[HN Gopher] Cistercian Numerals
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       Cistercian Numerals
        
       Author : DyslexicAtheist
       Score  : 126 points
       Date   : 2021-03-20 14:12 UTC (8 hours ago)
        
 (HTM) web link (en.wikipedia.org)
 (TXT) w3m dump (en.wikipedia.org)
        
       | ape4 wrote:
       | A single character able to hold 1 to 9,999 is pretty compact
        
         | VeninVidiaVicii wrote:
         | It seems like it'd take quite a bit of staring to decipher.
        
           | hpfr wrote:
           | After reading the page, it doesn't seem too bad. Each corner
           | represents a digit so you read each symbol one corner at a
           | time. Arithmetic wouldn't even be that different to learn
           | compared to Arabic numerals since each digit still has a
           | specific place.
        
           | kgeist wrote:
           | You only need to remember 9 permutations (which themselves
           | constitute a pretty logical sequence), the rest is a simple
           | combination of them
        
         | max_ wrote:
         | It cannot count beyond 10,000
         | 
         | Edit: I meant 10,000 not 1,000
        
           | popol12 wrote:
           | how about adding a second character next ? Then you would
           | count to 100,000,000.
           | 
           | Just like we do with arabic numbers actually, putting them
           | next to each others. With a single of our digits you can only
           | count to 10 !
        
           | detaro wrote:
           | How do you come to that conclusion?
        
             | max_ wrote:
             | was a typo sorry.
        
           | boygobbo wrote:
           | 4 boxes at 4 corners = 9,999
        
           | Jtsummers wrote:
           | It seems to use all 4 quadrants around the stave (vertical or
           | horizontal) at least in some forms. Each quadrant can mark
           | the digits 0-9 letting it represent 0-9999. Though 0 isn't
           | called out in the diagrams I'm seeing on the page, the stave
           | by itself should be sufficient to represent that whether the
           | users of it intended it that way or not.
           | 
           | https://upload.wikimedia.org/wikipedia/commons/d/d4/Cisterci.
           | ..
        
         | ed25519FUUU wrote:
         | I thought the same thing. We do have pretty compact ways to
         | write now though. For example 15,000 can be written as 15k.
        
         | alisonkisk wrote:
         | It's pretty similar to writing 4 Arabic digits in a square
         | formation.
        
       | hsablonniere wrote:
       | I created a clock with those numbers ;-)
       | 
       | https://www.hsablonniere.com/a-clock-based-on-cistercian-num...
        
         | Jtsummers wrote:
         | I was about to post this link, just saw it over on Reddit. Nice
         | project.
        
         | kukx wrote:
         | Nice idea.
         | 
         | Why not a single character for hours and minutes? It could make
         | a cool watch face.
        
       | throw0101a wrote:
       | The Cistercians have a long and fascinating history:
       | 
       | > _Andersen et al found that the location monasteries of the
       | Catholic Order of Cistercians, and specifically their density,
       | highly correlated to this work ethic in later centuries;[21]
       | ninety percent of these monasteries were founded before the year
       | 1300 AD. Joseph Henrich found that this correlation extends right
       | up to the twenty-first century.[22]_
       | 
       | * https://en.wikipedia.org/wiki/Protestant_work_ethic#Criticis...
        
         | vmilner wrote:
         | And they make nice beer - just had some with my lunch.
         | 
         | http://www.mountsaintbernard.org/tynt-meadow-ale
        
         | danielam wrote:
         | Also see the Benedictines in this regard (e.g., "Ora et Labora"
         | and the Rule of St. Benedict)[0].
         | 
         | [0] https://en.wikipedia.org/wiki/Pray_and_work
        
           | [deleted]
        
       | naringas wrote:
       | very reminiscent of 'freemason'-style secrecy
        
         | antipaul wrote:
         | There are relations between the two. See the link:
         | 
         | "In the late eighteenth century, Chevaliers de la Rose-Croix of
         | Paris briefly adopted the numerals for mystical use"
         | 
         | Then read more about the Chevaliers
        
       | MithrilTuxedo wrote:
       | This would go well with Elian script.
        
