8 ms·

Cistercian Numerals

140 points by maxutility 4y ago

dang 4y ago
Related: Show HN: A CLI tool to generate Cistercian numerals - https://news.ycombinator.com/item?id=27853033 https://news.ycombinator.com/item?id=27853033 - July 2021 (5 comments) Cistercian Numerals - https://news.ycombinator.com/item?id=26523363 https://news.ycombinator.com/item?id=26523363 - March 2021 (66 comments)
bookofjoe 4y ago
https://news.ycombinator.com/item?id=34579748 https://news.ycombinator.com/item?id=34579748
yborg 4y ago
It would be interesting to have a "Top-50" page of topics ranked by how many times they have been posted on HN.
- deleted 4y ago
  [deleted]
- NKosmatos 4y ago
  IMHO, Having something reposted every now and then is good. This gives the opportunity for people to see it if they missed it the first time. Judging for myself, this is the first time I’ve seen Cistercian numbers and although I’m a frequent HN user, I’ve never seen them before. If a topic is interesting it doesn’t hurt to repost it :-)
arh68 4y ago
Reminds me a lot of the D'ni numbers from Riven. D'ni numerals overlay two base-5 values in the same space, one horizontal & the other vertical, to represent 0–24. There's even a one-character numeral for 25, though it rarely comes up in-game. Different, of course, but I wouldn't be surprised if Cistercian was the inspiration. [1] https://www.omniglot.com/conscripts/dni.htm https://www.omniglot.com/conscripts/dni.htm [2] https://dni.fandom.com/wiki/D'ni_Numerals https://dni.fandom.com/wiki/D'ni_Numerals
- aendruk 4y ago
  It’s a fun task to generate these from the five base shapes. https://andrew.kvalhe.im/2020-04-28 https://andrew.kvalhe.im/2020-04-28
- kmill 4y ago
  Another number system, which I learned about recently on HN, are the Kaktovik numerals, which are even closer to D'ni. Interestingly, they were developed just a couple of years before Riven was released. https://en.wikipedia.org/wiki/Kaktovik_numerals https://en.wikipedia.org/wiki/Kaktovik_numerals It's not a base-5 system exactly. It's base-20, where the rotated-and-superimposed digit is only one of the first three numerals. I guess you could call it a mixed-radix system, where the bases alternate like 4 5 ... 4 5 4 5 and where each group of 4 5 combines into a single symbol.
mrled 4y ago
I am a fan of using Cistercian for date stamps, with a glyph for the year, month+day, hour+minute. Like this: <https://me.micahrl.com/blog/cistercian-dates/ https://me.micahrl.com/blog/cistercian-dates/> I also made a little decimal to Cistercian translator once. The numerals aren't in Unicode, so the font I use has to make use of private code points, which was kind of fun to get working properly. <https://cistercian.micahrl.com https://cistercian.micahrl.com>
- bediger4000 4y ago
  How did the Unicode people possibly miss Cistercian numerals?
  - mrled 4y ago
    Well there is a background document for future consideration: https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf However, it says: > It is not clear that there is any current need for Unicode support. Western Michigan University’s Medieval Institute (Cistercian and Monastic Studies) has a digitization project of Cistercian mss, but as of end 2020 they have not expressed any desire for computer encoding of the numerals. This document is therefore background information so that work is not duplicated if a need arises later.
  - aliqot 4y ago
    Luckily Unicode makes exceptions for charsets/languages that are overlooked, also they take encouragement (via joining the Unicode Consortium) if you have a special symbol that you need to add for a private interest.
  - MikeBattaglia 4y ago
    Unrelated rant: The Unicode people have missed a lot more than that. There are an enormous amount of, for instance, musical accidentals that are missing, including ones that have been in use for at least a hundred years, such as the half flats or half sharps in e.g. Arabic or Turkish music, which are used by probably hundreds of millions of people in the Middle East. (They do have a symbol called "half sharp" and "half flat", but it isn't the same symbol.) But at least they have the multiocular O, I guess.
astroalex 4y ago
There’s something very satisfying about the idea that the numerals themselves can be generated algorithmically. For example, here’s a nifty Cistercian numeral generator: https://shelby.cool/#/sketch/cistercian-numerals https://shelby.cool/#/sketch/cistercian-numerals
kijin 4y ago
This looks a lot like how Chinese characters are composed of individual "radicals", arranged like tetris blocks inside the same square box. Some of them affect the meaning of the letter, while others only signify the sound it's supposed to make. The resulting writing system is not easy for foreigners to learn, but it makes quite an efficient use of space. This might have been more valuable at a time when writable surfaces were expensive.
varenc 4y ago
If you like that, check out my favorite Cistercian numeral library: https://github.com/hsablonniere/cistercian-numerals https://github.com/hsablonniere/cistercian-numerals Here's a demo of it in action on the author's blog: https://www.hsablonniere.com/a-clock-based-on-cistercian-numerals--hptit8/ https://www.hsablonniere.com/a-clock-based-on-cistercian-num... I ended up using that library to create a simple Cistercian clock screensaver. My hope was that I'd learn to read Cistercian numbers fluently though I'm still working on that.
- hsablonniere 4y ago
  OMG, you made my day. Glad it helped you ;-)
cjdaly 4y ago
For your embedded cistercian projects: https://www.tindie.com/products/savageelectronics/rgb-cistercian-display/ https://www.tindie.com/products/savageelectronics/rgb-cister... (I'm not the maker, I just noticed these last year on Tindie and picked up a couple.)
olah_1 4y ago
here is some research that was done on adding cistercian to unicode https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf you can still email the author. he would love for someone to continue the research
AnimalMuppet 4y ago
