In my opinion absolutely everything can quantified. Whether everything should be quantified for the benefit of People is doubtful. Mathematics is an extremely broad field and to me it encompasses absolutley every field of study. Given the fact that anything can corrupted i would argue even with our best efforts to quantify everything, things will still go wrong. When i use the word quantification, i'm referring to approximate quantifications. Even NASA approximates their measurements when they quantify a concept or physical object. The absolute truth exists but it is very hard to obtain.

One argument that mathematics doesn't apply to everything is that there is essentially no known perfect witness. If a perfect witness exists, he/she doesn't make him/herself known.

I often see physicists say things like "we discovered some math that helps with problem so and so" and stuff like that. — Gregory

It is a particular branch of maths these days. Symmetry theory.

Although of course it used to be mostly geometry as you might expect. The maths of spatial relations.

Then geometry was found to have algebraic description too. Calculus helped to capture actions in time.

Symmetry groups finally emerged because symmetry breaking is what happens to reveal a world of particles once you have some kind of geometric description of nature that unfolds as a cooling~spreading manifold.

So it is not really a big surprise. Maths grew out of the everyday utility of modelling the everyday world in terms of "form". Spatial form, or geometric relations in Euclidean space, was the everyday starting point.

And the fact that maths has turned out to stay useful no matter how many different avenues it explores should tell us that the universe is itself in some sense a "mathematical operation". A process of mathematically-structured evolution.

Higher level of maths are created by relaxing constraints. Non-Euclidean geometry arose out of geometry by relaxing the constraint that parallel lines can never meet (because the world is perfectly flat). If you permit space to be curved (making flatness a special case), then you can see reality with greater generality.

In my opinion absolutely everything can quantified. — turkeyMan

That's key too. No point having a theory if it doesn't have measurements.

It is not a special feature of contemporary physics that says reality is made of mathematical objects; rather, it is a general feature of mathematics that whatever we find things in reality to be doing, we can always invent a mathematical structure that behaves exactly, indistinguishably like that, and so say that the things in reality are identical to that mathematical structure. If we should find tomorrow that our contemporary theories of physics are wrong, it could not possibly prove that those features of reality are not identical to some mathematical structure or another; only that they are not identical to the structures we thought they were identical to, and we need to better figure out which of the infinite possible structures we could come up with it is identical to. We just need to identify the rules that reality is obeying, and then define mathematical objects by their obedience to those same rules. It may be hard to identify what those rules are, but we can never conclusively say that reality simply does not obey rules, only that we have not figured out what rules it obeys, yet.

The mathematics is essentially just describing reality, and whatever reality should be like, we can always come up with some way of describing it. One may be tempted to say that that does not make the description identical to reality itself, as in the adage "the map is not the territory". In general that adage is true, and we should not arrogantly hold our current descriptions of reality to be certainly identical to reality itself. But a perfectly detailed, perfectly accurate map of any territory at 1:1 scale is just an exact replica of that territory, and so is itself a territory in its own right, indistinguishable from the original; and likewise, whatever the perfectly detailed, perfectly accurate mathematical of reality should turn out to be, that mathematical model is a reality: the features of it that are perfectly detailed, perfectly accurate models of people like us would find themselves experiencing it as their reality exactly like we experience our reality. Mathematics "merely models" reality in that we don't know exactly what reality is like and we're trying to make a map of it. But whatever model it is that would perfectly map reality in every detail, that would be identical to reality itself. We just don't know what model that is.

There necessarily must be some rigorous formal (i.e. mathematical) system or another that would be a perfect description of reality. The alternative to reality being describable by a formal language would be either that some phenomenon occurs, and we are somehow unable to even speak about it; or that we can speak about it, but only in vague poetic language using words and grammar that are not well-defined. I struggle to imagine any possible phenomenon that could cause either of those problems. In fact, it seems to me that such a phenomenon is, in principle, literally unimaginable: I cannot picture in my head some definite image of something happening, yet at the same time not be able to describe it, as rigorously as I should feel like, not even by inventing new terminology if I need to. At best, I can just kind of... not really definitely imagine anything in particular.

Humans have come up with paradoxes though. Zeno's directly targeted the intelligibility of the world. I'd rather talk about the Liars Paradox though, since Godel used it and Stephen Hawking used Godel's idea in a paper about the nature of reality. What if reality is a loopy paradox? Is it possible science's only defense is its apparent success? I am not putting down what people wrote above, just pushing the conversation..

