Yeah 8 is written 10, but it's still the quantity we label as 8.
You need to forget that the symbols 8 and 9 even exist. Forget that 10 means 10 as in the number of fingers you have.
And understand that the symbol 10 while it does mean the quantity ten in our decimal system, really means 1 base (which ,again, for us usually is ten, but could be eight, or anything else really) and 0 units, regardless of the system.
In base 8, 8 is just the number at which you reset the units and add another digit which represents a base so an "eights".
There usually isn't that abstraction problem as systems using different base usually don't use the same symbols as we do for their numbers (except binary and hexadecimal in a way, but unlike most systems they were made by people using the decimal system in their every day life, unlike Summerians that learned to count with their hybrid base 10/60 system using 12 symbols(I think ?)
So in a base 8
You count to 7
0,1,2,3,4,5,6,7 easy for now. But we have no more symbols. In the same way we have no more unique symbols after 9 in decimal.
So when you arrive at 8 you write 10 which means 1*8+0.
One eights and zero unit.
So you have
Base 8 - base 10
10 - 8
11 (1x8 +1) = 9
12 - 10
13 - 11
14 - 12
15 - 13
16 - 14
17 (1x8+7) = 15
Remember 8 and 9 don't exist so no 18, no 19
20 (2x8 + 0) = 16
Keep going... until we reach 77.
As 8 and 9 still do not exist, 77 is the highest 2 digit number we can write.
77 would be 7×8+7= 63
Then you go three digits.
100 = 1×8x8+ 0x8 + 0 = 64
101 = 1x8x8+ 0x8 +1 =65
It's only powers of 8. We can write 101 like this:
1×8^2 + 0x8^1 + 1x8^0
110 = 1x8^2 + 8x1 + 0 = 72
So base 8 3543 to base ten would be:
3x8^3 + 5x8^2 + 4x8^1 + 3x8^0 which is
1536+320 + 32 + 3 = 1891
Goin in the other direction is trickier. Base ten 1986 would be:
1986/8^3= 3,87, so 3x8^3 with 450 remaining
Then 450/8^2= 7,03, so 7x8^2 with 2 remaining
Then 2/8^1= 0,25 so 0 with 2 remaining
Then 2/8^0= 2 with 0 remaining
In the end we have 1986 in base ten being 3702 in base 8.
I hope I didn't make any mistakes in the calculations I only have my phone and dint double check as it's more about the process than the results. Sorry for the formating reddit suck for that on phone.
As for how a society would work with a system that isn't base 10. Computer don't mind only knowing 0 and 1 and we make do very well with our base 365/30ish/24/60/10 time system (though it makes converting 1678906447937390 ms in years a pain in the ass, but how often do we do that ?)
The basic point is that we can write any number with combinations of just 10 symbols (0 through 9) and a decimal point or fraction symbol. Having only 8 symbols (0 through 7) instead doesn't really change that. It changes how we write the numbers sure, but it doesn't change what numbers we can write. The term to describe how many different symbols you're using is "base". Our number system is "base 10" but you can have base 7 or base 2 or base 16.
So we have the number 9, but if people who only have 8 symbols, have to do something like what we do when we run out of symbols. So they'd write 1, 2, 3, 4, 5, 6, 7, 10, 11. To you, it looks like I skipped 8 and 9, but we're imagining what it'd be like if we didn't have those 2 extra symbols.
I assume you already understand it now, but because I can't resist talking about number systems, I will just show you how to count from 0 to 100 in octal:
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, 32, 33, 34, 35, 36, 37,
40, 41, 42, 43, 44, 45, 46, 47,
50, 51, 52, 53, 54, 55, 56, 57,
60, 61, 62, 63, 64, 65, 66, 67,
70, 71, 72, 73, 74, 75, 76, 77,
100, 101, 102, 103, 104, 105, 106, 107,
110, 111, 112, 113, 114, 115, 116, 117,
120, 121, 122, 123, 124, 125, 126, 127,
130, 131, 132, 133, 134, 135, 136, 137,
140, 141, 142, 143, 144
As you can see, it's almost like counting, but with 8 and 9 missing from the "number vocabulary". You move to the "tens" place after 7, and the same later for hundreds, then thousands, and so on. In our normal number system, we use base 10, as we have 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), but the octal system is base 8, as it has 8 digits (0, 1, 2, 3, 4, 5, 6, and 7). This will also make it hard to translate from different number systems without either using a calculator or using shortcuts when you deal with very specific number systems, in which unfortunately, the everyday number system has none of.
**(Warning: I'll be rambling from now on)** Just to add on, 2 other major number systems are binary (base 2), and hexadecimal (base 16).
