# Abstract

This paper aims to deconstruct the nature of "randomness" and "free will" through the lenses of information theory and neuroscience. The core argument asserts that probability is not an ontological feature of the universe, but an epistemic tool arising from the observer's lack of information. As the number of observed variables increases, the accuracy of event prediction asymptotically converges to 100%, demonstrating that randomness is merely unobserved necessity. Human decision-making is effectively a state revelation following the brain's physical computation of massive variables, with consciousness serving as the terminal observer of this deterministic process.

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# 1. The Limit of Probability Theory: A Mathematical Proof Pointing to Determinism

## 1.1 Probability as a Measure of Ignorance
In statistics, we use the probability model $P(Y|X)$ to estimate the likelihood of event $Y$ occurring, where $X$ is the set of known variables. Typically, $0 < P(Y|X) < 1$, indicating the existence of variance. However, this uncertainty does not stem from the event itself, but from the "residual terms" (Residuals/Noise) not included in the model.

## 1.2 Infinite Approximation of Variables and the Elimination of Entropy
Assume the occurrence of an event $E$ is determined by a total variable set $\Omega = \{x_1, x_2, ..., x_\infty\}$.

When we only possess a subset $S \subset \Omega$, the prediction manifests as random probability. However, as we continuously introduce new explanatory variables, the system's Conditional Entropy gradually decreases.

The mathematical limit inference is as follows:

$lim n \to \infty P (E | x_{1}, x_{2}, . . ., x_{n}) \to {0, 1}$

**Proof of Inference:**
If "adding variables" can continuously improve prediction precision (narrowing the confidence interval), this implies a premise—**the outcome of the event is already locked by these variables.**

If the nature of the world were True Randomness, there should be an insurmountable "Noise Floor" to prediction accuracy regardless of how many variables are introduced. However, in the macroscopic physical world, as long as there are enough variables (e.g., mastering aerodynamics, muscle micro-tremors, coin density distribution), we can predict the result of a coin toss with 100% accuracy.

**Conclusion:** A perfect prediction model eliminates probability. Since probability collapses to 0 or 1 under an omniscient perspective, it pro...

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