Thank you for the engaging discussion hendrik its been really cool to bounce ideas back and forth like this. I wanted to give you a thoughtful reply and it got a bit long so have to split this up for comment limit reasons. (P1/2)

Though in both the article you linked and in the associated video, they clearly state they haven’t achieved superposition yet. So […]

This is correct. It’s not a fully functioning quantum computer in the operational sense. It’s a breakthrough in physical qubit fabrication and layout. I should have been more precise. My intent wasn’t to claim it can run Shor’s algorithm, but to illustrate that we’ve made more progress on scaling than one might initially think. The significance isn’t that it can compute today but that we’ve crossed a threshold in building the physical hardware that has that potential. The jump from 50-100 qubit devices to a 6,100-qubit fabric is a monumental engineering step. A proof-of-principle for scaling, which remains the primary obstacle to practical quantum computing.

By the way, I think there is AI which doesn’t operate in a continuous space. It’s possible to have them operate in a discrete state-space. There are several approaches and papers out there.

On the discrete versus continuous AI point, you’re right that many AI models like Graph Neural Networks or certain reinforcement learning agents operate over discrete graphs or action spaces. However, there’s a crucial distinction between the problem space an AI/computer explores and the physical substrate that does the exploring. Classical computers at their core process information through transistors that are definitively on or off binary states. Even when a classical AI simulates continuous functions or explores continuous parameter spaces, it’s ultimately performing discrete math on binary states. The continuity is simulated through approximation usually floating point.

A quantum system is fundamentally different. The qubit’s ability to exist in superposition isn’t a simulation of continuity. It’s a direct exploitation of a continuous physical phenomenon inherent to quantum mechanics. This matters because certain computational problems, particularly those involving optimization over continuous spaces or exploring vast solution landscapes, may be naturally suited to a substrate that is natively continuous rather than one that must discretize and approximate. It’s the difference between having to paint a curve using pixels versus drawing it with an actual continuous line.

This native continuity could be relevant for problems that require exploring high-dimensional continuous spaces or finding optimal paths through complex topological boundaries. Precisely the kind of problems that might arise in navigating abstract cognitive activation atlas topological landscapes to arrive at highly ordered, algorithmically complex factual information structure points that depend on intricate proofs and multi-step computational paths. The search for a mathematical proof or a novel scientific insight isn’t just a random walk through possibility space. It’s a navigation problem through a landscape where most paths lead nowhere, and the valid path requires traversing a precise sequence of logically connected steps.

Uh, I think we’re confusing maths and physics here. First of all, the fact that we can make up algorithms which are undecidable… or Goedel’s incompleteness theorem tells us something about the theoretical concept of maths, not the world. In the real world there is no barber who shaves all people who don’t shave themselves (and he shaves himself). That’s a logic puzzle. We can formulate it and discuss it. But it’s not real. […]

You raise a fair point about distinguishing abstract mathematics from physical reality. Many mathematical constructs like Hilbert’s Hotel or the barber paradox are purely conceptual games without physical counterparts that exist to explore the limits of abstract logic. But what makes Gödel and Turing’s work different is that they weren’t just playing with abstract paradoxes. Instead, they uncovered fundamental limitations of any information-processing system. Since our physical universe operates through information processing, these limits turn out to be deeply physical.

When we talk about an “undecidable algorithm,” it’s not just a made-up puzzle. It’s a statement about what can ever be computed or predicted by any computational system using finite energy and time. Computation isn’t something that only happens in silicon. It occurs whenever any physical system evolves according to rules. Your brain thinking, a star burning, a quantum particle collapsing, an algorithm performing operations in a Turing machine, a natural language conversation evolving or an image being categorized by neural network activation and pattern recognition. All of these are forms of physical computation that actualize information from possible microstates at an action resource cost of time and energy. What Godel proved is that there are some questions that can never be answered/quantized into a discrete answer even with infinite compute resources. What Turing proved using Gödel’s incompleteness theorem is the halting problem, showing there are questions about these processes that cannot be answered without literally running the process itself.

It’s worth distinguishing two forms of uncomputability that constrain what any system can know or compute. The first is logical uncomputability which is the classically studied inherent limits established by Gödelian incompleteness and Turing undecidability. These show that within any formal system, there exist true statements that cannot be proven from within that system, and computational problems that cannot be decided by any algorithm, regardless of available resources. This is a fundamental limitation on what is logically computable.

