Cistercian Numbers | Hacker News Reader

Cistercian Numbers

omniglot.com

89 pointsdebo_17 comments

My minuscule pet peeve is that having only one source where the number 5 is depicted with a triangle (all others show it as a separated segment, like the number 6 but shorter), that's how every article or library draws it. It's all because the guy who wrote a book about them saw that source first so he based his figures on it.

Here's a small summary about the numbers with many examples: https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf

It would never have occurred to me that anyone would want to get these into a Unicode standard. This document you linked is excellent, thank you.

Being first matters :')

I wrote a font for these, which does use the triangle-5 and the vertical layout: https://bobbiec.github.io/cistercian-font.html (recent discussion here: https://news.ycombinator.com/item?id=46939312)

And my associated writeup: https://digitalseams.com/blog/making-a-font-with-9999-ligatu... .

As mentioned in the blog, I think the horizontal layout makes more sense too (in terms of writing order). But just like the triangle-5, the vertical layout is more commonly seen, so that's what I stuck with.

It might not be accurate but it does seem like it'd be easy to mistake a 5 and 6 without the triangle. Especially when the characters are being hurriedly written by hand. If I were going to use this system, I'd be sticking with the triangle.

I wish the 6 was a triangle in the other direction instead

In a Numberphile video [0], Alex Bellos also uses a triangle for 5.

[0]: https://www.youtube.com/watch?v=9p55Qgt7Ciw

Some people have said, use a unadorned staff for zero, and six being a triangle in the other direction instead; that is what I thought too, and some other people also do.

I also wrote a program in PostScript to draw Cistercian numbers (which uses the nonstandard sign for 6):

  % Specify a four-digit number as the command-line argument.
  /A ARGUMENTS 0 get def
  
  /Digit {
    get 48 sub {
      {} %0
      {24 0 rlineto} %1
      {0 -24 rmoveto 24 0 rlineto} %2
      {24 -24 rlineto} %3
      {0 -24 rmoveto 24 24 rlineto} %4
      {24 0 rlineto -24 -24 rlineto} %5
      {24 -24 rlineto -24 0 rlineto} %6 (nonstandard)
      {24 0 rlineto 0 -24 rlineto} %7
      {0 -24 rmoveto 24 0 rlineto 0 24 rlineto} %8
      {24 0 rlineto 0 -24 rlineto -24 0 rlineto} %9
    } exch get exec stroke
  } bind def
  
  4 setlinewidth
  6 6 moveto
  gsave
    36 0 rmoveto
    0 72 rlineto
    gsave
      -1 1 scale
      A 2 Digit
    grestore
    A 3 Digit
  grestore
  36 72 rmoveto
  1 -1 scale
  0 72 rlineto
  gsave
    -1 1 scale
    A 0 Digit
  grestore
  A 1 Digit
  
  showpage quit

I am a little sad that bare zero is not represented. This is my first exposure to Cistercian numbers but it looks like a unadorned staff would fit for the bare zero.

The whole thing is a lot of fun, feels like a Myst puzzle. Or more accuratly, I don't think Myst had a number puzzle but Riven did and I recently picked up Obduction and it had one, So probably fairer to say a Cyan type puzzle as they appear to love creating wierd numeric representations.

Two OEIS sequences for Cistercian numeral system: https://oeis.org/A341737 and https://oeis.org/A381327

Two odd things strike me:

1. 5 is the symbols for 4 and 1 combined, 6 is new, then 7=6+1, 8=6+2, and 9=6+3. It seems to me it would be more obvious to have 1 to 5 be unique symbols, then 6=5+1, 7=5+2, 8=5+3, and 9=5+4. Like how we do with tally marks.

2. The system is really just 4 digits combined in a square. I don't see the advantage over Arabic numerals.

They had limited space.

It's pretty cool but I'm surprised there wasn't confusion among the 2s (2 & 200, 20 & 2000) all the other symbols had enough to make it clear which side they're on, but the closer the 2-notch gets to the centre, the more ambiguous it gets. Could even be confused with a 1 if you're not careful

did a small raw binary-like implementation of an extended (base-16) version : https://www.onirom.fr/wiki/snippets/#JavaScript_:_Extended_C...

Shouldn't 523 in that list of "other numbers" actually be 522?

You're right

Wow, it's a while since I've seen one of those lists of hundreds of vampires that you have to deselect!

Actually, it would automatically translate when we scan it with the camera, like Google Translate.

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