Looks like no one complained about the long comment, so some further trivia I omitted mentioning:
• The problem that one cannot copy text from a PDF created via dvips and using METAFONT-generated bitmap fonts has recently been fixed — the original author of dvips, Tomas Rokicki ([1], [2]) has “come out of retirement” (as far as this program is concerned anyway) to fix this and is giving a talk about it next week at the TeX Users Group conference ([3], [4]):
> Admittedly this is a rare path these days; most people are using pdfTeX or using Type 1 fonts with dvips, but at least one prominent user continues to use bitmap fonts.
So in the future (when/if Knuth upgrades!) his PDFs too will be searchable. :-)
• In some sense, even Knuth's work on TeX and METAFONT can be seen as an extension of his drive to understand and explain (in his own unique way) others' work: at one point, suddenly having to worry about the appearance of his books, he took the time to learn intensively about typesetting and font design, then experiment and encode whatever he had learned into programs of production quality (given constraints of the time). This is in keeping with his philosophy: “Science is what we understand well enough to explain to a computer. Art is everything else we do.” and (paraphrasing from a few mentions like [5] and [6]) “The best way to understand something is to teach it to a computer”.
• Finally returning (somewhat) to the topic, and looking at the 2/3rds-page proof that Knuth posted [7], one may ask, is it really any “better”, or “simpler”, than Huang's original proof [8]? After all, Huang's proof is already very short: just about a page and a half, for a major open problem for 30 years; see the recent Quanta article ([9], HN discussion [10]). And by using Cauchy’s Interlace Theorem, graph terminology, and eigenvalues, it puts the theorem in context and (to researchers in the field) a “natural” setting, compared to Knuth's proof that cuts through all that and keeps only the unavoidable bare essentials. This is a valid objection; my response to that would be: different readers are different, and there are surely some readers to whom a proof that does not even involve eigenvalues is really more accessible. A personal story: in grad school I “learned” the simplex algorithm for linear programming. Actually I never quite learned it, and couldn't answer basic questions about it. Then more recently I discovered Knuth's “literate program” implementing and explaining the simplex algorithm [11], and that one I understood much better.
> The famous simplex procedure is subtle yet not difficult to fathom, even when we are careful to avoid infinite loops. But I always tend to forget the details a short time after seeing them explained in a book. Therefore I will try here to present the algorithm in my own favorite way—which tends to be algebraic and combinatoric rather than geometric—in hopes that the ideas will then be forever memorable, at least in my own mind.
I can relate: although the simplex algorithm has an elegant geometrical interpretation about what happens when it does pivoting etc., and this is the way one “ought” to think about it, somehow I am more comfortable with symbol-pushing, having an underdeveloped intuition for geometry and better intuition for computational processes (algorithms). Reading Knuth's exposition, which may seem pointless to someone more comfortable with the geometrical presentation, “clicked” for me in a way nothing had before.
This is one reason I am so fascinated by the work of Don Knuth: though I cannot hope to compare myself in either ability (even his exploits as a college kid are legendary [12]) or productivity or taste, I can relate to some of his aesthetic preferences such as for certain areas/styles of mathematics/programming over others, and being able to so well “relate” to someone this way gives you hope that maybe by adopting some of the same habits that worked for them (e.g.: somewhere, Knuth mentions that tries to start every day by doing whichever thing he's been dreading the most), you'll be able to move a few steps in somewhat the same direction, and if nothing else, this puts me in mind of what Bhavabhuti said many centuries ago [13] about finding someone with the same spirit, so to speak.
> The problem that one cannot copy text from a PDF created via dvips and using METAFONT-generated bitmap fonts has recently been fixed — the original author of dvips, Tomas Rokicki ([1], [2]) has “come out of retirement” (as far as this program is concerned anyway) to fix this and is giving a talk about it next week at the TeX Users Group conference ([3], [4])
Hope that will be filmed and put online, sounds like an intriguing talk to watch!
Wonderful insight into an interesting man. I’ve never understood why he’s spent so much time writing the Art of Computer Programming, but framing it as a deep inclination to explain and summarize the work of others in a beautiful way is such a wonderful perspective I’ve never heard anyone say before.
In 1993, Knuth requested of Stanford University (who granted his request) that he be allowed to retire early (and take up the title of “Professor Emeritus of The Art of Computer Programming”), so that he could complete TAOCP, which he regards as his life's work: https://cs.stanford.edu/~knuth/retd.html
Needless to say, the measly royalties from a technical book (especially one that is never going to be assigned as a textbook to large classes of undergraduate students) would be tiny in comparison to the Stanford professor salary that he gave up.
Also, if he were doing it as a source of income, he'd probably actually publish the long-awaited volumes so that they can sell and make money, rather than spend decades of full-time labour polishing each one (Vol 3 first came out in 1973; Vol 4A in 2011; Vol 4B is only about 1/3rd done), continually missing estimates, until they were at his desired level of quality.
