Water Molecules, Fluid Dynamics, and the Line Between Assembly and LLMs

Lately, I’ve been studying “why AI actually works” all over again.

To be precise, I always assumed I “understood” it. Sigmoid functions, vectors, dot products, backpropagation. I know the words, and I can follow the equations. When you’ve been an engineer long enough, you settle on “well, it’s probably just a giant statistical model” and let yourself be satisfied.

But recently, a thought struck me.

“Wait. Do I actually understand this?”

So I started carefully tracing through the Transformer again.

…To cut to the conclusion: somewhere along the way, I got lost again.

Especially after the Transformer. From here, it rapidly diverges from my “engineer’s gut feeling.”

The feeling of wiring circuits in university labs

Back when I built circuits in university labs and poked at microcontrollers.

You put a value into a register. A flag gets set. It jumps. An interrupt fires.

Everything had cause and effect.

It was complex, sure, but you could trace “why it worked.” You could always reach a point where you could say “this is the cause.”

Of course, the programming languages I use at work are nothing like the world of assembly, but it still feels like an extension of the same craft.

So the equations of neural networks themselves don’t really put me off.

Dot product? Sure, I get it.

Activation function? Makes sense.

Backpropagation? It’s unsettling, but I follow the logic.

Up to here it’s fine — I can just barely keep up through machine learning and deep learning.

But why does stacking all of that up turn into something “intelligence-like,” such as ChatGPT?

This is where my brain suddenly rejects it.

You can’t see a “wave” by looking at water molecules

While thinking about it, I suddenly remembered fluid dynamics.

Even if you chase water molecules (H₂O) one by one, there is no “wave” or “vortex” in them.

There’s just a world of tiny particles moving according to the laws of physics.

But once their number becomes astronomical, a “flow” suddenly emerges.

Viscosity. Turbulence. Waves. Vortices.

Macroscopic laws appear all at once — ones you could never intuit from the explanation of individual particles.

This is what they call “emergence.”

And looking at today’s LLMs, I get a feeling very close to this.

Around the Transformer, it suddenly turns “fluid”

Traditional programs were quite “mechanical.”

Input comes in, it branches, it processes.

But LLMs from the Transformer onward suddenly become “fluid”-like.

Attention especially.

When I first saw the concept, I thought,

“Why on earth compare every word with every other word?”

With a programmer’s brain, the sense of “process things in order” is just too strong.

But the Transformer is different.

It relates the words in a sentence to each other all at once, inside a vast space.

Does the word “broke” attach to “pen,” or to “system”?

It computes that simultaneously, in every direction.

How to put it —

The “sense of stacking up logic” suddenly vanishes.

This is where my gut feeling completely changes.

”Designed complexity” vs. “statistical complexity”

Old systems were a “designed complexity.”

If statements. Functions. State transitions. Design documents.

All of it, stacked up by humans who understood the meaning.

LLMs, on the other hand, are quite alien.

Humans didn’t write the “rules.”

It just relentlessly learned

“the probability of the next token (a fragment of a word)”

to the absolute limit.

And yet, as a result, “meaning” and “logic” have floated to the surface.

This is somehow eerie — and fascinating.

Maybe “intelligence” is a phenomenon

When a huge number of water molecules gather, waves are born.

When a huge number of simple computations gather, something thought-like is born.

Thinking about it that way, maybe “intelligence” itself isn’t some special designed artifact, but

a phenomenon that appears once complexity crosses a threshold.

Just like fluid dynamics.

That’s why I seem to understand it, yet can’t.

Just as knowing the molecule doesn’t let you intuit the “ocean,” knowing the dot product doesn’t let you intuit “intelligence.”

Closing

I used to chase a single register. Now I’m watching the “waves” that stand on an ocean of computation.

The layer has certainly changed.

But one question remains, one I can never answer.

Just as a gathering of water molecules becomes an “ocean,” if a gathering of computations becomes “intelligence” —

then this very feeling of having “understood” it, right now — isn’t it just another one of those waves?