# A fun thought-experiment: Not ten unique numbers, but twelve

Discussion in 'Off-Topic' started by Terxpahseyton, Mar 29, 2011.

1. ### TerxpahseytonKing, Warrior, Prophet, Magician, Lover

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We all know how it goes from 1 to 9. After that, a repetition of symbols begins and we deal with 1+Z-digit numbers (lets leave numbers beyond of Z out of it for the sake of not encouraging nit-pickers).
I assume this point is chosen because two hands have 10 fingers, so it makes sense that the biggest number we can most easily form in an symbolic way is the number most easiest to use for addition, subtraction, multiplication and division and which by that sort of is the skeleton of primary calculations, I suppose anyway.

But what if we had 12 fingers? Would we have two more unique number-symbols and would the two-digit numbers begin with 13? Would it make any difference except of course having different number-names and having bigger "intervals" between the "bones" (formerly 10, now 13) of simple calculation?

I guess what this hypothetical comes down to is: Has the number 10 as the "skeleton"-number any mathematical justification or is just an arbitrary choice caused by the number of our fingers? Right now it seems so to me and I find it fascinating how weird it still seems when I try to actually imagine it.

2. ### PeteAtomsFormulaRandom

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So the Decimal (Base 10) vs Duodecimal (Base 12) system thread?

From Wikipedia:

3. ### DachsHero of the Soviet Union

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You know, in theory, some ancient 'Germanic' groups counted in base 12. Entertaining coincidence that SiLL brought it up.

4. ### emziewicked witch of the North

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I find it really really hard to think outside of base-10. For the longest time, well into university, I didn't realize base10 was arbitrary and there's nothing special about 10.

Dunno about Scandanavian languages, but English and German have the same pattern, where we have unique names for 11, 12 and then 13 starts with the rehashing of 1-9.

eleven / elf
twelve / zwolf
thirteen / dreizehn

5. ### civ_kingDeus Caritas Est

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Chinese is definitely base 10
1 &#19968;
2 &#20108;
3 &#19977;
4 &#22235;
5 &#20116;
6 &#20845;
7 &#19971;
8 &#20843;
9 &#20061;
10 &#21313;
11 &#21313;&#19968;
12 &#21313;&#20108;
13 &#21313;&#19977;
&#12290;&#12290;&#12290;
20 &#20108;&#21313;
21 &#20108;&#21313;&#19968;
&#12290;&#12290;&#12290;
30 &#19977;&#21313;
&#12290;&#12290;&#12290;
100 &#19968;&#30334;
101 &#19968;&#30334;&#19968;
&#12290;&#12290;&#12290;
200 &#20108;&#30334;
1000 &#21315;
10000 &#19975;

6. ### GamezRuleInconceivable!

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I would like to see this in action. How would you write 367326 in a duodecimal system?

7. ### Defiant47Peace Sentinel

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I consider "ten" or "10" to be according to the base used.

So I will call 2 in binary "10" or "ten". Or 16 in hexadecimal "10" or "ten".

So basically, if we had 12 fingers and developed a duodecimal system, then we'd still have 10 fingers.

8. ### emziewicked witch of the North

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1586A6

Where A is an arbitrary symbol like 0-9 are.

edit: there are calculators that do the conversion for you, one which I used for that.

It's really hard for me to even try and think outside of Base 10. Understanding light is a wave/particle is easier.

9. ### PeteAtomsFormulaRandom

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For any other questions like that, online conversion tools for different Base N systems are easily found online:

Here's one,
and another.

EDIT:
@Arwon - Shi-shah-shah!, lol.

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11. ### TerxpahseytonKing, Warrior, Prophet, Magician, Lover

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Well PeteAtoms's wikipedia article disagrees.
However, according to the same article
Weird, why would that be?
Ah so it seems to be true. Neither did I, just arrived at this conclusion by coincidence while thinking about how people believe in structures as something universally given - I assume a result of a natural mechanism to accept authority which proved tribes with strength so they survive. And yes, it is freaking hard. Which is what makes it so much fun. It feels like a very vivid example of how human thinking is inherently flawed if you define such a hard-to-overcome bias as a flaw.

