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Tomabechi theory & Buddhist teachings

How can Tomabechi theory help us read Buddhist teachings?

When a proposal is rejected, what happened, how did you interpret it, and what will you do next? Use Tomabechi’s mathematical model and Buddhist teachings to separate these questions, then turn belief, effort, attention, concentration and judgment into observations you can record.

For readers curious about the relationship between Tomabechi theory and Buddhism, and how to examine their own practice. No knowledge of mathematical proofs is assumed.

About 25 minutes · Updated 5 October 2026

The focus is the mathematical interpretation of Buddhism in Tomabechi’s Four Dharma Seals paper, published in July 2026. Source-based explanation leads into this article’s own observational proposal.

Check the logic of an explanation, its fit with reality and changes in practice using the evidence appropriate to each question.

01

A judgment of a proposal is not a judgment of a whole person

Imagine a proposal rejected with the comment “The cost estimate is incomplete.” This fictional case runs through the article. The rejection and the actual comment are observable; “I have no value” adds an interpretation.

Separating the interpretation need not immediately remove disappointment. It does distinguish improving the estimate from examining a judgment about your entire worth. Whether the assessment was fair is another question to check.

The five aggregates—form, feeling, perception, formations and consciousness—analyse experience. SN 22.1 links identifying them as “me” or “mine” with distress when they change. We use this as a lens on treating one assessment as a judgment of the whole self. [S2]

SN 36.6 distinguishes bodily pain from additional mental distress. It offers a reference for separating an event from our response; the proposal case is our application, not a case from that discourse. [S3]

02

What does Tomabechi’s model try to explain?

The Four Dharma Seals paper mathematically represents changing states, evaluations of cost and choices of action, then discusses correspondences with Buddhist teachings. Check both the mathematical objects and the meanings assigned to them. [S1]

The following distinctions matter because each calls for a different kind of evidence.

LayerWhat to check
Buddhist textWhat is taught in this context?
Mathematical modelWhich aspect is represented by which variable?
Conditional theoremWhat follows if the assumptions hold?
Empirical scienceDo measurements support its predictions?

“A change in interpretation reduces suffering” could report a teaching, a model result or an experimental finding. Identify who showed what, under which conditions, before deciding how far the claim reaches.

03

Read state, evaluation and policy through one example

Place three model terms beside the proposal case. The final column is our explanatory illustration, not a measurement procedure specified by Tomabechi.

TermMeaningQuestion in the example
State xHow the system is at a given timeTension, thoughts and readiness to reply
Evaluation VWhat counts as a costWhether to measure distress, missing information or revision effort
Policy πHow actions are selected from statesObject, ask about requirements or revise the estimate

This separates becoming calm from getting a proposal accepted. To apply a model, one must additionally specify how states and evaluations are measured.

Now test one assumption. If every method has a positive cost, must the best attainable cost also be positive? Our teaching example assigns method n the cost 1/n. Compare a restricted choice with an unlimited set using the two buttons.

The distinction concerns theorem 24’s assumption that an optimal policy exists. Positive values may approach zero without attaining it. This is a mathematical illustration, not a measurement of human suffering. [S1 §13]

Optional: formulas and technical terms

TCZ uses the reachability and evaluation conditions defined in that edition. Abstraction is an order of inclusion. LUB, the least upper bound enclosing several concepts, is not their average. Self, Ego and TCZ are different types: operator, policy and set. [S1 §2]

Theorem 24 minimises discounted future nonnegative evaluations. Here ρ is a positive discount rate, a an abstraction level and T the starting time. [S1 §13]

The theorem also assumes measurable evaluation and at least one finite-cost policy.

The zero-impossibility condition applies below the highest abstraction level. “Almost everywhere” allows exceptions only on a set of times of measure zero.