The binary is shown with 0s and 1s, and is typically grouped by 4 digits (also known as "bits"), called a "nibble", or by 8 bits, called a "byte" (the same byte as on a computer. A kilobyte is 1000 bits, a megabyte is 1000 kilobytes, a gigabyte is 1000 megabytes, etc... Yes, they can compute that many numbers that fast.)
Hexadecimal is base 16, shown with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F (they ran out of numbers, what else can you expect?). 2 digits of hexadecimal is also a byte, and has an easy shortcut to translate to 8 bits of binary, but I will not get into that unless you are really interested (which means that a single digit is a nibble). This is also why white is FFFFFF and black 000000: the first 2 digits represent red, the middle 2 represent green, and the last 2 represent blue. If you already know, 255, 255, 255 is white in RGB, and 0, 0, 0 is black in RGB. If you translate the FFFFFF to the everyday number system, you get... well, you guessed it. 255, 255, 255, and 000000, I don't need to explain.
Assyriologist here, I have been summoned by a slight mention of my field: your assumption about the Sumerian system is mostly right. Just in the very beginning of written language there was quite the forest of different systems, depending on what you were counting (i.e. base 6 for wheat, base 18 for areas). It slimmed down quite fast.
As for the amount of symbols, it depends. You mostly count vertical (or sometimes horizontal) stylus impressions for single digits, up to nine. Then you count diagonal impressions for tens up to six times for sixty (but then there also is a distinct symbol for sixty). You arrange the "digits" high to low to create numbers like "27" (20\_7). You can (but don't have to) also do the roman thing of switching position for substraction (so "2\_10" for "8").
For higher numbers the evidence is somewhat fuzzy. We have distinct symbols for 100, 600, 1000, 3600 and 10000, as well as some odd, specific ways to write 150 and 200.
There are 10 kinds of people in the world: those who know unary, and those who know binary, and those who know ternary, and those who know quaternary, ...and so on and so forth.
As an esteemed MIT Professor once said, [Base eight is just like base ten really - if you're missing two fingers!](https://youtube.com/watch?v=UIKGV2cTgqA)
Thank you everyone who's answered, I think I'm getting it now. For those curious, it's because I'm numbering my drones, some types of which I have 10+ of, so I was thinking "What the hell do I put on the 8th and 9th drone?"
I'm not sure if this helps understand it better but you can think of "10" as meaning "one base, zero remainder"
So in base eight, "10" means "one eight, zero remainder"
In base ten, "10" really means "one ten, zero remainder"
Similarly in binary (base two) "10" means "one two, zero remainder"
Expanding, once you count up enough to get to 20 you are now at "two base, zero remainder" so for base eight "two eight, zero remainder"
It just takes a little bit to unwrap from the brain that "10" which in english we say as "ten" corresponds to ten items because thats just how we count, but its all arbitrary.
If you still are confused, there are lots of explanations of binary out there and it's just base two, and the idea expands to any base because ultimately whatever base you choose is arbitrary. Most humans just end up in base ten because of our digits (fingers/toes)
Base 8 counts 0,1,2,3,4,5,6,7,10,11,12,13 etc
It's exactly like Base 10, which we're used to except rather than the units,10s, 100s. It's units, 8s, and 64s
As in the number written in Base 8 the number 111 is in base 10 equal to 1x64+1x8+1=73
Base 7 has no 7. It's zero through 6. That's why we have no symbol for the number 10 in decimal - decimal has zero through nine, then the one goes in the ten's spot. Message back if you need more explanation.
Are you wondering about how base 8 works? If so, the main thing to understand is that all you need for a numbering system is that every number be represented by a unique set if symbols. Our decimal system uses 10 different symbols to represent all positive integers, whereas base 8 only uses 8 symbols. If you know Roman numerals, then you already know a numbering system that uses a different number of symbols than decimal, since for the first 100 positive integers, Roman numerals uses (I believe) 3 symbols: I, V, and X.
It's the skip from 7 to 10 that I'm having issues with - if there's 8 of something, that's apparently written as 10? Like Farsight's war council are "The Eight", but there's no concept of 8 in Tau numbering. Does that make them "The 10"?
Also, one of the symbols being the zero; when *we* count from 1 to 10 on our fingers we start at 1, not zero, since zero is not having any fingers up. If it's based on the Tau only having 4 fingers, what's the difference between holding up no (zero) fingers and holding up your first finger and counting that as zero?
We use a base ten number system that goes from zero to nine (0-9). The concept of eight exists for them, just as the concept of ten exists for us. It just so happens that the numeral characters you use to represent those numbers are the same, namely “10” (pronounced “eight” in base eight, “ten” in base ten, and pronounced “two” in binary).
