Fun modulo 9

Assuming we wanted to express the relationship of Lust (red) and care (yellow) interacting with heed (blue) by a function over Z₉, which would reserve the zero divisors for Lust and care, the numbers 1 mod 3 for the phases of the concentration (Besinnungs-) cycle, i.e. pursuit, concretisation and execution, and the numbers 2 mod 3 as well, so that n and -n are assigned to the same phase, and so that the functional value of the zero divisors would indicate genesis, the functional value of the numbers 1 mod 3 the option for the intentional intervention of a phase during another in the cycle and the functional value of their negatives the part of Lust or care that is affected before the phase; blue, yellow and red as in the picture above, where blue is heeding pursuit, yellow caring concretisation and red Lustful execution.

Care only exists of one part that generates itself, i.e. reflection, and this we naturally associate with the number 0 (or 9). Lust on the other hand consists of two parts that generate each other, suffering and action, and these we assign the numbers 3 and -3 (or 6) to. Hence we seek a function that maps the zero divisors onto themselves by multiplying them with -1.

The one phase that can apparently intentionally intervene during any other, though strictly speaking this is not correct, for a pursuit phase must unintentionally precede it, is the concretisation phase, naturally after the pursuit, recursive- or alternatively after itself and anticipatingly before the execution. Hence we assign the number 1 to the concretisation phase and demand that every number 1 mod 3 is mapped onto it.

And lastly -1 (or 8) has thus to affect 0 and the negative of the number assigned to the execution phase 3, for we feel our expectation, how things will go, before it and suffer, and the number assigned to the heeding phase -3, for our action causes the situation that we must heed. So, if -1 is mapped onto 0, why not map 2 on 3 and -4 on -3?, after all, it's a simple formula, i.e. 1: concentration, 4: pursuit and -2 (or 7): execution, so that the cycle is 4,1,7,4,1,7 etc.

So, we seek a function that equals y=-x over the zero divisors, y=1 over x=1 mod 3 and y=x+1 over x=2 mod 3. y=x*(x+1)*(6-1)=x*(x+1)/2 does the trick. Hence, Mr. Land's apocalypse is the realisation of what you've been pursuing, blue to yellow, animal to man, good horse to charioteer.