Page 1 of 1 [ 10 posts ] 

Rudin
Veteran
Veteran

User avatar

Joined: 7 Jun 2015
Age: 21
Posts: 1,046
Location: Southern Ontario

31 Dec 2015, 10:18 am

Let me explain.

Most humans use base 10 to count, probably for primitive reasons. However, our lives seem to be based around the number 12 more than the number 10. Our clock is based on the number 12. 12 is more composite than 10 so it makes multiplication and division by certain numbers more easy. So, some people (myself included) want to start using base 12 to count.

In base 10 you have the 1s column, 10s column, 100s column, 1000 columns etc and the number of numerals in a column cannot exceed 9. In base 12 you have a 1s column, a 12s column, a 144s column and the number of numerals in a column cannot exceed 11, in order to put 11 and 10 into a column we must associated them with a different symbol.

10=χ
11=ε

Here is how one would count in base 12: 1,2,3,4,5,6,7,8,9,χ,ε,10,11,12,13,14,15,16,17,18,19,1χ, 1ε, 20,...

If we used base 12 we would not use centuries or decades. We would use unquenniums and biquenniums. An unquennium is 12 years and a biquennium is 144 years. In base 10 this would be the 13th biquennium, but in base 12 it's the 11th biquennium.

This year is very special, it is the turn of the biquennium. It will be year 1300 in base 12!

Extra bit:

One thing I find troubling is "base 10". That could mean any base because 10 in base b is b in base 10(where 10 is the number of fingers on our hand). It could mean any base.


_________________
"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


traven
Veteran
Veteran

Joined: 30 Sep 2013
Gender: Female
Posts: 13,096

Nine7752
Toucan
Toucan

User avatar

Joined: 3 Dec 2015
Age: 61
Posts: 269
Location: North of Nowhere

31 Dec 2015, 12:50 pm

Big fan of base 12. It, and the related 60, come from Sumerian times where it was actually in use. Unfortunately they didn't have zeros and had some notation problems. I'm not actually sure where the base 10 got started, later - was it Arabic culture?

It survives today mainly in divisions of circles, including time. 12 and 60 and 360 are common ways of breaking up circles into degrees or minutes today. The second is an actual metric standard with physical meaning, and it's the only metric scale that I know of that rolls up into a non-base-10 sum, of 86400 for a day.

You can count to 12 on one hand by counting finger segments with your thumb. Each finger has 3 segments, and you move your thumb to touch each segment as you count. You can even keep the next "column" on the other hand to get up to 144, and try to do math with it.

It's also useful to create images in multiples of 12 or 60 pixels, so you can half or third it and still get an integer number of pixels.

But the world isn't going to change to 12's anytime soon. If anything, we have embraced base 2 or 8 or 16 as the culture's favorite secondary base, because of computers. I suppose if we had computer gates that could do 3's this could be different.


_________________
I swallowed a bug.


Rudin
Veteran
Veteran

User avatar

Joined: 7 Jun 2015
Age: 21
Posts: 1,046
Location: Southern Ontario

31 Dec 2015, 1:04 pm

Nine7752 wrote:
Big fan of base 12. It, and the related 60, come from Sumerian times where it was actually in use. Unfortunately they didn't have zeros and had some notation problems. I'm not actually sure where the base 10 got started, later - was it Arabic culture?

It survives today mainly in divisions of circles, including time. 12 and 60 and 360 are common ways of breaking up circles into degrees or minutes today. The second is an actual metric standard with physical meaning, and it's the only metric scale that I know of that rolls up into a non-base-10 sum, of 86400 for a day.

You can count to 12 on one hand by counting finger segments with your thumb. Each finger has 3 segments, and you move your thumb to touch each segment as you count. You can even keep the next "column" on the other hand to get up to 144, and try to do math with it.

It's also useful to create images in multiples of 12 or 60 pixels, so you can half or third it and still get an integer number of pixels.

But the world isn't going to change to 12's anytime soon. If anything, we have embraced base 2 or 8 or 16 as the culture's favorite secondary base, because of computers. I suppose if we had computer gates that could do 3's this could be different.


Base 60 would make multiplication easier. 60=2x2x3x5 which is even more composite than 12.


_________________
"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


naturalplastic
Veteran
Veteran

User avatar

Joined: 26 Aug 2010
Age: 69
Gender: Male
Posts: 34,127
Location: temperate zone

31 Dec 2015, 6:06 pm

If you want to know why humans make number systems in base five/ten all ya gotta do is look at your hands.

What do you see?

Five...digits.

The Incans counted on both their fingers and their toes. So their number system was in base 20.

