question for the math people

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

  1. Jeffsus

    Jeffsus TRIBE Member

    YAY.

    I agree with craig that it is j not i.

    Because i stands for current.

    "c" would have been good to use for current but it was taken by speed of light.

    "s" would have been good to use for speed of light but it was taken for distance.

    "d" would have been good to use for distance but it was taken for polarization vectors.

    "p" would have been good to use for polarization but it was already taken by momentum.

    "m" would have been good to use for momentum but it was already taken by junction widths

    "j" would have been good to use for junction but it was taken by imaginary numbers...

    And so the cycle continues....

    OK new debate:

    What is wonkier: the fibonnacci series or prime numbers? Do you think a GUT will relate the two sets?

    -jM
    A&D
     
  2. Plato

    Plato TRIBE Member

    2 + 2 is four
    2 + 2 is four...

    heh heh, i see why this show is so popular :)

    p[l]a+0
     
  3. Sporty Dan

    Sporty Dan TRIBE Member

    DUUUUDE......current is a capital I.



    BAH!
    ...... there is nothing wonky about the Fibonnacci series. Martin is wonkier than the Fibonnacci series. But Martin is NOT wonkier than {prime numbers}.
    .....unless he has forgotten to take his medication.....

    http://www.geocities.com/CollegePark/Residence/2001/


    dan.
     
  4. ADT

    ADT TRIBE Member

    im not sure why im bothering to explain this again..


    1> imaginary numbers DO NOT EXIST!.. they are a mathematical trick used to make the form of real equations more managable..

    2>just because you can use them to solve certain systems, doesnt mean you have to!!!! and it certainly doenst mean the soluctions dont exist without them!!!

    alot of the systems you are saying only have solutions through complex analysis have completely valid solutions that do not use j at all..

    you just dont know them, and I dont have time to explain them..

    believe it or not, complex analysis and all the phasor theory which your all touting as the one and only true way came along AFTER alot of AC signal theory had already been developed, infact the development of these simplified mathematical techniques were part of the motivation for our switch to AC power (on top of other benefits)...

    sorry.. maybe if I get some sleep today ill be able to give some examples later..

    and all that stuff about impedence is not true either..... impedence only exist in systems whos inputs are PHASORS, which have imaginary components added into represent their wave state... no imaginary component on the input, no reactance in the impedence

    v..abstractdatatype

    ps. i would like to see how this conservation of momentum for electrons thing works (or doesnt)
     
  5. AshG

    AshG Member

    hmm couple thoughts about the non-realness of i (or j if you get past high school)

    firstly, its probably a good idea to make a disinction between the Real set of numbers and would people would consider being physically "real."

    arguing that j doesn't exist in reality because there is no physical reality to a complex root is not valid for a couple reasons:

    1. this would imply that zero and all negative, transcenental, and irrational numbers do not really exist, because they don't physically exist (try to imagine zero of something - it simply isn't there!)

    2. mathematical numbers don't exist in reality anyway - they're purely imaginary (pun intended)

    3. mathematical models are used to mimic physical systems. just because we're queasy about how to interpret our solutions doesn't mean that they don't describe some physical reality o f which we're not yet aware.

    4. the convention (and it is a convention only), of using the root mean squared version of the power output to get a 'usable' result from electromagnetic calculations is there only because we don't like dealing with imaginary components. the imaginary portions do in fact add and subtract real energies from such systems throughout the life of the system in question. only at the end point of evaluating the system do we discard the imaginaries.
     
  6. quantumdj

    quantumdj TRIBE Member

    It's simple: You take stuff, and then you take away the same amount of stuff, and you're left with nothing.
     
  7. quantumdj

    quantumdj TRIBE Member

    let's say that 5/0=0. Then 5=0(0). Doesnt work.

    try it with any number, and you get an inequality.

    Try graphing this. m=5/0. This means that the graph rises 5 in zero run. This would also mean that the slope could be 4/0, 10/0, or even 13361490.293406/0. It can not be defined.
     
  8. sugar

    sugar TRIBE Member

    But, where did the stuff go?

    Hey, where did it come from?

    Where am I?
     
