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Mathematics: An Art Or A Science?


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#21
Dark Ainur

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I believe its both.
Maths whilst being the language of science also requires heavily creative skills. Most of the best proofs in maths require a creative mind and maths in itself is an art form.
The fact that it can be used as a tool in explaining the universe puts it as a very powerful discipline. Maths can easily be translated into emotion, for example Euler's identity
e^(i . pi) + 1 = 0 is oddly beautiful and reassuring (Kinda like a order from chaos). The problem with maths is you spend so much time having your hand held through questions you never really get to be creative with it.


#22
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Math is logic. Logic is irrelevant to art. Logic is everything to science.

If math = logic and science = logic. Math = science.

LAWL!



#23
DHC

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QUOTE (Extracheez @ Mar 9 2009, 10:55 AM) <{POST_SNAPBACK}>
Math is logic. Logic is irrelevant to art. Logic is everything to science.

If math = logic and science = logic. Math = science.

LAWL!


science isnt logic, though - it is a study of the world via the use of logical reasoning icon_wink.gif and to say that logic is irrelevant to art makes baby jesus cry!


to offer my opinion on the grand question at hand: Mathematics is neither created nor discovered, and thus does not fall into the categories of arts or sciences. to be extremely brief, i would almost consider Mathematics to be a philosophy - a way of looking at the world, through the use of logic, through a series of non-falsifiable claims. there is a certain intrinsic beauty to math that no true science can mimic, though despite this beauty, it is not an expression of the human experience, and thus cannot in my mind be called art.

#24
Rob`

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QUOTE (Extracheez @ Mar 9 2009, 02:55 PM) <{POST_SNAPBACK}>
If math = logic and science = logic. Math = science.


christianity = religion
islam = religion
christianity = islam
Perhaps if this signature is witty enough, someone will finally love me.


#25
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QUOTE (Rob` @ Mar 9 2009, 01:28 PM) <{POST_SNAPBACK}>
christianity = religion
islam = religion
christianity = islam

rofl
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#26
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QUOTE (DHC @ Mar 9 2009, 02:15 PM) <{POST_SNAPBACK}>
science isnt logic, though - it is a study of the world via the use of logical reasoning ;) and to say that logic is irrelevant to art makes baby jesus cry!


Math is the study of values and measurements via logic. If something in science is not logical it becomes not science(by this I mean that all theories are exhausted and there is no way of explaining something with science).

Logic is not needed in art. If something in art has no logic, it is still art.

QUOTE (Rob` @ Mar 9 2009, 02:28 PM) <{POST_SNAPBACK}>
christianity = religion
islam = religion
christianity = islam


Yah hence why I said "lawl" after that little display.



#27
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QUOTE (Extracheez @ Mar 10 2009, 05:28 AM) <{POST_SNAPBACK}>
Math is the study of values and measurements via logic. If something in science is not logical it becomes not science(by this I mean that all theories are exhausted and there is no way of explaining something with science).

Logic is not needed in art. If something in art has no logic, it is still art.

math is not math is not always logical. And art is more logical than you might imagine it to be.
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#28
Christron

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Art doesn't get a spaceship on the moon, you need cold hard numbers and equasions to expect it to work. Everything down to the shape is mathematical....

#29
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QUOTE (Christron @ Mar 10 2009, 01:11 PM) <{POST_SNAPBACK}>
Art doesn't get a spaceship on the moon, you need cold hard numbers and equasions to expect it to work. Everything down to the shape is mathematical....


Yeah but Math does not limit itself to flying spaceships to the mood.

And you could say that going to the moon could be an artistic performance.

P.S. going to the moon is probably the most useless thing humanity has ever done.
"Something tremendously powerful was lost when composers moved away from tonal harmony and regular pulses... Among other things the audience was lost" -John Adams

#30
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Since this is in the debate section i shall counteract your points

QUOTE (Verrückter @ Mar 11 2009, 01:19 PM) <{POST_SNAPBACK}>
Yeah but Math does not limit itself to flying spaceships to the mood.


I'm not sure i understand this one =(

QUOTE (Verrückter @ Mar 11 2009, 01:19 PM) <{POST_SNAPBACK}>
And you could say that going to the moon could be an artistic performance.


You definitely could, but you wouldn't be able to call it anything if math didn't make it happen in the first place

QUOTE (Verrückter @ Mar 11 2009, 01:19 PM) <{POST_SNAPBACK}>
P.S. going to the moon is probably the most useless thing humanity Russia America has ever done.

and isn't that the point? that we filmed did it.

sorry, i just learned how to use strikethrough and it's really exciting

ignore, that, i like cocks

#31
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Cocks huh ?

Honestly I have no counterpoints. You win the debate, sir.
"Something tremendously powerful was lost when composers moved away from tonal harmony and regular pulses... Among other things the audience was lost" -John Adams

#32
Christron

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i think that's the first time anyone's actually won a debate in the debate section. Well my work is obviously done here

/me twists his hat in one hand and tapdances back to GD

#33
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QUOTE (way2lazy2care @ Mar 10 2009, 11:49 AM) <{POST_SNAPBACK}>
math is not math is not always logical. And art is more logical than you might imagine it to be.


