Author Topic: The Number System  (Read 2216 times)

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Offline Skxawng

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The Number System
« on: December 21, 2009, 01:58:28 am »
Figure I'd bring this down from the e-mails, as its not on the site.

oe neu nume numbers, slä numbers lu incomplete. omum pe oe:
(directly: I want learn numbers, but numbers are incomplete. know what I:) <- early attempts :P

Na'vi number system is octal Based on 8.

Known numbers:

One - 'aw
Two - mune
Three - ??
Four - tsíng
Five - ??
Six - ??
Seven - kinä
Eight - ??

from there, thinking about numbers octally (base 8) can be pretty confusing at first, but you can break it down pretty simply: observe the following

Octal: 1,2,3,4,5,6,7
Decimal: 1,2,3,4,5,6,7

not different at all! here's where it gets confusing

Octal: 10,11,12,13,14,15,16,17
Decimal:8, 9,10,11,12,13,14,15

remember, 8 is essentially 0 in an octal system, and the new digit indicates how many of the base numbers are there. continuing on:

Octal:  20,21,22,23,24,25,26,27
Decimal:16,17,18,19,20,21,22,23

and you can go up and up. Here's a quick trick to quick number conversions:

For each 2nd digit increment, subtract an additional 2 from the octal number to get the decimal number.

Example:

Octal number is 25
since its in the twenties, multiply the number 2 by 2 again, and subtract the resulting 4 from the octal number:

25-(2x2) = ?
25-4
21 << decimal number

Example 2:

Octal number is: 47
47-(4x2) = ?
47-8
39 << decimal number

so quite simply, if the octal number is in the
10s, minus 2 from the number to get decimal equivalent
20s, minus 4 from the number to get decimal equivalent
30s, minus 6 from the number to get decimal equivalent
40s, minus 8 from the number to get decimal equivalent
50s, minus 10 from the number to get decimal equivalent
60s, minus 12 from the number to get decimal equivalent

and up and up and up.


-----------------

Numerical confusion:
past the first seven numbers, only two other numbers are known:

Sixteen, or vofu (octal: 20)
Thirty Two, or Tsìvol (octal: 40)


The question then is...

if o20 is vofu
is o21 vofu'aw? 'aw-vofu? 'awvofu?
is o22 vofumune? mune-vofu? munevofu?

and so fourth.
(forgot to mention, the o before the number indicates that its an octal, or na'vi number)

so again, for reference, here are the current known numbers:

One - 'aw
Two - mune
Three - ??
Four - tsíng
Five - ??
Six - ??
Seven - kinä
Eight - ??
o10 - ??
o20 - vofu
o30 - ??
o40 - tsìvol
o50 - ??
o60 - ??
o70 - ??
o100 - ??
« Last Edit: December 23, 2009, 03:30:20 pm by Skxawng »


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Offline Sarkath

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Re: The Number System
« Reply #1 on: December 21, 2009, 01:59:56 am »
This is what the blog would be nice for. Have like a new lesson every so often so there isn't a wall of text on the forum :D

Offline Taikomochi

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Re: The Number System
« Reply #2 on: December 22, 2009, 03:00:21 am »
Why oh why am I still so confused about all this? :(
I feel like something important and big is getting past me.

For example, how would you say "13", or "22"... or "51"

I'm just trying to get it. Tsap'alute if I seem kinda slow. :(

Offline Seze

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Re: The Number System
« Reply #3 on: December 22, 2009, 03:53:58 am »
Why oh why am I still so confused about all this? :(
I feel like something important and big is getting past me.

For example, how would you say "13", or "22"... or "51"

I'm just trying to get it. Tsap'alute if I seem kinda slow. :(

I may lose you on this, but I am going to try this analogy anyway.  Do you remember the older car odometers?  They were built with disks of numbers stacked together, generally 6 number wheels with 10 digits on each wheel (0 - 9).  The idea on how it works is that the wheel on the far right moves one position for every mile driven.  When that wheel gets to 9 and rolls over to 0 it turns the next wheel one place and repeats.  This is how base 10 works.  Now lets take away 2 digits from each wheel ( now our wheels are 0-7 ).  Now we can count from 0 to 7 and then when the wheel rolls over we get 10, which is actually 8.  If you ever wondered how binary works, its the same principle except its base 2.  There are only 10 types of people in the world, those that know binary and those that don't.  If you understand this joke, I think you will have gotten the idea of number bases but I digress.  Below is a Base 8 and Base 2 number scale, hope it helps some.  Again, I apologize if I've lost you on any of this, its past my bed time...