The problems are that this is 1) hard to use for arithmetic, and 2) brittle. "Brittle" because you're peacefully sitting there at 9999 coins or whatever, and you earn another one, and suddenly you can't represent it. Arabic (Hindu) numerals just slap another digit to the left, but Cistercian numerals break. (You could fix that by using an Arabic notation - two Cistercian numbers, with the left one meaning "multiply this by 10,000". At that point, Cistercian numbers become a compressed Arabic notation. Still harder to use for arithmetic, but that's true of many compressed formats.)
- Tepix 4y ago
  It's like a 16 bit integer, you can only store so much…
- college_physics 4y ago
  > The problems are that this is 1) hard to use for arithmetic, and 2) brittle. I wonder if these constraints are inate to the problem (inescapable trade-offs) or circumstantial to the particular choices of the Cistercian monks...
  - AnimalMuppet 4y ago
    Any fixed-number-of-digits (or bits, or whatever) system is brittle against overflow. Any compressed format is hard(er) to use for arithmetic. Pretty much any grade-school kid can memorize the addition table, and can work it out on their fingers if they forget. But that table only has 100 entries. The addition tables for Cistercian numbers has 100,000,000 entries; nobody will memorize that. But maybe I'm thinking wrong. Cistercian numbers really only have 0-9, in four possible orientations. So maybe you can just add them, going from units up through thousands, writing down each quadrant as you go. (Multiplying still looks like a mess, though...)
extra88 4y ago
One SVG to display 1 to 9,999 by using just a bit of JavaScript to toggle CSS classes to show/hide segments and update the SVG's accessible name. https://adrianroselli.com/2021/02/cistercian-svg.html https://adrianroselli.com/2021/02/cistercian-svg.html
_9hey 4y ago
Oh how I wish the glyphs started at the top right and moved anti clockwise one quadrant for each power of two, to be consistent with right handed coordinate systems
- timeaway 4y ago
  Yup, and besides the counter-clockwise for consistency, I would like them even more if: * Each stroke were 1 bit, so the numerals would be just a more "compact" representation for binary numbers. * Even better if they can be represented with a seven-segment display (or other similar displays). (Though I can't blame them, since these two things didn't even exist back then.)
- downvotetruth 4y ago
  Glyphs have to be written in an orientation; bidirection (or higher symmetric) layouts would impose either writing the words left to right & right to left, which would cause smearing when writing with ink with a dominant hand, or mirroring the glyphs themselves, which would make reading & writing words much more difficult.
_9hey 4y ago
As an interview question I might ask how to one might extend this system
- deleted 4y ago
  [deleted]
- NeoTar 4y ago
  Out of interest, what would you consider to be a good reply? The 'obvious' answer is to have a second glyph (and third, etc.), but that's rather a boring answer. Perhaps making a cross-shape so you have four-arms to work with (and can thus get to 10.000.000). Or making a capital H shape would let you have the next four digits, which could then be extended out indefinitely; |-|-| etc.
  - edent 4y ago
    You could use multiple dimensions. Or colours. Or fractals. Or any one of a hundred things. But the real answer to any "how would you...?" questions is to reply with "Who are the users and what are their needs?"
  - MayeulC 4y ago
    Well, another obvious extension would be to prolong the vertical line, since it's already ordered by rows (two of them). Or, indeed, you could make an array out of them, making a super-glyph (kind of like a block matrix). Four blocks of four digits would get you to 10^4^4 = 10^16 so 100,00,00,00,00,00,00,00 (or 10000,0000,0000,0000, or 10,000,000,000,000,000 depending on your grouping), which is 10 Quadrillions in short- scale. Obviously grouping digits by blocks of 2 or 4 makes mor sense, since that's a row or a glyph. Interesting discussion though, which is probably the goal here, rather than a good or bad reply: it allows you to see how the candidate thinks or approaches a problem.
  - _9hey 4y ago
    It’s intentionally open-ended to engage in discussions about functional and quality attributes. Does the candidate ask questions or just jump into an answer? I love it because it’s very open-ended and demonstrates problem solving. It’s a great conversation piece.
Ostrogoth 4y ago
Not my work, but I found this 3d printed digital clock using cistercian numeral system online. It looks like a cool project: https://www.instructables.com/Cistercian-Digital-Clock/ https://www.instructables.com/Cistercian-Digital-Clock/
- maw 4y ago
  Until someone makes a Cistercian display automatic wristwatch I'm not interested.
jhncls 4y ago
There is also a Numberphile video going into their history [0]. About monks with a vow of silence. [0]: https://youtu.be/9p55Qgt7Ciw https://youtu.be/9p55Qgt7Ciw
aendruk 4y ago
Can you generate the higher valued numerals using OpenType ligatures?
Animats 4y ago
That probably came from a culture where writing materials were really expensive. Did they use vellum?
- rob74 4y ago
  Plus I can imagine that it also helped as a form of encryption...
IanCal 4y ago
I like these. I feel like there's a missed symmetry here though and almost symmetrical things are like a wobbly tooth in my brain. The right line appears at 6, but if you added that at 5 you could repeat the pattern you did for 1-4 for the horizontal lines, which it almost does. 7 and 8 are 6+1 and 6+2. https://imgur.com/a/NE36rIW https://imgur.com/a/NE36rIW
- MayeulC 4y ago
  I'd make it binary-like, like another commenter said. Change 3 to 2+1, 6 to 4+2. 8 takes the current 6, and 7 becomes 6+1, 9 becomes 8+1 (current 7). That also gives you hex digits to work with for free, each symbol could store up to FFFF. It wouldn't change a lot, just removes the downstroke from 3. Of course, 4 bits is an arbitrary choice, one could keep the current 5 bit/segments as well, but not much is needed to normalize it to 4 bits, which is interesting in itself.
rfmoz 4y ago
This method could be used to compress numbers? You get a conversion from 4 to 1 digit.