I play guitar and do graphics design here and there, I understand the logic in art.

How is math not always logical?



#34
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The fact that mathematical results have been used in both art and science is pretty irrelevant. Philosophy is being applied to science all the time (ex. bioethics), but does this make philosophy a science? Results in physics are addressed all the time in different fields of philosophy to do with the all these stereotypical questions on "reality/nature of life/blabla". So, since physics is being applied in philosophy, does this now make physics an art? The real way to check is to look at how the field functions on its own. Does it only expand by the scientific method? That question is as sufficient as it is necessary. Math certainly does. Suppose there is a new idea. Once enough experimentation is done and the idea goes through peer-review, it is referred to as a conjecture. Should this idea also come with a proof, which is then peer-reviewed, it is then called a theorem. And only then can this result be used to justify further results(theorems). Hence math is a science.
QED

#35
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QUOTE (Gordo @ Mar 13 2009, 07:49 PM) <{POST_SNAPBACK}>
The fact that mathematical results have been used in both art and science is pretty irrelevant. Philosophy is being applied to science all the time (ex. bioethics), but does this make philosophy a science? Results in physics are addressed all the time in different fields of philosophy to do with the all these stereotypical questions on "reality/nature of life/blabla". So, since physics is being applied in philosophy, does this now make physics an art? The real way to check is to look at how the field functions on its own. Does it only expand by the scientific method? That question is as sufficient as it is necessary. Math certainly does. Suppose there is a new idea. Once enough experimentation is done and the idea goes through peer-review, it is referred to as a conjecture. Should this idea also come with a proof, which is then peer-reviewed, it is then called a theorem. And only then can this result be used to justify further results(theorems). Hence math is a science.
QED


Math is not an experimental science the way chemistry and physics are experimental sciences.
The closest thing to a math laboratory would be a room with a computer in it that performs complex manual mathematical operations...
but the outcome is not a mystery... the way it is when you do a physics or chemistry experiment.

physicists and chemists may use mathematics as a tool .... and math never lies.. but its up to the physicist to interprete the mathematic result

so chemistry, physics, and biology as experimental sciences really should not be grouped together with mathematics.

Math is not a science.
since you used a cool acronym i'll finish my reply with one as well....
GG No Re.
icon_smile.gif

QUOTE (Extracheez @ Mar 13 2009, 06:37 AM) <{POST_SNAPBACK}>
I play guitar and do graphics design here and there, I understand the logic in art.
How is math not always logical?


starting with the basic number system
the number system itself is always based in reality...
0 is nothing.
1 is a unit of something .. .say playing cards.
2 is just 1 more than 1 ... it is 1+1 .. 2 playing cards...
and 3 is just 1 more than 2 ... so it is 2+1 = 1+1+1. .. 3 playing cards...
with this system we can add, subtract multiply and divide.. and its results are reality based...

now here is where the number system becomes "illogical/voodoo"

any number to the power of zero was arbitrarily assigned the value of 1 only because it made the algebra model work in a simple way.
there is no logical reason based in reality for (x) to the power of 0 to be assigned the value 1.

i got some applied combinatorics anomolies dealing with Ramsey numbers i could go over with you as well...
these are the examples that stick out in my head... i'm sure there are a tonne more i dont know about

Edited by JimRaynor, 21 May 2009 - 01:34 AM.

QUOTE (James Madison @ Aug 25 1781, 11:48 AM)
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#36
DHC

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QUOTE (Gordo @ Mar 13 2009, 07:49 PM) <{POST_SNAPBACK}>
The fact that mathematical results have been used in both art and science is pretty irrelevant. Philosophy is being applied to science all the time (ex. bioethics), but does this make philosophy a science? Results in physics are addressed all the time in different fields of philosophy to do with the all these stereotypical questions on "reality/nature of life/blabla". So, since physics is being applied in philosophy, does this now make physics an art? The real way to check is to look at how the field functions on its own. Does it only expand by the scientific method? That question is as sufficient as it is necessary. Math certainly does. Suppose there is a new idea. Once enough experimentation is done and the idea goes through peer-review, it is referred to as a conjecture. Should this idea also come with a proof, which is then peer-reviewed, it is then called a theorem. And only then can this result be used to justify further results(theorems). Hence math is a science.
QED


here's a fun proof for you:

Science = {fields of study: knowledge is acquired via the scientific method}
assume Math is an element in Science
then math knowledge must be acquired via the scientific method
thus math knowledge is obtained via observation and hypothesis testing
false, hence Math is not an element in Science □

(btw - only pretentious people write "QED" for such small lemmas icon_wink.gif )

#37
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QUOTE (JimRaynor @ May 21 2009, 01:43 AM) <{POST_SNAPBACK}>
now here is where the number system becomes "illogical/voodoo"

any number to the power of zero was arbitrarily assigned the value of 1 only because it made the algebra model work in a simple way.
there is no logical reason based in reality for (x) to the power of 0 to be assigned the value 1.

i got some applied combinatorics anomolies dealing with Ramsey numbers i could go over with you as well...
these are the examples that stick out in my head... i'm sure there are a tonne more i dont know about

That's not why it's assigned the value of 1.

