On Monday 22 October 2012 01:10:18 Mike Speciner wrote:

Well, maybe I'm just too fussy. (My first job, in the early '70s, was writing software to typeset mathematics beautifully, and I always thought that TeX was a big step backwards from the state of the art.) Your png looks quite similar to what I see. Should I not expect the first two 1s to be at the same height? Should I not expect the ; between 1/qz and 1/q to be vertically centered around the fraction bars so that the semicolon's dot doesn't look like a center dot? And should I not expect the spacing to be a bit looser in several places?

I'm fairly sure that texify.com is not in fact running TeX; it's doing some simpler cheaper thing, probably involving MathML or something. If you typeset that same formula in TeX then ... well, actually you still get something pretty ugly, but it's ugly in quite different ways. What was the state of the art of computerized mathematical typesetting before TeX? -- g

interesting. are there any well-known books that were typeset with this language? Tippy-tapped on my iPad On Oct 21, 2012, at 6:12 PM, Mike Speciner <ms@alum.mit.edu> wrote:

There was this company called Composition Technology [CTI] in the early '70s that typeset mathematics for various journals and textbooks using cottage-industry typists who had been trained to do markup from the manuscripts. For mathematical markup, the language they used was fairly straightforward (e.g., "sub ... base" for subscripts "div ... den ... base" for built-up fractions); overall a couple of dozen constructs of that type, each with their own spacing rules. All the common math symbols had short mnemonic names as well. The typed pages were scanned and then processed by a PDP-6 using a pile of software, eventually producing camera-ready pages on a phototypesetter. [The downfall of the company was the cost of commercial PDP-6 time; they didn't have the capital to buy their own computer. Remember, this was forty years ago.] The software knew about fonts and characters and did kerning to properly position operators, sub- and superscripts, over and under characters [e.g., accents, overbars, sum and integral limits], particularly important with the beautiful Times Italic font. AFAIK, no one does kerning anymore, and so special, more upright fonts are used to make things look less bad. CTI had software for creating new characters for the phototypesetter [mathematicians are very inventive], which used a surprisingly wierd incremental bitmap format. CTI also "invented" a new relative character position (besides sub, sup, over, under, leftsub, leftsup) called overlay, which allowed users [e.g., typists] to create useful combinations of symbols by plopping existing symbols on top of each other.

CTI was owned by Alpha Industries, and when CTI failed, the technology was carefully documented and archived somewhere, presumably to remain a trade secret for eternity.

On 2012-10-21 20:34, Gareth McCaughan wrote:

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On Monday 22 October 2012 01:10:18 Mike Speciner wrote:

...

Well, maybe I'm just too fussy. (My first job, in the early '70s, was writing software to typeset mathematics beautifully, and I always thought that TeX was a big step backwards from the state of the art.) Your png looks quite similar to what I see. Should I not expect the first two 1s to be at the same height? Should I not expect the ; between 1/qz and 1/q to be vertically centered around the fraction bars so that the semicolon's dot doesn't look like a center dot? And should I not expect the spacing to be a bit looser in several places? I'm fairly sure that texify.com is not in fact running TeX; it's doing some simpler cheaper thing, probably involving MathML or something. If you typeset that same formula in TeX then ... well, actually you still get something pretty ugly, but it's ugly in quite different ways.

What was the state of the art of computerized mathematical typesetting before TeX?

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Times italic "f" usually has the most egregious issue with superscripts and accents (particularly hacek and macron (overbar)), since its top hangs quite far over. (That's also the reason for the ff, fi, fl, ffi, ffl ligatures--in the really old days of metallic type, if you tried to put those combinations together with single letters, you'd break off the f's overhang!) As far as samples of CTI's composition, I don't remember the names of the books that were done, just some of the publishers--Houghton Mifflin, Prentice Hall, Addison Wesley, and John Wiley come to mind, but I'm not certain. I do know that a number of AMS journals were produced by CTI, probably around 1972-1973. I might be able to recognize the typesetting if I saw it. I do remember one jr high or high school math textbook that was done with non-standard (i.e., not Times-Roman) fonts; I think they decided to use a sans serif font resulting in something not very pretty. I'm not familiar with TeX's kerning facility (and the last I looked, which was a very long time ago, it didn't have any), but typical kerning is done by a table of character pairs within the same font and size. CTI kerning was done by letter shape and could handle any horizontal juxtaposition of characters, even if they were from different fonts and at different sizes/obliquenesses/baseline (as would happen with subscripts and superscripts, math symbols, greek letters, etc.). --ms On 2012-10-22 17:55, Gareth McCaughan wrote:

