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 Post subject: The Multipliers
PostPosted: Fri Sep 13, 2013 8:34 am 
Avisaru
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Wondered where and when it was set, thought it had to be Wede:i, as the narrator is literate. Have found most of the towns mentioned on this map.

I am guessing that the city is Bi:dau and the date around -650 Z.E. Am I right?


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 Post subject: Re: The Multipliers
PostPosted: Fri Sep 13, 2013 11:45 am 
Boardlord
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Close enough— I'd probably put it a little earlier than the empire. And Bi:dau would make sense as it's the only Delta city to have a king at that time.


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 Post subject: Re: The Multipliers
PostPosted: Sat Sep 14, 2013 6:29 pm 
Lebom
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It is rumored that Munśuk is still at large, hiding in the marshes of the lower Euphrates. The King was going to send an expedition there led by his favorite prince Muku, but in fact Muku was one of the princes of the harem infiltration. It’s a tricky situation.


Euphrates?

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 Post subject: Re: The Multipliers
PostPosted: Sun Sep 15, 2013 12:23 pm 
Avisaru
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What clued me in was the incipient boom in copper. It had to be around the time bronze working was getting started. I also thought it was telling that a lot of the towns, like Na:iwor and Śinji, seem to be independent.

Interesting to note the major god seems to be Akśim, the river ("Euphrates"?) and not Wila:r (Meśa). EDIT: Going down the Meśaism page I realised that positively identifies the town as Bi:dau.


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 Post subject: Re: The Multipliers
PostPosted: Sun Sep 15, 2013 2:10 pm 
Boardlord
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Brel wrote:
Quote:
It is rumored that Munśuk is still at large, hiding in the marshes of the lower Euphrates. The King was going to send an expedition there led by his favorite prince Muku, but in fact Muku was one of the princes of the harem infiltration. It’s a tricky situation.


Euphrates?


Fixed. (I wrote it years ago about Earth and adapted it to Almea.)


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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 16, 2013 8:48 am 
Lebom
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Ah, okay.

I'm pretty in the dark about the history of math. Addition and subtraction are things we (and the uesti) can do with our fingers, but multiplication and division couldn't have become important before agriculture. Anyone have any books on the topic?

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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 16, 2013 9:36 am 
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Huh?
"We gathered 14 mushrooms today, and have three children. How many mushrooms should each child get?"
"We need four logs for each side of the building and the building has four sides. How many logs do we need to get in total?"

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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 16, 2013 9:43 am 
Smeric
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Salmoneus wrote:
"We gathered 14 mushrooms today, and have three children. How many mushrooms should each child get?"

Wrong example. In the Stone Age, children weren't allowed to get stoned.


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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 16, 2013 4:33 pm 
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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 16, 2013 6:32 pm 
Boardlord
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Salmoneus wrote:
Huh?
"We gathered 14 mushrooms today, and have three children. How many mushrooms should each child get?"
"We need four logs for each side of the building and the building has four sides. How many logs do we need to get in total?"


If the intended implication is "multiplication and division are things every human culture would have", then no, it seems pretty clear from number systems that not all cultures can ask or answer these questions. Quite a few languages don't count past two, or if they do, use addition-based expressions which would make counting past 10, much less multiplication, cumbersome or impossible.

Ethnologists would have to answer what hunter-gatherers actually do, but I'd note that equitable distribution doesn't require calculation at all-- you can evaluate the size of a pile of mushrooms by eye, and if it's really important you just distribute one mushroom at a time till your pile runs out. Or just let people grab what they need.

(That said, it can certainly be argued that multiplication comes way too late in the story, But it's not intended as rigorous ethnomathematics.)


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 Post subject: Re: The Multipliers
PostPosted: Thu Sep 19, 2013 11:30 am 
Avisaru
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Not necessarily. The Sumerians had a writing system of sorts for nearly a millennium before they had multiplication tables. (They had pictographs as early as 3500 BC.)


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 Post subject: Re: The Multipliers
PostPosted: Sat Sep 21, 2013 5:36 pm 
Avisaru
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Early mathematics could be weird — it seems that the Egyptians never got the idea of multiplication tables and decomposed one operand into powers of two instead.
(So, to calculate 111 * 15, for instance they did 111 * 8 + 111 * 4 + 111 * 2 + 111).


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 Post subject: Re: The Multipliers
PostPosted: Sat Sep 21, 2013 6:58 pm 
Avisaru
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The Egyptians never really bothered with the theory of mathematics, only the necessary utilitarian properties of it. This is made obvious by the sheer mathematics of the Pyramds--just googling about mathematics and Pyramids reveals some interesting and amazing topics on the subject. There is little evidence that the Egyptians knew of such mathematics, so evidence more leans on that they applied math, they did not study it. (On the other hand, they may have known about it, but the evidence doesn't exist. My college math courses were a fascinating study of a variety of different mathematical topics, including Egyptian geometry, which sticks out the most. My professor chalked it up to just not caring about the intricate theories, but more of what gets the results done--he could be wrong, and therefore I could be wrong too.)

