Mathematics: Invention or Discovery
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loosehead99 wrote...
Some what similar (maybe) to Schrodinger's cat. Quantum mechanicsWill research and get back to you, lol.
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Invention, since the system was entirely product of man's mental labor.
had the people involved in developing this system. not existed would it still exist? No. perhaps somethng diffrent. an example would be standard and metric systems, they have the same functions. after all
to invent something, man must have some hand in the creation
at least this is how i see it
in short, Necessity is the Mother of invention. If there was no need mathematics i would'nt be. Its product/creation of humans.
had the people involved in developing this system. not existed would it still exist? No. perhaps somethng diffrent. an example would be standard and metric systems, they have the same functions. after all
to invent something, man must have some hand in the creation
at least this is how i see it
in short, Necessity is the Mother of invention. If there was no need mathematics i would'nt be. Its product/creation of humans.
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mibuchiha
Fakku Elder
film_orange wrote...
This reminds me of Plato's discussion of Heraclitean flux. To me, math is an invention, down to something that seems basic and obvious as arithmetic. Take two pieces of chalk that are nearly identical except one has a slight nub. Place one on a table and we would constitute it as "one." If both pieces of chalk are on the table, there are "two." One piece of chalk is slightly less than the other, we still constitute each item as one. Math doesn't have a form for measurement. It doesn't tell you that in order to truly measure the oneness of objects, you must grind them down - in this case, for chalk. If you grind both down into fine, fine powder, can you then measure, piece for piece, the oneness of one or the oneness of another? Math doesn't make these distinctions.that has almost nothing to do with maths though. that's measurement and how you define it. maths are about the laws, not the method.
@fenex: physics are also product of mental labors, based on math to top things off. invention huh?
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mibuchiha wrote...
@fenex: physics are also product of mental labors, based on math to top things off. invention huh?Yes. Physics as a discipline (i.e. a systematic superset of tools of description) is an invention, the phenomena described by way of axioms are the discoveries.
The discipline of mathematics likewise is a system of abstraction (man-made) that provides (like physics) tools (invented) to describe observed phenomena (discovered).
Mathematics is an invention.
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Harmonian wrote...
My father introduced me to this "heated" debate recently, my father being the head of the math department at his college was very passionate about the subject, and I'm curious as to what the Fakku! community has to say about it.You'll have to forgive me if my opinion seems rather undeveloped as I'm somewhat in a rush.
I personally feel man invented math to suit our needs.
how about both? man kinda invent math to do everyday job but in the same time it's a discovery to all human kind. yes it is true that human invent math but before they even invent they discover 1st am i right. so with this i can conclude that invent and discover in mathematic are actually the same they need each other.
how about that?
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A Discovery.... yet cannot be denied to be an invented ideology which lead to the discovery, in other word a paradox
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The way we use math was invented. The actuallity itself however, had to be discovered. After all, 1+1 existed before humans did... But stating the 1+1 did not.
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I think that math was discovered because of the fact that stick(s). What makes stick(s) have mathmatic value? Its the number of sticks like 5 sticks.
Then we go on to rows of sticks placed like a rectangle like 5 sticks across and 4 down. They counted the sticks and its 20 sticks. They discovered that if they multiplied 4 and 5 that they got 20 as well.
If anyone understood what I just said then I explained very well.
Then we go on to rows of sticks placed like a rectangle like 5 sticks across and 4 down. They counted the sticks and its 20 sticks. They discovered that if they multiplied 4 and 5 that they got 20 as well.
If anyone understood what I just said then I explained very well.
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sounds more like invention. I mean to discovery something means to find something which is already there. While invention means to make something to fit means... since math is a system that would mean it is man made right? Like human language. like symbols and such. the things are there we need something to count it.
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seagull123 wrote...
Math is the language of the universe and physics is the law that governs the universe.Binary code, hexadecimals and more.
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loosehead99 wrote...
seagull123 wrote...
Math is the language of the universe and physics is the law that governs the universe.Binary code, hexadecimals and more.
isnt it more like the way we understand the universe?
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Man did not discover numbers. Man invented them.
1+1=2 is not a given. We did not discover such an equation that has been the "basic equation" for mathematics. It took Bertrand Russell hundreds upon hundreds of pages to prove that the above equation was true.
If mathematics was a discovery that would imply that that which it is built upon was also discovered, yes?
1+1=2 is not a given. We did not discover such an equation that has been the "basic equation" for mathematics. It took Bertrand Russell hundreds upon hundreds of pages to prove that the above equation was true.
If mathematics was a discovery that would imply that that which it is built upon was also discovered, yes?
Spoiler:
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Which is the point im trying to make!
If man did not need to count things and did not evolve to the point to need them math would not have been made. I mean numbers is just a symbol with meaning our minds makes the connection.
