Inca counting boards and the table yupana

[@MrVil1]

see kids, we're completely lost when things don't come with the *ORIGINAL* manual.

[@N.A._McBee]

Only the Staecker fanboys know what the ORIGINAL manual really is 😄

[@qtheplatypus]

Well killed out the people who understood things.

[@agesileus]

This is one of my favorite KZbin channels. The sense of humor and deep thoughts are really original, sometimes profound and always entertaining. The short format, editing and structure of of the videos reflect serious film making skills. I can’t understand why so few people are watching but I do like the idea that I discovered something rare and well made . Maybe similar to how I’d feel spotting a working antique adding machine in the wild

[@marcuspepperoni]

came for the history, left with existential crisis. 10/10 would recommend.

[@MrEMeat-kk9tc]

7:14 Your line reading of “It costs more than the Cuerta!” was great but the addition of the animation made it *chef’s kiss* perfect!

[@jamesforrest9837]

hell yeah! my favorite esoteric numerical device youtuber is back!

Given the symmetric nature I think this is a game board.

[@ChrisStaecker]

Yes I didn't really give my opinion, but this is the idea I like best too. I like the idea of a common ruleset that could be played on different layouts- like golf I guess.

[@jaapsch2]

I agree, especially when you consider all the shape variations. They all have two paths of squares leading up to a larger, usually raised, area. It is easy to imagine it as a board for a two-player game. Did they have dice?

@@jaapsch2 You don't even need dice for that. Start by tossing a handful of seeds in the middle compartment, then take turns in moving them closer to your tower according to some rules. The first to put a seed there wins. Similar to mancala, except the two players don't interact much.

[@Minty1337]

that's what i thought too, beat me to it

[@just_a_quick_ride]

I like the idea that a couple of Incans were playing their board game in work time, and when the dopey Conquistador asked what they were doing they said, "Accountancy" to get rid of him.

[@bertino6]

That ending was beautiful - what a great channel

[@normalperson4sure]

this was such a beautiful and respectful video. thank you so much for the acknowledgement, the nuance, and the zen joy you expressed in this video. i was just looking up base ten numeral systems and how to use an abacus and then got on a wikipedia deep until i found this video and it has stopped me right in my tracks. i can't wait to watch more of your videos but for now i'm content to sit in the feeling you've left me with now, thinking about the yupana.

[@turtle_soda]

Personally I think they represent the levels on a hill and you would tally out how much of each crop you would plant in each section/level. This would also explain why they’re all different. Maybe they had templates that would suite a different region which could also be why they look different.

[@mr_oger]

I also think that it has something to do with land, but more in the counting side. Like, it could be a counting/current-state bookkeeping device for trade between two cities or two major communities, raised portions representing them, outer ring representing in/out of goods, and central portions for something more abstract.

[@pamdemonia]

Oh now, you're at least a Y list youtuber. Really wish KZbin would actually show me your vids when they come out, without me having to turn on notifications on my phone. Love this stuff. Keep on rocking in the free world!

[@nashvillain171]

9:30 "But, can a man really love something that he doesn't understand?" * looks at wife *

[@ChrisStaecker]

It crossed my mind too but I decided not to go there

[@nashvillain171]

@@ChrisStaecker 😂

[@nunyabiznes33]

​@@ChrisStaeckerblink twice if wife is listening off cam.

[@TheGelatinousSnake]

I think you can use that for string/yarn multiplication. On two adjacent sides of the board arrange the strings. To multiply 12x12 you need 6 strings. 1 single in each Tens column, 2 strings in each ones column. All straight across the grid. When calculating 12x12, you will find four bundles of intersections. Each bundle is above a grid on the board. Count how many intersections in each grid and place that many seed counters. 1x1 string has 1 intersection, 1x2 has 2 intersections. 2x2 strings has 4 intersections. You should end up with counters 100+20+20+4 With the 2s occupying the fun center section reminding you those counters are actually representing 20s and need to be combined to 40. So basically 100+40+4

[@TheGelatinousSnake]

You can also use fewer strings if you have strings knotted to represent numbers 2-9. Or at least unknotted =1, little knot = 3, big knot = 5. With 1s, 3s and 5… all numbers 1-9 can be made in as little as 3 strands

[@tonyennis1787]

@@TheGelatinousSnake It would be a hard sell to ask accountants to make a new knotted structure from the kee-pu (sp) they already have.

[@tonyennis1787]

I like how you're thinking. I'd expect the boards to be square if kee-pu are used on adjacent sides. Also, kee-pu sizes weren't standardized so a little cleverness and technique would be needed to use any kee-pu on any board.

