Behavioral Prediction Model: Knowledge–Emotion–Confidence–Trust–Fatigue–Attention–Memory Load–Curiosity

@kungfufk

Sample for The Physics of Bounded Rationality:Why AI Needs a "Cognitive Mechanics" Engine(Virtual Intelligence)
STATUS: SAMPLE / ILLUSTRATIVE MODEL — NOT EMPIRICALLY VALIDATED
This model does not predict truth, belief, or what is correct. It predicts behavior — latency, hesitation, stability, degradation — following the reframing that this only claims to model observable outputs, not internal states as fact. That reframing is the reason this version is more testable than earlier ones: latency and mind-changing are measurable; "emotional energy" is not. Every physics borrow is still flagged as an Assumption. Free parameters ( $k_i$ , $\lambda_{ij}$ , $\beta$ , $\theta$ , $\gamma$ ) are unfit — they'd need calibration against real response-time and behavior data before any number here means anything quantitatively. Directional claims (does latency rise when load rises?) are at least checkable in principle.

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1. Variable roles (Assumption 0)

The eight inputs don't behave the same way, so they're split into three functional groups instead of being treated as eight identical oscillators:

Group	Traits	Role
Active / energy-contributing	Knowledge ( $K$ ), Emotion ( $Em$ ), Trust ( $Tr$ ), Attention ( $At$ ), Curiosity ( $Cu$ )	Behave like the trait-waves in the earlier model — they superpose and interfere to produce a composite "cognitive energy"
Capacity-draining	Fatigue ( $Fa$ ), Memory Load ( $ML$ )	Don't add engagement energy — they shrink the ceiling the active traits are operating under
Calibration / output	Confidence ( $Cf$ )	Kept as a real input (self-reported/observed amplitude) and compared against a value the model predicts from the other traits — the gap between the two is itself a useful signal

Assumption 0: This split is a modeling choice, not a fact about cognition. Fatigue and Memory Load could instead be modeled as active traits with negative coupling; Confidence could be treated as fully independent. This version was chosen because it matches the behavior of your own worked examples (Fatigue/overload degrading capacity; Confidence as an outcome of Knowledge/Emotion/Capacity).

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2. Assumptions

• Assumption 1 — Wave representation. Each active trait is approximated as $\Psi_i(t) = A_i(t)\sin(\omega t + \phi_i)$ , with amplitude $A_i(t)$ varying slowly relative to $\omega$ (a "slowly-varying envelope" borrow from signal processing/AM modulation). No evidence these traits actually oscillate.
• Assumption 2 — Shared frequency. All active traits assumed to share $\omega$ within one exchange, for tractability only.
• Assumption 3 — Energy $\propto$ amplitude $^2$ . Same simple-harmonic-motion borrow as before.
• Assumption 4 — Fatigue/Memory Load drain capacity linearly. $\gamma_{Fa}, \gamma_{ML}$ are free "drain rate" constants with no measured value.
• Assumption 5 — Confidence has a predictable component. Modeled as a function of Knowledge, Emotion, and spare capacity, matching your stated example directly.
• Assumption 6 — Incoming information is itself a wave. Represented as $\Phi_{info}(t) = A_{info}\sin(\omega t + \phi_{info})$ hitting the Trust wave — a direct continuation of the interference idea from the original framework.
• Assumption 7 — All thresholds ( $\beta, \theta, N_0$ ) are free parameters. Chosen for plausible direction of effect, not fit to data.

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3. Derivation

Step 1 — Active traits as waves (Assumption 1, 2)

$$\Psi_i(t) = A_i(t)\sin(\omega t + \phi_i), \qquad i \in {K, Em, Tr, At, Cu}$$

Step 2 — Composite active energy (same method as the EEAH model: superpose, square, time-average)

$$E_{cognitive}(t) = \frac{1}{2}\sum_i k_i A_i(t)^2 \;+\; \sum_{i<j} \lambda_{ij}\, A_i(t) A_j(t)\cos(\phi_i-\phi_j), \qquad i,j \in {K, Em, Tr, At, Cu}$$

Step 3 — Dynamic capacity ceiling (Assumption 4)

$$C(t) = C_0 - \gamma_{Fa} A_{Fa}(t) - \gamma_{ML} A_{ML}(t)$$

Fatigue and Memory Load don't add to $E_{cognitive}$ — they lower the ceiling everything else has to operate under.

Step 4 — Load ratio

$$R(t) = \frac{E_{cognitive}(t)}{C(t)}$$

This single number is what most of the seven predictions below are built from: $R \ll 1$ means spare capacity, $R \approx 1$ is the bounded-rationality regime, $R > 1$ is forced degradation.

Step 5 — Interference from incoming information (Assumption 6)

$$D(t) = A_{info}\cdot A_{Tr}(t)\cdot\bigl[1-\cos(\phi_{info}-\phi_{Tr})\bigr]$$

Small disagreement ( $\phi_{info}\approx\phi_{Tr}$ ) $\Rightarrow \cos\approx1 \Rightarrow D\approx0$ . Direct contradiction ( $\phi_{info}\approx\phi_{Tr}+\pi$ ) $\Rightarrow \cos\approx-1 \Rightarrow D\approx 2A_{info}A_{Tr}$ , maximal disturbance.

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4. The seven predictions

1. Decision latency (reasoning cycles)

$$N_{cycles}(t) \approx \frac{N_0\,(1+R(t))^{\beta}}{A_K(t)}$$

Carries over $T \propto 1/K$ from the original framework, now compounded by load. Rising $R(t)$ (more load, less spare capacity) increases the number of cycles needed; more knowledge reduces it.

