Computational irreducibility in Wolfram’s digital physics, and free will

Giulio Prisco
Turing Church
Published in
4 min readApr 18, 2020

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I am thinking about the new framework for fundamental physics proposed by Stephen Wolfram and its philosophical aspects discussed in the video “Wolfram Physics Project: Philosophical Implications & Q&A.”

In reply to a question from the audience, Wolfram says that his research program can be seen as related to traditional “sacred geometry.” I guess this is only a diplomatic reply, but I like it!

Wolfram’s collaborator Jonathan Gorard, who reminds me of Sheldon Cooper, appears in the video now and then, providing very clear explanations.

Wolfram’s framework is discrete, finite, and digital (based on a generalization of the cellular automata described in “A New Kind of Science”). Matter, energy, space, time, and quantum behavior emerge from underlying digital graphs. Gorard has written two papers, recommended as the best starting point for physicists, on the derivations of relativity and quantum mechanics in Wolfram’s framework.

Wolfram’s digital physics is fully deterministic, which seems to exclude free will.

But there is computational irreducibility: The strong unpredictability found in finite digital computations with simple evolution rules.

If you want to know what happens in the future of an irreducible digital computation, you must run the computation through all intermediate steps. There is no shortcut that permits predicting, with total certainty, what will happen in the future, without actually running the computation.

At this moment the question that I’m interested in is: Is computational irreducibility an “acceptable” replacement for free will?

In Wolfram’s words, computational irreducibility implies that

“the actual evolution of the universe… can only be observed, not predicted.”

Of course one can predict the end state of an irreducible computation running on a given computer, by simply running the computation on a faster computer. But this prediction is really an observation, because the computation has been run. Observers within the computation would observe an unpredictable evolution on both computers. Also, if the computation is our whole universe, there’s no faster computer.

Rudy Rucker says:

“I’m quite happy with this resolution of the conflict between determinism and free will…

By ‘free will’ do you mean ability to make an utterly random decision? But what is ‘utterly random’? If something’s unpredictable, it’s all but indistinguishable from being random, no?”

I concede that computational irreducibility seems practically indistinguishable from free will. If “fake” free will looks and feels like “real” free will and nobody can tell the difference (“If it looks like a duck…”), then it seems that computational irreducibility is a proxy for free will, if not the same thing.

I also concede that, besides “fake” free will, consciousness as we experience it could arise in a computationally irreducible digital universe.

However, even if it turns out that Wolfram’s digital physics permits deriving what we know of fundamental physics, real free will could be at work deeper down in the foundations of physical reality.

Ray Kurzweil noted that, even if Wolfram’s digital physics works, deeper mechanisms could be “implementing the computations and links of the cellular automata.”

“Perhaps underlying the cellular automata that run the universe are yet more basic analog phenomena… Thus, establishing a digital basis for physics will not settle the philosophical debate as to whether reality is ultimately digital or analog. Nonetheless, establishing a viable computational model of physics would be a major accomplishment.”

I agree, and I think that at this moment the main merit of Wolfram’s research is to suggest that what we know of fundamental physics, including relativity and quantum mechanics, could be elegantly derived from underlying models of reality different from current ones. In my book [*], I sketch models of reality compatible with free will, and suggest that real free will is a fundamental, primary aspect of physical reality.

In Wolfram’s digital physics, the universe is a computation, and the computation is all that is. But we can think (Wolfram doesn’t, but the idea can’t be ruled out) that digital physics “runs” on a computing substrate in a deeper level of reality (simulation hypothesis) [*].

We can think that a simulator (aka God) set the universe in motion with an initial configuration and digital evolution rules, without further interventions.

We can also think that God intervenes in the universe by violating the digital evolution rules now and then. But if I were the simulator, I would find it much more elegant to design the universe with an interface that allows interventions from outside, without violating the rules but rather by exploiting causal gaps in the rules (e.g. quantum collapse, strong chaos) [*].

I will continue to study Wolfram’s digital physics, but at this moment I have a strong esthetic bias against it.

[*] My book “Tales of the Turing Church: Hacking religion, enlightening science, awakening technology” is available for readers to buy on Amazon (Kindle | paperback).

Please buy my book, and/or donate to support other Turing Church projects.

Cover picture, picture from Wikimedia Commons.

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Writer, futurist, sometime philosopher. Author of “Tales of the Turing Church” and “Futurist spaceflight meditations.”