WOLFRAM NOTEBOOK

Biology 101 - Lesson 01: Background, The Road to Rule 30

Willem Nielsen

Introduction

What is the nature of biological processes? How do they look? What can they achieve? What happens when they go wrong? These are such simple questions, and yet the field of biology, in my view, has largely failed to give people good answers.

In my experience, modern academic institutions are really bad at answering big questions like this, and most of the best “scientists” of our time have found ways to make progress not because of these institutions but despite them.

So okay these are bold statements, who do I think I am, right? Well, I think most biologists have largely missed a powerful new class of models: those based on simple computational rules. And because of this, they have been limited in their ability to give good high-level descriptions of what is going on in biology.

For thirty years now, Stephen Wolfram has been filling this gap, and has pioneered some groundbreaking computational models for biological systems. Starting as a fan of the research, and eventually becoming a collaborator, I’ve become convinced that with Wolfram’s models, we’ve struck gold, and are now in a position to understand and communicate the high-level features of biology better than ever before.

Despite this, most people outside of the Wolfram circle don’t know about his work in biology. So, myself and others at the Wolfram Institute thought it would be a good idea to bring all of Wolfram’s work in biology into one place, so that those who are curious can get up to speed as fast as possible.

Stephen has published a ton of work that is very accessible, and I will link to it as we go. But my goal with this article is to provide a single chronological and theoretical thread through his research in theoretical biology. Even by telling this story, I’ve felt my intuition for biology growing. Not only that, I’ve felt that understanding Stephen’s biological work in its entirety, has sparked ideas for interesting future directions of research in biology. And my hope is that the reader will have a similar experience.

Okay, so, where to start? The first important piece of the story is understanding Stephen himself, so who the hell is this guy? And what makes him special?

The Road to Rule 30

From my observations and interactions with Stephen at Wolfram Summer School and working with him on the medicine post, my impression is he was basically born to be a scientist.

The one sentence summary is that he’s just an extremely curious, intelligent, friendly, and independent-minded person. This combination is very unique, and so it makes him a powerful force in the world of science and technology.

In addition to Stephen’s personality, I believe his story can also tell us a lot about what makes his research in biology different.

So what was that story?

Well, he’s been doing serious science since he was a teenager. He famously got interested in the second law of thermodynamics from this textbook on the subject at the age of twelve:

The book, was unique from other physics books in that its conclusions did not require a trust in authority, rather one could “reach the truth” simply by understanding the ideas in the book. In Stephen’s words “what was so exciting that day was that I got a first taste of the idea that one didn’t have to be told how the world works; one could just figure it out”:

This idea, that the arrangement of gas particles tends towards disorder, was also his first introduction to the “science of complexity” (although it didn’t have that name at the time) and importantly for us, it was this interest that would eventually lead him to model the origin of complexity in biological systems. This connection, was by no means a linear path though.

He spent his teens and early twenties deep in the field of particle physics. While very far from biology, it was during this time that he figured out that computers could be useful for doing science, often using them to do physics calculations. And this appreciation for the computer as a tool for science would grow and become an essential theme in his future work, including, in biology.

In his words, Stephen “quickly outgrew” the computational tools he was using. And after getting his PhD in physics, he decided to work on building a software system that could, once-and-for-all, fulfill all his scientific needs.

This famously turned into Mathematica, which ended up being extremely useful for Stephen (and others) in doing science. But more than being a useful tool, the process of building Mathematica continued to help develop Wolfram’s intuition that many of these “human creations” like mathematical equations, and the models of physics, could indeed be boiled down to computational rules.

With this powerful new tool and understanding, and with the rapid improvement of computers, Stephen began to separate himself from the traditions of physics, mostly using computational models instead of mathematical ones.

But what did all this mean for his childhood interest in complexity? Well after having success with Mathematica by stripping things down to their computational essentials, he began to use the same approach in his scientific endeavors. In particular, he started developing a “minimal model for complexity”.

After repeatedly refining and simplifying, he arrived at what he would call a 1-dimensional cellular automata, some early print-outs of these 1D automata are shown below:

And with these powerful new minimal models, he began to make significant progress in answering his long held questions about the origin of complexity.

The first step, was the formulation of the concept of “computational irreducibility”. In exploring the behavior of cellular automata, he started to realize that “unpredictability” was actually quite common, and he began to speculate about what that could mean for science. Here is an amusing piece of a transcript from the conference where he first spoke publicly about computational irreducibility:

The next crucial step, came from Rule 30. Interestingly, Stephen had looked at Rule 30 two years earlier in 1982, but he hadn’t yet understood its importance. After more study of cellular automata and after printing it out in higher resolution, its significance hit him, and he realized, that surprisingly, complex phenomena can originate not just from complex programs but even from simple ones. Here we show the earlier low resolution printout of Rule 30 on the left and the higher resolution one on the right:

And seeing these two images side-by-side, you can see why the second one was what made things click. What rule 30 so beautifully shows, is that, starting from a simple initial condition (with one black cell) and running a simple set of rules (eight rules in this case) one can already generate complex, or random behavior.

Digressing slightly, this story also nicely illustrates how the accessibility of Stephen’s models played an important role in expediting his thinking.

I mentioned earlier that Wolfram was born to do science. But I also believe, that he was extremely lucky to find a path that enabled him to become well-versed in both the world of computation and the world of science. And it turned out, that there were a lot of low-hanging fruit in that intersection.

In particular, nobody had captured the essence of complexity in such a simple model as in rule 30. And I think the fact that the model was so simple, gave him the mental clarity to realize its importance, and eventually connect the idea to so many different fields, as he did in New Kind of Science.

You might imagine that good ideas come from the mind, and the smartest minds have the best ideas. But even for someone as talented as Stephen, it was seeing the right picture that made all the difference in the formulation of his career-defining idea.

And I’ve definitely experienced this phenomena in my own intellectual journey. Being able to readily visualize the behavior of cellular automata, I believe, has allowed me to understand things that I would’ve never understood otherwise, like the ubiquity of hierarchy in animals societies, or understanding why treating cancer is so difficult. Oddly enough, I can feel myself getting smarter by staring at looking at these computational creatures.

Anyways, these two insights, computational irreducibility and the idea that simple programs can create complex behavior, were the seeds that grew into what would become New Kind of Science (NKS), where Stephen would make his first well-known foray into the field of theoretical biology.

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