[@TheGelatinousSnake]

@@tonyennis1787 now that im awake, after you learn string multiplication and you are move on to representative strings instead of bundle’s individual strands. You can do it all in a 6x6 grid with just counters. No longer counting intersections just remembering multiplication 1-9

[@dwagincon4841]

love this channel. I learn something new every time Chris uploads

[@gorgenfol]

That thing looks so much like chocolate, I wanna eat it

[@ChrisStaecker]

Yes- THAT is what the museum gift shops should be selling!

[@anthonyrepetto3474]

I had been inspired, years ago, by the quippu! Thank you for bringing attention to these alternate systems, even when we don't know exactly how they worked. I wondered, when I first heard about quippu, if there would be a way to link/unlink adjacent strands with beads, and move the beads over the knots, to perform operations? Not just arithmetic... you might be able to encode dependencies, weaving among protocols? Textile compiler! I would make icon-beads, stamped with each pictogram!

[@jamesonhardy2126]

Z-list? You don't give yourself enough credit. You're an x-list at least.

[@vuuvovuuv]

that's z list like the z axis: above the rest

[@kaisalmon1646]

I'm just gonna assume its a boardgame until further information develops

[@KarenSDR]

How fascinating! I read the book "Yupana Inka - Decoding the Inka's Math. Tawa Pukllay® " by Dhavit Prem , which is based on the drawing from the 1500s by Guaman Poma de Ayala that you showed. I made a video summarizing and giving examples of the method in the book. But i've never seen anything like these before. I love how mysterious they are. The same kind of mystery that surrounds the ancient Chinese boardgame Liubo: there are hundreds of physical boards, but not much on how they were used (in 2019 a tomb hoard was found which apparently has many pages of explanations, but I haven't been able to find out more information than just the fact that it exists.) Also those mysterious Roman dodecahedrons. There are lots of theories, but no actual explanations from ancient sources. Thanks for making this video!

[@devinhiatt9995]

You'll always be an A list youtuber to me.

[@markgreco1962]

I always watch till the end

[@4xlr6]

At least a napier is not killed to make these.

[@argonwheatbelly637]

Killing napiers out of season....*tsk tsk*...shameful! I remember seeing a box of dead napiers, and they weren't big. 2" long, if, even.

[@lafcursiax]

I had never heard of these, even once! Thanks for the lovely introduction. (And even though I've watched your Gerbert abacus video, I still momentarily thought you said "Care Bear abacus." There's a product idea......... It's been a long day!)

[@ptmusicalboxes]

I think I understand this. It’s a device to sort out numbers. I think I figured out a division on it. It truly is interesting.

[@echtopia1]

A base10 relish/hors d'oeuvre tray?

[@PraxZimmerman]

It's a calculator to compute just how much better you are than your friends, much like modern-day Monopoly.

[@tomnewsom9124]

Really thoughtful words. Nice :)

[@xremming]

Really looks like a boardgame to me. Also, you are an a-tier youtuber for me!

[@A1goritmatico]

The Incas were the first to invent Parcheesi, perhaps? There are symmetrical tracks going around the outside. The raised portions might be starting or ending (perhaps starting and ending) platforms for your grains of seed. Dice thrown in the jogged middle portions, or maybe numbered tops were spun to see how they fell and determine the next move. Of course all of that would be hard to do on the smaller boards; the tops, I mean. But, were there any dice or tops laying nearby these boards when they found them, or any where else in Inca findings? BTW I like to call dice, "random number generators."

[@txikitofandango]

I think it's a board game because of the two-way symmetry and there's kind of like a home square in most of those, I don't know. But yes the mystery, the thingness, it is good

[@timetraveller6643]

Hello Mr. Staecker. I keep trying to post a link to a film that shows a table yupana being used on screen but yuotube keeps deleting it. "Secret of the Incas" 1954. at 16:30, Charlton Heston examines one in a local museum.

[@ChrisStaecker]

Wow! Thanks- I’ll check it out

[@timetraveller6643]

@@ChrisStaecker - Search youtube for the title. the channel is "nexus verbal"

[@timetraveller6643]

@@ChrisStaecker -- I studied these and the Pomo de Ayala manuscript at university. I spent weeks and weeks making models and using coloured beads to try to figure out how to add and subtract. I am inclined towards the game supposition. The Inca farmed on terraced fields and carried grain/produce many kilometers to state controlled granaries for redistribution. As this was an important part of the daily life, a game representing harvest and transport makes perfect sense. It was easy to create rules for a Mancala/Backgammon type game with this artifact. The two terraced corners are to be harvested. The grain/beads then get transported seven cells to the center. All of the examples I saw had two terraces and seven cells to a center compartment. Even the ones that had a different symmetry. I am still moved to angry tears thinking about the conquistadors that destroyed every culture they met. I curse them before breakfast every day. --Molly J.

