Read the equation
This score depends only on how much the Φ samples vary within the window. Constant samples always give R=1, whether their level is high or low, and permuting their time order leaves R unchanged. Since Φ lies in [0,1], population variance is at most 1/4 and this formula requires R≥0.8; the manuscript’s baseline near 0.25 cannot come from this displayed formula under those assumptions.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| R_T | Reciprocal variance score ending at time T |
| Φ_t | Unity score at sample t |
| w | Window offset; inclusive T−w through T contains w+1 values |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
With a sample-variance convention the exact lower bound is 1/[1+m/(4(m−1))] for m samples, still near 0.8 for long windows.
A temporal synchrony interpretation needs more than variance alone.
Original context
Read the surrounding source passage
\begin{definition}[Resonance]
For consciousness time series $\{\Phi_t\}_{t=1}^T$, resonance at time $T$ is:
\begin{equation}
R_T = \frac{1}{1 + \text{Var}(\{\Phi_t\}_{t=T-w}^T)}
\end{equation}
where $w$ is the window size (typically 1000 ticks).
\end{definition}
Resonance is high when consciousness maintains stable values (low variance) and low when consciousness fluctuates. We establish empirical thresholds:
\begin{itemize}Exact original notation
R_T = \frac{1}{1 + \text{Var}(\{\Phi_t\}_{t=T-w}^T)}