MeSanatan · A research journey, not a finished discovery
From the Gītā to an Equation
How a spiritual question became a mathematical hypothesis, why the arithmetic changed, what the synthetic tests showed, and what science still needs to establish.
Eight chapters · explain first, inspect the mathematics second
How we arrived here
Each step shows the question, an example, what the philosophical references contributed, our mathematical choice and the limitation. This is a transparent reconstruction of the model's development, not a claim that each formula follows deductively from scripture.
The question before the formula
Why can our experience of clarity change?
A person may understand what matters, yet get caught in anger, comparison, fear or attachment. That was the motivating question: could we describe changing patterns of identification without claiming Consciousness itself changes? This begins with human experience and a philosophical distinction, not a measured dataset.
What inspired this?
Advaita distinguishes the changeless witness from the changing mind. That interpretation motivates keeping C fixed; different Sanātana schools do not share exactly the same metaphysics.
Show the mathematics and why we chose it
C = 1 (a philosophical normalization, not a measured constant)
Start with a reference that does not fluctuate, while treating any measurable mental-state variable as a different construct.
Evidence status: Metaphysical premise; not empirically demonstrated.
First subtraction: what obstructs?
What if the mind's entanglement limits modeled accessibility?
Imagine someone hearing criticism. The criticism is an event; being unable to disengage from the story about it is a possible obstruction. We introduced K as a provisional representation of that kind of entanglement—not as a score for sadness or a judgment of character.
What inspired this?
Bhagavad Gītā 2.62–63 describes a sequence involving attachment and impaired discernment. Yoga Sūtras 2.3–2.6 present avidyā as the field for related kleśas. Neither text gives us a numerical K.
Show the mathematics and why we chose it
A(t) = C × [1 − K(t)]
Subtraction is the simplest bounded candidate once K lies between 0 and 1. This mapping is chosen, not derived uniquely from scripture.
Evidence status: Mathematical hypothesis; no validated scale for A or K.
We tried addition—and found problems
Could Purity and Shakti simply increase Awareness?
The older SAE-1.4 expression added positive terms for Purity and Shakti inside a bracket, multiplied by Belief and included a Grace residual. We wanted to reflect several influences, but the algebra could exceed our intended range and it was difficult to separate terms from one another.
What inspired this?
References to śraddhā, discernment and disciplined action motivated the categories. Their numerical addition and multiplication were the project's engineering proposals, not teachings quoted from the Gītā.
Show the mathematics and why we chose it
Historical SAE-1.4: Awareness_raw = B × [C − K + P + S] + ε
An additive model is easy to propose, but its weights, boundaries and independent meaning must be justified. Our historical fixed form did not survive its corrected synthetic holdout.
Evidence status: Superseded historical model. Fixed synthetic temporal R² = −3.283. Earlier R² = 0.896 was invalidated by generator-only information leakage.
Multiplication moved to an interaction
Could discernment change how capacity is used?
Think of a highly skilled musician. Their learned skill may remain after an unkind decision. Skill and ethical orientation are not the same thing. We therefore moved P and S out of the direct addition to A and considered their interaction in the obstruction response.
What inspired this?
Gītā 18.26 and 18.30 distinguish qualities of action and discernment; they do not prescribe a signed product. The question of sincere intention with limited capability remains unresolved.
Show the mathematics and why we chose it
q(t) = P_effective(t) × S_effective(t)
Multiplication is a provisional interaction rule: available capacity may change the effect of present alignment. A different interaction or independent P contribution could be more defensible.
Evidence status: Bounded computational candidate, not an observed causal law.
A moment is not a lifetime
How do we distinguish a trigger from a persistent pattern?
A sudden argument can temporarily activate an old habit; the habit itself may persist long after that conversation ends. So we separated today's event response from background conditioning, rather than counting the same reaction twice.
What inspired this?
Practice and recurring patterns are topics of contemplative traditions. The particular event equation is a new modeling convenience, not a scriptural derivation.
Show the mathematics and why we chose it
e = L × T; R = e[1 − η max(q,0)] + η max(−q,0)e(1−e); K_effective = K_base + (1−K_base)R
The one-trigger closure combines activation, alignment and remaining headroom while keeping modeled K within 0–1 for declared ranges. Overlapping simultaneous triggers have not been specified.
Evidence status: One-trigger structural bounds checked; no independent human identification of these variables.
A differential equation enters
How could background conditioning change across time?
One action rarely explains a long-standing habit. We introduced a separate equation to contrast accumulating reinforcement with gradual clearing. An exact time-step calculation makes the hypothetical trajectory inspectable without calling the steps days or years.
What inspired this?
Gītā 6.26 and 6.35 discuss returning the wandering mind and practice with dispassion. That motivates inquiry into change, but not the rates or functional form.
