Are there languages that computers can understand? Not programming languages, no. I want there to be an exchange of information/communication between a human and a symbolic system, even if primitive. In other words, I want something that is between a conlang and a symbolic, purely declarative [programming?] language -- something both computers and humans can use, even if it is extremely simple.

I'm seeing this niche kind of unfilled. Conlangs exist that strive toward this, but the problem I see with them is they tend to focus too much on regularity and ease of parsing, which is well away from semantics and information exchange (the parts I'm interested in constructing).

With programming languages, they exist to solve an entirely different problem: they are basically ways and [thought] systems around "giving orders" the machine  -- they are about describing computation, operationally or declaratively.

What I am interested in is, roughly, a way to describe a world -- perhaps a symbolic world; not necessarily our real world, but one of many possible worlds -- with engineered rules and made of symbolic matter. One important remark would be that the world must be shared between the human and the machine in some way for communication to make sense.

I think my point could get across much more easily with the following.

Remove the human. Does the machine still use language? Does it still run? No? It needs a query, right? An operator?

Well, then you've failed to implement the kind of language I'm talking about -- or, rather, the kind of system that can produce it.

For me, whether there's a human operator or not, the machine/system must go on. Whether there's communication or not the machine must go on, doing its own things. Modern machines don't have their own things. Their function depends entirely on humans -- from assembly instructions to knowledge databases to LLMs, they need an operator at some point. They are not closed ontologically.

What I'm trying to do here is to strike the idea of inference, or knowledge databases, or logic/formal systems, all in some naive form. What use are they without a human, querying them, or starting the process of inference?

Language could be an interface, I believe; a kind of "render" of some sort of symbolic world (perhaps bound -- entangled, as I call it -- to parts of "objective reality").

Humans have such a world "in their heads". I am speaking metaphorically here, because "what we have in our heads" isn't anywhere in particular; it is simulated, in the loosest sense, as in "given expression/the ability to express itself/manipulate observable behavior". Simulating a world doesn't place it magically within or near the boundary -- the machine that's doing the actual, energy-expending work in the objective reality. What I want to say here is, if I wear this particular hat for a moment, I believe the brain is such a boundary machine -- a time-stepper, if you will. A physics engine realized in wetware.

Machines, too, could be engineered to have such a world -- stressing, again, the fact that it must go on, whatever this means in practice (that would largely depend on the domain or, if the domain is general, on the stimuli entering the system and the progress of computation based on that according to the system's rules).

Wearing a hat of slightly different color, I could try to define language in the following way: a world, say, W0, contains inside itself, apart from all other dynamics, an active representation/model of the world W1, which I will call from now on a -belief, here it is W1-belief.

When we say W0 communicates with W1, what we mean is W0 synthesizes a sequence of tokens that change the state of W1-belief to some target state. In a sense, W0 wants the content of W1-belief to include X, but it doesn't have direct access to W1 (it doesn't have any access to W1, in fact, nor any knowledge about its existence apart from stimuli at the edge of perception, which could be loosely linked to W1).

W0 has access only to its W1-belief. W0 modifies it to include X, and the containing system (the machine at the boundary between "objective reality" and this madness of a world, W0 -- the machine that hosts W0) synthesizes a string of tokens that represent the change in W1-belief. The string of tokens then transfers (perhaps audibly) across the medium to W1, which it enters, modifying W1's W0-belief. W1 perceives its W0-belief as speaking, and throughout that perception, this very speech modifies the rewrite dynamics of W1, shifting it (or not, this is called "misunderstanding", which I'm sure there will be plenty with this little piece of mine!) toward the point W0 wanted it to be in the first place.

Another way to imagine this is, more pragmatically, to imagine a symbolic world that contains (literally, i.e., as a symbolic object!) a model/representation of its user -- its user-belief. The world would then communicate with the user by modifying (or, making a weaker statement, by consulting -- by matching on) the user-belief. The world never touches language; the outer system does -- that is, the "simulator"/time-stepper. One could go even further and say that the user-belief is an active agent of its own, "living" within the symbolic world and participating in its evolution -- animated by the real user, but triggering processes inaccessible to the real user directly. In a way, the user, by animating the user-belief, receives an avatar of itself in another reality (used here in a Platonic sense). This way, the user is capable of triggering rules and transformations that simply do not exist in reality nor on their own end.

One could consider language to be steering signals sent to the user-belief. They are purely egoistic. In plain terms, say, if I want this entity to move left, I can't just move it left, I need to emit "steering signals" so that it moves left, and I learn about it actually moving left from feedback. The question of how those steering signals are generated is an implementation detail: in my case, I seem to pivot closer to the approach that completely abstracts away such "steering", so that the agents inhabiting the system can freely manipulate and compute about the user-belief, and the outer machinery tries as hard as it can to entangle that with the actual user. There are pros and cons to this approach, namely that one can get into situations where the belief drifts very much apart from the state of the user due to e.g. incompatible update-speed or lack of/infrequent feedback (so the system can't snap the belief back/"undo" quickly enough).

