SAE-1.5 · Plain-English first
A path, a rut, and a helping hand
A simple story can explain the model before we introduce a single differential equation. The story is an analogy—not a claim that spiritual awakening, addiction or human consciousness has been mathematically measured.
1. A familiar pattern develops
Imagine a traveler walking along the same muddy path. Each repetition wears a rut. In the model, K_base represents accumulated conditioning or entanglement. It is not a diagnosis, a measure of spiritual worth, or a literal brain measurement.
The next stage can happen gradually, abruptly, or not at all in real life; the numerical model captures only selected possibilities.
2. Something happens today
A difficult conversation or a tempting situation may activate an old pattern. The temporary response is represented separately from the background rut. Having a feeling or craving is not automatically an ethical failure.
The next stage can happen gradually, abruptly, or not at all in real life; the numerical model captures only selected possibilities.
3. Effort can change the path
Through ordinary practice, considered choices, reflection and nonattachment, a person may gradually develop more flexible responses. The model proposes this as one clearing route; the specific rate has not been demonstrated in people.
The next stage can happen gradually, abruptly, or not at all in real life; the numerical model captures only selected possibilities.
4. Sometimes a hand is needed before effort is possible
A person can be overwhelmed, low on energy, or unable to begin practicing consistently. Effective help, safer circumstances or supportive relationships may offer an independent recovery route. We call its modeled clearing influence H. It is the effectiveness of a restorative process in a thought experiment, not a count of helpers or a score of someone's character.
The next stage can happen gradually, abruptly, or not at all in real life; the numerical model captures only selected possibilities.
5. Recovery is possible, never guaranteed
The same environment may continue reinforcing old patterns. A helping influence can make the rut shallower only when the combined clearing effect exceeds continuing reinforcement. A setback does not erase personal dignity, and the curve is not a prediction of recovery from addiction.
Only then, the mathematics
Our present-state proposal asks how much of a hypothesized obstruction remains accessible at a particular moment:
A(t) = C × [1 − K_effective(t)]
The background state develops as a balance between factors that deepen the rut and factors that help clear it:
Change in K = reinforcement − clearing
dK_base/dt = u(1−K_base) − vK_base
u = αM + γD max(−q,0)
v = βD max(q,0) + H
H≥0 is an effective independent recovery-support rate; it does not require positive q or D. Whether K actually falls depends on the balance. When H=0, the earlier mathematical model is unchanged. All rates are hypothetical and uncalibrated.
Where is Belief?
Belief or Śraddhā is not used as a direct multiplier of this moment's A. The current Option B hypothesis is that truth orientation and voluntary commitment may support cultivated integrity over time through practice and choices. That delayed relationship has not been assigned a numerical law or established scientifically. A person does not need religious faith to possess consciousness or dignity.