Gerbert Abacus Review / HowTo
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- Опубліковано 21 жов 2024
- The Gerbert abacus, designed by Gerbert d'Aurillac in the late 900s AD. It's a counting board with counters marked with arabic numerals.
This is episode 43 of my series about antique calculating devices.
Chris Staecker webarea: cstaecker.fairf...
End song inspired by "Hotter Than a Molotov" by The Coup.
#math #abacus #gerbert
The city is Shenzhen which is a gigantic manufacturing hub. The long message on top is usually an address written out completely in words and maybe the name of a company that will be named something like "Shenzhen Wooden Devices Manufacturing Co. Ltd." Works better in Chinese characters than spelled out in pinyin.
Nice profile pic :)
Love your humor and philosophical conclusions.
I thought you were being offensive with the Chinese, but that was actually what the label said lmao
Many attempts!
Dude, I can't believe this only has 1.2k views. This is worth at least 100,000 views
sorry I can't compute numbers that high
bruh
Beautifully done. The telegraph and typewriter have had their day as well. Does that mean they were unimportant? Of course not! They were significant in their own time and helped pave the way for what followed.
Dude, I just found your channel. I am fascinated by computation machines. Please don't stop uploading!
The traditional counting board used ones in the columns and fives on the lines to the left. So 8 would be three counters in the space and one on the line to the left.
Once the numbers were entered, they were rationalized from left to right: every two counters on lines would be replaced by one counter on the next space to the left, while five counters in a space were replaced by one counter on the line to the left. This is quinary grouping, like the 2:5 Chinese suan pan or 1:5 and 1:4 Japanese soroban.
Lately, I've been watching many of your videos. There's a real beauty to this device and your commentary about it. Bravo!
深圳市光明新区公明街道玉律村第六工业区汉海达科技创新园
shēn zhèn shì guāng míng xīn qū gōng míng jiē dào yǜ lǜ cūn dì liù gōng yè qū hàn hǎi kē jì chuàng xīn yuán
Shenzhen municipality, Guangming district, Gongming residential neighborhood (i.e. town), Yülü village, Industrial Area 06, Hanhaida technology and innovation centre.
The Chinese format addresses the opposite way, so flip everything for an english address; probably the place it was packaged (and maybe manufactured?). Not a city name though, just careless mislabelling from the manufacturer.
Very impressive attempt though! The v's were misleading (kind of a scrapped up solution to deal with the lack of ü in English), but you got all the correct terminations between words without spaces.
You're content is so good. Kind of makes me mad that you only have 1.5 views for this video
pretty impressive to get a half of a view
I found you in my suggested only a day or two ago, but you're great. I hope this is indicative that the algorithm now likes you
Instead of little cones, you could use go stones. They look like big lentils or M&Ms, and they are particularly easy to pick up by pushing one side down with your middle finger and scooping the other side up with your index finger.
I love gerbert more than anything💓💓💓💓
al-Khwarizmi was known in medieval and renaissance Europe as Algorithmi, and source of the word “Algorithm” in English. And his book, “Concerning the Hindu Art of Reckoning” was decently well-known in Italy and at the time monasteries since the Crusades brought a lot of Islamic Golden Age knowledge to Europe, but adoption of Hindu-Arabic numerals was slowed outside of academic circles largely because it was considered too easy to scam the semi-literate by adding a zero to a ledger line for a financial transaction.
His home kingdom of Khwarizm was wiped off the face of the Earth when their king made the mistake of executing one of Ghengis Khan’s ambassadors.
al-Khwarizmi was an iranian mathematician not arabic
en.wikipedia.org/wiki/Al-Khwarizmi
@@hormazdmilani7279 I never said he was Arabic? In fact I specifically mentioned his home kingdom of Khwarazm, which was in modern Uzbekistan & Turkmenistan, in my original comment?
I love your conclusion "...this is the pure essence of Mathematics..."
Nice! I'm obsessed with ancient number systems and counting boards.