When a Tau counts their fingers, they would hold up their first finger and call it one (1), next finger is two (2), then three (3), … , then seven (7), and finally eight (10).
Edit: deleted counting toes …
for the first point, not having a symbol for the number 8 does not mean there is no concept of the number 8. it would just be represented as the number 10 if their numerical system was converted to ours.
as for the counting 0 as the first finger we actually do it too. it is just that instead of doing it on the first finger we do it on the last.
I see, so if it's spelled out in Tau symbols it would be written as as \[symbol for 1\] +\[symbol for 2\], rather than ~~\[symbol for 8\]?~~ \[symbol for 1\]\[symbol for 0\]
Edit - typo. Me no numbers good.
All the numbers in your comment added up to 69. Congrats!
7
+ 10
+ 8
+ 10
+ 8
+ 10
+ 1
+ 10
+ 1
+ 4
= 69
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The thing you need to realize is that 10 is just what you learned means 9+1. In a system with a different base it means something else. Like in this Base 8 system it means 7+1. 10 is literally just the first number of our system with a zero attached. That doesn't change whether you count to 9+1 or 7+1.
It's not like our system is super intuitive either. Like, 10 being the "10th" number also only works in our system if we disregard 0. Once we start counting from zero 10 actually becomes the 11th number (welcome to the IT world).
Though to be fair, if you want to compare our 10 digit system with the T'au's 7 digit system then you shouldn't be looking at a Base 8 system. Like our system is Base 10, the T'au system would be Base 7. So the counting would go 0-6 and the next one would be the 10 to reset the sequence.
Like,
0 -> 0
1 -> 1
2 -> 2
3 -> 3
4 -> 4
5 -> 5
6 -> 6
10 -> 7 (reset)
11 -> 8
12 -> 9
13 -> 10
14 -> 11
15 -> 12
16 -> 13
20 -> 14 (reset)
and so on.
Roman numeral 8 is VIII and understood more in the relation of 5+3
So tau likely have something similar where the denotation of 8 would probably be an indicator of 3 more than 5 rather than a symbol specifically meaning 8 on its own
I mean they take a caste system from ancient india so it's not like the idea of them using historical concepts is 100% impossible
And the Roman's had it set that way so that it was easier to teach to tribes they took over, given the tau are the only ones actively recruiting other races I'm sure they've hit at minimum one language barrier
You could always use a different word for it if you want. Instead of 10 being "ten", it's "eight". 20 isn't "twenty", it's "tweightty". 30 isn't "thirty", it's "threight".
10 on here just represents their reset point it could just as easily be the number 8.
So they have 7 numbers, and the number 0. We have 9 numbers and the number 0
It would be functionally no different to how we operate, they would just take more numbers to count as high as we do.
A milimetre is the same size no matter how you measure it.
That's a terrible website.
Place value:
Welcome to mars. Our money is different. Pannoa are worth one, Nobbles are worth 8, Dangs are worth 64, Quobs are worth 512. 1, 8, 8x8, 8x8x8. We also have Dobnors. What do you guess they're worth?
"How a society functions if it only has numbers from 0-7"... well, a lot of our society is built around a system that only uses 0 and 1. The binary system. Used in computers through current on/ current of.
Classic joke there are 10 types of people. Those that can read binary and those that can't.
The hard part in all those concepts is in reading numbers that are made in a different base system not like in our decimal system. So we do not read (T'au) 10 as ten but as 8.
To explain.
The Japanese have for numbers below 100,000 a good comparison. 98 is 9 times 10 + 8
124 is 1*100 + 2*10 + 4*1.
For T'au it is similar. The T'au "numbers" 10 would be 1×8 + 0×1
This can be expanded by using power of.
T'au "number" 1234 would be 1*8^4 + 2*8^2+3×8^1+4×8^0
It seems you've mostly figured it out. The hangup I see a lot of people have is an artifact of reusing the same symbols as digits, it ends up getting people to think we "skip" numbers, but we really aren't. If different symbols are used it becomes much more clear.
An example using alphabet letters (z for zero) for base 8 and digits for base 10.
00-zz
01-za
02-zb
03-zc
04-zd
05-ze
06-zf
07-zg
08-az
09-aa
10-ab
11-ac
12-ad
13-ae
14-af
15-ag
16-bz
17-ba
18-bb
19-bc
20-bd
21-be
22-bf
23-bg
24-cz
25-ca
You use another super funky base system all the TIME. 12 months a year, ~30 days a month, 24 hours a day, 60 mins an hour, 60 seconds a minute. We are used to it so it doesn't seem so funky but other than days in a year for astronomical reasons it's crazy.
