Mathematical Emotional Reality - A Fun Thought Exercise
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1. "Everything can be true at once"

In a vector space, a point simultaneously has components along many axes. There's no contradiction in being large in one dimension and small in another.

Similarly, lived experience isn't a single scalar truth ("good" or "bad"), but a high-dimensional state: grief, gratitude, fear, hope, boredom, meaning, all co-existing. They don't cancel each other out; they simply occupy different dimensions.


2. "Magnitude and angle of our emotions are projections"

A vector has an intrinsic position, but what you observe depends on the basis you project it onto.

Deciding whether a situation is worse or better is choosing a particular axis (or low-dimensional subspace) and projecting the full emotional vector onto it. The story you tell yourself is the coordinate system. Change the basis, and the same underlying state yields a different scalar feeling.


3. "The story we tell ourselves"

The latent vector is stable, but its representations ca vary.

Two narratives are two different transformations applied to the same latent vector. One narrative emphasizes loss, another emphasizes growth. Neither is false --- they are different slices through the same manifold.


4. "Things are both a lot better and a lot worse"

Better and worse are not orthogonal dimensions. They overlap, interfere, and correlate.

In a curved manifold, local directions can point up and down depending on where you stand. So improvement in one region can feel like decline in another. This is not inconsistency; it's curvature.


5. "And that's okay"

No single projection is privileged unless you impose a task function.

Emotionally insisting on a single scalar evaluation is an unnecessary loss of information. Acceptance is recognizing that compression is optional. You don't have to collapse the state into one number.