The Wanda Maximoff Illusion

So far the laws of physics have dictated that the world is ruled by causal relationships. Given an initial state, it will evolve following a set of rules, giving place to a new state.

If just for the sake of the argument, we assume a simple initial state and a simple set of rules, most people will assume the new state will also be simple, and that the rules can be inferred by observing enough state transitions. This is, after all, how we learned most of physics, put stuff in a box, mess with it, see what happens, rinse and repeat.

It turns out that things are not that, well, simple. First, simple rules applied to a simple scenario repeatedly can yield very complex scenarios. That very idea is the basis of Wolfram’s “New Kind of Science”. And as entropy expands, there is no guarantee we can look back. But here is a funny thing, Heisenberg’s uncertainty principle says we cannot look forward either. Even if you know the rules of the universe, to apply them you need to observe the initial state, but once you try to do it, you will destroy it.

Wolfram’s cellular automata number 30 shows that simple rules applied to neighboring states yield complex outcomes. Like in nature.

There are several hints that the universe is completely deterministic. But there is also evidence that we will never be able to prove this. Wittgenstein, Turing, and many others have shown that unsolvable contradictions arise when someone tries to reason about a system from inside it. But the fact that we cannot do it does not disprove the fact that the universe is deterministic. As is the case for the existence of god, the non-determinism of the universe may very well be unfalsifiable.

This amazing tweet from Joscha Bach triggered me to capture the thoughts here:

Given that we truly want to believe that we are independent agents in the universe, not just some fancy rocks, despite all the evidence on the contrary, and that no one will ever be able to disprove this for the reasons above, where can we find some solace? What is the part of the universe that could be subject to our will, and not to the laws of nature? And by laws of nature, it doesn’t matter if it is the pure scientific definition, Spinoza’s god, or the almighty bearded man in the sky who puppets us with his gift of freedom.

Quantum mechanics seems to have forced us to do the leap from causality reasoning to pure probabilities, due to its inherent observability limitations. It seems someone is playing dice with the universe. But just because something cannot be predicted, it does not mean it is nondeterministic. Let me craft my secret dice and let us play some d&d. I will roll my d20 for infernal breath plus full healing every turn.

Slime-like visualization of an atom highlighting the probabilistic distribution of electrons. Check this video for even more fun:

And maybe, it is about that. Maybe, in the course of evolution, the universe gave birth to a microscopic Wanda Maximoff. Maybe it evolved some atom arrangements that can fiddle with quantum probability distributions given their surroundings. Evolution is this neat theory, that offers a post-fact explanation for surprising outcomes. It is almost a tautology with its luxury of putting the improbable and the abundant in the same bucket. After all, anyone who can disagree is, by definition, dead. And it may have given this very special building block that can emit electrons not just out of the blue, but maybe when we are feeling blue.

In virtually any system, surprising orderly local minima will arise, as will chaos. The orderly way electrons arrange themselves in metal is surprising, as are water solvent properties coming from the H2O structure. What about those electrical discharges from our brains? We have strong hints that they implement some learning and command and control mechanism. But why do they exist? Are they the orchestration of those tiny scarlet witches?

In the Plantastic Voyage, writer Fabio Michelini and illustrator Giorgio Cavazzano use a beautiful anthropomorphism to represent the chloroplasts as Donald duck learns about how nature captures energy. We are doing the same here with our marvel heroine to talk about the electrical triggers in the brain.

Evolution limits itself to the survival part. It does tell us that beings that can control limbs, move around, and build tools, are likely to survive and grow complex due to their adaptability. But it does not tell us anything about will, even the will to survive. From its perspective, the neural networks in living beings are not different than those we have implemented in machines. Yes, different learning rates and sensorial apparatus, distinct sampling needs, and mechanisms, but ultimately all equally capable of minimizing to some extent a target function. Machines do lack an enormous number of pieces that will let them play the game of evolution, but it is very impressive how we made them mimic the brain.

Text-to-image models are a fascinating glimpse of the inside of a machine brain. Through bits they were fed, they developed their own WorldSense.

What artificial neural networks definitively lack is non-determinism. Given its initial state, we can compute the outcomes. Gödel’s paradox does not apply to finite computation. There is no halting problem with limited RAM, 64-bit math, and current energy prices. I will seed what I want in my perfectly controlled greenhouse, and I will wait for the crop. That is why even though the improvement of current technology may give us machines that can do any human task, they will not let us predict our next thought. We are nowhere near developing that ability.

What about quantum computing? Well, if the magical spark in our brains is these tiny Wanda Maximoffs arrangements manipulating probability fields, quantum computing is our House of M moment where we scream no more mutants. Take everything that makes us unpredictable, and put it in a tiny controlled box, neutralizing it. Quantum computing is this layer of control on top of the powerful subatomic probabilistic rules of the universe to make them more deterministic so that they can be useful for us. From that angle, it seems that the ultimate computer is not a superior form of life, but the opposite of it.

Life is, after all, in its most desirable definition, synonym with free will. We strive for agency, to be masters of our own, even if tiny, universe. Sadly, in the absence of nondeterminism in the laws of nature, we control nothing, not even our thoughts. Computers are fancy rocks of silicon and it would be sad for us to figure out we are just fancy rocks of carbon.

But what if deep in the brain we have these subatomic arrangements biasing quantum probabilities, entangling particles as we do to form qubits. What if this improbable and abundant phenomenon is making us be kind to our loved ones, feel part of our community, and be eager to persevere as a species and conquer the universe? This inscrutable initial state and its rules inside the brain, or even much simpler natural neural systems, may never be observable for the same reason we cannot prove determinism of the universe. Those pesky asymptotes trap the picture of the big bang inside black holes and make our deepest thoughts fall apart on the smallest photonic inspection.