       | NoOneNew wrote:
       | I've yet to see this brought up, but I hope a wandering historian
       | might speak up about this along with reference a book I can read
       | more about this.
       | 
       | Wasn't the marvel to Arabic-Hindu (edit) numerals the math system
       | behind them? Beyond counting, no one really discusses the actual
       | use of these other number systems. Maybe the actual number
       | representation with our modern numerals is the worst way to track
       | count, but the way to manipulate those numbers is the best that
       | ever was from what I can tell. All thanks to the folks that laid
       | down the foundation to Arabic-Hindu numerals. Using our current
       | methods of math does not translate directly to other numerals
       | systems... so it's just hard for me to gain an appreciation of
       | these other numeral styles?
       | 
       | Years ago I watched a documentary that focused on, I think on
       | Cuneiform writing or maybe another ancient writing system. What
       | was known on how accounting was done, the mathematic usage of
       | that system was a complete pain in the ass. It made me think
       | about how much we take for granted how easy it is to add and
       | subtract, let alone multiply and divide, with our current system.
       | This used to be a specialized skill. Now it's considered the
       | beginning to even knowing anything remotely useful.
       | 
       | Weird scatterbrained rant, but is anyone able to point to a good,
       | recommended resource on the history of math, ideally comparing
       | other methodologies?
        
         | krastanov wrote:
         | Tangentially related: in modern math we do have alternative
         | number systems to use for problems that are cumbersome with
         | Arabic-Hindu numerals. Check out p-adic numbers on Wikipedia,
         | for instance.
        
           | lambda_obrien wrote:
           | Yes, if I remember correctly, any n-ary number system is
           | equivalent and you can translate any proof between them. It's
           | just easier to work in one or another system.
        
             | tgb wrote:
             | p-adic is quite different though. It's not really that
             | relevant to this conversation though as far as I can tell
             | as it's not just about representing the integers or
             | rationals in a different way.
             | 
             | https://en.wikipedia.org/wiki/P-adic_number
        
         | anthony_romeo wrote:
         | So one element which kinda wraps all of these concepts together
         | is what some have called the "Golden Age of Islam".[1] The
         | [literal] Empire which emerged from Muhammad's legacy became a
         | source of great intellectual thinking (while Europe had just
         | entered its dark age). This makes sense, being the place of
         | some of the oldest civilizations on Earth, and surrounded by
         | several other great civilizations.
         | 
         | During this time (a few hundred years after the fall of Rome)
         | the texts of the ancient Greek philosophers and scientists
         | became quite popular among Muslim thinkers. One could argue
         | that this Golden Age included a natural continuation of the
         | works of Aristotle, Plato, etc. Furthermore, they adopted a new
         | system of representing numbers from India which turned out to
         | be a convenient language for formalizing the concepts of
         | Algebra (done by Muhammad ibn Musa al-Khwarizmi in the early
         | 800's [2]).
         | 
         | Sadly I can't recommend any books -- this was conjured up from
         | my memories of this subject from College some time ago (with
         | the guiding help of Wikipedia to fill in some gaps).
         | 
         | [1] https://en.wikipedia.org/wiki/Islamic_Golden_Age
         | 
         | [2] https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-
         | Khwarizmi
        
         | FlyingSnake wrote:
         | > All thanks to the folks that laid down the foundation to
         | Arabic numerals.
         | 
         | As an Indian, it is particularly weird for me to see the
         | achievements on Indian pioneer mathematicians attributed to a
         | totally different group of people. Brahmagupta, Pingala,
         | Aryabhatta etc. should be correctly attributed and celebrated
         | for their towering contributions to laying the foundations of
         | Maths as we see today.
        
           | NoOneNew wrote:
           | Right, yes, sorry. I'm just a casual to the history of math.
           | My bad.
        
           | reaperducer wrote:
           | _As an Indian, it is particularly weird for me to see the
           | achievements on Indian pioneer mathematicians attributed to a
           | totally different group of people._
           | 
           | Unfortunately, the internet is full of this sort of thing.
           | Wikipedia is especially rife with revisions that change
           | inventors and originators in jingoistic ways.
           | 
           | See also: The eight thousand tiny museums in villages
           | scattered across the U.K. all celebrating the local
           | "inventors" of different things that were already invented in
           | other countries long before.
        
             | scythe wrote:
             | The Internet did not trick Leonardo "Fibonacci" of Pisa
             | into calling the number system he was advocating "Arabic"
             | in the thirteenth century.
        
               | NoOneNew wrote:
               | I just wanted to have a casual, nerdy discussion of math
               | god damn it. That's all. How did this turn to a
               | politically correct issue already?
        
         | thaumasiotes wrote:
         | > Maybe the actual number representation with our modern
         | numerals is the worst way to track count, but the way to
         | manipulate those numbers is the best that ever was from what I
         | can tell. All thanks to the folks that laid down the foundation
         | to Arabic-Hindu numerals.
         | 
         | Hmm? The manipulation and the written form are fully
         | independent. Before the introduction of Arabic numerals to
         | Europe, this manipulation was already common; that's what an
         | abacus was for. It's just that you wrote your result down in
         | Roman numerals rather than as a picture of an arrangement of
         | beads.
        