Mike Speciner wrote:

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There was this company called Composition Technology [CTI] in the early '70s ... The software knew about fonts and characters and did kerning to properly position operators, sub- and superscripts, over and under characters [e.g., accents, overbars, sum and integral limits], particularly important with the beautiful Times Italic font. AFAIK, no one does kerning anymore, and so special, more upright fonts are used to make things look less bad. TeX is semi-smart about these things. It doesn't have separate positions for each (character,accent) pair -- it has general facilities for kerning, of course, but accented characters aren't considered instances of that -- but does let you say "this font slants by so much, so adjust accents accordingly". Empirically, I haven't noticed TeX-typeset accent positions being bad. (There *are* positioning and spacing things TeX does that I find very unsatisfactory, but that isn't one.) But then, I suspect that our tastes differ. I agree that the Times italic is elegant, but I find its roman so ugly that I'd never use it.

I too would be interested in examples of books typeset with CTI's software.

The character pair kerning you describe is what is used for text, and is typically NOT what you want to do for typesetting mathematics. For example, if you have a sequence of unsubscripted variables concatenated (as for multiplication), you don't want them to kern--e.g., f times i times n would look wrong in the mathematical sense if kerned, it would look like the italicized word fin instead. What CTI did, in those days of limited processing power, was to preprocess each character's bitmap, computing a quantized sequence of 12 values describing the left and right outlines of the character relative to its bounding box (the horizontal escapement of the character when typeset by the actual vertical extent). The bounding box was broken vertically into 6 equal pieces. The left and right outlines of the character were then each represented by 6 integers, with the horizontal increments being .05 em, and ranging from something like -2 (farthest inside the bounding box) to +4 (farthest outside the bounding box). (I'm not sure I have the details exactly right--it's been a couple of lifetimes ago.) The kerning algorithm matched the right side of one character with the left side of the next, handling such things as different baselines and sizes (e.g., for sub and superscript), and even different obliquing (greek letters were typically obliqued, as were sans serif fonts which typically didn't have separate italic subfonts). Larger constructs, like accented characters and built-up fractions, had their left and right sides computed on the fly if they needed to be kerned with adjoining characters or constructs. During the development of the kerning algorithm, it was discovered that some smoothing and limiting was necessary to avoid undesirable results such as the exponent in e**-x from sliding over the e! --ms On 2012-10-23 04:58, Gareth McCaughan wrote:

On Tuesday 23 October 2012 04:05:15 Mike Speciner wrote:

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I'm not familiar with TeX's kerning facility (and the last I looked, which was a very long time ago, it didn't have any), Wow.

Kerning is described in the "TEXDRA.FT" document Knuth put out in May 1977, well before any version of TeX was actually released. On the other hand, the next version of that document, TEX.ONE in July of the same year, seems to imply no kerning. The first book made with TeX, a keepsake for Knuth's wife's relations made in late 1978, has no kerning. There was definitely kerning by 1981 (in particular, before the big transition from TeX78 to TeX82).

Does anyone know more exactly when kerning was introduced to TeX?

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but typical kerning is done by a table of character pairs within the same font and size. CTI kerning was done by letter shape and could handle any horizontal juxtaposition of characters, even if they were from different fonts and at different sizes/obliquenesses/baseline (as would happen with subscripts and superscripts, math symbols, greek letters, etc.).

Yes, TeX uses a table of character pairs within each font. So CTI did some kind of optical kerning? Can you say anything about the algorithms used?