2025.03.27

The Broken Equation of Power

∀ x ∈ A, ∃! y ∈ B Inputs should get outputs. Fair. But reality? Some x get none. Millions of x are mapped to the same y.

asymmetry · math · power

The World Is Not a Function

And That’s the Problem

Mathematically, a function is simple. It’s a relationship where every input gets exactly one output.

No duplicates, no leftovers, no cheating.

A function f is a subset of a Cartesian product A × B, where for every x in A, there exists exactly one y in B such that (x, y) ∈ f.

∀ x ∈ A, ∃! y ∈ B

Translation? Every element in the domain is mapped to a unique counterpart in the codomain. Clean. Elegant. Balanced

Reality Check

Now, take a look at reality. We have a planet of 8 billion inputs, but only a fraction receive a meaningful output. Meanwhile, a handful of nodes—the top 1% are hoarding thousands of outputs each.

In set theory, we call that invalid. In economics, we call it “just how the system works.”

But it shouldn’t.

Because what we’re witnessing isn’t a function.
It’s a corrupted relation where:

  • Some x have no y.

  • Millions of x are mapped to the same y.

  • Entire subsets of A are unmapped, forgotten, null.

It’s a glitch in the foundational logic of civilization.

This is bad math masquerading as meritocracy.

Nature Knows Better

In every balanced system—biological, ecological, even quantum—resources flow like a proper function. Each node gets its share. No domination, no dangling variables.

But somewhere along the way, we rewrote the logic.

The few started collecting codomain values like trophies, and the many became phantom inputs, present in the domain, but never mapped.

The Function That Failed

Let’s be clear, this isn’t about left or right. This is about a fundamental break in the mapping system of civilization.

The world has become a relation with:

  • Broken Injectivity: f(x₁) = f(x₂) for wildly unequal x.

  • Failed Surjectivity: Entire sectors of the codomain are never reached.

  • Zero Chance at Bijectivity: True balance is a mathematical impossibility.

If our world were a program, we’d throw a DomainError and refactor the code. Instead? we call it normal.

So What Now?

Maybe it’s time to rewrite the function.

Because the longer we treat this corrupted mapping as natural, the deeper the null set grows. And what does nature do with imbalance?

It doesn’t ask politely.

It reconfigures.

The world isn’t a function. It’s a mess. And it won’t be fixed by those who broke the mapping.