           | jk7tarYZAQNpTQa wrote:
           | > The manipulation and the written form are fully
           | independent.
           | 
           | No, they are related. The optimal written form for a base 10
           | manipulation system is a base 10 numeral written system.
           | 
           | > Before the introduction of Arabic numerals to Europe, this
           | manipulation was already common; that's what an abacus was
           | for.
           | 
           | And the abacus was base 10, wasn't it? So the natural (and
           | optimal) way to write down that result is in a base 10
           | notation.
           | 
           | This Cistercian numerals are base 10000. Try doing a pen and
           | paper multiplication or division using this system. No,
           | seriously, try it. You'll understand why historically we
           | settled on our decimal system. It's basically "divide and
           | conquer" applied to mental math.
           | 
           | The good news is that 10000 has 10 as a factor, so base 10000
           | numerals come sort of natural to us, the learning curve isn't
           | that high.
        
             | thaumasiotes wrote:
             | > This Cistercian numerals are base 10000. Try doing a pen
             | and paper multiplication or division using this system.
             | 
             | Sure, in the same way that Babylonian cuneiform numerals
             | are base 60, which is "they're in base 10, but you combine
             | multiple symbols into the space of one glyph". The
             | Cistercian numerals don't have 10,000 separate symbols.
             | They have 10 symbols, and one glyph includes four
             | positional slots in which a symbol appears. They're exactly
             | equivalent to the Arabic numeral system we use now, and the
             | pencil-and-paper multiplication system we use now transfers
             | directly without problems.
        
               | kadoban wrote:
               | It's a bit like hexadecimal and octal and binary like
               | that, in that it's really trivial to convert between
               | those and just see at a glance what the conversion is.
               | Except with Cistercian it's even easier.
        
               | thaumasiotes wrote:
               | It would be exactly like hexadecimal and binary if the
               | hex glyph for 11, instead of being "A", looked like
               | 1 0       1 1
        
           | NoOneNew wrote:
           | Yes and no. The format of numbers is important to how you end
           | up manipulating them. The way we do long division with 3 or
           | more digit numbers cannot translate to roman numerals. A
           | different method is required. This is part of my point. No
           | one goes into how to do complex maths with Roman numerals,
           | Cunieform or anything else. They're just "look at how you can
           | display a count". Once you learn to add, substract, multiply
           | or divide 2 digit numbers on paper with Arabic-Hindu
           | numerals, 30 digit numbers are trivial, only time consuming.
           | Having a system that uses entirely different characters to
           | represent hundreds, five-hundreds, thousands and more, that
           | changes the math system.
           | 
           | There was a British show I watched as a kid that played in
           | the US which made a light hearted joke regarding this. I
           | think it was called How 2 or something like that. But it was
           | a Welsh woman that showed how 12/2 can equal 7. XII, when you
           | erase the bottom half, it gives you VII. While a joke, it
           | always bothered me that no one ever talked about how the
           | Roman ACTUALLY did math with their number system. How in the
           | hell do you XII/II on paper by showing your work? Because our
           | 12/2 long division method can translate easily to 1212/2. How
           | do you do the same with MCCXII/II? I find it hard to believe
           | there isn't one. Just, no one talks about it.
        
             | fao_ wrote:
             | It's why arithmetical calculation was a role one had. They
             | used an abacus for the calculation of complex sums.
             | 
             | https://thatsmaths.com/2019/07/04/what-did-the-romans-
             | ever-d...
        
               | NoOneNew wrote:
               | So wait... math was never really done long hand in
               | ancient times, but calculators (the abacus or any other
               | form) were used instead?
               | 
               | In some respects, that makes sense. Paper like materials
               | were never cheap and long-hand math uses a whole lot of
               | paper. Bead calculators makes sense. I'd be curious to
               | see if there's a correlation to "cheap" paper being
               | plentiful right before the invention of complex math like
               | Algebra.
               | 
               | With a quick 5 minute peek, "cheap" paper came from China
               | to the middle east in the ~8th century. Algebra was
               | recorded in the 9th in the middle east. So... eh, maybe.
               | Requires more reading, but it's interesting. Sounds like
               | an interesting infrastructure like correlation to
               | technology.
        
