• He had already published the first editions of Volume 1, 2, 3, and the second edition of Volume 1, by 1973. It was in 1977 when the publishers sent him galley proofs for the second edition of Volume 2, having switched to phototypesetting (away from hot-metal typesetting a la Linotype, though IIRC it was actually Monotype) that he was disappointed with the results. And he had some back-and-forth with them and they did improve their fonts (https://tex.stackexchange.com/a/367133/48), but he was still dissatisfied.
> I didn't know what to do. I had spent 15 years writing those books, but if they were going to look awful I didn't want to write any more.
• At this time he came to know of the existence of digital typesetters. Typesetting with computers had existed before, but it had always seemed a crude toy, rather than something suitable for “real books”. But he saw Patrick Winston's Artificial Intelligence that had been just published (I think he got an early proof copy to review or something), and he realized for the first time that digital typesetting was an option (apparently Winston's book was printed at >1000dpi, and Knuth later got his hands on a machine that claimed a resolution of 5333 dpi: see this wonderful comment from Knuth's student and “right-hand man”, David Fuchs: https://news.ycombinator.com/item?id=20009875)
• In fact it was the fonts that he was dissatisfied with rather than the typesetting, so METAFONT was in some sense the primary/motivating project and TeX was only written in order to be able to use METAFONT.
• Actually his first idea was to simply take the old fonts, get high-resolution scans of them (not easy to obtain at that time) and use them directly. He approached Xerox Research Center but:
> I asked if I could use Xerox's lab facilities to create my fonts. The answer was yes, but there was a catch: Xerox insisted on all rights to the use of any fonts that I developed with their equipment. Of course that was their privilege, but such a deal was unacceptable to me: A mathematical formula should never be "owned" by anybody! Mathematics belongs to God.
• So he went home and (after trying a bit with TV cameras) tried projecting photographs of the pages onto the wall and tracing the outlines, and it was while staring at these images that he realized that the shapes of letters were not arbitrary but there was some logic to them (e.g. in the font he was using, the spacing between the vertical strokes in 'm' was equal, and equal to that in 'n'), and he decided (as a computer programmer) to capture this design in code — something that had never before been done. The hardest letter to capture this way is S, hence the paper in the OP.
> Finally, a simple thought struck me. Those letters were designed by people. If I could understand what those people had in their minds when they were drawing the letters, then I could program a computer to carry out the same ideas. Instead of merely copying the form of the letters my new goal was therefore to copy the intelligence underlying that form. I decided to learn what type designers knew, and to teach that knowledge to a computer.
• This is also why METAFONT never really caught on among typographers: as Charles Bigelow (quoted by Richard Southall, https://luc.devroye.org/Southall-METAFONT1986.pdf) observed, “the designer thinks with images, not about images”. Knuth did not want crude “geometric” constructions of letters (as some prior 16th century typographers had attempted: https://www.ams.org/journals/bull/1979-01-02/S0273-0979-1979... and as some typographers only passingly familiar with METAFONT think!). He wanted actual real typographically beautiful shapes, but to be able to generate those shapes with code. This is obviously much harder than simply drawing the shapes using visual intuition, even if it enables variation. (See “The Concept of a Meta-Font”: https://gwern.net/doc/design/typography/1982-knuth.pdf — again, many people in the typography world confuse the abstract concept of a meta-font introduced in this paper with (their incorrect impressions of) the METAFONT program, and omit crediting Knuth for variable fonts).
• The second edition of Volume 2 was not printed with Linotype. Yes the machines still existed in Europe and he talked to typesetters (he mentions in particular a person from Belfast), but it was in fact published using TeX (the first version, TeX77 and MF78). He was still unhappy with the results, though, and spent a few more years learning more about typography and working with people like Bigelow and Hermann Zapf, before the rewrite into the current TeX82 and MF84 (and current version of Computer Modern). I think it's only with the third edition (1997) that he's finally satisfied.
