Math And The World. Who Obeys Who?

Every child learns to count on their fingers. 

One, two, three—up to ten, then start over. 

It seems natural, inevitable, like we're tapping into some fundamental truth about numbers. But here's a thought that should unsettle our confidence in mathematical absolutes: we count in tens only because we happen to have ten fingers.

If evolution had given us thirteen fingers instead, we'd probably count in base thirteen. Our multiplication tables would look completely different. 

The decimal point would be the tridecimal point. 

Every calculation, every equation, every mathematical framework we consider natural would be built around a completely different foundation.

This isn't just a curious hypothetical, it reveals something profound about the relationship between mathematics and reality that most people get backwards.

This simple fact reveals something profound: mathematics emerges from observing natural patterns, rather than nature somehow "knowing" mathematical rules. 

We watch how objects fall, how planets move, how quantities combine, and then we create mathematical descriptions that match what we've observed. 

The equations come after the phenomena, not before.

Think about basic arithmetic. 

We didn't discover that 2+2=4 as some eternal truth floating in space. 

We noticed that combining two objects with two other objects consistently resulted in four objects. 

We then created a symbolic system to describe this pattern. 

The pattern existed in the world; mathematics followed.

Geometry follows a similar pattern. 

We observed roughly triangular forms in nature—the approximate angles of crystals, the general patterns in leaves, the structures that emerge when materials reach equilibrium, and abstracted mathematical principles from these imperfect examples. 

We took the messy reality of natural shapes and created idealized mathematical descriptions.

Even advanced mathematics follows this sequence. 

Calculus wasn't invented in a vacuum; it was developed to describe rates of change that already existed in the physical world. 

Newton and Leibniz created mathematical tools to capture what was already happening with moving objects and changing quantities.

If we had evolved differently, with different sensory capabilities, different anatomy, different environments, our mathematics would be different too. 

This doesn't make mathematics arbitrary or invalid. 

The patterns we describe are real, and our descriptions often work remarkably well for prediction and control. But it does suggest that mathematics is more like language than like fundamental law. 

Languages evolve to express the experiences and needs of their speakers. 

Mathematics evolved to express the patterns and relationships we observe in our particular corner of reality.

The danger comes when we flip this relationship and start believing that the world must conform to our mathematical descriptions. 

When we encounter phenomena that don't fit our current mathematical frameworks, the problem isn't with reality, it's with our frameworks. The world keeps doing what it's always done; we just need better mathematics to describe it.

This perspective makes mathematics more humble and more human. 

Instead of discovering eternal truths, we're creating useful tools for understanding and manipulating our environment. 

These tools can be incredibly powerful and precise, but they remain tools, shaped by our biology, our history, and our particular way of experiencing reality.

The world existed for billions of years before the first consciousness developed the concept of number. 

Planets orbited, waves propagated, and complex systems evolved without any need for equations or proofs. 

Mathematics is our attempt to make sense of this reality, not reality's attempt to follow our rules.

The universe doesn't speak mathematics. 

We developed mathematics to help us listen to what the universe was already saying.