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 Post subject: Re: The Multipliers
PostPosted: Tue Sep 24, 2013 6:04 am 
Avisaru
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In this early story the Wedei civilization does have merchants. The class must have died out under the empire. I wonder how that happened. Perhaps certain wealthy people would be granted monopolies (like Miriŋi:l with elcarin steel) as royal favours, which could then be revoked, and either retained in royal hands or granted to the priesthood. In this way a market economy might end up as mostly a command economy. Is that how it happened?


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 Post subject: Re: The Multipliers
PostPosted: Tue Sep 24, 2013 10:26 am 
Boardlord
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That's kind of in flux. I'm in the middle of a book on early civilizations-- I feel like I don't know enough about how certain things develop, especially economies.

However, what's pretty certain is that the Wede:i weren't what we'd call a market economy. They mostly deal in bulk items, luxury goods, and inter-city trade, and there is no single currency. It's possible that they weren't independent entrepreneurs, but agents of temples and landowners, or perhaps minor landless nobility. Not sure yet.


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 Post subject: Re: The Multipliers
PostPosted: Tue Sep 24, 2013 10:29 am 
Smeric
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CAUNEAS

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 Post subject: Re: The Multipliers
PostPosted: Wed Sep 25, 2013 7:28 am 
Avisaru
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Interesting. It sounds from what you say, Zompist, as though the borderline between the two types of economy could be fluid. What is the title of that book you're reading? I think I'd like to read it too.


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 Post subject: Re: The Multipliers
PostPosted: Wed Sep 25, 2013 3:46 pm 
Boardlord
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It's Understanding Early Civilizations by Bruce G. Trigger. It focuses on Egypt, Mesopotamia, Shang China, the Aztecs, the Maya, the Incas, and the Yoruba. It's also very huge and dense, so I'm not far into it. :)


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 Post subject: Re: The Multipliers
PostPosted: Sun Sep 29, 2013 3:43 am 
Niš
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Very interesting. For a start, how much trade was there between Munkhash and the Wede:i, and what did the Wede:i know about the ktuvoks? What kind of rebellion was Munsuk's and why did the philosopher support it? More importantly why does the merchant take so long to realise they're fighting Muku - it seems fairly obvious. Are they using something like peasants’ multiplication? And does anyone know what sort of economy Mesopotamian city-states had for comparison purposes?


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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 30, 2013 3:33 am 
Sanci
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I'm not quite getting how multiplication could have been a new thing to them. 'Cause I'm looking at the Wede:i numbers, and multiplication is kind of built-in, right? To say "twelve," you have to say "two sixes." Is that kind of multiplication okay by the priests, and Bokugo is just the first guy to make a table based on "Hey, if this works with six, it'll work with one through five"?

Also, in the multiplication table at the top, do the two dots underneath read -ka?
And why is the numeral for 36 a picture of a person? What are there thirty-six of on a person? Or is that not a person?

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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 30, 2013 2:44 pm 
Boardlord
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Owain wrote:
Very interesting. For a start, how much trade was there between Munkhash and the Wede:i, and what did the Wede:i know about the ktuvoks?


Xengiman is far enough from Munkhash that it could be dealt with as a normal country. (You may recall the later episode where the province of Moun made a deal with Munkhash). However, trade would have been over the mountains, and thus most likely restricted to small amounts of luxury goods. The Wede:i almost certainly met no ktuvoks, and from what they heard about them probably assumed they were deities.

Quote:
What kind of rebellion was Munsuk's and why did the philosopher support it?


We don't have any additional information, but it'd be some sort of intra-elite power struggle.

Quote:
More importantly why does the merchant take so long to realise they're fighting Muku - it seems fairly obvious.


Fog of war in a premodern state. The narrator only knows what he can see, and that's severely limited when the streets are full of rioters and then soldiers. He expresses no surprise when Muku comes out on top, however.

Quote:
Are they using something like peasants’ multiplication?


I don't want to get too specific, but this pageis pretty neat, and suggests that it's really not that outlandish to think about multiplication as difficult higher mathematics! (All the more so when it was done without a positional representation system.)


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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 30, 2013 3:05 pm 
Boardlord
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justin wrote:
I'm not quite getting how multiplication could have been a new thing to them. 'Cause I'm looking at the Wede:i numbers, and multiplication is kind of built-in, right? To say "twelve," you have to say "two sixes." Is that kind of multiplication okay by the priests, and Bokugo is just the first guy to make a table based on "Hey, if this works with six, it'll work with one through five"?


I worried about this a bit in adapting the story! One possibility is that, as you suggest, multiplication was understood with the base itself (6), but not arbitrary numbers.

Another is that the names of the numbers in the grammar are post-Bokugo. Very possibly he (or others) introduced a new notation and some new number names, which would make the system easier to use but also require a good deal of adaptation for those who knew the previous system.

Quote:
Also, in the multiplication table at the top, do the two dots underneath read -ka?


Yep.

Quote:
And why is the numeral for 36 a picture of a person? What are there thirty-six of on a person? Or is that not a person?


