
Boiling lead and black art: a history of mathematical typography - fanf2
http://www.practicallyefficient.com/2017/10/13/from-boiling-lead-and-black-art.html
======
Turing_Machine
"Gutenberg revolutionized hot metal typesetting by coming up with an alloy
mostly made of lead that could be melted and poured into a letter mold called
a matrix."

The key feature of Gutenberg's alloy was that it _expands_ when it solidifies,
rather than shrinking. That's a very unusual property; most substances shrink
when they freeze, rather than expanding (water is another exception to this
general rule, which is why pipes break when they freeze).

The expansion is critical to getting a high-quality casting, because it forces
the metal into every nook and cranny.

~~~
whathaschanged
Expansion does nothing for air bubbles around edges and detail, even with vent
holes. Not sure what you are basing that on.

~~~
jacoblambda
The issue with normal alloys is more so having to handle contraction. With an
alloy that expands as it cools, while bubbles may still be an issue, you no
longer have to worry with working out how much the alloy will contract.

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taeric

        I strongly believe that an 
        unchanging system has great
        value, even though it is 
        axiomatic that any complex 
        system can be improved.
    
    

I have really grown to appreciate this attitude. I understand progress is a
great thing. And all things can progress. It is also great knowing that
progress won't have to lose things.

------
peter303
I was at Stanford when Prof Knuth developed his TeX system in the 1980s. It
was wonderful to watchthe user group meetings develop these systems. For
themost TeX semed to spring in a fully developed fashion like Athena born from
the head of Zeus.

At the same time as TEX Knuth developed literate programming. It was a method
of writing code and documentation simultaneously with empathsis on the latter.

The main disappointment with TeX is that it postponed Knuth finishing his
algorithms magus opus The Art of Computer Programming by a decade or so. And
perhaps unfinished in his lifetime.

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zokier
What seems amazing is that despite the incredible challenges in math
typesetting over the centuries, there seems to have been relatively little
movement to reform or adapt the notation to be more easily typesettable. You'd
think that the difficulty of getting your work printed would produce a
pressure to direct the evolution, but apparently not.

~~~
svat
Wouldn't that be backwards? The purpose of notation is to aid human thought
and communication. Technology should adapt to whatever notation would be most
useful to mathematicians, rather than mathematicians adapting their notation
for the sake of technology (like “more easily typesettable”).

The blackboard-bold fonts are an interesting example of this, with computer
typefaces being created for what mathematicians use in the real world. (Though
Knuth and Serre and some other mathematicians don't approve of them in
typesetting.) Besides, typesetting is a small part of the usage of notation;
most of it is written in private by mathematicians for themselves or
collaborators, in the classroom for students, in talks for each other, etc.
(Typeset papers are a low-bandwidth communication medium, though good for
broadcast and archival.) While it may make sense to optimize the ease of
creation of typeset mathematics (and that is what Knuth etc. have done to some
extent), changing the notation (for this reason) is not a sensible place to do
that.

(Some related links:
[https://micromath.wordpress.com/2010/09/24/psychophysiology-...](https://micromath.wordpress.com/2010/09/24/psychophysiology-
of-blackboard-teaching-2/)
[http://sites.math.rutgers.edu/~zeilberg/Opinion60.html](http://sites.math.rutgers.edu/~zeilberg/Opinion60.html)
[http://okasaki.blogspot.com/2008/01/why-i-dont-use-
powerpoin...](http://okasaki.blogspot.com/2008/01/why-i-dont-use-powerpoint-
for-teaching.html)
[http://sites.math.rutgers.edu/~zeilberg/Opinion78.html](http://sites.math.rutgers.edu/~zeilberg/Opinion78.html)
Section 3 of
[https://arxiv.org/abs/math/9404236](https://arxiv.org/abs/math/9404236))

~~~
canjobear
The cryptic nature of math notation is a major hindrance for people learning
and using it: for detailed arguments along these lines see [1].

Maybe if math notation were forced to be easily typesettable, it would be
simpler or more programming-language-like.

