7 ms·

Fraktur is used in mathematics, chiefly when discussing/denoting Lie groups. I've listed some sources but you can probably Google for more. [0] https://en.wiki

Fraktur is used in mathematics, chiefly when discussing/denoting Lie groups. I've listed some sources but you can probably Google for more. [0] https://en.wikipedia.org/wiki/Fraktur#After_1941 https://en.wikipedia.org/wiki/Fraktur#After_1941 [1] https://mathoverflow.net/questions/87627/fraktur-symbols-for-lie-algebras https://mathoverflow.net/questions/87627/fraktur-symbols-for...

banana_giraffe 6y ago
That's fair, but why stop there? The example that comes to mind is "Courier 12pt is the only font ever for screenplays". It's required to convey a screenplay, to my mind, like using Fraktur is required in the math space. Despite what it may seem like, I'm really not trying to mis-parse the reasons here, I'm honestly trying to figure out where the line is, and why it's there.
- plutonic 6y ago
  I really don't know, but my guess would be that in mathematics particular symbols denote particular meanings depending on the shape of / decorations on the character. Big g is different from little g which is different from bold g which is different from italic g which is different from Fraktur g. Because Fraktur g is different in meaning from just g, Fraktur gets a spot in the Unicode specs. Courier, while it is standard for screenplays, does not affect the meaning of the text of the screenplay as opposed to the use of another font.
- QuesnayJr 6y ago
  You mix the Fraktur and Roman letters in the same mathematical manuscript, the way you mix Greek and Roman letters in the same mathematical manuscript.
- kps 6y ago
  Historically, a few were included in the Letterlike Symbols block¹ because they were present in some pre-Unicode character set. Much later it was argued that since a few were present, they all should be present. ¹ https://en.wikipedia.org/wiki/Letterlike_Symbols https://en.wikipedia.org/wiki/Letterlike_Symbols
  - chungy 6y ago
    Also note that these selective ones were part of the basic multilingual plane, where space was always a bit at a premium. They were assigned before Unicode expanded to have 17 complete 16-bit planes and space stopped being a problem.
- thotsBgone 6y ago
  The introduction of the Fraktur font introduces different meaning. 'R' in Fraktur would mean something different than R in another font in the same text.
  - anamexis 6y ago
    I think you could argue the same for typewriter (monospace serif) fonts. Plenty of texts use them to denote the name of a variable or function in-line, much as we would use backticks to talk about `leftPad` here.
    - thotsBgone 6y ago
      𝚃𝚑𝚊𝚝'𝚜 𝚊 𝚐𝚘𝚘𝚍 𝚙𝚘𝚒𝚗𝚝. 𝚃𝚑𝚎𝚢 𝚜𝚑𝚘𝚞𝚕𝚍 𝚒𝚗𝚌𝚕𝚞𝚍𝚎 𝚝𝚑𝚘𝚜𝚎 𝚒𝚗 𝚄𝚗𝚒𝚌𝚘𝚍𝚎. 𝙾𝚑.
      - anamexis 6y ago
        Welp!
      - banana_giraffe 6y ago
        This is actually what started me down this path a while ago. I had to do a full text search feature for some text of questionable sources, and some users had taken to using the full width characters for emphasis (I think, they clearly had rules in their head for whey they'd use it, but I didn't know what the rules were). There are libraries that can handle the official Unicode normalization rules, but users don't exactly always pay attention to the official rules, so I get to start finding all sorts of weird little corners of Unicode. Though, as I understand it, the full-width characters are there not for any modern use cases, but for historical reasons having to deal with older character sets. Still interesting.
        phonon 6y ago
        Full-width latin characters are used to fit in the grid of Chinese/Japanese/Korean characters...they're not going anywhere. https://en.wikipedia.org/wiki/Halfwidth_and_fullwidth_forms https://en.wikipedia.org/wiki/Halfwidth_and_fullwidth_forms
- gumby 6y ago
  Fractur is more than a font difference as it has a few ligatures (e.g. tz) that are not found in the Roman alphabet as used in modern German (ß is the only one that made the transition). And these “ligatures” aren’t really true ligatures in the sense of, say, the “fi” ligature in some fonts; they are glyphs that are close to being fully fledged letters, as, say, ö, which is an accented (umlautened) letter in Germany is a fully-fledged letter in Swedish, or how W became a freestanding letter in English.
- thaumasiotes 6y ago
  > why stop there? The example that comes to mind is "Courier 12pt is the only font ever for screenplays". It's required to convey a screenplay, to my mind, like using Fraktur is required in the math space. The screenplay is still being written in letters. Mathematical ℝ is more accurately thought of as an ideogram than a letter. If you were to write "let r be a member of ℝ", the "ℝ" would be structurally parallel to the full word "member", not to the "r" within it. Courier for screenplays is a choice you make at the document level; blackboard bold for mathematical entities is not. ℝ is always ℝ no matter what styles apply to your document.