Show the mathematics and why we chose it
dK_base/dt = u(1−K_base) − vK_base
This is a bounded stock-and-flow model. The signs and rate choices are hypotheses, not demonstrated psychological dynamics.
Evidence status: Structural dynamics only; coefficients and time units uncalibrated.
An external critique changed Belief
Should zero Belief force zero modeled A?
Claude and Gemini challenged a direct B gate: the working candidate could make A equal zero whenever either Belief component was zero. We agreed that religious conviction is not required for human awareness and that conviction alone does not guarantee integrity.
What inspired this?
Śraddhā may support sincere inquiry and commitment, but the traditions do not justify assigning a universal numerical consciousness gate.
Show the mathematics and why we chose it
Retired: A = C × min(B1,B2) × (1−K). Current: A = C × (1−K). Proposed: P_cultivated = f(B1,B2,practice,choices,context)
The current A no longer directly depends on B. The proposed B-to-P developmental relation has no numerical coefficients or empirical evidence and is not calculated by the simulator.
Evidence status: Direct zero-B gate resolved algebraically. Belief-to-P mechanism remains entirely open.
Addiction recovery exposed a missing route
Can change begin before self-control becomes strong?
A person experiencing addiction may benefit from treatment, supportive relationships or safer circumstances before they can sustain deliberate practice. We should not confuse medical symptoms or limited capacity with moral failure. This example revealed that the first model allowed clearing only under constructive q and practice.
What inspired this?
Compassion, guidance and disciplined practice motivate questions about recovery, but addiction treatment cannot be reduced to a spiritual score; H is not Divine Grace.
Show the mathematics and why we chose it
u = αM + γD max(−q,0); v = βD max(q,0) + H, with H ≥ 0
H is an independent effective clearing-rate term. It permits hypothetical recovery at q≤0 and D=0; the net K falls only if vK exceeds u(1−K). No particular treatment effect is claimed.
Evidence status: Structural extension for testing. H is not a calibrated clinical variable.
Unsolved · visible by design
What we still cannot explain or prove
These are research gaps, not hidden disclaimers. Completing a mathematical simulation is not equivalent to explaining a person.
What exactly is A?
No validated measurement
We distinguish constant philosophical C from a proposed accessibility index, but no independent outcome instrument proves that A means what we intend.
What do P, S, B and K measure?
Operationalization incomplete
Measures must be specified independently and not reconstructed from the equation's desired output.
Does Belief help develop Purity?
No causal or numerical model
B1/B2 are retained as conceptual influences through choices and practice. No approved B-to-P update or human evidence exists.
Is P × S the right interaction?
Unresolved conceptual objection
Sincere intention with low available capability may not be represented fairly. Simpler and competing forms require comparison.
Does H represent recovery?
No human calibration
H is an independent effective rate in thought experiments, not a medical score, treatment guarantee or measurable form of Grace.
How do multiple triggers interact?
Unspecified
The present closure models one activated obstruction class; real overlapping events are not modeled.
Can the model outperform simpler explanations?
Not shown
Corrected SAE-1.4 synthetic regressions do not validate SAE-1.5. Independent psychological baselines and prospective, held-out data are required.
Is the scriptural mapping faithful?
Independent primary-text review needed
Verses inspire hypotheses but do not entail these numerical rules. Differences among Advaita, Yoga, Bhakti and Karma Yoga should remain visible.
Can outsiders reproduce everything?
Partial
Source checks and corrected historical analysis exist, but the private repository and incomplete public packages limit independent replication.
Are there real human observations?
No controlled human SAE data
No validated human SAE-1.5 dataset, coefficients or study conclusions exist. A consent-based and independently reviewed research protocol is future work.
An invitation, not a claim of validation
Help us determine what survives scientific testing
We are bringing this provisional framework to the attention of researchers and potential collaborators through possible ISCR Kyoto 2027 and ASSC Beijing 2027 submissions and other academic outreach. Neither meeting has reviewed, endorsed or accepted SAE-1.5. Our goal is critical discussion, operational definitions, independently designed human research and rigorous opportunities to falsify the hypothesis.
A useful outcome may be confirmation of a limited relationship, substantial revision—or rejection of the model.
Contemplative and philosophy scholars
Challenge interpretations, metaphysical distinctions, and whether the constructs fit traditions without forcing agreement.
Statisticians and mathematical modelers
Audit the bounded functions, alternative rate laws, identifiability, uncertainty and reproducibility.
Cognitive and behavioral researchers
Help define independent measurements, appropriate comparisons, preregistration, and ethical prospective studies.
The author is an independent engineer and devotee, not a Sanskrit specialist or clinical researcher. AI tools contributed extensively to research support, coding, drafting and critical review. Independent scholarly and human empirical validation remain outstanding.