Math: Did we discover or create it?

[Drip Curl Magic]

I guess it's a question as to whether or not nature is created with a base of mathematics. I think that natures possiblities are limitless beyond our simple mathematics system. But I guess you could say that our mathematics system also seems to be limitless as well. Obviously there is no end to counting. No highest number.

A lot of scientists have come up with formulas to explain our surroundings... but those formulas were based around the mathematics system that we already know. It's possible that if we were to make a new counting system, that we'd still be able to come up with just as many workable calculations.... but we'd have to re-work every formula that scientists have ever come up with.

It's a confusing topic... And I could come up with evidence supporting both sides of the arguement.... but it makes more sence to me to say that it's been created.

But then again, what do I know? I'm only human.

[Edge]

Other people say that maybe math is a language. Think about it, in some sort of way it can be true. On languages there are no errors, you define it. So with math. Languages do not need any proof to prove that there's no flaws (well, actually there can be flaws on language), and so with math.

[Qfwfq]

Originally Posted by virtualmeet

I don't agree with this for the simple reason that a "consistent systems" is a system that all it's rules have to fulfill our mathematical postulates and laws...so we can only say that thoses "systems" are "deduced" and not invented.

The only inescapable basic thing in mathematics is logic and the principle of non-contradiction. Without defining and constructing anything, you have nothing beyond logic. Peano's axioms are the standard way of defining the natural numbers, that isn't a "discovery" it's an invention! The same goes for integers, rationals and ordinary arithmetic, next come the real numbers(by topological completion of the rationals). The only reason it doesn't seem that way is because the natural numbers and arithmetic are so very fundamentally useful in describing basic facts of reality. They were constructed that way because they are very useful, that way.

Like any language, German, Hindi etc... it can be used to represent facts about reality. A mathematician is however not in the least concerned with reality. The sentence "Every cow is an excellent Tango dancer" is a perfectly correct, spotless English sentence, regardless of reality.

[virtualmeet]

Originally Posted by Qfwfq

Peano's axioms are the standard way of defining the natural numbers, that isn't a "discovery" it's an invention!

"invent" = "to design and/or create something which has never been made before" (from Cambridge Advanced Learner's Dictionary )

We can't say that Peano's axioms is an invention simply because it was in nature before Pean's born...Peano did just discovered them like any of us, between all seen and sensed nature's laws but took only those who are the most relevant (because of his mathematical great thinking), then put them down on a paper by using mathematical words (created by other mathematiciens). I think that mathematics is the most useless science for creating or inventing new things..Why? becasue if it did then we can be sure we have made a mistake somewhere in our reasoning.
All created things in mathematics are just "a new view" of it's basics laws...for example :
1+1 = 2 but we can also say that : 3*2 -6 +(9-7) =2. Suppose that human's QI was less than 1...if the first operation took hours to be solved...then the second can be called "Theory of 2" . I'm pretty sure that our most advanced mathematical theorys reflects only our limitations. We are using mathematics to only understand what we already have discovered in nature's laws. Perhaps we already have keys of all the understanding but we can't go much more than we are made for...

[Turtle]

Originally Posted by Qfwfq

...Like any language, German, Hindi etc... it can be used to represent facts about reality....

From Buckminster Fuller's Synergetics:
http://www.rwgrayprojects.com/synerg...s12/p0000.html

Tobias Dantzig, author of Number: The Language of Science,
Has traced the etymological history
Of the names for the numbers
In all the known languages of the Earth.
He finds the names for numbers all classifiable
As amongst the "oldest" known words....

[Qfwfq]

Obviously, Turtle, counting was amongst the first essential necessities for survival. A British ornithologist discovered that a wild bird he was trying to observe could count to around six, he had difficulty tricking the critter into thinking that he was no longer hiding in a disused hunting shack. Peolple find Z_30 less often useful than N, that's why it's only cranks like you and I, that play with such things.

(Apart from the odd cryptographer of course!)

Virtualmeet, I obviously did not mean to say that it was Giuseppe Peano (1858-1932) that first invented the natural numbers!!!!!! He simply formalized the age-old concept. You seem to have missed my point even more, about what is real and natural vs. some "language" or symbolism that we invent to the purpose of describing it. Not that I would strictly say there are any numbers in nature, there are only things, and quantities of them that we describe usng numbers.

[Turtle]

Originally Posted by Qfwfq

Obviously, Turtle, counting was amongst the first essential necessities for survival. A British ornithologist discovered that a wild bird he was trying to observe could count to around six, he had difficulty tricking the critter into thinking that he was no longer hiding in a disused hunting shack. Peolple find Z_30 less often useful than N, that's why it's only cranks like you and I, that play with such things.

(Apart from the odd cryptographer of course!)

___I heard a similar bird anecdote; no nationality mentioned, but it involved a crow counting to ten & not approaching a barn until all ten men left it. Nothing like a good crank to set the gears in motion. Nice to hear from you again Q. Epicycle anyone?

[virtualmeet]

Originally Posted by Qfwfq

Virtualmeet, I obviously did not mean to say that it was Giuseppe Peano (1858-1932) that first invented the natural numbers!!!!!! He simply formalized the age-old concept. You seem to have missed my point even more, about what is real and natural vs. some "language" or symbolism that we invent to the purpose of describing it. Not that I would strictly say there are any numbers in nature, there are only things, and quantities of them that we describe usng numbers.

Sorry about my misunderstanding. Sometimes, I can have more difficulties to read natural languages (specialy english) that I can do with the mathematical one

[virtualmeet]

Originally Posted by Edge

Other people say that maybe math is a language. Think about it, in some sort of way it can be true. On languages there are no errors, you define it. So with math. Languages do not need any proof to prove that there's no flaws (well, actually there can be flaws on language), and so with math.

I think you're right when you're saying that mathematics is just a language between others used by humains to describe their feelings... The main difference between The mathematical language and the others comes from the fact that in the first one, there are no flaws inherent in it's basics because they are not made by humans. Other languages can contain flaws (in fact all of them have some well known and very popular ones) as rules !!
Humans like to contradict themselfs, just for fun...we are indeed very complicated creatures (more than nature can ever build by itself).

[Pyrotex]

Originally Posted by Edge

We all know how important math is on the world, not arguing that. However, there are people that think that we discovered the laws of math, while others say that we created them (kinda like a language). There is also debate about if it's really a science or not? So, what do you think?

This question is easy to answer with a thought experiment.
Pretend that there is another inhabited planet in another galaxy, say that big one in the constellation Andromeda. The people on this planet get tired of making stone arrow points and turn their thoughts to more abstract subjects. Like 'lines' and 'triangles' and 'circles'. A million planetary rotations later, they have 'higher mathematics'.

Now, is it the SAME mathematics that WE have? Ignore the irrelevant details, like we use 'X' but they use '@', we use '=' and they use '}'. Is it the SAME math?

The answer has to be YES. Math will work the same for them. The relationships they discover will be the same relationships we have discovered. The applications of math to the physical world will be the same applications that we have used.

Therefore, mathematics is NOT an 'invented' concept. It is universal, and therefore 'discovered'.