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Math: Did we discover or create it?


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So, what do you think?  

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  1. 1. So, what do you think?

    • We discovered math.
    • We created math.
    • We discovered and then improved math.


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I think that math is science that was created by humans to make it easy for them to study nature more in depth. Thus, math is just an universale "language" that we use to formulate nature's laws that was discovered by others sciences like physics.
Or perhaps it can be seen as the fabrication of a tautology based on logic which allows us to extend our deductive logic to situations which are too complex to be held in our conscious mind as a closed entity. Note Feynman's position, "mathematics is the distilled essence of logic!" :naughty:

 

I suspect mathematics could probably be defined to be the design and study of internally self consistent systems. That would make the "systems" invented; however, if one conceives of mathematics as the entire set of all possible self consistent systems, then it would clearly be something to be discovered. There is something to be said for exactness in one's assertions. :doh:

 

On the other hand, if you disagree with my position, I challenge you to create a logically self consistent system which can not either be mapped into a known mathematical representation or be accepted as a "new" mathematics system by mathematicians. :confused:

 

Have fun -- Dick

 

Knowledge is Power

and the most common abuse of that power is to use it to hide stupidity

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I suspect mathematics could probably be defined to be the design and study of internally self consistent systems.

I agree with you and we can also add, it's also a set of logical rules

That would make the "systems" invented;

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.

however, if one conceives of mathematics as the entire set of all possible self consistent systems, then it would clearly be something to be discovered.

Mathematics can never make discovery, only deductions from it's basics laws (logic). Saying that mathematics can make discovery (or that it's discovered) is like saying that mathematics discovered the number "2" just because we can write in mathematical words : 1+1 = 2.

Can we say that mathematics discovered all numbers just because we can write [For every number "n" , there is a number "m" = "n+1"] ????? I don't think so...in fact, this is something that I have discovered long ago and that I simply used mathematics to put it down on a paper.

 

Sometime, a mathematicien can write down a very long and beautiful formula (based on simples mathematical and logical rules) but it'll be called a "theory" or "philosophy" until it'll be discovered by experimental science: I can say that, depending on my feeling (my own logic), an extraterrestrial life exist somewhere in the universe, we can call it "theory" or"philosophy" or SF. Suppose now that humans (in 1000 years from now) discovered that an extraterrestrial life exist in other planets... can we say that's it's me who discovered the extraterrestrial life? i don't think so even if I like the idea...

I think that mathematics was created and can only make theorys (which is mainly a very complicated and not simple or obvious deduction) which have to be discovered by other sciences.

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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.

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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.

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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.

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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...

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

 

From Buckminster Fuller's Synergetics:

http://www.rwgrayprojects.com/synergetics/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....

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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. :umno:

 

(Apart from the odd cryptographer of course!) :shrug:

 

Virtualmeet, I obviously did not mean to say that it was Giuseppe Peano (1858-1932) that first invented the natural numbers!!!!!! :hihi: 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.

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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. :hihi:

 

(Apart from the odd cryptographer of course!) :umno:

___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. :shrug: Nothing like a good crank to set the gears in motion. :eek: Nice to hear from you again Q. Epicycle anyone? :hihi:

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Virtualmeet, I obviously did not mean to say that it was Giuseppe Peano (1858-1932) that first invented the natural numbers!!!!!! :QuestionM 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 :eek2:

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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).

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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 :QuestionM 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'.

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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.

 

:QuestionM I take exception to that. I am a mathematician, and I am totally concerned with reality. "4 + 3 = 8" is a perfectly correct, spotless mathematical expression. It is also contra-reality ((WRONG)) and therefore worthless.

 

I disagree that mathematics is a "language". We only say things like that, and confuse ourselves in the process, because we have no abstract meta-word ((class)) to include 'mathematics' and 'German' as members. We try to cram 'mathematics' into the class of 'languages' and do ourselves a great disservice. When we speak of math as a 'language' on a par with German, we muddy the conversational waters. And we wind up making deductions about as worthless as "4 + 3 = 8".

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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 :evil: 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'.

Woa, interesting answer. Well, it seems true, there has been many mathematical languages (mayan, egiptian, etc.) and all of them were not good until the discovery of the zero, negatives, etc...

 

This can get tricky since math can also have another base other than a decimal one...

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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).

That's the thing. Does really language have flaws?

 

I have seen some pages trying to prove math is wrong...

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That's the thing. Does really language have flaws?

 

I have seen some pages trying to prove math is wrong...

Oh yes...for example, if you write an SF novell, wich is mainly a lot of unverifiable facts and non logical statements, then your is book is a big flaw. BUT, it can be accepted and even rewarded by humains because the language you used is not supposed to be 100% true, so no one will ask you to prouf every single word in your book. Writing someting with the mathematical language is an another story because you have to respect a lot of rules. You can put your imagination and creativity away and just act like a "machine". Math in fact can never make something wrong because it doesn't create or invente new things...other languages did and this is why they are more accepted by humains :evil: .

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