In this article, I want to get more philosophical about some concepts I’ve been thinking about for years now.

I’ve studied quantum mechanics and went down the rabbit hole, dove into the uncertainty principles, the spooky actions at a distance, the inversion of causal order, the time crystals, and the myriad of interpretation of quantum mechanics.

Recently I watched this video from Machine Learning Street Talk, and suddenly a certain number of disparate elements started to click and fall into one coherent place.

Something that became more and more clear to me with the advance and spreading of LLM’s (Large Language Model) is how language might not be so special after all. In this so-called modern era, we often hear that humans are superior to animals because we have the unique capacity to put our internal mind state into a precise language. The verbal communication, as some anthropologists suggest, is probably the root of our assumed, superiority over the animal kingdom. I remember in a class about cognition at McGill university, the teachers were probing us into thinking about what set us apart from other animals. And all the discussions lead to the eureka moment, where we all concluded that, we are more intelligent because knowledge is transmitted from one generation to another. Hence, verbal language is actually the most prominent technology that is putting us at the top of the hierarchy. An ability that, we like to comfort ourselves, is only reserved to humans, … Right?

Well, I guess if the west listened to other traditions, it might realize that actually, this is not true at all. But no need to go as far as doing cultural appropriation, since our current state of science is now providing evidence that language might actually be much more common through the animal kingdom than what we thought… very surprising, is it? So yes, actually some bird might have verbal language, such as the Japanese Tit, along other birds, with a syntax, and precise wording, for example, for naming specific predators. Whales and, as other Cetacea, also have patterns of language very similar to humans, and Elephant might be able to give names to their peers. These are just a small sample of the recent discoveries, or should I say more adequately, rediscovery, the modern world, is making.

Wording the world, is thus something not only human can do. Except that one might still argue, that we do have something more than other animals doesn’t seem to have. An obsession for words. The world of words then began to word everything that the world has to offer to the wording world. Words were not merely a useful technology, serving humans to exchange their emotions and need. Over the million of years, it is as if, words became entities themselves, alive in us, fighting wars with us, playing with us, playing us.

Opinions, then, seemed to matter more than anything else, into defining an identity. A sexual attraction, a desire to belong, accept and welcome, a desire to befriend, and spend time, with. Opinions, at the glorious era of, the near AGI, or so are we told to believe, become the most defining principle of unification / boundary. The stories about who we are, became more important that what we actually are, and in fact, the push to the marketization of identity as products, tied to brands, labels, and objects, is very revealing of that shallowing and superficiality into which oneself can so easily fall into. Swept away in an endless stream of distraction, gamification of the horror, in accumulation of likes and dislikes, forming gigantic casinos of the obscene, all feeding our omnissia-god like machines, GAFAM gluttons.

So what does this all have to do with Gödel’s incompleteness theorem, you might ask, and I would answer : everything.

The issue with verbal and written language, is in the realization of it’s limit, it is, and will forever be, inconsistent and incomplete. For example, as a friend of mine was proposing sarcastically : “try to explain, only by written text, what is left, and right.” You’ll often end up in tautology like, “well left is the side where I write (or not)”. In most cases, you will have to assume an embodied knowledge of space, that no word can in fact capture. Now my friend adding : “try that without using your body as reference, …” There is, indeed, a presupposition in the wording. It can only work as a pointer to a lived experience, but can never indicate what the experience is, in itself. That is to someone who is oblivious to said experience. In other “words”, I can only talk to someone about what is relatable to that person. Other than that, I am going to point in an abstract cognitive space that has not yet been mapped.

This is why it is for example absolutely impossible to explain to someone who never did psychedelics what it is like, to have a trip. The only thing you can do, is give a very rough pointer, an approximation, that will just left the person feeling confused, and in the best case, maybe curious, but that’s all. You cannot do much.

I could talk to you about the time dilation, the inversion of causal order, the dilation and contraction of space, the fractals, the holograms, and the synaesthesia, but that would again assume that you have an embodied experience related to each of these specific terms, in order for you to roughly get a sense of, “oh, this might be where he is projecting in the lived experience space”. That approximation you will make will be “false”, so to speak, and when you actually live the experience yourself, suddenly, you realize the mismatch between the initial language based pointer, and the actual lived experience vector : “Ah wow, this is what you were talking about, now I get it!”.

Now the interesting thing about this : “I get what you mean”, is that, there is no guarantee that is it the case. We might think that we map certain words to similar lived experience, but this job of pointing from the abstract space of words, to the embodied space of experience, inevitably leads to quiproquos and misunderstanding, since words in themselves have no intrinsic meaning. So anyway, yes, (verbal) language is a lost cause, as I was provokingly rapping about, but not all language are equal, right? In fact, some person with a minimal mathematical background could eloquently react to my initial statement about explaining left and right, and come with their smart explanation :

Yes, you can actually describe this, it is rather trivial in fact. For any given scene or object, take a reference line separating it into two parts, take another orthogonal line separating the first line into two parts, and now you have a coordinate system. Everything on the $x$ coordinate (horizontal axis) with negative value will be what we call left, from the point of reference being $x=0$, aligned with the vertical line, and everything that is to the right, correspond to a positive value of $x$. You see, easy I said!