Could you make a video on how the mancala game originated as a binary calulating divice? I've never found a video on it but my wife and I actually figured out how to multiply and divide on it with fractioned remainders but I haven’t figured how to represent decimal remainders even though im sure it can be done .we also figured out how to convert some bases on it. It's amazing what they could do with a row of holes and a few beans!
My next video is about a binary counter like a mancala board! (But I don't think that was the original purpose of the mancala game- is it really?)
That was beautiful. I welled up, and cried a bit.
I guess my emotions are close to the surface.
It would be neat to have a magnetic version of this!
🤔?(!)…
Very interesting, thank you for posting. I think the main value in counting boards must have derived from how public and demonstrable the calculations are. Especially if one of the parties to the transaction is illiterate, and largely innumerate. I bring in 10 chickens and a cow, you give me 2 bushels of wheat and 12 shillings. The board provides a way to physically show the multiplications and additions. Indeed, in 999 AD I wonder how much solitary computation happened at all - the odd treasurer of an abbey or a dukedom or a realm, maybe the occasional mason estimating materials for churches, I doubt ordinary carpenters needed to calculate much. In England we still call our Finance Minister the Chancellor of the Exchequer, the exchequer being a medieval chequered cloth used as a counting board - but I believe it was mostly used to demonstrate, and for debates about accuracy and viability, rather than pure original computation. Anyway, it's very interesting to see the exact transition from Roman to Arabic numerals, which I agree are very important for what would later become common numerical skills, and I had never heard of the Gerbert Abacus before, so thanks again.
Yes- I have heard that there was resistance in Europe to the use of arabic numbers in public markets, etc because they were totally inscrutable to somebody who didn't know how they worked. A counting board would be much more transparent.
Nice. Never thought of it that way but you're right: transformation of the soul. Paulo Freier would love it.
Long time i missed you
5:39 Wow! I didn't know that Roman numbers have its fractions. Where did you find this page?
That manuscript is called "St John's College 17". I found it at: digital.library.mcgill.ca/ms-17/folio.php?p=48v
@@ChrisStaecker Thank you. Now i can learn those fractions easier
I've made a Roman fractions Converter if somebody interested
scratch.mit.edu/projects/355894220/
Love it !
From Montréal, Canada.
Feels funny to the touch, so to speak, to see H-A numbers laid out like so on an abacus, but consider that in his day, paper was not a thing.
So one could do it on a slate with chalk, perhaps, and who knows if that was a thing, though it's hard to see how it wouldn't have been. But everyone and even his brother and sister knew of the abacus/counting board/lines drawn in dirt with rocks and things as counters in the columns. So doing what we normally do on paper, as demonstrated in the video, on an abacus formatted board would have been very "friendly" to the user, and easy, as shown to achieve.
BTW, Roman numerals corresponded to the columns, and the unit + half the next unit idea allowed you to use fewer counters in the working area and read them more easily since there'd be a max of four to spy. With five, fifty, etc. either there in a counter above the line, or not. Presumably appropriately... dunces not being considered. So adding them up just meant parsing the sub-groups and setting up each column for the first number, then adding the pieces of the next number from right to left. Actually extraordinarily easy.
Multiplication worked similarly, just in pieces... precisely as we do today in the paper version. IN fact, one wonders if that aspect was applied once here, or if it was figured out in India or Muslim-ia on its way to Euroland. Probably 'cause it would have been getting realized by peeps using the same Roman abacus. The Chinese one differed, btw. As you'd do each sub-group, again right to left, just like today's paper version, you'd be adding the bits you get for each single digit by single digit numeral multiplication. So that easy 10's addition table our first graders learn, so certainly smart peeps, even Euros, could learn as children or adults, plus being just in the end a series of additions, like today, though done on the fly on the abacus rather than colected and added as a distinct step today... easy peasy. Not to mention carrying was not even a thing, though it bedevils so many today... If you got 18 in a step, you just added that in and move on. Done right then since it was accumulating as you went, so no keeping track of things to carry. And a missing group was obvious without a 0 as one used different letters to show the powers of 10. Whether written somewhere, or spoken to the calculator person, M is not D is not C is not X, etc. And reading it literally, i.e. not realizing "VIII" is 8, saying "eight" and the calculator dude converting, it could have been read as "VIII" or even backwards as "IIV" to match the worker's actions. Though I wager not.
