Mathematical Numbers are Theoretical; Not Proven

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Originally Posted by Inside This Fantasy

I can say "asjdh jkahsldkah jvhkjlhl" and tell you it makes sense in another language, but it doesn't mean it does. Just like you can spout gibberish in language, you can spout gibberish in math. Just like a dog is a dog no matter what the name, adding the idea of one to the idea of one will create the idea of two. Changing the symbols used to represent that just changes how it looks on paper.

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He's actually saying that he can construct a language such that "asjdh jkahsldkah jvhkjlhl" has a meaning. That doesn't mean just substituting symbols so they represent different letters/sounds , but creating an entire system (grammar, syntax, etc)

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Originally Posted by Inside This Fantasy

Changing the symbols used to represent that just changes how it looks on paper.

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That's the point, you don't just change the symbols, you can also change the relationships between them. You can do that and still get a consistent system.

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Originally Posted by SnakeCharmer

He's actually saying that he can construct a language such that "asjdh jkahsldkah jvhkjlhl" has a meaning. That doesn't mean just substituting symbols so they represent different letters/sounds , but creating an entire system (grammar, syntax, etc)


That's the point, you don't just change the symbols, you can also change the relationships between them. You can do that and still get a consistent system.

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If he does create an entire system from those words, then he has succesfully made a new language to describe the world of math. He hasn't changed the world of math. You can change the symbols and the relations to get a consistent system, but it just makes a new language to describe the same world. I was just trying to say you don't change the world itself when you use a different set of symbols to describe it.

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Originally Posted by Xei

You can change the symbols to mean anything you want, and the rules of manipulating the symbols. Each time you would get a new, different system, only true in itself. You say one system of maths is real; then what about other, contradictory systems?

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This many ** plus this many *** is this many *****. There is no way around that. (for example)

Indeed, from the axioms of addition, which are really just based upon common experience.

There are other modes of addition, for example addition modulo 4, in which that wouldn't necessarily be true.

And it all becomes a lot less clear when you ask still very simple questions like,

Does x^n + y^n ever = z^n, for n>2?

Obviously the answer is either yes or no, but whether or not you can prove it with mathematics is a different matter (in this case you actually can determine the answer is no, but there are other problems which you can't).

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The world of math is exactly the same. There is only one world of mathematics, and it exists without language. You can use different languages to describe it (decimal, hex, binary, etc...) but they only make sense if they are coherent throughout the whole world of mathematics. You say you can throw random symbols together and they would make a coherent system...it doesn't work like that. I can say "asjdh jkahsldkah jvhkjlhl" and tell you it makes sense in another language, but it doesn't mean it does. Just like you can spout gibberish in language, you can spout gibberish in math. Just like a dog is a dog no matter what the name, adding the idea of one to the idea of one will create the idea of two. Changing the symbols used to represent that just changes how it looks on paper.

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I'm afraid this isn't true.

Mathematics is essentially the 'language'. To speak of langauge describing the world of mathematics is not true; mathematics is the language which describes various aspects of our reality. Whatever rules you come up with for what you are allowed to do in mathematics, there will always be some statements which are true, but unprovable. Mathematics is not only a language; it is also a limited language.

I didn't say anything about new systems of maths being 'random'. There are still precisely defined rules; it's just that the rules are different.

For example, one consistent mathematical system is that of Euclidean geometry, which has six (I think) axioms, and then builds upon them. This system, as with all mathematical systems, will be limited. There will be some isolated geometric facts which are true but you can't prove with Euclid's rules. Another consistent system is hyperbolic geometry, which uses different, and mutually exclusive axioms, and will establish new facts within that system which are completely wrong in the other.

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Originally Posted by Xei

For example, one consistent mathematical system is that of Euclidean geometry, which has six (I think) axioms, and then builds upon them. This system, as with all mathematical systems, will be limited. There will be some isolated geometric facts which are true but you can't prove with Euclid's rules. Another consistent system is hyperbolic geometry, which uses different, and mutually exclusive axioms, and will establish new facts within that system which are completely wrong in the other.

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Don't these systems of geometry fit what I said? Different languages describing the same world?

But the systems describe mutually contradictory facts..?

How can any world exist if it negates its own existence? It simply makes no sense.

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Originally Posted by Xei

But the systems describe mutually contradictory facts..?

How can any world exist if it negates its own existence? It simply makes no sense.

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The languages are imperfect ways of describing reality. If they are in fact describing the same aspect of reality and make contradictory claims, wouldn't that be a fault of the language? Even if the systems work within themselves, one would have to be wrong when it comes to reality, because the universe doesn't change depending on whether or not you are using euclidean or hyperbolic geometry. They are just different ways of describing what is.

I don't think you're being very consistent. You were saying that there is a mathematical reality. Now you're saying that physical reality is real and mathematics just describes various models which may apply to it, which is what I was saying...

Mathematics is a just series of logical systems in which you start with a small number of facts and rules which you can apply to them, and build up from there. Whether or not they have any bearing upon reality depends on how closely your facts and rules model those of reality. Some will appear quite similar, others will have no relevance at all, but all will only be true in themselves, not describing some single coherent otherworld, and all of them will be limited in the fact that they will be unable to determine various truths in that system.

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Originally Posted by Artelis

lol, this bullshit in the middle of actual discussion. I agree with Universal. The way we communicate math is made by mankind, but the truths represented are universal constants.

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What else am I supposed to type? This whole forum is Bullshit.

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Originally Posted by Xei

Indeed, from the axioms of addition, which are really just based upon common experience.

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They are factual whether they are experienced or not. This many *** ** and this many ***** are the same. A thing is the thing that it is. That is pure logic. It might even be the most fundamental principle of existence.