The motivation behind METAFONT is amusing to me because it seems to have some of the same hubris of the most extreme AI proponents nowadays: we can replace art by technology. I'm fascinated with TeX (and have spent a lot of my life rewriting it http://github.com/jamespfennell/texcraft) but I always found the situation with fonts in the TeX ecosystem a bit odd. There are people in our society whose vocation is font design (e.g. https://en.wikipedia.org/wiki/Robert_Slimbach). But the TeX ecosystem landed in a place where we use fonts created by computer scientists rather than font designers.
>Why don't you make them _S_ shaped?
To some degree, this problem was eventually solved, c.f., the five volume set _Computers and Typesetting_:
https://www-cs-faculty.stanford.edu/~knuth/abcde.html
but then one had the effort to create a new typeface set for math equations by the AMS, eventually named Euler as written up in "AMS Euler — a new typeface for mathematics". _Scholarly Publishing_ and so forth, but arguably, things went awry in that rather than capture the ductus of Prof. Zapf's pen, and model based on that stroke and a pen shape, the expedient approach of simply modeling the outline was arrived at and implemented due to the difficulty and lengthy time required for the idealized approach.
Another consideration may have been that there doesn't seem to be an available algorithm which is robust and accurate and automatic for determining the curves which describe the union of arbitrary Bézier curves (some projects get around this by making high resolution pixel images and tracing them).
Fig 9 stood out to me as obviously wrong. The two glyphs on the left are pixel by pixel identical, as are the three middle ones, and the two on the right. Quite mysterious though considering this PDF appears to be a scan.
https://www.dkriesel.com/en/blog/2013/0802_xerox-workcentres...
Thanks for giving us beautiful layout and better-looking fonts. Every time I write a new paper when I press "compile" in Overleaf I'm greatful that he made our work more beautiful, and it motivates me to make the content matter, too.
See the definitions of "O" and related glyphs for a good example[2].
[1] https://github.com/be5invis/PatEL
[2] https://github.com/be5invis/Iosevka/blob/main/packages/font-...
This results in a more complex and less obvious mathematical definition.
Also, a naively symmetrical "S" tends not to look good, probably because of these same issues, so needs further adjustment to match our visual expectations. This complicates the definition further.
Having models attempt an SVG letter S remains one of my personal/informal LLM benchmarks. They are still pretty bad at it.
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The motivation was not to replace art with technology, but to preserve/resurrect an art that was going away, by truly capturing the human understanding[^1]. When the rest of the industry was perfectly content with the deterioration of typesetting, Knuth set out to capture the aesthetics of the best journals of the past. A quote from the Mathematical Typography paper I linked above (https://websites.umich.edu/~millerpd//docs/501_Winter13/Knut...):
> At this point I regretfully stopped submitting papers to the American Mathematical Society, since the finished product was just too painful for me to look at. Similar fluctuations of typographical quality have appeared recently in all technical fields, especially in physics where the situation has gotten even worse.
Frankly, I think the "replace art by technology" impression is a very shallow one, that I alluded to earlier. When Knuth wrote his “The Concept of a Meta-Font” in a journal (Visible Language) mostly read by designers/typographers, many of them wrote letters in response (https://shreevatsa.net/tex/metafont/concept#reactions). What you can see is that the best of them were supportive (even bringing up new points like how it could be useful in educating the next generation of font designers), but some were sharply critical, more or less resenting this intrusion of technology into their art medium. But now a few decades later, basically all fonts are distributed and stored digitally anyway, except that (without METAFONT) the shapes of letters are now basically just stored as binary blobs / sequences of numbers, without any METAFONT-like understanding of typographically relevant quantities like (say) x-height, comma depth, slab thickness, etc. Which one is truer to the art?
(Not a rhetorical question BTW: as in the Bigelow/Southall quote above, one could say that Knuth's approach is to achieve typographical/artistic excellence through understanding, but the artistic approach is visual and intuitive without a cognitive component. But this is a different complaint from the "replace art by technology" take.)
(BTW apart from the default Computer Modern fonts designed by Knuth, who based them on earlier Monotype fonts, almost all fonts used by people with TeX too are designed by font designers, not computer scientists.)