If man did not need to count things and did not evolve to the point to need them math would not have been made. I mean numbers is just a symbol with meaning our minds makes the connection.
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I vote for discovery.
This I can understand. But how does it mean that man invented mathematics? The numbers are merely values, mathematics does not need them to function. The world has followed these rules long before man existed, so how could have man invented them?
Harmonian wrote...
Man did not discover numbers. Man invented them.This I can understand. But how does it mean that man invented mathematics? The numbers are merely values, mathematics does not need them to function. The world has followed these rules long before man existed, so how could have man invented them?
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As someone who majored in math in college, these are my feelings on the matter:
First off, it's kind of a misconception to say that math is about numbers. Number theory is about numbers and their properties, but math in general is about structures, patterns, and their properties. If you take upper level abstract math courses(generally past calculus), much of what you do has very little to do with numbers and computation. Instead, you focus on structures such as sets and groups and their properties and relationships. At a basic level, numbers are merely a way to describe certain types of relationships between structures.
I would say that just as language was something man invented to describe himself and the world he lives in, math was invented by humans to help them answer questions about the world. However, math doesn't necessarily have to have a basis in reality as something than can be "discovered" by looking at the natural world. Just as one can write nonsensical statements in a language that do not reflect reality, one can create mathematical systems in which things that would seem absurd based on real world happenings are mathematically true.
The reason that most of math does relate to problems found in reality is because those are generally the problems that are of most use to humans. For example, building bridges that don't collapse is useful and important and requires creating mathematical models that do have a basis in reality.
To me, claiming that math is discovered because it is often used to model reality is akin to claiming language is discovered because it describes reality. One might discover a rock, but one invents the term "rock" to describe that discovery. Similarly, one might discover a rate of change occurrence in reality, but one invents a mathematical model to describe it. Discovery does occur in math in the sense of discovering new theorems that hold true in already existing systems, but at a basic level, those systems had to be invented and defined by humans before discovering things about them was possible.
First off, it's kind of a misconception to say that math is about numbers. Number theory is about numbers and their properties, but math in general is about structures, patterns, and their properties. If you take upper level abstract math courses(generally past calculus), much of what you do has very little to do with numbers and computation. Instead, you focus on structures such as sets and groups and their properties and relationships. At a basic level, numbers are merely a way to describe certain types of relationships between structures.
I would say that just as language was something man invented to describe himself and the world he lives in, math was invented by humans to help them answer questions about the world. However, math doesn't necessarily have to have a basis in reality as something than can be "discovered" by looking at the natural world. Just as one can write nonsensical statements in a language that do not reflect reality, one can create mathematical systems in which things that would seem absurd based on real world happenings are mathematically true.
The reason that most of math does relate to problems found in reality is because those are generally the problems that are of most use to humans. For example, building bridges that don't collapse is useful and important and requires creating mathematical models that do have a basis in reality.
To me, claiming that math is discovered because it is often used to model reality is akin to claiming language is discovered because it describes reality. One might discover a rock, but one invents the term "rock" to describe that discovery. Similarly, one might discover a rate of change occurrence in reality, but one invents a mathematical model to describe it. Discovery does occur in math in the sense of discovering new theorems that hold true in already existing systems, but at a basic level, those systems had to be invented and defined by humans before discovering things about them was possible.
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WhiteLion wrote...
As someone who majored in math in college, these are my feelings on the matter:First off, it's kind of a misconception to say that math is about numbers. Number theory is about numbers and their properties, but math in general is about structures, patterns, and their properties. If you take upper level abstract math courses(generally past calculus), much of what you do has very little to do with numbers and computation. Instead, you focus on structures such as sets and groups and their properties and relationships. At a basic level, numbers are merely a way to describe certain types of relationships between structures.
I would say that just as language was something man invented to describe himself and the world he lives in, math was invented by humans to help them answer questions about the world. However, math doesn't necessarily have to have a basis in reality as something than can be "discovered" by looking at the natural world. Just as one can write nonsensical statements in a language that do not reflect reality, one can create mathematical systems in which things that would seem absurd based on real world happenings are mathematically true.
The reason that most of math does relate to problems found in reality is because those are generally the problems that are of most use to humans. For example, building bridges that don't collapse is useful and important and requires creating mathematical models that do have a basis in reality.
To me, claiming that math is discovered because it is often used to model reality is akin to claiming language is discovered because it describes reality. One might discover a rock, but one invents the term "rock" to describe that discovery. Similarly, one might discover a rate of change occurrence in reality, but one invents a mathematical model to describe it. Discovery does occur in math in the sense of discovering new theorems that hold true in already existing systems, but at a basic level, those systems had to be invented and defined by humans before discovering things about them was possible.
i agree