Last semester we taught “scalar reality.” We took Actual divided by Expectation, kept only the size of the denominator, and called that single number the aperture: tight vs. wide. We deliberately threw away the angle to keep the spine simple.
This semester we stop throwing away information. The law doesn’t change, but the readout now has two numbers:
- Aperture r — how tight or wide the current frame is. It’s Actual divided by the size of Expectation (unitless).
- Angle α — which way the unconscious is steering the denominator along the horizon between Prediction and Ideal.
Those two numbers are not a picture of the whole sky. They are instructions for where to take a sample next.
Whole sky vs. a sample
Actual, Predicted, Ideal, Expected, and Desired are all “whole-sky” renderings—different ways of depicting the entire night sky. Only Actual is the true sky as it is. The eyepiece never shows the whole sky; it shows a sample chosen by the two numbers (in auto) or by you (in manual). This single distinction—whole-sky renderings on the right, samples on the left—prevents most confusions.
What α tells you (and what it doesn’t)
α is the mix between Prediction and Ideal in the plane you already know:
• Near 0° → prediction-heavy (realistic).
• Near 90° → ideal-heavy (idealistic).
• Near 45° → balanced influence.
Angle tells you who’s steering the denominator at that moment. It does not tell you how tight the frame is; α and r are independent in the law. You can have a high angle with a wide aperture or a low angle with a tiny aperture. They often move together only after certain histories (e.g., prolonged manual fixation on an idea-saturated patch).
Two branches from the same numbers
When the pair (r, α) arrives, it immediately splits in two.
• Seat of witness (eyes closed): you only need r. The subjective felt experience tracks r (think “log of r” if you want a single scalar). α plays no role in feeling.
• Participant (eyes open): you use both r and α to aim the instrument and actually take the sample. What you then see through the eyepiece depends on those instructions (if auto) or on your choice (if manual).
Auto vs. Manual (binary)
• Auto (hands off): the autoguide enacts the incoming pair. Because the view roams with the world, the predictor remains the best representation of the whole sky available at that moment. If you had been manual before, the next few pairs may still carry that history; with auto left on, they relax back on their own.
• Manual (hands on): any contact means the autoguide cannot enact the pair. You choose the sample. Manual appears in two distinct behaviors:
– Search (roaming): you keep moving and swapping views, hunting for confirmation of a left-side desired outcome. Because no single niche is fed for long, the denominator drifts slowly and noisily.
– Fixation (camping): you park on one patch. Now the right side keeps seeing the same niche. Over trials the steering angle slides toward that niche’s axis (often closer to 90° if the niche is idea-heavy), and the size of Expectation grows for that niche, so the aperture r shrinks (a tunnel).
Desired vs. Ideal (left vs. right)
An idea’s desired outcome is Ideal (right side). Your desired outcome is Desire (left side). Desire shows up only as behavior—going manual (search or fixation). Ideal is inherently biased: excellent for its niche, worst as a whole-sky map.
Why we dropped α in the fall—and why we keep it now
Dropping α let you master tight vs. wide with one scalar. Keeping α now lets you interpret that same aperture in context—are you being steered by history’s momentum (prediction) or by a preferred outcome (ideal)? That second number is often enough to decode why two equally “tight” frames feel very different in lived experience.
A canonical example to anchor the intuition
Actual = $5. Predictor = $6. Ideal = $5.29.
The size of Expectation is about $8, so the aperture is 5/8 = 0.625 (a decent chunk of sky).
The angle is ~41°, which says the frame leans toward Ideal but not by much.
If Ideal were 1000 with Predictor still 6, the angle would be ~89.66° (almost pure Ideal) and the aperture would collapse near 0.005 (a tunnel on one object). Same law, very different readouts.
Advanced note: γ (gamma)
γ is not a knob you turn; it’s a diagnostic word for coherence or “lock.” When the scene is phase-aligned with an idea—think of a highly self-reinforcing niche—γ is effectively high. In that condition the ideal side contributes more coherently to Expectation, which makes the denominator larger and the aperture smaller (r shrinks, the felt log of r goes down). You infer γ from patterns across trials: prolonged manual fixation on one patch tends to show up as “γ-like” behavior (angle marching toward that niche, aperture tightening), whereas roaming manual or auto leave it low. Keep γ in the text as an explanation for why r can collapse even when P and I magnitudes weren’t huge to start with; don’t teach it as a control.
What to do in practice
- Read the pair (r, α).
- Decide mode: auto or manual.
- If auto, let the instrument go where the pair says; the predictor will keep learning the world you actually live under.
- If manual-search, expect slow, noisy drift in the denominator.
- If manual-fixation, expect α to slide toward the niche and r to shrink over sessions.
- When you return to auto, give it time; without reinforcement the numbers unwind toward baseline.
Common confusions to retire
• “If r = 1 then α must be 45°.” No—r and α talk about different things. r=1 means the size of Expectation matches Actual; 45° means P and I are equal in influence.
• “Looking through the eyepiece shows me the Actual.” No—the eyepiece always shows a sample. Actual is the whole sky.
• “Tighter means truer.” No—tighter means a larger denominator for that niche. Truth is the whole sky.
• “Angle tells me the aperture.” No—angle tells you who’s steering; only the size of Expectation vs. Actual sets r.
One-minute classroom demo
• Baseline: 0.625 and ~41°.
• Manual-fixation on a single idea-heavy patch: across short trials, watch the angle creep upward and the aperture shrink.
• Back to auto: watch both drift back as the instrument resumes sampling the world.
Takeaway
Complex Reality in 2D is two numbers—how tight the frame is and who’s steering it. Your only real choice is auto or manual; whatever you feed the instrument, it learns, and tomorrow’s two numbers will faithfully report what you’ve been teaching it.