I started delving into Steven Wolfram’s new book, “A Fundamental Theory of Physics.” I followed his work since the early ’90s when I first used Mathematica on an 80386 system. I was impressed by Mathematica’s ability to handle symbolic calculations and its graphics capabilities.
After Mathematica, Wolfram released “A New Kind of Science” in 2001, a comprehensive work on cellular automata, their properties, and implications. The book generated quite a buzz. Wolfram was one of many to demonstrate how simple cellular automata could produce complex patterns. His magnum opus collected more examples and discussions on the phenomenon than I saw in one place. The illustrations were captivating and would have been impossible in the ’70s or ’80s due to computational limitations.
Wolfram’s Books
One particularly fascinating concept was the Turing-completeness of Game of Life-like automata, which Wolfram discussed in depth. This idea suggests that these automata can perform any computation that a modern computer can execute. The simple rules governing these computations could be easily specified and generated, allowing for a captivating exploration of a universe filled with all such machines. If cellular automata could solve any computable problem and there existed a universe with all such automata, discovering computational solutions would no longer involve constructing a program but instead plucking it from this vast computational universe.
Another exciting aspect of cellular automata systems is that they also demonstrate emergence. Straightforward rules and shapes can result in repetitive, complex behaviors in terms of contributing to the build-up and upkeep of complex shapes and structures. For example, some simulations involving these systems demonstrate “gliders,”; forms that fly and travel across the board while maintaining their shape. There are also far more complex emergent phenomena possible, with entire giant spaceships moving through the game board, supported by individual patterns that retain their structural integrity. Some factories can produce objects like gliders. The world of Life can genuinely be quite complex. And all this complexity speaks to the emergence of complex phenomena, even useful ones, from the simplest rules.
If simple rules lead to unpredictable outcomes and deep complexity in the game of Life, why not in real life? And the universe?
Wolfram Mathematica
When “A New Kind of Science” was released, my fascination with genetic algorithms had already taken hold. I had a great time learning and experimenting by combining the concepts in Wolfram’s book with genetic techniques to generate programs efficiently and evaluate their “fitness” – their ability to solve a desired problem. However, another idea presented in the book introduced a limitation that could have helped the swift evaluation of generated programs: computational irreducibility. This concept posits that the only way to understand what some programs do is to run them and observe the results; there is no way to “fast forward” to a projection without performing all the intermediate steps. Computational irreducibility is not necessarily intuitive; it asserts that simply “reading” a program is insufficient to grasp its function – one must run the program to find out. Unlike Newtonian equations of motion that allow specific values to be plugged in to predict parameters at a particular moment, many programs are irreducible to such a model.
On a less practical but still enjoyable note, the ideas of Ed Fredkin, which I had been pondering since my teenage years, and the subsequent release of “A New Kind of Science” inspired me to contemplate whether the universe is a computer. I wrote a brief essay on the topic, questioning if the continuity we assume in the universe is not a reality but an artifact of the mathematical tools we use to examine everything around us. For example, Zeno’s paradox assumes that space can be divided infinitely, but we have seen in mathematics that this assumption may not necessarily hold true.
Conway’s Game of Life
I thought and even wrote about whether the Universe was a computer for much of my teen years. In one conceptual model I built, I imagined that we were living in a digitized, quantized world due to the finite indivisibility of space-time. If space-time can be no smaller than an indivisible unit of Planck length, then what it can contain is also similarly bound. And if we have quantized space-time and quantized unique “symbols” to populate in this space-time, what we essentially have is something that resembles a real computer data structure. Could entanglement, or “spooky action at a distance,” be a pointer between two memory locations? Could the evolution of the Universe as a system merely be algorithms acting upon the space-time data structure? And could it be that we somehow cause a selection of a dynamic slice of this vast data allowing us to perceive the current instance of time?
While these flights of fancy are fun and connected to deep questions, for a professional scientist and engineer, balancing these questions with pursuits that can have real, measurable, and tangible goals is essential. I have found some balance in this way throughout my career. I enjoy investigating such cosmically mysterious questions for fun, but much of my time is spent in figuring out how emergence is practically helpful in the context of Generative AI. How one can find inspiration from the idea of computational irreducibility to impose minimum resource costs on an operation, a “proof of work,” if you will.
Computer science is truly an ocean, and it is connected to other deep science in a very unique way. Ideas that originate here often lead to insights in other disciplines, and it is also the science that allows tools to be developed which broadly advance all science. So it is a noble pursuit for sure.
I read and enjoy the work of Stephen Wolfram. He has a practical side to his pursuits in building products and the courage and desire to take those crucial journeys of discovery that may or may not lead. Whether or not others consider it hard science, Wolfram’s work has been a great source of intellectual stimulation and learning.