Mathmatics is the language we use to understand the properties of the universe and everything truly

"There is another relevant consideration here too. If quantity is adopted directly from our representations consciousness without being mediated by pure thinking, it can happen very easily that its range of validity is exaggerated, and indeed that quantity is elevated to the rank of an absolute category. This is what does happen in fact when those sciences whose object can be submitted to a mathematical calculus are recognized as exact science." Hegel in the lesser Logic.

He was the philosopher of contradiction. He often says we are all reality, and fleshes out a philosophy where contradictions within our nature result in the world, which contains both these contradictions and the symmetry of the future we are headed to.

I wonder if there's anything in our universe that can't be mathematically described or anything whose mathematical aspect is just incidental.

What about logic? Logic seems more fundamental, at least more broader in application, than math.

How about things like black holes? I remember Michio Kaku (I hope I got the name right) saying that Einstein's equations "break down" inside of black holes? Quite possibly we just need a better but still mathematical theory but who knows, black holes maybe nonmathematical. :chin:

Scientists look for ways to apply maths to observation.

I often see physicists say things like "we discovered some math that helps with problem so and so" and stuff like that. — Gregory

This should be read as the scientists claiming a way to present the problem that leads to some greater clarity.

it is a general feature of mathematics that whatever we find things in reality to be doing, we can always invent a mathematical structure that behaves exactly, indistinguishably like that, — Pfhorrest

Yes.

Paradoxes are examples of language gone astray. Zeno's Achilles is a case in point; where Zeno articulated the problem into a paradox, the maths of limits articulates the paradox away.

The oddity discovered by Zeno of Elea (an ancient Greek living in Italy) is explained by Hegel in that section. Infinity and finitude are in every thing; they are for ever together and apart. Infinitesimals about endlessly, all within a world we quantize as finite. This is what strict logic can get out of observation. APPLYING math to the world seems like an illegal move, or at least is a strange choice of words

Paradoxes are examples of language gone astray. Zeno's Achilles is a case in point; where Zeno articulated the problem into a paradox, the maths of limits articulates the paradox away. — Banno

I suppose you could say that but language is nothing apart from semantics - concepts - and being so, paradoxes must be about flawed or inappropriate concepts.

Sure; so throw out the flawed concepts.

Sure; so throw out the flawed concepts. — Banno

:ok:

Well guys, even the debate that went on the middle ages over "how many angels can dance on the head of a pin" was about the question of points, limits, infinity, and quanity-magnitude. It was literally a topic about measure, since angels were understood to be simple but not in the Divine sense. So this is not some obscure topic

If you strip everything mathematical or physical from the idea of the finite, and have finite-ness in its pure naked form before you, you can know instantly that it could not form one with an infinity of numbers. Hegel says they cancel each other and their death is motion. Hence Zeno

If you strip everything mathematical or physical from the idea of the finite... — Gregory

...you would have nothing left.

Hegel speaks of pure conceptualization through intuition. Actually looking at an idea in the mind.
Kant had separated reality from perception. This was done with his Antimonies. Today it is done by science. They say we don't see things as they are. And they say stuff is flying all around us which we can't perceive. I believe the dresser over there and the desk to my right are in reality exactly as they look to me. My eyes go out and touch them, to be poorly poetic about it. My eyes know of contradiction and there is beauty there

...ok...?

It was Galileo, Descartes and Newton who lead the way in the mathematization of nature. But it doesn't describe all of reality - only that which is amenable to quantification, such as mass, velocity, relative position, and so on. Res extensa, in Descartes’ terms. The observing mind, however, was by the same method turned into the ‘ghost in the machine’.

True. The traditional scholastics (a term used for Thomists, Scotians, ect) thought an object was divided into accidents and substance. The former are how it is, the latter is what it is. The only difference between this belief and what Kant said is that accidents say something about substance, while phenomena says nothing about noumena. Scholastic tradition believed in a "ghost in the machine". Descartes's ghost was the soul

Form and matter, for Aristotle (the originator of this idea) are united in an object and produce the accidents vs substance relation. Descartes rejected form (rightly), and so took out the root, and. his discussion of the Eucharist is interesting. Aside from all that though, I think physicists are too obsessed with mathematics. I believe they should study logic and philosophy more. Their claim that my perceptions of the world are 99% inaccurate i take as bullshit. There are too many factors for their math to be accurate. You can't put your hands on all the forces that produces the universe either, so their claim that they can trace the casual line back 13.8 billion years back I find just ridiculous.

