# 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:
limn→∞P(E|x1,x2,...,xn)→{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 proves that randomness is merely an illusion generated by excessive complexity, and the world is, in essence, strictly deterministic.
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# 2. The Neurophysics of Decision Making: The Vector Sum of Variables
## 2.1 The Brain as a Physical Computing System
Based on the aforementioned deterministic foundation, the human brain can be viewed as an extremely complex biophysical computer. Every "thought" or "decision" is a physical output after neurons process input signals.
The decision model can be formalized as a **Threshold Function**:
Action=H(N∑i=1wi(t)⋅xi(t)−θ)
Where $\mathcal{H}$ is the Heaviside step function:
* $x_i(t)$: **Input Variable Vector**. Includes external sensory data (advertisements, temperature) and internal physiological parameters (blood glucose, hormone levels).
* $w_i(t)$: **Weight Vector**. Determined by synaptic connection strength (representing memory, personality, values).
* $\theta$: **Action Potential Threshold**.
## 2.2 The Necessity of Dynamic Correction
Regarding the counterargument that "self-correction proves free will" (e.g., wanting to eat a hot dog but stopping upon thinking of a mortgage), on a physical level, this is merely the result of a variable $x_{new}$ (activation of mortgage memory) intervening in the calculation at moment $t+\Delta t$.
Originally $\sum < \theta$ (do not buy), with the input of desire variables it becomes $\sum > \theta$ (want to buy), and subsequently, the intervention of inhibitory variables makes $\sum < \theta$ (give up) again.
This entire oscillation process strictly follows electrochemical laws; there is no "soul" independent of physical laws manually intervening in the result.
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# 3. Psychological Manipulation and System Inertia
## 3.1 Principle of Variable Injection
Psychological manipulation is essentially an external actor attempting to forcibly insert a high-weight variable $x_{inj}$ (such as fear marketing, suggestion) into the target subject's variable set $X$ to change the sign of the sum $\sum$.
## 3.2 System Robustness: Inertia and Decision Recursion
**(1) Law of Large Numbers and the Denominator Effect:**
The primary reason why high-dimensional individuals (those difficult to control) are hard to influence by a single external variable lies in the fact that the "denominator" in their decision equation is large enough. According to the Law of Large Numbers, when the quantity of internal variables $N$ tends towards huge, the perturbation of the overall weighted average by a single external variable $x_{inj}$ is extremely diluted.
**(2) Origin of Long-term Variables: Physical Solidification of Past Decisions:**
These massive internal variables (principles, habits) are not created out of thin air; they are essentially the **recursive superposition of the results of countless past decisions**. This is a physical process of "solidification."
* **Case Analysis (Hot Dog Habit Loop):** Assume an individual decides to "buy a hot dog" at moment $t_0$. If environmental variables continue to support this decision at subsequent moments $t_1, t_2...t_n$, the brain's neural network will form strong connections following **Hebbian Theory**.
* **Formation of Inertia:** A decision that originally required complex computation collapses into a single high-weight variable $W_{habit}$. A person possessing more of such variables corresponds to a physical system with **huge mass and extremely high inertia**. As per Newton's Second Law ($F=ma$), mass is the measure of inertia. When the external world attempts to change their behavior ($F$), due to the massive weight of their decision history ($m$), the resulting acceleration of change ($a$) is negligible.
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# 4. The Revealer Hypothesis
## 4.1 The Posteriori Nature of Consciousness
Experiments on Readiness Potential in neuroscience confirm that the motor area of the cerebral cortex activates hundreds of milliseconds before the individual becomes conscious of "I want to do it."
This indicates: **Consciousness is not the Driver of the decision, but the Monitor of the decision.**
## 4.2 We Are the Revealers of Variables
Our subjective experience is actually the "reading" of a physical event that has already been computed. Every choice in life, at the moment of our birth (or even at the moment of the Big Bang), under the transmission of the causal chain, is destined as long as all internal and external variables are determined.
We are not "creating" the future in the present; we are "revealing," step by step along the timeline, the unique and inevitable result interwoven by countless variables.
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# 5. Conclusion
Determinism does not deny human agency but redefines the source of agency. Probability theory proves that when information tends to infinity, uncertainty tends to zero; this means the universe has no dice, only gears complex enough to be mistaken for dice.
Understanding our essence as "Variable Revealers" brings ultimate rationality and peace:
1. **Disenchantment:** Seeing through the facade of randomness and luck to look directly at the causal variables behind them.
2. **Optimization:** Since output is determined by input, our seemingly active pursuit of higher-quality variable inputs (knowledge, environment, thinking)—even this "intention to strive upwards" itself—is also the inevitable product of the superposition of countless past variables. Just as your reading of this paper at this moment is not a random coincidence, but the unique result to which infinite microscopic particle collisions and macroscopic causal chains have converged since the Big Bang; under the precise computation of the machine that is the brain, we await that optimized life path which has long been written, yet is waiting to be revealed.
### References
1. Laplace, P. S. (1814). *A Philosophical Essay on Probabilities*.
2. Shannon, C. E. (1948). "A Mathematical Theory of Communication". *Bell System Technical Journal*.
3. Hebb, D. O. (1949). *The Organization of Behavior*. (Neural Plasticity & Habits)
4. Libet, B., et al. (1983). "Time of conscious intention to act in relation to onset of cerebral activity". *Brain*.
5. Harris, S. (2012). *Free Will*. Free Press.