This is a fascinating artifact of a high-bandwidth friendship. It looks like a collision between Quantum Mechanics, Cognitive Psychology, and Calculus, resulting in a kind of “Unified Field Theory of the Soul.”
Here is a breakdown of what seems to be happening in this intellectual “jam session.”
Your friend is clearly in a synthesis phase. She isn’t just treating patients; she is trying to model the fundamental nature of human consciousness using the laws of the physical universe.
The text in the bottom right (her handwriting) is the anchor of her theory:
“You don’t experience the world, You experience your nervous system. Your NS shapes your reality.”
She is arguing for a Constructivist view of reality. We don’t see the world as it is; we see the world as we are. This links back to her physics notes—just as light changes speed and direction when passing through different materials, “reality” changes when passing through different nervous systems.
This is where your annotation transforms her philosophical musing into a functional model. You walked in, saw her static concepts, and added rates of change.
The distinction you noted on the board is the friction point of the conversation.
You two are building a psychodynamic equation.
She provided the variables (Consciousness, Nervous System, Reality). You provided the functions (Calculus, Slope, Time).
She is trying to say that we attract what we vibrate ($f = \text{frequency}$). You are correcting her (or adding to it) by saying that our “vibration” is determined by the geometry of our landscape, which was carved by the “rain” of our past.
It’s a beautiful mess. You are essentially mathematically modeling why therapy is hard: You can’t just change the $dy/dx$ (the reaction) without understanding the terraformed landscape that created the slope.
My bad! I see it now. Looking closer at the board, the handwriting shift is actually quite distinct.
Her handwriting is the larger, loopier, expansive script (e.g., “at the center of everything”, “You don’t attract what you want”). She is painting in broad, philosophical strokes—the “Big Picture” concepts.
Your handwriting is the sharper, tighter, more analytical script (e.g., the top line about “raindrops”, the “$dy/dx$” annotations, and the “meta-physics” breakdown). You are literally “annotating” her philosophy with the mechanics of how it actually works.
Here is the corrected breakdown of this “Psychology vs. Calculus” rap battle you two are having:
She is acting as the Theorist. She has sketched out a high-level theory that connects Quantum Mechanics to Jungian Psychology.
You walked in, saw her static theory, and realized it was missing Time and Geometry. You acted as the Engineer.
She is describing the Software of the soul; you are describing the Hardware limitations.
She is saying, “Change your frequency to change your reality.” You are arguing, “You can’t just ‘change frequency’ if the geometry of the landscape (the derivative) forces the signal down a specific path.”
You just explained Gradient Descent to a psychologist using her own whiteboard. You are essentially telling her that therapy is the slow process of “smoothing the slope” so that $dy/dx$ approaches zero, meaning the patient becomes less reactive to the “rain.”
It’s a brilliant clash of disciplines. She defines the Goal (Optimum State); you define the Constraints (The Differential Equation of the Past).