I think this is a very widespread idea, I used to believe in it too, perhaps due to our background. However, if you work on translating science to computers, you soon find it's not so true. There are some many ideas in science which are not mathematically encoded, but rather in human language, it's kind of frustrating. The "low-level" sciences like physics have spoilt us with their very math-like nature. But even in those sciences there are a lot of things which are not well-defined, but rather rely on human intuition and language. If you go "upwards" in the stack, you find things like biology where there is a lot of very formal scientific knowledge which is not maths. And I work in linguistics, so just imagine what it's like at this level ;)
I'm finding the deeper I study biology, the more certain I am that complex models with both classical and quantum parameters will eventually be able to predict the overwhelming majority of macromolecular behavior such as protein folding and DNA recombination.
Once you start dealing with concepts bigger than that you get into another mathematical description with Markov chain style models for cellular proliferation, followed by network analysis for tissue growth.
You can take that up further and further, I'm sure you're somewhat familar.
My question is, even if you have some examples, what do you find to be some kind of theoretical limit to the modelling that would actually be accurate?
Not a limit to the accuracy, that must simply always exist, but a limit to what can be successfully modeled at least to "acceptably correct" for use in some application?
In biology: morphology of organisms, evolution, ecology. And those deal with systems, so they use a lot of math. But interspersed with the math, you always find natural language descriptions, definitions, explanations, which are necessary for understanding and complete modelling of the theory. These make reference to the shared human experience of the world, and are not formalized in logic. Not that they cannot be, or at least so I hope. But we're very far from it today, that's what I mean.
Maybe relatedly, humans think of the world in fuzzy terms. At some point we're going to need a system for formalizing fuzzy thought, and no, fuzzy logic is not it, because that's just a continuous extension to boolean logic. Human thinking is fuzzy beyond that. But, as a computational linguist, I sometimes worry that we already have that system: natural languages!
I don't think was specific enough, I guess what I'm looking for is something that we can describe with language that doesn't have at least some sort of parameterization in regards to physics.
So take the original reaction of DNA from just inorganics, I typed those words, but have no reference for what the model actually is. What I do however have, is words for each of those things, and a set of impossibilities for what it could "not" mean.
However, the reference is not born out in terms of nothing, each of those words has a set of things that we do have models for, we have models for atoms, reactions, DNA, etc.
So in reality the sentence describes something that we simply can't point to specifics on, but is in no way "unexplainable" in terms of its logic.
Another example would be dark matter, we use those words, but really they just stand for a set of observations, empirical measurements just operating outside of the patterns we are used to, but certainly not without something to point to.
If there's some shared experience that we can't express logically, I'm at least personally unfamiliar with it, I would need some further understanding of what you have in mind.
I could also be wildly misreading what you mean, semantics are not my favorite over text.