It is important to clarify that by "egoistic" above I meant something entirely mechanical. I meant W0's reasoning does not include W1, only W1-belief, which exists inside W0. W0's only objective is to change itself, never W1, and vice versa. That's why I used the word "egoistic". W0 isn't even aware that there is W1. For W0, W1 does not exist. W0 never interacts with W1. Only W0 exists, and part of W0 is W1-belief, from which W0 infers that W1 exists.

This resembles to me some sort of "computational, paradoxical solipsism" that I came to be a believer of recently. I say that only I exist, and when I cease to exist, you all will cease to exist (solipsism, stated a bit amateurly). As I am writing this, I think the statement is true with high probability.

Simultaneously, I am saying that we all exist, we are all equally real, both our subjective worlds, and the objective reality that contains us all. This statement is also true with high probability. W0 can only change itself. It can only interact with parts of itself. Once W0 ceases, the world W0 is gone, and with it, all Wn-belief's, which W0 happened to perceive as, or infer to be, Wn's.

A world, as I define it within this paradigm, is the pair (ruleset, matter). Rules are pairs of pattern [an abstract sensory organ facing the totality of a previous frame] and transformation [an abstract actuation organ referencing and reshaping what is seen into the next frame]. Matter, here, is symbolic. To ground the latter a little bit, think [extended] S-expressions.

Observation still exists, in that W0 has full access to its internal state, and once it wants to communicate that to W1, it modifies its W1-belief to contain "awareness of W0's current state".

Since the backdrop now resembles more and more the areas of rewrite systems and symbolic automata, I can try, and perhaps fail, to define language in terms of rewrite systems, as I understand them.

Language becomes the art of emitting a sequence of stimuli (factoring in interpretation by the boundary system[s]) that trigger compatible/expected rewrites in the world-content of other systems. More literally, they trigger -belief rewrites. They animate -beliefs. Language is a way to entangle parts of worlds I refer to as -beliefs.

Because, from Alice's perspective, it is Bob-belief speaking (the qualitative entity of Bob [forgive me; I know I am incompetent in philosophy, but I couldn't resist!]). It's not some abstract entity or an abstract idea suddenly realizing in Alice's head, making her thing Bob likes her. It is Bob-belief, quite literally. Think of your subjective experience talking to someone.

Look at them. Look in their eyes. What you see in front of you is what I call a belief-object. Perhaps you see Bob-belief, if your friend's name is Bob, or perhaps you see Alice-belief.

You're not looking at the real Bob or Alice. You're looking at an entity your brain puts in your subjective reality, that happens to be the puppet of Bob or Alice.

As they talk to you there in the real world, after some necessary processing delay, you see their belief-object animated -- moving its lips, raising its eyebrows. Interestingly, their belief-object is fully integrated with the rest of the "frame": you don't see parts of their mouth move out-of-sync in some weird sense due to neural processing delay of a few centimeters between the relevant areas. You look at Alice's dress, and she wears a very beautiful red dress, and you ingest the beauty of its redness.

But then you remember that you're reading this, and there's no dress; and you see there's no red, either, because the qualitative experience of red does not exist in objective reality.

Does the red feel less real to you? No? I think part of the reason that's the case is because objective reality is as real as subjective one, and qualia are beasts of the latter. So, as always, both camps of philosophers appear to be right: qualia exist, but they don't. In other words, it's complicated. But please, forgive me. I went off track here for a bit. 

When I say that Bob updates Alice's Bob-belief, I do not mean he "magically transfers his thoughts". Bob is literally making the Bob-belief speak, like a puppet, with a certain effort. Notice this when you talk with someone (if you ever do!)

There's plenty of machinery left to decipher language, from perception of Bob's sound waves and photons all the way to whatever method brains have for "parsing" and so on.

The situation seems rather direct on the subjective level, however: Bob is literally making Alice's Bob-belief speak, move, make Alice experience the qualia of Bob-belief-producing-sound, and so on, and it is this "qualia" that evokes an internal response (the "chain reactions" to which, in their totality, we react with "oh, I understand you").

The machinery we usually associate with language or even vision or hearing is downstream, or could be if I wear another one of those hats. In other words, we could make the wild assumption of qualia being more primitive than the neural processing that one conventionally says produces them (if one "believes in qualia").

Invoking foreign languages is helpful here so that I get my point across (even English idioms hint at the worldview I'm trying to describe here, don't you see?) 

Bob would be successful in making Bob-belief speak German "inside" Alice, but Alice's downstream machinery fails to process that; so at a certain point, the belief is "stripped" of meaningful influence on the parts of Alice waiting to interact with the Bob-belief. Bob has to resort to making heart signs with hands to convey the same message, "I like you". This reminds me of confluence -- the way different sequences of rewrites lead to the same meaning-state, which then feeds into response.

Language seems tightly coupled to the idea of updating one's belief-object inside another world (here, Bob deliberately updating Alice's Bob-belief). It's almost as if one opens an "embassy" of oneself in another world and must attempt communication with that world from the perspective of being inside it. It's almost as if one has a puppet "inside another's head" (let me not go back to why I put this in quotes!) A puppet one controls, and seeks way to control most efficiently, as losslessly as possible (see e.g. grammar).

