đź“š Learning as the Quest for Constants

This essay explores a simple but profound idea: our drive to learn may be fundamentally rooted in physics — in the search for what stays the same. If you're curious how stable patterns fuel intelligence, both biological and artificial, this is a good place to start.

👉 Read the full paper (arXiv: Dynamical Invariants and Learning)

The ideas below build on concepts from a previous piece: On the Physical Origins of Learning — but this time, we dive deeper into dynamics, predictability, and the thermodynamic foundations of learning.

Introduction

We often say that predictable information has value. In everyday life, we’re drawn to stable patterns — not just because they feel comforting, but because they help us act more effectively. We rely on them to plan, respond, and make sense of the world.

At a deeper level, much of human knowledge is built upon what stays the same: physical laws, mathematical truths, and slowly evolving social constructs. These constants form the invisible backbone of our lives. If everything changed too fast — faster than we could adapt — our systems, our decisions, and our very survival would be at risk.

As a result, we intuitively organize learning into layers. First, we master the most stable truths. Then, we move to slowly shifting ideas. Only later do we attempt to grasp fast-changing or unpredictable phenomena. And even in chaotic situations, we instinctively search for "islands of stability" — patterns we can trust, use, and build upon.

This tendency is everywhere. It's how physicists discovered conservation laws, how economists designed riskless portfolios, and how scientists identify invariant structures across complex systems. But while this learning behavior seems natural, it invites a much deeper question: why does predictability have value in the first place?

This essay explores that question through the lens of physics — building on a simple yet powerful insight by Rolf Landauer, who showed that predictable information carries usable energy. From this principle emerges a striking idea: that the drive to learn — and perhaps even the origins of intelligence — can be rooted in the thermodynamic benefits of recognizing what stays the same.

The sections below introduce this perspective and connect it to real-world examples, energetic efficiency, and the broader implications for both biological and artificial learning systems. Whether you’re a researcher, educator, or just curious about how intelligence may arise from simplicity, this framework offers a new way to understand why we learn — and what we’re really looking for.

Why Predictability Feels Valuable

We are drawn to stable patterns because they help us navigate a complex world. Whether following a familiar routine, interpreting body language, or reading a weather forecast, our ability to function relies on recognizing regularities.

Much of our knowledge rests on these enduring elements — the laws of nature, the rules of logic, and core social norms. These “constants” allow for planning, control, and understanding. If they changed too rapidly, our responses would always lag behind, and life would become unmanageable.

How We Learn: A Hierarchy of Change

We naturally structure our learning based on the stability of the subject matter:

Even in fast-changing environments, we seek “islands of stability.” This instinct drives major insights:

From Intuition to Physics

While our preference for stability seems intuitive, it reflects something deeper. Why is predictability not just useful, but valuable in a physical sense? Can this preference be traced to the laws of nature themselves?

In the 1960s, physicist Rolf Landauer uncovered the energetic cost — and value — of information. His work showed that predictability isn’t just a mental shortcut; it’s something that can carry **real physical energy**.

Landauer’s Principle and the Energy of Information

Landauer’s principle states that any bit of reliably predicted information carries a minimum amount of usable energy:

E = kT ln 2

This equation might look simple, but its implications are profound. It means that predictability can be energetically harvested — even by non-living systems. Constants, by being the most predictable features of reality, become the most efficient sources of usable energy.

From this lens, the search for constants isn’t just an intellectual or practical pursuit — it’s a thermodynamically rewarding one.

Learning as a Self-Sustaining Loop

Once this connection is made, learning takes on a new role: it becomes a self-fueling cycle.

Find what stays constant → extract energy → explore further

This process creates a feedback loop. The more stable patterns a system identifies, the more efficiently it can operate — and the more resources it has to keep learning. This may explain how early forms of “proto-intelligence” could arise even in simple physical or chemical systems: as a consequence of energy optimization.

In other words, the ability to learn may not require a brain, a goal, or even life itself. It may simply require a universe with structure — and a system that can benefit from finding it.

Why Learning Is the Search for Invariants

At its deepest level, learning is about finding what doesn't change in a changing world. These invariants form the anchors of understanding — the reference points that allow us to interpret everything else.

Whether it's a neuron, an algorithm, or a human mind, the process is the same: identify patterns, extract structure, build models, and act accordingly. And all of it begins with the search for constants.

This essay is a continuation of ideas introduced in On the Physical Origins of Learning, now extended to include dynamical invariants, energy flows, and the autonomous nature of intelligent systems.

If you're interested in cognition, AI, or the physical basis of intelligence, I'd love to hear your thoughts.

đź“„ Full Paper:
Understanding Learning through the Lens of Dynamical Invariants