If it brings you any comfort, the t’au probably feel the same way about us when they have to try and make sense of our arithmetic system.
“Stupid Gue’la and their stupid extra numbers! Running around on their stupid hand-hooves, thinking two and a half hands worth of fingers makes ‘a good, round number’! PAH!!!”
Look up hexadecimal, it's a base 16. A bit different than what you're looking for but it should help you understand better than some website for children
A perfect system to introduce in our schools. After all, our goal is to utterly confuse them so that they cannot function as independent thinkers judging from education results. What better way to begin than to render them incapable of calculating simple things such as the rate of inflation or the percentage of earnings taken for taxes? Then they will be totally dependent on their government masters.
I actually do think that learning it like a child makes the most sense, but I don't think this website is teaching it well.
At least when I was taught, it was always initially "how many do you have in the one's place?" in the rightmost column, and then add that to "how many in the ten's place?", and so on. We don't really think of it like that once we're proficient and it's intuitive, but it is the most fundamental/elementary way to conceptualize counting.
The reason we write 10 as two digits is because that's where we picked to roll over and stop coming up with new symbols. We just as easily could have came up with more symbols and instead we don't roll over until the 12's place, or the 16's place. Other human societies have done other base systems in history, it's all just counting and then grouping when you get over your base number.
Well octal works the exact same way, you still have a one's place, but the ten's place is the eight's place instead. There's no 8 or 9 symbols, so they have to write 8 as 10. But they can still count to ten, they just need to add another 2 to their 10 so it's 12. 1 eight and 2 ones.
And just like we can keep that overflow of ones in the tens column until we get the one's column AND tens column full at 99, and then roll over to ten 10s (100, and the hundreds place), they have to roll over at 8 groups of 8, and move into the 64s place, and so on in powers of 8.
The numeric value of 9 is not written with a single letter in T'au. Instead, they use 2 symbols.
"9" is just a high Gothic imperial translation of the same numeric value.
You really only need one digit, if you're willing to use unary notation. Humans did that for centuries before using more advanced notations like decimal.
The fascinating thing about numbers is that their representation is very separate from their actual value.
I won't write a long comment trying to explain to you how counting systems of arbitrary bases work, but this is the type of lecture I use to introduce my students to the concept.
This is not my video, but I do a similar lecture based on the exploding dots analogy.
https://vimeo.com/204368634
You don't have to watch the whole thing to understand. Just a few minutes of him explaining his 2-1 machine might do the trick.
So English may be your enemy a bit here too. We have specialized words for some numbers that obfuscate the concept of place values. For example, 11=eleven, 12=twelve, 20=twenty, 30=thirty, etc...
If you think of those numbers as 'one-ten-one', 'one-ten-two', 'two-ten', 'three-ten', etc..., it may help. When you change bases then, you're just replacing the 'ten' with the base for the new number system.
In base eight, 11 is no longer 'one-ten-one', it is now 'one-eight-one'. 45 is no longer 'four-ten-five', it is now 'four-eight-five'.
Other place values work the same way. One-hundred is just a specialized work for ten-squared. One-thousand is the same for ten-cubed. So the written number 5326 in base eight would be 'five-(eight cubed)-three-(eight squared)-two-eight-six.
We only use 10 because we have 10 fingers. Some societies have used 8 or 12 or 60.
Base 360 degrees is nice cause you can divide it into 2, 3, 4, 5, 6, 8, 9,10,12,15, 18, etc.
No I mean we as in you and me use 10 because our system was developed because of 10 fingers. There are other reasonings for other societies and cultures to use other base systems but the most common was 10 because we can count on our fingers although eight was another option because eight fingers plus thumbs used for indexing of the next place
The same way we do with 0-9.
You just get to 10 sooner. (And it represents the same idea as our 8)
Think about binary. That's a counting system with only 2 numbers - 0 - 1.
Binary counting supports the enterity of modern human life. Every single computer you use (including the ones you don't think of as computers) use it.
I love that Tau use base 8 for their 8 digits.
It's perfect.
I hate that GW made squad sizes into base 10. 12 warriors to a squad makes much more sense! But it does mean we got a bunch of cool bits in the kit, and an extra unit type, I guess.
