# Adopt a new numeral system

I am creating a fictional off-solar system colony. In this colony people started to use a duodecimal positional number system. The people were all cultured in science and practical with numbers. They didn't have any sort of amnesia or contact with alien cultures, their new world is similar enough to Earth to allow using the old system, they don't have to hide any technical secrets from each other.

My question is: Why would a group stop using a decimal system and start using a dozenal system?

Could it be because of an event (like a war) that happened before they started the colony (assuming they started using it only once they started the colony)?

Has it already happened in the world? What kind of results could it have in their culture, technical development and science?

• Welcome to the site Eithne, can you provide a bit more detail on the scenario, mainly, what kind of technology the people have access to? – James Oct 6 '15 at 15:51
• worldbuilding.stackexchange.com/questions/9741/… – Dan Smolinske Oct 6 '15 at 15:52
• @DanSmolinske Good add Dan, that explains the system pretty well...now we can make up reasons for switching to base 12... – James Oct 6 '15 at 15:58
• @James Sounds like idea generation, then. – Frostfyre Oct 6 '15 at 16:00
• Does it have to be a switch? We are still in the process of shifting our sense of time off of base 12 (Egyptians) and base 60(Greek/Babylonian), so the shifts of base can be gradual. Likewise, we are slowly progressing towards base 16 being particularly useful for interacting with computers, though we don't yet teach it in elementary schools. – Cort Ammon Oct 6 '15 at 16:05

Picture a planet with a year of 288 days in a year which has a large near moon with a orbital period of 12 days, with a week of 6 days being measured from Full Moon to New Moon and then from New Moon to Full Moon.

It is decided to use 12 months of 24 days each.

The days coincidently measure 24 hours long.

Imperial units of measure are used, with 12 inches to a foot.

Why have people started new colonies in the past? Setting up a community with their own ideals is one historical reason, and is a good bet moving forward.

A group of people are obsessed with 12 or with ancient cultures like Babylonians that used 12/60 stuff. They start with this idea, and go off to found their own world.

• This doesn't really feel like in the spirit of OP's question. He explicitly mentioned a scientific, cultured people. Even the babylonians are theorized to have a practical origin of their base 12 (counting on their knuckles) – knowads Dec 23 '19 at 18:50

Hmm.. there are still many occasions where dozens or half-dozens are used (so we already have a word for it!). Also, while we have 10 Fingers (altogether), we have 12 Finger Segments on each Hand, not counting the Thumbs. So it is possible to show Numbers up to 12 with just one Hand.

• So why do people switch from counting fingers (including thumbs) on both hands to finger segments (not including thumbs) on one hand? Yes, it's possible to do so, but what happened that made them do it? – Brythan Dec 8 '16 at 21:12
• hm, nice, ability to show numbers with one hand interesting. Using thumb all numbers can be shown by touching particular segment of particular finger. Hm, and with both hands I can show a number from 1 to 144 - that's handy. – MolbOrg Dec 9 '16 at 1:23

I can think about one idea, a political one... Let's think for a while about the French Revolution. Ignore slogans concerning human rights... Which does does not matter much when one starts new era of industrial scale extermination of political opponents... think more about revolutionary minded gov, huge concentration of unbalanced power and serious efforts to make mess tolerated under ancien régime finally cleaned up. No more ambiguous and impractical units...

https://en.wikipedia.org/wiki/Units_of_measurement_in_France#Revolutionary_France_.281795.E2.80.931812.29

Got proper mood? OK, so then rearrange all units in to more clear and logic version. As extra point for mass one may actually reuse "unified atomic mass unit" which in RL is defined as 1/12 of mass of carbon-12.

https://en.wikipedia.org/wiki/Unified_atomic_mass_unit

Decimal number system originated basically because we humans have 10 fingers in our hands (total, including thumbs). Number systems arise with the need of counting originates.

A number system of 12 will originate if your alien race has 6 fingers on each hand.

Or if have 12 small protrudings on their body which can be used for counting.

Something on those lines.

• Or if they use a method for counting other than extending fingers. – Gilles 'SO- stop being evil' Oct 6 '15 at 22:32
• Or if they count by touching phalanges with thumbs. – Trang Oul Oct 8 '15 at 9:17
• There are many real world historical examples of finger counting beyond the absurdly simple one digit = one digit. Some early counting was base 12 simply because that is what they counted on one hand (4 fingers which count 3 each - put thumb on end of index finger for '1', then slide it down the finger to the first knuckle for '2', then second knuckle for '3', then move the thumb to the end of the second finger for '4', first knuckle of second finger for '5', etc. etc.). – pluckedkiwi Oct 8 '15 at 16:41
• @pluckedkiwi: And then all those faded into obscurity and were swept in the waves of time. Only the solid, 10 fingers system remained and became global. The mayans and aztecs used base 20 counting system (they included their feet digits too), but their numeral system faded as did they ... – Youstay Igo Oct 8 '15 at 17:09

I've always thought that if humans had made a stronger distinction between fingers and thumbs, we'd have counted in eights (octal). That makes conversion to binary trivially easy and computers (mechanical ones) might have arrived a lot sooner.

