# Numerical systems

Discussion in 'History' started by Edont Knoff, Dec 18, 2015.

1. ### Edont KnoffRegistered Senior Member

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I'm under the impression that old numismatic systems had 6 or 12 based systems, while newer systems use a 10 or 100 based currency.

The 12 is more handy than the 10, because it can be split (without fraction) in 2, 3, 4, and 6 parts, while 10 only can be split in 2 or 5 parts.

Why did the 12 based system slowly vanish and werre replaced by 10/100 based systems?

3. ### sculptorValued Senior Member

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why 6?
Try a little exercise.
Get a bag of coins. Place a coin on a table
then place equal size coins around the first-this ring has 6 coins
then place equal size coins around the 2nd ring---this ring has 18 coins
then place equal size coins around the 3rd ring---this ring has 24 coins
then place equal size coins around the 4th ring---this ring has 30 coins
etc. ... etc. ... etc. ...

the number of coins in each ring progresses by 6
So much for "why 6?"
as to: Why change to base 10?------------------------------?????

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5. ### sideshowbobSorry, wrong number.Valued Senior Member

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Cute. But what's the practical value?

7. ### sculptorValued Senior Member

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I do not know the answer to that.

I was always just curious as to why some ancient civilizations chose base 6.
What I posted comes closer than all of the anthropology/archaeology lectures and writings I have heard/read on the subject.
So:
I posted the above.
Coincidence? or: Causation?
..............
count to 5 with digits of one hand, then flip a digit on the other hand for 6
repeat
when all the digits on the other hand are used, you will have 36 (6x6)
..
Is that practical?
................................
Everything I write on the subject is translated into base 10.
Does that translation introduce some alteration in the use or meaning?
...............................
caveat: I ain't no mathematician. On a good day, I consider myself barely literate.

Last edited: Dec 18, 2015
8. ### sideshowbobSorry, wrong number.Valued Senior Member

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Years ago I was introduced to something called https://en.wikipedia.org/wiki/Chisanbop (Korean finger math). You count to five but you use the thumb to represent five and then continue on to nine with the other four fingers. For ten, you put down a finger on the other hand, eventually using the other thumb for fifty. That way you can count to 99.

9. ### Dr_ToadIt's green!Valued Senior Member

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I can count up to 1023 with my fingers in binary.

So?

10. ### Edont KnoffRegistered Senior Member

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547
I didn't really ask "why 6". Even that I didn't know the ring example, 6 and 12 are more handy numbers than 5 and 10. Particularly 5 is impractical, because it is prime (not dividable in integral parts anymore, but 1 and 5 itself). 6 and it's double 12 are much better. The ring of disks thing is very interesting though.

Many ancient civilizations chose 6 or 12 based systems - e.g. our time is a 6/12 based system, 2*12 hours per day, 5*12 minutes per hour.
Circles and degrees the same - 360 degrees for a circle. 60*6 . Also in trade, a dozen is 12, that was a very common quantity, and still is.

I rather was asking why these old systems were given up in favor to 10/100 based systems. In coins the old systems are mostly gone, degrees are still common in 360, although mathematicians use PI as base, and time is also still 2*12 and 12*5 for the hour, but we usually take it as 10*6 for the hour, so a ten sneaked in there, too.

So since the other systems are kept, but numismatic systems changed so much, I was asking about the coins.

11. ### Fraggle RockerStaff Member

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24,690
Most primitive tribes had either base-five or base-ten number systems. The language of the Basques, who are not Indo-Europeans and therefore possibly the descendants of the Cro-Magnon, has no word for "six." They borrowed the Spanish word seis, although they left off the final S.

The duodecimal (base-twelve) system is rare and recent. It appears to have been an artifact of commerce, since a group of twelve objects for sale can be divided into groups of two, three, four or six, whereas a group of ten can only be divided into twos or fives.

The French language hints at an ancient vigesimal (base-20) system. They express the number 92 as quatre-vingts douze, "four twenties (and) twelve."

There's a tribe in New Guinea (or a nearby island, forgive my imprecision) in which the word for "eleven" is "now I have to start using my toes."

Oh, and by the way, a "numismatist" is a collector of coins. The word you were looking for is "numerical." I changed the thread title to avoid confusing our members.

Fraggle Rocker,
Moderator of Linguistics

12. ### Edont KnoffRegistered Senior Member

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547
I meant the coin systems. The other debate of the numbers emerged in the thread, but it was not what I wanted to know.

My question was, why were the old 6/12 division based coin systems abandoned in favor of 10/100 based coin systems?

I don't know what the proper english word for "coin system" is, but number system is too broad. I neither meant to discuss the circle/degrees, nor the time systems, that just popped up as examples of 12 based system which had been kept, while the coins were changed.

13. ### sideshowbobSorry, wrong number.Valued Senior Member

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Dairy Queen used to sell ice-cream sandwiches in "family packs" of eleven. My mother used to complain that there was no way to divide them up with our family of six. Even as a child, I understood the commercial implication - you have to buy more than one package.

14. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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finger counting. It is a great misfortune that we have 5 instead of 6 fingers.