It works like this 3^2 = 1*3*3 3^1 = 1*3 3^0=1. You need the multiplicative identity to apply otherwise the answers won't be right. Since anything to a power of anything is the multiplicative identity times the number however many times it is to the power, 3^0 is the multiplicative identity times 3 zero times.
QUOTE
Math is not an experimental science the way chemistry and physics are experimental sciences.
The closest thing to a math laboratory would be a room with a computer in it that performs complex manual mathematical operations...
but the outcome is not a mystery... the way it is when you do a physics or chemistry experiment.

Not true. I just got done doing a research study with Curm on roundness in graphs, and half the group that researched with me spent the whole time calculating the roundness of every possible graph with 7, 8, and 9 vertices just to see the spread of the roundnesses. They ended up finding holes in the apparent roundnesses at certain values, then proceeded to try to prove why they exist and if they exist for all graphs. idk if they ever did, because I wasn't working on that with them, but it's still observational.

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QUOTE (Virus52 @ Mar 3 2008, 09:44 AM) <{POST_SNAPBACK}>
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#38
JimRaynor

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QUOTE (way2lazy2care @ May 24 2009, 12:22 PM) <{POST_SNAPBACK}>
You need the multiplicative identity to apply otherwise the answers won't be right. Since anything to a power of anything is the multiplicative identity times the number however many times it is to the power, 3^0 is the multiplicative identity times 3 zero times.

which was arbitrarily assigned value 1... and it has no relation to physical reality whatsoever...


QUOTE (way2lazy2care @ May 24 2009, 12:22 PM) <{POST_SNAPBACK}>
Not true. I just got done doing a research study with Curm on roundness in graphs, and half the group that researched with me spent the whole time calculating the roundness of every possible graph with 7, 8, and 9 vertices just to see the spread of the roundnesses. They ended up finding holes in the apparent roundnesses at certain values, then proceeded to try to prove why they exist and if they exist for all graphs. idk if they ever did, because I wasn't working on that with them, but it's still observational.

If you'd like to provide a defenition for "graph" then we can begin. But, if I think I understand the context of "graph" here... so I'll take a stab at it...
This "graph" is probably just an abstraction that does not exist in reality.

good ole wikipedia icon_smile.gif
http://en.wikipedia....iki/Mathematics

If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. Albert Einstein has stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
Mathematics is the study of quantity, structure, space, relation, change, and various topics of pattern, form and entity. Mathematicians seek out patterns and other quantitative dimensions, whether dealing with numbers, spaces, natural science, computers, imaginary abstractions, or other entities.

3 is a human created abstraction and does not exist in reality.. 3 "keyboards" is something in reality.
Mathematics studies the abstraction... not the "keyboards" that exist in reality.
Math manipulates and examines the "3" not the "keyboards".

Edited by JimRaynor, 25 May 2009 - 02:07 PM.

QUOTE (James Madison @ Aug 25 1781, 11:48 AM)
If Tyranny and oppression come to this land it will be under the guise of fighting a foreign enemy

#39
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QUOTE (JimRaynor @ May 25 2009, 02:02 PM) <{POST_SNAPBACK}>
which was arbitrarily assigned value 1... and it has no relation to physical reality whatsoever...

It was arbitrary because you decided it was arbitrary? I just told you exactly why the 1 has to be there. Because there is never nothing on a side of the equation. Every equation in mathematics is built off the equation "1=1" not because it is arbitrary, but because it is necessary.

If you don't build off that equation, nothing can be there. "1=" is not an equation. Taking the definition of equation as "an expression or a proposition, often algebraic, asserting the equality of two quantities" there must be two quantities. To have two quantities, you need to have an identity. It is a requirement of mathematical being. It has to be there. If it isn't there, then there wouldn't even be an equation.

QUOTE
If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. Albert Einstein has stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

is "one" you? it certainly isn't the collective english speaking peoples who consider it to be:

sci⋅ence  [sahy-uhns] Show IPA
–noun
1. a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws: the mathematical sciences.
2. systematic knowledge of the physical or material world gained through observation and experimentation.
3. any of the branches of natural or physical science.
4. systematized knowledge in general.
5. knowledge, as of facts or principles; knowledge gained by systematic study.
6. a particular branch of knowledge.
7. skill, esp. reflecting a precise application of facts or principles; proficiency.


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#40
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I would say science based on the fact that the skill set needed to excel in math is more similar to those needed in science than in arts.




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