140 points by maxutility 4y ago

dang 4y ago

Related: Show HN: A CLI tool to generate Cistercian numerals - https://news.ycombinator.com/item?id=27853033 https://news.ycombinator.com/item?id=27853033 - July 2021 (5 comments) Cistercian Numerals - https://news.ycombinator.com/item?id=26523363 https://news.ycombinator.com/item?id=26523363 - March 2021 (66 comments)

bookofjoe 4y ago

https://news.ycombinator.com/item?id=34579748 https://news.ycombinator.com/item?id=34579748

yborg 4y ago

It would be interesting to have a "Top-50" page of topics ranked by how many times they have been posted on HN.

deleted 4y ago
[deleted]
NKosmatos 4y ago
IMHO, Having something reposted every now and then is good. This gives the opportunity for people to see it if they missed it the first time. Judging for myself, this is the first time I’ve seen Cistercian numbers and although I’m a frequent HN user, I’ve never seen them before. If a topic is interesting it doesn’t hurt to repost it :-)

arh68 4y ago

Reminds me a lot of the D'ni numbers from Riven. D'ni numerals overlay two base-5 values in the same space, one horizontal & the other vertical, to represent 0–24. There's even a one-character numeral for 25, though it rarely comes up in-game. Different, of course, but I wouldn't be surprised if Cistercian was the inspiration. [1] https://www.omniglot.com/conscripts/dni.htm https://www.omniglot.com/conscripts/dni.htm [2] https://dni.fandom.com/wiki/D'ni_Numerals https://dni.fandom.com/wiki/D'ni_Numerals

aendruk 4y ago
It’s a fun task to generate these from the five base shapes. https://andrew.kvalhe.im/2020-04-28 https://andrew.kvalhe.im/2020-04-28
kmill 4y ago
Another number system, which I learned about recently on HN, are the Kaktovik numerals, which are even closer to D'ni. Interestingly, they were developed just a couple of years before Riven was released. https://en.wikipedia.org/wiki/Kaktovik_numerals https://en.wikipedia.org/wiki/Kaktovik_numerals It's not a base-5 system exactly. It's base-20, where the rotated-and-superimposed digit is only one of the first three numerals. I guess you could call it a mixed-radix system, where the bases alternate like 4 5 ... 4 5 4 5 and where each group of 4 5 combines into a single symbol.

