question for the math people

Discussion in 'TRIBE Main Forum' started by roo, Feb 25, 2002.

  1. Ditto Much

    Ditto Much TRIBE Member

    1.9999... < 2 this statement is true!
    1.9999... = 2 this statement is only true is we allow the limit of approach to be the final value.


    1.9999... != 2

    It can only be true if you allow rounding, if you allow rounding then by default your using limits.


    Our
    Hippies

    Are
    High

    On
    Acid

    SohCahToa
     
  2. Sporty Dan

    Sporty Dan TRIBE Member

    ....No you don;t......I do.....re-read your original statement.



    Whether it has a physical meaning or not is not relavent.

    Your original contention was that imaginary numbers are only a tool 'invented' to make calculations easier and that problems can be solved without them. You said that no known phyical systems require i to be solved......I have given examples to the contrary.

    Whether imaginary mass has a physical meaning or not doesn;t change the fact that techyons and electron tunneling are real, observed phenomena that cannot be described at all without the use of imaginary numbers.



    dan.
     
  3. R4V4G3D_SKU11S

    R4V4G3D_SKU11S TRIBE Member

    You may already have given them (I'm lost here), but I want to see these explanations...
     
  4. ~atp~

    ~atp~ TRIBE Member

    Number theory's a lot of fun. Usually depends on how you define the formal system that you want to discuss; my background is in applied math, and some pure math--have any of you read "GEB" for short, or more formally: "Goedel, Escher, Bach: an eternal golden braid" by Douglas R Hofstader??

    If you're interested in these issues, you should read the book. Very thought provoking. ;)

    -keith
     
  5. ADT

    ADT TRIBE Member

    HAHA Sorry dan.. wrong again

    from www.physics-qa.com

    Atilla Gurel - Author of 'The Objectivist Quantum'



    but here is where I really started laughing my ass off..


    Who's the cat that won't cop out
    when there's physicists all about
    (ADT!)
    Right on

    You see this cat ADT is a bad mother--
    (Shut your mouth)
    But I'm talkin' about ADT
    (Then we can dig it)

    He's a complicated man
    but no one understands him but his woman
    (ADT)

    v.. abstractdatatype :cool:
     
  6. Jeffsus

    Jeffsus TRIBE Member

    What AshG was pointing out is the same as what Labrat mentioned right at the beginning, what PosTMOd also elaborated, and that which I reiterated:

    That imaginary numbers are no more or less existential than real numbers.

    All numbers, not merely imaginary ones, are mathematical tools that have no manifestation in 'existence'. Our familiarity with real number systems leads to the illusion that 'real' numbers are existential (hence their name).

    I said and still contend:

    To this end, I ask (and basically rephrase labrat's question) the question: show me a "one". Not one "apple", or one "meter", or one "watt"... please show me a "one" that exists. (if that is too hard, try to show me a two.. I will even allow you to show me a 'zero' if you can)

    I'm sure you will find it as just as impossible as an "i".

    That is my stance, and what I am pretty sure AshG, PosTMOd and Labrat were getting at: mostly #2 that real numbers are no more existential than complex ones.

    Dan's point was that the complex numbers are no less existential than the real ones, using the illustrations he did.

    The quotes in the texts, that there are no physical instances of "i", are irrelevent, because they make no comment on imaginary number's significance relevent to the significance of real numbers; nor does it make any comment on relative existentiality of either number set....

    so...

    -jM
    A&D
     
  7. ADT

    ADT TRIBE Member

    whatever..

    you cant argue that imaginary numbers exist one minute and then that numbers dont exist the next..

    what was that about talking out your ass?

    i have shown that real numbers have a basis in reality, imaginary numbers do not (despite Dans valiant effort)..

    the numbers are as real because they represent something real (real quantities vs ficticious quantities)

    5 oranges vs j oranges..

    v..abstractdatatype

    ps. i have a great line on weed right now, interested? $15/ j grams..

    what..? dont worry

    >imaginary weed exists as much as real weed does
    >real weed is as imaginary as complex weed

    the symbol exists because you can interperate and experience it
     
  8. PosTMOd

    PosTMOd Well-Known Member

    Oh, the world of a seven-year old, how I miss thee.
    The world of bliss, of ignorance, of simplicity.

    Oh, how I miss thee.

    Yet, I wonder, and cannot recall, if I was as amused back then.

    I know only that I was certain, and simple, and I longed for a teat to suckle, and had not a care in the world.

    Back when I was seven.
     
  9. AshG

    AshG Member

    Let's understand something about all numbers from the get-go:

    Numbers are inventions of man - they do not physically exist - not any of them. Oh yes, i too can count the "number" of pointless times i post about this topic and assign it a name - say "3", but that does not mean that the number 3 exists, only that it exists as a tool for labeling a quantity.

    We are so familiar with them we really think they do physically exist, but its worth noting that there is a human culture that traditionally, had no concept of quantity.
    Think about that. What would that mean?
    Well for the aboriginal peoples of australia, it meant saying things like "i will collect only some of the turtle eggs", as opposed to saying "i will collect 3 and leave 2".

    But that does not mean that the eggs don't exist; only that our invention of assigning quantitative value to them does.

    Remember that there was a time when "zero" and negative numbers did not exist in the number system - does that mean that they have have no physical meaning? of course not, it only means that we hadn't yet understood how to interpret its meaning in the physical world.

    Same goes for transcendental and irrational numbers - just because their is no physical way to represent these numbers doesn't mean they don't physicall show up somewhere. try measuring root(2) sometime - if you're like pythagorus, you'd end up killing people to keep a secret of the fact that it CAN'T BE DONE. To the greeks, who equated all mathematics with physical geometrical constructs, this was heresay, and they rejected it outright SIMPLY BECAUSE THEY COULDN'T ACCEPT THE MATHEMATICS AT FACE VALUE. They had to try and make it fit their reality. Well guess what? The mathematics wasn't wrong; their perception of reality was.

    This brings up a very important point: physics and all physical modeling tools are slaves to mathematics, never the other way around.

    A great deal of modern mathematics does away with numbers altogether and instead focuses on assigning more abstract VALUE to sets with certain properties, etc. So just because you're not happy with the value that gets spit out of an equation doesn't mean that the value is wrong - it means your interpretation of its meaning is flawed (probably due to the fact that you have yet to observe phenomena that match these strange values - but it doesn't mean this phenomena doesn't exist, rather its a signpost to go looking for this stuff)

    Also keep in mind that all models have their flaws and that wave equations in particular were done away with long ago because their matrix equivalents are so much more powerful. Wave equations (Shroedingers is a prime example) tell, at most, half the story. But since physicists like waves, they usually stick stubbornly by their waves, despite 50 years of evidence to suggest its by far the inferior model of choice.

    Even the very best make mistakes. Einstein insisted on his E =mc^2 formula, and ignored the fact that the equations actually work out to say:

    E = +/- mc^2

    he didn't like the fact that this would imply there are negative energies in the universe - for physicists of his day this was impossible (so the math must be wrong!)
    but it took a mathematician named Dirac to develop the negative energy level states theory to explain the existance of anti-matter. Easily Einstein' biggest blunder.

    And all because he couldn't fit the math to his view of the world, rather than try to fit his view to the math.

    Math rules! - on your knees physics!
     
  10. ADT

    ADT TRIBE Member

    Pfft .. Math does not exist, it is purely theoretical :p
     
  11. Bass-Invader

    Bass-Invader TRIBE Member

    what happened to this argument?
     
  12. ADT

    ADT TRIBE Member

    I Won...
     
  13. Bass-Invader

    Bass-Invader TRIBE Member

    you don't seem to be arguing the same thing anymore...
     
  14. PosTMOd

    PosTMOd Well-Known Member

    The sandbox?
     
  15. ADT

    ADT TRIBE Member

    indeed, i am playing in it know..

    :D

    [​IMG]

    ill open up a thread on ideas that are mostly BS but sound cool and are easy to understand

    so you can win the sandbox for that one...

    v..abstractdatatype
     
  16. ~atp~

    ~atp~ TRIBE Member

    The number 1, for example, is simply an abstract representation of something that we as humans can collectively identify singularly. In fact, numbers are really just sets: a collection of identifiable objects.
    Whether a number actually exists in "real life" is irrelevant: similarly, the imaginary number scheme is a consequence of the mathematical system in use. To be clear, ask yourself the question: "How big is i??" (that is, the "i" in imaginary number notation). You can't say, "i is about half of 14" or something similar. You must respond with "i squared is -1" since it is a result of the system we accept as true.
    So the question to whether "i" or the imaginary number system is directly observed in "physical reality" is irrelevant as well.
    Here's a question: if "i" is defined such that its square is -1, then could we not use "-i" in place of "i"??? In fact, is one form more correct than the other?

    ;)

    -keith
     
  17. ADT

    ADT TRIBE Member

    the difference between the symbols is that 1 reflects the universe that does exist, and j reflects the universe that may exist..

    my consciousness is a reflection of the design universe that does exist, therefore I exists..

    just as real numbers exist..

    and complex numbers may exists..

    v..abstractdatatype
     
  18. MKMIRAGE

    MKMIRAGE TRIBE Member

    I don't really have time for a longer lecture:

    1. 1.99999.... is NOT 2, come on, only 2 is 2! (Doesnt get much more obvious than that!)
    2. It IS a limit as the more 9s you got the closer you get to 2.

    2 Rules:
    - Your maths teacher is right
    - If s/he is wrong re-read the 1st rule

    M.
     
  19. PosTMOd

    PosTMOd Well-Known Member

    I really *do* wish I was 7 years old again.

    If you want to think it is a limit, go right ahead...

    What is 8/9? It is 0.8888888...
    What is 1/9? It is 0.1111111...

    What is (8/9) + (1/9)? It is 9/9.

    What is 0.88888... + 0.111111...? It is 0.99999...

    Get it, or should I wait until you are a bit older? I bet if I showed you a tall skinny glass with 250mL of juice in it, and a short fat glass with 250mL in it, you would think the tall one had more... ;)

    I think you are mixing up an infinite number of nines with an infinite function-- they are NOT the same.
     
  20. Guest

    Guest Guest

    "two plus two is four"
    [​IMG]
     
  21. PosTMOd

    PosTMOd Well-Known Member

    Here's another simple way of looking at it ;)

    Let x=0.99999999...

    Multiply both sides by 10, so

    10x = 9.999999999....

    Now, subtract one equation from the other:

    10x=9.999999999...
    - x = 0.999999999...
    -------------------------
    9x = 9.0000000000...

    Therefore, x=1
    But, we already defined x=0.999999999...

    Thus 1 = 0.999999999...
     
  22. air-bag

    air-bag TRIBE Member

    ^^ oh no! catastrophical cancellation! (i.e. postmod is cheating as always)
    now we must die :D


    p.s.
    what is this thread about? Is there any question that is being debated? i dont wanna read all 4 pages.. someone plz summarize ....
     
  23. PosTMOd

    PosTMOd Well-Known Member

    It's about some people thinking that some convergent series is some sort of limit.

    Oh, and some people (the youngsters) not being able to think abstractly enough, even though the word is part of their moniker. 'Not abstractly enough' meaning stuck in some strange land where some abstract ideas are allowed (and even seen as "real"), but others aren't.
     
  24. ~atp~

    ~atp~ TRIBE Member

    I believe much of that lack of abstract thinking is a direct result of the teaching we get in school (be it high school or university). The teaching, IMO, often steers far away from the fundamentals of math even in "pure" math courses. In my personal experience this has certainly been the case, and if it wasn't for my strong interest in literature, I'd be hard put to talk about some of the more abstract issues.

    Postmod's reference to the difference between infinite sums, and functional limits is a good point--the mathematical system upon which Calculus is based allows for such (seemingly) impossible relationships. However, some formal mathematical systems do not allow for it...

    -keith
     
  25. ADT

    ADT TRIBE Member

    i think it has alot more to do with people who only have a BASIC understanding of a topic thinking that the correct interpretation is corollary to fundamental axioms of the philosophy ONLY..

    mathematics and physics are as much a holistic philosophy as any other less rigid study..

    the laws have to be experienced before they can be understood completely, and that takes a perspective more 'hands on'..

    plays on words and definitions are the forte of showboaters..

    and just because it looks like a BLT to you..

    doesnt mean that it tastes like JUST bacon lettuce and tomatoes to me...

    working with it every day that is..

    v..abstractdatatype
     

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