@civ_king

You will notice that only until 9 unique symbols are used and only 100, 1000 and 10000 introduce new ones, which happen to be different versions of 10 multiplied with itself.

But this reminds me of an article in a news magazine I read where it was said that Chinese people's brain dealt with mathematics in very different ways compared to Western people because of the different way their language deals with mathematics (though civ_king failed to outline said difference).

12. ### PeteAtomsFormulaRandom

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Is zero "0" not a number? Aren't there 10 unique symbols?

Doesn't '10' represent the base value in the system +0 in all systems?

13. ### IntegralCan't you hear it?

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I have a particular affinity for base-16; my old TI in middle school had options for binary, octal, and hex bases along with the usual base-10.

Despite that, base-16 is a bit hard to work with in my head. Base=2, on the other hand, is nice and fun.
0 -> 0
1 -> 1
2 -> 10
3 -> 11
4 -> 100
5 -> 101
6 -> 110
7 -> 111
8 -> 1000

pi = 11.00100100 00111111 01101010 10001000 10000101 10100011 00001000 11010011 (etc)

edit: base-12 is still the most aesthetically pleasing base.

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binary(bit representation) and hexadecimal(byte representation) number systems aren't uncommon in the field of computer science

15. ### EarthlingDeity

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If humans had a different number of digits it is a justifiable speculation that we'd have developed a different base to use rather than base 10.

There actually is a real reason why base 10 is better than some arbitrary bases - it's the product of two distinct prime numbers. As such, writing many numbers in decimal or fraction forms is easier. A base like base 7, or base 11, etc... would be much more inconvenient.

Now, this doesn't really make base 10 (2x5) better than base 12 (2x2x3) for instance. But the inclusion of the factor of two is at least useful compared to an arbitrary radix. And because of the sheer convenience of binary number systems and operations it could be argued that octal or hexadecimal is superior though that's with the assumption any hypothetically developed intelligence species would similarly make use of binary, but if humans had say 12 fingers, binary/hex would probably still be worked out the same in all of our technology.

16. ### LeifmkDeity

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Yeah, oldschool computer programmers could often (and might still) work faster mentally in hexadecimal than decimal.

17. ### KozmosJew Detective

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We should all switch to hex so when we merge with computers the transition will go smoother.

18. ### Leoreth心の怪盗団Moderator

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Didn't the Babylonians also have a base 12 system because they counted on the tips and knuckles of the four fingers of one hand (so without thumb)?

At least this idea seems widespread enough to have our whole time measurement system built around it.

19. ### wolfigorEmperor

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It seems they used a sexagesimal sistem (base 60): http://en.wikipedia.org/wiki/Sexagesimal

The system somehow remains even today: 360 (60x60) degrees in a circle, 60 minutes in a hour, 60 seconds in a minute, 360 days in a year (until we fixed adding the missing days), etc.

The 12 sign of the zodiac are connected with the Babylonian calendar (http://en.wikipedia.org/wiki/Babylonian_calendar).

[Curious enough, also a 7 days week comes from the Babylonians "Counting from the new moon, the Babylonians celebrated the 7th, 14th, 21st, and 28th as "holy-days", also called "evil days" (meaning "unsuitable" for prohibited activities)"]

It's funny to see how some arbitrary decisions takes thousands of years ago still bind us today.

Base 10 is as arbitrary as any other base (I discovered it in my early teens when I studied binary numbers at school) .
As a "old school" computer programmer I was "fluent" in base16 as in base10 (until I finished university).

20. ### Leoreth心の怪盗団Moderator

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From the look of their symbols, it seems to be decimal as well. Would be interesting to know their names.