J* = minπ ∫[T,∞) exp(−ρ(t−T)) Vₐ(xπ(t),t) dt

04

Compare the four seal names with their mathematical scope

The Four Dharma Seals paper associates the seals with theorems 23–26. Buddhist terms are interpretive names for mathematical structures; the table points to conditions in the published version. [S1 §§12–15]

Interpretive nameConditions and scope
23 ImpermanenceChange in condition-dependent phenomena. The mathematical question concerns recurrence of a complete state, under stated conditions.
24 SufferingCan satisfaction be sustained? Theorem 24 concerns a positive cost remaining after optimization.
25 Non-selfIs there a fixed independent essence? Distinguish that claim from denying a functioning self.
26 QuiescenceCompare the quieting of suffering with mathematical stability. Model stability and actual liberation need separate checks.

Matching a model’s definitions to Buddhist usage is a separate comparison. Naming the greatest abstraction level “emptiness” does not make that definition the shared meaning of emptiness in every school.

Optional: formulas and technical terms

23 Impermanence: Non-recurrence of a complete state needs conditions including persistent strict dissipation. It does not mean every observable changes at every instant.

24 Suffering: Assumes permanent zero is impossible and an optimal policy exists. It does not mean constant pain or a uniform positive lower bound for all states.

25 Non-self: Uses history sensitivity and functional completeness, among other conditions. Distinguish a functional self from an independent fixed essence.

26 Quiescence: Uses a nonempty invariant zero residual-cost set and stability conditions. Model convergence is distinct from a practitioner attaining liberation.

05

Moving into practice: keep two tasks distinct

Apply the reading to the same case. You can improve the estimate while observing anger or self-criticism. Work improvement and the response to suffering need separate assessments.

TaskWhat to examinePossible next action
Work problemMissing costs, requirements and fairness of assessmentAsk for requirements and revise the estimate
Personal responseTension, anger and the interpretation “I have no value”Notice the response and check facts before replying

The four noble truths distinguish understanding suffering, abandoning its cause, realizing cessation and developing the path. They help distinguish understanding an explanation from accomplishing a practice. [S4]

Becoming calm does not resolve an unfair assessment. Keep external problems in view. When reading the faculties and powers, distinguish professional success from the purpose of Buddhist practice.

06

Five faculties and five powers: a comparison with limits

SN 48.10 describes faith, energy, mindfulness, concentration and wisdom. These comparisons offer an entry into early Buddhist teachings, not interchangeable translations of workplace skills. [S6]

Modern entry pointFacultyMeaning in the discourse
BeliefFaith · saddhāConfidence in the Tathāgata’s awakening
EffortEnergy · viriyaAbandoning unskillful qualities and developing skillful ones
AttentionMindfulness · satiRemembering and sustaining observation of body, feelings, mind and phenomena
ConcentrationConcentration · samādhiUnification of mind, including the four absorptions
JudgmentWisdom · paññāDiscerning arising and passing; understanding suffering, origin, cessation and path

At work we can assess attention through detection and judgment through choices. Mindfulness also retains the object of observation; wisdom understands conditions of suffering and cessation. High performance alone cannot certify their completion.

SN 48.43 describes a way of seeing the five faculties and five powers as the same five qualities. They need not be read as ten separate capacities or two compulsory successive stages. [S7]

Conze explains faculties as guiding practice and powers as those qualities unshaken by their opposites. This is commentary, distinguished here from the discourse. [S8]

For practical records, distinguish ordinary conditions from difficulty. This is our observational suggestion: record maintaining trust, continuing skillful practice, remembering observation, returning from distraction and reconsidering assumptions. A short personal record cannot certify liberation or a spiritual stage.

07

Development: make five capacities observable

How can we check whether practice changed? This article proposes observations for five workplace capacities. The previous comparison with Buddhist terms is a bridge for reading, not a scale of spiritual attainment.

Add records of choices and outcomes to claims such as “I tried” or “I believe.” Resources, opponents and luck affect competitive results, so separate effort, acquired capacity and final outcome.