Base 8       Base 2
000 = 0     0000 = 0
001 = 1     0001 = 1
002 = 2     0010 = 2
003 = 3     0011 = 3
004 = 4     0100 = 4
005 = 5     0101 = 5
006 = 6     0110 = 6
007 = 7     0111 = 7
010 = 8     1000 = 8
011 = 9     1001 = 9
012 = 10    1010 = 10
...             1011 = 11
017 = 15    1100 = 12
020 = 16    1101 = 13
021 = 7     1110 = 14
...             1111 = 15
077 = 63
100 = 64


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Offline Taikomochi

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Re: The Number System
« Reply #4 on: December 22, 2009, 04:05:57 am »
Well I think I understand, but how would you write/translate them to Na'Vi?

That was also my question, and a good reason as to maybe why I don't get it all

(although the 4am factor doesn't help either way <.<)

Nonetheless, irayo Seze, for trying to help me out on this, I appreciate. :)

Offline Seze

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Re: The Number System
« Reply #5 on: December 22, 2009, 04:14:29 am »
Well I think I understand, but how would you write/translate them to Na'Vi?

That was also my question, and a good reason as to maybe why I don't get it all

(although the 4am factor doesn't help either way <.<)

Nonetheless, irayo Seze, for trying to help me out on this, I appreciate. :)

If you are referring to how to write out the numbers, like 10 = ten in English, that hasn't really been answered yet.  Only certain numbers are known at this point. ’aw 1, mune 2, tsìng 4, vofu 16, and tsìvol 32.  If you are referring to converting base 10 to base 8 and back again, I would recommend google if you don't want to worry about the math.  To go from base 10 to base 8 use: <number in base 10> to base 8.  To go from base 8 to base 10 use: 0o<number in base 8> to base 10.


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Offline TrueJournals

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Re: The Number System
« Reply #6 on: December 22, 2009, 10:48:08 am »
The problem with numbers is exactly what's just been pointed out: Na'vi uses a base-8 number system, because they have four fingers on each hand (except for Avatars, that is).  Because humans have five fingers on each hand, we use a base-10 number system: we have 10 base digits (0,1,2,3,4,5,6,7,8,9).

So, if we want to translate a sentence with a number in it, we first have to pause and convert the number to the base-8 number system.  I have a feeling some people may never get accustomed to this, so the pause will always be there.  Others, however, might pick it up easily and do the conversions quickly in their head.

For example, let's try to construct the sentence: I hunted 32 thanators. (A rather silly sentence, I know...)
For the first step, let's convert our number.  32 in decimal (using http://www.statman.info/conversions/octal.html) is o40.  Another way to think of this is "four eights" (just like we think of forty as "four tens", even though we don't use this pronunciation).  I'm going to ignore the grammar in the rest of the sentence, because I'm focusing on the numbers here.
The root for four appears to be tsì, and the root for eight appears to be vo.  Combining these, o40 (remember, that's 32!) comes out to: tsìvol.

On to the sentence:
Oe-l t‹ìm›aron tsìvol-a ayfalulukan.
(I hunted 32 thanators).

I'm quite unsure of my grammar and sentence construction here.  In fact, I'm almost certain that the grammar is wrong, and would love someone to correct me on that :)  However, this should give you a good idea of how we translate numbers.

All that being said, we currently can't translate numbers like 24 (o30), because we don't know the Na'vi word for three!  However, it would be translated as "three eights".
« Last Edit: December 23, 2009, 02:38:58 pm by TrueJournals »

Offline Taikomochi

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Re: The Number System
« Reply #7 on: December 22, 2009, 11:02:52 am »
Oh no no, I understand the system, by eights and tens and all. It's the morning, it's all fine for me now.

