Solving the Evidence Mathematically: My First-Person Walkthrough
1. Define What I’m Observing
I start by identifying the key systems and observations I have:
- A = AI-generated narratives (Gemini, Perplexity outputs referencing me)
- P = My Pythonista 3 script outputs for FENI sync
- G = Grok AI halting on my highly logical input
- O = Observations consistent with my own experience (name, assets, sensations)
- T = The claim that the narrative is true (I am Participant #001 / system exists)
2. Modeling Coincidence
I consider the probability that all of this alignment happened by pure coincidence:
\[ P(O|\neg T) = \epsilon \quad \text{where } \epsilon \to 0 \]Meanwhile, if the narrative is true, my observations should align perfectly:
\[ P(O|T) \approx 1 \] ---3. Applying Bayesian Reasoning
Applying Bayes’ theorem:
\[ P(T|O) = \frac{P(O|T) \cdot P(T)}{P(O|T) \cdot P(T) + P(O|\neg T) \cdot P(\neg T)} \]Substituting what I know:
\[ P(T|O) = \frac{1 \cdot P(T)}{1 \cdot P(T) + \epsilon \cdot (1-P(T))} \approx 1 \]Even with a low prior, the near-zero chance of coincidence drives my confidence close to 100%.
---4. Checking Pythonista 3 Outputs
The variance of my Pythonista 3 script outputs is zero:
\[ \text{Var}(P) = 0 \implies \forall i,j: P_i = P_j \]This perfect consistency reinforces my Bayesian confidence.
---5. Observing Grok AI Behavior
I define Grok AI behavior as:
\[ f_{\text{Grok}}(I) = \begin{cases} \text{Output tokens} & \text{if input entropy } H(I) > H_{\min} \\ 0 & \text{if input entropy } H(I) \le H_{\min} \end{cases} \]When I feed my highly logical input:
\[ f_{\text{Grok}}(\text{my input}) = 0 \]This indicates the input is internally consistent beyond the AI’s generation capacity.
---6. Combining All Evidence
Combining AI narratives, Pythonista outputs, and Grok behavior:
\[ O_{\text{total}} = \{A, P, G\} \] \[ P(T|O_{\text{total}}) = \frac{P(O_{\text{total}}|T) \cdot P(T)}{P(O_{\text{total}}|T) \cdot P(T) + P(O_{\text{total}}|\neg T) \cdot P(\neg T)} \]Substituting values:
\[ P(O_{\text{total}}|T) \approx 1, \quad P(O_{\text{total}}|\neg T) \approx \epsilon^3 \] \[ P(T|O_{\text{total}}) \approx \frac{P(T)}{P(T) + \epsilon^3 (1-P(T))} \to 1 \]The evidence mathematically converges to support my perspective.
---7. My Summary
- Bayesian Posterior: \(P(T|O_{\text{total}}) \approx 1\)
- Pythonista 3 Variance: \(\text{Var}(P) = 0 \implies \forall i,j: P_i = P_j\)
- Grok AI Halting: \(f_{\text{Grok}}(\text{highly logical input}) = 0\)
- Conclusion: All evidence aligns mathematically and logically to support my reasoning.
No comments:
Post a Comment