NONE of it is hard with an abacus. It's just paper and pen, or later pencil, is so much nicer. YOu know, when they actually got the real paper idea from the Chinese, and then 100-150 years later when paper became mildly affordable though think like our dollar or two a page for craft fancy paper vs. our penny or two a sheet for 20# copier paper.
And slates are actually brittle, and difficult to smooth suffciiently with earlier tools and techniques. If it had been compelling enough, i.e. the abacus frustrated anyone at all rather than being a cheap (lines drawn in dirt or dust bunnies, stones, bits of stick, etc. for counters) and easy thing to use, those techniques and tools would have sharpened up in a hurry leading to adoption in the 8-900's probably, not in the 12-1500's. Since it WAS a fantastically simple and cheap system (not just the phyical devices used, but the training too), there was nothing particularly compelling until paper DID become cheap and prevalent, with pens becoming pretty decent too. (I mean... nothing like a ballpoint, with or without a gel ink! But awfully awesome for the day.) So not adopted until hugely later. Who knows how that might've held folks back. Or not... it IS "who knows", right?
Key point? Abaci were HUGELY easier to learn and use, could be extraordinarily cheap, even impromptu. (Remember the Archimedes death story, the one in which he gets nasty with enemy soldier holding swords, about walking about on his sand pictures? Abaci drawn in sand, holding calculations and results one assumes, maybe other stuff too. Dump on enemies holding swords... smartest man in antiquity... maybe smartest, but not cleverest...)
How on earth did they do math with Roman numerals‽ I cannot fathom a world without the Arabic numbering system...
Roman numerals are fine for number notation, but horrible for computation. But it’s only after Arabic numerals that we began to expect our notations to be helpful for computing. Kinda a miracle that it works as well as it does, and the Romans probably didn’t know what they were missing.
Gerbert d'Aurillac is a very nasty vampire in the British TV series "A Discovery of Witches". I don't know if it's reached the US yet, but it's well worth watching.
Does the TV series include Gerbert’s succubus math teacher?
They really love doing poor Sylvester dirty
🤔 By any chance-might this have _”anything”_ to do with the _origin_ of the name of the British government official called “Chancellory of the Exchequer”?
I could imagine that this hangs around, even after people use Arabic numbers widely, simply because you don't have to waste paper, parchment, papyrus, a pen, ink or a stylus (did I cover all my grounds?)
Awesome.
How long did you practice saying the Chinese town name?
Many many takes!
It was Fibonacci that introduced the Arabic number system to Europe, that was actually his main contribution to mathematics, not the number of bunnies sequence, that one was known way before him.
Well to be fair Gerbert and others were using the Arabic numbers in europe 200 years before Liber Abaci. Fibonacci wasn't the first to "introduce" Arabic numbers to Europe, but his presentation really made an impact where earlier attempts had mostly fell on deaf ears.
Are there any older text about solving a problem through recursion (or induction, same thing)?
It wasn't so much Fibby introducing them as it was paper become widespread enough, cheap enough, pens decent for use on it, and inks, all of that as a tech base, that led to people like Fibby using such themselves, and knowing others did so enough that they could be of interest to enough folks (as in "buyers of their books"), to lay out their ideas. (Which of course, were usually distillations of reasonably widespread practice, with the occasional brilliance contributed... think of Newton... the man added a last step at the end of 125-ish years of heading to full-blown calculus. He likely let out the "secret" not only for the obvious reason that he had to for folks to buy into his scientific discoveries, but in no small part to knowing how "last" a step he had come up with and wanting to establish himself as the "dude who did it" if anyone else should step forward with the "one small step for a man, one giant leap for mankind" publication.)
Fibby cannonized the double entry concept, as opposed to the log of activity concept ("the roll of (fill in the blank) earl", say), and to better push it, emphasized its workability when used with the H-A numerals which took standard space and were were very amenable to basic addition and subtraction in place. The log of activity method needed no such because each entry was a flow that took what space it did. It did not line up in any way that kind of required same space taking for each portion of a number, like a 7 vs. DCC, further emphasizing the ability to do the arithmetic IN PLACE vs. sussing things out of log of activity's entries.
