Why this old debate matters again
On quiet nights a familiar argument resurfaces in cafés, podcasts and pre‑print comment sections: do we truly have free will, or is everything already written in the source‑code of the cosmos? The other day I attended a lecture on Free Will from the perspective of a biologist and a philosopher. They framed it in terms of genes and brains and how biological systems are indeterministic etc. Unfortunately, I was not convinced, especially since they simply brushed away any and all scientific aspects made by physicists and their discovery of nature’s laws. But of course, there’s always quantum randomness which at first glance seems like an entry to the debate, but it’s really not.
Nevertheless, the conversation seems rebooted in 2025, even though I thought it was settled long ago. But this time around we have quantum processors on the horizon and Stephen Wolfram’s ambitious “Physics Project,” which proposes that the universe itself may be the output of a simple, deterministic computation. Let’s look into how we can bring all these ideas together into a new framework and how we can expand a little upon the idea I proposed a few years back about reality being an emergent phenomenon. [read more]
To see why the stakes have never been higher, we need to travel from a humble fractal to cutting‑edge qudits and back again to the human urge to believe “I could have done otherwise.”
A fractal cautionary tale: the Sierpiński triangle
Imagine you draw an equilateral triangle and pick any starting point in its interior. Now follow two simple rules – often called the Chaos Game:
1. Randomly choose one of the triangle’s three vertices.
2. Plot a point halfway between your current position and that vertex.
3. Repeat.
After a few iterations the dots look scattered (because you chose randomly), but by the time you reach a few hundred or thousand dots, a well-known self‑similar pattern emerges: the Sierpiński triangle. Every run of the game, no matter the first point or the stream of random vertex choices, brings forward exactly the same fractal shape.
Insight 1: Local randomness does not guarantee global unpredictability – instead, simple rules can lock apparently free choices onto a predetermined attractor.
That insight puts pressure on an intuitive account of free will, the sense that because we could have chosen differently, the future must branch into radically separate histories. Yet even when randomness is injected at every step, the outcome can be structurally inevitable. Hold that mental image...
Quantum randomness: a crack in the wall?
Classical physics is famously deterministic, but the quantum world is not. When a qubit, an elementary quantum bit, gets measured, its state collapses probabilistically. This genuine randomness cannot, as far as we know, be reduced to any hidden variables.
Does that somehow rescue free will? Not really. Indeterminism may break strict predictability, but a dice roll injected into your neurons is no more “you” than a gust of wind. Compatibilist philosophers therefore argue that what matters is whether actions flow from your character and reasoning, even if those processes are implemented in physical hardware that follows rules.
Enter Stephen Wolfram’s computational universe
Wolfram’s 2020 Physics Project proposes that space, time, matter and even quantum mechanics emerge from an underlying rewrite system on discrete elements, essentially a vast hypergraph whose evolution is fully deterministic. Apparent randomness and the probabilistic structure of quantum theory arise because any local observer samples only a thin thread through this multiway graph. Yet the whole graph itself unfolds law‑fully, step by step, with no room for “external” choice.
Insight 2: Even phenomena we label “quantum” could, in principle, be the shadow of an inexorable algorithm, one so complex that most branches are computationally irreducible (Wolfram’s term for processes that cannot be shortcut).
If Wolfram is right, free will might shrink to a perspectival artifact: each of us rides one causal path and perceives the garden of forking possibilities, while the meta‑computation tallies every branch in parallel.
Qubits vs. Qudits
Modern quantum computers manipulate qubits, two‑level systems that can encode a superposition of 0 and
1. Let's imagine a labyrinth e.g. While a classical
computer explores one path through the labyrinth at a time, or with parallel processors, several in parallel – but each one separately, a quantum computer puts the entire labyrinth into a quantum superposition – representing all
paths at once.
But: It can’t just look and see “which one is the exit.”
Instead, quantum interference is used to cancel out wrong paths and amplify the probability of the correct ones.
The result of the computation gives a high probability of getting the right answer – but only if the algorithm is carefully designed to guide the
interference.
Qudits generalize this idea to d‑level systems: In physical hardware these extra levels might be higher orbital states of an ion, frequency modes of a photon or spin states beyond up/down. This creates higher information density. A single qudit of dimension d carries log2 d bits of information. For equal numbers of particles, higher‑dimensional qudits can encode richer quantum states.
This will lead also to the development of algorithmic shortcuts, because we’re finally leaving the binary approach behind. Tenary system that are processing closer to Euler’s number would already be so much more efficient than normal binary systems. Certain quantum algorithms, error correction codes, Fourier transforms on non‑binary groups, topological simulations, become simpler or more hardware‑friendly when native gates match the problem’s algebraic structure.
