Fall 2025 · Logos first, templates second
One‐screen overview. This semester we isolate ideas and keep infinity in the foreground.
- Reality Equation We freeze the outside parts: Actual = 1, Predictor = 1.
- Where ideas live The unit circle is the idea ring: angles are distinct ideas (later translated by a template).
- How signal appears Start with all diameters fully adhered (perfect balance). What’s missing in a time window leaves the signal we sum.
- What we compute the resultant vector M, its length C, angle φ, and its projections j and k. Only k enters the denominator this term.
Step 1 — State the Reality Equation (ideas isolated)
We work with a fixed numerator and predictor to spotlight the contribution of ideas:
so the witness sees the denominator
and the reality ratio
.
Interpretations come later via a template (our case study is Love, The Cosmic Dance). First we just do the math.
Step 2 — Ideas as diameters, infinity up front
An idea is a diameter with two poles at angles . A system is always in relation with an infinite set of ideas.
Negative-photograph rule (one trial): if a pole at angle α fails to adhere in this snapshot, it contributes a unit arrow at its antipole . If both poles adhere (balanced), contribute nothing.
Step 3 — Build the resultant vector M over a time window
Across T trials (e.g., 10 prompts in one minute), sum the unit arrows from all missing poles:
If nothing is missing in a trial, skip that term.
Step 4 — Read C, φ, and the projections j, k
Write . Then
.
Why only k enters E this term? We reserve the real axis for the frozen predictor (P = 1). The imaginary contribution from ideas is the single scalar k. Thus , and
.
Worked micro example (10 trials, one missing pole)
Suppose the same pole is missing every time at , so arrows land at the antipole
.
Sum ten identical unit arrows:
Reality (ideas-only pass)
How the “negative photograph” reveals bias over time
- Macro: many small cancellations →
.
- Meso: recurring missing poles → stable “lines” (characteristic angles).
- Micro: a small set of missing poles repeats → larger
and a clear
.
Key sentence: If a system has a non-zero resultant vector, it’s because something is missing. We discover the “what” by the angles that repeatedly fail to adhere.
From math to meaning: apply a template (after the computation)
Angles are semantically blank until we apply a template (lens). For the case study Love, The Cosmic Dance, one simple lens is the four cardinal families.
Example lens (cardinal families) Fix a baseline angle and define axes
. Soft membership by cosine (clipped below zero):
.
We always compute M, C, φ, j, k first. Only then do we translate via the lens.
Classroom mini-lab (3 prompts, end-to-end)
- Pick 3 stimuli (image, sound, quote). For each stimulus n, fix a pole angle
and its antipole
.
- Partner labels each response: choose pole (meaning the antipole failed to adhere) or indifferent (both adhered).
- For each chosen pole at angle
, add a unit arrow at
).
- Sum the 3 arrows → M; compute C, φ, then j and k.
- Finish the pass:
.
Tip: spread your template angles so the three arrows don’t trivially cancel; e.g., 20°, 140°, 300°.
Guardrails
- Infinity foreground. We conceptually begin with all diameters adhered; only missing poles leave traces.
- Math before mythos. Do not assign meanings to angles until after you compute M, C, φ, j, k.
- Use k, not I. This term the imaginary contribution is the scalar k, nothing else.
- Stick to unit arrows. Each missing pole contributes one unit arrow; no weights needed.
Takeaway
The resultant vector is the fingerprint of what’s missing. Sum the antipoles of failed adherences to get , read
, and complete the ideas-only pass with
. Templates—like Love, The Cosmic Dance—come after.