mrled 4y ago

I am a fan of using Cistercian for date stamps, with a glyph for the year, month+day, hour+minute. Like this: <https://me.micahrl.com/blog/cistercian-dates/ https://me.micahrl.com/blog/cistercian-dates/> I also made a little decimal to Cistercian translator once. The numerals aren't in Unicode, so the font I use has to make use of private code points, which was kind of fun to get working properly. <https://cistercian.micahrl.com https://cistercian.micahrl.com>

bediger4000 4y ago
How did the Unicode people possibly miss Cistercian numerals?
- mrled 4y ago
  Well there is a background document for future consideration: https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf However, it says: > It is not clear that there is any current need for Unicode support. Western Michigan University’s Medieval Institute (Cistercian and Monastic Studies) has a digitization project of Cistercian mss, but as of end 2020 they have not expressed any desire for computer encoding of the numerals. This document is therefore background information so that work is not duplicated if a need arises later.
- aliqot 4y ago
  Luckily Unicode makes exceptions for charsets/languages that are overlooked, also they take encouragement (via joining the Unicode Consortium) if you have a special symbol that you need to add for a private interest.
- MikeBattaglia 4y ago
  Unrelated rant: The Unicode people have missed a lot more than that. There are an enormous amount of, for instance, musical accidentals that are missing, including ones that have been in use for at least a hundred years, such as the half flats or half sharps in e.g. Arabic or Turkish music, which are used by probably hundreds of millions of people in the Middle East. (They do have a symbol called "half sharp" and "half flat", but it isn't the same symbol.) But at least they have the multiocular O, I guess.

astroalex 4y ago

There’s something very satisfying about the idea that the numerals themselves can be generated algorithmically. For example, here’s a nifty Cistercian numeral generator: https://shelby.cool/#/sketch/cistercian-numerals https://shelby.cool/#/sketch/cistercian-numerals

kijin 4y ago

This looks a lot like how Chinese characters are composed of individual "radicals", arranged like tetris blocks inside the same square box. Some of them affect the meaning of the letter, while others only signify the sound it's supposed to make. The resulting writing system is not easy for foreigners to learn, but it makes quite an efficient use of space. This might have been more valuable at a time when writable surfaces were expensive.

varenc 4y ago

If you like that, check out my favorite Cistercian numeral library: https://github.com/hsablonniere/cistercian-numerals https://github.com/hsablonniere/cistercian-numerals Here's a demo of it in action on the author's blog: https://www.hsablonniere.com/a-clock-based-on-cistercian-numerals--hptit8/ https://www.hsablonniere.com/a-clock-based-on-cistercian-num... I ended up using that library to create a simple Cistercian clock screensaver. My hope was that I'd learn to read Cistercian numbers fluently though I'm still working on that.

hsablonniere 4y ago
OMG, you made my day. Glad it helped you ;-)

cjdaly 4y ago

For your embedded cistercian projects: https://www.tindie.com/products/savageelectronics/rgb-cistercian-display/ https://www.tindie.com/products/savageelectronics/rgb-cister... (I'm not the maker, I just noticed these last year on Tindie and picked up a couple.)

olah_1 4y ago

here is some research that was done on adding cistercian to unicode https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf you can still email the author. he would love for someone to continue the research

AnimalMuppet 4y ago

The problems are that this is 1) hard to use for arithmetic, and 2) brittle. "Brittle" because you're peacefully sitting there at 9999 coins or whatever, and you earn another one, and suddenly you can't represent it. Arabic (Hindu) numerals just slap another digit to the left, but Cistercian numerals break. (You could fix that by using an Arabic notation - two Cistercian numbers, with the left one meaning "multiply this by 10,000". At that point, Cistercian numbers become a compressed Arabic notation. Still harder to use for arithmetic, but that's true of many compressed formats.)

Tepix 4y ago
It's like a 16 bit integer, you can only store so much…
college_physics 4y ago
> The problems are that this is 1) hard to use for arithmetic, and 2) brittle. I wonder if these constraints are inate to the problem (inescapable trade-offs) or circumstantial to the particular choices of the Cistercian monks...
- AnimalMuppet 4y ago
  Any fixed-number-of-digits (or bits, or whatever) system is brittle against overflow. Any compressed format is hard(er) to use for arithmetic. Pretty much any grade-school kid can memorize the addition table, and can work it out on their fingers if they forget. But that table only has 100 entries. The addition tables for Cistercian numbers has 100,000,000 entries; nobody will memorize that. But maybe I'm thinking wrong. Cistercian numbers really only have 0-9, in four possible orientations. So maybe you can just add them, going from units up through thousands, writing down each quadrant as you go. (Multiplying still looks like a mess, though...)

