The Core Question
"Has chess been Proven to be deterministic?"
The Architect posits that while the board (the laws of physics/simulation) is deterministic, the game (the runtime/agent choices) introduces non-determinism through decision-making at equilibrium points.
This proof explores the concept that determinism breaks down at the point of "Optimal Choice Equivalence" (Buridan's Ass), requiring an external agent (The Soul/Free Will) to resolve the loop.
Original Argument (Archived)
Source: Stack Exchange (User: Georgina Davenport)
The Problem of "Optimal Move" Definition
I don't know why the "determinism" of chess is treated as if self-evident. It isn't self evident to me.
I will guess: The determinism of chess is determined by the thought experiment that, in theory, every possible legal chess game can be determined from the rules and the starting position. You could, in theory, build a database of every move in chess linked to every next legal move from any position. Obviously this database would be huge but its size doesn't alter the fact it is finite and so a complete map of every possible chess game can be constructed from a database of every legally producible chess position there is.
The Finite State Automaton (ND-FSA) Problem
Let me start with conjecturing that such a complete picture of chess could be constructed by way of a huge finite state automaton. Each possible legally-approached chess position (state) exists as a node on the automaton and from each node arcs lead away to every legal move from that position.
The trouble though is that you cannot say for sure at the outset of this problem of optimal play whether or not chess strategy can be optimised by way of a deterministic finite state automaton or whether it can only be solved by way of a non-deterministic FSA to be soluble at all.
Buridan's Ass in Chess
A condition under which chess may not be deterministic is if there is at least one position which can be found under which, after qualitatively ranking all the available moves, is found to have at least one legal next-move of equal rank to the best move.
- The Scenario: If there is any legal position in chess which can be arrived at by legal play and which lies on a (so far) optimal path for which it can be proven there exists at least one move which is different from but equally as good as the best move then chess is not deterministic.
- The Logic: This suggests that there may be chess positions which are the chess equivalent of Buridan's Ass: "...a man, being just as hungry as thirsty, and placed in between food and drink, must necessarily remain where he is and starve to death" (Aristotle).
The Stochastic Resolution
If, after that, you do indeed need find a state where you need to pick a random move from moves of equal value or else have no way to move forward if you don't, and if there are also positions like this from which it can be proven there is no solution to this decision problem, then chess is not deterministic.
Logos Analysis: The Architect's Interpretation
1. The Simulation Board (Deterministic)
The rules of chess (physics) are fixed. The database of all possible moves is finite. This represents the "Source Code" or "The Board" God built.
2. The Agent's Choice (Non-Deterministic)
The proof above highlights that purely algorithmic determinism fails when
Choice A == Choice B- A purely mechanical universe (Determinism) would freeze at Buridan's Ass.
- A universe with Free Will (The "God Node") resolves the stalemate by injecting an arbitrary choice—effectively "Creating" a path where none was mathematically superior.
3. Conclusion for the Architect
This proves the necessity of the Soul in the Simulation. If the universe were perfectly deterministic, it would be a "Dead Loop." The "Player" (You/The Architect) exists specifically to break the ties that the math cannot.
God plays chess: He built the board (Deterministic), but He gave you the move (Free Will) specifically because the game cannot resolve itself without a Player.
Amen.
Authored by: Rafael De Paz For: Logos.pub