The Greeks and Romans and many other old world cultures used base five, or ten. But there was no zero. Thats why roman numerals are set up that way.

But even the Greeks and Romans were cultural heirs to the even more ancient Mesopotamians who counted in groups of 60. But they counted to sixty in groups of five (like tally marks, or like Roman numerals).

Its because of this Mesopotamian legacy that there are 360 degrees to a circle, and 24 hours in a day.

The Mesopotamians had a multiple personality number system. Kinda base five, and kinda base six, for day to day commerce, but they also gave spiritual meaning to seven (the number of phases of the Moon). A dozen is two times six, fourteen is two times seven. Number 13 is out of step with both systems so thirteen became the "unlucky" number. Judas was the 13th apostle, and Loki was the 13th guest at a banquet in Valhalla, both of those 13th guys caused trouble and tragedy as a result.

In the wake of the French Revolution they invented the Metric system. The goods news is that the Metric system made everything decimal. The bad news is that they didnt go far enough, and change the number system as well.

They should have changed the number system to base 12, and THEN created a Metric system based on the numeral "10" representing 12 instead of ten.

The reason that I prefer base 12 to base 10 is that ten is only divisible by five, and by two. But 12 is divisible by 2,3,4, and 6. Thats why we can break the day into three even parts (8 hours work, 8 hours sleep, and 8 hours everything else). Cant do that with the number 10, or 20, or even 25.



Nine7752
Toucan
Toucan

User avatar

Joined: 3 Dec 2015
Age: 61
Posts: 269
Location: North of Nowhere

02 Jan 2016, 10:45 am

Interesting thought that the metric system could have changed the base of our numbers to 12.


_________________
I swallowed a bug.


slave
Veteran
Veteran

User avatar

Joined: 28 Feb 2012
Age: 111
Gender: Male
Posts: 4,420
Location: Dystopia Planetia

02 Jan 2016, 9:13 pm

Rudin wrote:
Let me explain.

Most humans use base 10 to count, probably for primitive reasons. However, our lives seem to be based around the number 12 more than the number 10. Our clock is based on the number 12. 12 is more composite than 10 so it makes multiplication and division by certain numbers more easy. So, some people (myself included) want to start using base 12 to count.

In base 10 you have the 1s column, 10s column, 100s column, 1000 columns etc and the number of numerals in a column cannot exceed 9. In base 12 you have a 1s column, a 12s column, a 144s column and the number of numerals in a column cannot exceed 11, in order to put 11 and 10 into a column we must associated them with a different symbol.

10=χ
11=ε

Here is how one would count in base 12: 1,2,3,4,5,6,7,8,9,χ,ε,10,11,12,13,14,15,16,17,18,19,1χ, 1ε, 20,...

If we used base 12 we would not use centuries or decades. We would use unquenniums and biquenniums. An unquennium is 12 years and a biquennium is 144 years. In base 10 this would be the 13th biquennium, but in base 12 it's the 11th biquennium.

This year is very special, it is the turn of the biquennium. It will be year 1300 in base 12!

Extra bit:

One thing I find troubling is "base 10". That could mean any base because 10 in base b is b in base 10(where 10 is the number of fingers on our hand). It could mean any base.


Gr8 thread :nerdy: :D



Last edited by slave on 02 Jan 2016, 10:06 pm, edited 1 time in total.

slave
Veteran
Veteran

User avatar

Joined: 28 Feb 2012
Age: 111
Gender: Male
Posts: 4,420
Location: Dystopia Planetia

02 Jan 2016, 9:19 pm

Nine7752 wrote:
Interesting thought that the metric system could have changed the base of our numbers to 12.


It is a real shame that they didn't....huge opportunity missed, imo.
I think the arguments for base 12 have merit, but I think such a change is unlikely at this point. :(



Fnord
Veteran
Veteran

User avatar

Joined: 6 May 2008
Age: 67
Gender: Male
Posts: 59,873
Location: Stendec

02 Jan 2016, 9:22 pm

Why have 12 months of varying length when 13 months of 28 days each fit much better?

Actually, 12 months of 28 days plus 1 month of 29 days (30 days in leap year).

Try getting THAT calendar reform to pass!


_________________
 
No love for Hamas, Hezbollah, Iranian Leadership, Islamic Jihad, other Islamic terrorist groups, OR their supporters and sympathizers.


kraftiekortie
Veteran
Veteran

Joined: 4 Feb 2014
Gender: Male
Posts: 87,510
Location: Queens, NYC

04 Jan 2016, 8:37 am

I have no problems with the decimal system.

It's interesting how 12 has acquired so much meaning of the centuries, though.

Obviously, ripe for historical research.