I like J. Especially because it has a saner way to write it (it doesn't have to look like as if you accidentally forgot a null terminator in C strings, all the traditionally short identifiers have a long and understandable form).
I feel like it's very regrettable that the superficial aspect of J (the very hard to read syntax) is standing in the way of some very nice ideas.
To comment on mathematical notation. Before I was a programmer, I was a typographer. During my study in art academy, I invented a bunch of fonts, one of my long time projects was to make Hebrew look more like Latin fonts for example (this is a long-standing issue in Hebrew typography, with several historical attempts, but still not quite resolved). Afterwards I worked in a printing house, paginated a newspaper, typeset a bunch of books etc.
Among my coworkers (esp. in the newspaper) I was sort of known for trying to automate stuff, so, I was often suggested as a candidate for "difficult" typographical tasks, like setting sports tables, chess diagrams, music sheets and the most damned and hated kind of typographical work: math formulas.
I've helped publish a course book on linear algebra for a university. It was a multi-year project which I joined in the middle. I have never seen so much pain, struggle and reluctance as I've encountered while working on this thing. People tasked with proofreading demanded extra pay for proof-reading this stuff, and still wouldn't do it. Just put it away and later explain that they had other things to do. The lady who had to translate the mostly hand-written, or sometimes typed on a typewriter manuscript would just skip work on the days she was supposed to input the manuscript into our digital system.
Everyone passionately wanted this project to burn in hell. And the reason for this was the mathematical notation. Typical proofreading techniques don't work on math formulas. The text is impenetrable to anyone, often even to the people who wrote it, including both the author and the editor. Parenthesis are a curse, because in the manuscript they are one of the elements that is most commonly forgotten or misplaced. Single-letter variables are the other one. Overloading the same symbols with different meaning is yet another one. It gets worse when the same symbol is used in its normal size, subscript and superscript.
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When I talked about my experiences to people with degrees in math, they way they tend to respond to this is by saying that "math is overall so hard, that mathematicians don't typically notice the extra struggle they incur on themselves by the bad language choices, it pales in comparison to the difficulty of the main problem they need to solve".
And, I kind of can see it... on the other hand, I see no reason _the students_ have to endure the same torture. They aren't solving any novel mathematical problems. Their task is usually reading-comprehension combined with memorization.
And then I saw Sussman book where he uses Scheme to write math formulas (I think it was about physics, but it still used a lot of math). Dear lord, it was so immeasurably better than the traditional mathematical notation. I really wish more people joined this movement of ditching the mathematical notation in favor of something more regular and typography-friendly as Scheme...
I, on the other hand, am dreaming of being able to use mathematical notation in my code. Sort of like what Fortran has helped with, only on a much larger scale.
As with a lot of things, some people may enjoy arduous and very low-yield process for all sorts of reasons. I, for example, like baking sourdough bread.
As with the bread, which comes out more or less comparable quality to what I can buy from the local grocery in exchange for much less effort, I get certain satisfaction from doing it myself. But, if I had to do this on an industrial scale (and I worked in a bakery, although very briefly), I'd want to kill myself if I had to deal with the same kind of process.
Math language is very similar in this regard. It's kind of nice, like a calligraphy piece. Sometimes it takes a master month to write just a few words in a visually appealing way, but if this was the expectation for everyday boring tasks, that'd be a completely different story.
Low-effort may be if you are writing with a pen on paper, or chalk on the board. It's anything but even with systems like LaTeX.
Just to put this in perspective: in the days of me being a student, I got a gig at the state hotel for official guests. They had a guest book and the honored guests would usually leave an autograph in it. They hired me to use calligraphy to write the name and the title of the guest. Usually, that meant two, sometimes one line with just two or three words each. So, let's say four words per page. I would do about ten pages per day (they had couple years of backlog).
My typical workload in the newspaper for a day was somewhere between 16 and 24 A3 pages (this includes everything from inputting the text into the system, editor editing it, proof-readers reading it and me running back and forth between the editor and proof-readers to convince the editor to find a different image / add or remove a paragraph etc. If memory serves, that's about under 1K words per page. So, 16K-24K words per day (compared to 40 words per day of calligraphy).
