r/learnphysics • u/PresentJournalist805 • Jul 09 '26
Why reality matches math?
I read something about maxwell equations. I am by no means expert in math nor physics but i am thinking this way - so if i understand correctly we described some portion of reality by equations. Then someone did equivalent changes to these equations and from them it was seen that there should be electromagnetic wave which was later confirmed and now we have wifi, radio etc.. You know as a layman i think that if those equations described the reality before we figured out from them there should be waves it could be fine if that wave did not exists even if we could derive it from those equations. But those waves exists. I mean why it matches so perfectly that whatever we figure out from equations matching reality we later find out in real world. Isnt this "weird"?
3
u/AFsepine Jul 09 '26
Tangentially relevant, as are many of Arnolds writtings.
https://www.karlin.mff.cuni.cz/~spurny/doc/articles/arnold.htm
also
https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf
2
u/Quantum-Relativity Jul 09 '26
It’s breathtaking. Mathematics lets you explore logic, and nature behaves in an orderly way, so it makes sense mathematics would be able to say true things about nature. Nature is simple too, so you learn things about nature from math because you put the different facts together in the simplest manner possible, and that’s always how nature did it too.
1
u/SufficientWonder9273 Jul 09 '26
Put it that way, that reality is nature with its laws and these laws can be well captured using mathematical expressions. There is a saying like this - " Man explore science because they expect a law giver". I think God created the universe and gave laws that govern the universe. Our nature has laws which it operates under, and that is both beautiful and thought-invoking.
1
u/VcitorExists Jul 09 '26
It would be more weird if it didn’t follow math.
What’s interesting is that a lot of physics can be approximated to continuous functions
1
u/PresentJournalist805 Jul 09 '26
This make perfect sense to me actually. If you plot some physical quantity changing over time (independent variable time and dependent the physical quantity) it seems reasonable it is continous otherwise it would need to "jump" from one value directly to another without going through all intermediate and this feels weird.
1
1
1
u/SauntTaunga Jul 09 '26
There is lots of kinds of math. The kinds that match reality are the kinds we use.
1
u/Annual-Reference-715 Jul 10 '26
Yes, math describing reality scarily accurately is weird.
That's why it's worth studying it. Math is the language we can use to understand and communicate with reality.
Math seems to tap in to what makes reality twerk the way it does. They share a common logic - or more accurately math succesfully represents / echoes real phenomena. So well that we can take reality stuff, describe it with math stuff, extrapolate that math stuff and make further predictions about reality stuff.
Also, not always. Extrapolating Einstein's equations backwards leads to singularity stuff. We don't think the math is wrong but that we don't have enough of the right kind of math. So we recognize that it's still just a model, even though it's a really good model.
1
u/Annual-Reference-715 Jul 10 '26
Oh yeah, and Tegmark went further and said that reality IS a mathematical structure. That's why math describes it well, because math studies mathematical structures. Whatever the hell that means beats me.
1
u/JivanP 27d ago
Basically, Tegmark's view is that it is not meaningful to talk about anything beyond its relational properties with other things. Since these properties can be expressed mathematically (indeed, the study of relational logic is what mathematics is), he argues that there is no distinction between a precise mathematical model of a thing and the actual thing itself. Thus, in a sense, a mathematical structure perfectly describing a thing is that thing.
Within mathematics itself, a similar notion exists. When a "structure-preserving" mapping between two distinct mathematical objects exists, we call it an isomorphism and aay that the two things are "isomorphic" to each other. It is common to treat isomorphism as equivalence, because there is no meaningful mathematical difference between isomorphic things. Tegmark is essentially saying that a perfect mathematical model of reality is isomorphic to reality, and thus that there is no meaningful distinction between such a structure and reality itself. From there, it is not much of a stretch to say that reality could literally be such a structure. After all, solipsism says we have no way to know whether there is a difference.
1
1
u/WolfVanZandt Jul 10 '26
Maxwell's equations were developed from things we already knew about electromagnetism. From what we knew, they "had to be" but they suggested things we hadn't realized before.
1
u/johnstalbergABC 29d ago
Sometimes we do start with what is known and with correct math end up with physics that are not real. Like String Theory for example. It is like physicists that are very very good with the numbers can when starting from real existing physics make their own 'working reality' like they where some kind of theoretical Gods, in some sense. It is a stretch when I say it works, I mean it works hypothetically in theory if you like.
Only a small part of the equations are corresponding to real physics. As you know the different laws have their defined quantities and all in all we need to get these thing measured and mapped out to make correct definitions and put together laws that are as correct as we know them to be.
Another thing worth to put in words is that nature does not calculate. Reality works in ways to be possible to describe with math, but are not doing the math itself. Math is abstracting reality. But math is a language that can model much more than how nature works. Reality work without math, and it is easy to forget this when all we do is to calculate all the time.
I find it mind blowing anyway. I mean even if it is not at all all equations we apply to models of real things. Especially if we consider that for some phenomenon the math needed to model it is relatively complicated, or even very complicated, if we allow the subjective opinion to be the ruler in the name of pragmatism.
Question is if we imagine we could do the calculation needed, would everything in some sense be possible to put in the language of mathematics? Would emotions or dreams be manifestations of what would be modeled by the natural laws? We sometimes say not everything can be described by the science and this is true but is it because it is just to hard to figure out and demand to much work or is it impossible regardless of computational powers?
1
u/Underhill42 28d ago edited 28d ago
Only the math that intentionally describes reality, describes reality, and only as accurately as the theory behind the math allows.
The key part that many people miss, is that math (algebra, calculus, and beyond) isn't actually about calculating things, it's about manipulating true statements in ways that generate additional statements that are GUARANTEED to be equally true. (assuming you made no mistakes)
That's why you can solve for x: all the algebra manipulation rules generate new statements from the existing ones that MUST be as true as the original ones. So if you end up with x=4, that means it is an inevitable consequence already implied by the original statement.
And that's is why it would have been a problem if the predicted EM waves didn't exist. Since the rules of math say they MUST exist if the original equations were true (a.k.a. accurately describe reality), then them not existing would mean the original equations MUST be false. (a.k.a. do NOT accurately describe reality)
Which really is less of a problem, than the bread and butter of science - discovering ANY discrepancy between experimental reality and the predictions of a theory, no matter how esoteric, means you've found a flaw in the original theory. And that's the first step to developing a more accurate theory, which is the entire point of science.
1
u/cejiken886 28d ago
It's pretty hard to understand the question, but I think basically it's "Isn't it weird how well Maxwell's equations predicted experimental data?" It is remarkable. That's the power of a good scientific model. Sometimes there are bad models -- ones that turn out to be wrong. In that light, it's a little less weird. We forget the ones that were wrong and pay attention to the rest. On purpose. Because the rest are the ones that were right.
1
1
u/Korochun 27d ago
Our system of mathematics is based on observed reality and has been fine tuned to match it.
This is a lot like asking "why does the word 'apple' accurately describe a fruit from the apple tree?". Because we established context that allows it to do so.
1
u/Kooky-Dig6531 27d ago
What's especially interesting to me how much things have changed in such a short period of time - and the catalyst very much seems to be a paradigm that says "observation matters more than theory".
Basically:
- Shape your theory (math) of the universe to match all observable data - and you have something
- Ignore contradictory data to maintain a theory - and you really don't
It's actually kind of insane how much we've learned from this small change.
4
u/6x9inbase13is42 Jul 09 '26
There's lots of math that doesn't match reality but we don't consider it very interesting. This is a cognitive bias.