15. ### Fraggle RockerStaff Member

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The term "baker's dozen," meaning 13, has been around for about 400 years. There are various explanations. The one that (to me) seems most likely accounts for the fact that baked goods are somewhat fragile. If one is smooshed in transit, the buyer will still receive an honest dozen.
Most mammals have five phalanges on each foot--or hand, in the case of primates. Like many results of evolution, it may very well be the luck of the draw. I can certainly imagine that six would be too many. Either our hands would be larger and heavier (probably an inconvenience), or our fingers would be narrower and more fragile.

Of course the artiodactyls (even-toed ungulates including sheep, deer, swine, cattle, giraffes, camels and most other familiar grazers) are the exception, with only four toes--although in both artiodactyls and perissodactyls (the small taxon of five-toed ungulates, including only equines, rhinos and tapirs) the toes are nothing more than bones and a few muscles inside the foot.

Birds, of course, have only four toes. The psittacines (parrots, cockatoos, budgies, etc.) are zygodactyl, meaning that two toes point forward and two backward. This allows them to grasp things, such as branches for climbing up into trees with too much foliage to permit flying, and to grasp food as well as objects that might serve as tools.

16. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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Me too (can imagine that). I can also imagine a more symteric hand with two opposible thumbs for the heavier task and four finer finger for more delicate work. - No increase in hand mass, just greater flexibility.

But "mother nature" did not know we would be come so dependent on number systems.

17. ### Edont KnoffRegistered Senior Member

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Our ancestors had also 5 fingers, and still they chose 12 based systems, as we can still see from our time (2*12 hours with 5*12 minutes each) and the angles (360 degrees, 5*6*12) and the 12 astrologic signs. Also, the old trade units of a dozen (12) and a gross (12*12).

It's strange that these systems were invented by people with 10 fingers, if finger counting is the reason why we now prefer 10/100 based systems.

Actually I suspect Arabic numbers to be the reason. There are 10 glyphs from 0 to 9 in our alphabet, but none for 11 and 12. So with the adoption of Arabic numbers 0-9, the 12 based systems were not matching the way anymore numbers were written. With 10 number glyphs, 10 based systems were more fitting.

18. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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You are probably correct.

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19. ### Edont KnoffRegistered Senior Member

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Computer scientists use A-F as number glyph extensions and a hexadecimal system that fits the memory organization of common computers - a 2-digit number fits exactly into one memory cell (one byte, 8 bits, the smallest directly addressable memory unit).

Still, while thios worked for the computer sciencetist, I think there is little hope to establish a 12 based system for everyday use, even if it'd have benefits, since the 12 includes so many small numbers. 2,3,4 and 6 are all evenly contained in 12. The next better base is 30, which has 2,3,4,5 and 6, all of the first 6 numbers (I didn't count the 1, because it's not useful). But 30 number glyphs are difficult to remember, so the 12 is likely more practical for this reason, even if it lacks the 5.

While doing my research on the question of the 10 vs 12, I also found this:

http://www.dozenal.org/

There is a real organization trying to promote the 12 based systems. I had not heard of this before. A pity, but I think it's good that there is an organization trying to promote the 12 based system and explain it's benefits.

I have not yet found out though which glyphs they suggest for the 10 and 11.

But I found another 12 based system: Musik - in western music an octave (the interval of a base frequency to double the base frequency) is split into 12 notes.

20. ### James RJust this guy, you know?Staff Member

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If I had to guess (and I do), I'd say the most likely reason that base 10 is so common is that we have tend to have ten fingers.

21. ### Fraggle RockerStaff Member

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You overlooked the fact that the "new moon" rises twelve times a year. For people who were dependent on the stars to keep track of the seasons and manage their food supply, this would be a strong influence on their number system.

The Wikipedia article points out that very few cultures actually used a duodecimal system for everyday counting, as shown in their languages. Their wider use after the invention of the technology of city-building and the subsequent paradigm-shifting technologies of bronze metallurgy, iron metallurgy, and industrial processes, strongly suggests that the utility of duodecimal numbering grows with post-agricultural technologies, and is not actually useful enough in Stone Age cultures to be worth the trouble of learning how to perform duodecimal arithmetic for any purpose except astronomy.
The so-called Arabic numbers were adopted wholesale from India and simply redrawn in strokes that fit in better with their abjad. (An abjad is an alphabet with no vowels, which works fine for the Semitic languages, in which vowels are not phonemic). Nonetheless, it's quite fair to give them credit for it because it was they who invented a symbol for zero, giving us, at long last, a true positional notational system.

22. ### Edont KnoffRegistered Senior Member

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For counting, 12 based systems have no benefits. The benefits only show if you want to do some calculations, particlarly calculations which includes divisions, and at the same time one wants to avoid fractions.

I assume you are right that the need for such calculation grew with technology level, well rather science.

And yes, the moon might also have triggered the idea that 12 is a good number, since many agricultural dates were derived from the moon in ancient times. The sun was less useful, at least until more precise instruments were made. Counting new moons was easier, and one only needed one sun-related point "new year" from when to start the new moon counting.

Also interesting that women in average experience their period 12 times a year (rounded). Maybe a biological dependency on the moon from ancient times? Anyways, the 12 is an interesting number in many ways.

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