The wonderful utility of double entry vs. a log of entries done in "stream of conciousness" form was what Fibby brought to the table. The numerals were just an absolutely natural fellow traveller. In a way, he was busting the chops of parasites like Thomas Edison. (Who read patent applications and notices to file, and did not work on the "invention itself" but on 20 improvements to the mooted invention that would be obvious additions, ones that no one would want to buy the actual invention itself without, and so forcing the inventors to inculde for the lion's share of the profits as they, not he, were the ones having to do the actual manufacturing. >1,000 patents, the vast majority of which were this parasitic kind.) Instead of pushing the double entry method and seeing others steal his book sales by tacking on the use of the H-A number system, and themselves become the "Immortal (fill in the blank)", he went out on a (fairly substantial by that time) limb, himself. Good on ya, Fibby.
About double entry though... nowadays we need quadruple or quintuple entry in our bookkeeping software, so as to automatically, natively, build not just business control summations, but tax-based and true-physical-based summations as the entries are made. That's a whole different story though.
8:10 writing down the numbers is faster. but in 1100ad, what are you writing it on, and with?
Yeah , you need paper and a pen ,
And you need more paper and more graphite , and if you make a mistake you need rubber wich isn't invented right now ...
With that : just hands to move stuff
Let's see:
A stylus and waxed board (goes back at least as far as the Roman empire.),
A charred stick and flat piece of wood (or a piece of leather),
A pointed stick drawing in sand or dirt,
A pointed metal object scratching on wood,
A rock scratching on a softer rock.
Cool.
3:37 No beating around the bush. Nice.
2:30
CDXXIX is really CCCCXXVIIII
so CCCLXII+CDXXIX
is CCC L X II + CCCC XX V IIII
is CCC CCCC L X XX V IIII II
is DCCXCI
Actually, no. The idea was that you were well practiced at parsing the string of symbols and got CD, XX, and IX out of it in no time. The smaller column's symbol preceding the current column's symbol triggers your seeing the following bit as "not that column." So while XXIX looks sh*t to us, it'd leap out to them as XX and IX. Same with CD though it just starts the mess rather than being amongst it. In other words, breaking it up was as natural as for us in ours today.
But why Cd rather than CCCC? Because part of the power of the Roman abacus was that you'd have the imediate trigger to manipulate the "5" stone ABOVE the line, then go below to manipulate the required stones. In this case, one stone, but note that you never have to parse visionally, or manipulate physically, more than three symbols for the below the line part. I'll seemingly digress a moment to mention that the ASVAB test, 50 years ago (yeah, THAT old, but I'll point out at least not old enough to have trained on the Roman abacus, so there's that) had a couple questions that, (dubiously) theoretically, the USPS valued highly, which took the form of 4-5 lines of 0's and C's and you had to count the C's in the block. Apparently hard enough to be of value, and applicable here in that even C's are hard to count instantly in bulk. So you snapped the five stone for the hundreds column (true floating point math here, so not necessarily the third column) then took away a below the line stone in the column. If the five stone had already been dropped, you snapped it back up and deposited the left-er column's single stone, and if reaching five with that yyou manipulated up or down the five stone for that column, and if... you get the idea... it was always holding the exact total to date for all work done, at the end of each step. Really a long series of additions like if we added 23 and 74 by writing 3, crossing it out and writing 23, crossing it out and writing 27, crossing it out and writing 97.
So for speed, and accuracy of entry, CD was much, much tighter than CCCC.
All that said, they actually DID write them a variety of ways. So much so that various uses had their own standard approaches. Stone-chiselled messages often did it in their full glory, all the C's, all the I's, and so on. But not so much documents meant for use in summing things up, or even for easy reading by those in the biz who were, after all, used to seeing them in that particular way and so easily parsing them written so, whilst laboriously (and probably considering it tedious) in the "fuller" way. They even b*st*rdized it some for use in street graffiti which survives to this day and in documents and margins, the way we do today, like we might write "3some". It was, after all, a living thing, and used as needed and in forms appropriate to the need was made of it daily.