And yes, this is a relatively satisfying answer, except that all of this is based on geometry, and it already completely assumes knowledge about space. It is built from the analysis of space, done by a certain specie who is very reliant on its visual system, who inferred the rules governing it. Now someone could even go as far as saying : “yeah well okay, forget about geometry, I can also give a purely algebraic definition”. But then again, who, without an already pre-existing sense of space embodiment, could actually make sense of the algebra ? You are still trapped into words, without it, and meaning eludes you.

This is it. We are exactly at the same state as the most successful scientific model we have, quantum mechanics, and let’s be honest: nobody truly knows what it means.

And this is not a joke, we reached a limit in our ability to know what this model really means about reality. We are now in an era, of “opinions”, about what reality is, fundamentally, composed of, and coming from. Scientists prefer the term interpretation, probably to avoid feeling insulted, but the distinction is subtle. You have more than a dozen different interpretation of what the so-called “wavefunction” actually represents. Some say “shut up and calculate”, loosely linked to the Copenhagen interpretation, and there is some wisdom to it. In a way it says : “In the absence of clarity about what it all means, let’s suspend our judgment, and use it, as long as it works, i.e., is not contradicted by experiments”. As a dear friend reminded me, this is very much aligned with the thinking of Ludwig Wittgenstein:

“Whereof one cannot speak, thereof one must be silent.”
— Tractatus Logico-Philosophicus (1921), Proposition 7

Maybe in the silence might we find a much needed introspection. This is the point where the lived experience breaks, and no one knows anymore what all this math means. My culture has no lived experience that can really unambiguously resonate with the direction that the math is pointing toward, as it points to a direction in the cognitive space that has not yet been mapped. Richard Feynman, famously said “I think I can safely say that nobody understands quantum mechanics”, capturing the idea that it escapes any mental model we can fully visualize.

I like very much that approach because it is kind of putting us back into our place. It is a sort of lesson of humility from the universe. I was once a partisan of the Leibniz school of thought that, “If we had complete information, we could deduce everything about the world.”, only to see my world view completely shatter after my first course of quantum mechanics. The wavefunction, our best description of particles, could only talk about probabilities. And ever since, I’ve been wondering whether altered states of consciousness might provide a lived experience that hints, however indirectly, at what the math is pointing toward. Of course, in doing so, I may still be trapped, unknowingly, in Leibniz’s deterministic camp.

I mean, not that it is not interesting, nor useful. After all, the splitting we are seeing in science might only be temporary, and it is possible that a set of experiment might validate, or for instance invalidate, some or all of the existing interpretations. At the current state of affair, it seems we know that mucn about reality :

• either it is real, but non‑local;
• or it is local, but not real (at least not in the classical sense).

Whatever this means, is also subject to interpretation, but you have partisans in each camp, defending their version of reality, and trying to argue why it is better, all the while working to provide falsifiable experiments. Still, physicists have largely converged on one hard fact: quantum systems violate Bell’s inequalities, which rules out local realism. Technically, we say that particles violate Bell’s inequality, and this rule out “local realism”. This is the the idea that physical properties exist independently of measurement and that no influence can travel faster than light.

In practice, this means that two distinct particles, regardless of the distance separating them, can become entangled, behaving as a single indivisible system. Alain Aspect, John F. Clauser and Anton Zeilinger won the Nobel Prize in 2022, for showing that. Now whether Nobel Prize are worth something or not is beyond the scope of this article, and anyway, you probably already know my position about this by now, but the fact remains, that the particles seems to follow the equation of quantum mechanics very religiously, so to speak!

And yet, we are back to the same problem: what do these equations actually mean?

Is the wave function describing a physical object, or is it just a mathematical abstraction giving good results, much like the geocentric model from Ptolemy ?

Some people try to treat the wavefunction as something physically real. In the case of Böhm’s interpretation, particles have definite positions and move under the guidance of a real wavefunction, at the cost of accepting explicit non‑locality. This would also mean the current model is incomplete, and some some hidden global variables need to be added. Other approaches treat the wavefunction as nothing more than a bookkeeping device for computing probabilities, without committing to any underlying ontology.

Then comes the real nightmare: measurement, and everybody seem confused as to what this actually means.

• Some say measurement is nothing special, just an interaction like any other.
• Some say it necessarily involves observers, and even consciousness.
• Some say measurement doesn’t exist at all.

In the Many‑Worlds interpretation (Everett), the wavefunction never collapses. Every possible outcome occurs, each branching in its own universe, and measurement is merely our subjective experience of being stuck in one branch. In QBism, the wavefunction doesn’t describe the world at all, but it describes an agent’s personal beliefs about future experiences. In retrocausal models, effects can propagate backward in time, relaxing our usual notions of causality.

This is all nice and very exciting that debates in science like that exist, but this is also very concerning in a way. The polarization that is very present in our societies, from opposing opinions, seems to be, in a way, also projected into these quantum interpretations. In fact, you could say that all the flavors of philosophies have their own interpretation of the theory, from the most ardent defender of Leibniz worldview, in the form of superdeterminism, to the materialist aficionado, as in Bohemian mechanics. Then there are interpretations that feel profoundly spiritual and which, at least for me, echo strongly with experiences from psychedelic trips: Wheeler’s participatory universe, in which reality itself depends on observers actively participating in its unfolding; and panpsychism, the idea that consciousness, or at least proto-consciousness, is a fundamental feature of the universe.

So yeah, the divide in the lived experience, is projected onto the unknown direction that this abstract, but so precise, math is pointing towards, and I am starting to wonder, after all the years invested in trying to learn about all this, if a given “camp”, can in fact ever win the game of interpretation, or if we will be left wondering, forever, in this, alright universe.

Now that might sound a bit depressing for some people but fear not. Since the article was about Gödel’s incompleteness, I am kind of obliged to integrate this at some point, right, otherwise, it would be somewhat misleading, like these fake news article selling you pills to heal your joint, but in fact making you sick.

So yeah. At this point, I feel like, what I am pointing at is almost as big as the freaking Burj Khalifa and its 828 meters. But hey, I am going to name the elephant in the room.

What if logic is not enough?

What if, beyond all our models of reality, lies something untouched — maybe even untouchable? In a sense, this is what Gödel’s incompleteness theorem tells us about formal systems:

In every consistent formal system containing elementary arithmetic, there are propositions that can neither be proved nor disproved within the system.

In mathematics, this is a hard limit on formal proof. Even though in physics, we have a slightly different twist: while the universe doesn’t give us formal proofs, it does give us experiments, or at least, it can… sometimes. We are seing something interesting where it becomes more and more difficult to devise experiment to valide or invalidate our theories.

This is the problem of underdetermination: multiple, mutually incompatible models can make exactly the same predictions. You can have different interpretations of quantum mechanics, Bohmian mechanics, Many-Worlds, QBism, retrocausal models, and no experiment, at least currently, can tell you which one “really” describes reality.

Put these two together, Gödelian incompleteness and physical underdetermination, and you get a universe that is infinitely rich, partially inaccessible, and fundamentally indeterminate. Our formal proofs stop working at the edges, our experiments can only go so far, and the unknown stretches out beyond our grasp.

What if, with quantum mechanics, we have just touched something so deep about the universe that mathematics alone is not sufficient to capture it? Our intuitions, sensations, feelings, and embodied experience then might become the sole source of meaning, if not truth, a kind of epistemic replacement when formal proof and experiment can no longer fully guide us.

What if multiple interpretations of quantum mechanics might all be true, even while being mutually exclusive? What if, the quest for the simplest explanation and more elegant models, was a projection of our fears of the complexity and the unknown. What if beyond lies a reality so complex, that no model can every fully grasp it? No equation can ever explain, and only belief, opinions, and ultimately faith remains.

I mean, this might be experienced as a loss, to be grieved for sure, but what about the gains?

The gains might be huge !

I mean, after the painful realization that there are fundamental limits to what we can know, there might also suddenly be room, a lot of room, for so many cosmogonies, to be, and be accepted as equally valid. There might be a reopening of Western thinking to older traditions, and maybe even a reckoning of its own shadow.

Maybe pluralism might emerge as the most natural thing in the universe, and maybe, in the acceptance that our cognition, as these formal models, have axioms that are true, that can never be proved, we will find unity in the plural, union in the dual, true and not true, might then be held, at the same time and space. Right and wrong, cherished, as the same child. Smart and dumb, seen, as the same lie. Separation from opinions, boundaries from cognition, from words splitting, as in Young’s experiment, as photons passing through both slits and collapsing into particular patterns. We confuse the map for the territory, the syntax for meaning, the logic for truths.

Obsessed that we are by naming, calling, labelling, we are now teaching our obsession to learning machines, and we are impressed at their ability to reproduce our thinking. But who is naming the thing, that if they can do this, with such rudimentary mechanics, maybe language is actually not so much our thing. Not our essence by any means, not the end goal of the evolution tree, but just a temporary meme. Not the miracle that we thought, nor the pinnacle that we ought.

So yes, a mechanical system might reproduce your thinking. But will it ever, give it meaning?

We will always need you, for that.

~ Special mention to my wife for inspiring this vision. In shaping my thinking and refining the weaving of my technological and scientific background, with a touch of more than human wisdom. <3