Why Humans Are Obsessed With Numbers Too Big to Understand

The Evolution of Scale: Why Our Obsession With Huge Numbers is Just Beginning

For most of us, a “considerable number” is something like a billion dollars or the distance to the next star. But as mathematician Richard Elwes points out in his recent work, “big” is entirely contextual. To a toddler, ten is massive. To a cognitive scientist, anything beyond 4.5—the limit of our innate ability to instantly recognize quantity, known as subitizing—is technically “big.”

As we move further into an era defined by quantum computing, galactic exploration, and artificial intelligence, our relationship with scale is shifting. We are moving away from numbers we can visualize and toward numbers that can only be managed by the systems we build.

From Human Intuition to Algorithmic Scale

Historically, our number systems evolved out of necessity. The shift from Roman numerals to the Indian-origin system we use today wasn’t just about convenience; it was about scalability. Roman numerals effectively “ran out” of practical utility, whereas our current system is infinite.

Today, we are seeing a similar transition. We are entering the age of algorithmic scale. When we discuss Large Language Models (LLMs) like GPT-4, we aren’t talking about millions of parameters, but trillions. These numbers are so large they evoke what Elwes calls “scale vertigo”—a sense of dizziness when the mind tries to grasp a magnitude it wasn’t evolved to handle.

In the future, we can expect a further decoupling of “mathematical truth” and “human intuition.” We will increasingly rely on abstraction layers—simplified representations of massive numbers—to make decisions about everything from global climate models to the distribution of wealth in digital economies.

Quantum Computing and the Death of Linear Counting

If scientific notation (using superscripts like 10¹²) allowed us to map the stars, quantum computing is forcing us to rethink the very nature of a “result.” In a classical computer, a bit is 0 or 1. In a quantum system, superposition allows for a complexity that grows exponentially.

The number of possible states in a sufficiently large quantum computer quickly exceeds the number of atoms in the observable universe. This isn’t just a theoretical exercise in mathematical logic; it’s a practical boundary. We are approaching a point where the “answers” provided by machines will be derived from numbers so vast that no human could ever verify them through traditional counting.

This trend suggests a future where we treat numbers not as quantities, but as topologies—shapes and patterns of data rather than a sequence of digits.

The Psychology of the Infinite: Numbers as Emotional Tools

Why do we care about numbers like “Fish 7” (one of the largest described numbers in mathematical logic)? It isn’t for taxes or engineering; it’s for the aesthetic of the infinite. Much like the Maya engraved massive numbers on monuments, modern humans use “big data” and cosmic scales to find a sense of wonder—or terror.

As we integrate more deeply with AI, we may develop a new “digital intuition.” Just as we learned to trust scientific notation to describe the microscopic world of atoms, we may develop a mental framework to “feel” the scale of petabytes and exabytes without needing to translate them back into units of one.

This psychological shift will likely lead to new forms of art and philosophy that explore the “spaces between” these incomprehensible numbers, treating the void of the ultra-large as a canvas for human expression.

Frequently Asked Questions

What is subitizing?
Subitizing is the ability to instantly recognize the number of objects in a small group without counting them one by one. For most people, this limit is around 4 or 5 objects.

Why is scientific notation vital?
It allows scientists to express incredibly large or small numbers (like the mass of a galaxy or the charge of an electron) using a concise format, preventing errors and making calculations manageable.

What is a “googologist”?
A googologist is someone who studies and attempts to define the largest possible numbers, often using advanced mathematical logic and set theory to push the boundaries of what can be named.

Want to dive deeper into how mathematics shapes our reality? Check out our previous analysis on the intersection of math and consciousness or explore the Numberphile archives for more visual explorations of these concepts.