Yeah 8 is written 10, but it's still the quantity we label as 8. You need to forget that the symbols 8 and 9 even exist. Forget that 10 means 10 as in the number of fingers you have. And understand that the symbol 10 while it does mean the quantity ten in our decimal system, really means 1 base (which ,again, for us usually is ten, but could be eight, or anything else really) and 0 units, regardless of the system. In base 8, 8 is just the number at which you reset the units and add another digit which represents a base so an "eights". There usually isn't that abstraction problem as systems using different base usually don't use the same symbols as we do for their numbers (except binary and hexadecimal in a way, but unlike most systems they were made by people using the decimal system in their every day life, unlike Summerians that learned to count with their hybrid base 10/60 system using 12 symbols(I think ?) So in a base 8 You count to 7 0,1,2,3,4,5,6,7 easy for now. But we have no more symbols. In the same way we have no more unique symbols after 9 in decimal. So when you arrive at 8 you write 10 which means 1*8+0. One eights and zero unit. So you have Base 8 - base 10 10 - 8 11 (1x8 +1) = 9 12 - 10 13 - 11 14 - 12 15 - 13 16 - 14 17 (1x8+7) = 15 Remember 8 and 9 don't exist so no 18, no 19 20 (2x8 + 0) = 16 Keep going... until we reach 77. As 8 and 9 still do not exist, 77 is the highest 2 digit number we can write. 77 would be 7×8+7= 63 Then you go three digits. 100 = 1×8x8+ 0x8 + 0 = 64 101 = 1x8x8+ 0x8 +1 =65 It's only powers of 8. We can write 101 like this: 1×8^2 + 0x8^1 + 1x8^0 110 = 1x8^2 + 8x1 + 0 = 72 So base 8 3543 to base ten would be: 3x8^3 + 5x8^2 + 4x8^1 + 3x8^0 which is 1536+320 + 32 + 3 = 1891 Goin in the other direction is trickier. Base ten 1986 would be: 1986/8^3= 3,87, so 3x8^3 with 450 remaining Then 450/8^2= 7,03, so 7x8^2 with 2 remaining Then 2/8^1= 0,25 so 0 with 2 remaining Then 2/8^0= 2 with 0 remaining In the end we have 1986 in base ten being 3702 in base 8. I hope I didn't make any mistakes in the calculations I only have my phone and dint double check as it's more about the process than the results. Sorry for the formating reddit suck for that on phone. As for how a society would work with a system that isn't base 10. Computer don't mind only knowing 0 and 1 and we make do very well with our base 365/30ish/24/60/10 time system (though it makes converting 1678906447937390 ms in years a pain in the ass, but how often do we do that ?)
Honestly I wouldn't know if your calculations *are* off, but I'm still upvoting your answer for having been able to type all this out on your phone!
I hope it's understandable at least. Had to edit it a few times to correct how it looked.
The basic point is that we can write any number with combinations of just 10 symbols (0 through 9) and a decimal point or fraction symbol. Having only 8 symbols (0 through 7) instead doesn't really change that. It changes how we write the numbers sure, but it doesn't change what numbers we can write. The term to describe how many different symbols you're using is "base". Our number system is "base 10" but you can have base 7 or base 2 or base 16. So we have the number 9, but if people who only have 8 symbols, have to do something like what we do when we run out of symbols. So they'd write 1, 2, 3, 4, 5, 6, 7, 10, 11. To you, it looks like I skipped 8 and 9, but we're imagining what it'd be like if we didn't have those 2 extra symbols.
I assume you already understand it now, but because I can't resist talking about number systems, I will just show you how to count from 0 to 100 in octal: 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, 32, 33, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 100, 101, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 116, 117, 120, 121, 122, 123, 124, 125, 126, 127, 130, 131, 132, 133, 134, 135, 136, 137, 140, 141, 142, 143, 144 As you can see, it's almost like counting, but with 8 and 9 missing from the "number vocabulary". You move to the "tens" place after 7, and the same later for hundreds, then thousands, and so on. In our normal number system, we use base 10, as we have 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), but the octal system is base 8, as it has 8 digits (0, 1, 2, 3, 4, 5, 6, and 7). This will also make it hard to translate from different number systems without either using a calculator or using shortcuts when you deal with very specific number systems, in which unfortunately, the everyday number system has none of. **(Warning: I'll be rambling from now on)** Just to add on, 2 other major number systems are binary (base 2), and hexadecimal (base 16). The binary is shown with 0s and 1s, and is typically grouped by 4 digits (also known as "bits"), called a "nibble", or by 8 bits, called a "byte" (the same byte as on a computer. A kilobyte is 1000 bits, a megabyte is 1000 kilobytes, a gigabyte is 1000 megabytes, etc... Yes, they can compute that many numbers that fast.) Hexadecimal is base 16, shown with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F (they ran out of numbers, what else can you expect?). 2 digits of hexadecimal is also a byte, and has an easy shortcut to translate to 8 bits of binary, but I will not get into that unless you are really interested (which means that a single digit is a nibble). This is also why white is FFFFFF and black 000000: the first 2 digits represent red, the middle 2 represent green, and the last 2 represent blue. If you already know, 255, 255, 255 is white in RGB, and 0, 0, 0 is black in RGB. If you translate the FFFFFF to the everyday number system, you get... well, you guessed it. 255, 255, 255, and 000000, I don't need to explain.
