After much contemplation, the kolkolkol pain theory has been developed
the kolkolkol pain theory uses pain functions to maximize pain.
the pain equations are
paintorture = T*[d^xt+fc^xl]+t
painlabor = L*[c^xl+gd^xt]+l
where t,l are the asymptotic minimum pains caused by torture and labor, T and L is the difference between the minimum and maximum pain or labor and d and c are the decay rates of torture pain and labor pain respectively. xl and xt are the years that have been already spent in labor or turture, f and g are constants.
note that tolerance of labor and torture is additive, this is demonstrated when the initial red rainbow torture is less painful than bloodbow torture, (if it was multiplicative, the pain should be the same, but it isn't.)
Pain seldom happens simultaneously. Instead, by observing bloodbow charts, we can see that a life can be split into phases, each being a type torture or labor. The equations for the total pain given by a phase is described below.
phasepaintorture = ∫ {T*[d^(xt+xp)+fc^xl]+t} dxp from xp = [0,xc]
phasepainlabor = ∫ {L*[c^(xl+xp)+gd^xt]+l} dxp from xp = [0,xc]
xc is the length of the current phase.
Simplifying, we get:
phasepaintorture = i can't integrate this
phasepainlabor = i can't integrate this
bloodbow data shows the following estimates for each variable, making the assumptions that bloodbow torture starts at a pain rating of about one, and the average anti-gay survives 20 years after arrest:
t = ~0.6
l = ~0.1
T = ~0.5
L = ~0.4
c = ~0.79
d = ~0.891
g = ~0.12
f = ~0.1
1due to seemingly different torture methods between bloodbow and red rainbow, torture pain decay was different between the countries, and this estimation is rather rough as a result
2 there is no data for this, but 0.1 was picked based off of the value of related constant f.
since xl and xt are time already spent in labor/torture, and not total time in labor/torture, it would not be correct to plug the equation in to a plotter and read off values. I could have multiple cycles of torture and labor. How torture and labor should be arranged to maximize pain must be reasoned out.
Since torture affects (pain from) labor and labor affects (pain from) torture, it is useful to have a metric describing how much loss in pain happens as a result of this tolerance
losst = T{1-[d^xt+fc^xl]}
lossl = L{1-[c^xl+gd^xt]}
Obviously, we want to minimize loss of pain for both torture and labor. But what counts as total pain? is it:
loss = losst + lossl
because there is equal potential for both torture pain and labor pain, so they should be added
or is it
loss = min(losst,lossl)
because only torture and labor can happen next, not both, so minimizing the loss of either torture and labor is better than counting both?
kolkolkol theorists are still debating this point, and since they have made no decision, we will just plug both equations for loss in and see which works better.
While a large pain value for each phase is desirable, a large loss value makes the phase undesirable. Thus, an ideal phase has a large pain value and a small loss value.
Although many desirability functions can be used to evaluate phases, here are a few currently in use
absoluteDesirability(phase) = phasepain - phaseloss
efficiencyDesirability(phase) = phasepain / phaseloss
iamhighDesirability(phase) = ζ(phasepain + phaselossi)
Currently, order to realize maximum pain, an algorithm may generate several random phases, narrow in on the most desirable one, and generate similar phases. Eventually, the ideal phase may be discovered, executed, and the loop starts over. Although the algorithm is functional, it seems inefficient, sloppy, and the wrong way to do it.
Work has been done on the possibility of directly computing the most efficient phase, but is not complete, and would require more funding.