The traditional scholastics (a term used for Thomists, Scotians, ect) thought an object was divided into accidents and substance. The former are how it is, the latter is what it is. — Gregory

An idea that I find quite congenial.

I think in conclusion that I should clarify that I believe in corona virus research. That is organic science. Physics? Well.. they are good at making gadgets, big and small. I don't know what to compare the rate of technological advances to, but this has nothing to do with physics of hundreds of years ago, let alone billions. There is literally no end to the number of factors that could have interfered with the casual series they set up from now till 13.8 BC.I

A couple of months ago articles were popping up about "new mathematical techniques that can prove causality", which I find to be a bold face lie. Certain philosophers spend their whole lives studying causality and the different ways it could work. Then some physicists come along and say they can topple this with math techniques? That's pretty embarrassing

I've said my peace

I don't think we should assume the world is mathematical. A more accurate statement would be that the world can be expressed mathematically. Out of all the ways nature can be represented, modeled, and expressed, mathematics is one of them. Language and art are others. Biologically the world is presented and expressed to us as experience and emotion. If all of this were to also have a mathematical representation, great. It would be because they are all part of the natural world. But they also pre-exist their mathematically representations because for much of it we still need to figure it out.

And not only can most of us do without mathematical representations, often they're not even relevant.

Since nature can be expressed mathematically, those who assume the world is mathematical do have a mathematical viewpoint of nature at hand they can point to and say "see!". Good. But to then not be able to point to anything else would be their loss.

Anyone willing to help me reason through this issue? — Gregory

I would be hard pressed to describe anything that is demonstrably anti mathematical.

It often seems like that are taking math a priori and assuming that the world must accord with it. That would be a Pythagorean position though. It would need defending. Anyone willing to help me reason through this issue? — Gregory

Sure, great question! Math/a priori abstract concepts go way back to Platonism which of course is still popular today. Numbers or other abstract objects are supposed to be objective, timeless entities, independent of the physical world and/or of the symbols used to represent them. However, we know that there are other problems associated with those descriptions and concepts of reality.

For example, we know that running mathematical calcs. to size-up a structural beam is an abstract way of describing a physical object. And similarly, also running calcs. to compute or describe unseen things (metaphysical) like the laws of gravity. Of course neither are necessary for building certain things or for dodging falling things/objects. And so you have this ancillary feature of human existence that just is. Why we have this ability is a mystery. But the mystery also extends to the paradox of existence (timeless truth's v. time dependent truth's).

Platonic realms, mathematics and reality relate to contradictions in temporal time and time dependency (contingency & causation in nature) v. timelessness. Since mathematical truth's are known to be timeless abstract truth's that can effectively describe physical things (though not perfectly complete viz Gödel and Heisenberg), yet at the same time we live in a time dependent reality, we have to confront the contradiction between those concepts from our reality. And that could also lead to the other intriguing questions about whether math itself has an independent existence or whether it's a human invention, or other problems relative to logically necessary truth's which are based on formal logic/mathematics, like the infamous ontological argument.

But here's the thing, living life itself is not strictly binary either/or like much in the world of mathematics, computers and mathematical abstracts. Instead, it's more akin to the dialectic reasoning of both/and.

So I think it's just another means to and end. It's a tool that is obviously useful yet has its limitations. When discussing the nature of reality and existence, you have to confront the paradoxes associated with timelessness and time dependent things in nature. But it's ironic that we ourselves have this capability to compute timelessness (Platonic realms) through the use of mathematics and mathematical abstracts in our thinking, yet we live in a world of time dependent * reality.

(*Though I suppose one could make a case for relativity insofar as the speed of light being timeless and eternal like mathematical abstracts.)

Humans assume the world is mathematical, I think, for two reasons. 1) Because math is powerful in terms of approximation and 2) because it makes them feel like reality is full of order and that it can be controlled. It always gives me a laugh when I meet a mathematical supernaturalist. They just can't handle the fact that numbers are simply useful symbols and concepts. They want more, they want to turn math into a kind of God. Pity one always has to use another language to make math intelligible.

They want more, they want to turn math into a kind of God. — JerseyFlight

No mathematical physics - no internet, no computers. You'd be writing that post on paper, or on the wall.

Maybe thru evolution we will, someday, build newer computers using only our intuition

:up: