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Mathematics Is Completely Relative

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    Cornelius Ellsonpeter

    No, really, think about it. It is a completely made up system of rules and symbols with no basis in anything, not even nature. You could easily make up your own symbols, give them functions, and the only way they become accepted is if everybody can agree on them.

    It's like the concept of "math research" or even "computer research". Both systems are completely manmade...how can truly research something "manmade"?

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    ScanIAm

    Cornelius Ellsonpeter wrote:
    No, really, think about it. It is a completely made up system of rules and symbols with no basis in anything, not even nature. You could easily make up your own symbols, give them functions, and the only way they become accepted is if everybody can agree on them.


    Paging Captain Obvious.  Come in Captain Obvious.  Smiley

    Seriously, yes, you are right, but for example, the relationships between the constants would stay the same.  This is the whole point of theoretical (and applied) mathmatics:  To determine those constants and formulas.

     

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    shreyasonli​ne

    ScanIAm wrote:
    
    Cornelius Ellsonpeter wrote:No, really, think about it. It is a completely made up system of rules and symbols with no basis in anything, not even nature. You could easily make up your own symbols, give them functions, and the only way they become accepted is if everybody can agree on them.


    Paging Captain Obvious.  Come in Captain Obvious. 

    Seriously, yes, you are right, but for example, the relationships between the constants would stay the same.  This is the whole point of theoretical (and applied) mathmatics:  To determine those constants and formulas.

     


    Constants are like wedge under a leg of your table, just to keep it balanced, isnt it ?

    Shreyas Zare

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    DoomBringer

    Math exists in nature, if you know where to look.

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    Cornelius Ellsonpeter

    DoomBringer wrote:
    Math exists in nature, if you know where to look.
    Oh yes, you are right.

    Like pi. Or fractals. Or how cells divide.

    It's still relative, because the system of mathematics is made up of symbols. The symbols are arbitrary, as are the relationships between them and their functions.

    For instance, let's say instead of counting by ones, I create a whole new system of mathematics where they count by twos, but I would have to call it something else to avoid confusion. I suppose this is like the concept of "base number" systems. But, the functions in my new system could be arbitrary, too, and I could easily retrofit them to line up with whatever is going on in nature. Yet it would look completely different from anything we know.

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    Cybermagell​an

    Cornelius Ellsonpeter wrote:
    No, really, think about it. It is a completely made up system of rules and symbols with no basis in anything, not even nature. You could easily make up your own symbols, give them functions, and the only way they become accepted is if everybody can agree on them.


    Same thing with money....

    There is no law saying you MUST accept dollars in exchange for goods, you could trade computers, toenails, or *ahem* women....

    That being said "dollars" is the most accepted form (Besides credit)

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    DoomBringer

    Cornelius Ellsonpeter wrote:
    
    DoomBringer wrote: Math exists in nature, if you know where to look.
    Oh yes, you are right.

    Like pi. Or fractals. Or how cells divide.

    It's still relative, because the system of mathematics is made up of symbols. The symbols are arbitrary, as are the relationships between them and their functions.

    For instance, let's say instead of counting by ones, I create a whole new system of mathematics where they count by twos, but I would have to call it something else to avoid confusion. I suppose this is like the concept of "base number" systems. But, the functions in my new system could be arbitrary, too, and I could easily retrofit them to line up with whatever is going on in nature. Yet it would look completely different from anything we know.

    Thing is, you're wrong.
    Pi is a relationship between the diameter of a circle and its circumference.  Pi is always going to be pi, no matter what system you're using.

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    julianbenja​min

    Cornelius Ellsonpeter wrote:
    
    DoomBringer wrote: Math exists in nature, if you know where to look.
    Oh yes, you are right.

    Like pi. Or fractals. Or how cells divide.

    It's still relative, because the system of mathematics is made up of symbols. The symbols are arbitrary, as are the relationships between them and their functions.

    For instance, let's say instead of counting by ones, I create a whole new system of mathematics where they count by twos, but I would have to call it something else to avoid confusion. I suppose this is like the concept of "base number" systems. But, the functions in my new system could be arbitrary, too, and I could easily retrofit them to line up with whatever is going on in nature. Yet it would look completely different from anything we know.


    But here you're talking about the symbols used in mathematics, not mathematics itself.  The system of mathematics is not made up of symbols; symbols are used to convey ideas, for which the basis does exist in nature (addition, subtraction, etc).  The fact that everyone agreed on one system just makes it easier.  Yet, look at computers, with their binary system.  It still uses the same concepts of mathematics (addition, subtraction, multiplication, etc); the methodology is different, but ultimately, you get the same result if you add in binary or you add in decimal.

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    Cornelius Ellsonpeter

    DoomBringer wrote:
    Thing is, you're wrong.
    Pi is a relationship between the diameter of a circle and its circumference.  Pi is always going to be pi, no matter what system you're using.
    Yes and no. The relationship would still be there in some form...I'll give you that. If you deciding to only work in binary, you could still calculate diameters and circumferences based on that relationship, although the numbers would be very difficult to work with without a PC. However, what if, in my new system, I stop counting by ones, and only allow you to count by twos? Let's say I call that new number a "Scoble". Example:

    In decimal:

    1 apple + 1 apple = 2 apples

    In the new system:

    1 now equals 1/2 a Scoble, so that:

    1 Scoble apple + 1 Scoble apple = 2 Scoble apples, or 4 apples in decimal

    If I tried to figure out the circumference of that apple by knowing it's diameter, yes, pi would still be there in either system, but it would probably be like this:

    1/2 pi in decimal = pi in the new system

    ...so even the term "constant" is relative, because the definition of that constant (or the agreed upon representation of it) is dependent on my symbol system.