A zenith is always present in a recursive system, traversed as zero or the infinite. The Brahma and the Shiva, as Vishnu live and dies, again and again. The father, the son, and the holy spirit are all Elohim, as is Dattatreya. Black holes trap the big picture and photons destroy the details, and we are left with piling turtles all the way as we reason about the universe from inside.

But it is precisely those limits that may give rise to the exact definition of free will. The ability to operate on a system that is deterministic, but non-predictable. The guarantee that your thoughts are your own, and can never be seen by any technology since, as Schrondiger’s cat, they would collapse with the interference the moment someone tries. This is freedom.

The recent hit show, Wanda and Vision, borrowed heavily from Pleasantville, a movie that attributes colors to deviance and blandness is left black and white, like in the 50s family shows. In its final scene, the characters sit on a bench and ask themselves what is going to happen next. Their answer, that they don’t know, summarizes the whole notion that life and color can only grow in the presence of uncertainty. Whereas religious stories leverage the idea of discovering the underpinning powers of the world, removing chance, and granting guidance, there seems to be this universal counter-meme that embraces randomness and resonates with many, especially in the dawn of their youth, when arrogance starts to fade, but before the fear of old age kicks in.

The actress portraying Betty seems uncomfortably excited with her new colorful existence while George continues attached to his predictable (un)life.

Do we have any evidence that this quantum regularization layer powering our neurons actually exists? Does feeling happy or trying to run fast correlate with changes in the electrical patterns in our brain? That we know to be true. But when it comes to causation, how does it work? External stimuli, like music, can trigger happiness, but what is the chain of events that will prevent me from stopping writing now and seeing how fast I can run? Do I have the free will to do that choice?

We can’t define causality between happiness and your brain’s electrical patterns because we cannot inspect the initial state of each electron in the brain. Were they arranged in a way to induce a discharge and make you happy, so happiness was unavoidable or were they arranged in a boring way and some soul-like power made them do unlikely jumps to create the current so you could feel the happiness you wanted? Because we are talking about a large visible effect on the macro world, we feel it ought to be decidable. But as you keep shrinking definitions, from neurons to electrons, from uncontrollable heartbeats to dopamine releases, you soon find the barriers of observability.

But we are seeing these very pronounceable composite effects on the macro world, so something is biasing the computations being made by your brain. Something improbable and abundant. The Wanda Maximoff illusion, evolution’s ultimate trick. The initialization priors, the distributions of the dropouts, are forever hidden behind the curtains of the magical spectacle of life. We can’t say whether we live the unlikely or the unavoidable. We can only wish it is neither, we can only wish, against all odds, it is us.

Scientists have mapped the twenty thousand neurons of the Aplysia Californica (the cute sea hare below). Due to its simple neuron system, this species has been studied for over 50 years, and we discovered that with the right stimuli regimen we can condition new behaviors in an individual. Both short and long-term learning. It could be said that conditioning, habituation, or even the more general concept of learning are means of removing freedom. As we gaze into this primitive animal, we make it more predictable. Maybe scientific curiosity is like the eyes of the Medusa, turning live beings into fancy rocks.

We have mapped the ~20k neurons of the California Sea Hare. Can we use it to predict where it will swim next?

Inherent unpredictability is not an exclusive trait of complex neural networks. The weather is so hard to predict that we have attributed it to external, powerful wills in the past. Even today people still dance to gods for the rain to come. The branch of mathematics known as Chaos Theory was born when Edward Lorenz got a surprising outcome from a weather forecast due to a very small mistake in initial conditions. As he would put it later, in a chaotic system, the present determines the future, but the approximate present does not approximately determine the future.

Nonetheless, we no longer perceive the weather as possessing some form of free will. This could be because we can capture enough of the initial state to do meaningful predictions in some limited window, say, for a week or two. This suffices for us as an explanation of underlying the mechanisms. We can look at the micro components, like the individual drops, or the macro ones, like the monsoons, and feel we have a good grasp of what is going on.

In our brains, it seems cause and effect, the micro and the macro are so tightly packed, in space and time, that we cannot tell whether are just seeing the same kind of chaos arising, or witchery is in control. Because of observability limits, we cannot ever know that when I think about raising my arms, that is happening because we are seeing some big bang residue manifesting itself out of some chaos system fed by quantum state, or because I want to. Maybe the brain of a primate is to Earth's climate as the aplysia california neuron system is to Monterey Bay Aquarium’s. Fortunately (or not), evidence hints that we will never be able to prove this.

We seem to be discussing a tautology, because we defined free will as the ability to act outside of the chains of causality, and also took as an axiom that it is impossible to confirm whether anything (or everything) can act outside those chains. We cannot devise an experiment that proves that our thoughts are our own. Something can only be truly free outside a system, but if your system is the universe and you are part of it, you are trapped in recursion. We cannot devise its dual either, because even if we knew all the rules of the universe, we cannot capture the state to feed them and produce the counter-proof showing that an external force is bending those rules.

These are not bad news. There is no palpable distinction between something you control, and something no one else in the world controls. What is interesting though is that anything that can be predicted belongs to the mundane, and anything that cannot is humane. We are the deviations. Free will is the courage to embrace the unpredictable. This is why I say yes to more mutants. To more diversity. Freedom is letting each rock roll its own way. Even if it is a bit scary. Because the alternative, that everyone behaves the way they were taught they should, well, that will turn us into fancy rocks.

The ignorance of the kids is the ultimate form of freedom — for them, everything is a choice



Frustrated writer, happy coder. I like what is inside people’s mind and I can’t avoid spending a lot of time in mine.

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Davi De Castro Reis

Frustrated writer, happy coder. I like what is inside people’s mind and I can’t avoid spending a lot of time in mine.