Around the year 2012 I got caught in a storm of synchronicities. I was led there through a bunch of things and ideas that happened in my life at that time. I found some "strange attractors" (looks like it, I don't have the rigorous phase space characterizations, nor the knowledge to do it). Pick one language. Find two frequency lists. Remove words that aren't present in both and establish ranks (Or establish ranks then remove words that are not share, the order is critical, it was a long time ago and my memories have faded). Then do as if you were plotting a Zipf distribution but instead of comparing rank against frequency, compare each rank with (absolute) distance to the rank in other frequency list. You observe some structures merging amid a mist of points and continuity lines emerge. Because some frequencies come multiple times, the order of the list is partial but the plot demands total order anyway. There is some arbitrary ordering to do, so randomize those choices and make the seed vary: the points in the cloud change, but the metastable structure remains. Change your sorting algorithm, the shape of the structure changes. It remains (meta)stable.
Around the same time I play a philosophical game with a friend. Pivot subjects and nouns around their verb and observe. Don't say "I smoke a cigarette" but say "the cigarette smokes me". It often makes sense. And not just because the verb meaning implies the subject and object are naturally interchangeable. It creates meaning figuratively. I start envisioning a generalized commutation operation for linguistics (was studying this field at the time) that would not just be a tool to probe the structure of meaning. It would be its very foundation. The commutation would be like a geometric pivot: it's continuous. I sketch ideas about mapping the space of these commutation that create meaning figuratively, even oracularly. And I have that picture in mind that I can now convey by evoking scales weighting scales ... weighting the scales they sit on. I need a "fractal" byte, where each bit can be seen as a sub-byte, ad-infinitum, and operate computations at every scale at the same time. That's when it striked me what I needed was a quantum bit of some sort. At this point I have no interest in QM, it's just that I have that sudden realization that I need that stuff I read about in pop science magazines. It's as if the quantum came to me, not the other way around. Saying this now that I introduced that idea of linguistic pivot may make you smile. But it was the bread butter of my life at that time, it was the consubstantial mud at the bottom of synchronicity pit I was at the bottom of. Anyway it's not like I was coming up with a new idea, a representation of something (sketchy or not). No it was about incarnating that very idea, discovering the element that motivated your search in the first place. Imagine: a theory of how ideas emerge in theoreticians was emerging in me. It's everywhere in fact. Einstein elaborated a philosophical relativity theory with a "bro" when he was younger. Heisenberg too. There is some will for eternal return a need to close his inner loop in Strogatz when he concludes his chaos theory popularization book by saying sync may even explain how he wrote that book. Ditto with that woman quanta magazine interviewed about her work around geometrical forms whose interaction in a system make the entropy decrease. She says her objects of study are at play in the chaos that is her department as she oversees 40 phd students. This is what I call incarnation.

The story continues: 2012. Start studying computer science. Math teacher is a chaos theorician. He introduces himself and presents his main contribution to science. He draws on the blackboard what I would draw if I had to schematize those Zipfian pseudo-attractors I was trying to capture at that time. Incarnation strikes again, yet another synchronicity to add to the list. I thought I had caught an attractor, and now it seemed as if it was the the attractor that had caught me. Nonetheless nothing came out with my interaction with that researcher. I kept the secret of my formula (explained above), he thought I was spooky.

Some 10 years after the facts what can I tell ? Quantum linguistics is a booming field and there are people running question answering algorithms, on quantum hardware, with quantum native theories of language. The dude behind this says "language is quantum native". His master, Aerts, has views that goes along the line of "quantum physics is in fact a quantum linguistics construct". I'm exaggerating, but just a bit. Concretely, what do I have ? Nothing but juxtaposition and future-proves-past kind of non-points. Like this:

2019

https://deepai.org/publication/the-role-of-grammar-in-transi...

> Sentence formation is a highly structured, history-dependent, and sample-space reducing (SSR) process. While the first word in a sentence can be chosen from the entire vocabulary, typically, the freedom of choosing subsequent words gets more and more constrained by grammar and context, as the sentence progresses. This sample-space reducing property offers a natural explanation of Zipf's law in word frequencies, however, it fails to capture the structure of the word-to-word transition probability matrices of English text. Here we adopt the view that grammatical constraints (such as subject--predicate--object) locally re-order the word order in sentences that are sampled with a SSR word generation process. We demonstrate that superimposing grammatical structure -- as a local word re-ordering (permutation) process -- on a sample-space reducing process is sufficient to explain both, word frequencies and word-to-word transition probabilities. We compare the quality of the grammatically ordered SSR model in reproducing several test statistics of real texts with other text generation models, such as the Bernoulli model, the Simon model, and the Monkey typewriting model.