A geometric guide to balanced expectation and clear perception
Start with a simple diagram: draw a horizontal axis and label it the real axis. This is your X-axis. Now draw a vertical axis, perpendicular to the real axis, and label it the imaginary axis—your Y-axis. Where they meet at the center, mark that origin point as (0, 0). Now draw a circle with radius 1 centered on that point. You’ve just constructed the unit circle.
Next, label four points:
(1, 0)→ 0° or 2π radians (horizontal line)(-1, 0)→ 180° or π radians (horizontal line)(0, 1)→ 90° or π⁄2 radians (vertical line)(0, -1)→ 270° or 3π⁄2 radians (vertical line)
Let’s focus on a special point: 45° (π⁄4 radians). Draw a line from the origin to that point on the unit circle. Now drop perpendicular lines from that point to both the real and imaginary axes. You’ve just drawn a square—literally. This is what we mean by “squaring it.”
Why 45 Degrees?
At 45°, your real and imaginary components are equal: one axis measures subconscious prediction (habit), the other measures ideation (the influence of ideas). When these two are balanced, the expectation is geometrically square—neither skewed toward blind repetition nor swallowed by chaos.
This is how you achieve clarity. This is how you “square it.”
And this geometric balance is not just visual. It maps directly onto your lived experience. The real axis is your subconscious pattern recognition. The imaginary axis is the influence of third-party thoughtforms—ideas as Jungian entities. Your current expectation is a vector in this space, and its angle—theta—determines your skewed view of the actual pattern.
Case 1: The Habitual Mind (Low Theta, e.g., 5°)
Most people fall here: strong subconscious prediction, low ideation. Their expectation vector lies close to the real axis. The rectangle formed with the imaginary axis is nearly flat—minimal height, maximum width.
How do they square it?
- They must increase ideation.
- They must enter a symbiotic relationship with a powerful idea.
- They must allow the idea to disrupt their habitual structure.
As Jung said: “Ideas have people.” You don’t choose an idea. It chooses you. And it chooses you because you’re a good actualizer—a host capable of bringing it into the historical record. It’s a mutual relationship: the idea gets actualized; you get access to the pattern. You square it.
Case 2: The Possessed Creative (High Theta, e.g., 85°)
These are the mad hatters. Big ideas dominate them. But their subconscious prediction—i.e., groundedness in habitual pattern—is weak. Their expectation is mostly vertical. Their rectangle is tall and narrow. They live in a fantasy of ideas but cannot reliably predict what happens next.
How do they square it?
- They must become grounded.
- They must build routines, structures, and repetitions.
- They must develop a predictable base for the idea to express itself through.
It is the opposite journey: from 85° down to 45°. From being overwhelmed by the imaginary to becoming an interpreter of the pattern. The key is not to silence the idea, but to give it structure.
The Goal: 45° (π⁄4 radians)
At this angle, your real and imaginary components are both √2⁄2. Equal contributions. Balanced expectation. A square projection. This is when you see clearly—not perfectly (that would be Reality = Actual, which no one achieves), but as clearly as a human being can.
This is why squaring it is not just important. It is essential. Until you square it, you are either habitual or possessed. After you square it, you become a participant—not just in behavior, but in comprehension.
Geometric Clarity for Metaphysical Living
The unit circle gives us a way to visualize how far off we are. Theta is not moral. It is not evaluative. It is simply your current alignment of habit and idea.
To square it is to commit yourself to seeing the pattern. If you are too flat, embrace a symbiotic idea. If you are too vertical, build a daily routine. Either way, the angle will shift. And when you hit 45°, you’ll know it:
- The pattern becomes visible.
- The buttons don’t matter anymore.
- You are watching the video—not just holding the phone.
Square it. Then rotate around it. You’ll never go back.