extra88 4y ago

One SVG to display 1 to 9,999 by using just a bit of JavaScript to toggle CSS classes to show/hide segments and update the SVG's accessible name. https://adrianroselli.com/2021/02/cistercian-svg.html https://adrianroselli.com/2021/02/cistercian-svg.html

_9hey 4y ago

Oh how I wish the glyphs started at the top right and moved anti clockwise one quadrant for each power of two, to be consistent with right handed coordinate systems

timeaway 4y ago
Yup, and besides the counter-clockwise for consistency, I would like them even more if: * Each stroke were 1 bit, so the numerals would be just a more "compact" representation for binary numbers. * Even better if they can be represented with a seven-segment display (or other similar displays). (Though I can't blame them, since these two things didn't even exist back then.)
downvotetruth 4y ago
Glyphs have to be written in an orientation; bidirection (or higher symmetric) layouts would impose either writing the words left to right & right to left, which would cause smearing when writing with ink with a dominant hand, or mirroring the glyphs themselves, which would make reading & writing words much more difficult.

_9hey 4y ago

As an interview question I might ask how to one might extend this system

deleted 4y ago
[deleted]
NeoTar 4y ago
Out of interest, what would you consider to be a good reply? The 'obvious' answer is to have a second glyph (and third, etc.), but that's rather a boring answer. Perhaps making a cross-shape so you have four-arms to work with (and can thus get to 10.000.000). Or making a capital H shape would let you have the next four digits, which could then be extended out indefinitely; |-|-| etc.
- edent 4y ago
  You could use multiple dimensions. Or colours. Or fractals. Or any one of a hundred things. But the real answer to any "how would you...?" questions is to reply with "Who are the users and what are their needs?"
- MayeulC 4y ago
  Well, another obvious extension would be to prolong the vertical line, since it's already ordered by rows (two of them). Or, indeed, you could make an array out of them, making a super-glyph (kind of like a block matrix). Four blocks of four digits would get you to 10^4^4 = 10^16 so 100,00,00,00,00,00,00,00 (or 10000,0000,0000,0000, or 10,000,000,000,000,000 depending on your grouping), which is 10 Quadrillions in short- scale. Obviously grouping digits by blocks of 2 or 4 makes mor sense, since that's a row or a glyph. Interesting discussion though, which is probably the goal here, rather than a good or bad reply: it allows you to see how the candidate thinks or approaches a problem.
- _9hey 4y ago
  It’s intentionally open-ended to engage in discussions about functional and quality attributes. Does the candidate ask questions or just jump into an answer? I love it because it’s very open-ended and demonstrates problem solving. It’s a great conversation piece.

Ostrogoth 4y ago

Not my work, but I found this 3d printed digital clock using cistercian numeral system online. It looks like a cool project: https://www.instructables.com/Cistercian-Digital-Clock/ https://www.instructables.com/Cistercian-Digital-Clock/

maw 4y ago
Until someone makes a Cistercian display automatic wristwatch I'm not interested.

jhncls 4y ago

There is also a Numberphile video going into their history [0]. About monks with a vow of silence. [0]: https://youtu.be/9p55Qgt7Ciw https://youtu.be/9p55Qgt7Ciw

aendruk 4y ago

Can you generate the higher valued numerals using OpenType ligatures?

Animats 4y ago

That probably came from a culture where writing materials were really expensive. Did they use vellum?

rob74 4y ago
Plus I can imagine that it also helped as a form of encryption...

IanCal 4y ago

I like these. I feel like there's a missed symmetry here though and almost symmetrical things are like a wobbly tooth in my brain. The right line appears at 6, but if you added that at 5 you could repeat the pattern you did for 1-4 for the horizontal lines, which it almost does. 7 and 8 are 6+1 and 6+2. https://imgur.com/a/NE36rIW https://imgur.com/a/NE36rIW

MayeulC 4y ago
I'd make it binary-like, like another commenter said. Change 3 to 2+1, 6 to 4+2. 8 takes the current 6, and 7 becomes 6+1, 9 becomes 8+1 (current 7). That also gives you hex digits to work with for free, each symbol could store up to FFFF. It wouldn't change a lot, just removes the downstroke from 3. Of course, 4 bits is an arbitrary choice, one could keep the current 5 bit/segments as well, but not much is needed to normalize it to 4 bits, which is interesting in itself.

rfmoz 4y ago

This method could be used to compress numbers? You get a conversion from 4 to 1 digit.