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**1** Consider a world `W`

where there are many `x`

s (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 `t`

if `max(M(x0,t), M(x1,t), M(x2,t), ... ,M(xi,t), ...) == M(x(i),t)`

.

Let's say,

(1) Each `x`

can utilise some strategy `S(x,M)`

to increase their `M`

value between `t`

and `t+1`

, i.e. `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)`

.

(3) `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 `S(x(j),M(x(j),t))`

. Therefore `x(i)`

and `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 `S(t)`

and `THRESH`

is some global threshold of wellness of all the people in the world.

(2) There will be a better ideal utopian world `S(t+1)`

, where `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)`

into `S(t+1)`

. Clearly, `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`

?

```
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)?
```

Then, `∀ 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].