2. Confidence — predicted vs. self-reported

Predicted confidence from Knowledge, Emotion, and spare capacity, floored at zero:

$$Cf_{predicted}(t) = \frac{A_K(t)}{A_K(t)+A_{Em}(t)} \cdot \max\bigl(0,\ 1-R(t)\bigr)$$

This reproduces your example directly: high $K$ , low $Em$ , low $R(t)$ (high spare capacity) $\Rightarrow Cf_{predicted}\to1$ . Low $K$ , high $Em$ $\Rightarrow Cf_{predicted}\to0$ (hesitation, heuristics).

Calibration gap (a genuinely new derived quantity, not just a restatement of the input):

$\Delta Cf(t) = A_{Cf}(t) - Cf_{predicted}(t)$

$\Delta Cf > 0$ : expressed confidence exceeds what Knowledge/Emotion/load would justify (overconfidence). $\Delta Cf < 0$ : underconfidence — the person has grounds for more certainty than they're showing.

3. Emotional stability under incoming information

Directly from Step 5's disturbance $D(t)$ :

• Small disagreement $\rightarrow D\approx0 \rightarrow$ minor disturbance
• Huge contradiction $\rightarrow D\approx 2A_{info}A_{Tr} \rightarrow$ large interference

This is the same constructive/destructive interference idea from the original framework's Section 2, now given an actual formula instead of just a description.

4. Cognitive overload

Directly from Step 4: when $R(t) > 1$ (i.e. $E_{cognitive} > C$ ), predicted symptoms are qualitative, not separately derived — slower thinking (rising $N_{cycles}$ from #1), more heuristic shortcuts, degraded encoding (which would show up as rising $A_{ML}$ , a feedback loop back into Step 3), simplified problem framing.

5. Attention switching

$$\frac{dA_{Em}}{dt} > 0 \ \text{ and } \ \frac{dA_{At}}{dt} < 0 \ \Rightarrow \ \text{reasoning quality falls}$$

A reasoning-quality proxy, built the same way as the confidence ratio in #2:

$$Q(t) = \frac{A_{At}(t)}{A_{At}(t) + A_{Em}(t)}$$

$Q$ falls as emotion rises relative to attention.

6. Learning speed

This isn't a new formula — it's a direct corollary of #1: as $A_K(t)$ rises over time, $N_{cycles}(t)$ falls, matching $T\propto 1/K$ . Internal consistency, not new machinery.

7. Information acceptance — contradiction tolerance

Reframes "will they believe it" as "how much contradiction can the current state absorb," using Step 5's disturbance formula solved for a tolerance threshold:

$$A_{info}^{tolerable}(t) \approx \frac{\theta(t)\cdot C(t)}{A_{Tr}(t)\cdot\bigl[1-\cos(\phi_{info}-\phi_{Tr})\bigr]}$$

Higher trust and more spare capacity raise the tolerable contradiction amplitude. Curiosity's role: rather than sitting unused, Curiosity is assumed to raise the disruption threshold itself — a curious state treats contradiction as interesting rather than destabilizing:

$$\theta(t) = \theta_0 + \delta \cdot A_{Cu}(t)$$

( $\theta_0$ , $\delta$ free parameters — Assumption 7.) Note: at $\phi_{info}=\phi_{Tr}$ exactly (perfect agreement) the denominator is zero and the expression is undefined — the trivial case where there's nothing to tolerate.

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5. Worked toy example (synthetic numbers, illustration only)

$A_K=0.7,\ A_{Em}=0.3,\ A_{Fa}=0.6,\ A_{ML}=0.5,\ C_0=1.5,\ \gamma_{Fa}=\gamma_{ML}=0.5$

Capacity: $C = 1.5 - 0.5(0.6) - 0.5(0.5) = 1.5 - 0.3 - 0.25 = 0.95$

Suppose $E_{cognitive}=0.8$ at this moment $\Rightarrow R = 0.8/0.95 \approx 0.84$ (near capacity, not yet over).

Predicted confidence: $Cf_{predicted} = \frac{0.7}{0.7+0.3}\times(1-0.84) = 0.7\times0.16 \approx 0.11$ — low, despite decent knowledge, because the system is running near its (fatigue/memory-load-reduced) ceiling. This is the model's way of saying: knowledge alone doesn't guarantee confidence if capacity is already spent elsewhere.

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6. Limitations

• Same free-parameter problem as before. $k_i, \lambda_{ij}, \gamma_{Fa}, \gamma_{ML}, \beta, \theta_0, \delta$ are all unfit. Until they're calibrated against real latency/behavior data, only the direction of predictions is meaningful, not the magnitude.
• The active/drain/output split (Assumption 0) is a design choice, not a discovery. A different, equally defensible split could be made.
• Behavior $\neq$ ground truth, and that's the point — but it's also a limit. This model can, in principle, predict that someone hesitates or takes longer; it cannot say whether their eventual answer is correct.
• The interference formulas (Step 5, Prediction 7) inherit the same shared-frequency and phase assumptions flagged in the earlier model — still the weakest structural assumption in the whole framework.
• Nothing here has been tested against real response-time or behavioral data. The toy example in Section 5 is illustrative arithmetic, not a finding.

This is a sample model of what a testable version of the framework could look like — the next real step is picking one prediction (decision latency is the easiest to measure) and checking whether real response-time data moves in the direction this model predicts.