CapacityWhat to observeEvidence to keep
EffortSustained practice and improvementPractice conditions, changes and performance on comparable tasks
BeliefChoices consistent with a view despite uncertaintyActions, costs, duration and conditions for revision
AttentionDetection of consequential informationDetection rate, false alarms and time against a defined answer key
ConcentrationMaintaining work and returning after interruptionQuality, errors, recovery time, rest and working conditions
JudgmentChoosing with incomplete informationPrior predictions and probabilities, reasons, outcomes and a benchmark

Separate consistency of belief-guided action from the truth of a belief. A costly choice may show influence on action; the prediction still needs comparison with outcomes. Costs also depend on resources and alternatives.

“Respect the other person” is a value; “asking will reveal what is missing” is a testable prediction. Keeping them distinct lets you preserve a value while changing an ineffective method.

Do not judge decisions from one success or failure. Record available information, possible losses and a benchmark, as well as success rate. An adverse outcome may reflect a poor choice or an uncertainty that was anticipated.

08

What a record shows, and what evidence of effectiveness requires

A record first clarifies what you predicted, tried and will revise. One calm day after recording does not establish effectiveness. Task difficulty, sleep or another person’s response may also explain the result.

To investigate an effect, specify comparison conditions, measures, timing and results that would count against the prediction in advance. Personal reflection and testing a causal claim that applies to others are different tasks.

Farb and colleagues studied narrative and present-experience attention experimentally and examined brain activity in relation to training. This illustrates a researchable question about attention, not evidence for this record method or Tomabechi’s complete theory. [S5]

09

Record a prediction, action and outcome for one task

Write the opening case in two parts: before action and after action. The reply and outcome below are fictional too; they illustrate a concrete record, not a reported improvement.

RecordExample
Purpose and valueRespect the other person and clarify missing cost assumptions
Prediction before actionAsking what is missing will identify one item to revise
Action and cost limitWithin five minutes, separate the comment from my interpretation and ask “Which cost item is missing?”
Observation after actionThe reply was “operating costs.” Anger remained, but an item to revise was identified
What this supportsThe clarification task succeeded. Emotional improvement and whether recording caused the result remain undecided
Next revisionIf no item emerges, make the question more specific; shorten notes if they obstruct work

The five capacities can be anchored in this event: effort in improving the estimate, belief in a respectful reply, attention in finding the missing item, concentration in returning to clarification, and judgment in the reason for asking. No single overall ability score is needed.

Choose one upcoming situation. Before acting, write one sentence each for the prediction, action and revision condition. Append the outcome afterwards. Preserve the original prediction and record revisions as the next prediction.

Success can coexist with greater attachment; calm can coexist with an unresolved work problem. Separate records help you choose what to address next.

10

Decide how far to accept an explanation

Transfer the distinctions to these situations. Before opening an answer, consider what evidence would be needed.

A proposal was rejected. What is fact, and what is interpretation?

The rejection and actual comment are facts; “I have no value” is an added interpretation. Check the missing estimate and fairness of the assessment.

If every cost is positive, must a positive minimum exist?

Check whether a candidate attains a minimum. Every 1/n is positive, but over all natural numbers the infimum is zero and no minimum exists.

Someone paid a large price to maintain a belief. What was established?

You can examine whether the choice followed the belief. Its truth and the method’s effectiveness need separate evidence.

A question identified a missing item, but anger remained. Was it a failure?

Work clarification progressed while an emotional issue remained. Record both and choose the next action.

Sources and reading locations

  1. S1苫米地四法印定理

    §2; §§12–15 / Theorems 23–26

  2. S2SN 22.1 — Nakulapitar Sutta

    Five aggregates; bodily and mental distress

  3. S3SN 36.6 — Sallatha Sutta

    The two arrows

  4. S4SN 56.11 — Dhammacakkappavattana Sutta

    Four truths and their duties

  5. S5Farb et al. (2007) — Attending to the present

    Abstract; narrative and experiential focus

  6. S6SN 48.10 · Indriya-Vibhaṅga Sutta

    Definitions of the five faculties

  7. S7SN 48.43 · Sāketasutta

    The faculties and powers as the same five qualities

  8. S8Edward Conze · The Way of Wisdom: The Five Spiritual Faculties

    Part I, opening: commentary on faculties and powers

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