Emergence

For a long time, my instinct in physics was to understand things by taking them apart.

A material into its microstructure.
A microstructure into atoms.
A physical process into equations.
And, quite often in my case, an equation into something I could eventually simulate on a computer.

It is still one of the ways I like to think.

I started in materials science, so looking for explanations at smaller scales felt natural. Why does a material behave this way? What is happening in its structure? What happens if we go further down and look at atoms, interactions, or electronic structure?

Later, as I moved closer to computational physics, the tools changed, but the instinct remained similar. Differential equations, numerical simulations, machine learning: different ways of trying to describe a physical system from the rules underneath it.

Somewhere along the way, however, I became interested in almost the opposite direction.

Not only in what the pieces are and what laws they follow, but in how those pieces become something else when they are together.

That question is what brought me to emergence.

A single spin is not a magnet.

A single molecule does not undergo a phase transition.

A single neuron is not a mind.

Yet the collective system can acquire behavior that is difficult to see by looking at any one component in isolation.

There is something about that transition that I find beautiful.

P. W. Anderson gave one of the clearest expressions of this idea in his 1972 essay More Is Different. I first encountered the idea when I was around twenty, and the title stayed in my head long after I had forgotten many of the details I was reading at the time.

More is different.

It is such a short sentence, but it changes the way the problem is framed.

Knowing the microscopic laws does not automatically mean that we understand everything that happens at larger scales. When enough components interact, entirely new descriptions become useful: phases, collective modes, order parameters, patterns, networks, and structures that do not really make sense at the level of an isolated component.

This did not make me less interested in reductionism. If anything, I became more interested in it.

I still want to know the atoms. I still care about electronic structure, equations of motion, molecular dynamics, numerical methods, and simulations.

But now I am just as interested in the bridge between those microscopic descriptions and the collective behavior that eventually appears.

That is probably where my interest in complexity started becoming something more than a passing curiosity.

I began noticing the same ideas appearing in very different places: collective behavior, self-organization, criticality, feedback, networks, information. Systems that looked unrelated on the surface sometimes seemed to share similar ways of organizing themselves.

At the same time, I became more careful about the word complexity itself.

Having many components is clearly not enough. A gas can contain an absurd number of molecules and still be described remarkably well using only a few macroscopic variables.

So the interesting part is not simply the number of pieces, but the structure of their interactions, the feedback between them, the presence of several scales, and the way organization can appear without being explicitly imposed from outside.

I do not yet have a clean definition that I am completely satisfied with.

And I am fine with that.

One reason I created this website is precisely because there are many things I am still trying to understand.

Most of what I write here is personal in that sense.

These are not meant to be authoritative articles or polished lecture notes. They are closer to traces of what I am studying, things I want to remember, connections I notice, and ideas I want to return to later.

Writing is also one of the ways I test whether I actually understand something.

I often come back to my own notes weeks or months later, read them again, change my mind about parts of them, or suddenly see a connection that I had missed the first time.

So, in some sense, I am the main reader of this website.

But it is still a website, not a private notebook.

If someone happens to find one of these posts useful, interesting, or worth sharing, that makes me genuinely happy. Science has always been more enjoyable to me when an idea escapes the page I found it on and becomes part of another conversation.

That is also why the language of this site will not always be the same.

Some things I will write in English, especially ideas connected to my scientific work or things I would like to discuss with people beyond my immediate circle.

Other things I will write in Persian. Sometimes I simply want to explain something to friends, or write about an idea in the language in which I would naturally talk about it with them.

There will also be gaps.

If something I am currently interested in does not appear here, it may simply be because this site is new and I have not had time to bring all my old notes into it.

Or, more importantly, it may be because I am still studying it.

I would rather leave something missing for a while than fill the website with explanations I do not yet believe I understand.

This means the posts will probably appear in a slightly strange order.

That is fine with me.

This is not supposed to be a finished map of what I know. It is closer to a record of how that map changes.

And that brings me back to the title.

This first post is called Emergence for three different reasons.

The first is the physical one: the appearance of collective phenomena that are not obvious from the individual pieces that produce them.

The second belongs to Anderson.

More Is Different was one of the ideas that made me look at physics differently when I was younger, and it feels appropriate that the first page of this site leaves a small reminder of that essay here. In that sense, this post is also a modest tribute to P. W. Anderson and to a sentence that quietly opened a new direction of curiosity for me.

And the third emergence is much less scientific.

It is simply this website itself.

For a long time, I had notes, unfinished ideas, simulations, questions, bits of physics I wanted to return to, and subjects I kept telling myself I would write about later.

At some point, I had to stop waiting for them to become complete.

So this is the beginning.

I still come from materials science and physics. I still enjoy building models, solving equations, running simulations, and finding ways to use computation and machine learning to understand physical systems.

But I am increasingly interested in what happens between the levels: between atoms and materials, local interactions and collective behavior, microscopic rules and macroscopic structure, simulation and understanding.

I do not know yet whether complexity will eventually become the center of my work or remain one of the lenses through which I look at other problems.

For now, I am happy to leave that unresolved.

What I do know is that I want to keep following the same underlying idea: how simple rules, repeated interactions, and many components can give rise to structures and behaviors that feel genuinely new.

And whether computation and machine learning can help us not only reproduce those behaviors, but understand where they come from.

I do not have the answers yet.

That is probably why I am writing things down.

And it seems fitting that the first thing to emerge on this website is a post about emergence.