Purpose. Start from the Reality Equation, lock the numerator and predictor to isolate the imaginary part of the denominator, and compute it from event samples via the resultant vector. The template family for the semester is Love, The Cosmic Dance; math first (logos), then translation (mythos).
0) The Reality Equation
Reality is the ratio of Actual to Expectation:
Expectation is complex:
Witness readouts:
Axiom. The past is immutable. Consequences: the center is a permanent node; the predictor stays strictly positive (); absolute actualization (
) is impossible.
1) Fall scope (locks to isolate ideas)
- Lock
and
for all computations.
- All variation in Reality comes from the imaginary component
.
- Predictor modeling (stochastic, Markovian, Bayesian) is deferred to Spring.
2) Logos (math lens): event-sample definition of the resultant vector
Resultant vector. For a chosen time window, each idea event contributes one unit arrow at its angle on the unit circle. Add them tip-to-tail to get the single arrow .
Split once into perpendicular components:
- j: realization component (many realized instances when large).
- k: mark component (the only part that reaches the denominator).
Plug into Reality (ideas-only locks):
Mantras. Add unit arrows first. Split once. Only k reaches the denominator. Every M is the fingerprint of an infinity.
3) Mythos (template lens): Love, The Cosmic Dance
Template family for the semester. We keep the math agnostic, then translate with this case study after the computation.
Line we use: “Ideas have people; people do not have ideas.” Mathematically, idea space is continuous (infinite). A system is always in relation with all ideas; opposite directions cancel in the round; the remainder in a window yields .
Overlay rule. Compute first; only then place names on sectors (for example, your four cardinal ideas). Translation is template-specific and always comes after logos.
4) Levels and windows
- Micro. Short windows (seconds to weeks). Angles jump;
breathe.
- Mezzo. Structured windows (months to decades). The angle can drift like a clock hand;
roughly steady.
- Macro. Large aggregation and long windows. Signed contributions cancel; Reality tends toward one.
5) Canonical Fall pipeline (what students do)
- Gather event angles for a window; place unit arrows; sum to get
.
- Read
.
- Compute
via projections.
- With
, compute
.
- Optional: alignment score
as the idea’s view of how well the system carries the mark.
- Only after the math: overlay the template names (mythos).
6) Quick interpretive anchors
- Angle near
:
→ many realized instances, fuzzy mark.
- Angle near
:
→ few realized instances, sharp mark.
: perfect cancellation in this lens; Reality reduces to Actual over Predictor (both locked to one).
7) Stock exercises (Fall)
- One-minute micro drill. Each student logs angles for sixty seconds, computes
. Pool the class to show macro cancellation.
- MLK window. Tight cluster near seventy to eighty degrees →
.
- Everyday circles. Tight cluster near twenty-five to thirty-five degrees →
.
- Split detection. Equal crowds at
: direction along
. Reveal two-fold structure by doubling angles before summing.
- Three-fold symmetry. Equal at
:
8) Laws and guardrails
- Law. No one has ever seen a perfect storm: with
and finite
always.
- Ban naming sectors until after the math. Compute first; translate second.
- If students revert to “spin,” redirect: event counts, cancellation, resultant.
9) Assessment map (Fall)
- Quiz 1 (week 3): compute
from given angle sets; one-sentence interpretations.
- Midterm (week 7): micro and mezzo windows; simple cycle plot of the angle over rolling windows; annotate where Surprise compressed or relaxed.
- Final (week 14): full pipeline on unseen data plus a brief template overlay; students must explicitly state “only k reaches the denominator.”
10) Spring preview
Spring is the predictor semester. We unfreeze and model it (stochastic baselines, Markov transitions, Bayesian updates). Ideas stay as
. The full readout is
with both parts moving.
One-line takeaway. Compute the resultant from event samples, split once into realization and mark
; pass only k to the denominator of the Reality Equation.