Saturday, October 16, 2010

12 is the loveliest number. # naming conventions.

Twelves appears in many places and many guises.
It flies in the face of our modern sensibilities.
We just assume that a 1-size-fits-all 10-base system is the way to go.

I will make my case for the need to name #s simply right up to 12.

In physics, the Planck length, denoted ℓP, is a unit of length, equal to 1.616252(81)×10−35 meters. It is a base unit in the system of Planck units.

D - metric-style prefixes to a power-multiple of 3x12 is desirable to easily encapsulate the Planck length. So instead of yocto at 10 -24, we could have something else at 10 -36- Planck length territory.

The imperial system is still widely used. I worked in construction, and can tell you we still do everything with the Imperial measuring system.
We all know inch-feet-yards-miles.
There are a few more but those are the important ones.
Once we reach lengths smaller than inches, we typically use a fraction-2-power system.
I.e. 1/2 ,1/4, 1/8, 1/16ths...
Here we see the importance of a to-the-power # naming convention.
That is also true of the metric-style prefix names, as well as the #s 1,10, and 100.
Really, 10 and 1000 with various powers are the basis for our modern decimal/metric system.

Twelve also appears in time, and has resisted every effort to displace it.

Behind this use of 12 is the backdrop of the sexagesimal system - 60 base.
Sexagesimal (base 60) is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, it was passed down to the ancient Babylonians, and it is still used — in a modified form — for measuring time, angles, and the geographic coordinates that are angles.

The number 60, a highly composite number, has twelve factors, namely { 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 } of which two, three, and five are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, six minutes, five minutes, etc. Sixty is the smallest number that is divisible by every number from one to six. This is because 60 = 2 × 2 × 3 × 5 = 4 × 3 × 5.

D: take a circle with 360 degrees. Dividing progressively in half, we get 360,180,90, 45 .... 22.5.
Whereas a 100-base system would divide to 100, 50, 25, .... 12.5.
To avoid decimals/fractions for one more division, we'd hafta go up to a 1000 base system.

The importance of the 12-base system is apparent in our English # naming conventions.
We have eleven, twelve and only then the 13-19 "teen" ending.

Finally, we have our 360 (plus a bit) days of the year. Our calendar has 12 months.

Very few aux-langs think to make # names simple beyond 10.
We see above that there are many benefits to a # naming convention that is compact to 12 for brevity of speech.

As always, take Espo for example. ( I dare not utter utter this demonic language's true name - it attracts spammers! <:)
16 Dek ses (one ten and six)
Lojban, et al typically also fall into this trap.
Lojban cycles through the aeiou vowel set twice to reach names to 10.

One last thought. In time, we have the following naming conventions.
Second-minute-hour-day-week-month-year. Only day and year have any natural-world meaning.
We see a similar progression of names for Imperial distances.
The option of a measuring-unit system with a 1-7 or so scale for names, much like #s, may be desirable.
Alternatively, a day-less-1-scale (hour) system could be attractive.
Possibly, a naming convention that uses very brief terms for common multiples could work. E.g. Second is day /24 hours/ 60 minutes/ 60 seconds.

I vaguely entertained a notion to use a time unit convention for the day that reflects geometry. I.e. 360 degrees vs 12 hours. That is 30 degrees per hour. Each degree would be 2 minutes. From there, arc minutes and arc seconds.
It'd be interesting to show time on an old hand-based clock for the year.
The best argument I've heard for why our time-unit second is a second is the rate that the human heart beats at.


1 comment:

dino snider said...

It may seem strange that I am bashing a pure 10-base system, instead opting for a supplementary terse naming convention for 11 and 12. Well, I may call it 7 now - CVN (consonant - vowel - nasal), pronounced seven. There are 7 continents so it is a nice inclusive # too. It also works well with the heptagram symbol - I use alchemy as an analogy for my vocabulary approach.