I could understand if this were a non-alphabet system like Chinese where the information coding is that dense per character. But for an alphabet system, why the mismatch between the bits of information per character and the bits needed to visually represent that character? The Latin alphabet mostly fits on a 7 seg display, and 26 letters requires a theoretical minimum of 5 bits to encode, so the graphical efficiency is close to optimal. What is it about the way other alphabets are encoding information that makes them hard or impossible to reduce down to a small number of segments?

Because the information coding is dense. Arabic script has a lot of tiny shapes that indicate what letter it is and it also has diacritic marks, which on their own are similarly intricate and small. You can't represent one line, two lines, a dot, a circle, a hamza, etc. above, below, to the side of particular characters, without a lot of resolution.

Another challenge for representing Arabic a display made of line segments is all the curves. If it weren't for the dots, I imagine you could write consonant-only Arabic on something close to a seven-segment display, although it would look bizarre because all the letters would be isolated and there would be so many more straight line segments than in normal Arabic script. (An absolute majority of the isolated forms of Arabic letters are made up only of curves, whereas an absolute majority of Latin capital letters are made up only of straight line segments!)

I wonder how Arabic ended up with characters that differ only by dot positioning (like ب ت ث, and also ن whose combining form is especially similar to the combining forms of those). By contrast, the most similar Latin characters might be EF / CG / IJ / MN / UV which I think are clearly more different than the Arabic characters that differ only by dot quantity and positioning.

(The Il1| are also famously confusable in some Latin fonts, but one could say having to worry about these comes late in the history of Latin script writing. Although the scribal minim https://en.wikipedia.org/wiki/Minim_(palaeography) used at some points to write u, i, m, and n is every bit as confusing as any Arabic character.)

I don't think curves are a technological problem for a segmented display. You can easily make curved segments and dots. Its all just an LED behind a window painted over with the negative image of the curve. In principle you could make a display that is optimized for OCGDU rather than EIFHTL.

Much like latin characters, at some point a segmented display is just going to have to compromise on the tradeoff between correct an the number of parts. We see it work just fine casting the curvy latin letters to squares. So the real question I reckon is how much can you mangle the diacritics / curves / other parts and still read it? In other words, what is the bandwidth redundancy of this writing system?

Yes, I wasn't thinking flexibly enough there (no pun intended). Interesting questions!

hold up. Representing a line, two lines, a dot, a circle... in one of several fixed positions relative to the character...that's exactly what a segmented display is good at. I think you may not have got what I meant by "dense". I'm looking at it from a pure information theoretic view. There's something like 5000 Chinese characters overall. Even if I could find a system of on/off segments to represent them all, I would still have to use at least 13 segments, because it takes at least 13 bits to encode 5000 possibilities. Chinese is dense in the sense that a whole 13 bits have to fit in the space of a single character. Granted diacrtics and other markers do add one or two new bits, but adding permutations isn't the same as adding complexity. Every time you learn one diacritic, you've doubled the number of letters you know how to write. Whereas in Chinese, when you learn a new character, you've learned a new character.

Other commenter nailed the real technical hurdle. Context dependent spacing system. How do monotypes do it (or do those not exist)?

There's certainly a finite set of combinations but in order for you to create a segmented display that isn't just a dot matrix, you need to have few enough variations that it can 1) actually encode all of the characters and their context-specific variations, 2) have segments that at least somewhat resemble the characters they are supposed to represent and 3) if they are overlapping must be able to to render all of the components of every letter distinctly. So If you have a line that you also want to be two or three dots and a hamza or some other diacritic, you need to break each segment down to the lowest common denominators.

A 7-segment display works by turning on and off each of the segments in order to render a glyph that is supposed to represent English alphanumeric characters. It mostly accomplishes this, though just barely and honestly a lot of characters do not render well at all (like the lowercase "i"). How would you shape the segments in such a way that could accomplish at least that level of clarity in Arabic?

I personally think that what you'd end up with would very closely resemble a dot matrix.