The Curiosity and the Cat: Innovation, Exploration, and Assembly Theory

yuval bloch

We’ve all heard the saying, “Curiosity killed the cat.” It may be time to flip the script. Without curiosity, cats—and every other living thing—might never have come into existence at all.

Of course, curiosity alone doesn’t spark life. Complexity arises from a dynamic tension: the urge to explore new possibilities and the need to consolidate what has already been discovered. Innovation without a foundation leads nowhere. Consolidation without curiosity stalls progress. Life—and all complex systems—depend on the interplay between the two.

In this post, we’ll revisit assembly theory to explore how this same balance plays out across biology, technology, and beyond—from evolution and immune responses to artificial intelligence and economics.

“Would you tell me, please, which way I ought to go from here?”
“That depends a good deal on where you want to get to,” said the Cat.
“I don’t much care where—” said Alice.
“Then it doesn’t matter which way you go,” said the Cat.
— Lewis Carroll, Alice’s Adventures in Wonderland

Slime mold creating optimal networks
The Cheshire Cat and Alice — a moment of pure exploration. Without a fixed destination, every path is possible.

Assembly Index: Building from the Ground Up

Imagine trying to build a bicycle from scratch. You see one and note its components: wheels, a frame, gears, chain, handlebars, brakes. So you begin with the gears—but gears require a chain. The chain is made of metal links. And so it goes.

Soon, you realize: a bicycle isn’t a singular object. It’s a layered construction—an assembly of parts, many of which are assemblies themselves. Without these components already in place, building a bike randomly would be nearly impossible.

That’s because complex systems aren’t just assembled—they evolve. Bicycles didn’t appear fully formed. Simpler technologies like wheels, axles, and gears were built for other uses, then later recombined.

This is the essence of assembly theory, which measures how many steps are required to build something from basic building blocks, reusing parts as you go. A higher assembly index means greater complexity—something unlikely to emerge by chance, shaped instead by history, selection, and reuse.

A Soviet Lesson in Skipping Steps

This layered building process applies beyond biology. Consider the Soviet Union’s attempt to shortcut innovation in computing.

From the 1940s to 1960s, Soviet engineers made steady, iterative progress in developing early computers. But under pressure to compete with the West, Soviet leadership chose to abandon this organic growth and instead reverse-engineer IBM’s System/360.

At first, it seemed efficient. But reproducing the IBM system without having built the intermediate steps resulted in fragile, inflexible machines that weren’t well understood. By skipping the necessary layers of learning and iteration, the Soviets lost their innovative edge.

The lesson? You can’t shortcut complexity. Real innovation only emerges through a layered process of exploration, feedback, and construction.

Slime mold creating optimal networks
The IBM System/360 — the Soviet Union knew exactly where it wanted to go, but left no room to explore how to get there..

The Balance

Innovation relies on a balance between stochastic exploration (trying many things at random) and deterministic selection (filtering out what doesn’t work). Too much randomness leads to chaos. Too much control leads to stagnation. Assembly theory helps us understand how complex systems maintain this balance.

We see this tension everywhere:

  • Evolution relies on mutation and recombination for novelty, and on natural selection to filter what survives.

  • Brains form new neural connections through experience, then prune unused ones. Psychedelics seem to tip this balance—promoting excess connectivity while reducing pruning—leading to more creative but less focused states. Interestingly, some researchers suggest that in specific contexts, this altered state may be cognitively useful.

  • Ant colonies use fixed trails for efficiency but also send out scouts to discover new food sources.

  • Immune systems deploy targeted responses while allowing exploratory immune cells to search for unknown threats.

Machine Learning

Machine learning mirrors natural systems by balancing exploration and selection. Algorithms like neural networks, evolutionary models, and reinforcement learning use meta-parameters—learning rate, mutation rate, temperature—to regulate this dynamic. Too much of either can stall learning or lead to instability. Success lies in keeping exploration and exploitation within a balanced range.

Assembly Theory in Action

In the paper “Assembly Theory Explains and Quantifies Selection and Evolution”, the authors demonstrate a simple model: Start with elements A, B, and C. Combine A and C to form AC. Then AB. Then ABA. Over time, longer structures emerge from combining simpler parts.

But random combinations rarely produce long, complex sequences. To build meaningful complexity, the system must reuse and replicate useful structures—effectively introducing selection.

If reproduction dominates, the system repeats itself endlessly. If novelty dominates, it never builds anything coherent. But in the right range of balance, the system can generate and regenerate layered complexity—a hallmark of life, learning, and innovation.

Range of exploration and reproduction supporting innovation
The range of exploration and reproduction that enables innovation, adapted from the paper Assembly Theory Explains and Quantifies Selection and Evolution.

Diverse Paths to Innovation

We often associate innovation with freedom—especially in democracies. These systems tend to strike a good balance between exploration and consolidation.

But assembly theory suggests that innovation isn’t tied to one system alone. What’s essential is that systems operate within an effective zone of balance—and that zone can be surprisingly wide.

Centralized or authoritarian regimes may temporarily support innovation by focusing effort, reducing noise, or accelerating decisions. This doesn’t mean they’re better—but it does mean we shouldn’t underestimate them.

Recognizing the diversity of innovation pathways isn’t an endorsement of authoritarianism. It’s a call to understand global dynamics with nuance. Innovation thrives not because of any one structure, but because a system enables exploration and consolidation to coexist.

I believe in democracy—not just as a space for innovation, but as the morally superior system, one that protects dignity and dissent. But acknowledging that innovation can arise elsewhere helps us defend democracy more clearly—not by assumption, but by strategy.