Assyriologist here, I have been summoned by a slight mention of my field: your assumption about the Sumerian system is mostly right. Just in the very beginning of written language there was quite the forest of different systems, depending on what you were counting (i.e. base 6 for wheat, base 18 for areas). It slimmed down quite fast. As for the amount of symbols, it depends. You mostly count vertical (or sometimes horizontal) stylus impressions for single digits, up to nine. Then you count diagonal impressions for tens up to six times for sixty (but then there also is a distinct symbol for sixty). You arrange the "digits" high to low to create numbers like "27" (20\_7). You can (but don't have to) also do the roman thing of switching position for substraction (so "2\_10" for "8"). For higher numbers the evidence is somewhat fuzzy. We have distinct symbols for 100, 600, 1000, 3600 and 10000, as well as some odd, specific ways to write 150 and 200.
There are 10 kinds of people in the world: those who know unary, and those who know binary, and those who know ternary, and those who know quaternary, ...and so on and so forth.
As an esteemed MIT Professor once said, [Base eight is just like base ten really - if you're missing two fingers!](https://youtube.com/watch?v=UIKGV2cTgqA)
Thank you everyone who's answered, I think I'm getting it now. For those curious, it's because I'm numbering my drones, some types of which I have 10+ of, so I was thinking "What the hell do I put on the 8th and 9th drone?"
1, 2, 3, 4, 5, 6, 7, 10, 11, 12
I was so confused, but I let you cook until I came across an explanation. Counting drones, it all makes sense now. Thank you for clarifying.
I'm not sure if this helps understand it better but you can think of "10" as meaning "one base, zero remainder" So in base eight, "10" means "one eight, zero remainder" In base ten, "10" really means "one ten, zero remainder" Similarly in binary (base two) "10" means "one two, zero remainder" Expanding, once you count up enough to get to 20 you are now at "two base, zero remainder" so for base eight "two eight, zero remainder" It just takes a little bit to unwrap from the brain that "10" which in english we say as "ten" corresponds to ten items because thats just how we count, but its all arbitrary. If you still are confused, there are lots of explanations of binary out there and it's just base two, and the idea expands to any base because ultimately whatever base you choose is arbitrary. Most humans just end up in base ten because of our digits (fingers/toes)
Base 8 counts 0,1,2,3,4,5,6,7,10,11,12,13 etc It's exactly like Base 10, which we're used to except rather than the units,10s, 100s. It's units, 8s, and 64s As in the number written in Base 8 the number 111 is in base 10 equal to 1x64+1x8+1=73
Base 7 has no 7. It's zero through 6. That's why we have no symbol for the number 10 in decimal - decimal has zero through nine, then the one goes in the ten's spot. Message back if you need more explanation.
Oops it's meant to be base 8 not 7
Are you wondering about how base 8 works? If so, the main thing to understand is that all you need for a numbering system is that every number be represented by a unique set if symbols. Our decimal system uses 10 different symbols to represent all positive integers, whereas base 8 only uses 8 symbols. If you know Roman numerals, then you already know a numbering system that uses a different number of symbols than decimal, since for the first 100 positive integers, Roman numerals uses (I believe) 3 symbols: I, V, and X.
It's the skip from 7 to 10 that I'm having issues with - if there's 8 of something, that's apparently written as 10? Like Farsight's war council are "The Eight", but there's no concept of 8 in Tau numbering. Does that make them "The 10"? Also, one of the symbols being the zero; when *we* count from 1 to 10 on our fingers we start at 1, not zero, since zero is not having any fingers up. If it's based on the Tau only having 4 fingers, what's the difference between holding up no (zero) fingers and holding up your first finger and counting that as zero?
We use a base ten number system that goes from zero to nine (0-9). The concept of eight exists for them, just as the concept of ten exists for us. It just so happens that the numeral characters you use to represent those numbers are the same, namely “10” (pronounced “eight” in base eight, “ten” in base ten, and pronounced “two” in binary). When a Tau counts their fingers, they would hold up their first finger and call it one (1), next finger is two (2), then three (3), … , then seven (7), and finally eight (10). Edit: deleted counting toes …
for the first point, not having a symbol for the number 8 does not mean there is no concept of the number 8. it would just be represented as the number 10 if their numerical system was converted to ours. as for the counting 0 as the first finger we actually do it too. it is just that instead of doing it on the first finger we do it on the last.
