Invented or Discovered?
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We have discovered it. We have however invented ways of expressing mathematics. -- standing so tall, the ground behind no trespassers, on every floor a garden swing, and another door she makes it clear, that everything is hers A place of abode, not far from here, Ms. Van de Veer
Jörgen Sigvardsson wrote: We have discovered it. We have however invented ways of expressing mathematics. => knowledges are discovered, tools are invented :)
A rock pile ceases to be a rock pile the moment a single man contemplates it, bearing within him the image of a Cathedral[^]. Antoine de Saint-Exupery (1900-1944)
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Hey, here is a interesting question....someone asked me this...Was Math Invented or Discovered? What are ur opinions ? I think it was discovered because for example...2+2=4..nobody invented that...it just is Let the discussions begin!
I remember having a long discussion/argument with a friend of mine about this years ago. I was on the "Discovered" side which is the typical techie repsonse to the question but now I'm older and wiser (?!), I'm not so sure. Taking your example of 2+2=4, Nature has no concept of 2 or 4 or even addition. Things just work the way they do because that's how they work. Numbers and the operations we perform on them are simply constructs that we have devised to help us explain what we see happening around us. So in that respect, mathematics is "invented".
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Hey, here is a interesting question....someone asked me this...Was Math Invented or Discovered? What are ur opinions ? I think it was discovered because for example...2+2=4..nobody invented that...it just is Let the discussions begin!
Invented. Why? Because math is a process of manipulating symbols. It reveals and mirrors an underlying reality. The fact that reality conforms to a set of laws is discovered. The fact that math mirrors that reality is discovered. But, math itself is invented. Additionally, this is the same reason we say that (for example) the steam engine was invented. Sure, all the laws were in place before the steam engine was actually created. But, the steam engine did not exist in nature -- as if Columbus came over a hill one day and said, "look at that!" The same is true of math: the process of manipulating symbols did not exist in nature. ------------------------------------------ "Isn't it funny how people say they'll never grow up to be their parents, then one day they look in the mirror and they're moving aircraft carriers into the Gulf region?" - The Onion # rm /bin/laden /bin/laden: Not found
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Hey, here is a interesting question....someone asked me this...Was Math Invented or Discovered? What are ur opinions ? I think it was discovered because for example...2+2=4..nobody invented that...it just is Let the discussions begin!
Math is nothing more than a model that we mere humans invented in our ongoing attempt to comprehend the nature of our universe (something we still have very little understanding of). It is invented, abstract, and doesn't really exist. The phenomena it attempts to reveal does however.
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Define math. Todd Smith
#define math maths Regardz Colin J Davies
Sonork ID 100.9197:Colin
You are the intrepid one, always willing to leap into the fray! A serious character flaw, I might add, but entertaining. Said by Roger Wright about me.
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#define math maths Regardz Colin J Davies
Sonork ID 100.9197:Colin
You are the intrepid one, always willing to leap into the fray! A serious character flaw, I might add, but entertaining. Said by Roger Wright about me.
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Hey, here is a interesting question....someone asked me this...Was Math Invented or Discovered? What are ur opinions ? I think it was discovered because for example...2+2=4..nobody invented that...it just is Let the discussions begin!
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I remember having a long discussion/argument with a friend of mine about this years ago. I was on the "Discovered" side which is the typical techie repsonse to the question but now I'm older and wiser (?!), I'm not so sure. Taking your example of 2+2=4, Nature has no concept of 2 or 4 or even addition. Things just work the way they do because that's how they work. Numbers and the operations we perform on them are simply constructs that we have devised to help us explain what we see happening around us. So in that respect, mathematics is "invented".
Taka Muraoka wrote: Nature has no concept of 2 or 4 or even addition. That's because those are symbols for our interpretations. Four flowers in a pot are still four flowers in a pot whether we grasp natural numbers or not. You see, we cannot escape the natural numbers. And all the stuff that comes with it. We did not devise that the successor to the value zero is the value one, successor to value one is value two, and so on. All we did was to call the values, zero, one, two, ... . All that is built into nature [what is nature anyway?], we're just a bunch of name callers. ;) -- standing so tall, the ground behind no trespassers, on every floor a garden swing, and another door she makes it clear, that everything is hers A place of abode, not far from here, Ms. Van de Veer
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Invented. Why? Because math is a process of manipulating symbols. It reveals and mirrors an underlying reality. The fact that reality conforms to a set of laws is discovered. The fact that math mirrors that reality is discovered. But, math itself is invented. Additionally, this is the same reason we say that (for example) the steam engine was invented. Sure, all the laws were in place before the steam engine was actually created. But, the steam engine did not exist in nature -- as if Columbus came over a hill one day and said, "look at that!" The same is true of math: the process of manipulating symbols did not exist in nature. ------------------------------------------ "Isn't it funny how people say they'll never grow up to be their parents, then one day they look in the mirror and they're moving aircraft carriers into the Gulf region?" - The Onion # rm /bin/laden /bin/laden: Not found
One could argue that we discovered the natural numbers. Then we invented a way to express them with symbols. Everything from that point to here is derived. Is derivation invention or discovery? -- standing so tall, the ground behind no trespassers, on every floor a garden swing, and another door she makes it clear, that everything is hers A place of abode, not far from here, Ms. Van de Veer
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Math is nothing more than a model that we mere humans invented in our ongoing attempt to comprehend the nature of our universe (something we still have very little understanding of). It is invented, abstract, and doesn't really exist. The phenomena it attempts to reveal does however.
Nope, not IMO. By definition mathematics are absolute. Using numbers and operations is a model of this reality, but it's different. Wherever in the Universe 2 and 2 make 4, at the level of the concept, its written expression "2+2=4" is "locally" defined.
A rock pile ceases to be a rock pile the moment a single man contemplates it, bearing within him the image of a Cathedral[^]. Antoine de Saint-Exupery (1900-1944)
