Honestly, you are just confused.
With LLMs, The "knowing" you're describing is trivial and doesn't really constitute knowing at all. It's just the physics of the substrate. When people say LLMs are a black box, they aren't talking about the hardware or the fact that it's "math all the way down." They are talking about interpretability.
If I hand you a 175-billion parameter tensor, your 'knowledge' of logic gates doesn't help you explain why a specific circuit within that model represents "the concept of justice" or how it decided to pivot a sentence in a specific direction.
On the other hand, the very professions you cited rely on interpretability. A civil engineer doesn't look at a bridge and dismiss it as "a collection of atoms" unable to go further. They can point to a specific truss and explain exactly how it manages tension and compression, tell you why it could collapse in certain conditions. A software engineer can step through a debugger and tell you why a specific if statement triggered.
We don't even have that much for LLMs so why would you say we have an idea of what's going on ?
It sounds like you're looking for something more than the simple reality that the math is what's going on. It's a complex system that can't simply be debugged through[1], but that doesn't mean it isn't "understood".
This reminds me of Searle's insipid Chinese Room; the rebuttal (which he never had an answer for) is that "the room understands Chinese". It's just not satisfying to someone steeped in cultural traditions that see people as "souls". But the room understands Chinese; the LLM understands language. It is what it is.
[1] Since it's deterministic, it certainly can be debugged through, but you probably don't have the patience to step through trillions of operations. That's not the technology's fault.
>It sounds like you're looking for something more than the simple reality that the math is what's going on.
Train a tiny transformer on addition pairs (i.e i.e '38393 + 79628 = 118021') and it will learn an algorithm for addition to minimize next token error. This is not immediately obvious. You won't be able to just look at the matrix multiplications and see what addition implementation it subscribes to but we know this from tedious interpretability research on the features of the model. See, this addition transformer is an example of a model we do understand.
So those inscrutable matrix multiplications do have underlying meaning and multiple interpretability papers have alluded as much, even if we don't understand it 99% of the time.
I'm very fine with simply saying 'LLMs understand Language' and calling it a day. I don't care for Searle's Chinese Room either. What I'm not going to tell you is that we understand how LLMs understand language.
No one relies on "interpretability" in quantum mechanics. It is famously uninterpretable. In any case, I don't think any further engagement is going to be productive for anyone here so I'm dropping out of this thread. Good luck.
Quantum mechanics has competing interpretations (Copenhagen, Many-Worlds, etc.) about what the math means philosophically, but we still have precise mathematical models that let us predict outcomes and engineer devices.
Again, we lack even this much with LLMs so why say we know how they work ?
Unless I'm missing what you mean by a mile, this isn't true at all. We have infinitely precise models for the outcomes of LLMs because they're digital. We are also able to engineer them pretty effectively.
The ML Research world (so this isn't simply a matter of being ignorant/uninformed) was surprised by the performance of GPT-2 and utterly shocked by GPT-3. Why ? Isn't that strange ? Did the transformer architecture fundamentally change between these releases ? No, it did not at all.
So why ? Because even in 2026, nevermind 18 and 19, the only way to really know exactly how a neural network will perform trained with x data at y scale is to train it and see. No elaborate "laws", no neat equations. Modern Artificial Intelligence is an extremely empirical, trial and error field, with researchers often giving post-hoc rationalizations for architectural decisions. So no, we do not have any precise models that tell us how a LLM will respond to any query. If we did, we wouldn't need to spend months and millions of dollars training them.