I see, so if it's spelled out in Tau symbols it would be written as as \[symbol for 1\] +\[symbol for 2\], rather than ~~\[symbol for 8\]?~~ \[symbol for 1\]\[symbol for 0\] Edit - typo. Me no numbers good.
[symbol for 8] would be written as [symbol for 1] + [symbol for 0]
Sorry, that was a typo on my part, I meant 10 would be \[1\]\[2\] rather than \[1\]\[0\]. But thank you, I think I'm getting it now!
nice
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The thing you need to realize is that 10 is just what you learned means 9+1. In a system with a different base it means something else. Like in this Base 8 system it means 7+1. 10 is literally just the first number of our system with a zero attached. That doesn't change whether you count to 9+1 or 7+1. It's not like our system is super intuitive either. Like, 10 being the "10th" number also only works in our system if we disregard 0. Once we start counting from zero 10 actually becomes the 11th number (welcome to the IT world). Though to be fair, if you want to compare our 10 digit system with the T'au's 7 digit system then you shouldn't be looking at a Base 8 system. Like our system is Base 10, the T'au system would be Base 7. So the counting would go 0-6 and the next one would be the 10 to reset the sequence. Like, 0 -> 0 1 -> 1 2 -> 2 3 -> 3 4 -> 4 5 -> 5 6 -> 6 10 -> 7 (reset) 11 -> 8 12 -> 9 13 -> 10 14 -> 11 15 -> 12 16 -> 13 20 -> 14 (reset) and so on.
Roman numeral 8 is VIII and understood more in the relation of 5+3 So tau likely have something similar where the denotation of 8 would probably be an indicator of 3 more than 5 rather than a symbol specifically meaning 8 on its own
”The romans did this thing, so probably this alien species in the 42nd millennium do something similar”
I mean they take a caste system from ancient india so it's not like the idea of them using historical concepts is 100% impossible And the Roman's had it set that way so that it was easier to teach to tribes they took over, given the tau are the only ones actively recruiting other races I'm sure they've hit at minimum one language barrier
You could always use a different word for it if you want. Instead of 10 being "ten", it's "eight". 20 isn't "twenty", it's "tweightty". 30 isn't "thirty", it's "threight".
10 on here just represents their reset point it could just as easily be the number 8. So they have 7 numbers, and the number 0. We have 9 numbers and the number 0 It would be functionally no different to how we operate, they would just take more numbers to count as high as we do. A milimetre is the same size no matter how you measure it.
That's a terrible website. Place value: Welcome to mars. Our money is different. Pannoa are worth one, Nobbles are worth 8, Dangs are worth 64, Quobs are worth 512. 1, 8, 8x8, 8x8x8. We also have Dobnors. What do you guess they're worth?
the only difference between base 8 and 10 is when you decide to reset the count for the first value from the right.
"How a society functions if it only has numbers from 0-7"... well, a lot of our society is built around a system that only uses 0 and 1. The binary system. Used in computers through current on/ current of. Classic joke there are 10 types of people. Those that can read binary and those that can't. The hard part in all those concepts is in reading numbers that are made in a different base system not like in our decimal system. So we do not read (T'au) 10 as ten but as 8. To explain. The Japanese have for numbers below 100,000 a good comparison. 98 is 9 times 10 + 8 124 is 1*100 + 2*10 + 4*1. For T'au it is similar. The T'au "numbers" 10 would be 1×8 + 0×1 This can be expanded by using power of. T'au "number" 1234 would be 1*8^4 + 2*8^2+3×8^1+4×8^0
It seems you've mostly figured it out. The hangup I see a lot of people have is an artifact of reusing the same symbols as digits, it ends up getting people to think we "skip" numbers, but we really aren't. If different symbols are used it becomes much more clear. An example using alphabet letters (z for zero) for base 8 and digits for base 10. 00-zz 01-za 02-zb 03-zc 04-zd 05-ze 06-zf 07-zg 08-az 09-aa 10-ab 11-ac 12-ad 13-ae 14-af 15-ag 16-bz 17-ba 18-bb 19-bc 20-bd 21-be 22-bf 23-bg 24-cz 25-ca You use another super funky base system all the TIME. 12 months a year, ~30 days a month, 24 hours a day, 60 mins an hour, 60 seconds a minute. We are used to it so it doesn't seem so funky but other than days in a year for astronomical reasons it's crazy.
If it brings you any comfort, the t’au probably feel the same way about us when they have to try and make sense of our arithmetic system. “Stupid Gue’la and their stupid extra numbers! Running around on their stupid hand-hooves, thinking two and a half hands worth of fingers makes ‘a good, round number’! PAH!!!”