  9. Sporty Dan

    Sporty Dan TRIBE Member

    Schrodinger;s Equation = Conservation of energy

    -(h^2/2m)*(d^2/dx^2)(Psi) + V*Psi = i*h*(d/dt)(Psi)
    V = V(x,t) = potential energy
    Psi = Psi(x,t) = wave function
    and 'h' = h/2*pi...since my keyboard does not have an h-bar key.

    It;s potential energy V is always real & it;s mass is real. This means that either the electron must occupy imaginary space, imaginary time, or have imaginary energy.......

    ...trying to derive this equation only considering real numbers gives you the result that electrons cannot tunnel through an energy barrier.......since empirical evidence suggests that they can, there must be an imaginary component to the electron;s 4-vector {x,y,z,E}.


    dan.
     
  10. MKMIRAGE

    MKMIRAGE TRIBE Member


    Limits mate, limits... as a number of 9s in 1.999999999... approaches infinity, the value approaches 2.
     
  11. roo

    roo Well-Known Member

    that's really dumb. the calculators cheat. 5/0 should = 5. simple.
     
  12. PosTMOd

    PosTMOd Well-Known Member

    Not a limit, since it ain't approaching infinite... it *IS* an infinite number of 9's... and it *IS* 2, not approaching 2.
     
  13. miguel

    miguel TRIBE Member



    boy you sure sound condescending! you take some of our knowledge for granted here. no need to talk down to anyone, you don't know us or what we're about (or how much pure math background some of us may or may not have).

    many differential equations cannot be solved by "standard" methods without the use of complex numbers, and yet their solutions are actually real. (unless you consider trial and error another solution method)
     
  14. labRat

    labRat TRIBE Member

    miguel: don't fret, i think ADT is trying to win a losing battle. he'll soon come over to the dark /complex side of the force.

    as someone else pointed out, irrational numbers are in the same league as ''imaginary" numbers. try showing me something real that represents pi. pi is an integral part to almost anything mathematical that helps to realise many models, but it is something that can't be fully determined although it is only a simple ratio.

    although i am quite sure that pi is rational in another base, something logarithmic i'm sure.

    --craig
     
  15. ADT

    ADT TRIBE Member

    let me put it this way.. did complex numbers exist before we invented them?

    no

    every characteristic of every system you are describing is a reflection of something that is happening in the REAL world..

    the complex number system is simply a transform of sorts of our own real number system, much like fourier in a way...

    they are added in to the equation only to be taken out again in the end when you want a physical solution..

    %60 of the math I do is some form of complex analysis (mainly Fourier and a lot of EM wve theory).. and while j may seem to make sense when in the context of reactance.. you can also see what it does to wave equations.. it essenstially turns them into nonsensical gibberish with no physical interperetation.. only when you bring them back into the purely real domain do you have something that makes any kind of sense at all..

    v..abstractdatatype
     
  16. PosTMOd

    PosTMOd Well-Known Member

    Since you didn't bother to read this very good post the first time, ADT, here it is again (you're backed into a corner, and you are now arguing out YOUR ASS)... numbers, "real" or "imaginary", do NOT exist in reality no matter what... give it up...


     
  17. ADT

    ADT TRIBE Member

    pfft.....

    seeing as we are all made of waves, that is they are the true fundamental matter of the universe.. and the only valid context for this argument..

    in wave mechanics: zero amplitude > exists; negative amplitude > exists; irrational amplituted> DOES NOT EXIST

    what is a number? that is a very difficult question to answer and if we chose to twist this around we could send this whole discussion to the shitter..

    >> my definition: a symbolic representation of physical relationship or relativeness, contextually starting with wave mechanics and expanding to other representations. Every number that exists is reflected in the relative characteristics of EM waves. Just as every thing that exist in our universe is a product of those wave relationships, every number that exist must be as well.

    if mathematical models mimic physical systems, conversely physical systems should mimic mathematical models (correct ones at least), hence my interest in Picards Theorem

    there are no known physical systems that exibit complex properties (yet).. this is a physics discussion, not a math one really...

    more importantly..


    exactly my point, if they need to be discarded then they are tainting the correctness of the result and are not a reflection of the true system being analyzed, otherwise why would we have to discard them

    more importantly, if they exist already, then why do we have to add them in?

    rather than looking at the big picture, you have to look at where these numbers come from.. or how they found their way into wave theory in the first place

    one place..

    sinx = (1/2i)(exp(ix) - exp(-ix))


    this equation elequently shows how complex components are physically realizable ONLY when they cancel each other out (the two exponents will negate the imaginary parts of each other).

