The Symmetry of Overthinking: Math Models for Everyday Anxiety

Have you ever found yourself caught in a spiral of overthinking? That recursive loop where one anxious thought leads to another, and another, until you're several layers deep in a problem that started as a minor concern?

As a math student, I've started to notice interesting parallels between certain mathematical concepts and the way our minds process anxiety. This isn't just a cute metaphor—I think there's something deeper here that might help us understand why we overthink and how to break the cycle.

Feedback Loops and Recursive Thinking

In mathematics, a feedback loop occurs when the output of a system is routed back as input, creating a circuit of cause and effect. This is precisely what happens when we overthink:

1. We have an initial thought (input)
2. Our mind processes it and generates a response (output)
3. That response becomes the new input
4. The cycle continues

This can be modeled as a recursive function: