## Thought Experiments

Posted on , 3 min read

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].