1 Consider a world
W where there are many
xs (such that
x ∈ X). In this experiment, we define the winner of the game as having the maximum
M value (think of it to stand for "money", perhaps), i.e. more formally,
x(i) is the winner at some time
max(M(x0,t), M(x1,t), M(x2,t), ... ,M(xi,t), ...) == M(x(i),t).
x can utilise some strategy
S(x,M) to increase their
M value between
M(x,t+1) = S(x,M(x,t)) such that
M(x,t+1) > M(x,t).
(2) Since this is an unfair experiment, each
x has a different initial
M value, i.e.
M(x=x(i),t=0) != M(x=x(j),t=0). In some extreme cases there could, of course, be a very large difference,
M(x=x(k),t=0) >>> M(x=x(q),t=0).
x=x(i)'s strategy function
S(x(i),M(x(i),t)) at some time
t may or may not have adverserial affect on another
x=x(j)'s strategy function
x(j) must know that their strategies can adverserially affect each other to one's benefit and the other's decline.
The question then that this thought experiment proposes is this -- is only the knowledge of the above three statements enough to win the game in world
W (i.e. to pick the best strategy
S in each epoch t, t+1, t+2 ...)?
2 A standard narrative of the utopians can be somewhat formally deduced as such:
(1) There exists a current state of the world, say,
S(t), with the life of all people being sub-optimal, say,
avg(P(t)) <<< THRESH; where
P(t) is the wellness of people in
THRESH is some global threshold of wellness of all the people in the world.
(2) There will be a better ideal utopian world
P(t+1) >= THRESH or ideally,
P(t+1) >>> THRESH.
Given the above two statements as the axiomatic statements of the utopians, the missing element seems to be an understanding of the nature of the function that transforms
S(t+1) is dependant on
S(t)? And clearly we must need multiple iterations
t, t+1, t+2,... t + n until really
S(t+n) > S(t); because it might be impossible that one epoch yields a better
S(t+1) = transform_world(current_state = S(t)) def transform_world(current_state: S) -> S: # what happens here? # does this have side effects? # how does it affect P(t)?
∀ p ∈ P, what will
p(t+1) be? The question of course is; what is acceptable? Must it be that
p(t+1) > p(t) ∀ p ∈ P? or is it good enough that for
i ∈ P and
j ∈ P,
j(t+1) >>> i(t+1), where
len(i) >>> len(j), however of course satisfying the utopian condition of
P(t+1) = i(t+1) + j(t+1) >>> THRESH >>> P(t)?
If you know of any literature that extensively talks about the algorithm of the tranformation function itself, i.e. the actual inner details of
transform_world() and the resulting
S in each iteration than the usual ones which usually state that
S(t) is bad, but
S(t+1) can be better immediately, or if you wish to contribute to develop the above two thought experiments further, write to [email protected].