               | thaumasiotes wrote:
               | > math was never really done long hand in ancient times,
               | but calculators (the abacus or any other form) were used
               | instead?
               | 
               | No. I provided an example of peasant multiplication in my
               | response sidethread. (Well, "yes" if you mean using
               | paper. Paper is hard to get. But you can multiply without
               | needing a special tool; the algorithm is commonly
               | executed by using piles of rocks and pits in the ground.)
               | The abacus is a more advanced technology that took time
               | to develop. (It does appear early in some form; see
               | https://en.wikipedia.org/wiki/Abacus#History )
        
             | thaumasiotes wrote:
             | > The format of numbers is important to how you end up
             | manipulating them.
             | 
             | I just pointed out:
             | 
             | >> Before the introduction of Arabic numerals to Europe,
             | this manipulation was already common; that's what an abacus
             | was for.
             | 
             | The abacus doesn't represent numbers in Roman numerals. It
             | represents them positionally. This poses no problems
             | because conversion between representations is trivial.
             | 
             | > How in the hell do you XII/II on paper by showing your
             | work?
             | 
             | That's as easy as it gets; half of X is V and half of II is
             | I. This is like asking "how in the hell do you do 7 - 2 on
             | paper by showing your work?". Dividing by 2 is a primitive
             | that is always easy to do in Roman numerals, and is relied
             | on heavily in the method you'd use to multiply them, which
             | you can in fact read about. I'll do 47x9:
             | XXXXVII  *  VIIII         XXIII  *  XVIII            XI  *
             | XXXVI             V  *  LXXII            II  _  CXXXXIIII
             | I  *  CCLXXXVIII              CCLXXXVIII + LXXII + XXXVI +
             | XVIII + VIIII =       = CC LL XXXXXXXXX VVVV IIIIIIIIIIIII
             | =       = CC C LXXXX XX XIII =       = CCCCXXIII = 423
        
         | gumby wrote:
         | > What was known on how accounting was done, the mathematic
         | usage of that system was a complete pain in the ass.
         | 
         | Actually it wasn't that difficult and was even rather
         | convenient given how they viewed the rest of the world (among
         | other things they only had rationals, and a limited number)
         | 
         | Decimal systems didn't take over the circle, or timekeeping
         | (and for the circle sometimes radians are easier). Decimal
         | stock trading in the US is only a couple of decades old and
         | within my memory countries switched to decimal currencies
         | replacing systems that had survived centuries.
         | 
         | In fact the US uses a non-decimal measurement system which has
         | numerous advantages (as well as disadvantages) for daily use.
        
         | Balgair wrote:
         | Cuneiform math isn't the most terrible. It's 'column' based,
         | like the modern arabic version we have. However, at some times
         | they lacked the 0 representation.
         | 
         | Roman numerals, however, are quite difficult. In addition to
         | the problems with basic manipulations (27-9, or XXVI - IX),
         | they also lacked any higher symbols than 1000 (M in Roman). So
         | for 15,000 you have to write MMMMMMMMMMMMMMM. I'll spare you
         | numbers like 1,000,000.
         | 
         | Here's a good video on how to do math in Cuneiform, and a brief
         | discussion on Roman numerals:
         | 
         | https://www.youtube.com/watch?v=RR3zzQP3bII
         | 
         | Strangely, _Numberphile_ has yet to do a video on Roman
         | /Chinese number systems. Maybe because it's really hard to do
         | math with them, and that's a bit boring to just show that it's
         | hard.
        
           | kccqzy wrote:
           | The Roman system is indeed difficult? What's difficult about
           | the Chinese one? It seems basically identical to Arabic
           | numerals except using different symbols.
        
       | jephson wrote:
       | A great little front-end project for generating these numerals:
       | https://adrianroselli.com/2021/02/cistercian-svg.html
        
       | thebradbain wrote:
       | Haha, this is surreal to see. I attended the only Cistercian
       | high-/middle-school in the US, which of all places is in Texas.
       | How they ended up there was due to a series of happy (and many
       | not-so-happy) accidents while fleeing Nazi/USSR occupation. Many
       | of whom would come to be the original Hungario-Texan monks who
       | fled in their teens/twenties (some of them students themselves at
       | a Cistercian school in Hungary who had no intention of ever
       | entering the priesthood) were my teachers, and some still are
       | alive today.
       | 
       | I'm not particularly religious, but I always found their order's
       | history and personal stories fascinating, and a living example of
       | adapting to the cards you're dealt.
        
       | mynegation wrote:
       | Written this way, numerals reminded me of the Ted Chiang's "Story
       | of your life" (which served as a basis for the movie "Arrival").
       | Both are recommended.
       | 
       | Also I could not help but notice poster's nick name. Question to
       | them: is there a connection?
        
       | max_ wrote:
       | Numberphile did a video on this.
       | 
       | https://youtu.be/9p55Qgt7Ciw
        
       | marcodiego wrote:
       | Image a segment display of these!
        
       | jccalhoun wrote:
       | It seems like someone watched the episode of Modern Rogue that
       | was released yesterday: https://youtu.be/VKB2-gOH7G0
        
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       (page generated 2021-03-20 23:00 UTC)