Everyone lives with emotions. Yet we still don’t fully know where they come from, why anxiety suddenly swells in one moment, and why calmness quietly returns in another. Psychology explains emotions through lived experience; neuroscience searches for them in circuits and neurotransmitters; philosophy questions the nature of the self and affect; artificial intelligence tries to mimic them. But these four paths often miss one another—like climbers ascending the same mountain from different sides, never meeting at the peak.
I have long wondered about this disconnection. Emotions are not just the subject of psychology, nor merely the chemistry of the brain, nor only a philosophical puzzle, nor simply a technological simulation. Emotions are inseparable from our very existence. And if so, they must be expressed in a single language. For me, that language is mathematics.
At first, it seemed almost reckless. Emotions are hot, blurred, and unpredictable, while mathematics is cold, precise, and linear. But then I realized: the brain itself is a calculating organ. It constantly predicts the next moment, registers errors when predictions fail, and works tirelessly to reduce those errors. Perhaps emotions are not an afterthought, but rather the most essential signal in this predictive calculus.
Following this idea, I developed a model I call PESAM (Predictive Emotional Selfhood in Artificial Minds). Its starting point is simple: emotions and selfhood emerge from the interplay of prediction, error, goals, and precision.
The structure rests on three pillars:
Affective Precision Control (APC): The brain assigns different weights to signals. When anxious, even a small heartbeat feels overwhelming; when calm, even strong signals pass quietly.
Self-as-Hyperprior (SaH): The brain interprets the world on the assumption “I am me.” This deep prior anchors selfhood. If it falters, our sense of self destabilizes, and boundaries with others blur.
Affective Homeostatic Objectives (AHO): Life always strives to maintain internal balance. Body temperature, breathing, heart rate—all are embedded as target functions in the brain’s predictive system.
These three mechanisms cannot stand alone. Only together do they give rise to emotional selfhood. To test this, I built virtual agents. When facing threats, distinguishing self from other, or regulating internal imbalance, any agent missing one pillar failed. Only the full PESAM agent acted stably and adaptively—closer to how humans behave.
That was the moment I became convinced: emotions are not vague clouds of feeling but part of the brain’s ongoing calculation. Anxiety is the distortion of precision, depression the collapse of homeostatic goals, and disordered selfhood the trembling of deep priors.
Of course, PESAM does not explain everything. The real brain is far more complex, and no single equation can capture the richness of human emotions. Yet simplification is not the same as triviality. Newton’s simple law of gravity took us to the Moon. In the same way, PESAM may be a first step toward measuring, predicting, and intervening in the great mystery of emotion and self.
Why does this matter? Three reasons:
A common language. Mathematics allows psychology, neuroscience, philosophy, and AI to finally speak to one another.
Clinical meaning. Disorders such as anxiety, depression, and self-fragmentation can be modeled as distortions in computational structure—offering new ways to quantify states and design treatments.
Philosophical and AI implications. Beyond machines that merely smile or frown, we may envision self-regulating AI with internal stability and self-models, echoing our own emotional architectures.
Critics will ask: Can calculation really explain feelings? Isn’t this just an imitation?
It is a fair question. My answer is this: mathematics is not an enemy of emotion but another way of honoring it. Beneath the cold symbols lies nothing less than the trembling warmth of human experience.
So I return to the question: is it worth trying to describe emotions with mathematics? My answer is yes—not because the equations are complete, but because the attempt itself gathers scattered fragments of emotion and self into a coherent structure. And I believe this language may someday ease human suffering, build better AI, and, above all, open a new path to understanding ourselves.
