slave
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 Posted: Wed Mar 07, 2012 7:28 pm Post subject: Mathematics: created or discovered? |
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Are Mathematicians discovering mathematical structures, laws,etc... that, in some sense, already exist or are they creating same?
Fractal geometry, in nature, has existed for non- trivial time periods and Benoit Mandelbrot delineated the mathematics for us. Did he discover or did he create?
Pal Erdos believed that all of the correct mathematics already exist in a metaphorical "book of proofs" and that the role of the Mathematician is to uncover them for humanity.
What about pure abstract math(s) for which there is no application and no apparent relationship with reality?
What is your opinion on this philosophical question?
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Fnord
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| Posted: Wed Mar 07, 2012 7:58 pm Post subject: |
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The principles of natural mathematics, just like the principles of natural physics, are discovered.
Creativity is for art, fantasy, and religion. |
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abacacus
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| Posted: Wed Mar 07, 2012 8:51 pm Post subject: |
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| Fnord wrote: | The principles of natural mathematics, just like the principles of natural physics, are discovered.
Creativity is for art, fantasy, and religion. |
What he said.
Someone did not sit down and arbitrarily decide to invent the concept of zero, he discovered that adding a zero in to some equations can dramatically change the results (the obvious examples are division and multiplication, dividing by zero nets you an impossible number and multiplying by zero will ALWAYS give you a zero).
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Vigilans
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| Posted: Wed Mar 07, 2012 8:53 pm Post subject: |
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I created math
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shrox
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| Posted: Wed Mar 07, 2012 9:00 pm Post subject: |
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| Fnord wrote: | The principles of natural mathematics, just like the principles of natural physics, are discovered.
Creativity is for art, fantasy, and religion. |
Creativity moves science along when reason fails...or else we would only understand Newtonian physics. |
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slave
Always stuck between 13-38Hz and tired of it.
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| Posted: Wed Mar 07, 2012 9:52 pm Post subject: |
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| Vigilans wrote: | | I created math |
care to elaborate?
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Vigilans
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| Posted: Wed Mar 07, 2012 10:45 pm Post subject: |
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| slave wrote: | | Vigilans wrote: | | I created math |
care to elaborate? |
6.853
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Opportunities multiply as they are seized. -Sun Tzu
Nature creates few men brave, industry and training makes many -Machiavelli
You can safely assume that you've created God in your own image when it turns out that God hates all the same people you do |
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slave
Always stuck between 13-38Hz and tired of it.
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| Posted: Thu Mar 08, 2012 12:38 am Post subject: |
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Your response is not an elaboration IMO
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Burzum
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| Posted: Thu Mar 08, 2012 2:41 am Post subject: |
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| slave wrote: | | Your response is not an elaboration IMO |
It seems like a perfectly valid elaboration to me.  |
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Declension
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| Posted: Thu Mar 08, 2012 4:12 am Post subject: |
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It depends what you mean. While playing a game such as ZFC, a mathematician really is discovering which theorems can be proven in the game.
However, the game was created by mathematicians in the first place.
Here is an analogy: a chemist might create a new chemical, and then discover things about it through experimentation. The "chemicals" that a mathematician creates and studies are formal systems of first-order predicate logic. However, the people who make the chemicals and the people who study the chemicals aren't usually the same people. The former are set theorists and logicians, and the latter are specialists in various mathematical fields.
But I should add that the chemicals are not just randomly generated. They are created for a certain purpose, and if they are not fit for purpose, nobody studies them. This explains why mathematics is useful for science. It's because that's what we care about, so that's what we make the chemicals for. There are all sorts of other weird chemicals that we will never study, and they are simply seen as pathological. |
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heavenlyabyss
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| Posted: Thu Mar 08, 2012 5:42 am Post subject: |
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Mathematics is discovered in the same way that physical laws of nature are discovered.
However, mathematical notations and systems for describing mathematical concepts are created. We think of the number 0 as denoting "nothingness" - ie no pencils, no slices of pizza, no marbles in a jar. In a different society, 0 might mean infinity and infinity might mean 0.
I'm stating this obvious but you get my point. Mathematics is discovered. |
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Fnord
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| Posted: Thu Mar 08, 2012 10:58 am Post subject: |
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| heavenlyabyss wrote: | | Mathematics is discovered in the same way that physical laws of nature are discovered. However, mathematical notations and systems for describing mathematical concepts are created. We think of the number 0 as denoting "nothingness" - ie no pencils, no slices of pizza, no marbles in a jar. In a different society, 0 might mean infinity and infinity might mean 0. I'm stating this obvious but you get my point. Mathematics is discovered. |
Agreed.
The only times creativity is ever applied to maths are when someone uses "creative accounting" in an attempt to conceal embezzlement or tax fraud. |
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Oodain
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| Posted: Thu Mar 08, 2012 12:33 pm Post subject: |
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the field of mathematics was created to discover the relationships of nature.
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Ancalagon
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| Posted: Thu Mar 08, 2012 8:14 pm Post subject: |
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| Declension wrote: | | They are created for a certain purpose, and if they are not fit for purpose, nobody studies them. This explains why mathematics is useful for science. It's because that's what we care about, so that's what we make the chemicals for. |
This doesn't explain the many times that pure math which nobody thought could be applied in any practical way actually turned out to be very useful for a practical purpose which did not exist when that mathematical idea was discovered.
| Fnord wrote: | | The only times creativity is ever applied to maths are when someone uses "creative accounting" in an attempt to conceal embezzlement or tax fraud. |
It takes a lot of creativity to discover mathematical truths.
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Fnord
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| Posted: Thu Mar 08, 2012 8:37 pm Post subject: |
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| Ancalagon wrote: | | Fnord wrote: | | The only times creativity is ever applied to maths are when someone uses "creative accounting" in an attempt to conceal embezzlement or tax fraud. |
It takes a lot of creativity to discover mathematical truths. |
No, just diligent research supported by an already strong foundational understanding of valid mathematical principles.
Mathematics is not about what you feel, it's about what you know, and what you do with that knowledge. |
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