The second form is state representation uncomputability, which arises from the physical constraints of finite resources and size limits in any classical computational system. A classical turing machine computer, no matter how large, can only represent a finite discrete number of binary states. To perfectly simulate a physical system, you would need to track every particle, every field fluctuation, every quantum degree of freedom which requires a computational substrate at least as large and complex as the system being simulated. Even a coffee cup of water would need solar or even galaxy sized classical computers to completely represent every possible microstate the water molecules could be in.

This creates a hierarchy of knowability: the universe itself is the ultimate computer, containing maximal representational ability to compute its own evolution. All subsystems within it including brains and computers, are fundamentally limited in what they can know or predict about the whole system. They cannot step outside their own computational boundaries to gain a “view from nowhere.” A simulation of the universe would require a computer the size of the universe, and even then, it couldn’t include itself in the simulation without infinite regress. Even the universe itself is a finite system that faces ultimate bounds on state representability.

These two forms of uncomputability reinforce each other. Logical uncomputability tells us that even with infinite resources, some problems remain unsolvable. State representation uncomputability tells us that in practice, with finite resources, we face even more severe limitations there exist true facts about physical systems that cannot be represented or computed by any subsystem of finite size. This has profound implications for AI and cognition: no matter how advanced an AI becomes, it will always operate within these nested constraints, unable to fully model itself or perfectly predict systems of comparable complexity.

We see this play out in real physical systems. Predicting whether a fluid will become turbulent is suspected to be undecidable in that no equation can tell you the answer without simulating the entire system step by step. Similarly, determining the ground state of certain materials has been proven equivalent to the halting problem. These aren’t abstract mathematical curiosities but real limitations on what we can predict about nature. The reason mathematics works so beautifully in physics is precisely because both are constrained by the same computational principles. However Gödel and Turing show that this beautiful correspondence has limits. There will always be true physical statements that cannot be derived from any finite set of laws, and physical questions that cannot be answered by any possible computer, no matter how advanced.

The idea that the halting problem and physical limitations are merely abstract concerns with no bearing on cognition or AI misses a profound connection. If we accept that cognition involves information processing, then the same limits which apply to computation must also apply to cognition. For instance, an AI with self-referential capabilities would inevitably encounter truths it cannot prove within its own framework, creating fundamental limits in its ability to represent factual information. Moreover, the physical implementation of AI underscores these limits. Any AI system exists within the constraints of finite energy and time, which directly impacts what it can know or learn. The Margolus-Levitin theorem defines a maximum number of quantum computations possible given finite resources, and Landauer’s principle tells us that altering the microstate pattern of information during computation has a minimal energy cost for each operational step. Each step in the very process of cognitive thinking and learning/training has a real physical thermodynamic price bounded by laws set by the mathematical principles of undecidability and incompleteness.

(P2/2)

I don’t think this is the case. As far as I know a human brain consists of neurons which roughly either fire or don’t fire. That’s a bit like a 0 or 1. But that’s an oversimplification and not really true. But a human brain is closer to that than to an analog computer. And it certainly doesn’t use quantum effects. Yes, that has been proposed, but I think it’s mysticism and esoterica. Some people want to hide God in there and like to believe there is something mystic and special to sentience. But that’s not backed by science. Quantum effects have long collapsed at the scale of a brain cell.[…]

The skepticism about quantum effects in the brain is well-founded and represents the orthodox view. The “brain is a classical computer” model has driven most of our progress in neuroscience and AI. The strongest argument against a “quantum brain” is of decoherence. In a warm wet brain quantum coherence is rapid. However, quantum biology doesn’t require brain-wide, long-lived coherence. It investigates how biological systems exploit quantum effects on short timescales and in specific, protected environments.

We already have proven examples of this. In plant cells, energy transfer in photosynthetic complexes appears to use quantum coherence to find the most efficient path with near-100% efficiency, happening in a warm, wet, and noisy cellular environment. Its now proven that some enzymes use quantum tunneling to accelerate chemical reactions crucial for life. The leading hypothesis for how birds navigate using Earth’s magnetic field involves a quantum effect in a protein called cryptochrome in their eyes, where electron spins in a radical pair mechanism are sensitive to magnetic fields.

The claim isn’t that a neuron is a qubit, but that specific molecular machinery within neurons could utilize quantum principles to enhance their function.

