I this thread on Evolution I’m afraid I started a hijack on what is a “fact” by suggesting 2+2=4 is the only “true” facts we can count on (which is to say math…not just that equation).

Derelth responded by saying:

The conversation moves from there and most recently John Mace and I had this exchange:

John Mace’s response to that:

Now, I get that the Universe does not “care” about math. I understand that we use human words and concepts to try to describe the universe but they are inexact.

Nevertheless it seems, to me, that the language of the universe is math.

True a moon does not “understand” math and “agree” to follow a certain orbit. That said the orbit the moon follows is thoroughly described by math.

That gold record on Voyager uses math as a universal language because any reasonably intelligent alien will know that 2+2=4

Perhaps we are talking past each other here. I suspect we agree (in the other thread) more than we disagree on this point. Still, figured it was something for the Teeming Millions to have a go at.

I’m not sure I can say more than I already said on the subject other than to just repeat myself, but let’s give it a go.

The question is: did the universe “invent” math in order to exist (pardon the anthropomorphizing), or did humans invent math in order to understand the universe? I’m not sure how you would prove this, but it seems intuitively obvious to me that it’s the latter.

I agree the universe did not “invent” math but I am proposing that math is a fundamental aspect of the universe.

Math is a language and a human invention. The universe does not know what “two” is.

That said in a universe with two particles in it then there is a reality to the numbers. You can use whatever words you want (two or dos or два).

A planet orbits in a very predictable way. We can describe that with math very precisely (in theory to any precision you want till you bump into Heisenberg).

I think I’m going to have to go with the others to say that the universe acts in concordance with the mathematical language we made for ourselves, but is independent of it. The moon orbits in a ellipsoid because its momentum is conserved and it is acting under a force of gravity that is proportional to the product of the masses and the square of the distance. This is because there are certain additive forces and fields at work*. We can use math to manipulate symbols that correspond calculate what those additive forces and fields are, and so predict the future orbit of the moon and other satellites we put up. However all of this symbol manipulation is just an accounting system designed by man so that it matches what we see in the universe.

As another example, if I have 42 8oz cans of tomato sauce and a 5 gallon drum, one might want to know if I have enough sauce to fill the drum. This can be done entirely without math by opening all the cans and trying to fill the drum. That is the physical fact of the situation. But instead I use some math to find that 48x8oz cans = 384oz= 3 gal and so I know the drum won’t be filled. I could reduce this problem to a symbol manipulation problem because I designed the symbolic the laws of multiplication to be such that when 48x8oz < 5 gal, it will be the case that 48 8oz cans will fit into a 5 gallon drum.

There are many branches of mathematics which so far have no relevance to the universe, and similarly there are many things going on in the universe that as yet we have no mathematics to model. (ie quantum gravity)
*I’m no physicist so I’m leaving this intentionally ambiguous so as to not get in trouble

Depends on what you mean. To the extent that any sentient race, in any physical environment anywhere in this Universe, would come up with the same mathematics, I think you’d have to regard that math as inherent in the nature of things in this universe, rather than an invention.

For instance, having things to count, and counting them, gets you the counting numbers. Subtraction gets you zero and the negative numbers; division gets you the rationals; roots get you the real and complex numbers. If a sentient race has occasion to count, subtract, divide, and take roots, they’re going to come up with all the sets of numbers that are the basis of contemporary mathematics.

Math’s a way to represent what we see in the physical world, a language if you will.

The ratio of a circle’s circumference to it’s diameter is constant, whether it’s denoted as 3.14159, 22/7, 3.11037 or 3.243F6. (pi, if you haven’t figured that out)
What people are trying to say when they say that “math’s the language of the universe” is that instead of saying that an alien would look at 3.14159 and recognize pi, that there are abundant examples of mathematical “rosetta stones” (pi, etc…) out there, so that we and any other species could relatively easily reconcile our respective mathematical systems.

