[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)