I just wanted to know how to write stuff like the numbers we don't know. I was a bit too eager, I was well aware we didn't have them, my bad. I guess I'll just be more patient :)
Irayo for the help, everyone. :)

Offline Uniltìranyu

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Re: The Number System
« Reply #8 on: December 22, 2009, 08:16:41 pm »
Figure I'd bring this down from the e-mails, as its not on the site.

oe neu nume numbers, slä numbers lu incomplete. omum pe oe:
(directly: I want learn numbers, but numbers are incomplete. know what I:) <- early attempts :P

Na'vi number system is octal Based on 8.

Known numbers:

One - 'aw
Two - mune
Three - ??
Four - tsíng
Five - ??
Six - ??
Seven - kinä
Eight - ??

from there, thinking about numbers octally (base 8) can be pretty confusing at first, but you can break it down pretty simply: observe the following

Octal: 1,2,3,4,5,6,7
Decimal: 1,2,3,4,5,6,7

not different at all! here's where it gets confusing

Octal: 10,11,12,13,14,15,16,17
Decimal:8, 9,10,11,12,13,14,15

remember, 8 is essentially 0 in an octal system, and the new digit indicates how many of the base numbers are there. continuing on:

Octal:  20,21,22,23,24,25,26,27
Decimal:16,17,18,19,20,21,22,23

and you can go up and up. Here's a quick trick to quick number conversions:

For each 2nd digit increment, subtract an additional 2 from the octal number to get the decimal number.

Example:

Octal number is 25
since its in the twenties, multiply the number 2 by 2 again, and subtract the resulting 4 from the octal number:

25-(2x2) = ?
25-4
21 << decimal number

Example 2:

Octal number is: 47
47-(4x2) = ?
47-8
39 << decimal number

so quite simply, if the octal number is in the
10s, minus 2 from the number to get decimal equivalent
20s, minus 4 from the number to get decimal equivalent
30s, minus 6 from the number to get decimal equivalent
40s, minus 8 from the number to get decimal equivalent
50s, minus 10 from the number to get decimal equivalent
60s, minus 12 from the number to get decimal equivalent

and up and up and up.


-----------------

Numerical confusion:
past the first seven numbers, only two other numbers are known:

Sixteen, or vofu (octal: 20)
Thirty Two, or Tsìvol (octal: 40)


The question then is...

if o20 is vofu
is o21 vofu'aw? 'aw-vofu? 'awvofu?
is o22 vofumune? mune-vofu? munevofu?

and so fourth.
(forgot to mention, the o before the number indicates that its an octal, or na'vi number)

so again, for reference, here are the current known numbers:

One - 'aw
Two - mune
Three - ??
Four - tsíng
Five - ??
Six - ??
Seven - kinä
Eight - ??
o10 - ??
o20 - vofu
o30 - ??
o40 - tsìvol
o50 - ??
o60 - ??
o70 - ??
o80 - ??
o90 -  ??
o100 - ??

Well, from the numbers given, Couldn't you just compound certain numbers like for Ox3 wouldn't it be "'aw-ulte-mune" (one-and-two)? And for Ox5 "'aw-ulte-tsing" (one-and-four) etc.?
Eywa ayngahu, frapo nìNa'vi paylltxeie...
May Eywa be with you, all Na'vi speakers.

Offline Skxawng

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Re: The Number System
« Reply #9 on: December 22, 2009, 08:18:40 pm »
you could, but I'm going to say it would be better to wait until we know the information for sure from Frommer before committing anything to memory.


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Offline Uniltìranyu

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Re: The Number System
« Reply #10 on: December 22, 2009, 09:45:37 pm »
you could, but I'm going to say it would be better to wait until we know the information for sure from Frommer before committing anything to memory.
Good idea.
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Offline Seze

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Re: The Number System
« Reply #11 on: December 22, 2009, 10:23:05 pm »
Being a CS guy, I grew up around base 2 and base 8.  Its getting really confusing to me when we mix all our bases together.  Maybe its just me, but when I think vofo, I would much rather think 20 base 8 than 16 base 10.

It might be a good idea to note that there is an error in one of the above posts, there, is no 080 or 090.  The concept of 8 and 9 in any form does not exist in base 8, at all.  Just to make sure we are all on the same page on base 8, below is the number order Na'vi people would count with. 

0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 22 23 24 25 26 27 30 31 ... 76 77 100 101 102 103 ... 776 777 1000 1001

I think its worth noting that as we humans see it as normal to go 7 8 9 10 11, it is also just as normal for the Na'vi to go 5 6 7 10 11, since 8 and 9 are nonexistent.