[@ChrisStaecker]

Sounds like you're more of an expert than me- I had a hard time finding honest scholarship about it, and I never found answers to even basic questions. Like how old are the artifacts? Surely some have been carbon dated? Anyway thanks so much for the movie clip. That prop is huge! Are there really artifacts that tall? I was kind of guessing when I made the z-axis for mine. Interesting that they never tried to present it as a computing tool in the film.

[@timetraveller6643]

@@ChrisStaecker - You are right to point out that as Westerners, we are stepping far outside our lane in trying to interpret these cultures. Early interpretations of the Table Yupana included architectural models. The film's art director expanded on that debunked theory. I have never held a genuine one in my own hands but, the descriptions agree closely with your model. It is widely believed that the Inca inherited quite a bit from the previous Wari civilization so dating the artifacts would give little more data than we have regarding its function or social significance. I had a great deal of trouble getting hold of any deep scholarly study of the things and now mistrust most of what I read about them. There is an unfortunate tendency of modern interpretations to insert profound meaning based on two or three data points. The illustrations made by Pomo de Ayala are scant but show stones in groups of 2, 3, and 5. This launched an unfounded belief that the Inca used the Fibonacci sequence to perform arithmetic. Pd.A was likely mathematically illiterate and copied a grid scratched in the ground used to teach children. There is a book by David Esparza Hidalgo that started an Aztec/Mayan math craze in the seventies that has since been revealed as a hoax. "Nepohualtzintzin" claimed that the Aztecs and other Mesoamerican cultures used wrist abacus's to perform arithmetical operations. His diagrams will show up in any google search. Mr. Hidalgo included no bibliography, no list of sources, and no photographs of his artifacts. Yet the Nepohualtzintzin abacus continues to be sited in schools as a precolumbian calculator. On the bright side, the kipu are much better understood. Though there is quite a bit we still don't have regarding information coded by other means. colour, twist direction, fibre type, etc. You must have seen the Kipu hanging on the wall behind Mr. Heston. The film is fun to watch on its own merits. You get to see and hear Yma Sumak sing. Also, it is a direct ancestor to Indiana Jones. -- Molly J.

[@JeffreyMichaud]

I could see this layout being used for a type of board game. With your higher ranked pieces being placed higher in the castle

[@hujackus]

I think the symmetrical trays are for trade. Two people would sit on opposite ends and place seed tokens into their respective trays based on what they are trading. The central dish is for exchanging tokens from one side to another without removing them, reducing the odds of cheating. That's what I first thought when I saw the shape. This could explain why all the trays are symmetrical through the origin, but do not have the same number of trays or layout. m.kzbin.info/www/bejne/iJ6UnmCHq7uEna8

[@itwasrightthere]

I have the exact same feeling for the Gallo-Roman dodecahedron. I first learned about them when I went to Tongeren, Belgium.

[@farpointgamingdirect]

That zig-zag bit in the middle strikes me as something designed to assist in carrying over while making calculations

[@davidegaruti2582]

these where like their ram while the quipu where their hard drives

[@Torn_Shoe]

- Where's my yuopana? - Sorry, I ate it.

[@altaris6593]

I feel that central compartment is to store excess beads, rest is for calculating

[@Charles-oo3dw]

I think its a board game like backgammon , who knows though, great channel btw, love your content.

[@Charles-oo3dw]

Lots of early board games also were magical tools, also forgive me if this is something you have spoken about before, but are you familiar at all with the game Go, I think you would find it interesting, there is a steep learning curve despite it being so simple but it is very much worth the investment of studying.

[@sumdumbmick]

if it is in any way related to calculation it's probably just to settle payments/debts. one side is the payer's assets, the other is the payee's assets, and you just transfer tokens from one side to the other, indicating what the payment should be and where everyone should end up.

[@sumdumbmick]

that would mean it's just storing numbers that are only being manipulated via incrementation/decrementation. which is hardly amazing levels of math. but, it would allow that to be done very reliably and fairly, and thus it would have real value for basic commerce and governmental management of resources and populations.