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Originally Posted by grasshoppa

What else am I supposed to type? This whole forum is Bullshit.

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Oh ho ho, don't like it? Get the fuck off and quit trolling to screw it up for everyone that does like this forum. What are you supposed to type? Something pertaining to the the topic at hand. That's how forums work.

I agree with ninja: * added to * gives you **.

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Originally Posted by [SomeGuy]

Oh ho ho, don't like it? Get the fuck off and quit trolling to screw it up for everyone that does like this forum. What are you supposed to type? Something pertaining to the the topic at hand. That's how forums work.

I agree with ninja: * added to * gives you **.

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Cool. But... you didn't really just call me Ninja, did you? Not Ninja! :makeitstop:

Oh crap...wrong guy! I thought it was him whilst I was writing it. I needed to add some maths to it so I wasn't being a troll...while I was yelling at someone for trolling.

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They are factual whether they are experienced or not. This many *** ** and this many ***** are the same. A thing is the thing that it is. That is pure logic. It might even be the most fundamental principle of existence.

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It is indeed a fact based on reality, but it needn't be true or even have meaning in a mathematical system.

Reality is real; mathematics as an entity is not. There is no such thing as a 'mathematical number' as opposed to a 'real number', there are just numbers. Numbers of real, physical objects or properties of objects.

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Originally Posted by [SomeGuy]

Oh crap...wrong guy! I thought it was him whilst I was writing it. I needed to add some maths to it so I wasn't being a troll...while I was yelling at someone for trolling.

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:lol: I was totally joking. I was mainly screwing with Ninja, not you.

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Originally Posted by Xei

It is indeed a fact based on reality, but it needn't be true or even have meaning in a mathematical system.

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Mathematical systems are all about reality, except for imaginary numbers and such, which take imaginary concepts and apply reality's rules to them.

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Originally Posted by Xei

Reality is real; mathematics as an entity is not. There is no such thing as a 'mathematical number' as opposed to a 'real number', there are just numbers. Numbers of real, physical objects or properties of objects.

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I am a little confused on what you are saying at the beginning with that. Numbers are reality, and mathematics is about the nature of numbers.

Physical objects are not the only things that exist and that numbers apply to. They also apply to thoughts, metaphysical realities, and hypothetical situations.

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Mathematical systems are all about reality, except for imaginary numbers and such, which take imaginary concepts and apply reality's rules to them.

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Imaginary numbers are rotations of 90 degrees. Rotations of 90 degrees are real. :l

What imaginary concepts are you referring to? I'd say that multiplication of a negative by a negative has no striking physical counterpart.

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I am a little confused on what you are saying at the beginning with that. Numbers are reality, and mathematics is about the nature of numbers.

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Not really, numbers are idealised concepts. You will never be 100% accurate or certain about any physical number.

Mathematics can be any language with any set of particular rules. What I'm saying is that there is no 'world of mathematics', because different systems of mathematics contradict each other. It isn't really any different from any other language, for example, English; there is no 'world of English' in some other mystical plane. English is just a human invention, and resides only within human minds.

Both attempt to describe a 'world of truths' - that is to say, reality - but both are flawed and limited.

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Originally Posted by [SomeGuy]

Oh ho ho, don't like it? Get the fuck off and quit trolling to screw it up for everyone that does like this forum. What are you supposed to type? Something pertaining to the the topic at hand. That's how forums work.

I agree with ninja: * added to * gives you **.

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Ya, I'm the troll...Your the one saying you did my mom. And my initial post was completely serious.

The thread was kinda dead when I said that. I wasn,t complaining about how terrible the forums are in the middle of a math discussion. It was quiet until after that.

Anyway, the concept of numbers was created to describe physical things. Math and physical objects are undeniably tied into each other.

no they are not tied to each other, we create the link in our minds. Numbers are a system and product of rational thinking. It helps us systematically categorize objects

They are related to each other because of the fact thatwe created a system of numbers to describe physical objects. That seems like an undeniable link. While the link resides in our minds, there is a link.

Don't forget that we drew the lines on the map

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Originally Posted by grasshoppa

Don't forget that we drew the lines on the map

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doesn't mean the world doesn't exist.

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Originally Posted by Artelis

doesn't mean the world doesn't exist.

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I was referring to the boundaries we put up for ourselves mentally, socially, physically etc..

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Originally Posted by Xei

Imaginary numbers are rotations of 90 degrees. Rotations of 90 degrees are real. :l

What imaginary concepts are you referring to? I'd say that multiplication of a negative by a negative has no striking physical counterpart.

Not really, numbers are idealised concepts. You will never be 100% accurate or certain about any physical number.

Mathematics can be any language with any set of particular rules. What I'm saying is that there is no 'world of mathematics', because different systems of mathematics contradict each other. It isn't really any different from any other language, for example, English; there is no 'world of English' in some other mystical plane. English is just a human invention, and resides only within human minds.

Both attempt to describe a 'world of truths' - that is to say, reality - but both are flawed and limited.

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Then why bother making pi = 3.14...? Why not just make it 3, or 1... or 0? Wouldn't that make a ton of computations much easier? Why not change the quadratic formula to a + b + c = 3? Why not make the slope formula m = x1 + x2 + y1 + y2? Why not make the distance formula d = 1?

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Originally Posted by Universal Mind

Then why bother making pi = 3.14...? Why not just make it 3, or 1... or 0? Wouldn't that make a ton of computations much easier? Why not change the quadratic formula to a + b + c = 3? Why not make the slope formula m = x1 + x2 + y1 + y2? Why not make the distance formula d = 1?

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Because they attempt to to describe a 'world of truths.' These formulas don't even attempt to make sense.

But I'm actually on your side. Just pointing out holes in your argument.