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Offline Skxawng

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Re: The Number System
« Reply #12 on: December 22, 2009, 10:32:56 pm »
aha good point

I wrote that up when the group email was just beginning so it was a bit rushed, fixing ...


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Re: The Number System
« Reply #13 on: December 23, 2009, 01:39:21 pm »
A note on notation,

Something hit me today while I was taking a shower, (not literally).  When writing octal or hexadecimal numbers down, we prefix them so we know what base we are using.  Octal is 0o and Hexadecimal is 0x.  It never occurred to me until this morning that we use o for octal because octal starts with o and x for hexadecimal because well, theres an x in hexadecimal.  Never made that connection until now... 

I think our vocab pages also should be updated.  Since the entire Na'vi number system is in octal, we should stress octal more than decimal.  Vofu for instance is 0o20, but is listed as "sixteen".  Would it would be better to have it listed as Vofu, 0o20 (16) instead?  I know we don't know a whole lot about the numbers yet, but it seems highly probable that it will use the 20 30 40 etc root numbers like we are used to in decimal, and if thats the case, I think most people will miss the connection on why the root changes from vofu (0o20) to <unknown number> (0o30) to tsìvo (0o40).


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Offline Txur’Itan

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Re: The Number System
« Reply #14 on: December 23, 2009, 02:01:58 pm »
Figure I'd bring this down from the e-mails, as its not on the site.

oe neu nume numbers, slä numbers lu incomplete. omum pe oe:
(directly: I want learn numbers, but numbers are incomplete. know what I:) <- early attempts :P

Na'vi number system is octal Based on 8.

Known numbers:

One - 'aw
Two - mune
Three - ??
Four - tsíng
Five - ??
Six - ??
Seven - kinä
Eight - ??

from there, thinking about numbers octally (base 8) can be pretty confusing at first, but you can break it down pretty simply: observe the following

Octal: 1,2,3,4,5,6,7
Decimal: 1,2,3,4,5,6,7

not different at all! here's where it gets confusing

Octal: 10,11,12,13,14,15,16,17
Decimal:8, 9,10,11,12,13,14,15

remember, 8 is essentially 0 in an octal system, and the new digit indicates how many of the base numbers are there. continuing on:

Octal:  20,21,22,23,24,25,26,27
Decimal:16,17,18,19,20,21,22,23

and you can go up and up. Here's a quick trick to quick number conversions:

For each 2nd digit increment, subtract an additional 2 from the octal number to get the decimal number.

Example:

Octal number is 25
since its in the twenties, multiply the number 2 by 2 again, and subtract the resulting 4 from the octal number:

25-(2x2) = ?
25-4
21 << decimal number

Example 2:

Octal number is: 47
47-(4x2) = ?
47-8
39 << decimal number

so quite simply, if the octal number is in the
10s, minus 2 from the number to get decimal equivalent
20s, minus 4 from the number to get decimal equivalent
30s, minus 6 from the number to get decimal equivalent
40s, minus 8 from the number to get decimal equivalent
50s, minus 10 from the number to get decimal equivalent
60s, minus 12 from the number to get decimal equivalent

and up and up and up.


-----------------

Numerical confusion:
past the first seven numbers, only two other numbers are known:

Sixteen, or vofu (octal: 20)
Thirty Two, or Tsìvol (octal: 40)


The question then is...

if o20 is vofu
is o21 vofu'aw? 'aw-vofu? 'awvofu?
is o22 vofumune? mune-vofu? munevofu?

and so fourth.
(forgot to mention, the o before the number indicates that its an octal, or na'vi number)

so again, for reference, here are the current known numbers:

One - 'aw
Two - mune
Three - ??
Four - tsíng
Five - ??
Six - ??
Seven - kinä
Eight - ??
o10 - ??
o20 - vofu
o30 - ??
o40 - tsìvol
o50 - ??
o60 - ??
o70 - ??
o80 - ??
o90 -  ??
o100 - ??


Math, Yummy!

Since human numbering systems and Na'vi numbering systems appear to be based on finger counts, we may have to presume that the four fingered Na'vi hand is the basis for number progression, thus verbal choices for naming those numbers interelatively may work like this.

