Why is the universe describable with math?

nimzov said:
Euler did not create but discovered this relation between natural numbers and pi. What he actually created was the demonstration or the proof.

If he had died before he made this discovery, most likely someone else would have made the discovery later in history and maybe produced a different demonstration.

Euler dis not create this property of natural numbers, in the sense that the value pi^2/6 cannot be anything else.

Discovery vs creation or invention of mathematical objects are at the heart of the question of the OP. I believe mathematical objects are not created by man but what is the creation of the mathematicians is the demonstrations and proof of the properties of these objects.

nimzo
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We may not have created that relationship, but we did create the idea of natural numbers, pi, irrational numbers, equals, plus, summation, ect, and the idea that the relationship proven by Euler is significant. You can demonstrate that a bicycle can be used to deliver pizzas, that doesn't make bicycles or pizzas fundemental properties of the universe that exist without man.
 
T'ai Chi said:
The title kind of says it all. Why do you think the universe is describable with math?

(and please, let's not evoke fantasy multiple universes where math doesn't exist; let's talk about what there is evidence for)
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Why are colors and sounds describable with words?
 
nimzov said:
Don't we use math (and physics) to determine the self-consistency (or non-contradictory) of the universe.
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No. For example, if I leave an apple in my refrigerator and return tomorrow, unless someone else has taken it, it will still be there; not to mention the fact that the refrigerator will still be a refrigerator, not a television or an automobile. For that matter, when I walk around the corner, I don't, for example, turn into a penguin or a guitar.

Because of this self-consistency of the universe, over time, over space, and over rotation, we can define laws of physics, which we describe with mathematics, that describe the way the universe works. If it wasn't internally consistent in this manner, such a description would not be possible.
 
My suspicion is that the question is back to front. We design mathematics to fit the way reality is. There are many alternative mathematics imaginable which would describe something other than the observed reality. We reject them as "wrong" , for that reason, even if they are logically consistent.
(I also suspect mathematicians are plotting to take over the Universe by making it seem so complex that we will think only they understand it. This worked for lawyers ).
 
CaptainManacles said:
We may not have created that relationship, but we did create the idea of natural numbers, pi, irrational numbers, equals, plus, summation, ect, and the idea that the relationship proven by Euler is significant. You can demonstrate that a bicycle can be used to deliver pizzas, that doesn't make bicycles or pizzas fundemental properties of the universe that exist without man.
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If I have one stone and I put another stone with it, I have two stones. If I measure the circumference of a circle and divide see how many times bigger it is than the diameter, I have pi. We didn't create these numbers, they were there all along, unless you somehow believe that two stones lying on the ground by theselves weren't really two stones until someone counted them. We use mathematical language to describe these things, and discover new relationships, but this does not mean we are creating these concepts, we are merely describing them in a language that we can understand.

Comparing numbers with pizza is not even comparing apples and oranges, it is comparing apples and the colour blue. Pizza is not fundamental to the universe (although some might disagree :p) because it is a physical object, which may or may not be required for the universe to function/exist. Numbers are used to describe physical objects, regardless of what those objects are. The number two can be used to describe anything in the universe because it is always possible to have one of something and add another of something - this is what two means. Pizza cannot be used to describe most of the universe because most things are not pizza. If I have one electron and another electron, I have two electrons - I do not have pizza.
 
Soapy Sam said:
Do you see this as a conclusion or an assumption? How do you explain it?
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There is no conclusion or assumption. Whether you call it two or not, if I have a number of stones and a number of pizzas, I can put them in pairs and if there are no pizzas or stones left over then I have the same number of pizzas and stones. This is how numbers work. Mathematics is not an assumption about the universe or a conclusion derived from observation, it is just a language that we use to describe the universe.

What do you have if you remove both stones?
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A sad feeling of empty loneliness.
 
I remember standing outside of my guitar teacher's studio, listening to him instruct a fellow student. He was teaching fretboard theory - if you finger a string at a specific fret, then if you go one string over, and one fret lower, the note sounded is a third higher, etc. She (the student) marvelled about the genius of the inventor of the guitar. How could anybody conceive such a complicated fretting system, and then invent some strings, tunings, and fret intervals to actually implement that complicated system. The man must have been a genius, she concluded!!!!! She positively gushed.

