Re: Dividing by 12

alanmc95210@xxxxxxxxx wrote:
GeorgeD wrote:
Sam wrote:
Help me with this some...

In religion and mythology you see lots of examples where particular numbers
tend to show up repeatedly. Obviously they had some significance to the
culture. Seven is the best example and appears practically world wide.
From the Near East thanks to the Sumerians and Egyptians we also have 12 and
60.

Seven is easy, it comes from the solar system. The sun, moon, Mercury,
Venus, Mars, Jupiter, and Saturn. Practically all cultures deified them and
created the "seven hosts of heaven". It's where we get seven days of the
week from, and of course the western names in Latin tie to the Roman (from
Greek) names for the gods they represented. In several eastern languages
even the character for the planets and the day of the week are the same.

I'm fuzzy still on 12. The best connection I can come up with is this. By
2100 or so, the Sumerians were using a 360 day a year calendar. Out of that
the months came to be based on the moon. I would guess then that the
relationship between the cycle of the sun god and the cycle of the moon god,
that basically there was a 1:12 ratio, (even though wasn't a 13th month
sometimes added to keep things in sync?). The fact that the deities in the
divine world saw it fitting to divide things by 12 must have bubbled over
into the human realm. Examples of this is that the earliest sundials from
Sumerian and Egypt divided the daylight into 12 hours. With more daylight
in summer than winter, hours were just longer, but there were still 12 from
sunrise to sunset. Also in many ancient systems of weights and measure,
many "sub-units" are defined as 1/12 of it's "parent" unit. In both cases
humans are dividing by 12 because it was seen as divinely significant. I
can't help but wonder if that's not where the whole "12 tribes" of the
ancient Hebrews comes from. Not simply the mythology (achronistic) of where
they came from, but just the perceived significance of the idea that there
were 12. i.e., Israel was divided into 12 parts.

60 I'm even fuzzier on. It also shows up in weights and measure, and of
course further dividing an hour into 60 parts (minutes). But what exactly
was the significance of 60 in the 1st place? Does anyone know where it
comes from?

Another one is that 40 was near eastern slang for "a bunch". It also shows
up in texts where the intent is just to signify it was a lot of things
depending on the context.

Another is 70 from Ugarit and the Bible. El had seventy sons/daughters that
made up the pantheon.

A lesser one is 4, mainly because of the 4 cardinal directions. Shows up
most often only in that context, but sometimes with poetic use.


12 and 60 are not so much mystical as useful. 12 can be divided by 2,
3, 4, and 6. It has more divisors than and other number of comparable
size. Using feet (12 inches) as an example, you can easily find a half
a foot, a third of a foot, a quarter of a foot, and a sixth of a foot.
60 is the next number with a large number of divisor for its size.

And as an added factor in the simplicity of 12, our base 10 number
system hadn't been invented yet. Imagine trying to divide MCM by XL-
A. McIntire

You point is well taken but poorly stated. It doesn't matter the
base of your number system for "place" related system to work well.
Note that the Roman numbers given in your example is actually a
base 10 system. To that system was grafted the concept of "place"
and the addition of zero from the Hindu/Arabic number system.

It is just as easy to have a place related system using any base.
If it's base 12, it's called duodecimal. If it's base 8 it's called
octal and if it's base 16 it's called hexidecimal. The last being
VERY common in computer use.

The numeral base is not the key. "Place" and "zero" are the keys.

In a base twelve system, natural fractions (1/8, 1/4, 1/2, 1/3)
are more closely related to the decimal fractions (.125, .25,
..5, .33333..., etc for the decimal versions of the natural fractions
given). Hence a duodecimal system actually makes more sense. Or
at least it would if we had 6 fingers on each hand.


There is a whole branch or mathematics dealing with this subject. I
forget what it is called; rich something or other.

Regards,

.

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