Recall the Wede:i counting system: a fist is 1, with fingers held up for 2 to 6. When you can count to 6 on one hand, you can count to 36 on two. This is an extension of a fairly common idea in terrestrial numeration-- Shasta tsec '20' < 'man'.


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 Post subject: Re: The Multipliers
PostPosted: Mon Sep 30, 2013 7:17 pm 
Sanci
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zompist wrote:
Another is that the names of the numbers in the grammar are post-Bokugo. Very possibly he (or others) introduced a new notation and some new number names, which would make the system easier to use but also require a good deal of adaptation for those who knew the previous system.
So, for example, the word for "six" could have been "hand" and in order to say "twelve" you'd have to say "hand hand"?


Quote:
Quote:
And why is the numeral for 36 a picture of a person? What are there thirty-six of on a person? Or is that not a person?


Recall the Wede:i counting system: a fist is 1, with fingers held up for 2 to 6. When you can count to 6 on one hand, you can count to 36 on two. This is an extension of a fairly common idea in terrestrial numeration-- Shasta tsec '20' < 'man'.
Didn't think of it being a place-value thing. But again, that runs into an implicit understanding that 12=2*6. So for my own sanity, I'm going to go on in the assumption that multiplication was understood with the base itself (6), but not arbitrary numbers.

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 Post subject: Re: The Multipliers
PostPosted: Wed Dec 25, 2013 3:10 pm 
Avisaru
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In celebration of Christmas, and my copy of the Lexipedia arriving, I thought I would try out my Wede:i translation skills on Zompist's latest story.

The Multipliers

2 Tokn

"Dined with Bokugo tonight. Truly an unsung genius"
Go:źiok Bokugoli lil seki. Raluŋ, ŋinuulze to:magu.
eat-PAST Bokugo-WITH this night. Oracle-ADJ sing-PP-NEG clever-AUG-MAN

"It’s a shame he has to live in such a squalid quarter: the Dry Wells section,"
ŋerugesa yurma ŋa:unaak-do ra gau śa:uge : lu:sir lu:a:in gala:i,
live-DUR-CAUS bad-AUG street-COLL-LOC in THAT shame-DUR : water-WITHOUT water-PLACE-PL enclosure,

"virtually in the shadow of the Aklu:ma Gate"
Aklu:manodaunoraudo ru:sirdo ra liluŋ
Aklu:ma-GEN-city-GEN-door-LOC sun-WITHOUT-NOM-LOC in near-ADJ

"We were bothered by beggars all evening"
lila:ugun bauokingzerape sekibuge
approach-PERS-PL quiet-PAST-1-NEG-PASS-REP night-before-DUR

"till Bokugo brandished a sword at them."
Bokugo toawo jalanoknido bu
Bokugo sword-OBJ wave-PAST-IND.OBJ-LOC before

"Discussed King's Ear Nauroda's decree against the followers of Munśuk."
yoneningok moganopaźiwa Naurodano Munśukno la:utigun sa:un soŋur
speak-REF-1-PAST ear-GEN-king Naroda-GEN Munśuk-GEN come-after-PERS-PL law strike-GER

"Bokugo was worried that his own support for Munśuk would come out"
Munśukdo śaiuri la:urokju gau Bokugo paijokge
Munśuk-LOC support-GER-GEN3 come-out-ABIL THAT Bokugo fear-PAST-DUR

"but I assured him that no one would ever know."
dowugo ze:nuyuze gau lisaingnei
nobody know-TENT-NEG THAT explain-1-BUT-3

"The truth is, I doubt anyone in the palace even knows Bokugo's name."
Raluŋa, paun bogu nizdo Bokugono sim ze:nuze gau yediŋze
Oracle-GER-NOM, some person palace-LOC Bokugo-GEN word(name) know-NEG THAT think-1-NEG

"Still, I wish he would be more discreet about these things."
ŋozi, bauyonyuta lil bokando gau
same(pragmatic), quiet-speak-TENT-DES THIS thing-PL THAT

"Love what the king loves and prosper, as the proverb says."
paźiwa zu:rtaugeuŋ zu:rtaro yebi:li:ka gau ze:nsaju yonu
king love-DUR-ADJ love-IMP (be)rich-AND THAT teaching-thing say

"Bokugo seemed unusually excited about one of his projects."
Bono su:bokando Bokugo paun joka do:uŋ liraok
one-GEN new-thing-PL-LOC Bokugo some other-AND(more) breeze-ADJ(excited) see-PASS-PAST

"Something about addition. It was lost on me."
Bobokado paun boka. Soźokśino.
One-one-AND-LOC some thing. Lose -PAST-DAT.PASS-1OBJ

"I have no head for higher mathematics."
Duziŋ dowo śenuŋ boboze:insaka nituk yuma
have-1 no high-ADJ one-one-teach-NOM for head


Last edited by Mornche Geddick on Wed Dec 25, 2013 3:59 pm, edited 1 time in total.

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 Post subject: Re: The Multipliers
PostPosted: Wed Dec 25, 2013 3:26 pm 
Boardlord
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Impressive, especially with the limited Wede:i vocabulary! I'll check it over in more detail...


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