[1]
[https://mitpress.mit.edu/sites/default/files/titles/content/...](https://mitpress.mit.edu/sites/default/files/titles/content/sicm/book-
Z-H-5.html)

~~~
svat
My point was that the notation should be optimized for the people using it,
not for the technology used to typeset it. If the notation is suboptimal for
the _people_ then it can definitely be changed, but that's a different reason.

Note that some of these notational improvements may actually make it _harder_
to typeset. For example, the second part of Knuth's paper "Two Notes on
Notation"
([https://arxiv.org/abs/math/9205211](https://arxiv.org/abs/math/9205211))
introduced improved notation for the Stirling numbers "of the first kind" and
"second kind", replacing easier-to-typeset but less informative notation like
S(n,k). This notation has gained a good degree of acceptance, the paper won a
writing award ([https://www.maa.org/programs/maa-awards/writing-
awards/paul-...](https://www.maa.org/programs/maa-awards/writing-awards/paul-
halmos-lester-ford-awards)), and another paper citing it calls this “The best
thing that has happened to the Stirling numbers during their 400 years of
chequered history”
([https://www.jstor.org/stable/2974533?seq=1](https://www.jstor.org/stable/2974533?seq=1)).
(See also a talk of his on Notation
[https://www.youtube.com/watch?v=KjbuyB4dQa0&list=PLoROMvodv4...](https://www.youtube.com/watch?v=KjbuyB4dQa0&list=PLoROMvodv4rNMsVRnSJ44WuwbminUqXX2&index=14)
for which someone has taken notes:
[https://crypto.stanford.edu/pbc/notes/misc/notation.html](https://crypto.stanford.edu/pbc/notes/misc/notation.html))

I think there are valid questions to be raised on _which_ people to optimize
for: whether the students encountering the notation for the first time, or the
people who use it every day for years. In either case (to make my point again)
it's a question about people, and not about the technology — a programming-
like notation isn't better unless that's how the people who use it think (or
want to think).

------
nathell
The proper pronunciation of TeX is /ˈtɛx/, not /ˈtɛk/, ending with a voiceless
velar fricative.

~~~
lottin
Maybe in Greek, but English doesn't have the /x/ sound.

~~~
Y_Y
Maybe your dialect doesn't, but mine certainly does.

~~~
umanwizard
Genuine curiosity: what dialect is that? I live in the US and have met people
from several other English-speaking countries and I don't recall ever having
heard that sound from any native English speaker. (I'm not saying I don't
believe you; I'm just surprised).

~~~
Y_Y
Southern Irish, although as a sibling comment noted you'll also find it in
Scotland and Northern England. It helps that the Irish language uses this
sound copiously so most people are used to it from school.

~~~
umanwizard
What English words do you have that sound in?

------
ivan_ah
This was a fascinating historical article. We should all appreciate TeX more.
Yes it's 80s technology, but it will be really hard to replace...

Interesting to note the TiKZ example uses spheres and not boxes — boxes look
less good because TiKZ doesn't do perspective projections for the viewpoint,
only isometric. This makes boxes look "weird" if you're used to 3D graphics
from games and other 3D renderers.

------
spunker540
I found this worthwhile simply for the history of typesetting, regardless of
the difficulties of printing mathematics. I did not realize how much went into
typesetting and printing back in the day. Hard to believe daily papers were so
prevalent back in the 1800s when it was so challenging to print anything at
all! I definitely did not give printing enough credit in the pre-digital era.
It's amazing!

~~~
aomurphy
It's worth one day finding a printing press class and setting some type by
hand. For one thing, what you'll produce is beautiful, and it really gives a
sense of how much art, work, and mastery goes into type.

~~~
jeblair
Indeed. In the SF Bay area, a good option for introductory hands-on learning
about printing is the San Francisco Center for the Book:
[https://sfcb.org/](https://sfcb.org/)

------
agumonkey
People should watch Guy Steele CMS talk, he goes into the variations of
mathematical notation (grouping, lambdas, etc)

~~~
zokier
Link please? Couldn't readily find it via google.

~~~
agumonkey
Here's a slightly edited rendition at the latest conjure conf
[https://www.youtube.com/watch?v=dCuZkaaou0Q](https://www.youtube.com/watch?v=dCuZkaaou0Q)

~~~
DonHopkins
Thanks, this is a fascinating talk!

TIL not to confuse these people:

[https://en.wikipedia.org/wiki/Emil_Leon_Post](https://en.wikipedia.org/wiki/Emil_Leon_Post)

[https://en.wikipedia.org/wiki/Emily_Post](https://en.wikipedia.org/wiki/Emily_Post)

------
keithpeter
Interesting article with a challenge at the end.

Alas, no mention of the earlier and less versatile eqn/troff (along with tbl
and pic) to contrast with Knuth's end-to-end system.

[https://en.wikipedia.org/wiki/Eqn](https://en.wikipedia.org/wiki/Eqn)

------
skierscott
...I read the article in Safaris Reader mode. The font is too big for mobile.

But this is a great article.

~~~
dEnigma
I was able to read it just fine. In fact, if the text were any smaller, I
would probably have problems reading it. Especially on this shaky bus ride.