With the math textbook, we did about a page a day, and it was closer to A4, so, under 500 words. Also, of course, the formulas are just a small fraction of the algebra textbook: most of it is prose: proofs or some general discussion about the subject. Of course some diagrams (but that's comparable to the newspaper).
So, while not as bad as calligraphy, math textbook was at least two orders of magnitude harder than newspaper, and only an order of magnitude easier than calligraphy.
NB. Newspapers aren't the easiest job in terms of putting text on paper. It's actually quite involved and paginators are under quite a lot of pressure to finish things on time, especially for the daily papers. If you are looking for the lowest effort / highest yield, something like the War and People (or is the traditional English translation the War and Peace?) would be your best bet. You can do hundreds of pages per day, even with moderate amount of illustrations.
> math notation is indeed high-yield and low-effort
low-effort is perhaps “your mileage may wary”, as they say :) but the yield per square inch of paper does indeed make math the most powerful and expressive language known to humans. On that note, Ken Iverson was very concerned that tons of mathematical symbolic conventions and speak overlap and conflict with each other to an obscene degree. As we all know, that little book he wrote on this very subject eventually got him a Turing award when people finally realized what he did there.
That said (and please no offense APL and typography fiends who are reading this) a considerable portion of the funny APL chars was a hard compromise dictated by economics and physics of IBM Selectric typeball.
With that in mind, if you take a fresh look at the original APL charset, you will see that much of it is stone-stupid overtypes of two ASCII chars.
I feel like it's very regrettable that the superficial aspect of J (the very hard to read syntax) is standing in the way of some very nice ideas.
To comment on mathematical notation. Before I was a programmer, I was a typographer. During my study in art academy, I invented a bunch of fonts, one of my long time projects was to make Hebrew look more like Latin fonts for example (this is a long-standing issue in Hebrew typography, with several historical attempts, but still not quite resolved). Afterwards I worked in a printing house, paginated a newspaper, typeset a bunch of books etc.
Among my coworkers (esp. in the newspaper) I was sort of known for trying to automate stuff, so, I was often suggested as a candidate for "difficult" typographical tasks, like setting sports tables, chess diagrams, music sheets and the most damned and hated kind of typographical work: math formulas.
I've helped publish a course book on linear algebra for a university. It was a multi-year project which I joined in the middle. I have never seen so much pain, struggle and reluctance as I've encountered while working on this thing. People tasked with proofreading demanded extra pay for proof-reading this stuff, and still wouldn't do it. Just put it away and later explain that they had other things to do. The lady who had to translate the mostly hand-written, or sometimes typed on a typewriter manuscript would just skip work on the days she was supposed to input the manuscript into our digital system.
Everyone passionately wanted this project to burn in hell. And the reason for this was the mathematical notation. Typical proofreading techniques don't work on math formulas. The text is impenetrable to anyone, often even to the people who wrote it, including both the author and the editor. Parenthesis are a curse, because in the manuscript they are one of the elements that is most commonly forgotten or misplaced. Single-letter variables are the other one. Overloading the same symbols with different meaning is yet another one. It gets worse when the same symbol is used in its normal size, subscript and superscript.
----
When I talked about my experiences to people with degrees in math, they way they tend to respond to this is by saying that "math is overall so hard, that mathematicians don't typically notice the extra struggle they incur on themselves by the bad language choices, it pales in comparison to the difficulty of the main problem they need to solve".
And, I kind of can see it... on the other hand, I see no reason _the students_ have to endure the same torture. They aren't solving any novel mathematical problems. Their task is usually reading-comprehension combined with memorization.
And then I saw Sussman book where he uses Scheme to write math formulas (I think it was about physics, but it still used a lot of math). Dear lord, it was so immeasurably better than the traditional mathematical notation. I really wish more people joined this movement of ditching the mathematical notation in favor of something more regular and typography-friendly as Scheme...