banana_giraffe 6y ago

That's fair, but why stop there? The example that comes to mind is "Courier 12pt is the only font ever for screenplays". It's required to convey a screenplay, to my mind, like using Fraktur is required in the math space. Despite what it may seem like, I'm really not trying to mis-parse the reasons here, I'm honestly trying to figure out where the line is, and why it's there.

plutonic 6y ago
I really don't know, but my guess would be that in mathematics particular symbols denote particular meanings depending on the shape of / decorations on the character. Big g is different from little g which is different from bold g which is different from italic g which is different from Fraktur g. Because Fraktur g is different in meaning from just g, Fraktur gets a spot in the Unicode specs. Courier, while it is standard for screenplays, does not affect the meaning of the text of the screenplay as opposed to the use of another font.
QuesnayJr 6y ago
You mix the Fraktur and Roman letters in the same mathematical manuscript, the way you mix Greek and Roman letters in the same mathematical manuscript.
kps 6y ago
Historically, a few were included in the Letterlike Symbols block¹ because they were present in some pre-Unicode character set. Much later it was argued that since a few were present, they all should be present. ¹ https://en.wikipedia.org/wiki/Letterlike_Symbols https://en.wikipedia.org/wiki/Letterlike_Symbols
- chungy 6y ago
  Also note that these selective ones were part of the basic multilingual plane, where space was always a bit at a premium. They were assigned before Unicode expanded to have 17 complete 16-bit planes and space stopped being a problem.
thotsBgone 6y ago
The introduction of the Fraktur font introduces different meaning. 'R' in Fraktur would mean something different than R in another font in the same text.
- anamexis 6y ago
  I think you could argue the same for typewriter (monospace serif) fonts. Plenty of texts use them to denote the name of a variable or function in-line, much as we would use backticks to talk about `leftPad` here.
  - thotsBgone 6y ago
    𝚃𝚑𝚊𝚝'𝚜 𝚊 𝚐𝚘𝚘𝚍 𝚙𝚘𝚒𝚗𝚝. 𝚃𝚑𝚎𝚢 𝚜𝚑𝚘𝚞𝚕𝚍 𝚒𝚗𝚌𝚕𝚞𝚍𝚎 𝚝𝚑𝚘𝚜𝚎 𝚒𝚗 𝚄𝚗𝚒𝚌𝚘𝚍𝚎. 𝙾𝚑.
    - anamexis 6y ago
      Welp!
    - banana_giraffe 6y ago
      This is actually what started me down this path a while ago. I had to do a full text search feature for some text of questionable sources, and some users had taken to using the full width characters for emphasis (I think, they clearly had rules in their head for whey they'd use it, but I didn't know what the rules were). There are libraries that can handle the official Unicode normalization rules, but users don't exactly always pay attention to the official rules, so I get to start finding all sorts of weird little corners of Unicode. Though, as I understand it, the full-width characters are there not for any modern use cases, but for historical reasons having to deal with older character sets. Still interesting.
      - phonon 6y ago
        Full-width latin characters are used to fit in the grid of Chinese/Japanese/Korean characters...they're not going anywhere. https://en.wikipedia.org/wiki/Halfwidth_and_fullwidth_forms https://en.wikipedia.org/wiki/Halfwidth_and_fullwidth_forms
gumby 6y ago
Fractur is more than a font difference as it has a few ligatures (e.g. tz) that are not found in the Roman alphabet as used in modern German (ß is the only one that made the transition). And these “ligatures” aren’t really true ligatures in the sense of, say, the “fi” ligature in some fonts; they are glyphs that are close to being fully fledged letters, as, say, ö, which is an accented (umlautened) letter in Germany is a fully-fledged letter in Swedish, or how W became a freestanding letter in English.
thaumasiotes 6y ago
> why stop there? The example that comes to mind is "Courier 12pt is the only font ever for screenplays". It's required to convey a screenplay, to my mind, like using Fraktur is required in the math space. The screenplay is still being written in letters. Mathematical ℝ is more accurately thought of as an ideogram than a letter. If you were to write "let r be a member of ℝ", the "ℝ" would be structurally parallel to the full word "member", not to the "r" within it. Courier for screenplays is a choice you make at the document level; blackboard bold for mathematical entities is not. ℝ is always ℝ no matter what styles apply to your document.