[@sumdumbmick]

there is always a central region. this could be to hold tokens to use elsewhere. there is always a distinct end to each of the two strings of simple squares, somehow symmetrically opposed to the other. this is plausibly some sort of starting point, perhaps a space to indicate which string belongs to who. there are always two simple squares touching the distinct end of each string of simple squares. this is plausibly to emphasize which string belongs to which end. since the languages of the area used base-10 (which is actually weird for the Americas), then it's not ridiculous to assume that if these objects are at all for some sort of calculation, akin to what I'm suggesting, then each simple square probably just indicates power of 10 increments, exactly as Arabic numerals work. and so, since there's nearly always 7 simple squares per string, it's fair to guess that these things can handle values up to 10,000,000. given that Roman numerals top out at 4,000, and the Romans were pretty crap at math, this limit is somewhat large, but reasonable. especially since contemporaneous civilizations in the Americas could easily handle much larger values.

[@sumdumbmick]

it's also important to note that I'm merely speculating. I am in no way asserting that this is what these things are really for. but it is worthwhile to note that my above analysis is practical and sensical within the cultural context, and still doesn't render these objects as calculators of any real sort.

[@sumdumbmick]

kzbin.info/www/bejne/fWiqh6asiNaEY5o

[@bdot02]

It kinda looks like a plate for serving a bunch of tapas.

[@canobiecrazy]

The shape reminds me a lot of the inside of a jewelry box

[@pubcollize]

I don't know what this thing is, but if we compare it to any of the categories that were mentioned then it barely looks like it would fit any of them. However I've never seen a jewelry box, stationery box, tool box, sewing box, and small hardware items box, that don't have a very similar resemblance to these things. Especially when you compare them in aggregate.

[@bytesandbikes]

Very interesting. That we don't really know what it is makes it even more intreguing. My uneducated guess is that it's for taxes. Looks like a way to split things up rather than add them. Or a game board, like someone else said.

[@StrayCatHomestead]

Did the Inca create Ink?

[@satchell78]

We all learned something today, not sure what.

[@ARVash]

knowing the incas, I'm gonna say it was a board game

[@davidegaruti2582]

inca 1 " why did you make it like that ? it could have been an easier shape " inca 2 " yeah but it does look rad tho " inca 1 " ok no i get ya , you're right man "

[@AndyLundell]

It feels like a counting board with such high walls between the sections would be annoying. Doing calculations on that would be a real hassle, and pretty soon you'd wish there were ramps between the sections so you could quickly slide the seeds from one section to another. If I was an accountant in a culture that used a board like that, by my second day I would have given up and just DREW the board on my desk. If it IS a counting board, Perhaps they used it in a way very different than I would expect a counting board to be used. Perhaps it was literally for counting things. The ancient equivalent of a clicker with no real computing functionality. That way you'd never empty a segment until you were ready to zero the whole thing by holding it upside down over a bucket.

[@ChrisStaecker]

I agree- I think you can see that I had a hard time picking up and moving around the counters. But this may just be my design- I have no access to a real table yupana, so I had to build mine just by eyeballing photographs (though the total dimensions are published, so that's accurate). The vertical height and walls between sections are just my estimates. But anyway the oval one for example is way too small to be realistic for that purpose- those compartments wouldn't even hold 1 peanut.

[@biquinary]

You are wayyyy better than Z-list!

[@Pillowcase]

They're beautiful objects.

[@pierQRzt180]

Could it be a board game that mixes something like chess (that is, units on the board) and mancala ?

[@argonwheatbelly637]

Location arithmetic with a chess board.

[@juanguerreroquispe1545]

That would explain why the Sapac Inga Atahualpa managed to beat the Spaniards in chess during his capture in Cajamarca. They already had some knowledge of something similar to that table.

[@colinstu]

more than the curta!!? damn.

[@jurjenbos228]

If it is more expensive than a curta, you obviously should be able to calculate faster and more accurate than a curta. That's how the market works.

[@nunyabiznes33]

What if it's just a board game like mancala (even have spots for seeds) and the Spanish thought these were counting boards?

[@ChrisStaecker]

The Spanish really didn't notice them at all. They were only "discovered" much later archaeologically by Europeans who thought they were counting boards for really no good reason.

[@StrayCatHomestead]

You know some Inca guy comes home and has no place to put the things from his pockets. His wife constantly nags A place for everything and everything has a place.

[@yep_2431]

You're an a-list KZbinr to me brotha

[@TheGoodMorty]

I wanna 3D print one

[@ChrisStaecker]

Click the link to get my files-

[@ATOQ777]

Enjoyable video

[@TheBookDoctor]

Such a crime that this is a z-list channel. I mean, it's math channel. It should be an x-list channel, at least!

[@Cas1O]

I'm in the Mancala camp!

[@vuuvovuuv]

oo la la, are you counting with pine nuts? classy!