With that we also get closer to nature’s math. Many theoretical frameworks (e.g., balanced ternary logic, SU(3) symmetries in particle physics) are naturally non‑binary as described above. By trying to model the universe itself, qudits may prove a cleaner fit than forcing everything into zeros and ones.
If the cosmos really is executing a vast computation, then qudits might be the more faithful pixels of that simulation, allowing us to reproduce its behaviour with fewer resources. Viewed through this lens, each qudit behaves like a miniature “vertex‑selector” in the Sierpiński chaos game. Its multi‑level state guides which rewrite rule fires next, weaving a higher‑dimensional fractal inside the hypergraph.
Can unlimited compute reveal the road ahead?
Suppose we possessed a fault‑tolerant, large‑scale qudit processor and a perfect microscopic scanner of the present state of the universe. Could we “skip” time, calculate the Sierpiński‑like attractor of human history and jump straight to the ending?
Two obstacles right then and there:
1. Initial‑data explosion. Recording every relevant degree of freedom in even a cubic millimeter is wildly beyond current or foreseeable capacity.
2. Computational irreducibility. Wolfram’s core result says, that for most non‑trivial rules, the only way to know the state after n steps is to run the computation step‑by‑step. Shortcuts are rare and usually problem‑specific, so we must walk the talk and can’t really skip ahead or simulate it. Try STRATA if you want to give it a try - my simulation abstraction matrix.
In other words, a cosmic Sierpiński may well exist but lies behind an impenetrable wall of complexity. But that still doesn't give you Free Will. Qudits offer some hope of sampling that structure more efficiently, glimpsing statistical contours of the future without computing every micro‑branch.
What survives of free will?
Fractals teach us that randomness needs not free us from structure; Wolfram reminds us that apparently stochastic physics could be deterministic under the hood; qudits promise denser windows into that hidden machinery. Where does that leave free will?
- If libertarian free will requires uncaused choice, the news is bleak.
- If compatibilist free will only demands that actions align with our reasons and values, nothing here undermines agency, though it does suggest that our sense of open possibility is a feature of limited perspective, not a bug.
- And if computational irreducibility holds, practical unpredictability persists even in a lawful universe: no outside observer can cheaply forecast each personal decision.
In short, the end of meaphysical Free Will may coexist with the endurance of meaningful autonomy.
Light, paths and closing the loop
Richard Feynman taught that a photon explores all possible paths between source and detector; the interference pattern we observe is the weighted sum of those trajectories. By analogy, perhaps each of us browses a subset of the universal multiway graph, collapsing it into the story we call “my life.” The Sierpiński triangle and Wolfram’s graphs remind us that the grand design may be rigorously computable, even beautiful, yet hopelessly beyond exact compression.
Final insight: Whether the universe runs on qubits, qudits or still‑unknown primitives, its code seems to weave determinism, randomness and computational complexity into a single tapestry. Our lived experience of choice occupies just one luminous thread. What you have is the chance to momentarily reverse entropy in your corner of the universe that you call your life and rest assured that some of the threads you’re weaving (aspects that appear to be of Free Will) will eventually make it into the cosmic web of determinism but are just as much already determined by it.
All the pieces on one board
The Sierpiński triangle, qudits, Wolfram’s hypergraph and our day‑to‑day feeling of agency may look like distant curiosities, yet they resonate at three key frequencies:
1. Rule → Pattern. In both the Chaos Game and Wolfram’s model, a tiny rule set unfolds into a vast, self‑similar tapestry. Whether the state vector sits in a 2‑level qubit or a 7‑level qudit, the same principle holds: local choices (vertex picks, rewrite steps, gate operations) tunnel relentlessly toward a stable landscape of emergent regularities.
2. Superposition as navigation. A qudit’s ability to occupy many logical levels simultaneously is the quantum analogue of the photon’s “all possible paths” and of our own branching futures. From this viewpoint, free will is the subjective act of collapsing a personal superposition – choosing one edge of the hypergraph – while the global computation explores every possible option just like a photon.
3. Fractal irreducibility. The triangle teaches us that not all randomness yields novelty while Wolfram clarifies that not all determinism yields predictability; quantum theory grafts genuine indeterminism onto both. Together they imply a universe where freedom and necessity interlace like bright and dark pockets of a single fractal.
Realizing this does not empty human life of meaning, quite the opposite. It tells us that our decisions matter precisely because they are how the multiway engine registers one thread as the lived present. Every time we act, we carve a Sierpiński‑shaped groove through Hilbert space, leaving a trace that no other branch can overwrite.
by mario
