Desire, Attachment, Suffering, and Ignorance — Formal Ontology

Formal definitions for four left-hand constructs. The right-hand ratio is immutable; only the carried parameters (radius and angle) are passed to the left, and no numerator substitution ever occurs.

Preliminaries (Primitives)

The core law is:

We work with the following objects:

Actual $A>0$ (unseen on the left; no control).
Expectation $E = P + iI$ with real component $P$ (prediction) and imaginary component $I$ (ideal).
Carried parameters: $r = A / |E|$ and $alpha = atan2(I,P)$ .
Witness readout: $S = ln r$ .

Sampling (What Is Actually Seen)

On the left, nothing ever sees Actual; only a sample of it is observed. Let the effective setpoint be selected by a binary gate:

Invariant: the witness channel remains $S=ln r$ and does not depend on the gate.

Definitions

Desire

Type. Pre-sample target specification (pattern), not a control action and not an outcome.

Timing: exists prior to and independent of $(r,alpha)$ .
Object: a predicate or scoring rule $T$ on observations, optionally with priority $pi$ ; write $D=(T,pi)$ if needed.
Invariance: does not modify $A,E,r,alpha,S$ or $Sigma$ .
Gate independence: may be present with either $h=0 or h=1$ .
Relation to hope/fear: hope/fear are pre-sample evaluation commitments that may be parameterized by $T$ but are distinct from Desire.
Persistence: episode-level Desire ends at observation; trait-level Desire may persist across episodes.

Attachment

Type. Control state that determines which setpoint is used for sampling.

Definition: $h=0 uses s_R=(r,alpha); h=1 uses s_M=(r̄,ᾱ)$ .
Invariance: does not alter $A,E,r,alpha,S$ ; only chooses $s_eff$ .
Independence from Desire: Desire can influence the likelihood of $h=1$ but is not identical to it.
Modality: soft attachment = low dwell; hard attachment = persistent, high dwell.

Suffering

Type. Post-sample persistence in conflict with the observed $x$ .

Necessaries: after arrives, all of the following are required:
1. Mismatch: $x violates D$ .
2. Insistence: continued attempts to force alignment with $T$ (re-aim/re-tighten/re-interpret/replay).
3. Duration: persistence beyond the instant of observation (distinct from $S$ ).
Invariance: no change to $A,E,r,alpha,S$ ; later Expectation drift is ordinary learning.
Sufficiency: Mismatch ∧ Insistence ∧ Duration ⇒ Suffering.
Cessation (all required): full cessation occurs only when, over a settling interval,
1. Release Attachment: manual insistence ceases (effectively $h->0$ or $s_M not enforced$ ), and
2. Relax Episode-Desire: the active $T$ is let go or reframed so mismatch no longer drives insistence, and
3. Episode Turnover: attention advances without carrying forward the prior insistence.

Ignorance

Type. Epistemic/attentional condition about the carried parameters and the gate.

Definition: failure to represent that a sampling setpoint can equal the carried $(r,alpha)$ from the right-hand ratio ( $s_R=(r,alpha)$ ), and/or failure to track which setpoint ( $s_R vs s_M$ ) is active via $h$ .
Invariance: does not alter $A,E,r,alpha,S$ ; it concerns the agent’s internal model.
Relation to Attachment: can co-occur with $h=1$ yet is distinct; one can be attached while fully aware, or ignorant even with $h=0$ .
Effect: increases dwell in narrow sampling and raises persistence of Suffering by obscuring the pathways required for cessation.
Resolution: reduced by accurately representing the architecture: recognize carried $(r,alpha)$ , know $s_R and s_M$ , and monitor $h$ .

Edge Checks

Desire present, $h=0$ , match → no Suffering.
Desire present, $h=0$ , mismatch → Suffering only if Insistence and Duration occur; cessation requires all three conditions above.
Attachment without Desire → narrowed sampling, but Suffering not implied absent mismatch + insistence + duration.
Ignorance alone → not Suffering, but increases risk by hiding the steps needed for cessation.

Minimal Glossary

Actual ( $A$ ): outcome on the right; unseen on the left.
Expectation ( $E$ ): complex denominator with prediction and ideal.
Radius ( $r$ ): carried scalar $A/|E|$ .
Angle ( $alpha$ ): carried phase $atan2(I,P)$ .
Witness ( $S$ ): lawful felt readout $ln r$ .
Gate ( $h$ ): selects $s_R vs s_M$ .
Desire: pre-sample target specification $D=(T,pi)$ ; invariant to $(r,alpha),h$ .
Attachment: control state selecting $s_eff$ ; does not alter the ratio.
Suffering: post-sample mismatch + insistence + duration.
Ignorance: failure to represent carried $(r,alpha)$ and/or to track the active setpoint via $h$ .