    In any other form they are theoretical symbolism for an idea with no physical basis.

    In Summary:

    >Everything in the universe is made of waves.
    >Every number that exists has a corresponding wave somewhere whose amplitude defines it (corallory to Picard theorem!!!!:eek: )

    of course you can change the definition of numbers to include quanitities with no basis in reality; but thats your argument isnt it?

    numbers do not have to have a basis in reality, or is it just that your argument has no basis in reality?

    v..abstractdatatype
     
  18. ADT

    ADT TRIBE Member

    ps. [STOMP].... [/STOMP]
     
  19. ADT

    ADT TRIBE Member

    just so you dont twist the topic of discussion around while your arguing out your ass, lets remind you what we were discussing in the first place..

    this statement..

    that is, i/j exist in a theoretical form only and has no basis in physical reality..

    :cool:
     
  20. 416

    416 TRIBE Member

    That's kindof a weird thing to talk about without some other details.

    Typically, 2 and 1.999... can't really be compared to one another. Usually they're considered to be in different groups, making any comparison between the two impossible. When 2 is an integer and 1.999... is a real number, any attempt to prove that one equals the other or that one is greater then the other is impossible.

    Sorry, don't pay any attention to me, it's very possible that I've got no idea what I'm talking about.
     
  21. 416

    416 TRIBE Member

    I don't really understand the term "physical reality" as it relates to math. Take and elliptical curve defined over some weird assed polynomial in a group of integers. You can't draw it on a graph, but the curve still exists. Because it complies to all laws governing elliptical curves defined over real numbers. Which one "exists" and which doesn't?

    I'm lost. I guess what I'm trying to say is that I don't understand what you mean by "physical reality". All numbers "exist" within a set of parameters that are somehow conjured up in our head. Putting two apples together with two other apples is a simple analogy for a mathematical operation. It doesn't prove that the number two or the addition operation actually exists.
     
  22. Sporty Dan

    Sporty Dan TRIBE Member


    .....Well..... you haven;t acknowledged my electron problem from above......
    .....please demonstrate how you can differentiate a real function and get a complex number...............it can;t be done.

    .....and because I have nothing better to do, I will bring up tachyons.
    t = t0/SQRT(1-v^2/c^2)
    tachyons have been observed to exist and travel with v > c, so they must exist in imaginary time or have imaginary mass....
    http://www1.shore.net/~ewall/



    dan.
     
  23. Jeffsus

    Jeffsus TRIBE Member

    I declare that AshG and PosTMOd are right and that my physicist, Sporty Dan, has again proven an opponent who backs his claims.

    I also declare that ADT, although (s)he has a cool pseudonym, is wrong in this case, and is sounding remarkably similar to Christian dogma in the middle ages: ie.
    1. maybe if I say my point again, it will become more correct.
    2. I will ignore all contraindicated evidence, no matter how obvious it may be.
    3. If I can't see it or don't understand it, it must not exist

    YAY.

    ANd of course the smilie to pretend I am not serious ;)

    -jM
    A&D
     
  24. ADT

    ADT TRIBE Member

    ADT>> final stance

    AshG, Postmod, Jeffsus<< all definitely wrong, or at least lacking valid arguments to prove their position..

    im really surprised you see anything in AshG's arguments Jeffsus, they really seem... well ..... wishy washy and contrived.. or artsy fartsy at least.. (no offence AshG)

    they most definitely shoot no holes in my stance, in fact they strengthened it if anything (see above)

    as far as Sporty Dan is concerned; my knowledge of particle physics stopped with mechanics and relativity (i ran out of electives).. and kept me out of quantum mechanics..

    so I will admit at least to the plausability of a chink in the armour coming from his direction..

    v..abstractdatatype
     
    Last edited: Feb 27, 2002
  25. ADT

    ADT TRIBE Member

    I WIN :D

    thanks sporty dan.. i think ill read the rest of that web-page...

    sound familiar?

    or


    v..abstractdatatype << the baddest muthah of the TBK math poseee, and nobody understaaaaannndddssss him but his womaaaaannn... ADT :cool:
     
    Last edited: Feb 27, 2002

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