HUMAN: 5 and 5 are named 10  the total of both hands of fingers.

NA'VI: tsíng (4) and tsíng (4) are probably tsí<it>
the smallest value of one set of both fingers counted tsí<it>'aw would be 8 and one.  I am basing this on the number 40 octal which is named tsì<vol> which would be four counts of eight essentially. 

The concept of zero would be no fingers counted, so each rotation of an eight count would start at zero instead of end at it.
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Offline Skxawng

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Re: The Number System
« Reply #15 on: December 23, 2009, 03:32:27 pm »
I wrote this in the original mailing group,


As far as vofu goes, it could be similar to french, in that once you get past 10 in french, the numbers, the numbers become unique permutations of the first decimal equivalents up to 16. --

for example:
1 = un - 11 = onze
2 = deux - 12 = douze
3 = trois - 13 = treize
4 = quatre - 14 = quatorze
5 = cinq - 15 = quinze
6 = six - 16 = seize
but when you get past sixteen  it goes to the "ten and the base number system...'
7 = sept - 17 = dix-sept
8 = huit - 18 = dix-huit
9 = neuf - 19 = dix-neuf
... which then carries throughout the rest of the larger numbers

so perhaps the na'vi numbers are unique up until vofu, or perhaps a little beyond before going into the four-eights style system.


We can speculate on that but i think it might be safer to wait until frommer comes out with more and memorize what we have.


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Offline Txur’Itan

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Re: The Number System
« Reply #16 on: December 23, 2009, 04:00:46 pm »
It is a good probability that there are many ways for the numbers to be handled already presented in what he has told us so far.

Considering Frommer's Malay language influences, what I was thinking is he may most probably be using Asian or Polynesian counting which recycles names in a simpler context than the structures of European languages.  Like in the Japanese pictographic it works like this for counting in the arrangement of Kanji symbols as well as the verbal counting,

[Japanese Romaji example of counting]

1-ichi
2-ni
3-san
4-yon [shi] (same sound as the word for death so Yon is used more.)
5-go
6-roku
7-nana [shichi] (same deal as with number four)
8-hachi
9-kuu
10-juu
11-juu-ichi  (ten and one)
12-juu-ni (ten and two)
13-juu-san (ten and three)
14-juu-yon (ten and four)
15-juu-go (ten and five)
16-juu-roku (ten and six)
17-juu-nana (ten and seven)
18-juu-hachi (ten and eight)
19-juu-kuu (ten and nine)
20-ni-juu (two and ten)
21-ni-juu-ichi (two and ten and one)

and what you propose used more for working math a sort of dual naming structure.

Japanese also has shortcuts for quantities

Yokkai - <Yo>kkai (4th floor - trucating yon)

---

So I am thinking Na'vi numbers are named in this fashion, and that Frommer presumed we would be able to derive this structure based on the key examples.

« Last Edit: December 23, 2009, 04:44:55 pm by vidvamp01 »
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Offline Taikomochi

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Re: The Number System
« Reply #17 on: December 23, 2009, 04:38:05 pm »
They do say "five" in the movie though. Just thought about that.

Grace asks Norm "How's your Na'Vi?"
He answers many things. Don't remember it all by heart.

She says he's a bit formal.

He answers "I've been studying for 5 years, but I have a lot to learn." !

:O

Anyone?

Offline Taruia

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Re: The Number System
« Reply #18 on: December 23, 2009, 07:21:13 pm »
I'll try to get the sound clip from that scene, maybe one of the people more comfortable with Na'vi will be able to pick out the number 5.

Apparently megaupload fails...Skxawng is gonna host it for everyone...thanks Skxawng!
« Last Edit: December 23, 2009, 07:43:46 pm by Taruia »

Offline Skxawng

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Re: The Number System
« Reply #19 on: December 23, 2009, 07:34:56 pm »
I'll try to get the sound clip from that scene, maybe one of the people more comfortable with Na'vi will be able to pick out the number 5.

http://www.megaupload.com/?d=Z9KJSFSI
Here is the clip from that scene. It's just him saying "I've been studying for 5 years, but I have a lot to learn." Hopefully someone can pull the number 5 out of that.

is unavailible atm. Check your message box and I'll host it myself


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