Another View of Ethiopic Number Sequences

If you are like me you probably have not seen any Ethiopic numbers in any value larger than what would be used for writing years; and may be uncertain about the rules for writing numbers greater than 10,000. Also if you are like me, in fact you would have to be almost exactly like me, you were sketching out Arabic to Ethiopic number conversion algorithms during lunch today, and actually enjoying it. But if you were this much like me you would also be writing now in which case one or both of us would cease to exist under The Cosmic Absurdity Theorem which by requirement initiates the collapse of the known universe. So I hope it is just me...

...If you do find numbers interesting then read on...

The purpose of this posting is to get feedback to see if I am totally wrong on the mechanics of Ethiopic numbers as I have perceived them. Converting an Ethiopic string of numbers into a second system is trivial, converting from another system into Ethiopic I found requires a little more care.

Notation: A^B ==> B is the exponent of A A/B ==> integer division of A by B A*B ==> A multiplied by A A%B ==> A in the modulo class of B (A) ==> ``A'' is the Fidel equivalent [A](B) ==> A instances of (B), Example: [3](B) = (B)(B)(B)Lets take an arbitrary string of what we call Arabic numerals:

EeDdCcBbAaThe decimal expansion is the same in both systems, but to rewrite the string in Ethiopian numbers a delimiter of sorts appears:

(E*10)(e) + 10^8 + (D*10)(d) + 10^6 (C*10)(c) + 10^4 + (B*10)(b) + 10^2 + (A*10)(a)The delimiter that appears are the orders of 10 that must be inserted in the string as additional Ethiopic numerals. Observing that they are the exponents are all divisible by 2 we perform a simple shift of this index:

(E*10)(e) + 100^4 + (D*10)(d) + 100^3 (C*10)(c) + 100^2 + (B*10)(b) + 100^1 + (A*10)(a)This form is more insightful as it becomes apparent soon that the orders-of-100 delimiters are really sequences of the two Ethiopic numbers meto (100) and asr xi (10,000) -lets also abbreviate (10,000) with (10K).

The exponents ``i'' of 100^i then tells us how many (100) numbers and how many (10K) numbers are needed. It is also quick to see that we only need the number (100) when i is odd. We can take i-1 (or i alone when i is even) to tell us how many (10K) numerals to write. Our string is then:

(E*10)(e)(10K)(10K)(D*10)(d)(100)(10K)(C*10)(c)(10K)(B*10)(b)(100)(A*10)(a)The compacted formula for 100^i interpretation:

100^i = [i%2](100)[i/2](10K)An example I can verify is for a year such as 1988 which becomes:

1988 = (1*10)(9) + 100^1 + (8*10)(8) = (10)(9)(100)(80)(8)but this is a small number and again I truly don't know if dates are an exception or not. I would hope counting rules work independent of their application.