[@tonyennis1787]

9:15 I think decoding and deciphering these objects only makes them more beautiful, and makes the Inca more human, not less. Learning how this (alleged) device works only makes the Incas more real and shows respect for their accomplishments. It helps us understand the problems they faced and how they solved those problems in a way that made sense to them. Even the fact that some of these are made of stone is curious. So much work. Whatever it is, it must have been very important. Learning and conjecturing and thinking about the Inca honors the Inca. Making a video on the device (?) and then taking time to tell us how the Inca aren't there to be deciphered sounds like you're virtue signaling. And seriously, appreciating a human artifact for its mystery, as though the "mystery" is some higher level of purity, is hogwash. I love your channel just the same, but geez dude.

[@ChrisStaecker]

I agree that deciphering these kinds of artifacts is illuminating and does honor to the ancient culture that produced them. But this only works in contexts where there really is enough information to make that kind of analysis accurately. Earlier versions of this episode were a bit more specific in calling out particular cases of people claiming to "crack the code" of the yupana in ways that seem problematic to me. [Look up Nicolino De Pasquale- who media reports were happy to indicate knew nothing of the Inca and developed his entire theory in 40 minutes. But that work is still cited as if it were legitimate scholarship- Aimi & De Pasquale (2003). They published the paper with de Pasquale's "decoding" of the same table yupana that Aimi had just acquired as an exhibit at the museum that he was running. Not a great setup for honest scholarship.] But I want to be careful not to position MYSELF as an expert either, so I decided not to go too hard on people who seem to me to be bad actors. I've got no problem with speculation and conjecture- this is after all how real science is moved forward. But it's got to be honestly portrayed as speculation. One idea that I often try to communicate in my videos is that mathematical-type hyperlogical analysis is beautiful and powerful, but (for me) not the ultimate source of beauty and meaning in life. I know how to do mathematics when appropriate, but most truly meaningful things in my everyday experience are better understood as artworks to be appreciated rather than equations to be solved.

[@tonyennis1787]

@@ChrisStaecker Thank you for the reply

[@GregorShapiro]

It is a game board! (I think)

[@hawkfred2749]

I have a hunch you might be interested in this video about tally sticks: kzbin.info/www/bejne/aHXOqpSej9WffNE

[@ChrisStaecker]

Yes! very interesting- thanks

[@raulapaza1511]

Soy profesor de matemáticas ancastral puedo enseñarle el uso de la yupana y codificación de quipu

[@ChrisStaecker]

I’m interested- email me!

[@geniewiley4217]

I just wanna point out that the "Inca" still exist. They're not a lost culture or anything, there's still plenty of people who speak Quechua and Aymara in South America. The "Inca Empire" was just a specific historical-political configuration. Same with the Maya and Aztec; there's plenty of Maya people in Guatemala and Chiapas (Mexico) and over 1 million Nahuas in Mexico City.

[@giorgio84]

Oh come on, i wanted an answer

[@tilasole3252]

It's an ancient game board

[@bogdanvasut8915]

Oh, but the usage is quite obvious, it's similar with the usage of the roman dodecahedron

[@kamardbob]

🙄

[@nilsschenkel7149]

How would you knit glove fingers on this thing?

[@kamardbob]

@nilsschenkel7149 obviously this thing is a drop spindle

[@hughjanes4883]

Hey your not a Z list youtuber, X list minimum

[@briankgarland]

You don't need to "proceed with caution". You aren't responsible in any way for anything that came before you.

[@rlt9492]

There’s a big difference between personal responsibility and collective responsibility.

[@L.Mandrake]

looks yummy!

[@fkurcik]

I thought it’s a block of chocolate.

[@autismuskaefer]

I want this in chocolate

[@jolu2469]

Looks like a waffle maker for their ceremonial Sunday brunches (of course, all you can eat).

[@MIsterB716]

3D Chess Board

[@argonwheatbelly637]

But you can do math on a chessboard.

[@rildopilcochoque8181]

Eso no es una yupana, hay videos peruanos donde se explica como se suma de manera muy práctica muchos números, espero los vean, saludos.😅

[@ChrisStaecker]

As far as I can tell, those explanations are all speculative. There is no reliable historical description of exactly how a yupana was used, or even exactly what it is. (I agree that what I have is almost certainly not a true calculating yupana)

[@ChrisLeeW00]

I thought it was for charcuteries 🤷‍♂️

[@ChrisLeeW00]

Or a game board! It can do two things, why shouldn’t it!?

[@golovkaanna8757]

I think it's a backgammon. Looks too inconvenient for a calculator

[@diogoduarte369]

Looks like chocolate.

[@nicholasgromak7627]

Incan cafeteria trays

[@arturomateo3920]

long confusing and frustrating. Congratulations

[@pjwadd]

Z list? Hell no!