You correctly note that the “neuron as a binary switch” is an oversimplification. The reality is far more interesting. A neuron’s decision to fire integrates thousands of analog inputs, is modulated by neurotransmitters, and is exquisitely sensitive to the precise timing of incoming signals. This system operates in a regime that is often chaotic. In a classically chaotic system, infinitesimally small differences in initial conditions lead to vastly different outcomes. The brain, with its trillions of interconnected, non-linear neurons, is likely such a system.

Consider the scale of synaptic vesicle release, the event of neurotransmitter release triggered by the influx of a few thousand calcium ions. At this scale, the line between classical and quantum statistics blurs. The precise timing of a vesicle release could be influenced by quantum-level noise. Through chaotic amplification, a single quantum-scale event like the tunneling of a single calcium ion or a quantum fluctuation influencing a neurotransmitter molecule could, in theory, be amplified to alter the timing of a neuron’s firing. This wouldn’t require sustained coherence; it would leverage the brain’s chaotic dynamics to sample from a quantum probability distribution and amplify one possible outcome to the macroscopic level.

Classical computers use pseudo-random number generators with limited ability to truly choose between multiple possible states. A system that can sample from genuine quantum randomness has a potential advantage. If a decision process in the brain (like at the level of synaptic plasticity or neurotransmitter release)is sensitive to quantum events, then its output is not the result of a deterministic algorithm alone. It incorporates irreducible quantum randomness, which itself has roots in computational undecidability. This could provide a physical basis for the probabilistic, creative, and often unpredictable nature of thought. It’s about a biological mechanism for generating true novelty, and breaking out of deterministic periodic loops. These properties are a hallmark of human creativity and problem-solving.

To be clear, I’m not claiming the brain is primarily a quantum computer, or that complexity doesn’t matter. It absolutely does. The sheer scale and recursive plasticity of the human brain are undoubtedly the primary sources of its power. However, the proposal is that the brain is a hybrid system. It has a massive, classical, complex neural network as its substrate, operating in a chaotic, sensitive regime. At the finest scales of its functional units such as synaptic vesicles or ion channels, it may leverage quantum effects to inject genuine undecidably complex randomness to stimulate new exploration paths and optimize certain processes, as we see elsewhere in biology.

I acknowledge there’s currently no direct experimental evidence for quantum effects in neural computation, and testing these hypotheses presents extraordinary challenges. But this isn’t “hiding God in the gaps.” It’s a hypothesis grounded in the demonstrated principles of quantum biology and chaos theory. It suggests that the difference between classical neural networks and biological cognition might not just be one of scale, but also one of substrate and mechanism, where a classically complex system is subtly but fundamentally guided by the unique properties of the quantum world from which it emerged.

Exactly what an LLM-agent would reply. 😉

I would say that the LLM-based agent thinks. And thinking is not only “steps of reasoning”, but also using external tools for RAG. Like searching the internet, utilizing relationship databases, interpreters and proof assistants.

You just described your subjective experience of thinking. And maybe a vauge definition of what thinking is. We all know this subjective representation of thinking/reasoning/decision-making is not a good representation of some objective reality (countless of psychological and cognitive experiments have demonstrated this). That you are not able to make sense of intermediate LLM reasoning steps does not say much (except just that). The important thing is that the agent is able to make use of it.

The LLM can for sure make abstract models of reality, generalize, create analogies and then extrapolate. One might even claim that’s a fundamental function of the transformer.

I would classify myself as a rather intuitive person. I have flashes of insight which I later have to “manually” prove/deduc (if acting on the intuition implies risk). My thought process is usually quite fuzzy and chaotic. I may very well follow a lead which turns out to be dead end, and by that infer something which might seem completely unrelated.

A likely more accurate organic/brain analogy would be that the LLM is a part of the frontal cortex. The LLM must exist as a component in a larger heterogeneous ecosystem. It doesn’t even have to be an LLM. Some kind of generative or inference engine that produce useful information which can then be modified and corrected by other more specialized components and also inserted into some feedback loop. The thing which makes people excited is the generating part. And everyone who takes AI or LLMs seriously understands that the LLM is just one but vital component of at truly “intelligent” system.

Defining intelligence is another related subject. My favorite general definition is “lossless compression”. And the only useful definition of general intelligence is: the opposite of narrow/specific intelligence (it does not say anything about how good the system is).