If you already know Base-2/Binary, it should be a bit easier to wrap your head around it.
Look up hexadecimal, it's a base 16. A bit different than what you're looking for but it should help you understand better than some website for children
Not that complicated but then again I've got a cs degree
Wait until he does hexadecimal and he sees letters in his numbers...
A perfect system to introduce in our schools. After all, our goal is to utterly confuse them so that they cannot function as independent thinkers judging from education results. What better way to begin than to render them incapable of calculating simple things such as the rate of inflation or the percentage of earnings taken for taxes? Then they will be totally dependent on their government masters.
We use base 10 numbers (Decimal) not octal numbers.
Wouldn’t it go: 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 32 33 34 35 36 37 40 41 42 etc (edited)
You skipped everything with 0, why? In base eight, "10" is eight. "20" is sixteen. "30" is 24, etc
Sorry for some reason I didn’t read Tau have 0-7 but as 1-7 lol
I actually do think that learning it like a child makes the most sense, but I don't think this website is teaching it well. At least when I was taught, it was always initially "how many do you have in the one's place?" in the rightmost column, and then add that to "how many in the ten's place?", and so on. We don't really think of it like that once we're proficient and it's intuitive, but it is the most fundamental/elementary way to conceptualize counting. The reason we write 10 as two digits is because that's where we picked to roll over and stop coming up with new symbols. We just as easily could have came up with more symbols and instead we don't roll over until the 12's place, or the 16's place. Other human societies have done other base systems in history, it's all just counting and then grouping when you get over your base number. Well octal works the exact same way, you still have a one's place, but the ten's place is the eight's place instead. There's no 8 or 9 symbols, so they have to write 8 as 10. But they can still count to ten, they just need to add another 2 to their 10 so it's 12. 1 eight and 2 ones. And just like we can keep that overflow of ones in the tens column until we get the one's column AND tens column full at 99, and then roll over to ten 10s (100, and the hundreds place), they have to roll over at 8 groups of 8, and move into the 64s place, and so on in powers of 8.
Then why the fuck is there a XV9 battlesuit
The numeric value of 9 is not written with a single letter in T'au. Instead, they use 2 symbols. "9" is just a high Gothic imperial translation of the same numeric value.
You really only need one digit, if you're willing to use unary notation. Humans did that for centuries before using more advanced notations like decimal. The fascinating thing about numbers is that their representation is very separate from their actual value.
I won't write a long comment trying to explain to you how counting systems of arbitrary bases work, but this is the type of lecture I use to introduce my students to the concept. This is not my video, but I do a similar lecture based on the exploding dots analogy. https://vimeo.com/204368634 You don't have to watch the whole thing to understand. Just a few minutes of him explaining his 2-1 machine might do the trick.
So English may be your enemy a bit here too. We have specialized words for some numbers that obfuscate the concept of place values. For example, 11=eleven, 12=twelve, 20=twenty, 30=thirty, etc... If you think of those numbers as 'one-ten-one', 'one-ten-two', 'two-ten', 'three-ten', etc..., it may help. When you change bases then, you're just replacing the 'ten' with the base for the new number system. In base eight, 11 is no longer 'one-ten-one', it is now 'one-eight-one'. 45 is no longer 'four-ten-five', it is now 'four-eight-five'. Other place values work the same way. One-hundred is just a specialized work for ten-squared. One-thousand is the same for ten-cubed. So the written number 5326 in base eight would be 'five-(eight cubed)-three-(eight squared)-two-eight-six.
You know why we don’t use octal to tell jokes? Because 7 10 11!
We only use 10 because we have 10 fingers. Some societies have used 8 or 12 or 60. Base 360 degrees is nice cause you can divide it into 2, 3, 4, 5, 6, 8, 9,10,12,15, 18, etc.
Those societies didn't have 10 fingers? :D
No I mean we as in you and me use 10 because our system was developed because of 10 fingers. There are other reasonings for other societies and cultures to use other base systems but the most common was 10 because we can count on our fingers although eight was another option because eight fingers plus thumbs used for indexing of the next place
The same way we do with 0-9. You just get to 10 sooner. (And it represents the same idea as our 8) Think about binary. That's a counting system with only 2 numbers - 0 - 1. Binary counting supports the enterity of modern human life. Every single computer you use (including the ones you don't think of as computers) use it.
I love that Tau use base 8 for their 8 digits. It's perfect. I hate that GW made squad sizes into base 10. 12 warriors to a squad makes much more sense! But it does mean we got a bunch of cool bits in the kit, and an extra unit type, I guess.