)

I hope to spend some time in the library stacks today, and
may have more data by this afternoon.

Lee Rudolph

Dan Luecking

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Oct 6, 2003, 3:04:50 PM10/6/03
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I remember noticing as an undergraduate math major (1967-1971) that
the books that I read and that used a distinctive font for these sets,
all used some sort of ordinary bold (upright or slanted). While all my
teachers used blackboard bold on the blackboard. I jumped to the
conclusion that BBB was simply a way to make a bold-like distinction
in a medium where it was not otherwise possible. I have always felt
it is overused in print. Most articles in my field (complex analysis)
don't have any other bold C in them and a simple bold letter C would
be quite sufficient.

By the way, none of my teachers added more than one extra stroke to
their ordinary uppercase letters to produce BBB. The example BBB in
the TeXBook (my edition anyway) is pretty obviously a CMR I and R
run together. (I thing it looks better than any currently available
doublestroke font and have considered adapting cmr to produce something
along those lines.)


Dan

--
Dan Luecking Department of Mathematical Sciences
University of Arkansas Fayetteville, Arkansas 72701
luecking at uark dot edu

Dan Luecking

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Oct 6, 2003, 3:08:37 PM10/6/03
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On Mon, 06 Oct 2003 09:32:28 +0100, Robin Houston
<ro...@remove-this-bit.kitsite.com> wrote:

>G. A. Edgar wrote:
>> OK, here are the two AMS fonts:
>>
>> <http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>
>
>Very useful, thanks! I see now that I have misinterpreted
>Barbara's remark: she was talking only about the _location_
>of the doubled strokes, which is indees the same as in msbm.
>(This is different from Alan Jeffrey's bbold font, for
>example, which seems to be what's shown in
>http://www.w3.org/TR/MathML2/double-struck.html)
>
>> Don't you agree that msym looks like Mathematical Pi?
>
>Yes, absolutely. So perhaps msbm was indeed the first
>use of the "inline" style for blackboard bold.

When you say "inline" do you perhaps mean "outline"? I have never heard
"inline" used in this sense.

David Kastrup

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Oct 6, 2003, 3:14:03 PM10/6/03
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Dan Luecking <Look-...@uark.edu> writes:

> By the way, none of my teachers added more than one extra stroke to
> their ordinary uppercase letters to produce BBB. The example BBB in
> the TeXBook (my edition anyway) is pretty obviously a CMR I and R
> run together. (I thing it looks better than any currently available
> doublestroke font and have considered adapting cmr to produce
> something along those lines.)

You mean like the bbm.sty and fonts do?

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
UKTUG FAQ: <URL:http://www.tex.ac.uk/cgi-bin/texfaq2html>

Robin Houston

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Oct 6, 2003, 5:33:25 PM10/6/03
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Dan Luecking wrote:
> When you say "inline" do you perhaps mean "outline"? I have
> never heard "inline" used in this sense.

Let me quote from the typographic glossary in Robert
Bringhurst's excellent book _The Elements of Typographic Style_:

Inline: A letter in which the inner portions of the main
strokes have been carved away, leaving the edges more
or less intact. Inline faces lighten the color while
preserving the shapes and proportions of the original
face. _Outline_ letters, on the other hand, are produced
by drawing a line around the outsides of the letters
and removing the entire original form. Outline letters,
in consequence, are fatter than the originals and have
less definition.


Robin

Dan Luecking

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Oct 8, 2003, 4:44:54 PM10/8/03
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On 06 Oct 2003 21:14:03 +0200, David Kastrup <d...@gnu.org> wrote:

>Dan Luecking <Look-...@uark.edu> writes:
>> ... The example BBB in


>> the TeXBook (my edition anyway) is pretty obviously a CMR I and R

>> run together. (I think it looks better than any currently available


>> doublestroke font and have considered adapting cmr to produce
>> something along those lines.)
>
>You mean like the bbm.sty and fonts do?

No, I don't mean like that. I'm pretty sure I've checked all
"currently available" (free) doublestroke fonts. There's a
blackboard.ps by Olaf Kummer available on CTAN that lists them
(or at least those that were known to the author). And I usually
check out any new ones announced here.

As to bbm: compare the example "R" in the TeXBook (in index under
blackboard bold) to the bbm "R". Not at all alike.

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