Dozenal Numeric System

21 Januray 2012
By Andrew Craucamp

In order to understand what is going on here you will need some understanding of the Dozenal numeric system or alternate numeric systems in general.

There is nothing new about the dozenal numeric system however it has been incomplete for a long time, piggy backing off the decimal system in terms of phonetics and notation. I have created a phonetic structure from scratch which is independent of that of the English decimal system but has some similarities for ease of migration, coupled with the Devanagari numeral system for disassociation.

I used the Devanagari numerals instead of the standard Western Arabic numerals to disconnect association with a decimal numeric system, this is obviously lost on those who are already accustomed to the Devanagari system though. If one sees 100 they immediately think of one hundred decimal units which can create confusion when trying to do calculations in dozenal because of subconscious assumptions that are made.

Ideally we should use a set of characters that correspond to the groups of three in the dozenal phonetics (Di, Do, Da), (Ti, To, Ta), etc. but in order to be able to use the numeric system on present day computers and printers it makes sense to use a pre-existing system. The last two characters are the first two digits in modern Arabic numerals.

I believe that by keeping it simple and maintaining a logical pattern it will be easier to pick up on basic mathematical concepts. More importantly; an advanced numeric system coupled with systematic phonetics has the potential of making the core mathematical concepts such as geometry and trigonometry far more natural, for example 360 (degrees of a circle) divides into 12 exactly 30 times. This is simply a proof of concept, i strongly believe that we can and should improve on the fundamental systems we use daily.

Base Units:

0 - ० (Di)
1 - १ (Do)
2 - २ (Da)
3 - ३ (Ti)
4 - ४ (To)
5 - ५ (Ta)
6 - ६ (Si)
7 - ७ (So)
8 - ८ (Sa)
9 - ९ (Ni)
A - ١ (No)
B - ٢ (Na)
10 - १० (DoZi)

Exponents:

१० = १ (Do)
१० = १० (Zi)
१० = १०० (Zo)
१० = १ ००० (Za)
१० = १० ००० (Ki)
१० = १०० ००० (Ko)
१० = १ ००० ००० (Ka)
१० = १० ००० ००० (Mi)
१० = १०० ००० ००० (Mo)
१० = १ ००० ००० ००० (Ma)
१०١ = १० ००० ००० ००० (Bi)
१०٢ = १०० ००० ००० ००० (Bo)
१०१० = १ ००० ००० ००० ००० (Ba)


Examples

१० (12)
DoZi-Di (or just DoZi)
Do - The multiple of the exponent (in this case १)
Zi - The exponent used (in this case १०)
Di - Number of appended units (in this case ० which does not need to be enunciated)
(१ x १०) + ० = १०

१०० (144)
DoZo-Di (or just DoZo)
Same as above the only difference is the exponent.
(१ x १००) + ० = १००

२५ (29)
DaZi-Ta
Da - २
Zi - १०
Ta - ५
(२ x १०) + ५ = २५

१४८ (200)
DoZo-ToZi-Sa
Do - १
Zo - १००
To - ४
Zi - १०
Sa - ८
(१ x १००) + (४ x १०) + ८ = १४८

८४٢६ (14 538)
SaZa-ToZo-NaZi-Si
(८ x १०००) + (४ x १००) + (٢ x १०) + ६ = ८४٢६