Boiling lead and black art: a history of mathematical typography | Hacker News Reader

Boiling lead and black art: a history of mathematical typography

practicallyefficient.com

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"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.

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

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.

    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.

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.

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.

Who cares what it takes to set mathematical notation in type? It's skilled labour, but done just once. What really matters is ease of reading.

Not necessarily. Most papers are not read that often.

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.

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://xkcd.com/927/

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) 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-...), 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). (See also a talk of his on Notation https://www.youtube.com/watch?v=KjbuyB4dQa0&list=PLoROMvodv4... for which someone has taken notes: 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).

Thanks to TeX math is easy enough to typeset that it probably doesn't need to be simplified much further. I mean, I've seen a bunch of undergrads learn how to use TeX much faster (and better!) than they learn the math they use it for.

Don't forget handwriting here. For all these centuries, and perhaps even today, the vast majority of both writing and reading of mathematics wasn't typeset: on blackboards and in lecture notes, and on paper in the many attempts to understand what someone else did, and in turn to work out results that may one day end up on a printed page.

Introducing an easy to read & easy to typeset notation which doesn't work well by hand means you're creating a figure, an illustration to be looked at like a photo, not something to be worked with.

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

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

English doesn't have umlaute either. That never prevented typesetters from using them.

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

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).

I'm guessing Northern England or Scotland.

https://en.wikipedia.org/wiki/Voiceless_velar_fricative

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.

What English words do you have that sound in?

It's what Knuth asked for. Lots of people like him enough to oblige.

Indeed. Quoting "The Name of the Game", the very first chapter of Knuth's "The TeXbook": "Insiders pronounce the $\chi$ of TeX as a Greek chi, not as an `x', so that TeX rhymes with the word blecchhh. It's the `ch' sound in Scottish words like loch or German words like ach; it's a Spanish `j' and a Russian `kh'. When you say it correctly to your computer, the terminal may become slightly moist."

Interesting bit: The Idea of the name came from the Greek word τέχνη (/ˈtɛxnɛ/), wich can be translated as art, skill and craft. A combination that captures the purpose of the program very well.

A russian "kh" ? That sound is spelled "х" in Russian

"X" is the transliteration of the Cyrillic character in question as per the 1995 version of ISO/R 9; but the 1968 version that was in effect when The TeXbook was first published has it as "kh". See https://en.wikipedia.org/wiki/ISO_9

You may want to send Knuth a note that he should update this for the next printing; perhaps you'll get one of his rewards.

Yes, but I've literally never once heard someone pronounce it "correctly."

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.

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!

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.

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/

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

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

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

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/Emily_Post

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

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

But this is a great article.

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.

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