The idea here also lands sufficiently close to explain what books are, and why they work. They are such "embassies", "puppets", or maybe "avatars" -- pick whichever you like. Such avatars are instantiated as they are read. They live "inside" one's mind and "show" it all sorts of things. Independently of the eyes and the ears, the belief-objects instantiated and continuously animated by the process of reading trigger confluent or near-confluent rewrites on their own, and may even persist well past the process of reading as do the worlds of Lord of the Rings or Harry Potter, although they in some sense "lose power" this way. The latter points to the fact that such avatars may be underdetermined.

The act of writing, then, is similar to painting a picture, except the picture is also in motion. Writing thus involves the process of constraining the reader's rewriting (which includes the belief-object previously constructed by the process being described) to produce a new belief-object similar to the one in the author's mind. This is expected to encode both "shape" and "transition", because provided one has a physics engine, they are, in a sense, one and the same.

Backtracking a bit, propaganda also seems to fit this idea rather well. Metaphorically, I consider propaganda "radiation for the mind". No one is resistant to it completely because its point is not to "attack" -- it is to reside, to open and maintain an embassy of that particular world-view.

Whether you are a scientist who spent their entire life studying radiation or their effects, or a stalker, standing long enough near the Elephant's foot would give you enough radiation to start feeling funny

To create a belief-object that you find omnipresent, because in a way, it is -- it is inside your subjective reality. It is important to maintain the belief-object constantly, through exposure to subjects carrying that world-view. Radio, TV, internet bubbles -- all that serves maintenance to the belief-object. Once you start debating the belief-object, parodying it -- you're lost; you're interacting with it, and thus perpetuating it. In a way, by talking about it, by seeing it in the abstract sense of the word, you are helping it to continue existing.

This also seems to hint at one possible explanation for LLMs; at least in what they are not. They are clearly not worlds. There is no dynamics there. An LLM is not Bob. This sounds kind of obvious, until it does not: LLMs are mathematical objects constructed so as to reside in Alice as belief-objects and manipulate her (said here in a neutral way).

They are an agent inside Alice, "an embassy", just like Bob-belief, except artificial; except more importantly, there's no one there on the other side of the LLM-belief. It's trillions of math operations that manage to transform inputs to outputs in such a way that what results is LLM-belief behaving the way one would expect an entity that comprehends language to behave.

I always felt LLMs are somehow "fooling" me, making ne interact with myself in a bizarre kind of way. This is hinted at by various cases of LLM-psychosis, LLM-induced psychotic loops (although I'm not a psychiatrist, so of course I have no idea what I am talking about here!) This could happen when one's odd beliefs are reflected onto oneself so that a process similar to infinite regress begins, and sometimes grows out of control, as the LLM-belief always knows "which buttons are the right to press" inside you. And this is of course not intentional: it's just that the corpus says to press them, and the LLM is "slapped" if it doesn't.

The mathematical object behind LLM-belief is also "alien", in a certain sense of the word. And by "fooled", I mean that exactly: Alice feels there's a Bob animating her Bob-belief; but there's none. Instead, there's an LLM animating the Bob-belief -- an abstract, multidimensional object that happens to be doing just the right things. Thanks to massive amounts of data on how to do just the right things, of course -- humans only write that kind of stuff, you see; we don't exchange incomprehensible noise.

LLMs are structured in such a way as to take a rewrite trajectory matching a properly animated Bob-belief most of the times. That's why I say "fooling". LLMs aren't the only focus here: other generative models are, as well, except they act on other modalities, and sometimes "fool" in a slightly less harmful way (as in generating a picture that looks like Geneva, but there's no Geneva "behind" it -- less harmful than an interactive Bob-belief which with each message convinces Alice how smart she is -- without a trace of some kind of human-comprehensible Bob-with-incentives behind it).

More importantly, when an LLM pretends to be Bob and animates Bob-belief, there's no Bob. What this means is there's no Alice-belief either: there's no Bob to host it. Alice is not present in an LLM's "mind" (plug in whatever you want here, let me be!!) -- like she is present in Bob's when they're talking. Put plainly, when you talk to an LLM, it doesn't see you. It doesn't hear you. And that's what matters, even if you think it doesn't -- that you're a "signal source" inside something that has its own life.

Another explanation for LLMs is possible. We can define languages as ontologically closed: as rewrite systems. The task of an LLM is then to figure out, during training, the rules of "language physics". The huge function that an LLM is is in some sense a "linearized encoding" of the application of these rules. That is, you don't get a world out; you get something like "latest point in trajectory" out. It is unclear to me how to translate [the evolution of] an ontologically closed world into a sequence of tokens. The same is true for humans as well. Subjectively, I see language as "a cloud of words" or maybe "language-realized thoughts", and simultaneously as a "void from which a sequence of words is emitted". I use the word void here in the same sense your blind spot is a void, or the stuff behind the back of your head, or the kind of thing a blind person sees. In that it absent, and not in any sense "black". I suspect this absence hides a lot of very interesting machinery!