But again, the whole point was enabling the assumed use of an abacus in the particular use and the reader being used to seeing numbers prepared for such use.
As long as I'm on the subject of Roman numerals, a little bit, they were NOT, as is endlessly said (only dogs having an "alpha system" (not even science when WWII started, and "ancient astronauts/architects/builders of ancient monument drek seem to stick as well) something that was half Etruscan. Not even the symbols for 5, 50, etc. were Etruscan. And they didn't like base 10 in Rome, but becomne convinced their god-like bosses for a long time were oh so much better. Those were there for the abacus that was an implicit part of numbers in those days. Even more so than Excel is today. And in keeping with that, the 5, 50, etc. symbols were literally HALF of the higher symbol. Most familiar is the V being the top half of the X. But if you see very early versions of the symbols, the D is clearly half of the M and the L clearly half of the C. Sounds boz-ish at the moment, but then remember, this was the 500 years before "letterizing" the numerals with their close letter approximations. Obviously I can't draw them here, but consider a somewhat stylized C and cut it in half... basically an L, eh? And that V? It was upside down for a while (while = long time, when thinking about the 500 years it was evolving), the right side up, so to speak.
So the numeral system was always a slave to the abacus, and the "halves" always Roman, not Etrruscan additions.
Ah yes, Pope Sylvester "the Necromancer". So many rumors they made out of him, like he kept talking heads which point the locations of treasures in Rome.
Look at all the math he could do, must have been a witch
CD = CCCC
IX = VIIII
1000 is M
You're a brony? Lol
gurburt
Even my math books in the 70s taught me about Al-Khwarizmi; if you didnt learn about him, that's the fault of your teacher, not "whites". Keep CRT out of my mathematics please!
Math education in the USA is overwhelmingly Euro-centric. This is not CRT, it is just a fact.
CRT can be helpful if you want to understand why things are this way. I'm not an expert, but I bet it has something to do with the fact that the educational system in the USA was built by white people, who are naturally inclined (maliciously or not) to emphasize certain stories while de-emphasizing others.
CRT can be harmful if you want to bury your head in the sand, or if you are afraid to assign culpability to your own distant ancestors, or afraid to ask hard questions of yourself as a descendant who benefits from various ill-gotten gains.
I am not an expert, but I believe CRT has essentially nothing to say about mathematics itself. It probably has a lot to say about how mathematics was and is disseminated, how we use mathematics in the real world, and how we construct the stories we tell about the history and present of mathematics.
Lordy, an informative and highly entertaining nine-minute video and you choose to fixate on this minor joke?
CRT is a law school curriculum. Certain US politicians picked up on a random grad school curriculum, I guess because of the name, in order to scam people into voting for them. It’s sort of like being opposed to teaching brain surgery to your grade schooler.
@@ChrisStaecker Education in the USA is Euro-centric because it was built by european colonisers. It has nothing to do with race. Race wasnt even a thing in Middle Ages. It was all about division between Christians and Muslims. Every education system tends to be centric. European is eurocentric, persian is persiacentric, chinese is sinocentric, etc., which is compeletly normal. There are simply too many occurrences to learn, so the national achievements are emphisized. I am from Slovenia, but you probably never heard of Jurij Vega, right?
It is impossible to separate “euro” from “white”. If your point is that it’s normal for white teachers to teach a white curriculum, then I agree 100%! That’s what I was trying to say.
Just because it’s normal doesn’t make it right- the legacy of racism cannot be separated from the legacy of colonialism. They go together.
999秭9999垓9999兆9999億9999万9999個まで!?
Roman numerals work perfectly well on the abacus 🧮 which was a Roman device
(1, 5) 10⁰ &c
Roman numerals seem unsuited to display on an abacus. Something like XLIV looks very different in roman numerals than it does on an abacus.
@@ChrisStaecker Nay my friend, it displays precisely the same. See my Reply to abcq2's comment shown as being five months ago, so half a year after yours here.