And mathematical theory also not: it is immanent.
Mathematics doesn't help, at all, ever, in telling you what the universe is like. It's a system of rules about how to make statements and prove them correct (or incorrect), and then a set of axions from which one can derive statements and prove them correct. It is just a game that minds can play. Very much like chess.
Having said that, there is a very difficult to understand connection between mathematics and reality. How come that we can make models of the universe (for example Newton's theory of gravitation, which is proven every time we drop a wine glass on the hard floor of the kitchen), and the "game" of mathematics happens to help us build the models? Let me give you a much easier example of that. We have Peano's axioms, which in mathematics help us define what integers are and how they work. In a nutshell, Peano's axioms define the system of counting: We start with 0, we add 1 and get 1, we add 1 and get 2, and so on. You can try that in your kitchen, by pulling a few apples from the fruit basket: Put one apple on the counter. Put another apple next to it, and you have 2 apples. Put yet another apple next to it, and you have 3 apples. But mathematics doesn't know anything about apples. It only knows about integers, and rules for incrementing their number (and doing many other fascinating things with them).
What you just did is a scientific experiment. You counted apples, you built a model of how the number of apples increments when pulling them from the fruit basket, and that model happens to follow Peano's axioms and the properties of common integers. That shows that there is a connection between mathematics and the world.
And now comes the place where magic happens, where philosophers of science are dumbfounded: Find an orange in the fruit basket, put it on the counter. You have 1 orange. Put another orange next to it, and you have 2 oranges. The miracle is: Why does the same mathematical theorem apply to oranges that we have already experimentally proven (many times, since we learned to count when the kindergarten teacher brought apples) on apples? There is nothing in mathematics that says that counting oranges should follow the same law. I could make a mathematically consistent model that says: If you put another orange next to 1 orange, you now have 42 oranges, and if you remove one orange again, you go from 42 to e^(i*pi). Nothing in mathematics says that oranges have to follow the rules of normal integers. The miracle is that Peano's axioms apply to ALL fruit (and to squirrels and bricks and all objects we interact with in everyday life).
Yet, there are objects in the universe for which normal counting rules don't apply. An example are electrons: take one electron, put it on the counter. Take another electron in the same state (same energy level, same spin), and just try putting it next to it. It just won't work, you will never get to two electrons. Pauli's exclusion principle says so, and detailed studies of atomic spectra have proven that. In electrons, 1+1 is not 2, it can't be done. Another fun weirdness of electrons happens with normal geometry: Take one electron, put it in a an electron basket on your kitchen counter (a thing that is just like a fruit basket is for apples, it is possible to build magnetic "traps" that hold individual particles, but for electrons it is extremely difficult). Now take the fruit basket, and spin it around on the counter by exactly 360 degrees. You would think that after that rotation by exactly a full circle, the electron is exactly like it was before. You can try this experiment on apples and oranges (and on pions and Higgs bosons), and they work just like apples, and after a 360 degree rotation they're back in their original state. Well, I'm sorry to tell you that on an electron it WON'T work: after spinning it by 360 degrees, it internal rotation is backwards. To get it back to its original state, you have to spin it by a multiple of 720 degrees (two full rotations), not a single one.
Experimental physics does not help here: it is built from the perception.
This is yet another very deep and philosophical question. The wife (now ex-wife) of a physicist friend was a famous cultural anthropologist, and she often asked this question: Are the laws of physics (models of reality) that we have found through experimentation and theory dependent on our cultural background. As an example, European white men found F=ma=m d2x/dt2, and F=mg, Newton's laws of motion and of gravity. Would a different culture have found different laws? The example typically discussed (following Margaret Mead) is: Would Samoans have come to different results when studying coconuts falling from palms that Newton did when studying apples falling from trees?
I think the answer is the following. Yes, we can express the same laws of physics many different ways. For example, Newton did all that with differential calculus (which he helped invent in the process). But we don't have to say that a = d2x/dt2, we can instead use integrals, and say that the acceleration is fundamental, and x = Int Int a dt2 (where Int is the big S-like integration symbol). Similarly, when it comes to more complex problems in mechanical motion, every physics graduate student learns to prove that Lagrange's method of solving them (with a Lagrange function, posing it as a minimization problem) is equivalent to the Hamiltonian method of solving them (with an operator). In quantum mechanics, it was quickly discovered that Schroedinger's wave functions and Heisenberg's matrices give the same "results" (real-world predictions), they are just more or less convenient to use for different set of problems. A similar theoretical revolution happened when Feynman's diagram made it much easier to calculate particle physics cross sections, and it was quickly found that they are actually equivalent to the old Lagrangian approach or S-matrix approach.
So here is the answer: Yes, Samoans would find the same physical laws, but they might express then very differently. Not just in a different language, but in a completely different formalism. After all, Galileo proved that coconuts and apples fall the same way (remember his famous experiment using the tower of Pisa, except that he demonstrated that a pound of feathers and a pound of lead fall down at the same acceleration ... oh wait, that's an old joke). But we all believe that concrete predictions of "true" physical models are independent of perception, and independent of culture and of how they are presented. And in that sentence, the word "true" means that the models match reality well. For example, if a hypothetical culture (let's call them Elbonians) came up with a model of gravity that says that both apples and coconuts fall downwards, while wine glasses fly up in the air if dropped, the Elbonian theory of gravity would be very quickly proven "false", not "true".
So my answer is: No, it's not just perception. There is really a number 3 out there. Whether we call that spatial dimensions, or degrees of freedom, or anything else, it is as real as our experiments have shown it to be.
By the way: Using thermodynamics to prove anything about the universe tends to drive people insane. Here's the introduction to the best textbook on that topic, by Kerson Huang: "Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously."
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).
. Gunm/Gally, aka alita battle angel, was the same, several iterations; the original gunm manga was very good, it's all online if you search for it.
