Questions About Stephen Wolfram’s Principle of Computational Equivalence

Following up on my post about the philosophy of ruliology and cellular automata, I decided to look more into the concept of ruliology. And what better way to explore ruliology than by reading the writings of the term’s inventor Stephen Wolfram? So, over the past month, I have read "A New Kind of Science" by Steven Wolfram.

After diving into the book, however, the last chapter left me pondering the Principle of Computational Equivalence. And as I head into the Wolfram High School Summer Research Program this summer, I thought I might write some philosophical questions down about this concept. This principle proposes a profound idea that may reshape our thoughts about the universe and our place within it. But what does this principle really mean, and how does it connect to broader philosophical questions?

What is the Principle of Computational Equivalence?

Wolfram suggests that systems capable of doing computations, whether they are human brains or simple algorithms, have equal power of computation when they reach a certain level of complexity. Essentially, this means that even simple rules can lead to behaviors as complex as any we might consider. So, if we think about it, does this mean everything around us is computing at the same level?

In this Youtube video, Stephen Wolfram gives a retrospective on Chapter 12 of "A New Kind of Science"

Exploring the Implications for Free Will and Determinism

Wolfram actually has a section dedicated in Chapter 12 about the nature of free will. Esentially, one side of the argument is that if all complex systems have equivalent computational abilities, and our brains are such systems, does this mean our choices are not as free as we believe? Are our decisions the result of computations determined by rules we have yet to understand? In contrast, the other side of the argument (which Wolfram argues for) is that our brains are affected by emergent behavior and that even if our brains are constructed by simple rules, as the principle suggests, the combination of these rules creates something larger and complex. Thus, the combination of these rules creates our true free will. These two sides can be a startling idea—considering the implications, how do we reconcile our sense of autonomy with a deterministic universe defined by computational rules?

The Universe as a Computational Entity

Wolfram’s theory pushes us to view the universe not just as a physical space but as a computational entity, where every part of it follows rules that, despite their simplicity, can lead to incredibly complex outcomes. If everything from the smallest particles to the vast structures of the universe operates under this computational framework, what does this tell us about the nature of reality itself?

Computational Equivalence and Equality

An intriguing philosophical twist is the notion of equality embedded in the principle. If a simple cellular automaton can compute things as complex as a human mind can, doesn’t this level the playing field between all forms of matter and intelligence? This idea challenges our conventional hierarchies of intelligence and complexity. Does this mean that everything in the universe deserves a new kind of respect and consideration?

An elementary cellular automaton known as rule 110. In his book, Wolfram considers this, along with other rules with slight variations, as the elementary cellular automata that show the most complex behavior due to its combination of randomness and localized structures. According to the Principle of Computational Equivalence, this rule (showing universality) is computationally equivalent to the human mind or the universe.

Image source: Weisstein, Eric W. "Rule 110." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Rule110.html

Philosophical and Ethical Considerations

The Principle of Computational Equivalence opens up scientific inquiries and ethical and philosophical debates. For example, if we can create or simulate systems that are computationally equivalent to human brains, what are we responsible for these systems? And how do we address the moral implications of creating or destroying such systems?

What's Next?

Stephen Wolfram’s Principle of Computational Equivalence was first proposed over 20 years ago, but it still offers a radical way to view the world, blending science with deep philosophical questions. As we continue to explore this principle, we may find that the universe is far more interconnected and equal than we ever imagined. What other revelations might this new kind of science bring? And how will it continue to challenge our beliefs about complexity, intelligence, and the very fabric of reality?