Monday, August 27, 2007

Integers Nine to One and their significance in Gadaa (part II)

[Continued from Part I]

Let us examine the remaining numbers in a descending order. What happens to the number 8 when we apply the above formula? Observe that for 8xN = XY where X+Y = 9 only when N = 9. For all other numbers, X+Y < 9 and the sum falls away in a decreasing order as N increases. (Figure II) for the Graph of 8 and learn how it is falling down one step at a time. Therefore 8 is a feeble number that can not be used in any of the Gadaa function and the Oromos named it as “Saddettan dhalaa Nenxaa” the gestation period of a lion.

The next number is 7. We apply the same formula as we did for the number 9 and 8 i.e., 7xN = XY, where X+Y = 9 or X+Y < 9. Through this operation, the product of the number 7 adds up to 9 only when N = 9. When N is any number other than 9, the sum of X+Y rises and falls following an inconsistent cycle. The Graph of 7 (Figure III) shows how X+Y is falling down two steps and rising up one step at a time non-uniformly. Therefore 7 is a number that shows a reasonable strength but not sufficiently strong enough to serve in a Gadaa system. However, its function is limited to Sundays’ service and the Oromos named it “Torbban Nannoo Dilbataa”, the cycle of Sundays. It is a formal meeting day or prayer’s day to Waaqaa (God)

Let us take the next number, which is 6. Observe what happens if we use the formula as we did for the numbers 9, 8 & 7. 6xN = XY, where X+Y = 9 or X+Y < 9. Through this operation, this number merges to 9, when N = 9, 6 & 3. When N is a number other than 9, 6 & 3 the result falls away from the graph of nine in a descending order. See Figure IV for the Graph of 6 and learn how it is falling down double steps to reach its destination but only a single step to hit the graph of 9. Therefore, 6 is a medium number that can be used in the Gadaa function as a regional subdivision of Oromia (Biyyaa Oromo) and is referred to as “Jahan Jabbii Qaraxxaa”, the taxation which implies administration. A very strong and tangible proof for this scenario is that there are only six Odaa centers in Oromia. The six administrative (legislative) regions are Odaa Bisil, Odaa Bultum, Odaa Gaares, Odaa Makoodii, Odaa Nabee and Odaa Roobaa.

What happens when we apply the above formula to the number five? Through this operation, the sum of X+Y for 5xN = XY approaches 9, after only five uniform cycles. When N is a number other than 9, the result decreases and increases in a uniform pattern. The Graph of 5 (Figure V) clearly illustrates this pattern. Therefore, 5 is a sophisticated strong number that is used in the Gadaa function as a judiciary group of Oromia and is referred to as “Shanan Qubaa harkaa”. Just as we have five fingers for effective coordination and five senses for absolute judgment the Oromos trust a group of five Abbaa Gadaas to interpret the law of the Land (Orimia).

Observe what happens to the number 4 when we use the formula 4xN = XY, where X+Y = 9 or X+Y < 9. Through this operation the value of X+Y approaches 9, after only three cycles. As N increases (N = 1, 2,3…) the peaks of the three cycles fall away from the Graph of 9 in a decreasing order. However, when N = 9, the fourth peak merges with the Graph of 9 (Figure VI). Therefore 4 is classified as a weak number that can not be used in the Gadaa functions of Oromia (Biyyaa Oromo) and is referred to as “Arffan Muchaa Sayyaa”, the four teats on the udder of a cow.

The number 3 is very fascinating. For 3xN = XY where X+Y=9 or X+Y < 9, when N= 9, 6 & 3, the peaks for the Graph of 3 touch the Graph of 9. When N is any number other than 9, 6 & 3 the sum of X+Y falls away from 9 in a descending order. Observe Figure VII for the Graph of 3 and learn how it is falling down in one shot (a fact that 3 is much stronger than 6) and rises up and touches 9 in two steps. Therefore, 3 is a powerful number that is used in the Gadaa function as an administrative and defense committee. The number 3 is classified as “Sadan Sunsummanii”, broad based. A very solid and tangible proof for this scenario is the term “Sunsumaa” which translates into the word “tripod”. Therefore, the Oromos fixed the number of council in the area of defense and administration to 3.

Take the next number “2”. Observe what happens to the values for the formula 2 x N=XY, where X+Y=9 or X+Y < 9. The sum of X+Y reaches the Graph of 9 only when N = 9. See Figure VIII to learn that for all numbers other than 9, the graph shows one cycle, which rises to its peak in three steps and falls off to its lowest value in just one step. Therefore 2 is a feeble number that can not be used in any of the Gadaa function and the Oromos named it as “Laman Muchaa Re’ee”, the teats on the udder of the she goats.

The last number is 1. One does not change the value of any number that it is multiplied with (1xN = N). As N increases (N = 1,2,3…) the Graph of 1 approaches the Graph of 9. Therefore 1 is an impotent number that can not be used in any of the Gadaa functions and the Oromos refer to it, as “Tookken Tookkituma”, one is always one.

I hope you enjoyed reading this excerpt as much as I did.

4 comments:

Anonymous said...

I enjoyed reading it and it is fascinating to see how our past was glorious. One question that I have for you is that is there any way that you can find the graphs and include them in this article? Even though the writing on its own is descriptive and can be understood with out the graphs, the graphs would enhance and help the readers visualize the issue better, as the saying goes "A picture worth more than a thousand words".

Good job

T.O

Anonymous said...

To me, surprising more than it is interesting . I did not think people of that era would be mathimatically intellegent. Now, it seems like we had our own Galilios and Newtons back in the days.

Dhuga Dubataa

Torben said...

I must admit that I was tempted to rush to Number seven( you can guess why) but didn't. I loved the idea, which is basically an exercise in real anaysis, of digging the base ten numerals to comeup with some natural property. The author gets it right in consistently explaining the historical incidents and denominations with the numerals. Probably, there could be something that needs to analyzed seriously. The author needs to be encouraged to pin down the full fledged implications and associations with the tools he has now. It looks promising!

Anonymous said...

One can appreciate how our Oromo ancestors understood mathematical significances on organization and life. Interestingly enough, the numbers 1 and 0 have significance in terms of Space Exploration, Computers and Religion.

In most monotheistic religion, the 1 is Waqaa who is understood as being everywhere. At the same time, one can not say he is only here and not over there. The color blue (Gurachaa Garaa Waqaa or black as Waqaa's stomach) has a link with Waqaa illustrating the concept of 1. When our people pray to Waqaa, they say Waqaa Gurachaa. In terms of space, Gurachaa is the heat sink where there is debate on the black hole as being an energy deposit formed by a dead star. Thusly, if Waqaa Gurachaa is 1 and black is the high concentration of energy, then what is 0? In terms of Computers, 0 is the opposite of 1 meaning if 1 is on then 0 is off. The design of computers is a complex arrangement of 1 and 0. Such an arrangement has created a whole new form of communication and life. It is both real and abstract and one that has changed the way we live life in many aspects.

In my opinion, the number 1 is very significant but also dangerous since one can fall into unilateralism through “I” instead of “us.” Those who only believe in 1 compromise humanity when they believe life only exists in their nation and nowhere else. Other common statements by those that only believe in 1 are as follows:
My religion is the only true religion and it is #1.
My country is the only #1 because it is the most powerful super power.
I am not going to do anything for others unless I can get something out of it.

Our ancestors may have understood this very well and so minimized its significance. The author stated our ancestors set aside the number 1 as just that "Tookken Tookkituma."
Nagaan.

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