[lordnacho]

IMO math seems effective because everything that works is called math. So yeah, that quote from the beginning is right, it's selection.

There are many different math concepts used to describe the world, everything from calculus to graph theory, geometry, and so on. These things have a two way relationship with the real world: they don't necessarily have to correspond with anything real, like Hardy's quote about his number theory work that eventually ended up appearing in cryptography, but if something in the real world happens ahead of it, math will expand to swallow it.

Think of a scientific theory that isn't described with some kind of math. I'm not sure it can be done. My sense is that whatever you think of, even if it's completely new, will be called math. For instance general relativity relied on some quite new concepts at the time, but nobody would point at it and say it wasn't math.

[agarsev]

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 ;)

[qboltz]

Could you cite some specific examples?

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?

[agarsev]

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!

[qboltz]

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.

[d_tr]

> they don't necessarily have to correspond with anything real, ...

I would just say they correspond to encoded thought processes, encoded reasoning. If you can take a thought process and describe it in terms of sets and relations (i.e. subsets with certain properties), you have a mathematical structure and you can start trying to prove theorems.

You spend time thinking about a problem, then hopefully you start recognizing patterns, then you take the reasoning, clean it up, abstract it and generalize it to increase its ultimate utility, and package it for others to reuse and build upon.

> everything that works is called math

It is just fortunate that people have been able to "package" a lot of stuff this way. Like Riemann did with his geometry for example. It is not that mathematicians just decide to "take over" everything.

[_xnmw]

What? I'm sorry but this is utter bullshit. Math is not just anything that works. Every hot new theory is assumed to "work" in the era which it is produced, and not everything is called "math". There has been no significant "wrong" result in the entire history of math since ancient times, nor has any significant result been jettisoned from the field of math, whereas every other field or discipline of study has been wrong at some point. If math was just "anything that works", then we'd be regularly purging stuff from the "math" label, but I can't think of anything that was called "math" in history and not called "math" now.

[lordnacho]

Compare and contrast:

> everything that works is called math

> Math is not just anything that works

Can you see how you have read my comment wrong? "An A is a B" is not the same as "A B is and A", you're arguing against something that wasn't claimed.

If you wanted to come up with something sensible to say, you could bring up a theory that is backed up by something that isn't called math.

[asimpletune]

What about "experts"? Like, I would say there are people out there who are valuable because they know how to do stuff. It's not required for them to explain how they do it, and often times it's the case that they can't, otherwise they would simply explain and we'd all be experts. Rather, we need them precisely because the results they deliver are not able to be broken down into a sequence of steps that anyone could follow - since many of them can't explain. So it's something that "works" but isn't math.

I'll add that eventually experts are replaced, but then by that time there are new experts. The problem domain evolves and what used to require experts is replaced with math, and the new experts are working in the area where things can't be math.

Conceptually I think I'm on point for this, but I don't know if my examples are super good. I'd say business, human language, politics, medicine, and art are all examples of things that have experts. In each of these fields that are things that work, but it's not yet backed up by math.

Maybe it's more accurate to say, given an infinite amount of time and intelligence, everything becomes math? And I think that makes sense, but I'm sort of inclined to believing in an objective, yet logistically intractable reality.

[lordnacho]

Sure, tacit knowledge is a real thing that people talk about. But I see expertise as a kind of navigation through murky waters rather than "theory" which tends to be an explicit thing.

One thing experts can do is tell you when a theory is applicable.

[jacobolus]

> no significant "wrong" result in the entire history of math since ancient times, nor has any significant result been jettisoned

This is a bit of an exaggeration. If you search around you can e.g. find https://mathoverflow.net/questions/35468/widely-accepted-mat... https://math.stackexchange.com/questions/139503/in-the-histo... https://mathoverflow.net/questions/27749/what-are-some-corre... https://mathoverflow.net/questions/879/most-interesting-math...

[_xnmw]

Reading just the top answers from those threads, I see no significant results that have been disproved. Only the "intuitions" and "footnotes" and some "trivial assumptions" of mathematicians, but not an actual published result that was cited by other results and had significant consequences by invalidating other results.

[morelisp]

You can't open the conversation offering "the entire history of math since ancient times" and then demand thoroughly modern things like "an actual published result that was cited by other results" as counter-evidence.

Nonetheless many of the examples in the above links still fit your criteria.

[_xnmw]

A published result that cites another result is not "a thoroughly modern thing". Mathematicians have been citing each other since Pythagoras and Avicenna.

[leonry]

How about Hilbert‘s 16th problem, would that satisfy your conditions for a counterclaim to your assertion? For a short summary, see https://mathoverflow.net/a/116530/60775 or https://valentermz.github.io/documents/slides/olivetti-2013-... for instance.

In any case, there is still the foundational crisis in the late 19th and early 20th century that‘s worth a mention.

[jonsen]

I think you got the parent comment bacwards.

[TheOtherHobbes]

No. https://en.wikipedia.org/wiki/List_of_incomplete_proofs

You seem to be arguing from a personally idealised view of math, which doesn't match reality.

Real math is full of full of mis-starts, dead ends, and established mistakes which are later corrected.

Math is exactly like science. There's a cumulative core we can be very confident about, and more exploratory edges where results are more tentative and subject to review, correction, and expansion.

[_xnmw]

Sure there are incomplete proofs and dead ends. But I have yet to see an example of an "established mistake" which disproved an entire line of research that depended on the mistake. Sure, mistakes have been published. But it never led to an entire branch of "knowledge" based on a false belief -- something that happens regularly in other fields.