Insisting on reducing every motivation to whether or not it makes money is such a narrow-minded display of being unable to imagine other ways of viewing the world that it's almost insulting.
• The problem that one cannot copy text from a PDF created via dvips and using METAFONT-generated bitmap fonts has recently been fixed — the original author of dvips, Tomas Rokicki ([1], [2]) has “come out of retirement” (as far as this program is concerned anyway) to fix this and is giving a talk about it next week at the TeX Users Group conference ([3], [4]):
> Admittedly this is a rare path these days; most people are using pdfTeX or using Type 1 fonts with dvips, but at least one prominent user continues to use bitmap fonts.
So in the future (when/if Knuth upgrades!) his PDFs too will be searchable. :-)
• In some sense, even Knuth's work on TeX and METAFONT can be seen as an extension of his drive to understand and explain (in his own unique way) others' work: at one point, suddenly having to worry about the appearance of his books, he took the time to learn intensively about typesetting and font design, then experiment and encode whatever he had learned into programs of production quality (given constraints of the time). This is in keeping with his philosophy: “Science is what we understand well enough to explain to a computer. Art is everything else we do.” and (paraphrasing from a few mentions like [5] and [6]) “The best way to understand something is to teach it to a computer”.
• Finally returning (somewhat) to the topic, and looking at the 2/3rds-page proof that Knuth posted [7], one may ask, is it really any “better”, or “simpler”, than Huang's original proof [8]? After all, Huang's proof is already very short: just about a page and a half, for a major open problem for 30 years; see the recent Quanta article ([9], HN discussion [10]). And by using Cauchy’s Interlace Theorem, graph terminology, and eigenvalues, it puts the theorem in context and (to researchers in the field) a “natural” setting, compared to Knuth's proof that cuts through all that and keeps only the unavoidable bare essentials. This is a valid objection; my response to that would be: different readers are different, and there are surely some readers to whom a proof that does not even involve eigenvalues is really more accessible. A personal story: in grad school I “learned” the simplex algorithm for linear programming. Actually I never quite learned it, and couldn't answer basic questions about it. Then more recently I discovered Knuth's “literate program” implementing and explaining the simplex algorithm [11], and that one I understood much better.
> The famous simplex procedure is subtle yet not difficult to fathom, even when we are careful to avoid infinite loops. But I always tend to forget the details a short time after seeing them explained in a book. Therefore I will try here to present the algorithm in my own favorite way—which tends to be algebraic and combinatoric rather than geometric—in hopes that the ideas will then be forever memorable, at least in my own mind.
I can relate: although the simplex algorithm has an elegant geometrical interpretation about what happens when it does pivoting etc., and this is the way one “ought” to think about it, somehow I am more comfortable with symbol-pushing, having an underdeveloped intuition for geometry and better intuition for computational processes (algorithms). Reading Knuth's exposition, which may seem pointless to someone more comfortable with the geometrical presentation, “clicked” for me in a way nothing had before.
This is one reason I am so fascinated by the work of Don Knuth: though I cannot hope to compare myself in either ability (even his exploits as a college kid are legendary [12]) or productivity or taste, I can relate to some of his aesthetic preferences such as for certain areas/styles of mathematics/programming over others, and being able to so well “relate” to someone this way gives you hope that maybe by adopting some of the same habits that worked for them (e.g.: somewhere, Knuth mentions that tries to start every day by doing whichever thing he's been dreading the most), you'll be able to move a few steps in somewhat the same direction, and if nothing else, this puts me in mind of what Bhavabhuti said many centuries ago [13] about finding someone with the same spirit, so to speak.
[1]: https://tomas.rokicki.com [2]: https://www.maa.org/sites/default/files/pdf/upload_library/2... [3]: http://tug.org/tug2019/preprints/rokicki-pdfbitmap.pdf [4]: https://github.com/rokicki/type3search/blob/a70b5f3/README.m... [5]: https://www.maa.org/sites/default/files/pdf/upload_library/2... [6]: https://youtu.be/eDs4mRPJonU?t=1514 (25:14 to 26:46) [7]: https://www.cs.stanford.edu/~knuth/papers/huang.pdf [8]: http://www.mathcs.emory.edu/~hhuan30/papers/sensitivity_1.pd... [9]: https://www.quantamagazine.org/mathematician-solves-computer... [10]: https://news.ycombinator.com/item?id=20531987 [11]: https://github.com/shreevatsa/knuth-literate-programs/blob/9... [12]: http://ed-thelen.org/comp-hist/B5000-AlgolRWaychoff.html#7 [13]: https://shreevatsa.wordpress.com/2015/06/16/bhavabhuti-on-fi...