Anyway, there have been other number systems in history. Babylon used base-sixty, which can be subdivided as six tens or five twelves. Both were used. Sixty can be divided exactly by two, three, four, five, six, ten and twelve (and by eight using halves), which is useful to a mercantile society.

More recently base-20 was popular, subdivided in fours and fives. Vestiges survive in various somewhat obscure shepherd's dialects ( https://en.wikipedia.org/wiki/Yan_tan_tethera ) and in the French for ninety (quatre-vingt dix, four twenties and ten). "Dix" is ten in many of those shepherd's dialects, showing a common origin (Celtic ).

• Why would binary be that important for mechanical computers? Regarding fingers, how many languages even have a word for finger-excluding-thumb? – Gilles 'SO- stop being evil' Oct 6 '15 at 22:34
• The question was "why would a group switch systems?" and then some ancillaries about base 12. This post doesn't address the main question or the ancillaries. – nitsua60 Oct 7 '15 at 1:07
• Well, one reason is easy divisibility by 3 and 4. That matters more in a mercantile society lacking mechanical calculating aids, such as Babylon. It's the likely reason dozens have not completely died out in modern society. Another reason could be religion. The number five and multiples thereof might come to be regarded as suspect or demonic, or their prophet might have been one of those rare humans born with five perfectly formed fingers rather than the usual four. (It's much more common with cats). – nigel222 Oct 7 '15 at 18:28
• @Gilles French at least has a name for every finger (not toes, except the big one "thumb") : Index ; Major ; "ring finger" ; "ear scratching finger". – MakorDal Dec 8 '16 at 7:51
• @MakorDal You forgot thumb in that list. The French language has no word for finger-excluding-thumb, only for finger-including-thumb. And for the big toe we mostly say “big thumb” (gros orteil). – Gilles 'SO- stop being evil' Dec 8 '16 at 9:34

They were merchants who sold by the dozen and by the gross. It got to the point where they said "the heck with it" and adopted the duodecimal system as their "main" system.

If they kept all their records by computer, switching bases might well have been as easy as switching display formats.

A lot of people have answered how or why it could happen, but only a couple touch on what the effects of a switch would be.

Besides my snarky comment about the number of failed engineering projects where the incorrect unit was assigned to a number (which correlates to switching bases because does 10 mean ten or twelve or two?), there has been at least one such case in recorded history. The Norse and Germanic tribes did not use base 10, and as such, common words ended up with different meanings. For example, the Long Hundred. This had to be standardized in law to prevent fraud. Suppose you use 120 for the value of hundred, and suppose 1 fish sells for 1 pence. I promise to sell you 100 fish for 100 pence, and you think 'Wow! What a deal!", but then I only deliver 100 fish. You get angry and wonder where the other 20 fish are, but I point out that I sold you 100 fish, not a hundred fish.

You can also look at the various gauges for things sold in countries using Imperial and countries using Metric. Cars with analog dials have markings for both MPH and KPH. Rulers have a inch side and a centimeter side. Packages list both pounds/ounces as well as kilograms.

People who were raised using base 10 will often need cheat sheets that translates Duodecimal to base 10 numbers simply because counting is learned at such an early age that it becomes deeply ingrained in us by the time we're adults.

Not a full answer. But in base 12 you can divide nicely through all the factors: 2,3,4,6,12 (while base 10 only has 2 and five). This also means the decimal representation of the fractions become simpler - so is 1/3 in base 12 is 0.4 (exact) - while in base 10 it is 0.333333.... (infinte series). A computer working in this base 12 would make different rounding errors than in base 10.

On a side note - there is some research going on in mixed radix number systems. There is hope that there are systems in which complicated numbers such as roots, pi and e will have a simple form. You might make it that your (advanced) people have found such a system and 12 is the first radix - so people would for everyday things just work with this number. And computer working in such a system would make no rounding errors.

During the war, computer programmers were no more secure in their accommodations than anyone else. It's hard to program when your ship's axis of rotation changes suddenly as pieces break off, and fuel is low. So while waking up the systems from hibernation and hurriedly attempting to filter out insertions into the textual history databases, somebody typed 0-9a-b instead of 0-9a-f, and numerical records in ASCII hexadecimal representation were truncated. When people started to learn numbers again, and wanted to preserve their history, they looked to the latter day "Rosetta stone" and found the digits they need. Methusalah lived 39 years. Seemed reasonable.