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Are functionals united with the vector space which they operate on?

  1. May 5, 2010 #1

    jaketodd

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    Are functionals united with the vector space which they operate on? For example, Physics is a functional of Behavioral Psychology. However, Behavioral Psychology does not include Physics. Am I correct?

    Thank you,

    Jake
     
  2. jcsd
  3. May 5, 2010 #2

    Landau

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    Is this a joke?
     
  4. May 5, 2010 #3

    HallsofIvy

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    What does this have to do with "vector spaces"? For that matter what does it have to do with mathematics?

    Perhaps it would help if you gave a precise definion for your use of "functional" here.
     
  5. May 5, 2010 #4

    jaketodd

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    I assumed (apparently incorrectly) that functionals could be applied to the abstraction levels of concepts.

    Sorry about the confusion; I'm new to these concepts.

    What got me asking this question is from Wikipedia: "A spin network, immersed into a manifold, can be used to define a functional on the space of connections on this manifold."
    http://en.wikipedia.org/wiki/Spin_network

    So I guess what I'm really asking is: Is the map the functional provides, on the space of connections on a manifold, united with the spin network that is immersed into the manifold in order to obtain the functional?

    Thanks,

    Jake
     
  6. May 5, 2010 #5
    Also, could you give us a mathematical meaning to "united"?
     
  7. May 5, 2010 #6

    jaketodd

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    The best I can do is try conceptually: In the concept of spacetime, space is united with time. Does that bring to mind a mathematical representation?

    Thank you for bearing with me,

    Jake
     
  8. May 5, 2010 #7
    Lol, this is really funny actually. No offense, but you're not making any sense. :) . These math concepts have very precise meanings... if you want a philosophical discussion, you should ask in the philosophy forum. :)
     
  9. May 6, 2010 #8

    jaketodd

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    But isn't everything representable with math?
     
  10. May 7, 2010 #9

    HallsofIvy

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    No, why in the world would you think so?
     
  11. May 8, 2010 #10

    jaketodd

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    What can't be defined with math? That's kind of a philosophy question, and I can already hear objections to this thread turning into that. So if you don't want to, don't worry about not responding.
     
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