I came to a different conclusion - I concluded that she(the student) wasn't so bright.

I wonder if there is a parable in there somewhere?
 
A couple of peripheral notes, for what they're worth:
  1. Mathematics is the biggest and best-known example of a so-called axiomatic (formal) system, and
  2. Bertrand Russell and Alfred Whitehead in their Principia Mathematica (1910 - 1913) proved, among other things, on the basis of formal logic the proposition "1 + 1 = 2" where each of the symbols takes its usual meaning. Prior to the proof, the statement was an axiom of mathematics.
'Luthon64
 
Cuddles said:
There is no conclusion or assumption. Whether you call it two or not, if I have a number of stones and a number of pizzas, I can put them in pairs and if there are no pizzas or stones left over then I have the same number of pizzas and stones.
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What do you have if you put them in threes?
 
Soapy Sam said:
What do you have if you put them in threes?
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A mess. If you have pizzas and stones and want to compare them to see if you have the same number, what could possibly be the point in putting them in threes? That would mean either two stones and one pizza or two pizzas and one stone, or three of one of them. This would tell you absolutely nothing.

wollery said:
:D

You git Cuddles, I'm still coughing from the laughing fit that gave me!!
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My work here is done.:p
 
Math doesn't describe the universe. It simulates it.

Matter of an identical fundamental nature should be able to simulate other matter. That's basically math and semiotic's fundamental axiom.

But its simulation depends upon perception and its simulator's elegance.

To ask why math is doing such a good job predicting occurances in the universe is a more humble and accurate question.

I think it's because, when accurately applied, math gives interpretable data for us to attach to experience. Basic math at the heart is simpling a labelling of amounts of what we can interpret and reproduce, so long as we set strict guidlines in translation from numbers to what those numbers designate. More complicated math though, is less based on the physical or labelling, but on its logical conclusions, and those futher conclusions upon it. This math may or may not be 100% reliable in predicting, depending on the quality of logic, critical thinking, and the assumption that our logic is 100% foolproof. But I think things like Lorenz manifolds and m-theory have given us hope.
 
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I'm interested in why the Greeks discovered the conics and not until 2000 years later did Kepler discover their astronomical importance.
 
Anacoluthon64 said:
A couple of peripheral notes, for what they're worth:
  1. Mathematics is the biggest and best-known example of a so-called axiomatic (formal) system, and
  2. Bertrand Russell and Alfred Whitehead in their Principia Mathematica (1910 - 1913) proved, among other things, on the basis of formal logic the proposition "1 + 1 = 2" where each of the symbols takes its usual meaning. Prior to the proof, the statement was an axiom of mathematics.
'Luthon64
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Formal axiomatic systems aren't everything. See Turing and Godel.
 
No, all Godel said was that within a given formal axiomatic system that is powerful enough to describe number theory, there are statements whose truth value can't really be proven either way within the system. That doesn't mean that there is something beyond formal axiomatic systems.
 
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Well, hmmm, actually he said that either there are statements whose truth value can't be proven either way, or there are statements that are true that cannot be derived within the system. It's a matter of choice, you see, whether you declare it inconsistent or incomplete.
 
Cuddles said:
A mess. If you have pizzas and stones and want to compare them to see if you have the same number, what could possibly be the point in putting them in threes? That would mean either two stones and one pizza or two pizzas and one stone, or three of one of them. This would tell you absolutely nothing.



My work here is done.:p
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I thought Pizza was great if you were stoned.
 
Anacoluthon64 said:
How, please, did I imply that they were?
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And don't think I wasn't implying that you were implying they were. If it came across that way, sorry. I just think people need more reminders of those proofs. Math, logic, and the universe are all so much more interesting than we're taught in school.
Anacoluthon64 said:
Moreover, Turing and Gödel were exactly my unstated point.
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What was your unstated point? I'm interested now.
 
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