[1]: Related quote from Knuth (sorry paraphrasing from memory): “People say that the best way to understand something is to teach it. I say no: the best way to understand something is to teach it to a computer.” But then again he has also said: "Science is what we understand well enough to explain to a computer. Art is everything else we do."
One point concerning Metafont and Computer Modern (and TeX): A key overall goal of the whole kit and caboodle is that a document written in TeX and using the default fonts would produce exactly the same output on all capable computers and output devices, indefinitely into the future, with the same line breaks, page breaks, character shapes, etc. And in fact TeX files from over half a century ago still produce pixel-perfect results.
This requirement meant that the default fonts had to be portable between printers and typesetters with various resolutions (and other optical filtering attributes). There was simply no other way at the time to accomplish this than using a tool like Metafont to author a home-grown font family like Computer Modern (and even then it was a bit of a hope and a prayer).
And don't even get me started on how 5pt super-super-scripts aren't just 10pt characters scaled down by half, contrary to how post-hot-lead typesetters operated, and not fully addressed commercially until decades later.
Metafont users can specify point size, boldness, slant, and whatever other parameters they choose (plus device-specific info like resolution) that can then be used in the simultaneous equations that determine the coordinates of critical points and shapes of pens used to draw the characters. So, for the smaller-font issue, the width of the pen may be a non-linear function of the font point size; ditto for the x-height, etc. In Metafont, it's the responsibility of the font designer / coder to handle it all; there's no automated algorithmic monkeying with the pixels other than what you write. This all becomes much clearer with a perusal of The METAFONTbook.
https://tug.org/interviews/fuchs.html
a useful starting point.
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I have not heard if Butterfield has started a third company to develop a video game.
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1. Funnily enough this is the second time in two days that I’ve shared this article, albeit in different contexts.
2. As far as I know, although I could be wrong.
Surely Karow's Ikarus was earlier than that.
One of the main innovations of Metafont was the use of "pen"s, so that one would describe a single path and the software would trace it and imitate the use of one or more pens, to end with an outline of something with thickness, and essentially more curves. It mimics how drawing and writing actually happens.
AFAIK, Zapf did not like this approach at all, as he was used to design typefaces the traditional way, by specifying all the curves. Richard Southall embraced the new paradigm and used Metafont as it was supposed to be used, but produced only a couple of demo typefaces (mainly the nmt family) and a handful of commercial ones (I can now only remember Colorado, with Ladislas Mandel, used in the phone directories of US West). I think he also implemented Melior, but of course this was never distributed as it was a proprietary Zapf design.
Note: all the above are based on recollections of my discussions with Zapf, Southall, and Knuth, in the distant past. All my relevant printed materials are in a different country right now, and I don't have easy access to them.
_TeX and METAFONT_ (the book) was published in 1979 (I still vividly remember checking a copy out of the local college library as a high school student in 1983) having its initial release in 1978, after being precipitated by the infamous second edition galley proofs on TAoCP 30 March 1977.
Didn't mean for my post to come across as cavalier --- it's a _very_ tough row to hoe, and even now, I don't think that there are good solutions in this space (but I haven't checked for a while, been out of the typography scene for a while now --- I'd love to be wrong). Ironically, my current project
https://github.com/WillAdams/gcodepreview
is circling back to the underpinnings of this sort of thing (I need to make a single stroke font so as to make it easier to set text in CNC projects) and I'm hoping to approach this from the bottom up and eventually arrive at a visual and interactive version of METAFONT/POST which will also work as a general-purpose drawing program (so that I'll have one to use when I can no longer use Freehand/MX) --- hopefully that will then allow me to finish a compleat digital version of Warren Chappell's typeface designs as we discussed peripherally ages ago.
Burninating the peasants.
Burninating all the peoples.
This is all fine. What fascinates me with Knuth's work is how he applies mathematical rigour to concepts like these which are generally considered "artistic" and subjective. It underlines how mathematical ideas of symmetry etc. play a role in making the world we live in beautiful.
I remember seeing an animated documentary as a child called "Donald in Mathmagic Land" which ends with a quote attributed to Galileo.
> Mathematics is the language with which God has written the universe