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    DoomBringer

    Cornelius Ellsonpeter wrote:
    
    DoomBringer wrote: Thing is, you're wrong.
    Pi is a relationship between the diameter of a circle and its circumference.  Pi is always going to be pi, no matter what system you're using.
    Yes and no. The relationship would still be there in some form...I'll give you that. If you deciding to only work in binary, you could still calculate diameters and circumferences based on that relationship, although the numbers would be very difficult to work with without a PC. However, what if, in my new system, I stop counting by ones, and only allow you to count by twos? Let's say I call that new number a "Scoble". Example:

    In decimal:

    1 apple + 1 apple = 2 apples

    In the new system:

    1 now equals 1/2 a Scoble, so that:

    1 Scoble apple + 1 Scoble apple = 2 Scoble apples, or 4 apples in decimal

    If I tried to figure out the circumference of that apple by knowing it's diameter, yes, pi would still be there in either system, but it would probably be like this:

    1/2 pi in decimal = pi in the new system

    ...so even the term "constant" is relative, because the definition of that constant (or the agreed upon representation of it) is dependent on my symbol system.

    So you're just using a different number base then?  Well, pi is always going to be 3.14..., the number system to represent it will differ.  If I tried to represent it in Roman numerals, it would look different.  But its always going to be a constant, because it holds true for any size circle.

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    Cornelius Ellsonpeter

    DoomBringer wrote:
    So you're just using a different number base then?  Well, pi is always going to be 3.14..., the number system to represent it will differ.  If I tried to represent it in Roman numerals, it would look different.  But its always going to be a constant, because it holds true for any size circle.
    I'm also saying you can change the way you count in the new system. I could even throw out addition if I wanted to, which would take multiplication with it, and come up with a completely different name, and a different way of representing it. Right...or no?

    For instance, let's say I have five billard balls on a pool table. I add five more. If I threw out addition, you have to recount all the balls. Yes, that would be a pain with large numbers, but it could be done. However, what if I had a system that could identify a group of five billiard balls and called them a "zork"? So, one zork plus another zork is two zorks.

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    JohnAskew

    I completely disagree.

    Number wasn't invented by man, it was discovered by man, who found number in nature.

    Mathematics exists outside man's formalization and codification of it.
    Mathematics is the physics of number, it is not artificial, though consciousness of mathematics is "an art", imho.

    Number is so deeply embedded in our organistic existence that it is unrecognizable oftentimes.

    Read 'Number and Time', written by Marie Louise von Franz, a student of C.G. Jung's. 

    Imho, time is not a blank slate, either...

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    shreyasonli​ne

    JohnAskew wrote:
    

    I completely disagree.

    Number wasn't invented by man, it was discovered by man, who found number in nature.

    Mathematics exists outside man's formalization and codification of it.
    Mathematics is the physics of number, it is not artificial, though consciousness of mathematics is "an art", imho.

    Number is so deeply embedded in our organistic existence that it is unrecognizable oftentimes.

    Read 'Number and Time', written by Marie Louise von Franz, a student of C.G. Jung's. 

    Imho, time is not a blank slate, either...



    I agree. We count in decimal just because we have 10 fingers. Numbers always existed. The value of any constant remains same, no matter what system you use. The value of 1 meter will always be same at 1000 milimeter, isnt it?

    Shreyas Zare

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    julianbenja​min

    Cornelius Ellsonpeter wrote:
    
    DoomBringer wrote: So you're just using a different number base then?  Well, pi is always going to be 3.14..., the number system to represent it will differ.  If I tried to represent it in Roman numerals, it would look different.  But its always going to be a constant, because it holds true for any size circle.
    I'm also saying you can change the way you count in the new system. I could even throw out addition if I wanted to, which would take multiplication with it, and come up with a completely different name, and a different way of representing it. Right...or no?

    For instance, let's say I have five billard balls on a pool table. I add five more. If I threw out addition, you have to recount all the balls. Yes, that would be a pain with large numbers, but it could be done. However, what if I had a system that could identify a group of five billiard balls and called them a "zork"? So, one zork plus another zork is two zorks.


    You can change the way you count, but if you want to do a comparison between two different number systems, you have to convert one to the other before doing it.

    So, if I have 10 billiard balls, you'd say I have 2 zorks.  Which is fine, because when it comes to physical representation, they both refer to the same thing, i.e. 10 billiard balls.

    It's like the currency system.  You can't expect to pay 10 dollars for something that costs 10 pesos.  You'd have to convert to speak the same "language", but once converted, you're now speaking apples-to-apples instead of apples-to-oranges.

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    AdityaG

    Erm. Everything is relative. What exactly isn't relative to something else? Language, us, religion.. everything is relative to something. We don't know about EVERYTHING in the universe. Until then, everything we do know about will be relative and sometiems based on certain accepted postulates...

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    Minh

    Dude. What are you smoking? Can I have some?

  • User profile image
    Cornelius Ellsonpeter

    Minh wrote:
    Dude. What are you smoking? Can I have some?
    I'm not smoking anything. Some day I'll post a thread about prime numbers, too. Ever read "Music of the Primes" by Marcus du Satoy? I only got through part of it, but what I could understand was pretty interesting and quite deep.

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    Cornelius Ellsonpeter

    jaylittle wrote:
    
    Minh wrote: Dude. What are you smoking? Can I have some?

    Don't worry - the posting will stop as soon as he feels the munchies coming on.
    You know, I try to raise the bar here as far as discussion, and like always Jay, you turn around and take the discussion down about ten levels.

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