# Supergeek Stephen Wolfram on “computational irreducibility”

July 3, 2012 | Posted by News under Comp. Sci. / Eng., Intelligent Design, Irreducible Complexity |

In an interview with Martin Eiermann (“”I Like to Build Alien Artifacts”,” *The European,* July 2, 2012), Stephen Wolfram offers some interesting, maybe dubious, comments on cells and computational irreducibility:

Wolfram:A couple of points. There is a phenomenon which I call computational irreducibility. When you have a process where the behavior is quite simple – like a planet orbiting around a star – we are smart enough to use math to figure out what will happen in the future without having to wait for the planet to move around. We can compute the outcome by plugging the right numbers into a formula. But many systems are irreducible after a number of steps – you really have to simulate each step to see what will happen. We need a lot of computational effort for that. But it’s a fallacy to believe that our current technology is the only possible computational technology. The fact is, we can make computers from a lot of materials, not just transistors. The reason that’s exciting is because it opens up the possibility of making a computer out of molecules. It hasn’t been done yet, and there’s a lot of ambient technology that is required to make a molecular computer possible. But it reminds us that we must not shrink transistors – we can use much simpler components.

The European:Maybe it is helpful to talk a little bit more about what you call “computation in nature.” Our common sense tells us that there’s a big difference between animate and inanimate life, or between human technology and natural organisms.

Wolfram:Computation describes a system that starts somewhere, goes crunch-crunch-crunch, and produces a result. The question is whether all computations are like those that we program into computers with our current software engineering. The answer is no. But when you start enumerating programs at random, a lot of them look remarkably like the kinds of processes we see in nature. Today, we are using active algorithm discovery in our research, where we mine the computational universe for programs that might be useful for doing computer processing; and it’s becoming much more obvious that naturally occurring computations are not unlike the processes inside a computer: We start at one state, and end at another state.

The European:This equation of nature and technology raises a few very hard questions about the definition of life, about free will, and about intelligence. What are the mathematician’s answers to those questions? …[interesting claims about free will follow]

Wolfram:Computational irreducibility is a key feature of life: We cannot grasp life through a formula, but must really simulate and observe it to see what happens. That’s how we as humans end up freeing ourselves from the deterministic rules. I tend to think that the concept of computational irreducibility is probably the answer to the philosophical debates of the past two thousand years about the relationship between free will and determinism. Philosophy is always at a certain distance to human behavior, so a lot of questions really get answered by science.

Thoughts?

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### 10 Responses to *Supergeek Stephen Wolfram on “computational irreducibility”*

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One might probably say that a river computes its way through rocks. But I think that the word “compute” implies a formal process in a teleologic context rather than something obscure. Computation is causally linked to formalism and ultimately to intelligence. Inanimate nature does not compute anything in this sense, IMO.

Dr Wolfram, havent you heard of basic chaos theory 101?

“When you have a process where the behavior is quite simple – like a planet orbiting around a star – we are smart enough to use math to figure out what will happen in the future without having to wait for the planet to move around. We can compute the outcome by plugging the right numbers into a formula.”

Now take a “simple process”

Water in a pipe.

Is Dr Wolfram “smart enough to figure out what will happen in the future”, in turbulent flow, by “plugging the right numbers into a formula”.

Give it a try Doc. Yessirre. That should tell the world how smart you are.

Eugene S., here’s my take on it:

When I think ‘computation’ in the sense of teleology, I think ‘algorithmic’ is the better word. If we know the exact topography and the fluid equations that govern the behavior of water, we can theoretically ‘compute’ exactly what will happen when we open the floodgates. In this sense, the flow is following a set of equations. It is the laws of nature + the configuration of the system that determines the behavior of the river.

However, when you observe someone hiking across a landscape, or a driver making his way from point A to point B through a system of roads, this motion is determined by a set of instructions. i.e. go to point A, turn left, go to point C, turn right, etc. In this case the set of instructions originate from some source outside of the system. There is a flow, and a computation, but the behavior is determined by an algorithm that transcends the system. So it is with the processes that govern life.