I think you are making a mistake by confusing math with reality. The particles, as far as we know, obey physical laws that we represent using math. But the physical laws are not math. Not to mention that there isn’t any such thing as a particle in the first place. That, too, is a human construct.

Those words may be incomprehensible to someone else but no matter where you go in this universe the underlying premise is true.

Hence why we used math on that gold record on Voyager. As said above it is a Rosetta Stone (like that analogy). No matter where you go everyone will understand it (assuming some moderate intelligence).

First of all, we assume it’s universal. We don’t really know.

We also assume that diagrams are universal, since they are also used on that plaque that went with Voyager. There was some sort of symbol that was supposed to represent a Hydrogen atom. And there was a diagram of our solar system.

Eugene Wigner, a highly influential figure in quantum mechanics (though at the same time he did have a few controversial views, i.e. he believed conciousness played an importnat role in quantum physics) wrote the famous essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences.

As I said on the other thread, maths is about abstraction. If yous tart requiring maths to have some sort of roots planted firmly in the empircial then your in danger of losing the full power of abstraction.

I would say mathematics is the language of physics. ratehr than of the universe.

Actually I sort of disagree, nearly all areas of maths find practical application. Catergory theory which is a an area of maths about catergorizing abstract mathematical structures such as sets, fields, vector spaces, topological spaces, etc, etc was the first thing that sprangt o mind for me when thinking about areas of maths that are very abstract and don’t have applications that leap out at you. Howvwer it does seem from a quick google that compuetr programmers have used it for practical purposes.

The mathematics do actually exist to model quantum gravity (though it’s empircally untested for reasons that I’m just about to mention), you can derive the maths of quantum gravity using canocial quantization (i.e. the standard way of creating a quantum field theory from a classical field theory), the problem is that it has an in-built resistance to peturbative solutions (a method for obtainign approximate solutions) which makes it totally impractical as you can’t even obtain approximate solutions (by normal methods at least).

It can take centuries before a branch of mathematics finds an application in the real world. Sure, Newton invented calculus to solve a real-world problem, but that may be the exception rather than the rule.

I believe that the OP’s question cannot yet be answered. We know there are real physical phenomena that cannot presently be described by mathematics. We have some faith that this will not always be the case, but we can’t say this for certain.

If we ultimately find the math to describe all physical phenomena, then I think the OP’s conjecture can be said to be correct for all practical purposes. Even if it turns out that mathematics has uses beyond the description of reality, that doesn’t preclude it from being the “language” of it.

But if we fail to find the math to describe all physical phenomena, then the OP’s question cannot be answered yes or no. I’m not sure that one could prove a physical phenomenon to be not reducible to math, so we may never know for certain whether this is the case or whether we have simply failed to discover that correct math to describe it.

I don’t really know what the OP means by “[math is] the language of the universe”. Mathematics itself is probably “universal”, but that doesn’t seem to mean the same thing at all.

AFAIK, the truth is, we don’t really know what the relationship between logical and mathematical systems and “physical reality” is, or even if there really is a relationship other than that we can use one to make mental models of the other. We don’t even really know what exactly the relationship between either of those and our mental models is. These are old questions, going back at least to Plato.

Roger Penrose’s book “The Road to Reality” touches on these issues in the introduction, but it mostly makes it pretty clear that our mathematical descriptions of reality are if anything much more complicated than you’d expect (interesting, but complicated).

I don’t think the Universe is mathematical any more than it is based on the English language.

How many points are there along a 1 metre line; I mean in the real, physical universe?
1 / planck length? Infinity? Then how come I can do useful mathematics, and get correct answers, with a much lower granularity?

The answer is because mathematics is just a tool for deriving non-obvious facts from obvious facts. It’s a means of manipulating information in a way we would find difficult without the intermediate step of representing it symbolically.

That said, the fact that maths can be applied to the universe tells us something: that the universe is self-consistent and behaves in the same way as far as we can currently see.