Wolfram is not saying anything that has not already been said by others. He is a student of the school of digital physics pioneered by Edward Fredkin. It’s really a religion. The core belief is that the universe is a huge discrete computer and that everything is deterministic. Computational irreducibility, pioneered by Konrad Zuse, Fredkin and others, says that some computations (such as the universe itself) are so complex that they might as well be non-deterministic because the outcome can only be found by running the computations. In other words, Wolfram believes that free will is an illusion caused by the unpredictability of certain complex computations.

It’s all nonsense, however, since determinism makes no sense without randomness. There can be no reality that is purely random or purely deterministic. We live in a yin-yang universe.

Just because you can’t predict the result of the computation with a simple mathematical rule doesn’t rid the process of its fundamental determinism. Free will cannot be supported by anything within the physical world, at least as long as we expect the laws of physics to be universal within it.

Chris -

Wolfram’s research is on precisely the phenomena you describe, in fact that was quoted in the part that Denyse put forward: “But many systems are irreducible after a number of steps – you really have to simulate each step to see what will happen.”

In fact, Wolfram shows that you get this kind of erratic behavior even in some of the simplest systems conceivable. He and Matthew Cook proved the Turing-completeness of several elementary cellular automata.

For people wanting to see a linkage between Wolfram’s work and the Intelligent Design debate, you should checkout a paper of mine discussing exactly that issue:

Irreducible Complexity and Relative Irreducible Complexity: Foundations and Applications

Tragic mishap,

I totally agree with the first part of your comment. With the greatest respect to Professor Steve Wolfram, his point on computational irreducibility has no bearing on human freedom vs. determinism. As any competent philosopher would tell him, showing that human behavior cannot be predicted does not entail the conclusion that our behavior is undetermined. Unpredictability

per sedoes not make us free.However, you then go on to write:

I have written a post which touches on this topic: Is free will dead? (in response to an article in

USA Todayby Professor Jerry Coyne). If you have a look at the sections on quantum indeterminacy and top-down causation, you will see that I develop a simple model for reconciling free will with the laws of physics.Exactly how we (as human beings) manage to collapse wave functions on a holistic (i.e. personal rather than bio-molecular) level is a mystery, but there’s nothing in physics to say it can’t happen, as far as I can tell.

Vincent -

I think you have misread Wolfram. He does not say that it is undetermined, but rather that its unpredictability is what gives us the illusion of freedom.

Out of curiosity, have you read Stapp’s paper, Quantum Interactive Dualism?

I well remember that thread vj. As I recall I asked a question which you never answered: Is God the form of the universe? This would seem to be the obvious conclusion about Him from what you are saying. That idea is repugnant to me for the same reasons I reject your idea of free will. I’m not really sure what the difference is between what you’re saying and emergence.

Obviously I believe in top-down causation and interaction between the immaterial and material may even occur at the quantum level somehow. But I have a different idea of what the “top” is and a different idea of what “immaterial” means. “Immaterial” means “not material.” You seem satisfied with that. I want to know if not material, then what?

It is a simple exercise to prove that the universe is necessarily probabilistic and that a purely deterministic universe is crackpottery. Does this mean that Wolfram, Fredkin and the rest of the digital physics crowd are a bunch of crackpots or, at the very least, mistaken? You be the judge.

If the universe were deterministic it would have to be able to calculate the precise durations of various particle pair interactions, otherwise conservation laws would be violated. The duration of an interaction is determined by the energies involved.

The problem is that no such calculation can be performed. Why? Because a time dimension cannot exist. Why? Because that would require a changing time and a changing time is self-referential, leading to an infinite regress. Therefore, nature has only one recourse: probability. In the end, the conservation laws are obeyed.

This simple proof of the unchanging nature of time (hence a probabilistic universe) is the reason that nothing can move in spacetime (surprise) and that Sir Karl Popper compared Einstein’s spacetime to Parmenides’ (Zeno’s teacher and mentor) block universe in which nothing happens. Source: Conjectures and Refutations.